A NOVEL EQUATION-OF-STATE TO MODEL MICROEMULSION …
Transcript of A NOVEL EQUATION-OF-STATE TO MODEL MICROEMULSION …
The Pennsylvania State University
The Graduate School
Department of Energy and Mineral Engineering
A Dissertation in
A NOVEL EQUATION-OF-STATE TO MODEL MICROEMULSION PHASE
BEHAVIOR FOR ENHANCED OIL RECOVERY APPLICATIONS
Energy and Mineral Engineering
by
Soumyadeep Ghosh
2015 Soumyadeep Ghosh
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
December 2015
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The dissertation of Soumyadeep Ghosh was reviewed and approved* by the following:
Prof. Russell T. Johns
Professor of Petroleum and Natural Gas Engineering
Program Chair for Petroleum and Natural Gas Engineering
Pennsylvania State University
Dissertation Advisor
Chair of Committee
Luis F. Ayala H.
Professor of Petroleum and Natural Gas Engineering;
Associate Department Head for Graduate Education
Pennsylvania State University
Zuleima T. Karpyn
Associate Professor of Petroleum and Natural Gas Engineering;
Quentin E. and Louise L. Wood Faculty Fellow in Petroleum and Natural Gas
Engineering;
Pennsylvania State University
Andrew Belmonte
Professor of Mathematics and Materials Science and Engineering
Pennsylvania State University
*Signatures are on file in the Graduate School
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ABSTRACT
Surfactant-polymer (SP) floods have significant potential to recover waterflood residual oil in
shallow oil reservoirs. A thorough understanding of surfactant-oil-brine phase behavior is critical
to the design of chemical EOR floods. While considerable progress has been made in developing
surfactants and polymers that increase the potential of a chemical enhanced oil recovery (EOR)
project, very little progress has been made to predict phase behavior as a function of formulation
variables such as pressure, temperature, and oil equivalent alkane carbon number (EACN). The
empirical Hand’s plot is still used today to model the microemulsion phase behavior with little
predictive capability as these and other formulation variables change. Such models could lead to
incorrect recovery predictions and improper flood designs. Reservoir crudes also contain acidic
components (primarily naphthenic acids), which undergo neutralization to form soaps in the
presence of alkali. The generated soaps perform synergistically with injected synthetic surfactants
to mobilize waterflood residual oil in what is termed alkali-surfactant-polymer (ASP) flooding.
The addition of alkali, however, complicates the measurement and prediction of the
microemulsion phase behavior that forms with acidic crudes.
In this dissertation, we account for pressure changes in the hydrophilic-lipophilic
difference (HLD) equation. This new HLD equation is coupled with the net-average curvature
(NAC) model to predict phase volumes, solubilization ratios, and microemulsion phase
transitions (Winsor II-, III, and II+). This dissertation presents the first modified HLD-NAC
model to predict microemulsion phase behavior for live crudes, including optimal solubilization
ratio and the salinity width of the three-phase Winsor III region at different temperatures and
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pressures. This new equation-of-state-like model could significantly aid the design and forecast
of chemical floods where key variables change dynamically, and in screening of potential
candidate reservoirs for chemical EOR. The modified HLD-NAC model is also extended here for
ASP flooding. We use an empirical equation to calculate the acid distribution coefficient from
the molecular structure of the soap. Key HLD-NAC parameters like optimum salinities and
optimum solubilization ratios are calculated from soap mole fraction weighted equations. The
model is tuned to data from phase behavior experiments with real crudes to demonstrate the
procedure. We also examine the ability of the new model to predict fish plots and activity charts
that show the evolution of the three-phase region. The modified HLD-NAC equations are then
made dimensionless to develop important microemulsion phase behavior relationships and for use
in tuning the new model to measured data. Key dimensionless groups that govern phase behavior
and their effects are identified and analyzed.
A new correlation was developed to predict optimum solubilization ratios at different
temperatures, pressures and oil EACN with an average relative error of 10.55%. The prediction
of optimum salinities with the modified HLD approach resulted in average relative errors of
2.35%. We also present a robust method to precisely determine optimum salinities and optimum
solubilization ratios from salinity scan data with average relative errors of 1.17% and 2.44% for
the published data examined.
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TABLE OF CONTENTS
Glossary ................................................................................................................................... vii
List of Figures .......................................................................................................................... x
List of Tables ........................................................................................................................... xxiii
Acknowledgements .................................................................................................................. xxv
Chapter 1 Introduction ............................................................................................................. 1
1.1. Surfactants and Interfacial Tensions ......................................................................... 2 1.2. Winsor’s R-Ratio and the C-Layer ........................................................................... 3 1.3. Effect of Salinity on R-Ratio ..................................................................................... 5 1.4. Microemulsions ......................................................................................................... 6 1.5. Types of Microemulsions in Surfactant-Oil-Brine (SOB) systems and their
significance in EOR ................................................................................................. 7 1.6. Research Goals .......................................................................................................... 10 1.7. Organization of the Dissertation ............................................................................... 10
Chapter 2 Literature Review .................................................................................................... 17
2.1. The Equivalent Alkane Carbon Number and its Relevance to Microemulsion
Phase Behavior ......................................................................................................... 17 2.2. Effect of Temperature, Pressure and Solution Gas on Microemulsion Phase
Behavior ................................................................................................................... 19 2.3. Role of Alkali in Surfactant Enhanced Oil Recovery Processes ............................... 23 2.4. The Surfactant Affinity Difference ........................................................................... 24 2.5. The Hydrophilic – Lipophilic Difference.................................................................. 25 2.6. The HLD-NAC model............................................................................................... 27
2.6.1. Radii and Curvatures of Micelles in Solubilized Systems ............................. 27 2.6.2. The Average Curvature Equation ................................................................... 28 2.6.3. The Net Curvature Equation .......................................................................... 29 2.6.4. Flash Calculations using HLD-NAC .............................................................. 29
2.7. Summary ................................................................................................................... 35
Chapter 3 Development of a Modified HLD-NAC Equation-of-State to Predict
Surfactant-Oil-Brine Phase Behavior for Live Oil at Reservoir Pressure and
Temperature ..................................................................................................................... 39
3.1. Extension of The HLD Equation to Include Pressure ............................................... 39 3.2. New Relations for Prediction of Optimum Solubilization Ratio .............................. 42 3.3. Modifying the HLD-NAC Model ............................................................................. 44
3.3.1. Accounting for Surfactant Volume Fraction in The Average Curvature
Equation............................................................................................................ 44 3.4. Determining The Surfactant Length Parameter ........................................................ 46 3.5. Results ....................................................................................................................... 48
3.5.1. Example 1: Skauge and Fotland (1990) Experiments .................................... 48
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3.5.2. Example 2: Roshanfekr and Johns (2011), and Roshanfekr et al. (2013)
Experiments ...................................................................................................... 51 3.5.3. Example 3:Austad and Strand (1996) and Austad and Taugbol (1995)
Experiments ...................................................................................................... 54 3.6. Discussion ................................................................................................................. 57 3.7. Conclusions ............................................................................................................... 61
Chapter 4 A Modified HLD-NAC Equation of State to Predict Alkali-Surfactant-Oil-
Brine Phase Behavior ....................................................................................................... 83
4.1. Soap Formation Model .............................................................................................. 83 4.2. Equilibrium Constants and Their Dependence on the Molecular Structure of
Petroleum Acids ....................................................................................................... 85 4.3. Flash Calculations Including the Alkali Component ................................................ 86 4.4. Results ....................................................................................................................... 90
4.4.1. Case A from Mohammadi (2008), and Mohammadi et al. (2009) ................. 91 4.4.2. Case B from Mohammadi (2008), and Mohammadi et al. (2009) ................. 93
4.5. Conclusions ............................................................................................................... 97
Chapter 5 Dimensionless Solutions to Microemulsion Phase Behavior .................................. 108
5.1. Solubilization Ratio Relationships in Two-Phase Regions ....................................... 108 5.1.1. Dimensionless Solutions for Type II- Microemulsions.................................. 110 5.1.2. Dimensionless Solutions for Type II+ Microemulsions ................................. 111
5.2. Solubilization Ratio Relationships in The Three-phase Region ............................... 111 5.3. Two-phase Limits and Stability Criteria for Dimensionless Equations .................... 114 5.4. Results ....................................................................................................................... 117
5.4.1. Interpretation of Phase Behavior Experiments ............................................... 117 5.4.2. Analysis .......................................................................................................... 120 5.4.3. Dimensionless Solutions Applied to Temperature and Pressure Scans ......... 121 5.4.4. Interfacial Volume Ratio for Surfactant Mixtures.......................................... 123
5.5. Conclusions ............................................................................................................... 124
Chapter 6 Conclusions and Recommendations ........................................................................ 143
6.1. Conclusions ............................................................................................................... 143 6.2. Recommendations for Future Research .................................................................... 146
Appendix A Effect of Pressure on the Surfactant Affinity Difference and the
Hydrophilic-Lipophilic Difference .................................................................................. 148
Appendix B Alkalinity of Aqueous Sodium Carbonate Solution ........................................... 153
Appendix C Salinity Scan Experiments at Atmospheric Pressure .......................................... 155
References ................................................................................................................................ 160
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Glossary
Roman
As = Total interfacial area occupied by surfactant (Å2)
A1 = Constant slope for σ* vs 1/ΔHLD linear trend (dimensionless)
A2 = Constant intercept for σ* vs 1/ΔHLD linear trend (dimensionless)
B1 = Constant slope for lnS* vs 1/σ* linear trend (dimensionless)
B2 = Constant intercept for lnS* vs 1/σ* linear trend (dimensionless)
ai = Activity coefficient of surfactant in phase i. (dimensionless)
asurf = Area per surfactant molecule (Å2)
asoap = Area per soap molecule (Å2)
bi = constant value of partial derivative of µi* for a phase i with respect to a HLD
variable (dimensionless)
C1 = Constant slope for lnS* vs Xsoap linear trend (dimensionless)
C2 = Constant intercept for lnS* vs Xsoap linear trend (dimensionless)
Cc = Characteristic curvature of surfactant (dimensionless)
D1 = Constant slope for 1/σ* vs Xsoap linear trend (dimensionless)
D2 = Constant intercept for 1/σ* vs Xsoap linear trend (dimensionless)
EACN = Equivalent alkane carbon number (EACN unit)
f(A) = Function of alcohol type and concentration (dimensionless)
Ha = Average curvature (Å-1)
Hen = Net curvature (Å-1)
HLD = Hydrophilic lipophilic difference (dimensionless)
K = Slope of logarithm of optimum salinity as a function of EACN (per EACN unit)
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L = Surfactant length parameter (Å)
Lc = Maximum chain length of surfactant tail (Å)
nc = Effective number of carbon atoms in the tail of the surfactant
P = Pressure (bars)
RI = Radius of component i in the microemulsion (Å)
R = Universal gas constant (J mol-1 K-1 )
S = Salinity (g/100ml)
SAD = Surfactant affinity difference (J mol-1)
T = Temperature (°C or K)
Vi = Volume of component i (cm3)
Xi = HLD variable (mnemonic)
xi = Fraction of total system composition of surfactant in phase i.(dimensionless)
Xsoap = Soap mole fraction
Surfactant = Surfactant mole fraction
Greek
α = Temperature coefficient (°C -1 or K-1 )
β = Pressure coefficient (bar-1)
σ = Solubilization ratio (dimensionless)
ϕi = Fraction of component i in the microemulsion (dimensionless)
µi = Chemical potential of surfactant in phase i (J mol-1)
µi* = Reference state chemical potential of surfactant in phase i (J mol-1)
ξ = Correlation length (Å)
ξ* = Critical correlation length (Å)
χ = Overall composition parameter (dimensionless)
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Subscripts
U = Upper limit corresponding to a phase transition from type III to type II+ or vice
versa
L = Lower limit corresponding to a phase transition from type II- to type III or vice
versa
o = Oil
w = Water
s = Surfactant
ref = Reference state
Superscripts
* = Optimum state unless mentioned otherwise.
0 = Initial condition
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List of Figures
Figure 1-1 : Schematic of forces acting (in dynes or N) on unit length (e.g. 1 cm or m) on
an interface. The force per unit length is the interfacial tension (dynes/cm or N/m). ..... 13
Figure 1-2: Oil droplet with radius R suspended in water, separated from the oil bulk
phase. Adapted from Acosta et al. (2003). ....................................................................... 13
Figure 1-3: Interaction energies in the C-layer that govern the R-ratio. Adapted from
Bourrel and Schechter (2010). ......................................................................................... 14
Figure 1-4: Schematic of microemulsion formation. Adapted from Tadros (2006). ............... 14
Figure 1-5: Pseudo ternary diagram of a type II- system. (Lake et al., 2014) ......................... 15
Figure 1-6: Pseudo ternary diagram of a type II+ system. (Lake et al., 2014) ........................ 15
Figure 1-7: Pseudo ternary diagram of a type III system. (Lake et al., 2014) ......................... 16
Figure 2-1: Flowchart showing the protocol followed for the HLD-NAC model described
by Acosta et al. (2003). .................................................................................................... 38
Figure 3-1: Optimum salinity as a function of pressure for experiments reported for the
SAS surfactant (Skauge and Fotland 1990). The slope is the β factor for the HLD
equation. ........................................................................................................................... 68
Figure 3-2: Optimum salinity as a function of pressure for experiments reported for the
SDBS surfactant (Skauge and Fotland 1990). The slope is the β factor for the HLD
equation. ........................................................................................................................... 68
Figure 3-3: A schematic showing the trend lines for the optimum salinity, and the upper
and lower salinity limits. The width of the three-phase Winsor III region is shown. ..... 68
Figure 3-4: Reciprocal of optimum solubilization ratios as a function of logarithm of
optimum salinity. Red, green and blue represent data at 20°C, 50°C and 90°C
respectively. Oils used were heptane, octane and decane. B1 = 0.15 and B2 =-0.22.
Data from Sun et al. (2012). ............................................................................................. 68
Figure 3-5: Flowchart of the modified HLD-NAC Equation-of-State. .................................... 69
Figure 3-6: Phase volume fractions after tuning as a function of salinity for the SAS
surfactant. The value for interfacial area per molecule after tuning was 180 Å2. Data
from Skauge and Fotland (1990)...................................................................................... 70
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Figure 3-7: Phase volume fractions after tuning as a function of salinity for the SDBS
surfactant. The value of interfacial area per molecule after tuning was 97 Å2. Data
from Skauge and Fotland (1990)...................................................................................... 70
Figure 3-8: Logarithm of optimum salinity as a function of EACN for experiments
reported for SAS surfactant. The slope of the trend line gives the slope K for the
HLD equation. Data obtained from Skauge and Fotland (1990). ..................................... 70
Figure 3-9: Logarithm of optimum salinity as a function of EACN for experiments
reported for SDBS surfactant. The slope of the trend line gives the slope K for the
HLD equation. Data obtained from Skauge and Fotland (1990). ..................................... 70
Figure 3-10: Logarithm of optimum salinity as a function of reciprocal of optimum
solubilization ratio for experiments reported for SAS surfactant from the EACN
trend. B1 = 0.24 and B2 = -0.24. Data obtained from Skauge and Fotland (1990). .......... 71
Figure 3-11: Logarithm of optimum salinity as a function of reciprocal of optimum
solubilization ratio for experiments reported for SDBS surfactant from the EACN
trend. B1 = 0.18 and B2 = -0.02. Data obtained from Skauge and Fotland (1990). .......... 71
Figure 3-12: logarithm of optimum salinity as a function of temperature for experiments
reported for SAS surfactant. The slope of the trend line gives the α factor for the
HLD equation. Data obtained from Skauge and Fotland (1990). ..................................... 71
Figure 3-13: logarithm of optimum salinity as a function of temperature for experiments
reported for SDBS surfactant. The slope of the trend line gives the α factor for the
HLD equation. Data obtained from Skauge and Fotland (1990). ..................................... 71
Figure 3-14: Optimum solubilization ratio as a function of pressure for experiments
reported for SAS surfactant. The HLD equation and equation from Figure 3-10 was
used for prediction. Data obtained from Skauge and Fotland (1990). ............................. 72
Figure 3-15: Optimum solubilization ratio as a function of pressure for experiments
reported for SDBS surfactant. The HLD equation and equation from Figure 3-11 was
used for prediction. Data obtained from Skauge and Fotland (1990). ............................. 72
Figure 3-16: Optimum solubilization ratio as a function of temperature for experiments
reported for SAS surfactant. The HLD equation and equation from Figure 3-10 was
used for prediction. Data obtained from Skauge and Fotland (1990). ............................. 72
Figure 3-17: Optimum solubilization ratio as a function of temperature for experiments
reported for SDBS surfactant. The HLD equation and equation from Figure 3-11
was used for prediction. Data obtained from Skauge and Fotland (1990) ....................... 72
Figure 3-18: Tuned result for solubilization ratios as a function of salinity for octane. Red
represents oil solubilization ratios. Blue represents water solubilization ratios. The
solid lines are model results from HLD-NAC obtained by tuning as. .............................. 73
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Figure 3-19: Tuned result for solubilization ratios as a function of salinity for decane.
Red represents oil solubilization ratios. Blue represents water solubilization ratios.
The solid lines are model results from HLD-NAC obtained by tuning as. ...................... 73
Figure 3-20: Tuned result for solubilization ratios as a function of salinity for dodecane.
Red represents oil solubilization ratios. Blue represents water solubilization ratios.
The solid lines are model results from HLD-NAC obtained by tuning as. ...................... 73
Figure 3-21: logarithm of optimum salinity as a function of EACN. A mixture of tridecyl
alcohol propoxylate and C13-C18 internal olefin sulfonate was used along with iso-
propanol as cosurfactant. Data obtained from Roshanfekr et al. (2011). ......................... 73
Figure 3-22: Logarithm of optimum salinity as a function of reciprocal of optimum
solubilization ratio from experiments with varying EACN. B1 = 0.08 and B2 = 0.02.
Data obtained from Roshanfekr et al. (2011). .................................................................. 74
Figure 3-23: Prediction of phase behavior for dead oil at elevated pressure (68.95 bars)
using data from pure alkane series and estimated β factor of 7.71×10-4/bar. Red
represents oil solubilization ratios. Blue represents water solubilization ratios. .............. 74
Figure 3-24: Prediction of phase behavior for dead oil at atmospheric pressure using data
from pure alkane series. Red represents oil solubilization ratios. Blue represents
water solubilization ratios. The solid lines are model results from HLD-NAC. .............. 74
Figure 3-25: Prediction of phase behavior for live oil at high pressure using estimated β
factor of 7.71×10-4/bar. Red represents oil solubilization ratios. Blue represents
water solubilization ratios. The solid lines are model results from HLD-NAC. .............. 74
Figure 3-26: Phase volume fractions as a function of salinity using 0.5 wt. % dodecyl
orthoxylene sulfonate. The tuned as value was 98 Å2. Solid lines represent model
outputs with tuned alpha values. Circles represent experimentally obtained values.
Blue represents ................................................................................................................. 75
Figure 3-27: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil temperature scan at 50 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 75
Figure 3-28: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil temperature scan at 100 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 75
Figure 3-29: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil temperature scan at 150 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 75
Figure 3-30: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil temperature scan at 200 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 76
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Figure 3-31: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil temperature scan at 250 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 76
Figure 3-32: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil temperature scan at 300 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 76
Figure 3-33: Comparison of tuned result (solid lines) and actual values (circles) for live
oil temperature scan at 100 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 76
Figure 3-34: Comparison of tuned result (solid lines) and actual values (circles) for live
oil temperature scan at 200 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 77
Figure 3-35: Comparison of tuned result (solid lines) and actual values (circles) for live
oil temperature scan at 250 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 77
Figure 3-36: Comparison of tuned result (solid lines) and actual values (circles) for live
oil temperature scan at 300 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 77
Figure 3-37: Comparison of tuned result (solid lines) and actual values (circles) for live
oil temperature scan at 400 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 77
Figure 3-38: Comparison of tuned result (solid lines) and actual values (circles) for live
oil temperature scan at 450 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 78
Figure 3-39: Comparison of tuned result (solid lines) and actual values (circles) for live
oil temperature scan at 500 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 78
Figure 3-40: Comparison of tuned result (solid lines) and actual values (circles) for live
oil temperature scan at 600 bars. Red represents oil solubilization. Blue represents
water solubilization. Data from Austad and Strand (1996). ............................................. 78
Figure 3-41: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil pressure scan at 55°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 78
Figure 3-42: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil pressure scan at 60°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 79
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Figure 3-43: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil pressure scan at 65°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 79
Figure 3-44: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil pressure scan at 70°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 79
Figure 3-45: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil pressure scan at 75°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 79
Figure 3-46: Comparison of tuned result (solid lines) and actual values (circles) for dead
oil pressure scan at 80°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 80
Figure 3-47: Comparison of tuned result (solid lines) and actual values (circles) for live
oil pressure scan at 70°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 80
Figure 3-48: Comparison of tuned result (solid lines) and actual values (circles) for live
oil pressure scan at 75°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 80
Figure 3-49: Comparison of tuned result (solid lines) and actual values (circles) for live
oil pressure scan at 80°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 80
Figure 3-50: Comparison of tuned result (solid lines) and actual values (circles) for live
oil pressure scan at 85°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 81
Figure 3-51: Comparison of tuned result (solid lines) and actual values (circles) for live
oil pressure scan at 90°C. Red represents oil solubilization. Blue represents water
solubilization. Data from Austad and Strand (1996). ....................................................... 81
Figure 3-52: Variation of α with increasing pressure. Blue squares represent tuned α
values for dead oil. Red squares represent tuned α values for the live oil. Data
obtained by analysis of experimental results reported by Austad and Strand (1996). ..... 81
Figure 3-53: Variation of β with increasing temperature. Blue squares represent tuned β
values for dead oil. Red squares represent tuned β values for the live oil. Data
obtained by analysis of experimental results reported by Austad and Strand (1996). ..... 81
Figure 3-54: linear correlation of the optimum solubilization ratio inverse of the three-
phase region width and the inverse of the three-phase region width. The points
represent results from both live and dead oil at all pressures and temperatures
reported. A1 = 2.54 and A2 = 4.28. Data obtained by analysis of experimental
results reported by Austad and Strand (1996). ................................................................. 82
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Figure 3-55: A schematic showing the shifts in optimum salinity trend line due to
pressure. The shifts in the intercepts are caused by the β factor and the difference
between the pressure of interest and the reference pressure. The black dot shows the
optimum salinity at the reference condition. The green circles show the correct
interpretation of the shift due to pressure. The red circles show the incorrect
interpretation made in Jang et al. (2014). ......................................................................... 82
Figure 4-1: Linear relationship between the number of carbon atoms in the alkyl group of
a carboxylic acid and pKd for water-heptane systems. Data obtained from Smith &
Tanford (1973). ................................................................................................................ 101
Figure 4-2: Linear relationship between mole fraction of soap formed and log of optimum
salinity (in meq/ml) for Case A. Value of n used was 13. Data obtained from
Mohammadi (2008). ......................................................................................................... 101
Figure 4-3: Linear relationship between mole fraction of soap formed and inverse of
optimum solubilization ratio in cc/cc for Case A. Value of n used was 13. Data
obtained from Mohammadi (2008). ................................................................................. 101
Figure 4-4 Match of tuned HLD-NAC model (solid lines) for Case A at 50% oil overall
concentration (v/v). Red represents σo while blue represents σw. The tuned value of
asurf was 195 Å2. Circles are experimental data and dashed lines show UTCHEM
output reported by Mohammadi (2008). .......................................................................... 101
Figure 4-5: Match of tuned HLD-NAC (solid lines) model for Case A at 30 % oil overall
concentration (v/v). Red represents σo while blue represents σw. The tuned value of
asurf was 215 Å2. Circles are experimental data and dashed lines show UTCHEM
output reported by Mohammadi (2008). .......................................................................... 102
Figure 4-6: Prediction of solubility ratios using tuned HLD-NAC model for Case A at
10 % oil overall concentration (v/v). Red represents σo while blue represents σw. The
value of asurf used was 205 Å2. The green circle represents the optimum
experimentally measured by Mohammadi (2008). This point was used in tuning. ......... 102
Figure 4-7: Prediction of solubility ratios using tuned HLD-NAC model for Case A at
20 % oil overall concentration (v/v). Red represents σo while blue represents σw. The
value of asurf used was 205 Å2. The green circle represents the optimum
experimentally measured by Mohammadi (2008). This point was used in tuning. ......... 102
Figure 4-8: Prediction of solubility ratios for tuned HLD-NAC model for Case A at 40 %
oil overall concentration (v/v). Red represents σo while blue represents σw. The value
of asurf used was 205 Å2. The green circle represents the optimum experimentally
measured by Mohammadi (2008). This point was used in tuning. .................................. 102
Figure 4-9: Phase volume fraction diagram based on flash calculations for 10 % oil
concentration for Case A. Each bar represents a fixed sodium carbonate
concentration. Red represents excess oil phase, blue excess brine, and green the
microemulsion phase. ....................................................................................................... 103
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Figure 4-10: Phase volume fraction diagram based on flash calculations for 40 % oil
concentration in Case A. Each bar represents a fixed sodium carbonate
concentration. Red represents excess oil phase, blue excess brine, and green the
microemulsion phase. ....................................................................................................... 103
Figure 4-11: Activity map for Case A. Solid lines represent prediction from the model
used in this dissertation. Green represents type II-, red type III and blue type II+
regions found experimentally. The dashed lines show the three-phase window used
in the UTCHEM model by Mohammadi et al. (2009). .................................................... 103
Figure 4-12: Linear relationship between mole fraction of soap formed and log of
optimum salinity (in meq/ml) for Case B. Value of n used was 14. Data obtained
from Mohammadi (2008). ................................................................................................ 103
Figure 4-13: Linear relationship between mole fraction of soap formed and inverse of
optimum solubilization ratio in cc/cc for Case B. Value of n used was 14. Data
obtained from Mohammadi (2008). ................................................................................. 104
Figure 4-14 Match of tuned HLD-NAC model (solid lines) for Case B at 30 % oil overall
concentration (v/v) and 0.3 wt.% surfactant concentration. Red represents σo while
blue represents σw. The tuned value of asurf was 16 Å2. Circles are experimental data
and dashed lines show UTCHEM output reported by Mohammadi (2008). .................... 104
Figure 4-15: Match of tuned HLD-NAC model (solid lines) for Case B at 50 % oil overall
concentration (v/v) and 0.3 wt.% surfactant concentration. Red represents σo while
blue represents σw. The tuned value of asurf was 45 Å2. Circles are experimental data
and dashed lines show UTCHEM output reported by Mohammadi (2008). .................... 104
Figure 4-16: Prediction of tuned HLD-NAC model (solid lines) for Case B at 30 % oil
overall concentration (v/v) and 0.6 wt.% surfactant concentration. Red represents σo
while blue represents σw. Circles are experimental data and dashed lines show
UTCHEM output reported by Mohammadi (2008). ........................................................ 104
Figure 4-17: Prediction of tuned HLD-NAC model (solid lines) for Case B at 40 % oil
overall concentration (v/v) and 0.6 wt.% surfactant concentration. Red represents σo
while blue represents σw. Circles are experimental data and dashed lines show
UTCHEM output reported by Mohammadi (2008). ........................................................ 105
Figure 4-18: Prediction of tuned HLD-NAC model (solid lines) for Case B at 50 % oil
overall concentration (v/v) and 1 wt.% surfactant concentration. Red represents σo
while blue represents σw. Circles are experimental data and dashed lines show
UTCHEM output reported by Mohammadi (2008). ........................................................ 105
Figure 4-19: Phase volume fraction diagram based on flash calculation results for Case B
at 30 % oil overall concentration (v/v) and 0.6 wt.% surfactant concentration. Each
bar represents a sodium carbonate concentration. Red represents excess oil phase,
blue represents excess brine, and green represents microemulsion phase. ...................... 105
xvii
Figure 4-20: Phase volume fraction diagram based on flash calculation results for Case B
at 50 % oil overall concentration (v/v) and 1 wt.% surfactant concentration. Each
bar represents a sodium carbonate concentration. Red represents excess oil phase,
blue represents excess brine, and green represents microemulsion phase. ...................... 105
Figure 4-21: Activity map for Case B with 0.3 wt.% surfactant. Solid lines represent
prediction from the model used in this dissertation. Green represents type II-, red
type III and blue type II+ regions found experimentally. The dashed lines show the
window used in the UTCHEM model by Mohammadi (2008). ....................................... 106
Figure 4-22: Activity map for Case B with 0.6 wt.% surfactant. Solid lines represent
prediction from the model used in this dissertation. Green represents type II-, red
type III and blue type II+ regions found experimentally. The dashed lines show the
window used in the UTCHEM model by Mohammadi (2008). ....................................... 106
Figure 4-23: Activity map for Case B with 1 wt.% surfactant. Solid lines represent
prediction from the model used in this dissertation. Green represents type II-, red
type III and blue type II+ regions found experimentally. The dashed lines show the
window used in the UTCHEM model by Mohammadi (2008). ....................................... 106
Figure 4-24: Example of a fish diagram showing types of microemulsions with no alkali
for a pure surfactant. Only Nalco concentration in brine is varied. Model parameters
were obtained from Case A. Red shows the upper salinity limit and blue the lower
salinity limit. Dashed line shows the optima. .................................................................. 106
Figure 4-25: Fish diagrams using model parameters obtained from Case A. Red shows
the upper salinity limit and blue the lower salinity limit. Solid lines show the fish
diagram with 1.0 wt.% Na2CO3 and dashed lines show fish diagram in absence of
alkali. ................................................................................................................................ 107
Figure 4-26: Fish diagrams using model parameters obtained from Case B. Red shows the
upper salinity limit and blue the lower salinity limit. Solid lines show the fish
diagram with 1.0 wt.% Na2CO3 (fixed) and Nalco concentration varying. Dashed
lines show the fish diagram in absence of alkali. ............................................................. 107
Figure 4-27: Fish diagram using model parameters tuned for Case A. Red shows the
upper salinity limit and blue the lower salinity limit. Solid lines show the fish
diagram with Na2CO3 concentration varying (brine concentration fixed). Squares
indicate experimental data from Mohammadi (2008). ..................................................... 107
Figure 4-28: Fish diagram using model parameters tuned for Case B. Red shows the
upper salinity limit and blue the lower salinity limit. Solid lines show the fish
diagram with Na2CO3 concentration varying (brine concentration fixed). Squares
indicate experimental data from Mohammadi (2008). ..................................................... 107
Figure 5-1: An example showing the linear relationship between the inverse of oil
solubilization ratios and HLD for type II- microemulsions. Data obtained from
Sheng (2010). ................................................................................................................... 130
xviii
Figure 5-2: An example showing the linear relationship between the inverse of water
solubilization ratios and HLD for type II+ microemulsions. Data obtained from
Sheng (2010). ................................................................................................................... 130
Figure 5-3: An example showing the linear relationship between the inverse of
solubilization ratios (red for oil, blue for water) and HLD for type III
microemulsions. Data obtained from Sheng (2010). ........................................................ 130
Figure 5-4: An example showing the linear relationship between the inverse of
solubilization ratios and HLD. Red represents inverse of oil solubilization ratios.
Blue represents inverse of water solubilization ratios. (WOR=1, σ* = 13.5 cc/cc and
I-ratio = 0.129). ................................................................................................................ 131
Figure 5-5: Tuned phase behavior (solid lines) compared to data (circles) for experiments
with NaCl and SDS+SDBS+IBA surfactant mixture at 40 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. I-ratio = 0.21, σ* =
7.35 cc/cc and S*= 1.47 meq/ml. Oil used was heptane. .................................................. 131
Figure 5-6: Tuned phase behavior (solid lines) compared to data (circles) for experiments
with NaCl and SDS+SDBS+IBA surfactant mixture at 40 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. I-ratio = 0.34, σ* =
4.56 cc/cc and S*= 2.52 meq/ml. Oil used was dodecane. ............................................... 131
Figure 5-7: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with NaCl and SDS surfactant at 20 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 132
Figure 5-8: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with KCl and SDS surfactant at 20 °C. Red represents oil solubilization
ratios. Blue represents water solubilization ratios. Data from (Aarra et al., 1999) .......... 132
Figure 5-9: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with CaCl2 and SDS surfactant at 20 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 132
Figure 5-10: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with MgCl2 and SDS surfactant at 20 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 132
Figure 5-11: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with NaCl and SDS surfactant at 35 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 133
xix
Figure 5-12: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with KCl and SDS surfactant at 35 °C. Blue represents water
solubilization ratios. Data from (Aarra et al., 1999) ........................................................ 133
Figure 5-13: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with CaCl2 and SDS surfactant at 35 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 133
Figure 5-14: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with MgCl2 and SDS surfactant at 35 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 133
Figure 5-15: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with NaCl and SDS surfactant at 50 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 134
Figure 5-16: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with KCl and SDS surfactant at 50 °C. Red represents oil solubilization
ratios. Blue represents water solubilization ratios. Data from (Aarra et al., 1999) .......... 134
Figure 5-17: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with CaCl2, and SDS surfactant at 50 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 134
Figure 5-18: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with MgCl2, and SDS surfactant at 50 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 134
Figure 5-19: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with NaCl and AAS surfactant at 20 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 135
Figure 5-20: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with KCl and AAS surfactant at 20 °C. Red represents oil solubilization
ratios. Blue represents water solubilization ratios. Data from (Aarra et al., 1999) .......... 135
Figure 5-21: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with CaCl2, and AAS surfactant at 20 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 135
Figure 5-22: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with MgCl2, and AAS surfactant at 20 °C. Red represents oil
xx
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 135
Figure 5-23: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with NaCl and AAS surfactant at 50 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 136
Figure 5-24: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with KCl and AAS surfactant at 50 °C. Red represents oil solubilization
ratios. Blue represents water solubilization ratios. Data from (Aarra et al., 1999) .......... 136
Figure 5-25: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with CaCl2, and AAS surfactant at 50 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 136
Figure 5-26: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with MgCl2, and AAS surfactant at 50 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 136
Figure 5-27: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with NaCl and AAS surfactant at 90 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 137
Figure 5-28: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with KCl and AAS surfactant at 90 °C. Red represents oil solubilization
ratios. Blue represents water solubilization ratios. Data from (Aarra et al., 1999) .......... 137
Figure 5-29: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with CaCl2, and AAS surfactant at 90 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 137
Figure 5-30: Tuned phase behavior (solid lines) compared reported data (circles) for
experiments with MgCl2, and AAS surfactant at 90 °C. Red represents oil
solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et
al., 1999) .......................................................................................................................... 137
Figure 5-31: Average tuned interfacial volume ratios for experiments using SDS
surfactant at 20°C (Blue), 35°C (Red), 50°C (Green). Black lines represent average
interfacial volume ratios for each salt. ............................................................................. 138
Figure 5-32: Average tuned interfacial volume ratios for experiments using AAS
surfactant at 20°C (Blue), 50°C (Red), 90°C (Green). Black lines represent average
interfacial volume ratios for each salt. ............................................................................. 138
xxi
Figure 5-33: Width of the three-phase region as a function of the optimum solubilization
ratio and the interfacial volume ratio (I) for a fixed overall concentration of
ϕo=0.495, ϕw=0.495 and ϕs=0.01. ................................................................................... 138
Figure 5-34: Example of a modified fish diagram (interfacial volume ratio (I)=0.2). Red
shows the upper salinity limit and blue the lower salinity limit. Type III
microemulsions can only exist when χ is larger than σ* and, HLD is within the upper
and lower critical limits HLDU* and HLDL
* . ................................................................... 138
Figure 5-35: Locus of the invariant type III microemulsion composition in a ternary
space. (σ*= 3 cc/cc) ......................................................................................................... 139
Figure 5-36: Locus of the invariant type III microemulsion composition in a ternary
space. (σ*= 10 cc/cc) ........................................................................................................ 139
Figure 5-37: Locus of invariant type III microemulsion composition in a ternary space
(σ*= 30 cc/cc). ................................................................................................................. 139
Figure 5-38: Inverse of oil solubilization ratios as a function of pressure at different
constant temperatures using dead oil. Data from Austad and Strand (1996) ................... 140
Figure 5-39: Inverse of water solubilization ratios as a function of pressure at different
constant temperatures using dead oil. Data from Austad and Strand (1996) ................... 140
Figure 5-40: Inverse of oil solubilization ratios as a function of pressure at different
constant temperatures using live oil. Data from Austad and Strand (1996) ..................... 140
Figure 5-41: Inverse of water solubilization ratios as a function of pressure at different
constant temperatures using live oil. Data from Austad and Strand (1996) ..................... 140
Figure 5-42: Inverse of oil solubilization ratios as a function of temperature at different
constant pressures using dead oil. Data from Austad and Strand (1996). ........................ 141
Figure 5-43: Inverse of water solubilization ratios as a function of temperature at
different constant pressures using dead oil. Data from Austad and Strand (1996). ......... 141
Figure 5-44: Inverse of oil solubilization ratios as a function of temperature at different
constant pressures using live oil. Data from Austad and Strand (1996). ......................... 141
Figure 5-45: Inverse of water solubilization ratios as a function of temperature at
different constant pressures using live oil. Data from Austad and Strand (1996). ........... 141
Figure 5-46: Interfacial volume ratio for a surfactant mixture (sodium laurate and sodium
oleate) as a function of laurate soap mole fraction using Eq. (5.32). ............................... 142
Figure 5-47: Inverse of water solubilization ratios as a function of temperature at
different constant pressures using dead oil. Data from Austad and Strand (1996). ......... 142
xxii
Figure 5-48: Inverse of oil solubilization ratios as a function of temperature at different
constant pressures using live oil. Data from Austad and Strand (1996). ......................... 142
Figure C-1: Schematic of readings measured from a phase behavior pipette scan. O: oil,
W: water and ME: microemulsion. Total volume capacity of each pipette is 5 ml. ........ 159
xxiii
List of Tables
Table 1-1: General classification of micelles, microemulsions and macroemulsions.
(Tadros, 2006) .................................................................................................................. 12
Table 1-2: Summary of effects of SOB system variables on microemulsion phase
behavior. ........................................................................................................................... 12
Table 3-1: Summary of prediction of optima at various temperatures for SAS surfactant.
Predictions for S* were made by taking S* at 20°C as reference and using α = 0.0031
K-1. Data obtained from Skauge and Fotland (1990). ...................................................... 63
Table 3-2: Summary of prediction of optima at various pressures for SAS surfactant.
Predictions for S* were made by taking S* at 20°C and atmospheric pressure as
reference. β is 0.0006 bar-1. Data obtained from Skauge and Fotland (1990). ................. 63
Table 3-3: Summary of prediction of optima at various temperatures for SDBS surfactant.
Predictions for S* were made by taking the S* at 20°C as reference. α is 0.0077 K-1.
Data obtained from Skauge and Fotland (1990). ............................................................. 64
Table 3-4: Summary of prediction of optima at various pressures for SDBS surfactant.
Predictions for S* were made by taking S* at 20°C and atmospheric pressure as
reference. β is 0.0008 bar-1. Data obtained from Skauge and Fotland (1990). ................. 64
Table 3-5: Summary of results obtained by matching pressure scans for dead oil. Data
obtained from Austad and Strand (1996). ........................................................................ 65
Table 3-6: Summary of results obtained by matching pressure scans for live oil. Data
obtained from Austad and Strand (1996). ........................................................................ 65
Table 3-7: Summary of results obtained by matching temperature scans for dead oil. Data
obtained from Austad and Strand (1996). ........................................................................ 66
Table 3-8: Summary of results obtained by matching temperature scans for live oil. Data
obtained from Austad and Strand (1996). ........................................................................ 66
Table 3-9: Summary showing β values obtained from tuning. Data from Skauge and
Fotland (1990), Roshanfekr and Johns (2011) and Austad and Strand (1996). ............... 67
Table 4-1: : Summary of optima for experiments for crude oil case A. Data from
Mohammadi, (2008). ........................................................................................................ 99
Table 4-2: : Summary of model parameters for Case A. ......................................................... 99
xxiv
Table 4-3: Summary of optima for experiments for crude oil case B. Data from
Mohammadi, (2008). ........................................................................................................ 100
Table 4-4: Summary of model parameters for Case B. ............................................................ 100
Table 5-1: Summary of optima and tuned interfacial volume ratio (I) for experiments
using SDS surfactant reported by Aarra et al. (1999) ...................................................... 126
Table 5-2: Summary of optima and tuned interfacial volume ratio (I) for experiments
using AAS surfactant reported by Aarra et al. (1999) ...................................................... 127
Table 5-3: Summary of interfacial volume ratio at different temperatures from analysis of
pressure scans reported by Austad and Strand (1996). .................................................... 128
Table 5-4: Summary of interfacial volume ratio at different pressures from analysis of
temperature scans reported by Austad and Strand (1996). ............................................... 128
Table 5-5: Statistical summary of interfacial volume ratio data obtained from pressure
and temperature scans reported by Austad and Strand (1996). ........................................ 129
Table C-1: Summary of observations and calculations in a salinity scan. Total volume
capacity of each pipette is 5 ml. ....................................................................................... 158
xxv
Acknowledgements
I would like to thank my advisor Prof. Russell T. Johns for the support and guidance I received
from him during the course of this research. His insightful questions and perseverance helped
expand this research and make it impactful. He has constantly shown faith in my ability and has
encouraged me to excel in both academic and professional environments. I have learned a lot
from him and it has been an honor to have him as my PhD mentor.
I would also like to thank the rest of my committee, Prof. Luis Ayala, Prof. Zuleima
Karpyn, and Prof. Andrew Belmonte. Their insightful comments and critique helped me to
significantly improve my research. Special thanks to Prof. Turgay Ertekin for his guidance, which
provided me with much needed direction at the nascent stages of my graduate school experience.
Special thanks to my friends Sarath Ketineni, Taha Husain and Vaibhav Rajput for the
stimulating discussions, for the sleepless nights we were working together before deadlines, and
for all the fun we have had in the last four years. Victor Torrealba, Pooya Khodaparast, Bahareh
Nojabaei, Liwei Li and Saeid Khorsandi ensured that the office we shared was full of life. I thank
them for their camaraderie. Special thanks to Atriya Ghosh, Phani Kiran, Manasi Kamat and
Sagnik Ray Choudhury for their support.
I am grateful to Sophany Thach for gifting me Bourrel and Schechter’s book
“Microemulsions and related systems: formulation, solvency, and physical properties.” It was a
gift that proved to be crucial in the development of this research. I also thank Adwait Chawathe
for being a strong moral support. I greatly acknowledge the members of the EOR industry
affiliates program at PennState and the US Department of Energy for their financial support.
Last but not least; I thank my family; my parents and my brother, for believing in
me. The unconditional love from my family has been a pillar of strength for me
xxvi
throughout my life. This dissertation would not have been possible without their
encouragement.
1
Chapter 1
Introduction
Capillary forces resist viscous forces during a waterflood, which causes significant trapping of oil
in pores. Trapping occurs at a small capillary number, where the capillary number is defined as
the ratio of viscous forces to capillary forces. One form of the capillary number is
/
w
c
o w
µ qN
. (1.1)
An increase in capillary number reduces the residual oil saturation (Foster, 1973).
Viscous forces must overcome capillary forces to improve oil recovery (Healy and Reed, 1977).
Enhanced oil recovery processes involving surfactants aims at achieving high capillary number
by reducing the oil and water interfacial tension (γo/w) to ultra-low values. Viscous forces are also
increased by using water-soluble polymers, which increases the viscosity of drive water (µw).
Typical capillary numbers using Eq. (1.1) are on the order of 10-6 during a waterflood.
Estimates for Berea sandstone showed that in order to recover 50% of the residual oil after a
waterflood, the capillary number must increase by three orders of magnitude to about 10-3 (Foster,
1973). Typical oil-brine interfacial tensions lie in the range of 20-30 dynes/cm. Thus ultra-low
interfacial tensions (less than 10 -3 dynes/cm) are desirable.
Surfactants are compounds that have an ability to seek an interface between two
immiscible fluids and alter the interfacial tension. The phases formed due to the presence of
surfactants in the system and the degree of interfacial tension alteration is critical to enhanced oil
recovery.
2
1.1. Surfactants and Interfacial Tensions
Surfactants contain polar groups (known as “heads”) and non-polar groups (known as “tails”).
The head groups attract polar molecules like water and are hence are known as hydrophiles. Due
to polarity, heads have a tendency to repel non-polar molecules (in oils or lipids) and hence are
also known as “lipophobes”. The hydrophilic head may be negatively charged (anionics),
positively charged (cationics) or neutral (non-ionics). Anionic surfactants are most effective for
IFT reduction as they are less expensive and have smaller retention/adsorption on negatively
charged surfaces like sandstones. The tail groups mostly consist of hydrocarbon chains that have
an affinity towards non-polar molecules in oils. Tails are thus known as “lipophiles”.
Consequently, lipophiles repel polar molecules in an aqueous phase and are hence also known as
“hydrophobes.”
The word “surfactant” comes from the term “surface active agent.” As defined by Rosen
(2004), a surfactant is “a substance that, when present at low concentration in a system, has the
property of adsorbing onto surfaces or interfaces of a system and of altering to a marked degree
the surface or interfacial free energies of those surfaces (or interfaces).” An interface is the
boundary separating two different phases. An interface may form between an insoluble solid and
a liquid as occurs in rock and fluid systems. An interface may also form between two immiscible
liquids (microemulsion phase behavior). Interface formation between a liquid and an insoluble
gas occurs in foams. Interfacial free energy is defined as the minimum work Wmin required to
create an interface with area A. Interfacial tension is defined as the interfacial free energy per unit
area. Hence, for an oil-water interface, when an incremental area of ΔA is created,
min /o wW A . (1.2)
3
From Eq. (1.2), it is evident that interfacial tensions will have units of force per unit length and
are commonly reported in N/m or dynes/cm.
Now consider an oil-water interface that is planar (ignoring curvature). The equal and
opposite force experienced by a line of unit length on such an interface is the force (see Figure
1-1) that contributes to the interfacial tension.
Oil may also be suspended in aqueous solution as a droplet with radius R. Such a
simplification (see Figure 1-2) was considered by Acosta et al. (2003). The oil has a molar
volume of vo. The interfacial energy of such a spherical interface would hence be
2
/4excess o wG R . (1.3)
The chemical potential change associated with transfer of an oil molecule from the bulk phase b
to the droplet d is obtained by averaging the excess free energy per mole of oil present in the
droplet. Hence,
2
/ /, , 3
4 3
4 / 3 (1/ )
o w o w oo d o b
o
R v
R v R
. (1.4)
Therefore, from Eq. (1.3) in order to determine interfacial tensions (IFT), the excess free energy
at the interface must be known. Also, the radius of the solubilized oil droplet (oil in water
micelle) is an important factor as shown in Eq. (1.4).
1.2. Winsor’s R-Ratio and the C-Layer
Winsor (1954) was the first to explain the R-ratio. Surfactants seek the oil-water interface.
Therefore, in a surfactant-oil-water system, three distinct regions exist: an aqueous region (W), a
4
non-polar oleic region (O) and an amphiphilic or bridging region (C). The interfacial zone (C) has
a definite composition separating the oil and water bulk phases (Bourrel and Schechter, 2010).
This interfacial region, also known as the C-layer, has a defined thickness. In addition to
amphiphiles (surfactants), the C-layer also contains some oil and water molecules and also co-
solvents such as short-chain alcohols. The interaction energies between the molecules in the C-
layer determines its stability.
Consider surfactant in the C-layer (see Figure 1-3) that contains hydrophiles “H” and
lipophiles “L”. The interaction energy between molecules is represented as “A”. The interaction
between oil molecules and the C-layer (ACO) is contributed by both H and L. Hence,
CO LCO HCOA A A . (1.5)
Similarly, the interaction between water molecules and the C-layer is contributed by both H and L
such that,
CW LCW HCWA A A . (1.6)
Interaction energy amongst oil molecules is represented by AOO and, amongst water
molecules by AWW. Interaction energy between hydrophobes is represented by ALL and, between
hydrophiles, by AHH. The R-ratio is then defined as,
CO OO LL
CW WW HH
A A AR ratio
A A A
. (1.7)
5
As interaction between the amphiphile and the oil molecules (ACO) increases, the
surfactant shows greater affinity to the oleic phase. This results in an R-ratio greater than one and
the surfactant becomes increasingly oil soluble. The converse is true for ACW. As ACW increases,
the R-ratio becomes less than unity and the affinity of the surfactant towards the water phase
increases. For an R-ratio equal to unity, the surfactant has equal affinities towards the oil and
water regions. This occurs at optimum conditions, which is explained in more detail in the next
section. In practice, interaction energies at the molecular level cannot be calculated from phase
behavior experiments.
1.3. Effect of Salinity on R-Ratio
Anionic surfactants have an ionic head that attracts counter ions. Addition of salt (like NaCl)
produces more counter-ions (Na+) in the aqueous phase. Anionic surfactants are typically
available as sodium (or potassium) salts. For an undissociated surfactant salt molecule, charge on
the hydrophile is neutralized by the metallic counter-ion and so the ionic character of the
molecule is reduced. Therefore, undissociated surfactant salts are oil soluble. Dissociated
anionic surfactants in aqueous solutions have negatively charged head groups. The ionic nature
of dissociated anionic surfactants makes them water soluble. An increase in salinity results in a
greater number of counter-ions (cations) in the aqueous solution resulting in a decrease of the
anionic surfactants’ degree of ionization. Thus, an increase in salinity in the aqueous phase
typically decreases the water solubility of anionic surfactants. From an R-ratio perspective, the
counter-ion neutralizes the hydrophile, which decreases the interaction of the C-layer with water.
Hence, the R-ratio increases with salinity, which gives an increase in the surfactant’s affinity to
the oleic phase.
6
1.4. Microemulsions
Microemulsions are homogeneous solutions consisting of surfactant, oil and brine (SOB).
The term “microemulsion” was first introduced by Hoar and Schulman (1943) who found that by
titration of a milky emulsion containing potassium oleate (a soap) with a medium-chain alcohol
(pentanol or hexanol), a stable oil-in-water emulsion was produced. The components did not
separate on settling. The emulsions produced were transparent or translucent. Winsor (1948)
later described microemulsions as “swollen micellar solutions.” Broadly, micelles (surfactant
aggregates in aqueous solution), macroemulsions (or simple emulsions), and microemulsions
(also known as micellar solutions) can be categorized by their dimensions (Tadros, 2006).
Table 1-1 shows a summary of the classifications.
Tadros (2006) further explained that microemulsion classifications solely based on size
or appearance is not adequate. He defined thermodynamic criteria for formation of
microemulsions by considering a system as shown in Figure 1-4. Consider oil being introduced
into an aqueous phase. A1 is the interfacial area of the oil bulk phase. A2 is the total interfacial
area of the dispersed oil droplets. Interfacial area increases as an emulsion is formed. Hence, the
surface free energy increases (from Eq. (1.2)) by γ (A1-A2). Formation of an oil dispersion
introduces a large number of oil droplets in the system. The degree of randomness therefore
increases and so does the entropy of the system. From the second law of thermodynamics, the
free energy of emulsion formation (ΔGm) is,
mG A T S . (1.8)
The magnitude of the free energy of emulsion formation determines if the resulting mixture will
form a macroemulsion or a microemulsion.
7
In macroemulsions, interfacial tensions are not low enough. Therefore, γ ΔA is larger
than TΔS. This results in a positive ΔGm. Hence macroemulsion formation is not a spontaneous
process. External energy (agitation or mixing) is required in order to facilitate such processes.
In microemulsions, the interfacial tensions are desired to be ultra-low. Such low
interfacial tensions result in γ ΔA being smaller than TΔS. Therefore ΔGm is negative, which
implies microemulsions are formed spontaneously and are thermodynamically stable.
In summary, macroemulsions and microemulsions can be differentiated on the basis of
thermodynamics. Reduction of residual oil saturation requires ultra-low interfacial tensions as
discussed and hence microemulsions are important in EOR applications. As a consequence,
microemulsions are the subject of interest in this dissertation.
1.5. Types of Microemulsions in Surfactant-Oil-Brine (SOB) systems and
their significance in EOR
The salinity of the aqueous phase affects the R-ratio and thus the microemulsion phase behavior.
The phase behavior observed in surfactant-oil-brine systems were first described by Winsor
(1948). Healy et al. (1976) and Nelson and Pope (1978) who applied Winsor’s characterization to
specific EOR chemicals. The phase behavior is expressed using ternary diagrams in which the oil,
brine and surfactant/cosurfactant mixture are treated as three pseudo-components. The formation
of different microemulsion systems at different salinities has been well represented schematically
using ternary diagrams by Lake et al. (2014).
At low salinities, the anionic surfactant has good water solubility. Thus, the system will
exhibit two phases: an excess oil phase, which is assumed to be pure oil component and a water-
external (with respect to the micelle) microemulsion. This microemulsion has brine, surfactant
and a low amount of solubilized oil. Microemulsions of this type are classified type II- (system
8
has two-phases with ternary tie lines having a negative slope). They are also referred to as lower-
phase microemulsion as the microemulsion phase settles below the excess oil phase at
equilibrium.
At high salinities, the anionic surfactant prefers the oil phase. The system again exhibits
two-phases: an oil-external microemulsion and an excess brine phase. The microemulsion phase
consists of oil, surfactant and a low amount of solubilized oil. Microemulsions of this type are
classified as type II+ (system has two phases with ternary tie lines having positive slopes). They
are also referred to as upper phase microemulsions since (being less dense) they form above the
excess brine phase.
As salinity is increased, the system moves from a type II- to a type II+ microemulsion
system. However the transition typically takes place through a third system at intermediate
salinities. The system here exhibits three-phases: excess oil, excess brine and a microemulsion,
which contains surfactant, solubilized oil and, solubilized water. Microemulsions of this type are
classified as type III (system has three-phases). They are also referred to as middle-phase
microemulsions. The composition of this microemulsion is invariant at a particular salinity within
the tie triangle according to the Gibbs phase rule as explained by Bourrel and Schechter (2010).
There are two interfacial tensions under consideration in this type of system (γ o/m and γ m/w).
Optimal salinities and optimal solubilization ratios relevant to surfactant flooding are encountered
in this region making this system particularly important.
Irrespective of the brine salinity, a single phase may form at high surfactant
concentrations. The single phase formed is known as a type IV microemulsion. Type IV
microemulsions are typically encountered in EOR processes. However, type IV microemulsions
are of importance in other chemical engineering applications. This thesis will discuss the criteria
that lead to formation of single phase systems.
9
In an ideal surfactant flooding process at optimum conditions, an excess oil bank forms in
front of the microemulsion slug as injection continues, which in turn is followed by a polymer
drive. Since all three-phases are immiscible, it is desirable for the microemulsion slug to
effectively displace oil at the front while the microemulsion itself (which contains oil) is
effectively displaced by brine (Healy and Reed, 1977). Minimal trapping of the oil or
microemulsion phase is desirable. Thus, a condition where interfacial tensions (IFT) γo/m and γm/w
are both ultra-low and equal is required and the salinity at which this occurs is known as optimum
salinity (denoted henceforth as S*).
Consequently, from Eq. (1.9) when the water and oil solubilization ratios are equal to
each other, the minimum optimal IFT is reached. Phase behavior experiments known as salinity
scans are done to obtain these solubilization ratios.
Equation (1.2) shows the relationship of excess free energies to interfacial tensions.
However, excess free energies are difficult to measure and hence interfacial tensions are
determined by using tensiometers. Alternatively, interfacial tensions can be easily calculated
from solubilization ratios by using Huh’s correlation (Huh 1979). Huh’s equation replaced the
need for cumbersome IFT measurements. Solubilization ratios can be obtained from phase
behavior scans. Solubilization ratio of a component i (σi) is defined as the ratio of the volume of
component i solubilized to the volume of surfactant in the microemulsion (m) phase. Hence,
/ 2i m
i
c
(1.9)
where c is a constant specific to a surfactant, typically around 0.3 and,
σ ( / )i i msV V . (1.10)
10
Component i can be oil (o) or water (w). The microemulsion phase and its types are explained in
the next section.
1.6. Research Goals
The objectives of this research are to:
1. Develop a novel, physically-based equation-of-state (EOS) to predict Winsor II-, II+,
and III microemulsion phase behavior at different pressures, temperatures, oil
compositions and overall compositions.
2. Extend the model to phase behavior with acidic oils in presence of alkali by
understanding soap formation mechanisms in such systems.
3. Identify key dimensionless groups that affect microemulsion phase behavior and to
analyze the impact of such groups.
1.7. Organization of the Dissertation
Chapter 1 gives a brief review of microemulsion phase behavior considerations that are important
when designing an effective EOR flood. Chapter 2 reviews the literature on the key concepts of
hydrophilic lipophilic difference (HLD) and net-average curvature (NAC) theory. Both are
important tools to predict microemulsion phase behavior. The effects of salinity, temperature,
pressure, solution gas and alkali content on phase behavior are explained. This dissertation
extends the HLD-NACs capabilities to fulfill the research objectives.
Chapter 3 presents a new HLD-NAC based equation-of-state approach to predict
surfactant-oil-brine (SOB) phase behavior for live oil at reservoir pressure and temperature. The
11
approach brings in a new pressure dependency to the HLD equation. Key empirical relationships
between lnS* and 1/σ* are developed. Experimental data from available literature are analyzed.
Chapter 4 presents a modified HLD-NAC equation of state to predict alkali-surfactant-
oil-brine phase behavior. The model developed in Chapter 3 is coupled with a pH dependent
soap formation model. A relationship between the soap to surfactant mole fraction ratio,
optimum salinity and optimum solubilization ratio is established. The model is then validated
using published data and experimental results.
Chapter 5 develops a dimensionless solution to microemulsion phase behavior. The net
and average curvature equations are used to develop a set of dimensionless equations. This
results in identification of key dimensionless groups that impact microemulsion phase behavior.
Chapter 6 summarizes the important contributions of this research. It contains overview
of this research, results, conclusions, and recommendations for future research.
12
Type
Radius in nm
Appearance
Micelles
(surfactant aggregates in
aqueous solutions)
< 5 Scatter little light, transparent
Microemulsions / Micellar
Solutions 5-50
5-10 nm: Transparent
10-50 nm: Translucent
Macroemulsions >50 Opaque or Milky
Table 1-1: General classification of micelles, microemulsions and macroemulsions. (Tadros,
2006)
Increasing Variable
Oil Solubility of
Surfactant
Water Solubility of
Surfactant
Phase Behavior
Change
Salinity Increases Decreases Towards type II+
Oil EACN Decreases Increases Towards type II-
Temperature
Decreases for
anionics
Increases for
nonionics
Increases for
anionics
Decreases for
nonionics
Towards type II-
Towards type II+
Pressure Decreases Increases Towards type II-
Solution Gas Content
(Addition of lower EACN
volatile components at
constant pressure in under
saturated oils)
Increases Decreases
Towards type II+
Table 1-2: Summary of effects of SOB system variables on microemulsion phase behavior.
13
Figure 1-1 : Schematic of forces acting (in dynes or N) on unit length (e.g. 1 cm or m) on an
interface. The force per unit length is the interfacial tension (dynes/cm or N/m).
Figure 1-2: Oil droplet with radius R suspended in water, separated from the oil bulk
phase. Adapted from Acosta et al. (2003).
F F
Top View
of an
interface
14
Figure 1-3: Interaction energies in the C-layer that govern the R-ratio. Adapted from
Bourrel and Schechter (2010).
Figure 1-4: Schematic of microemulsion formation. Adapted from Tadros (2006).
A1 A
2
γ γ
Initial condition Dispersion
15
Figure 1-5: Pseudo ternary diagram of a type II- system. (Lake et al., 2014)
Figure 1-6: Pseudo ternary diagram of a type II+ system. (Lake et al., 2014)
16
Figure 1-7: Pseudo ternary diagram of a type III system. (Lake et al., 2014)
17
Chapter 2
Literature Review
This chapter consists of a detailed literature survey that explains the basic concepts presented in
this dissertation. First, the equivalent alkane carbon number and its impact on microemulsion
phase behavior is discussed. Then, a review of temperature, pressure and alkali effects on
surfactant-oil-brine (SOB) is presented. The concept of surfactant affinity difference (SAD) along
with the dimensionless form of SAD, the hydrophilic lipophilic difference (HLD) is discussed.
Finally, net and average curvature equations are given, which relate micelle curvatures in
solubilized microemulsion systems as a function of the state variable HLD.
2.1. The Equivalent Alkane Carbon Number and its Relevance to
Microemulsion Phase Behavior
One of the first concepts developed for characterizing the oil phase and matching it with a
preferred surfactant is equivalent alkane carbon number (EACN). Crude oils are complex
mixtures of various hydrocarbon species and thus are not easy to characterize. The EACN
provides a way to characterize a complex fluid (like oil) by using just one parameter. Oils with
the same EACN should have the same phase behavior (at the same state conditions) if all
components partition equally.
Cayias et al. (1977) first studied oils with different EACNs using petroleum sulfonates.
The aqueous phase used had constant salinity (1 wt.% NaCl) and a constant surfactant
concentration of 0.2 wt.%. Hydrocarbons from three homologous series; alkanes, alkyl benzenes
and alkyl cyclohexanes were used. Interfacial tensions between the aqueous solution and oil
consisting each of hydrocarbons from these homologous series were then plotted against
increasing alkyl chain carbon number. An interfacial tension minimum was observed for an alkyl
18
chain carbon number of eight in all cases except for the alkyl cyclohexanes, which showed a
minimum at four. Since the alkane and alkyl benzene curves showed the minimum at the same
point, it was concluded that the aromatic character of a molecule played no role in phase behavior
for their system. It was also concluded that since the cyclohexanes produced a minimum at four,
the cyclohexane ring mimics a carbon chain with four carbon atoms. The following empirical
rule was developed for calculating EACN and is still widely used today (Solairaj, 2011),
– 2 – 4 / 3C R DBEACN N N N , (2.1)
where NC is the number of carbon atoms in the molecule, NR is the number of rings in the
molecule and NDB is the number of double bonds in the molecule.
Cash et al. (1977) used the empirical equation successfully to calculate EACNs of binary
mixtures. He found that the EACN followed a mole-fraction weighted formula for mixtures such
that,
avg i i
i
EACN EACN X . (2.2)
where EACNi is the EACN and Xi is the mole fraction of the i-th component. The authors first
carried out experiments by mixing hydrocarbons from a single homologous series and used them
as the oil phase for interfacial tension measurements. They then used binary mixtures containing
components from two different homologous series.
Salager et al. (1979 a.) found that the natural log of optimal salinity for a particular
surfactant formulation with constant alcohol concentration increased linearly with EACN of a
single component oil. Salager et al. (1979 b.) then confirmed the linear dependence of the natural
log of optimal salinity on the EACN using binary mixtures of alkanes and alkyl benzenes. Cayias
19
et al. (1976) and Cayias et al. (1977) showed that a particular surfactant formulation has a
preferred ACN (PACN) value at which it gives a minimum interfacial tension. EACN is an oil
property while PACN is the EACN of the oil that a surfactant prefers in an EACN scan (an
optimum EACN).
The affinity of a surfactant towards the oil is lowered as the EACN of the oil is increased.
Therefore, the optimum salinity increases with EACN. This implies that a system is likely to
move towards a type II- phase behavior if the oil EACN is increased.
2.2. Effect of Temperature, Pressure and Solution Gas on Microemulsion
Phase Behavior
Nelson (1983) was the first to study the effect of pressure on microemulsion phase behavior with
and without methane. Stock tank oils and synthetic oils were used for the experiments. He found
that pressure alone had negligible effect on microemulsion phase behavior when a stock tank oil/
iso-octane blend was used. For the synthetic oil, he observed that pressure alone caused the phase
behavior to shift towards type II–. Subsequent researchers have validated this phase behavior
shift. Pressurization of the stock tank oil using methane resulted in a shift towards the type II+
side, which is associated with greater oil solubilization ratios in the microemulsion phase.
However, when he used methane to pressurize the synthetic oil, he observed a phase behavior
shift towards type II–. Additionally, the shifts reported in all cases were small. However,
subsequent researchers have found substantially greater shifts depending on the fluids used.
Austad et al. (1990) used a single anionic surfactant system with no cosurfactant. For an
n-decane/surfactant/brine system, an increase in pressure or temperature led to shifts towards type
II –. Live oil phase behavior was then studied using methane and decane. They measured
solubilization parameters of oil and water while increasing pressure and temperature. A shift
20
towards II- was again observed further validating the findings of Nelson (1983). Austad and
Staurland (1990) studied the microemulsion phase behavior of live oil from the North Sea. Again
an increase in pressure led to a shift towards the type II- region. This was also confirmed by
Austad and Strand (1996), but they did not study the impact of solution gas content with pressure.
Austad et al. (1996) used different types of oils in order to study the effect of oil
composition on phase behavior as pressure or temperature is increased. They confirmed that the
trend towards type II- with increasing pressure was not affected by oil composition. However, an
anomaly was observed for temperature scans of a crude oil, brine and single component
surfactant system. Contrary to the findings by Austad et al. (1990), they observed that the crude
oil showed a tendency to move towards type II+ as temperature was increased. They concluded
that the presence of resin-type polar components are capable of establishing ionic interactions
with the surfactant, which is responsible for such a trend. This effect was also observed when
aromatic live oil was used in Austad and Staurland (1990). They observed that the surfactant
showed a tendency to migrate into the excess oil phase as temperature increased.
Kahlweit et al. (1988) and Sassen et al. (1991) both confirmed phase behavior changes
towards type II- with increasing pressure. However, contrary to the conclusions made by Austad
et al. (1990), both reported a phase behavior shift towards the type II+ side as temperature of the
oil/brine/surfactant system was increased. This behavior is attributed to the nonionic surfactants
(as opposed to anionics studied before) used in their experiments. Water solubility of nonionic
surfactants decreases with increasing temperature (Karlstrom and Lindman, 1992). Such a
behavior has also been observed for some alkyl alkoxylated sulfonates (Puerto et al., 2012) even
though they are typically classified as anionic surfactants. The effect is particularly pronounced
for highly ethoxylated anionics where the non-ionic character of the surfactant contributed by the
polyoxyethylene chain dominates over the anionic character of the head group (Velasquez et al.,
2010).
21
Skauge and Fotland (1990) reported an increase in interfacial tension between the
microemulsion-oil interface and a decrease in the microemulsion-water interfacial tension as the
pressure of a surfactant-oil-brine system increased. This is in good agreement with conclusions
made by other authors that an increase in pressure leads the phase behavior of a system towards
the II- type microemulsion. Importantly, they measured the variation of optimal salinity with
increasing oil-phase density. They found that optimal salinity increased with oil phase density.
Later, Roshanfekr and Johns (2011) found that for pure components (pure hydrocarbons), the
natural logarithm of optimal salinity varies linearly with oil phase density. However, this linear
behavior was not shown for hydrocarbon mixtures.
Skauge and Fotland (1990) also presented a thermodynamic explanation for the effect of
pressure on microemulsion phase behavior. They explained that the change in partial molar
volume of the surfactant upon micellization is positive. Therefore, the critical micelle
concentration increases with increasing pressure from Le Chatelier’s principle. This suggests that
the surfactant’s preference to remain in the aqueous phase in its dissociated monomeric form
increases with pressure. Hence, as pressure increases, a phase behavior shift towards the type II-
side is preferred.
Puerto and Reed (1983) used methane to pressurize a dead crude oil. Subsequent phase
behavior experiments were carried out in order to determine the change in optimal salinity with
respect to the change in the oil molar volume as the oil was saturated with methane at different
pressures. Addition of methane lowered the oil molar volume as expected. However, a decrease
in optimal salinity was also observed. The live oil was prepared by saturating dead oil with
methane at 1000 and 2000 psig. Thus only two other data points other than that of the dead crude
were available for comparison. In another set of experiments, phase maps of salinity and alkane
carbon numbers were also presented in order to observe phase behavior changes with increasing
22
temperature. Linear alkanes were used in these experiments and a shift towards the type II- side
was observed.
Further investigation of the effect of pressure, temperature and solution gas on
microemulsion phase behavior systems for surfactant-polymer flood applications have been
reported (Roshanfekr et al., 2012; Roshanfekr et al., 2009). They used resin cured tubes to make
salinity scans at high pressures. They concluded that an increase in pressure alone causes a phase
behavior shift towards type II-, however, addition of solution gas at the same pressure and
temperature lowered the EACN, which subsequently resulted in a phase behavior shift towards
type II+. Reduction in oil phase EACN increases the oil phase solubility of an anionic surfactant.
They mentioned that both of these effects must be taken into consideration. They also gave a
thermodynamic explanation of the linear dependency of the logarithms of solubilization ratios on
pressure and the inverse of temperature.
Roshanfekr and Johns (2011) also presented a procedure to predict optimal salinities and
optimal solubilization ratios at reservoir pressure. Their procedure used data at atmospheric
pressure, which were then corrected to reservoir conditions using an oil phase density correlation.
They used PR78 Peng-Robinson equation of state (Robinson and Peng, 1978) to calculate the
densities. They eliminated the need for performing cumbersome high pressure phase behavior
experiments.
Attempts at studying live-oil microemulsion phase behavior for ASP flood applications
have been made (Southwick et al., 2010). However, reported results show that the crude oil used
for the phase behavior experiments had a low total acid number. Optimal salinity did not change
for different water to oil ratios. Thus, the alkali added (sodium carbonate) acted more like a salt
rather than a saponifying agent.
A comprehensive list of effects on microemulsion phase behavior due to changes in
salinity, oil EACN, temperature, pressure and solution gas is included in Table 1-2.
23
2.3. Role of Alkali in Surfactant Enhanced Oil Recovery Processes
Hydrocarbons are believed to be formed from diagenesis of organic matter at high temperature.
Such processes can produce polar compounds, including a large fraction of oxygenated polar
compounds called carboxylic acids (Seifert, 1975). A majority of the carboxylic acids are
naphthenic acids that have straight or branched paraffinic chains (cyclopentane or cyclohexane
type). Such acids are known as naphthenic acids.
Nelson et al. (1984) initiated research on injection of alkali (a caustic agent) with
synthetic surfactants in a chemical slug for enhanced oil recovery (EOR). Alkali reacts with
acidic compounds in the crude oil (such as naphthenic acids) to produce soaps. The soaps cause
an in-situ emulsification of the crude oil (Castor et al., 1981; Johnson Jr, 1976; Sheng, 2010).
These soaps act as surfactants and aid in lowering interfacial tensions. The synthetic surfactants
along with the in-situ soaps were able to produce low IFTs. Soaps with injected synthetic
surfactant can synergistically contribute to achieve near 100% oil displacement efficiency.
Formation of in situ soap by injecting relatively inexpensive alkali can significantly
reduce the amount of expensive synthetic surfactants needed in the EOR process (Shuler et al.
1989). In such processes, polymers may be added to the aqueous phase for mobility control to
improve sweep. With all these chemicals injected, the process becomes an alkali-surfactant-
polymer (ASP) flood.
A wide variety of caustic agents have been used for field trials (Gogarty, 1983) including
sodium carbonate (Jackson, 2006), ammonium carbonate, sodium hydroxide and ammonium
hydroxide. The amount of soap formed as a result of saponification depends on many factors
including the alkali and oil concentration. Thus, alkali complicates the phase behavior present in
an ASP flood and has not been well understood or predicted.
24
2.4. The Surfactant Affinity Difference
Winsor’s R-ratio is a measure of the surfactant’s preference to be in the oil or water phase. The
R-ratio evaluates the preference by considering interaction energies between the oil region, water
region and the C-layer as discussed in Chapter 1. Alternatively, chemical potential of the
surfactant can also be analyzed in order to understand surfactant partitioning as shown by Salager
(1988).
Consider first the chemical potential of the surfactant in phase j to be µsj where j may be
either oil or water. Now, consider these chemical potentials at some reference state to be µsj*.
The equations for chemical potentials of the surfactant component in the water and oil phases can
therefore be expressed as
* ln( )sw sw sw swRT x a , (2.3)
and,
* ln( )so so so soRT x a , (2.4)
where xso and xsw represent relative concentrations of the surfactant in oil and water, respectively.
Activity coefficients of the surfactant in oil and water phase are represented by aso and asw
respectively. At equilibrium, the chemical potentials of the surfactant component are equal to
each other. The difference between the reference state chemical potentials of the surfactant in the
water and the oil phase at equilibrium is the surfactant affinity difference. The dimensionless
form of the SAD is the hydrophilic lipophilic difference. Therefore,
* * ln( / )sw so so so sw swSAD RT x a x a , (2.5)
25
and,
SADHLD
RT . (2.6)
In high quality formulations (those that have the potential to achieve ultra-low IFTs), the
concentration of the surfactant in the excess oil and water phases (Cso and Csw) is very small. This
implies that the activity coefficients are equal to 1 in those phases. Therefore, activities can be
replaced by concentrations (Cso and Csw) in the SAD equation. Equations (2.5) and (2.6) become,
ln( / )so swHLD C C . (2.7)
Furthermore, at optimum salinity, the concentrations of surfactant in the excess oil and water
phases are equal. Hence the SAD (and the HLD) at optimum condition is zero.
2.5. The Hydrophilic – Lipophilic Difference
Salager et al. (1979 a.) derived an empirical relation from experimental data at optimum
conditions for oil-water-brine systems in the presence of an anionic surfactant as,
*ln ( ) 0refS K EACN f A T T Cc (2.8)
where S* is the optimum salinity expressed as grams per 100 ml, EACN is the equivalent alkane
carbon number, f(A) is a function of alcohol type and amount, and Cc is a surfactant-dependent
parameter called the characteristic curvature (Acosta et al., 2008). The parameter K is the slope
26
obtained from the observed linear relationship between the logarithm of optimum salinity and the
EACN. That is, when all other formulation variables are fixed we have,
*lnconstant
SK
EACN
(2.9)
Similarly, the constant α is derived from the observed linear dependence of lnS* with temperature
(all other formulation variables are fixed):
*lnconstant
S
T
(2.10)
Equation (2.8), which is valid for microemulsion systems at optimum conditions, was also
extended to the concept of surfactant affinity difference (SAD). As discussed, SAD is the
difference between the standard chemical potential of the surfactant in the water and oil phases,
which relates directly to the partitioning of the surfactant between the water and oil phases
(Marquez et al., 1995; Marquez et al., 2002). The HLD is therefore a state function that accounts
for phase behavior changes owing to compensating effects of formulation variables (Salager et
al., 2005; Salager et al., 2000), and when coupled with Eq. (2.8) gives,
ln ( )refHLD S K EACN f A T T Cc (2.11)
where HLD is zero at optimum conditions (see Eq.(2.8)). Appendix A shows that there is a
thermodynamic basis for Eq. (2.11) where formulation variables like salinity are treated
independently of the other variables.
27
Pressure effects have been ignored in the SAD and HLD equations by previous
researchers. Chapter 3 adds a pressure term to the HLD equation, which is a key contribution of
this research.
2.6. The HLD-NAC model
The use of net and average curvature (NAC) of solubilized micelles to model a microemulsion
phase behavior scan was first introduced by Acosta et al. (2003). The theoretical premise of this
model has been well explained by these authors for the three pseudo-component system of oil (o),
water (w) and surfactant (s). The model assumes that the microemulsion phase is ideal, which
implies that there is no change in the total volume of the system upon mixing. The model also
assumes that the micelles formed are spherical. Such an assumption is good from the type II- and
type II+ regions, but is not true in the type III region. Nevertheless, spherical micelles are
assumed in all regions as a first approximation. The model developed by Acosta et al. (2003) is
not predictive outside the range of their measured data, but was shown to fit data from salinity
scans well.
2.6.1. Radii and Curvatures of Micelles in Solubilized Systems
The reciprocal of a spherical micelle radius is taken to be curvature of the solubilized component.
The micelle radii containing component i (oil or water) can be obtained from the volume of
component i solubilized (Vi,m) and the interfacial area occupied by the surfactant molecules at the
interface (As). The parameter As is dependent on the moles of surfactant in the system (ns) and
surface area per molecule of surfactant (as). For a mixture of surfactants, the term As is a
28
summation of the area contributed by every surfactant molecule (Avogadro’s number times nsas)
so that,
, ,
236.023 10
3 3i m i m
i
s ss
V VR
A n a
(2.12)
2.6.2. The Average Curvature Equation
The average curvature (Ha) can be expressed by the average radii of oil (Ro) and water (Rw)
micelles (or droplets) in the microemulsion phase and the characteristic or correlation length (ξ)
as defined by DeGennes and Taupin (1982). That is,
1 1 1 1
2a
o w
HR R
(2.13)
.
The correlation length ξ is equivalent to the average micelle diameter (Buijse et al., 2012) in
simple microemulsions with spherical micelles. As a consequence, the average curvature
describes the amount of oil and water solubilized in micelles in the microemulsion phase.
Equation (2.12) can be substituted into Eq. (2.13) to derive an expression for the
correlation length. The volume of surfactant (Vs,m) can be obtained from the concentration of the
surfactant and by assuming surfactant component density equal to water. The correlation length
(ξ) can then be expressed in terms of volume of surfactant (Vs,m) in the microemulsion, volume
fraction of oil, surfactant and water in the microemulsion (ϕo, ϕs and ϕw), and their solubilization
ratios (σo and σw) as reported by Buijse et al. (2012). The expression becomes,
29
6 6
1
s o w s o w
s s s o w
V V
A A
(2.14)
However, this expression has been updated and modified in Chapter 3 in order to account for the
surfactant component volume, which was previously ignored.
2.6.3. The Net Curvature Equation
The curvature of the surfactant interface is described by the net curvature (Hn). The net curvature
is related to the radii of oil (Ro) and water (Rw) micelles, the surfactant length parameter (L), and
to HLD (Acosta et al., 2003; Acosta et al., 2008). The net curvature was found to be proportional
to the HLD of the system with 1/L as the proportionality constant. Therefore, the parameter HLD
translates the changes in formulation variables into the NAC model as,
1 1n
o w
HLDH
R R L . (2.15)
At optimum, the oil and water curvatures (hence radii) are equal to each other. This is consistent
with the fact that oil and water solubilization ratios are equal to each other at optimum. This
satisfies the condition that HLD is zero at optimum in Eq. (2.15).
2.6.4. Flash Calculations using HLD-NAC
This section describes the flash calculation protocol required for the HLD-NAC to model
microemulsion phase behavior where two and three-phase regions may be present. The
30
procedure for flash calculation is modified in Chapter 3 so that it becomes predictive outside the
range of experimental conditions.
2.6.4.1. HLD-NAC to Model Type II- Microemulsions
For a high quality formulation, the excess phases should be pure oil or water component
depending on the type of excess phase. In the type II- region the oil micelles are assumed to be
dispersed in the continuous aqueous phase (oil in water microemulsion). Therefore, all water is
in the microemulsion phase and the volume of the water component solubilized (Vw,m) in the type
II- microemulsion is equal to the total volume of water component present in the system, which is
known from the initial composition of the system. Equation (2.12) can then be used to calculate
an effective Rw, which is hypothetical in that only oil micelles (and hence oil radii) exist in a
continuous water phase in such systems. Vw,m is therefore equal to the total volume of water in the
system Vw, so that,
,3 3w
s
m w
w
s
V VR
A A . (2.16)
The curvature of solubilized water component calculated is negative since the microemulsion
phase is of type II- (water external). Only absolute values of curvatures are used in the NAC
model. Using Eq.(2.12), Ro can then be obtained based on the HLD value of the formulation.
Equation (2.15) can now be used for the oil component to calculate the amount of oil solubilized
(Vo,m).
,
1
3
3
/ 3
1o m
w
s
s
s w
VHLD HLD
L V L V
A
A
A
(2.17)
31
Furthermore, we assume excess phases to be pure. Hence, all surfactant component is contained
only in the microemulsion phase. This implies,
,s m sV V . (2.18)
Therefore, with volumes Vo,m, Vw,m, and Vs,m known, σw (Vw,m / Vs,m ) and σo (Vo,m / Vs,m ) can be
calculated.
2.6.4.2. HLD-NAC to Model Type II+ Microemulsions
An analogous procedure is followed for type II+ microemulsions. In type II+ microemulsions, Ro
is known from the overall oil composition, where curvature is negative and oil is external to the
micelles (oil is continuous) so that,
,3 3o
s
m o
o
s
V VR
A A . (2.19)
Equation (2.15) can now be used to calculate the amount of water solubilized (Vw,m) in the
microemulsion. That is,
,
1
3
3
/ 3
1w m
o
s
s
s o
VHLD HLD
A
A
AL V L V
. (2.20)
32
2.6.4.3. HLD-NAC to Model Type III Microemulsions
Oil and water micelles coexist within the bi-continuous middle phase (type III microemulsion).
The optimum solubilization ratio (σ*) for type III is equal to σo and σw at the optimum salinity.
The correlation length at optimum conditions (ξ*), therefore, can be calculated using Eq. (2.14)
and an experimentally obtained (or predicted, as shown in the modified flash calculation
procedure in Chapter 3) value of σ*. The correlation length (and the average curvature) remains
constant and equal to ξ* for the type III microemulsion phase. That is, in type III microemulsions,
*
1 1 1 1
2a
o w
HR R
(2.21)
where,
*2*
*
6
1 2
s
s
V
A
. (2.22)
In the three-phase systems, two excess phases (oil and water) and one microemulsion exist. The
oil and water curvatures, are calculated by solving Eqs. (2.15) and (2.21) simultaneously.
*
1
2
1
o
HLD
R L (2.23)
and,
*
1
2
1
w
HLD
R L . (2.24)
Using Eq. (2.12) in Eqs. (2.23) and (2.24), solubilized volumes Vo,m and Vw,m can be obtained as,
33
,
*
2
33s
w m
AV
HLD
L
(2.25)
and,
,
*
33
2
s
o m
AV
HLD
L
. (2.26)
2.6.4.4. Phase Volumes
The phase volumes for excess oil (Voo), excess water (Vww) and microemulsions (Vm) are
calculated once the solubilized volumes Vo,m and Vw,m have been determined. That is,
,oo o o mV V V , (2.27)
,ww w w mV V V , (2.28)
and,
m total ww ooV V V V , (2.29)
where,
total w o sV V V V . (2.30)
With volumes of excess phases and solubilized components known, densities of surfactant, oil
and water components can then be used to compute molar and mass compositions.
34
2.6.4.5. Stability Criteria to Determine Two and Three-phase regions
The inverse of the average curvature is equal to ξ* at the two- and three-phase transition limits:
between type II- and type III, and type III and type II+ (Acosta et al. 2003). This criteria is used
to obtain the HLD values at which the correlation lengths ξ in the type II- and II+ environments
are equal to the critical correlation length ξ*. In the two-phase regions, the oil and water radii are
used in the average curvature equation Eq. (2.13) to obtain the correlation length ξ. Therefore
upper and lower HLD limits, HLDU and HLDL can be determined as follows,
*3 3
12 s
L
w
ALHLD
V
, (2.31)
and,
*
2
3
1
3
s
U
o
ALHLD
V
(2.32)
The stability criteria that determines if the system will form a type II-, type II+ or type III
microemulsion is as follows:
Case 1: If HLDL < HLDU,
HLD > HLDU , a type II+ microemulsion exists (two-phase system).
HLD < HLDL , a type II- microemulsion exists (two-phase system).
HLDL ≤ HLD ≤ HLDU a type III microemulsion exists (three-phase system).
Case 2: If HLDL = HLDU
The system will transition from type II- to type II+ as HLD increases, encountering a three-phase
region only at HLD = HLDL = HLDU. At that HLD, ξ is equal to the critical correlation length ξ*.
Case 3: If HLDL > HLDU,
35
The system will transition from type II- to type II+ as HLD increases, without
encountering a three-phase region.
HLD < HLDU , a type II- microemulsion exists (two-phase system).
HLD > HLDL , a type II+ microemulsion exists (two-phase system).
HLDL ≥ HLD ≥ HLDU a type IV microemulsion exists (single phase system).
2.7. Summary
The net curvature equation brings the state function HLD into the phase behavior model. Hence,
the effect of net curvature as formulation variables change can be modeled this way. Figure 2-1
shows a flowchart of the steps followed to perform a flash calculation using the original HLD-
NAC model. The following input parameters are required in HLD-NAC as described by Acosta
et al. (2003):
Overall composition (from surfactant concentration and water-oil ratio),
Interfacial area per molecule of surfactant,
Surfactant length parameter,
Optimum solubilization ratio, and,
HLD of the system.
The surfactant concentration and water-oil ratio are known in experiments. However, the
surfactant length parameter and the surfactant interfacial area per molecule are obtained from the
literature. The optimum solubilization ratio and optimum salinity are determined from a single
salinity scan. The flash calculation methodology explained in this chapter is based on the state-
of-the-art prior to this research.
The HLD-NAC flash calculation procedure has the following limitations:
36
1. There was no reliable way to predict σ* as a function of changing formulation variables.
From Eq. (2.14), it can easily be inferred that the value of ξ* is governed by the value of
σ*. The HLD-NAC described could only be used after determining σ* experimentally.
Therefore, the current HLD-NAC model cannot predict phase behavior outside the range
of experimental conditions.
2. Pressure effects are not accounted for in the HLD equation. Therefore, prior to this
research, the HLD-NAC was incapable of predicting changes in microemulsion phase
behavior as a function of pressure.
3. The surfactant length parameter L is not well known for different surfactants.
4. Interfacial area per molecule of the surfactant (as) used in HLD-NAC must also be
obtained from experimental results reported in the literature.
5. Surfactant volume fraction in the microemulsion phase is ignored while calculating the
correlation length (ξ).
We address the issues listed above in subsequent chapters. Chapter 3 presents a novel approach to
predict σ* and hence, ξ* , thereby modifying the existing HLD-NAC model and making it into a
true equation of state where relationships can be found between temperature, pressure and
volume. In this research, we include a pressure term similar to the functional form of the
temperature term in the HLD equation. Chapter 3 also presents a way to estimate the surfactant
length parameter L. The method is empirical. We estimate L parameters for complex surfactants
for which reliable experimental data is not available. In Chapter 3, we use the area parameter to
tune and match phase behavior data. Our method provides a way to obtain as for complex
surfactant formulations for which experimental data are not available. We also update the average
curvature equation to include the surfactant volume fraction in the microemulsion phase. In
Chapter 4, we extend the modified HLD-NAC approach to model phase behavior for systems
with acidic oils in presence of alkali. In Chapter 5, we rearrange the equations in the modified
37
HLD-NAC and make them dimensionless. We identify and study key dimensionless groups that
impact surfactant-oil-brine phase behavior.
38
Figure 2-1: Flowchart showing the protocol followed for the HLD-NAC model described by
Acosta et al. (2003).
HLD = ln (S/S*)
Initial
compositions
Vo, Vw , Vs
σ* from a
salinity scan
experiment
S*
from a
salinity scan
experiment
Salinity S at
which flash
is to be
performed
L from
literature as from
literature
Obtain HLDL and HLDU
If HLDL ≤ HLDU If HLDL > HLD
U :
HLD < HLDL
Type II-
HLDL < HLD <
HLDU
Type III
HLDU < HLD
Type II+
HLDL < HLD
Type II+
HLDU < HLD <
HLDL
Type IV
HLD < HLDU
Type II+
Solubilized
component
volumes
Vom and Vwm
Phase volumes Voo,
Vww and Vm
Solubilization ratios
σw and σo
39
Chapter 3
Development of a Modified HLD-NAC Equation-of-State to Predict
Surfactant-Oil-Brine Phase Behavior for Live Oil at Reservoir
Pressure and Temperature
Chapter 1 reviews the effect of formulation variables on microemulsion phase behavior. In this
Chapter, a robust physically-based methodology that uses the HLD-NAC model and associated
empirical equations to predict Winsor II-, II+, and III microemulsion phase behavior at different
pressures, temperatures, and varying oil compositions (with varying amounts of solution gas) are
developed. The concept of hydrophilic-lipophilic deviation (HLD) is used and empirically
established HLD equations are modified to account for pressure changes for anionic surfactants.
The new HLD equation is coupled with the net-average curvature (NAC) model to predict, after
tuning with limited experimental data, phase volumes, solubilization ratios, optimum conditions,
and phase transitions at conditions other than those that were measured. This research study
greatly expands the applicability of the HLD-NAC model to predict microemulsion phase
behavior for oils where many formulation variables are changing simultaneously.
3.1. Extension of The HLD Equation to Include Pressure
Experiments used to develop the empirically derived HLD equation were mostly carried out at
atmospheric pressure. This is likely because experiments at low pressure are relatively easy to
perform and experiments in the chemical engineering literature focused on the effect of large
temperature changes in their applications, not large pressure changes. Thus, the effect of
pressure, which may be needed for high-pressure petroleum engineering applications, has largely
40
been neglected in the literature. This research is the first to include the effect of pressure in the
HLD equation.
An increase in pressure (and temperature) shifts the microemulsion phase behavior
towards type II- as has already been discussed in the introduction. Further, like temperature, lnS*
exhibits a linear dependence with pressure. Skauge and Fotland (1990) for example made
pressure scans for pure heptane using the surfactants secondary alkane sulfonate (SAS) and
sodium dodecyl benzene sulfonate (SDBS). Figure 3-1 and Figure 3-2 show the linear
dependence of lnS* with pressure for these surfactants, where linear regression gives excellent R2
- values of 0.956 and 0.996 respectively. Thus, the effect of pressure on phase behavior can be
treated analogously to temperature in the HLD equation. That is, we introduce a new constant
factor β in the HLD equation to account for pressure changes as,
ln ( ) ( )HLD S K EACN f A T T P P Ccref ref
, (3.1)
where Tref and Pref are at reference conditions, typically at the conditions that are measured in a
standard salinity scan (reservoir temperature and atmospheric pressure). For optimum salinity,
where the HLD is equal to zero, Eq. (3.1) yields,
*ln 0ref refS K EACN f A T T P P Cc , (3.2)
where the pressure coefficient is defined as,
.
*ln
constant
S
P
. (3.3)
41
With all formulation variables now accounted for in Eq.(3.2), however, a more general
notation would be to indicate that all formulation variables are at optimum when HLD is zero.
Thus, optima can be defined in terms of optimum pressure or temperature, not just in terms of
optimum salinity. With this new way of thinking about optimum, the HLD equation for a salinity
scan will therefore be more strictly defined as,
, , , ( ), *| lnT P EACN f A Cc
SHLD
S . (3.4)
Similarly, the HLD equation for a temperature scan is,
*
, , , ( ),| S EACN P f A CcHLD T T , (3.5)
where T* is the optimum temperature. The HLD equation for a pressure scan,
*
, , , ( ),| S EACN T f A CcHLD P P , (3.6)
where P* is the optimum pressure. An even more general expression would be to allow all three
primary variables to change simultaneously, which leads to
* * *
* *
*, ( ), , , ,( , , ) | ln ( ) ( )
EACN f A Cc S P T
SHLD S T P T T P P
S . (3.7)
In Eq. (3.7), we assumed that the oil composition is fixed, along with the type and amount of
surfactant(s) and alcohol(s). However, Eq. (3.7) holds true for all oil compositions and anionic
surfactant formulations. For example, one could change the branching of a surfactant to shift the
optimum to the desired salinity, temperature, and pressure. The equation shows the hydrophilic
lipophilic deviation from a particular optimum state of (S*, T*, P*) that satisfies Eq. (3.2). When
42
all three formulation variables are at an optimum (S*, T*, P*) in Eq. (3.7) , HLD is zero. Equation
(3.7) shows that a particular value of HLD (including zero at an optimum condition) is
represented by a plane in (lnS, T, P) space.
3.2. New Relations for Prediction of Optimum Solubilization Ratio
The HLD equation can be used to determine the deviation of the state of an oil-surfactant-brine
system from the optimum condition. However, the HLD equation offers no explanation of how
oil and water solubilization in the microemulsion phase vary with salinity. The literature
provides insight into how one could link the optimum variables such as S* to the optimum
solubilization ratio (σ*) using the HLD concept. In particular,
Optimal salinity has been observed to increase with an increase in the oil EACN, while
optimum solubilization ratio decreases (Barakat, Fortney, Schechter, et al., 1983; Graciaa
et al., 1982). The change in logarithm of optimal salinity follows a linear trend with
EACN as has been already discussed.
Salager et al. (1979) showed that as the oil EACN is increased, the range of salinity over
which a type III microemulsion is formed also increases. This range can be expressed as
ΔEACN or ΔlnS (see Figure 3-3).
Similar to optimum salinities, the natural logarithms of the upper and lower salinity limits
also form linear trends with EACN (Salager, 1988). Such a linear trend was also used by
Roshanfekr et al. (2013).
Barakat, Fortney, Lalannecassou, et al. (1983) showed that σ* is proportional to the
inverse of the width of the three-phase region irrespective of temperature and oil EACN.
Bourrel and Schechter (2010) further demonstrated that,
43
* EACN d , (3.8)
where the dimensionless proportionality constant d is a constant value of 5.5 for alkyl
benzene sulfonates, 24.7 for alpha olefin sulfonates and 40.3 for ethoxylated oleyl
sulfonates. The value of d can also be determined from experiments for particular
surfactant-oil-brine systems.
Graciaa et al. (1982) showed that σ* is proportional to the inverse of the width of the
three-phase region in terms of the difference of the hydrophilic lipophilic balance
(ΔHLB). Salager et al. (2005) suggested replacing HLB by HLD because it is easier to
determine from the empirical equations.
Barakat, Fortney, Lalannecassou, et al. (1983) also found that a relationship for S* and σ*
exists that is unique to surfactant type. This means, irrespective of oil EACN or
temperature, such a relationship is always satisfied.
Based on these observations and conclusions, a new empirical relationship is proposed to relate
the optimum solubilization ratio with the width of the type III region expressed in terms of
ΔHLD. That is,
1*
2AH
A
LD
, (3.9)
where A1 and A2 are dimensionless constants. Further, from Figure 3-3, the width of the Winsor
III three-phase window (ΔEACN or ΔlnS) increases linearly with lnS*(or EACN).
.
*ln S EACN . (3.10)
That is, lnS*, like ΔEACN, should be inversely related to σ*. That is,
44
1 2
*
*
1lnB S B
. (3.11)
.
The dimensionless constants B1 and B2 can be determined by a linear regression of lnS* and 1/σ*
available from experiments. Subsequent sections show that tuning these constants yields
excellent predictions of optimum solubilization ratio from optimum salinities.
Figure 3-4 shows an example of the validity of Eq. (3.11) where we use data reported by
Sun et al. (2012). The experiments were conducted using a commercial internal olefin sulfonate
with pure alkanes; n-heptane, n-octane and n-decane (EACNs of 7, 8 and 10 respectively) at
temperatures of 20°C, 50°C and 90°C. The figure shows a clear linear correlation of lnS* with
1/σ* where a linear regression gives an R2-value of 0.96.
3.3. Modifying the HLD-NAC Model
3.3.1. Accounting for Surfactant Volume Fraction in The Average Curvature
Equation
The microemulsion phase consists of three components namely, oil (o), water (w) and surfactant
(s). Component volume fraction is the ratio of the volume of the component (Vi) solubilized in the
microemulsion to the total volume of the microemulsion phase (Vme). The summation of
component volume fractions (ϕi) in a phase is equal to unity, which implies,
1o w s . (3.12)
Hence, adding the inverse of the water and oil volume fractions, we obtain the expression,
11 1 s
o w w o
. (3.13)
45
Dividing Eq. (3.13) by the volume of microemulsion phase Vm we get,
, ,
11 1 s
o m w m m w oV V V
, (3.14)
where, Vo,m and Vw,m are solubilized volumes of the oil and water components in the
microemulsion phase. Acosta et al. (2003) assumed the solubilized micelles to be spherical. As
shown in Chapter 2, the radii of the spheres (and hence curvatures) are related to the total
interfacial area (As) and the solubilized volumes (Vi,m),
, ,
23
3 3
6.023 10
i m i m
i
s s s
V VR
n a A
, (3.15)
Hence, the average curvature equation can be expressed as
(1 )1 1 1
2 6
s s
o w me w o
A
R R V
. (3.16)
The NAC theory as presented by Acosta et al. (2003) relates the average curvature to the inverse
of the DeGennes correlation length ξ (DeGennes and Taupin, 1982). Hence, from Eq. (3.16) , the
correlation length can be redefined as
6
(1 )
me w o
s s
V
A
(3.17)
46
The correlation length in prior research (Acosta et al., 2003; Acosta and Bhakta, 2009; Buijse et
al., 2012), was not a function of the surfactant content in the microemulsion. This was probably
because the surfactant volume component was assumed to be negligible owing to low overall
surfactant concentrations in typical formulations. However, the NAC model assumes the excess
phases to be pure, which constrains the entirety of the surfactant component to be contained in the
microemulsion phase only. Therefore, as the overall surfactant concentration increases, ϕs
becomes increasingly significant.
The HLD-NAC model at its prior state of development is constrained by the knowledge
of the value of optimum salinity and solubilization ratio. From Eqs. (3.4) - (3.6) it can be seen
that the HLD values used in the net curvature equation are constrained by the optimum HLD
variable (for example, S* in a salinity scan). ξ* in the average curvature equation for type III
microemulsions is constrained by the optimum solubilization ratio σ*. This dissertation, therefore
presents a way to predict these optimum values at different oil EACNs, pressures, and
temperatures to extend the HLD-NAC’s modeling capabilities. Equation (3.2) is used to predict
optimum salinities. Equation (3.11) is then used to predict optimum solubilization ratios from
predicted optimum salinities. Surfactant concentration and water-oil ratio are known in
experiments. Estimation of the surfactant length parameter is explained in the next section. The
interfacial area of surfactant molecule can be obtained by tuning the phase behavior model to fit
experimental data. This procedure fully defines all input variables required for the HLD-NAC
model and presents a true equation-of-state like approach.
3.4. Determining The Surfactant Length Parameter
One of the required parameters in the model is the average surfactant length. The surfactants
considered here have anionic moieties so that only the HLD equation applicable for anionics is
47
considered in this dissertation. The approach could be easily extended to nonionic surfactants as
well (Salager et al., 2000). The surfactant length parameter L in the net curvature equation is
approximately 1.2 times the surfactant tail length (Lc in Å) for anionics and 1.4 times Lc for
nonionics (Acosta et al., 2003; Acosta and Bhakta, 2009; Acosta et al., 2008). We determined Lc
from the effective number of straight chain carbon atoms (nc) using the equation for maximum
chain length (Acosta et al., 2008; Tanford, 1980):
1.5 1.265c cL n . (3.18)
Equation (3.18) is convenient for simple surfactants with tails consisting of linear carbon chains.
In order to calculate the equivalent carbon numbers (or effective chain lengths) of surfactants
with complex hydrophobes, we use rules of equivalence as reported in Rosen (2004). These rules
apply to characterization of surfactant hydrophobes with respect to their critical micelle
concentrations (CMC). For a branched hydrophobe, the carbon atoms on the branch (shorter
secondary chain) have one-half the hydrophobic effect of the primary chain. For extended
surfactants like ethoxylates or propoxylates, the carbon atoms between the oxygen atoms
contribute half the effect that would have existed if the oxygen atoms were absent. A benzene
ring and an orthoxylene group have a net contribution of 3.5 and 2.5 carbon atoms, respectively.
Using these rules, nc can be obtained. If a mixture of surfactants is used, the surfactant length
parameter is obtained by using a surfactant mole fraction averaged mixing rule. One could also
tune this parameter to the available experimental data, but in this dissertation tuning on a
minimum number of parameters was preferred.
48
3.5. Results
In this section three examples using experimental data are given to demonstrate the validity of the
methodology presented. Matched results of tuning the HLD-NAC models to the experimentally
measured data are reported. The new model’s prediction capability is demonstrated by
comparing predictions to data not used in the tuning process.
3.5.1. Example 1: Skauge and Fotland (1990) Experiments
Very limited data is reported with both temperature and pressure changing simultaneously, and
often data that is reported does not give sufficient information regarding the experiments in the
analysis that follows. One of the best data sets reported in the literature for our purposes is that
by Skauge and Fotland (1990). In their experiments they used sodium dodecyl benzene sulfonate
(SDBS) and a mixture of C13 to C18 secondary alkane sulfonate (SAS) along with the co-solvent
n-Butanol. One salinity scan for each surfactant formulation at atmospheric pressure and 20°C
using heptane were reported. They then measured optimum salinities and solubilization ratios at
different temperatures, but at atmospheric pressure. Similarly, they measured optima at different
pressures keeping the temperature fixed at 20 °C. The following steps were followed in our
analysis of their data:
1. The surfactant length parameter was calculated based on surfactant structure. Other key
parameters such as surfactant concentration, S*, and σ* were known at 20°C and 1.01
bars from standard salinity scans they reported using n-heptane. The only unknown for
the HLD-NAC model, the interfacial area per molecule of the surfactant (as), was used as
a tuning parameter to match the phase fraction vs salinity data reported within the upper
49
and lower salinity limits. Equation (3.4) was used to determine HLD for use in the net
curvature equation.
2. Using the measured change in optima (S* and σ*) with respect to EACN (at 20°C and
atmospheric pressure), the following were calculated:
a. The slope (K) of the lnS* vs EACN trend.
b. The constants B1 and B2 based on the linear trend of lnS* vs 1/σ*.
3. Skauge and Fotland (1990) varied pressure keeping the temperature constant at 20°C and
reported optima at different pressures. They held pressure constant at 1.01 bars
(atmospheric) and varied temperature to show the change in optima due to increasing
temperature. The α and β factors in Eq. (3.2) were obtained from the linear dependence of
lnS* with temperature and pressure based on their elevated T and P data with all other
parameters constant (such as EACN).
4. Using the α and β factors from step (3), optimal salinities were calculated at different
pressures and temperatures from the value at atmospheric pressure and 20°C.
5. Using the slopes from the linear correlations from step (2), σ* at different temperatures
(pressure constant at atmospheric conditions) and pressures (temperature constant at
20°C) were predicted from the value of optimum solubilization ratio at atmospheric
pressure and 20°C.
6. The calculated values and actual experimental values were compared.
The surfactant length parameters calculated for sodium dodecyl benzene sulfonate
(SDBS) and secondary alkane sulfonate (SAS) surfactants were 23.05 Å and 25.33 Å
respectively. The tuning process using the HLD-NAC model gave a tuned as value of 97 Å2 for
SDBS and 180 Å2 for SAS. Figure 3-6 and Figure 3-7 compare experimental data and tuning
results. Acosta et al. (2008) reported a value for as of 50 Å2 for SDBS. The larger value
50
obtained from tuning can directly be attributed to use of n-butanol as a cosurfactant by Skauge
and Fotland (1990), which is known to seek the interface and make the surfactant layer at the
interface less rigid.
The slopes (K) for the linear dependence of lnS* on EACN were 0.12 (R2 - value 0.99)
and 0.14 (R2 - value 0.99) for SAS and SDBS respectively (Figure 3-8 and Figure 3-9). Figure
3-10 and Figure 3-11 show the linear regression of lnS* as a function of 1/σ* along with the
constants B1 and B2. The constants B1 and B2 as defined by Eq. (3.11) for SAS are 0.24 and -0.24
respectively. B1 and B2 for SDBS are 0.18 and -0.02 respectively. The R2 - values obtained for
SAS and SDBS was 0.99 and 0.98 respectively showing good linear correlations between lnS*
and 1/σ*.
Using the optimum salinities reported by Skauge and Fotland (1990) at different
pressures, β was found from the linear trends already discussed previously. However, all of these
experiments were conducted at 20°C. Therefore we could not determine any dependence of β on
temperature. Similarly, α was determined (Figure 3-12 and Figure 3-13) from experiments where
temperature changed at fixed atmospheric pressure. The β factors obtained from linear fits were
6×10-4 bar-1 (R2 - value 0.96) and 8×10-4 bar-1 (R2 - value 0.99) for SAS and SDBS respectively.
The α values obtained from linear regression were 3.1×10-3 K-1 (R2 - value 0.90) and 7.7×10-3 K-1
(R2 - value 0.97) for SAS and SDBS respectively.
Using the α and β values, optimum salinities were predicted for heptane from the
optimum at atmospheric pressure and 20°C. The average relative error in calculation of optimal
salinities is 2.35%. Using the predicted optimum salinities, optimum solubilization ratios were
predicted. As shown in the comparison of Figure 3-14 and Figure 3-15, the predicted and actual
values agree well up to pressures of 200 bars. The use of constant β under-predicts optimum
solubilization parameters somewhat beyond this range. However, constant α gives a very good
51
prediction of changing optimum solubilization ratios with increasing temperature (compare
Figure 3-16 and Figure 3-17). The average relative error in prediction of optimum solubilization
ratio is 10.55%. Table 3-1 to Table 3-4 summarize the prediction of optima using the procedure
described previously in this dissertation and the corresponding relative errors. For both errors, the
total number of data points considered was 24.
This section demonstrates that our new HLD equation with all constants known is a
powerful tool to determine optimum conditions in terms of temperature, pressure, oil EACN and
salinity for a given surfactant formulation. This is the first time optimum solubilization ratios
have been predicted at different temperatures and pressures using a simple empirical correlation.
3.5.2. Example 2: Roshanfekr and Johns (2011), and Roshanfekr et al. (2013)
Experiments
Measurements reported by Roshanfekr and Johns (2011), Roshanfekr et al. (2013) and
Roshanfekr (2010) were used to predict dead and live oil phase behavior by estimation of input
parameters for the HLD-NAC model. They used a mixture of tridecyl propoxylated alcohol
sulfate and a C13-C18 internal olefin sulfonate along with isopropanol as a cosolvent. All
experiments were performed at 25°C (77°F). They reported salinity scans using the same
surfactant formulation for three pure alkanes; octane, decane and dodecane. They also reported
salinity scans for a dead crude at atmospheric pressure, dead crude at elevated pressure (1000 psi
/ 68.95 bars) and live crude with 17 mole % of methane solubilized at the same elevated pressure.
WOR was reported to be 1.0. The following steps were taken to analyze their experimental data:
1. The surfactant length parameter was first estimated. A mole fraction averaged length
parameter was obtained based on the surfactant mole fractions
52
2. Salinity scans of octane, decane and dodecane were matched by tuning interfacial area
per molecule (as) using the values of S* and σ* reported. Tuning was done to fit the
experimentally obtained solubilization ratios as a function of salinity. An average tuned
value of the interfacial area obtained from three matches was used in the HLD-NAC
model to predict phase behavior for dead and live oils. Equation (3.4) was used to
determine HLD in the net curvature equation.
3. We estimated the β factor from optimum salinities of the dead oil at atmospheric pressure
and elevated pressure.
4. The constant K for the HLD equation was estimated from the EACN trend for pure
alkanes. Using K, the β factor, and known EACNs of the dead and live oils, optimum
salinities were estimated.
5. The linear dependence of lnS* on 1/σ* was found using data from pure alkane
experiments. The optimum solubilization ratios for the dead and live crudes were
estimated from the optimum salinities predicted in step (4).
6. Last, we used the surfactant length parameter from step (1), average tuned value of as
from step (2), estimated optimum salinities from step (4) and estimated optimum
solubilization ratios from step (5) to predict the phase behavior for live and dead oils. We
did not use the density correlations found in Roshanfekr and Johns (2011) for this
prediction.
Tridecyl alcohol has an effective carbon number of 12.9 (Hammond and Acosta, 2012).
Using the rules already discussed, each polyoxyethylene (POE) group was considered to have an
effective linear carbon contribution of 1.5 carbon atoms. The surfactant length parameter was
therefore calculated to be 50.98 Å. The internal olefin sulfonate was a mixture of surfactants
consisting of tails between 15 and 18 carbon atoms. An average effective carbon number of 16
was hence considered. The surfactant length parameter for this carbon number was estimated to
53
be 26.88 Å. The mixture consisted of 1.5 wt. % TDA propoxylated sulfate (molecular weight of
1059 g/mol) and 0.5 wt. % of the internal olefin sulfonate (average molecular weight of 232
g/mol from Barnes et al. (2010). The mole fraction averaged length parameter was therefore
35.96 Å. Using the L parameter from step (1) and reported values of S* and σ*, as was tuned and
phase behavior of the three pure alkanes (octane, decane and dodecane) were matched (see Figure
3-18 to Figure 3-20). The tuned values of interfacial area per molecule of surfactant (as) were 225
Å2, 163 Å2 and 114 Å2 respectively. The average value was 167.33 Å2.
The β factor was calculated to be 7.71×10-4 bar-1 based on the values of optimum
salinities of the dead oil at atmospheric and elevated pressure (1000 psi / 68.95bars). The constant
K as defined by Eq. (3.2) was found to be 0.18 (see Figure 3-21) by using pure alkane data only.
Figure 3-21 shows a linear regression of lnS* and EACN with an R2 - value of 0.98. This K value
was used in order to predict phase behavior of the crude oil A, which was reported to have an
EACN of 9.9. The optimum salinity for the crude oil was predicted to be 2.33 g / 100 ml
(compared to the actual measured value of 2.3 g / 100 ml) at atmospheric conditions. From the β
factor, optimum salinity for dead oil at high pressure was calculated to be 2.45 g / 100 ml
(measured value is 2.35 g / 100 ml).
The live oil contained 17 mole % of methane. The EACN follows a mole-fraction
weighted formula for mixtures (Cash et al. 1977). The EACN of the live oil, as reported by
Roshanfekr and Johns (2011) was 8.4 where they considered EACN of methane to be 1. Using
the modified HLD equation, the predicted optimum salinity for the live oil is 1.88 g/100 ml
(measured value is 1.98 g/100ml).
The linear relationship for lnS* and 1/σ* are shown in Figure 3-22. The constants B1 and
B2 as defined by Eq. (3.11) are 0.08 and 0.02 respectively. Figure 3-22 shows a linear regression
with an R2- value of 0.91. The regression was used to predict optimum solubilization ratios for
the predicted optimum salinities from step (4). For the dead oil at atmospheric pressure, optimum
54
solubilization ratio was estimated to be 10.84 cc/cc (measured value is 11 cc/cc). For dead oil at
high pressure, the estimated optimum solubilization ratio was 11.32 cc/cc (measured value is 11.2
cc/cc). For live oil at high pressure, the estimated optimum solubilization ratio was 14.22 cc/cc
(measured value is 13 cc/cc).
The average length parameter L (35.96 Å), average interfacial area per molecule of
surfactant as (167.33 Å2), and the predicted optimum values were then used in the HLD-NAC
model in order to predict the salinity scans of the crude at dead and live conditions. Figure 3-23 to
Figure 3-25 show the predicted salinity scans and the actual data for comparison.
This example shows that if the β factor and EACN of the crude are known, salinity scans
using pure alkanes at atmospheric conditions are enough to predict phase behavior at high
pressures (with or without solution gas). Thus, no measurements with solution gas at high
pressure are necessary, except to verify the claims of our new modified HLD-NAC model.
3.5.3. Example 3:Austad and Strand (1996) and Austad and Taugbol (1995)
Experiments
Austad and Strand (1996) measured pressure and temperature scans using dead and live synthetic
oils in a PVT cell. Salinity and overall composition of the system were kept constant, but
pressure and temperature were varied to assess their effect on solubilization and optimum
conditions. Temperatures in their experiments ranged from 55°C to 120°C while pressures ranged
from 50 bars to 200 bars. The surfactant used was a dodecyl-ortho xylene sulfonate. Austad and
Taugbol (1995) used the same surfactant where they reported a salinity scan using n-heptane at
50°C. To analyze their data we performed the following steps:
1. The surfactant length parameter was first calculated. Using this value, the salinity scan
(phase fraction vs salinity) at atmospheric pressure and 50°C reported by Austad and
55
Taugbol (1995) was matched. The interfacial area per surfactant molecule (as) was again
used as a tuning parameter.
2. The HLD equations applicable to temperature and pressure scans (Eqs. (3.5) and (3.6))
were used in the net curvature equation.
3. Using the reported values of surfactant concentration and optimum variables (σ*, T* and
P*), matches to experimental results were obtained by tuning α for temperature scans and
β for pressure scans.
4. All “scans” were matched using the modified HLD Eqs. (3.5) and (3.6) coupled with the
NAC model. The width of the three-phase regions for each scan was estimated in HLD
units (ΔHLD). Eq. (3.9) was then validated.
The surfactant length parameter was 23.8 Å. The tuning process was completed and
Figure 3-26 shows the match obtained for the salinity scan reported by Austad and Taugbol
(1995). The tuned value of as was 98 Å2. The modified HLD equations Eqs. (3.5) and (3.6) were
then coupled with NAC to tune temperature and pressure scans reported by Austad and Strand
(1996). The calculated length parameter and tuned as value of 23.8 Å were used in the HLD-NAC
model.
Figure 3-27 to Figure 3-40 show matches obtained for temperature scans of live and dead
oils by tuning α. Figure 3-41 to Figure 3-51 show matches obtained for pressure scans of both
live and dead oils by tuning β. The matches obtained were excellent, which affirms the inclusion
of the factor β in the HLD equation. However, since only experimental data within the type III
window were available, we were unable to match data in the type II- and II+ regions. Table 3-5 to
Table 3-8 summarize the tuning results.
An interesting observation was made during the process of tuning these data. The tuned α
values, which affect the system’s temperature dependence on HLD, decrease with increasing
pressure (see Figure 3-52). This is a new observation since all α values reported previously were
56
obtained by analyzing experimental data obtained at atmospheric pressures. This result suggests
that the effect of temperature on microemulsion phase behavior as expressed by the HLD
equation decreases with an increase in pressure. Also, Salager et al. (1979 a.) concluded that the
surfactants they considered showed an average α value of 0.01 K-1. However, they could only
estimate α from experiments at atmospheric pressures. From Figure 3-52, it can be seen that the
tuned α values converge towards a value that is similar to their observation at atmospheric
pressures. However not much can be concluded about the dependence of β on temperature (see
Figure 3-53). The constant β is smaller than α so it is more noisy given experimental uncertainty.
The upper limit is defined at the transition between the type III and the type II+ regions
(type II+ microemulsions are also known as upper phase microemulsions). Similarly the lower
limit is defined at the transition between type II- and type III regions (type II- microemulsions are
also known as lower phase microemulsions). Since with increasing pressure, the system shifts
towards type II- (HLD decreases as pressure increases), the upper pressure limit is always lower
than the lower pressure limit. This is contrary to the traditionally popular salinity scans, where an
increase in salinity causes the phase behavior to shift towards type II+. The same is true for
temperature scans. Furthermore, we calculated the width of the three-phase regions using the
HLD equations. From Eq. (3.5), for a temperature scan, the ΔHLD in terms of the upper
temperature limit (TU) and lower temperature limit (TL) can be expressed as:
L UHLD T T . (3.19)
Similarly, for a pressure scan, from Eq. (3.6), the ΔHLD in terms of the upper pressure
limit (PU) and lower pressure limit (PL) can be expressed as:
L UHLD P P . (3.20)
57
Figure 3-54 shows the dependence of the optimum solubilization ratio on 1/ΔHLD (R2 -
value 0.99) and shows the validity of Eq. (3.9). Constants A1 and A2 are 2.54 and 4.28
respectively. The correlation satisfies all conditions of temperature and pressure for both dead and
live oils. These results provide new understandings of microemulsion phase behavior and suggest
that correlations exist that are unique to a particular surfactant, but are independent of oil
composition, temperature and pressure.
3.6. Discussion
The results show that the modified HLD coupled with NAC is a valuable tool for prediction of
microemulsion phase behavior of oils with different EACNs at different conditions of
temperature, pressure, and salinity. Furthermore, it is an excellent tool to interpret PVT
experiments like the ones conducted by Austad and Strand (1996). Such PVT experiments are
easier and faster to make compared to the traditional salinity scans at high pressures like the ones
reported by Roshanfekr and Johns (2011) and Jang et al. (2014). High pressure salinity scans
require sophisticated equipment and furnish phase behavior data at only one condition of
temperature and pressure. Alternatively, a PVT experiment furnishes data over a wide range of
temperatures and pressures and gives vital information required for proper interpretation of the
HLD factors α and β.
The effect of pressure on microemulsion phase behavior is also more important than
previously recognized. From the HLD equation for optimum conditions (Eq. (3.2)), it can be
seen that the linear trend of lnS* vs EACN translates by a factor of β(ΔP) where ΔP is the
difference between the pressure of interest and the reference pressure. Hence, a family of
58
parallel lines of different pressures (see Figure 3-55) results when lnS* is plotted as a function of
EACN. This is analogous to the family of parallel lines obtained at different temperatures but
constant pressure (Sun et al. 2012). Hence the method adopted by Jang et al. (2014), which
forced optimum salinities of lnS* vs EACN to lie on the same straight line could lead to an
incorrect interpretation. They did include the change in optima due to changing EACN as
solution gas is introduced into the oil phase. However, the effect of the translation based on
β(ΔP) was not included so they adjusted the EACN of methane to 10. Using the data reported by
Roshanfekr and Johns (2011), for example, if we forced the lnS* value for live oil on the EACN
trend at atmospheric pressure (see Figure 3-55), the EACN of the live oil would be 9, as compared
to the reported value of 8.2. Based on this value of EACN for the crude, the EACN of methane
must be incorrectly adjusted to 4.6 to lie on the same trend and to satisfy the approach presented
by Jang et al. (2014). From Figure 3-55, the error in EACN of methane will increase as pressure
increases owing to the shift of β(ΔP). Our approach shows that using the traditionally accepted
value of 1.0 for the EACN of methane, the entire phase behavior (not just optima) of live crude
can be predicted.
The EACN concept must also be used with caution. The traditionally used empirical rule
that determines the EACN of alkyl benzenes has been found to give inconclusive results (Puerto
and Reed, 1983). Queste et al. (2007) recently revisited the EACN rule and found that using fish
diagrams, the values of EACNs of alkyl benzenes can be drastically different from the ones
obtained from the traditional empirical equation. They also describe the limitations of
determining the EACNs of lower alkyl benzenes like benzene and toluene. Hence the dilution of
crude oils using toluene while assuming the toluene EACN to be 1.0 can lead to an error in
calculation of the crude oil EACN. Queste et al. (2007) suggested that EACN of toluene is -3,
but at the same time cautioned readers on the use of this value since it was obtained by
extrapolation and not by actual experiments. Therefore use of surrogate oils to match the
59
optimum salinity of a live oil is potentially an incorrect way to characterize the crude in a
microemulsion system. It is strongly recommended to use pure alkanes to obtain crude oil EACN.
Since the EACN concept attempts to scale the crude to an alkane, our recommendation will
potentially minimize errors in analysis of experimental results.
From the results obtained, we observe that β factors are approximately one-tenth of α
values. This does imply that pressure has a weak effect on phase behavior in comparison to
temperature if the magnitude of change in temperature is same as the change in pressure. But the
difference in pressures between atmospheric and reservoir conditions is larger than that for
temperature and therefore pressure effects can be equally significant when designing a
formulation for enhanced oil recovery. For example, if α is 0.01 K-1 and β is 0.001 bar-1, the
phase behavior change caused by a change of 20°C is about the same as that caused by 200 bars
(2900.8 psi). These differences in temperature and pressure might be representative of the
difference between laboratory and reservoir conditions and therefore, surfactant EOR
formulations must be optimized for both temperature and pressure.
The present research also demonstrates that in addition to the existence of an optimum
salinity at a particular temperature and pressure for a particular surfactant formulation, optimum
pressures and temperatures also exist. A scan can be performed experimentally by varying one
HLD variable while keeping all other variables fixed. The optima in a P, T and EACN space can
be determined easily if the HLD equation (Eq. (3.1)) is known. Therefore if relevant correlations
are known, phase behavior at different HLD values can be predicted using one single salinity scan
as a reference.
Reasonable estimates based on α values are available in the literature. This dissertation
provides reasonable estimates for β values as well (see Table 3-9). Similarly an estimate of K can
be made from the type of surfactant used. Salager et al. (1979) estimated K to be 0.16 (±0.01) for
the sulfonates used in their research. Acosta and Bhakta (2009) reported that a broad range of
60
surfactants have K values ranging from 0.1 to 0.2 with most surfactants having an average K
value of 0.17. Thus from one phase behavior experiment, using Eq. (3.2), a rough estimate of
optimum salinities can be made for different oils at any pressure and temperature. However for a
more robust flood design, we recommend the following steps to be followed to characterize
microemulsion phase behavior:
1. Salinity scans at atmospheric pressure and a reference temperature must be done using
pure alkanes. At least three experiments using alkanes of different EACNs should be
used. This provides the value for constant K and the constant intercept from in the HLD
equation. Additionally, a salinity scan of the oil of interest must be done under the same
conditions in order to assess its EACN by fitting its optimal salinity to the alkane trend.
Alternatively, the crude of interest may be diluted by two pure alkanes. Salinity scans
using these two model oils and the crude by itself can then be performed. The EACN of
the crude can be found iteratively by fitting the linear relationship between logarithm of
optimum salinity and EACN as shown by Roshanfekr and Johns (2011). Both approaches
also give a correlation between optimum solubilization ratios and optimum salinities that
satisfy Eq. (3.11).
2. Interfacial area per surfactant molecule and the surfactant length parameter can be
obtained from step (1). The HLD-NAC model can be tuned to match the salinity scan
experiments using the procedure described in this dissertation.
3. PVT experiments similar to the ones performed by Austad and Strand (1996) should then
be done at dead and live oil conditions at constant salinity of interest for a particular
reservoir. Matching procedures described in this dissertation can then be followed to
obtain α and β.
4. The HLD equation, now complete with pressure, temperature and EACN effects, coupled
with the NAC model becomes an equation of state (EOS) like tool that can be easily used
61
in simulators.
It is also worth pointing out that in our research we did not consider the effect of EACN,
temperature and pressure on as. The interfacial area parameter was always held constant.
However, Rosen (2004) reported a list of published results that show that as can vary with oil type
and temperature. Incorporating a model that captures changes in the area per surfactant molecule
due to pressure, temperature and EACN can potentially make the approach described in this
dissertation more accurate.
3.7. Conclusions
A new HLD-NAC based model for microemulsion phase behavior was developed. The approach
was validated by using available published data. The following conclusions are made:
1. Microemulsion phase behavior depends on pressure changes. The logarithm of optimum
salinity varies linearly with pressure.
2. The existing HLD equation was updated to include a new β factor to account for the
change in HLD due to pressure.
3. We confirm that temperature dependence on the HLD equation can be modeled by the α
factor, as defined by Salager et al. (1979 a.).
4. The optimum solubilization ratio depends inversely on the width of the three-phase
window expressed in HLD units. This dependence can be used to obtain a relationship
between optimum salinities and solubilization ratios. Based on salinity scans using
different pure alkanes, these relationships can be easily determined and used for
prediction.
5. The modified HLD equation we developed can be coupled with NAC and used to
interpret temperature and pressure scans.
62
6. PVT experiments like those reported by Austad and Strand (1996) are critical in
understanding the effect of pressure and temperature on phase behavior. They provide a
quick and easy way to obtain phase behavior data, specifically α and β in the HLD
equation, over a wide range of temperature and pressure. In comparison, salinity scans at
high pressures give limited information and are more cumbersome and expensive.
7. It is important to understand the implications of using surrogate oils to analyze high
pressure microemulsion phase behavior. Pressure and solution gas both affect phase
behavior and in a compensating manner. Therefore ignoring either one of them can lead
to errors. We do not recommend the use of surrogate oils or forcing the EACN of
methane to be values other than 1.0.
63
Table 3-1: Summary of prediction of optima at various temperatures for SAS surfactant.
Predictions for S* were made by taking S
* at 20°C as reference and using α = 0.0031 K
-1.
Data obtained from Skauge and Fotland (1990).
T in °C S* in g/100 ml S* in g/100 ml σ* in
cc/cc σ*
in cc/cc % relative error in S*
% relative error in σ*
Actual Predicted from α
Actual Predicted
20.00 4.60 4.60 7.60 7.55 0.72 55.00 4.89 5.13 6.00 6.61 4.96 10.25 65.00 5.08 5.29 5.70 6.37 4.16 11.77 80.00 5.29 5.54 5.20 6.02 4.79 15.81 85.00 5.43 5.63 4.90 5.91 3.74 20.62 90.00 5.84 5.72 5.50 5.80 2.04 5.46 Average 3.94 10.77
Table 3-2: Summary of prediction of optima at various pressures for SAS surfactant.
Predictions for S* were made by taking S
* at 20°C and atmospheric pressure as reference. β
is 0.0006 bar-1
. Data obtained from Skauge and Fotland (1990).
P in bars
S* in g/100 ml S* in g/100 ml σ* in
cc/cc σ*
in cc/cc % relative error in S*
% relative error in σ*
Actual Predicted from β
Actual predicted
1.01 4.60 4.60 7.60 7.55 0.72 197.30 5.48 5.18 6.90 6.54 5.58 5.20 250.77 5.69 5.35 7.10 6.29 6.01 11.38 395.78 5.92 5.83 7.50 5.66 1.55 24.51 480.36 6.26 6.14 7.30 5.32 1.98 27.09 553.31 6.47 6.41 7.30 5.04 0.99 30.90 Average 3.22 16.63
64
Table 3-3: Summary of prediction of optima at various temperatures for SDBS surfactant.
Predictions for S* were made by taking the S
* at 20°C as reference. α is 0.0077 K
-1. Data
obtained from Skauge and Fotland (1990).
T in °C S* in g/100 ml S* in g/100 ml σ* in
cc/cc σ*
in cc/cc % relative error in S*
% relative error in σ*
Actual Predicted from α
Actual predicted
20.00 2.10 2.10 7.90 8.46 7.14 35.00 2.29 2.36 7.20 7.31 2.90 1.56 45.00 2.49 2.54 6.60 6.70 2.09 1.55 50.00 2.58 2.64 6.70 6.43 2.68 3.97 55.00 2.64 2.75 6.00 6.19 4.02 3.10 60.00 2.83 2.86 6.00 5.96 0.83 0.73 65.00 3.05 2.97 5.20 5.74 2.64 10.43 Average 2.53 4.07
Table 3-4: Summary of prediction of optima at various pressures for SDBS surfactant.
Predictions for S* were made by taking S
* at 20°C and atmospheric pressure as reference. β
is 0.0008 bar-1
. Data obtained from Skauge and Fotland (1990).
P in bars
S* in g/100 ml S* in g/100 ml σ* in
cc/cc σ*
in cc/cc % relative error in S*
% relative error in σ*
Actual Predicted from β
Actual predicted
1.01 2.15 2.15 8.30 8.22 1.01 138.69 2.37 2.40 7.70 7.17 0.91 6.88 284.49 2.63 2.69 7.40 6.32 2.47 14.64 350.15 2.80 2.84 7.20 5.99 1.49 16.75 421.00 2.99 3.00 7.20 5.68 0.48 21.10 Average 1.34 12.07
65
Table 3-5: Summary of results obtained by matching pressure scans for dead oil. Data
obtained from Austad and Strand (1996).
T in °C P* in bars σ*
in cc/cc
β in bars-1 ΔHLD PU in bars PL in bars
55.00 291.65 16.07 7.70E-04 0.22 148.79 434.51
60.00 247.16 14.31 7.60E-04 0.26 76.11 418.21
65.00 201.37 13.01 7.30E-04 0.30 -2.74 405.48
70.00 154.91 11.67 7.10E-04 0.35 -88.75 398.57
75.00 101.45 10.51 8.30E-04 0.40 -137.10 340.01
80.00 45.00 9.45 9.80E-04 0.45 -186.63 276.63
85.00 -9.26 8.39 1.00E-03 0.53 -273.26 254.74
Table 3-6: Summary of results obtained by matching pressure scans for live oil. Data
obtained from Austad and Strand (1996).
T in °C P* in bars σ* in
cc/cc β in bars-1
ΔHLD PU in bars PL in bars
70.00 612.37 20.15 2.50E-04 0.15 304.37 920.37 75.00 528.00 18.03 3.80E-04 0.18 285.90 770.11 80.00 478.38 16.27 3.00E-04 0.22 118.38 838.38 85.00 394.06 14.48 3.70E-04 0.26 48.11 740.00 90.00 318.57 12.85 2.90E-04 0.30 -205.57 842.71
66
Table 3-7: Summary of results obtained by matching temperature scans for dead oil. Data
obtained from Austad and Strand (1996).
P in bars T* in °C σ* in
cc/cc α in K-1 ΔHLD TU in °C TL in °C
50.00 79.75 9.61 8.90E-03 0.45 54.69 104.80 100.00 75.23 10.58 8.30E-03 0.39 51.50 98.97 150.00 70.47 11.61 7.70E-03 0.35 47.87 93.07 200.00 65.17 13.01 6.40E-03 0.30 41.89 88.45 250.00 59.75 14.42 5.90E-03 0.26 37.89 81.62 300.00 53.97 16.37 5.00E-03 0.21 32.57 75.37
Table 3-8: Summary of results obtained by matching temperature scans for live oil. Data
obtained from Austad and Strand (1996).
P in bars T* in °C σ* in
cc/cc α in K-1 ΔHLD TU in °C TL in °C
600.00 70.37 20.06 3.20E-03 0.15 46.31 94.43 500.00 77.61 17.07 5.10E-03 0.20 58.00 97.22 450.00 82.11 15.80 4.20E-03 0.23 55.21 109.02 400.00 84.71 14.71 4.40E-03 0.25 56.30 113.12 300.00 91.01 12.75 6.40E-03 0.31 67.11 114.92 250.00 93.87 12.40 5.40E-03 0.32 64.43 123.32 200.00 96.33 11.79 7.30E-03 0.34 73.04 119.62 100.00 98.87 10.30 8.40E-03 0.41 74.58 123.15
67
Table 3-9: Summary showing β values obtained from tuning. Data from Skauge and
Fotland (1990), Roshanfekr and Johns (2011) and Austad and Strand (1996).
Source β in bars-1
Example 1: SAS data from Skauge and Fotland (1990) 6.00E-04
Example 1: SDBS data from Skauge and Fotland (1990) 8.00E-04
Example 2: Roshanfekr and Johns (2011) 7.71E-04
Example 3: Dead oil pressure scan at 55°C (Austad and Strand 1996) 7.70E-04
Example 3: Dead oil pressure scan at 60°C (Austad and Strand 1996) 7.60E-04
Example 3: Dead oil pressure scan at 65°C (Austad and Strand 1996) 7.30E-04
Example 3: Dead oil pressure scan at 70°C (Austad and Strand 1996) 7.10E-04
Example 3: Dead oil pressure scan at 75°C (Austad and Strand 1996) 8.30E-04
Example 3: Dead oil pressure scan at 80°C (Austad and Strand 1996) 9.80E-04
Example 3: Dead oil pressure scan at 85°C (Austad and Strand 1996) 1.00E-03
Example 3: Live oil pressure scan at 70°C (Austad and Strand 1996) 2.50E-04
Example 3: Live oil pressure scan at 75°C (Austad and Strand 1996) 3.80E-04
Example 3: Live oil pressure scan at 80°C (Austad and Strand 1996) 3.00E-04
Example 3: Live oil pressure scan at 85°C (Austad and Strand 1996) 3.70E-04
Example 3: Live oil pressure scan at 90°C (Austad and Strand 1996) 2.90E-04
Average 6.36E-04
Standard Error 6.55E-05
68
Figure 3-1: Optimum salinity as a function of
pressure for experiments reported for the SAS
surfactant (Skauge and Fotland 1990). The slope is
the β factor for the HLD equation.
Figure 3-2: Optimum salinity as a function of
pressure for experiments reported for the SDBS
surfactant (Skauge and Fotland 1990). The slope is
the β factor for the HLD equation.
Figure 3-3: A schematic showing the trend lines
for the optimum salinity, and the upper and lower
salinity limits. The width of the three-phase
Winsor III region is shown.
Figure 3-4: Reciprocal of optimum solubilization
ratios as a function of logarithm of optimum
salinity. Red, green and blue represent data at
20°C, 50°C and 90°C respectively. Oils used were
heptane, octane and decane. B1 = 0.15 and B2 =-
0.22. Data from Sun et al. (2012).
y = 0.0006x + 1.56 R² = 0.9555
1.5
1.6
1.7
1.8
1.9
0 200 400 600
ln S
*
Pressure (bars)
y = 0.0008x + 0.76 R² = 0.9958
0.6
0.8
1
1.2
0 100 200 300 400 500
ln S
*
Pressure (bars)
y = 0.15x - 0.22 R² = 0.96
0.04
0.12
0.2
1.8 2 2.2 2.4 2.6
1/σ
* (c
c/c
c)
lnS* (g/100 ml)
E
nS
Δ EACN Δ lnS
69
Figure 3-5: Flowchart of the modified HLD-NAC Equation-of-State.
HLD from
Eq.(3.1)
Initial
compositions
Vo,Vw,Vs
σ* from
Eq. (3.11)
Constants K,
α, β, f(A), Cc
Salinity
Oil EACN
Temperature
Pressure
Lc from Eq.
(3.12)
Tuned
as
Obtain HLDL and HLDU If HLDL ≤ HLDU
If HLDL > HLD
U :
HLD < HLDL
Type II-
HLDL < HLD <
HLDU
Type III
HLDU < HLD
Type II+
HLDL < HLD
Type II+
HLDU < HLD <
HLDL
Type IV
HLD < HLDU
Type II+
Solubilized
component
volumes
Vom and Vwm
Phase volumes Voo,
Vww and Vm
Solubilization ratios
σw and σo
lnS* from
Eq.(3.2)
Constants B1
and B2
nc of
surfactant
component
L=1.2Lc
70
Figure 3-6: Phase volume fractions after tuning as
a function of salinity for the SAS surfactant. The
value for interfacial area per molecule after tuning
was 180 Å2. Data from Skauge and Fotland (1990).
Figure 3-7: Phase volume fractions after tuning as
a function of salinity for the SDBS surfactant. The
value of interfacial area per molecule after tuning
was 97 Å2. Data from Skauge and Fotland (1990).
Figure 3-8: Logarithm of optimum salinity as a
function of EACN for experiments reported for
SAS surfactant. The slope of the trend line gives
the slope K for the HLD equation. Data obtained
from Skauge and Fotland (1990).
Figure 3-9: Logarithm of optimum salinity as a
function of EACN for experiments reported for
SDBS surfactant. The slope of the trend line gives
the slope K for the HLD equation. Data obtained
from Skauge and Fotland (1990).
2 3 4 5 6 7 80
0.2
0.4
0.6
0.8
1
Salinity in g/100 ml
Ph
ase v
olu
me f
racti
on
Type II+
Type II-
Excess
oil
Type III
Excess
water
0 1 2 3 4 50
0.2
0.4
0.6
0.8
1
Salinity in g/100 ml
Ph
ase v
olu
me f
racti
on
Type II+
Type III
Type II-
Excess
oil
Excess
water
y = 0.12x + 0.69 R² = 0.99
1
1.5
2
2.5
6 8 10 12
ln S
* (g
/100 m
l)
EACN
y = 0.14x - 0.18 R² = 0.99
0.4
0.8
1.2
1.6
6 8 10 12 14
ln S
* (g
/100 m
l)
EACN
71
Figure 3-10: Logarithm of optimum salinity as a
function of reciprocal of optimum solubilization
ratio for experiments reported for SAS surfactant
from the EACN trend. B1 = 0.24 and B2 = -0.24.
Data obtained from Skauge and Fotland (1990).
Figure 3-11: Logarithm of optimum salinity as a
function of reciprocal of optimum solubilization
ratio for experiments reported for SDBS
surfactant from the EACN trend. B1 = 0.18 and B2
= -0.02. Data obtained from Skauge and Fotland
(1990).
Figure 3-12: logarithm of optimum salinity as a
function of temperature for experiments reported
for SAS surfactant. The slope of the trend line
gives the α factor for the HLD equation. Data
obtained from Skauge and Fotland (1990).
Figure 3-13: logarithm of optimum salinity as a
function of temperature for experiments reported
for SDBS surfactant. The slope of the trend line
gives the α factor for the HLD equation. Data
obtained from Skauge and Fotland (1990).
y = 0.24x - 0.24 R² = 0.99
0.10
0.15
0.20
0.25
0.30
1.40 1.60 1.80 2.00 2.20
1/σ
*
ln S* (g/100 ml)
y = 0.18x - 0.02 R² = 0.98
0.08
0.13
0.18
0.23
0.28
0.60 0.80 1.00 1.20 1.40 1.60
1/σ
*
ln S* (g/100 ml)
y = 0.003x + 1.45 R² = 0.8819
1.40
1.50
1.60
1.70
1.80
15.00 35.00 55.00 75.00 95.00
ln S
* (g
/100 m
l)
Temperature in °C
y = 0.0077x + 0.56 R² = 0.9682
0.6
0.8
1
1.2
15 35 55 75
ln S
* (g
/100 m
l)
Temperature in °C
72
Figure 3-14: Optimum solubilization ratio as a
function of pressure for experiments reported for
SAS surfactant. The HLD equation and equation
from Figure 3-10 was used for prediction. Data
obtained from Skauge and Fotland (1990).
Figure 3-15: Optimum solubilization ratio as a
function of pressure for experiments reported for
SDBS surfactant. The HLD equation and equation
from Figure 3-11 was used for prediction. Data
obtained from Skauge and Fotland (1990).
Figure 3-16: Optimum solubilization ratio as a
function of temperature for experiments reported
for SAS surfactant. The HLD equation and
equation from Figure 3-10 was used for
prediction. Data obtained from Skauge and
Fotland (1990).
Figure 3-17: Optimum solubilization ratio as a
function of temperature for experiments reported
for SDBS surfactant. The HLD equation and
equation from Figure 3-11 was used for
prediction. Data obtained from Skauge and
Fotland (1990)
73
Figure 3-18: Tuned result for solubilization ratios
as a function of salinity for octane. Red represents
oil solubilization ratios. Blue represents water
solubilization ratios. The solid lines are model
results from HLD-NAC obtained by tuning as.
Figure 3-19: Tuned result for solubilization ratios
as a function of salinity for decane. Red represents
oil solubilization ratios. Blue represents water
solubilization ratios. The solid lines are model
results from HLD-NAC obtained by tuning as.
Figure 3-20: Tuned result for solubilization ratios
as a function of salinity for dodecane. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. The solid lines are
model results from HLD-NAC obtained by tuning
as.
Figure 3-21: logarithm of optimum salinity as a
function of EACN. A mixture of tridecyl alcohol
propoxylate and C13-C18 internal olefin sulfonate
was used along with iso-propanol as cosurfactant.
Data obtained from Roshanfekr et al. (2011).
0.5 1 1.5 20
5
10
15
20
25
30
Salinity in gms/100 ml
So
lub
iliz
ati
on
rati
o (
cc/c
c)
1.4 1.6 1.8 2 2.2 2.4 2.6 2.80
5
10
15
20
25
30
Salinity in gms/100 ml
So
lub
iliz
ati
on
rati
o (
cc/c
c)
2.8 3 3.2 3.4 3.6 3.8 4 4.20
5
10
15
20
Salinity in gms/100 ml
So
lub
iliz
ati
on
rati
o (
cc/c
c)
y = 0.18x - 0.91 R² = 0.98
0.4
0.8
1.2
7 9 11 13
ln S
* (g
/100 m
l)
EACN
74
Figure 3-22: Logarithm of optimum salinity as a
function of reciprocal of optimum solubilization
ratio from experiments with varying EACN. B1 =
0.08 and B2 = 0.02. Data obtained from
Roshanfekr et al. (2011).
Figure 3-23: Prediction of phase behavior for dead
oil at elevated pressure (68.95 bars) using data
from pure alkane series and estimated β factor of
7.71×10-4/bar. Red represents oil solubilization
ratios. Blue represents water solubilization ratios.
Figure 3-24: Prediction of phase behavior for dead
oil at atmospheric pressure using data from pure
alkane series. Red represents oil solubilization
ratios. Blue represents water solubilization ratios.
The solid lines are model results from HLD-NAC.
Figure 3-25: Prediction of phase behavior for live
oil at high pressure using estimated β factor of
7.71×10-4/bar. Red represents oil solubilization
ratios. Blue represents water solubilization ratios.
The solid lines are model results from HLD-NAC.
y = 0.08x + 0.02 R² = 0.91
0.04
0.06
0.08
0.1
0.12
0.14
0.4 0.6 0.8 1 1.2 1.4
1/σ
*
lnS* (g/100 ml)
2 2.2 2.4 2.6 2.80
10
20
30
Salinity in gms/100 ml
So
lub
iliz
ati
on
rati
o (
cc/c
c)
2 2.5 3 3.5 4 4.50
10
20
30
Salinity in gms/100 ml
So
lub
iliz
ati
on
rati
o (
cc/c
c)
1.5 2 2.5 3 3.50
10
20
30
Salinity in gms/100 ml
So
lub
iliz
ati
on
rati
o (
cc/c
c)
75
Figure 3-26: Phase volume fractions as a function
of salinity using 0.5 wt. % dodecyl orthoxylene
sulfonate. The tuned as value was 98 Å2. Solid
lines represent model outputs with tuned alpha
values. Circles represent experimentally obtained
values. Blue represents
Figure 3-27: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
temperature scan at 50 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-28: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
temperature scan at 100 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-29: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
temperature scan at 150 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
2 2.5 30
0.2
0.4
0.6
0.8
1
Salinity in g/100 ml
Ph
ase v
olu
me f
racti
on
Type
II-
Excess
oil
Type III
Excess water
Type
II+
65 70 75 80 85 90 95 1000
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
60 65 70 75 80 85 90 950
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
55 60 65 70 75 80 85 900
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
76
Figure 3-30: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
temperature scan at 200 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-31: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
temperature scan at 250 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-32: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
temperature scan at 300 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-33: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
temperature scan at 100 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
50 55 60 65 70 75 80 850
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
45 50 55 60 65 70 75 800
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
45 50 55 60 65 700
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
80 90 100 110 1200
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
77
Figure 3-34: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
temperature scan at 200 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-35: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
temperature scan at 250 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-36: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
temperature scan at 300 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-37: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
temperature scan at 400 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
80 90 100 110 1200
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
70 75 80 85 90 95 100 1050
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
70 75 80 85 90 95 100 1050
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
70 75 80 85 90 95 1000
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
78
Figure 3-38: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
temperature scan at 450 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-39: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
temperature scan at 500 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-40: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
temperature scan at 600 bars. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-41: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
pressure scan at 55°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
70 75 80 85 90 950
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
60 65 70 75 80 85 900
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
60 65 70 75 80 85 900
10
20
30
40
Temperature in oC
So
lub
iliz
ati
on
rati
o (
cc/c
c)
240 260 280 300 320 340 3600
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
79
Figure 3-42: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
pressure scan at 60°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-43: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
pressure scan at 65°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-44: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
pressure scan at 70°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-45: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
pressure scan at 75°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
200 220 240 260 280 3000
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
140 160 180 200 220 240 2600
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
0 50 100 150 200 2500
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
0 50 100 150 2000
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
80
Figure 3-46: Comparison of tuned result (solid
lines) and actual values (circles) for dead oil
pressure scan at 80°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-47: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
pressure scan at 70°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-48: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
pressure scan at 75°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-49: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
pressure scan at 80°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
0 50 100 1500
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
500 520 540 560 580 6000
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
500 520 540 560 580 6000
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
300 350 400 450 500 550 6000
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
81
Figure 3-50: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
pressure scan at 85°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-51: Comparison of tuned result (solid
lines) and actual values (circles) for live oil
pressure scan at 90°C. Red represents oil
solubilization. Blue represents water
solubilization. Data from Austad and Strand
(1996).
Figure 3-52: Variation of α with increasing
pressure. Blue squares represent tuned α values
for dead oil. Red squares represent tuned α values
for the live oil. Data obtained by analysis of
experimental results reported by Austad and
Strand (1996).
Figure 3-53: Variation of β with increasing
temperature. Blue squares represent tuned β
values for dead oil. Red squares represent tuned β
values for the live oil. Data obtained by analysis of
experimental results reported by Austad and
Strand (1996).
340 360 380 400 420 440 4600
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
100 200 300 400 5000
5
10
15
20
25
30
Pressure in bars
So
lub
iliz
ati
on
rati
o (
cc/c
c)
y = -1E-05x + 0.0089 R² = 0.8672
0
0.005
0.01
0.00 200.00 400.00 600.00 800.00
α (
K-1
)
Pressure (bars)
0.00E+00
4.00E-04
8.00E-04
1.20E-03
40 60 80 100
β (
bar-
1)
Temperature (°C)
82
Figure 3-54: linear correlation of the optimum
solubilization ratio inverse of the three-phase
region width and the inverse of the three-phase
region width. The points represent results from
both live and dead oil at all pressures and
temperatures reported. A1 = 2.54 and A2 = 4.28.
Data obtained by analysis of experimental results
reported by Austad and Strand (1996).
Figure 3-55: A schematic showing the shifts in
optimum salinity trend line due to pressure. The
shifts in the intercepts are caused by the β factor
and the difference between the pressure of interest
and the reference pressure. The black dot shows
the optimum salinity at the reference condition.
The green circles show the correct interpretation
of the shift due to pressure. The red circles show
the incorrect interpretation made in Jang et al.
(2014).
y = 2.54x + 4.28 R² = 0.99
0.00
5.00
10.00
15.00
20.00
25.00
1.00 2.00 3.00 4.00 5.00 6.00 7.00
σ*
(cc/c
c)
1/ΔHLD EACN
lnS
*
Pref, Tref
P1, T
ref
P2, T
ref
83
Chapter 4
A Modified HLD-NAC Equation of State to Predict Alkali-Surfactant-
Oil-Brine Phase Behavior
This chapter discusses tuning of the model and modifications that were made to the flash
calculation procedure to allow for two or more surface active agents; one or more synthetic
surfactants, and the soap formed in-situ as a result of saponification. The model parameters are
dependent on the soap mole fraction and can be obtained by simple mixing rules developed here.
A variety of examples show that the model is capable of predicting complex phase behavior
diagrams such as ternary diagrams, activity charts and fish plots. The pH dependent soap
formation mode is introduced, where petroleum acids are represented by one pseudo component
labeled HA. The mole fraction of soap is then included in the hydrophilic-lipophilic difference
(HLD) and net-average curvature (NAC) model. The required inputs and the approach to tuning
of experimental data are discussed, followed by an illustration of the flash calculation procedure.
4.1. Soap Formation Model
The acid number (AN) of oil is defined as the milligrams of potassium hydroxide required to
neutralize one gram of oil (ASTM, 2005). Specifically for EOR applications, the acid number of
reservoir crude is a measure of its acid content at equilibrium with the reservoir brine. The model
of deZabala et al. (1982) predicts soap formation as a function of the equilibrium acid content in
the oil using equilibrium partition coefficients. We use the soap formation model presented by
84
Sharma and Yen (1983), where the equilibrium partition constants are dependent on the structure
of the acid pseudo component.
The unsaponified acid species HA partitions between the oil (o) and water (w) phase.
Hence the distribution equilibrium constant (Kd) can be represented by,
and W
O
HA
O W d
HA
CHA HA K
C (4.1)
where Ci represents concentration of species i. Dissociation of the acid in the aqueous phase at
equilibrium forms the soap. The dissociation constant Ka is dependent on the aqueous H+
concentration (pH) of the system. More soap is formed at high pH such that,
and
W
H AW a
HA
C CHA H A K
C
. (4.2)
From mass conservation, Sharma and Yen (1983) showed that the concentration of the
dissociated acid A- (soap) is dependent on the equilibrium constants Ka and Kd by,
0
1 1
o
oHA
w
A
w OH d o
a w
SC
SC
K C K S
K S
(4.3)
where Kw is the dissociation constant for water and So and Sw are oil and water saturations
respectively. C0HAo is the initial acid concentration in the oil phase, which is calculated from the
acid number. Rock-fluid reactions associated in alkali processes are beyond the scope of this
85
dissertation, but could be coupled by including the pH and chemical species concentrations in Eq.
(4.3).
4.2. Equilibrium Constants and Their Dependence on the Molecular
Structure of Petroleum Acids
The equilibrium reaction constants are dependent on the molecular structure of the acids present
in the oil. Furthermore, the distribution of acids between the oil and water phases is dependent on
additional factors like oil type and temperature. Temperature will also affect the dissociation
reaction. Values of equilibrium constants are traditionally assumed owing to lack of sufficient
data. Mohammadi (2008) and Mohammadi et al. (2009) for example, used fixed values of Kd
=10-4 and Ka =10-10, but in this dissertation we use empirical trends in estimating these
equilibrium constants.
Smith and Tanford (1973) examined partitioning of straight-chain paraffinic acids in
heptane-water systems at 25°C. They found that the free energy involved in the transfer of
carboxylic acids between the oleic and aqueous phases is a linear function of the number of
carbon atoms in the aliphatic tail (n). Consequently, they concluded that the negative logarithm
of the distribution constant (pKd) is nearly a linear function of n. We fit their data and obtained
the following linear relationship (see Figure 4-1),
0.601 3.389dpK n . (4.4)
With limited data for reservoir crudes at high temperature, Eq. (4.4) is useful for estimating more
physical values of the partitioning coefficient.
Smith and Tanford (1973) and Goodman (1958) showed that the pKa values of fatty acids
are independent of the alkyl chain length. This is a reasonable assumption because the pKa values
86
are strong functions of the acidic functional group, which for naphthenic acids is the carboxylic
group. Consequently, we use a pKa of 4.76 as reported by Smith and Tanford (1973) for all
calculations in this dissertation. This value of pKa does not agree with the fixed value used by
Mohammadi (2008).
4.3. Flash Calculations Including the Alkali Component
This section describes coupling of the soap formation equations with modified HLD-NAC using
the same flash calculation protocol described previously in Chapter 3. From Eq. (4.3), the
amount of soap formed is calculated from the acid content in the oil (AN), the concentration COH-
(the pH or pOH) of the aqueous phase, the distribution coefficient of the undissociated acid HA
(from pKd), the dissociation constant of HA (from pKa), and the water-oil ratio (ratio of water and
oil saturations). The molecular weight contribution of the –COOH group is 45.016 g/mol. The
molecular weight contribution of the CH3- and CH2- group is 15.034 g/mol and 14.026 g/mol,
respectively. Hence, for a given value of n, the molecular weight (in g/mol) of a carboxylic acid
is,
60.05 14.026( 1)HAMW n . (4.5)
The total volume of the surfactant pseudo component (Vs) is a function of the moles of
soap formed and the molecular weight of soap. Also, for a given value of n, pKd is calculated
using Eq. (4.5), while pKa is fixed at 4.76 as discussed previously. Hence, the concentration of the
soap formed in our approach becomes solely dependent on
1. the acid number of the oil, which is generally known from laboratory experiments;
87
2. the water-oil ratio from the initial overall composition (or from saturations in a grid
block);
3. Density of oil (to calculate C0HAo), which is also generally known from laboratory
experiments;
4. the pH, which is a function of alkali concentration; and
5. n, which is dependent on the structure of the acidic pseudo component.
Key HLD-NAC model parameters are taken as functions of the soap concentration
formed. The L parameter for soap (Lsoap) and synthetic surfactant (Lsurfactant) are calculated from
the effective number of carbon atoms (n) in the tail using the methodology described by Ghosh
and Johns (2014). They estimated the tail length for synthetic surfactant by calculating the
effective carbon number using rules established by Rosen (2004) and Tanford (1980). The
interfacial area per molecule for the -COO – head group is taken to be 60 Å2 based on the value
reported for oleic acid soap (asoap) by Acosta et al. (2008). The interfacial area per molecule for
the synthetic surfactant (asurf) is relatively unknown and is used as a tuning parameter in this
dissertation.
Acosta et al. (2008) applied HLD-NAC to mixtures of anionic surfactants. This
dissertation follows their procedure and lumps the soap and synthetic surfactant into one
surfactant pseudo component. They used a mole fraction weighted linear mixing rule in order to
calculate the L parameter. Hence,
soap soap surfactant surfactant
1
N
i i
i
L X L X L X L
, (4.6)
88
where N is the total number of surface active agents. In this research, two or more synthetic
surfactants are lumped into one surfactant pseudo component and distinguished from the soap.
That is,
soap surfactant
1
1N
i
i
X X X
. (4.7)
Similarly, the area term As can be obtained by adding the area contributions of the soap
and surfactant based on their concentrations. The surfactant pseudo component volume Vs is also
obtained by adding the volume contributions of all the surface active agents in the system. That
is,
23
soap soap surfactant surfactant6.023 10 ( )SA n a n a , (4.8)
and,
soap surfactantSV V V . (4.9)
Mole fraction based mixing rules are also used for calculating optimum salinities (Acosta
et al., 2008; Liu et al., 2010; Mohammadi et al., 2009; Salager et al., 1979 a.) as expressed by,
* * * *
soap soap surfactant surfactant
1
ln ln ln lnN
i i
i
S X S X S X S
. (4.10)
Equations (4.7) and (4.10) imply,
*
soapln S X . (4.11)
89
The logarithm of S* is also proportional to the inverse of optimum solubilization ratio (Ghosh
and Johns, 2014) so that,
* *ln 1/S . (4.12)
Hence, from Eqs. (4.11) and (4.12), the inverse of the optimum solubilization ratio is also
proportional to the soap mole fraction. That is,
*1/ soapX , (4.13)
and,
soap surfactant
* * * *1soap surfactant
1 Ni
i i
X X X
. (4.14)
Equations (4.13) and (4.14) are new relationships presented in this dissertation, which are
different from traditionally used linear and logarithmic mole fraction averaged rules
(Mohammadi, 2008). Equations (4.11) and (4.14) can be written using Eq. (4.7) as
*
1 soap 2ln S C X C , (4.15)
and,
1 soap 2*
1D X D
, (4.16)
where C1, C2, D1 and D2 are constants. The values of S* and σ* obtained are therefore dependent
on the amount of soap formed. These constants can be determined by having at least two points
90
at different alkali concentration (likely one of these is without alkali so that only synthetic
surfactant exists). Additionally, adding Eqs. (4.15) and (4.16) gives,
*
1 1 soap 2 2*
1ln ( ) ( ) 0S C D X C D
. (4.17)
Equation (4.17) represents a plane in the ( lnS*, 1/ σ*, Xsoap ) space.
The density of oil, acid number, pH of the solution and n determines Xsoap. Once the
constants in Eqs. (4.15) and (4.16) are known, the same flash calculation procedure used in
Chapter 3 is followed with an adjustment of several input parameters to account for Xsoap, namely
the L, AS, and HLD. For example, Eq. (4.15) is used to calculate the value of the HLD parameter
as a function of salinity. The constants (K, α, β and Cc) in the HLD equation would also follow a
mole fraction averaged rule (Acosta et al., 2008). Acosta et al. (2008) particularly mentioned
that the constant K, which varies over a small range from 0.1 to 0.19 for surfactants, can be
assumed to be independent of the surfactant mole fraction. This allows the model to perform
general flash calculations for all possible varying input parameters, such as salinity, temperature,
pressure, or oil composition (EACN).
4.4. Results
We demonstrate our modified HLD-NAC model using experimental data in the literature. We
further demonstrate how our model can be tuned and used to predict complicated phase behavior
in the presence of soap and synthetic surfactant. Solubilization ratios in phase behavior
experiments for alkali surfactant systems are typically reported in terms of volume of synthetic
surfactant because soap formation is unknown.
91
4.4.1. Case A from Mohammadi (2008), and Mohammadi et al. (2009)
These experiments were done using a blend of two anionic surfactants, C22-24 internal olefin
sulfonate (0.1 wt. %) and a branched C16 alkyl benzene sulfonate (0.1 wt. %). We calculated the
mean molecular weight of the surfactant blend to be 408.61 g/mol. Diethylene glycol butyl ether
was used as a cosolvent. The oil had an acid number of 0.5 mg of KOH/g of oil. Synthetic
brine at 0.6 wt.% NaCl concentration (0.103 meq/ml) was used. Scans using sodium carbonate as
the alkali were done for concentrations varying from 0 to 50,000 ppm. Experiments were
conducted for five different, evenly spaced oil concentrations (volume basis) ranging from 10 to
50%. The pH for sodium carbonate (alkali) in aqueous solution was calculated. All experiments
were performed at 62°C and atmospheric pressure.
4.4.1.1. Determinination of Soap Model Parameters
Mohammadi (2008) assumed values of equilibrium constants to calculate soap mole fractions.
Contrarily, in this research, the alkyl carbon number of the acid n is used to calculate Kd in a more
deterministic approach. The values of reported optimum solubilization ratios and salinities are
shown in Table 4-1. A linear fit to their data (see Eqs. (4.15) and (4.16)) gives the required
coefficients C1, C2, D1, and D2. The density of oil was assumed to be 0.9 g/cc to calculate C0HAo
from the acid number. The pH is calculated from the concentration of sodium carbonate in the
aqueous phase (see Appendix B). The initial composition and hence water-oil ratios are also
known. Therefore, only a simple iteration on n is needed to complete the soap formation model.
As discussed, the parameter n governs the distribution coefficient, molecular weight, and tail
length of the soap, thereby reducing the number of tuning variables. Excellent R2-values of 0.96
and 0.997 for n equal to 13 were obtained from linear regression of σ* and lnS*as a function of
92
Xsoap, respectively (see Figure 4-2 and Figure 4-3). Constants C1 and C2 were -1.19 and 0.001,
respectively, while D1 and D2 were -0.053 and 0.059, respectively.
4.4.1.2. Tuning the Phase Behavior Model
The modified HLD-NAC model was tuned to available experimental data, using only one tuning
parameter. All other parameters were calculated or known. The experimental data fit are
sodium carbonate scans for oil volume concentrations of 50% and 30% as reported by
Mohammadi. The length parameter L for the synthetic surfactant is 32.92 Å according to the
procedure described by Ghosh and Johns (2014). For the soap with an alkyl carbon number of
n=13, the length parameter L is calculated to be 21.53 Å. The area per molecule of the soap
(asoap) is 60 Å2 as discussed previously. Thus, the only adjustable parameter remaining is the
area per molecule of surfactant (asurf) since it is relatively unknown. This parameter is adjusted so
that the model matches the measured phase behavior data. Figure 4-4 shows the tuned result for
the case with 50% (v/v) oil concentration. The tuned value of asurf was found to be 215 Å. For
30% (v/v) oil concentration, the tuned value of asurf was found to be 195 Å (see Figure 4-5),
which is very close to the value for 50% oil concentration. Because the results for the area
parameter were consistent, we used an average value of asurf (205 Å) for predictions with our
modified HLD-NAC model. Comparisons between our tuned model and UTCHEM results
reported by Mohammadi are also shown in the figures, which show a better overall fit of the data
with our modified HLD-NAC model. The large value of asurf is likely due to the use of co-solvent
in the formulations.
93
4.4.1.3. Phase Behavior Predictions
Phase behavior diagrams were generated by making flash calculations with the modified HLD-
NAC model. The input parameters for Case A are summarized in Table 4-2. The first diagrams
generated are solubilization curves for various oil concentrations. Figure 4-6 shows the
predicted curves for 10% oil concentration, while Figure 4-7 is for 20% oil concentration and
Figure 4-8 for 40% oil concentration. Only the optima for these experiments were reported.
Flash calculation results for the 10% and 40% oil concentration cases at different sodium
carbonate concentrations can be seen in Figure 4-9 and Figure 4-10, respectively.
A common phase behavior diagram reported in the literature is activity maps. Activity
maps show the evolution of the three-phase region as a function of overall oil concentration and
salinity. UTCHEM uses parameters CSEU (upper salinity limit) and CSEL (lower salinity limit)
as input parameters for the Hand’s rule based model. CSEU and CSEL are determined from
experimental data using the procedure described in Sheng (2010). The limits for other
experiments are derived using a mixing rule similar to Eq.(4.10) . One of the main advantages of
using a modified and tuned HLD-NAC is that the three-phase salinity limits are calculated by the
model itself and can vary depending on the input parameters, such as temperature, pressure and
EACN. Figure 4-11 shows the activity map predicted by our model and compares it with the
tuned result reported by Mohammadi (2008). The results show that the new model is capable of
predicting well the evolution of the type III microemulsion window in the compositional space.
4.4.2. Case B from Mohammadi (2008), and Mohammadi et al. (2009)
The procedure followed for experiments in Case B was identical to Case A. Experiments
reported in Case B were done using an oil with a higher acid number (1.5 mg of KOH/ g of oil)
94
and a density of 0.93 g/cc. The surfactant formulation was different from Case A. In Case B,
equal quantities (weight basis) of tridecyl alcohol polyethoxy sulfate (7PO) and a C20-24 internal
olefin sulfonate was used. The surfactant concentration of this blend was varied from 0.3 wt.% to
1 wt.%. The molecular weight of the surfactant blend was reported to be 450 g/mol. Sodium
carbonate was again used as the alkali and concentrations were varied in a range from 0 to 60,000
ppm. Synthetic brine composition was provided and its salinity was calculated to be 0.072
meq/ml. A summary of the optima for the experiments in Case B is presented in Table 4-3. All
experiments were performed at 46°C and atmospheric pressure.
4.4.2.1. Determination of Soap Model Parameters
Iterations were done on n in order to obtain the constants for the linear Eqs. (4.15) and (4.16). The
value of alkyl carbon number of the acid component was found to be 14. The R2-values after
fitting Eqs. (4.15) and (4.16) were 0.95 and 0.99 respectively. Constants C1 and C2 were found to
be -1.52 and 0.48 respectively (see Figure 4-12). Constants D1 and D2 were found to -0.06 and
0.09 respectively (see Figure 4-13).
4.4.2.2. Tuning the Phase Behavior Model
The length parameter L for the surfactant was estimated to be 37.21 Å, while for the soap (n=14)
23.05 Å. Parameter asoap remained fixed at 60 Å2. The area per molecule of surfactant (asurf)
was tuned to fit the phase behavior data at 0.3 wt.% surfactant concentrations. There were two
experiments at different oil concentrations. For 30% oil concentration (v/v) asurf was tuned to 16
Å2 (see Figure 4-14). For 50% oil concentration (v/v) asurf was tuned to 45 Å2 (see Figure 4-15).
95
Both figures also compare UTCHEM phase behavior results reported by Mohammadi with our
model results. An average value of asurf (30.5 Å2) was considered for predictions.
4.4.2.3. Phase Behavior Predictions
Table 4-4 shows a summary of input parameters for Case B. With the model parameters known,
phase behavior for cases with 0.6 wt.% and 1 wt.% surfactant concentrations were predicted and
compared with experimental data. Figure 4-16 to Figure 4-18 show solubilization ratio
predictions for Case B. The results using tuned values of asurf agree well with experimental
values. Figure 4-19 shows flash calculation results at different sodium carbonate concentrations
for an oil volume concentration of 30%. Figure 4-20 shows flash calculation results for oil
volume concentration of 50%.
Mohammadi (2008) also reported activity maps generated from UTCHEM at the three
surfactant concentrations considered in Case B. Figure 4-21 to Figure 4-23 show the activity
maps predicted by the new model in comparison to UTCHEM results. Deviation from the
UTCHEM model can be seen as surfactant concentration is increased. However, as discussed
previously, UTCHEM employs a logarithmic mixing rule to predict the upper and lower limits,
while the new model predicted these limits.
4.4.2.4. Fish diagrams for alkali-surfactant systems
Activity maps are important to describe the evolution of the three-phase regions (salinity limits)
as a function of oil composition (or water-oil ratio) of the system. Fish (also known as gamma)
diagrams however, have been traditionally used to determine three-phase salinity limits in terms
of formulation variables (temperature, salinity, etc.) as a function of the total surfactant
96
concentration in the system (Salager, Forgiarini and Bullon, 2013; Salager, Forgiarini, Marquez,
et al., 2013; Salager et al., 2005). Fish diagrams are typically made for a water-oil ratio (WOR)
of one. Typically, pure surfactants tend to produce near symmetric fish diagrams (see Figure
4-24) as opposed to surfactant mixtures (or commercial surfactant blends) that form asymmetric
fish plots. Here, evolution of fish diagrams applicable to alkali-surfactant systems as a function of
lnS have been investigated using the model parameters determined for cases A and B. Fish
diagrams for different overall surfactant concentrations at unit WOR were generated.
Without alkali, the model predicts symmetric fish diagrams as shown in Figure 4-25 and
Figure 4-26. This is because the optimum does not change as a function of surfactant
concentration given other constant input parameters and the synthetic surfactant is assumed to be
pure. However, at a fixed alkali concentration of 1 wt.% sodium carbonate with NaCl
concentration varying, the optima are a function of the mole fraction of the soap formed. Thus,
the fish diagram becomes asymmetric as explained by Salager, Forgiarini, and Bullon (2013) and
Salager, Forgiarini, Marquez, et al. (2013). For a constant water-oil ratio of one, as the overall
surfactant concentration increases, the width of the three-phase region decreases. The point at
which the limits intersect is the beginning of the region where type IV microemulsion (single
phase) is formed.
Figure 4-27 and Figure 4-28 show fish diagrams where alkali concentrations were varied
keeping the brine concentration fixed for cases A and B. The results from the tuned models are
in agreement with measured data.
Typical values of surfactant concentration in EOR are less than 2 wt.%. The figures
show surfactant concentrations ranging up to 15% in order to show the fish tail and the full extent
of the three-phase region.
97
4.5. Conclusions
A modified HLD-NAC equation of state to model and predict microemulsion phase behavior
applicable to alkali-surfactant EOR was developed. The approach was validated by using
available published data. The following conclusions are made:
1. The soap formed under in-situ conditions is dependent on the alkyl carbon number
and molecular weight of the petroleum acid pseudo component.
2. The alkyl carbon number of the acid can be used to estimate distribution coefficients,
soap tail length, and soap mole fractions thereby reducing the number of input/tuning
variables.
3. The inverse of optimum solubilization ratio (1/σ*) is a linear function of the soap
mole fraction (Xsoap). This empirical relationship is new to this research.
4. The relationship between inverse of optimum solubilization ratio, lnS*, and mole
fraction of soap formed can be represented by a plane in three-dimensional
coordinates.
5. Relationships to predict optima can be used to constrain the soap model and
determine an effective alkyl carbon number for the acid pseudo component.
6. Flash calculations using the modified HLD-NAC model are non-iterative, fast, and
robust. Flash calculations were extended to model soap as a second component
lumped in the surfactant pseudo component. Additional synthetic surfactants can also
be added.
7. Only two tuning parameters are required (n and asurf). In comparison, the UTCHEM
model has seven input parameters that require tuning (Sheng, 2010) which can be
reduced to five if excess phases are assumed to be pure.
8. The new model predictions are in good agreement with un-tuned experimental data.
98
9. Activity maps can be predicted easily by our model without the need to fit three-
phase windows from experiments.
10. Fish diagrams for alkali-surfactant system are asymmetric, which is in agreement
with published literature.
Chapter 5 presents a dimensionless form of the modified HLD-NAC model developed so far.
Important design criteria with respect to dimensionless groups have then been presented.
99
Table 4-1: : Summary of optima for experiments for crude oil case A. Data from
Mohammadi, (2008).
Oil Volume % S* in meq/ml
Na2CO3 ppm at
optimum σ
* (cc/cc)
10% 0.80 37000 19.51
20% 0.72 32700 23.01
30% 0.65 29100 26.01
40% 0.54 23000 31.96
50% 0.46 19000 38.04
Table 4-2: : Summary of model parameters for Case A.
Input Parameter Value Units
Acid number 0.5 mg of KOH/g of oil
pH Dependent on alkali
concentration -
N 14 -
C1 -1.187 -
C2 0.001 -
D1 -0.053 cc/cc
D2 0.059 cc/cc
Oil density 0.9 g/cc
Lsurf 32.92 Å
Lsoap 21.53 Å
asurf 205 Å2
asoap 60 Å2
WOR 1 to 9 -
Surfactant concentration 0.2 wt. %
Surfactant molecular
weight 408 g/mol
100
Table 4-3: Summary of optima for experiments for crude oil case B. Data from
Mohammadi, (2008).
Oil
Volume
%
Surfactant
concentration
(wt.%)
S* in meq/ml Na2CO3 ppm at
optimum σ
* (cc/cc)
30% 0.6 0.86 41700 16.07
40% 0.6 0.67 31900 17.89
30% 0.3 0.66 31100 18.42
50% 0.3 0.49 22200 23.53
50% 1 0.69 32500 17.55
Table 4-4: Summary of model parameters for Case B.
Input Parameter Value Units
Acid number 1.5 mg of KOH/g of oil
pH Dependent on alkali
concentration -
n 14 -
C1 -1.789 -
C2 0.821 -
D1 -0.06 cc/cc
D2 0.09 cc/cc
Oil density 0.93 g/cc
Lsurf 37.21 Å
Lsoap 23.05 Å
asurf 30.5 Å2
asoap 60 Å2
WOR 1 to 9 -
Surfactant concentration 0.3,0.6, and 1 wt. %
Surfactant molecular
weight 450 g/mol
101
Figure 4-1: Linear relationship between the
number of carbon atoms in the alkyl group of a
carboxylic acid and pKd for water-heptane
systems. Data obtained from Smith & Tanford
(1973).
Figure 4-2: Linear relationship between mole
fraction of soap formed and log of optimum
salinity (in meq/ml) for Case A. Value of n used
was 13. Data obtained from Mohammadi
(2008).
Figure 4-3: Linear relationship between mole
fraction of soap formed and inverse of optimum
solubilization ratio in cc/cc for Case A. Value of n
used was 13. Data obtained from Mohammadi
(2008).
Figure 4-4 Match of tuned HLD-NAC model
(solid lines) for Case A at 50% oil overall
concentration (v/v). Red represents σo while
blue represents σw. The tuned value of asurf was
195 Å2. Circles are experimental data and
dashed lines show UTCHEM output reported
by Mohammadi (2008).
y = 0.601x - 3.389 R² = 0.999
0
1
2
3
4
5
6
7
8
9
10
5 7 9 11 13 15 17 19 21 23
pK
d
Number of carbon atoms in alkyl chain (n)
y = -1.187x - 0.001 R² = 0.965
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 0.2 0.4 0.6 0.8
lnS
*
Xsoap
y = -0.053x + 0.059 R² = 0.997
0
0.01
0.02
0.03
0.04
0.05
0.06
0 0.2 0.4 0.6 0.8
1/σ
*
Xsoap
0 1 2 3 4 5
x 104
0
10
20
30
40
50
60
70
Na2CO
3 concentration in ppm
So
lub
iliz
ati
on
rati
os (
cc/c
c)
102
Figure 4-5: Match of tuned HLD-NAC (solid lines)
model for Case A at 30 % oil overall concentration
(v/v). Red represents σo while blue represents σw.
The tuned value of asurf was 215 Å2. Circles are
experimental data and dashed lines show
UTCHEM output reported by Mohammadi (2008).
Figure 4-6: Prediction of solubility ratios using
tuned HLD-NAC model for Case A at 10 % oil
overall concentration (v/v). Red represents σo
while blue represents σw. The value of asurf used
was 205 Å2. The green circle represents the
optimum experimentally measured by
Mohammadi (2008). This point was used in
tuning.
Figure 4-7: Prediction of solubility ratios using
tuned HLD-NAC model for Case A at 20 % oil
overall concentration (v/v). Red represents σo while
blue represents σw. The value of asurf used was 205
Å2. The green circle represents the optimum
experimentally measured by Mohammadi (2008).
This point was used in tuning.
Figure 4-8: Prediction of solubility ratios for
tuned HLD-NAC model for Case A at 40 % oil
overall concentration (v/v). Red represents σo
while blue represents σw. The value of asurf used
was 205 Å2. The green circle represents the
optimum experimentally measured by
Mohammadi (2008). This point was used in
tuning.
0 1 2 3 4 5
x 104
0
10
20
30
40
50
60
70
Na2CO
3 concentration in ppm
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0 1 2 3 4 5
x 104
0
10
20
30
40
50
Na2CO
3 concentration in ppm
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0 1 2 3 4 5
x 104
0
10
20
30
40
50
Na2CO
3 concentration in ppm
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0 1 2 3 4 5
x 104
0
10
20
30
40
50
Na2CO
3 concentration in ppm
So
lub
iliz
ati
on
rati
os (
cc/c
c)
103
Figure 4-9: Phase volume fraction diagram based
on flash calculations for 10 % oil concentration for
Case A. Each bar represents a fixed sodium
carbonate concentration. Red represents excess oil
phase, blue excess brine, and green the
microemulsion phase.
Figure 4-10: Phase volume fraction diagram
based on flash calculations for 40 % oil
concentration in Case A. Each bar represents a
fixed sodium carbonate concentration. Red
represents excess oil phase, blue excess brine,
and green the microemulsion phase.
Figure 4-11: Activity map for Case A. Solid lines
represent prediction from the model used in this
dissertation. Green represents type II-, red type III
and blue type II+ regions found experimentally.
The dashed lines show the three-phase window
used in the UTCHEM model by Mohammadi et al.
(2009).
Figure 4-12: Linear relationship between mole
fraction of soap formed and log of optimum
salinity (in meq/ml) for Case B. Value of n used
was 14. Data obtained from Mohammadi
(2008).
0 1 2 3 4 5
x 104
0
20
40
60
80
100
Na2CO
3 concentration in ppm
Vo
lum
e (
cc)
0 0.5 1 1.5 2 2.5 3 3.5 4
x 104
0
20
40
60
80
100
Na2CO
3 concentration in ppm
Vo
lum
e (
cc)
0 10 20 30 40 50 600
1
2
3
4
5
6x 10
4
Na 2
CO
3 c
on
cen
trati
on
in
pp
m
Oil concentration in volume %
y = -1.519x + 0.479 R² = 0.953
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.3 0.5 0.7 0.9
ln S
*
Xsoap
104
Figure 4-13: Linear relationship between mole
fraction of soap formed and inverse of optimum
solubilization ratio in cc/cc for Case B. Value of n
used was 14. Data obtained from Mohammadi
(2008).
Figure 4-14 Match of tuned HLD-NAC model
(solid lines) for Case B at 30 % oil overall
concentration (v/v) and 0.3 wt.% surfactant
concentration. Red represents σo while blue
represents σw. The tuned value of asurf was 16
Å2. Circles are experimental data and dashed
lines show UTCHEM output reported by
Mohammadi (2008).
Figure 4-15: Match of tuned HLD-NAC model
(solid lines) for Case B at 50 % oil overall
concentration (v/v) and 0.3 wt.% surfactant
concentration. Red represents σo while blue
represents σw. The tuned value of asurf was 45 Å2.
Circles are experimental data and dashed lines
show UTCHEM output reported by Mohammadi
(2008).
Figure 4-16: Prediction of tuned HLD-NAC
model (solid lines) for Case B at 30 % oil
overall concentration (v/v) and 0.6 wt.%
surfactant concentration. Red represents σo
while blue represents σw. Circles are
experimental data and dashed lines show
UTCHEM output reported by Mohammadi
(2008).
y = -0.056x + 0.087 R² = 0.985
0.03
0.04
0.05
0.06
0.07
0.3 0.5 0.7 0.9
1/σ
*
Xsoap 0 1 2 3 4 5 6
x 104
0
10
20
30
40
50
60
70
Na2CO
3 concentration in ppm
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0 1 2 3 4 5 6
x 104
0
10
20
30
40
50
60
70
Na2CO
3 concentration in ppm
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0 1 2 3 4 5 6
x 104
0
10
20
30
40
Na2CO
3 concentration in ppm
So
lub
iliz
ati
on
rati
os (
cc/c
c)
105
Figure 4-17: Prediction of tuned HLD-NAC model
(solid lines) for Case B at 40 % oil overall
concentration (v/v) and 0.6 wt.% surfactant
concentration. Red represents σo while blue
represents σw. Circles are experimental data and
dashed lines show UTCHEM output reported by
Mohammadi (2008).
Figure 4-18: Prediction of tuned HLD-NAC
model (solid lines) for Case B at 50 % oil
overall concentration (v/v) and 1 wt.%
surfactant concentration. Red represents σo
while blue represents σw. Circles are
experimental data and dashed lines show
UTCHEM output reported by Mohammadi
(2008).
Figure 4-19: Phase volume fraction diagram based
on flash calculation results for Case B at 30 % oil
overall concentration (v/v) and 0.6 wt.% surfactant
concentration. Each bar represents a sodium
carbonate concentration. Red represents excess oil
phase, blue represents excess brine, and green
represents microemulsion phase.
Figure 4-20: Phase volume fraction diagram
based on flash calculation results for Case B at
50 % oil overall concentration (v/v) and 1 wt.%
surfactant concentration. Each bar represents
a sodium carbonate concentration. Red
represents excess oil phase, blue represents
excess brine, and green represents
microemulsion phase.
0 1 2 3 4 5 6
x 104
0
10
20
30
40
50
60
70
Na2CO
3 concentration in ppm
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0 1 2 3 4 5 6
x 104
0
10
20
30
40
50
60
70
Na2CO
3 concentration in ppm
So
lub
iliz
ati
on
rati
os (
cc/c
c)
3 3.5 4 4.5 5
x 104
0
20
40
60
80
100
Na2CO
3 concentration in ppm
Vo
lum
e (
cc)
2 2.5 3 3.5 4 4.5 5
x 104
0
20
40
60
80
100
Na2CO
3 concentration in ppm
Vo
lum
e (
cc)
106
Figure 4-21: Activity map for Case B with 0.3
wt.% surfactant. Solid lines represent prediction
from the model used in this dissertation. Green
represents type II-, red type III and blue type II+
regions found experimentally. The dashed lines
show the window used in the UTCHEM model by
Mohammadi (2008).
Figure 4-22: Activity map for Case B with 0.6
wt.% surfactant. Solid lines represent
prediction from the model used in this
dissertation. Green represents type II-, red
type III and blue type II+ regions found
experimentally. The dashed lines show the
window used in the UTCHEM model by
Mohammadi (2008).
Figure 4-23: Activity map for Case B with 1 wt.%
surfactant. Solid lines represent prediction from
the model used in this dissertation. Green
represents type II-, red type III and blue type II+
regions found experimentally. The dashed lines
show the window used in the UTCHEM model by
Mohammadi (2008).
Figure 4-24: Example of a fish diagram
showing types of microemulsions with no alkali
for a pure surfactant. Only Nalco
concentration in brine is varied. Model
parameters were obtained from Case A. Red
shows the upper salinity limit and blue the
lower salinity limit. Dashed line shows the
optima.
0 10 20 30 40 50 600
1
2
3
4
5
6
7x 10
4
Na 2
CO
3 c
on
cen
trati
on
in
pp
m
Oil concentration in volume %
0 10 20 30 40 50 600
1
2
3
4
5
6
7x 10
4
Na 2
CO
3 c
on
cen
trati
on
in
pp
m
Oil concentration in volume %
0 10 20 30 40 50 600
1
2
3
4
5
6
7x 10
4
Na 2
CO
3 c
on
cen
trati
on
in
pp
m
Oil concentration in volume %0 5 10 15
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
ln (
Na+
) co
ncen
trati
on
in
meq
/ml
w t % of synthetic surfactant in aqueous solution
Type II+
Type III
Type II-
Type IV
107
Figure 4-25: Fish diagrams using model
parameters obtained from Case A. Red shows the
upper salinity limit and blue the lower salinity
limit. Solid lines show the fish diagram with 1.0
wt.% Na2CO3 and dashed lines show fish diagram
in absence of alkali.
Figure 4-26: Fish diagrams using model
parameters obtained from Case B. Red shows
the upper salinity limit and blue the lower
salinity limit. Solid lines show the fish diagram
with 1.0 wt.% Na2CO3 (fixed) and Nalco
concentration varying. Dashed lines show the
fish diagram in absence of alkali.
Figure 4-27: Fish diagram using model parameters
tuned for Case A. Red shows the upper salinity
limit and blue the lower salinity limit. Solid lines
show the fish diagram with Na2CO3 concentration
varying (brine concentration fixed). Squares
indicate experimental data from Mohammadi
(2008).
Figure 4-28: Fish diagram using model
parameters tuned for Case B. Red shows the
upper salinity limit and blue the lower salinity
limit. Solid lines show the fish diagram with
Na2CO3 concentration varying (brine
concentration fixed). Squares indicate
experimental data from Mohammadi (2008).
0 5 10 15
-0.6
-0.4
-0.2
0
0.2
ln (
Na+
) co
ncen
trati
on
in
meq
/ml
w t % of synthetic surfactant in aqueous solution
0 5 10 15-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
ln (
Na+
) co
ncen
trati
on
in
meq
/ml
w t % of synthetic surfactant in aqueous solution
0 1 2 3 4 5 6 7
-1.5
-1
-0.5
0
ln (
Na+
) co
ncen
trati
on
in
meq
/ml
w t % of synthetic surfactant in aqueous solution
0 2 4 6 8 10-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
ln (
Na+
) co
ncen
trati
on
in
meq
/ml
w t % of synthetic surfactant in aqueous solution
108
Chapter 5
Dimensionless Solutions to Microemulsion Phase Behavior
This chapter develops the dimensionless form of our modified HLD-NAC EOS to interpret phase
behavior of surfactant-oil-brine systems. As discussed in Chapter 1, Huh (1979) found a
correlation between solubilization ratios and the interfacial tensions. The relationship made it
easier to deduce interfacial tensions from phase behavior experiments and eliminated the need for
performing cumbersome IFT measurements. Since then, phase behavior experiments known as
salinity scans have been routinely done with the primary goal of determining oil and water
solubilization ratios as a function of salinity. Therefore, prediction of solubilization ratios is of
high importance.
The solubilization ratio is a dimensionless term. The following sections revisit the net
and average curvature equations to provide useful relationships for oil and water solubilization
ratios as a function of the HLD.
5.1. Solubilization Ratio Relationships in Two-Phase Regions
This section illustrates the use of the net curvature equation to derive useful relationships between
the solubilization ratios and the HLD of the system. The net curvature equation relates the oil and
water curvatures to the HLD of the system and the surfactant length parameter L. From (3.15) and
the net curvature equation,
1 1
3
s
o w
A HLD
V V L
. (5.1)
109
Multiplication of Eq. (5.1) by the volume of surfactant in the system (Vs), and rearranging the
terms we get the relationship,
1 1
3( )( )o w
I HLD
, (5.2)
where,
s
s
VI
LA . (5.3)
I, referred to as the interfacial volume ratio henceforward, is a dimensionless group that is a ratio
of the volume of the surfactant component to the volume of the interface. The interface is defined
with a thickness L contributed by the surfactant length parameter and As, which is the total area of
all surface active molecules at the interface. The volume of the surfactant at the interface is LAs.
A large I indicate the surfactant is well packed at the interface. I must be less than one.
As discussed in Chapter 3, the HLD in a traditional salinity scan is expressed by,
, , , , ( ) *
( ) | lnEACN T P Cc f A
SHLD S
S . (5.4)
Hence, (5.2) provides a simple mathematical relationship between the solubilization ratios and the
salinity of the system in a salinity scan. Similar relationships can be developed for temperature
and pressure scans.
Chapter 2 introduced equations to calculate solubilized component volumes in type II-
and type II+ microemulsions. The excess phases were assumed to be pure. Hence from Eq. (5.2),
110
dimensionless solutions for the microemulsions in the two-phase regions can be developed as is
done next.
5.1.1. Dimensionless Solutions for Type II- Microemulsions
The system consists of an excess oil phase and a microemulsion where water is the continuous
phase. This implies Vw,m is equal to Vw of the system. Dividing this by the surfactant volume
(Vs), which by assuming pure excess phases, is equal to Vs,m, we obtain a constant water
solubilization ratio of Vw/Vs in the type II- microemulsion for a fixed overall composition,
regardless of the value of HLD (as long as the criteria for formation of type II- microemulsions
are satisfied as discussed in Section 5.3). The constant water solubilization ratio in type II-
microemulsions is henceforward denoted as σ0w. Therefore, in type II- microemulsions,
0
1 13
o w
IHLD
. (5.5)
Specifically, for a salinity scan, from Eq. (5.4),
* 0
1 13 ln
o w
SI
S . (5.6)
Therefore, the inverse of solubilization ratios varies linearly with the logarithm of the aqueous
phase salinity. This is an important new result of this research. The slope of this line is always
equal to -3I. Figure 5-1 shows evidence of a linear trend between the inverse of oil solubilization
ratios (from experiments) and HLD in the type II- region. Experimental data used here was
reported by Sheng (2010).
111
5.1.2. Dimensionless Solutions for Type II+ Microemulsions
For type II+ microemulsions, Vo,m is equal to Vo in the system. Dividing by the surfactant volume
(Vs), we obtain a constant oil solubilization ratio of Vo/Vs in the type II+ microemulsion for a
particular overall composition, regardless of the value of HLD. The constant oil solubilization
ratio in type II+ microemulsions is σ0o. Hence, in type II+ microemulsions,
0
1 13 ( )
w o
I HLD
. (5.7)
Specifically, for a salinity scan, from Eq. (5.4),
* 0
1 13 ln
w o
SI
S
. (5.8)
This result is similar to Eq. (5.6). However, the slope of the linear relationship between the
inverse of water solubilization ratio and logarithm of salinity is +3I (as opposed to -3I in Eq.
(5.6)). Figure 5-2 shows inverse of water solubilization ratios (from experiments) are linearly
related to the HLD of the system in the type II+ region. Experimental data used here was
reported by Sheng (2010).
5.2. Solubilization Ratio Relationships in The Three-phase Region
The type III system consists of three-phases, an excess oil phase, an excess brine phase and the
middle phase microemulsion. As explained in Chapter 2, neither σw nor σo in type III
microemulsions are constrained by the overall composition alone. Therefore, Eq. (5.2) is not
sufficient to determine the composition of type III microemulsions. In this section we derive a
112
second dimensionless equation from the modified average curvature equation Eq.(3.16) to
calculate the solubilization ratios.
In type III microemulsions, the correlation length is constant at ξ*. This is a good
assumption for type III microemulsions where the oil and water both form continuous planar
micelles (spheres with large radii of curvatures), but not necessarily true near the two phase
boundaries where cylindrical micellar structures may exist. Furthermore, at optimum, the oil and
water component volume fractions in the microemulsion are equal. Therefore, at optimum,
o w (5.9)
and,
*
o w . (5.10)
Consequently, from Eq. (3.17) , ξ* can be expressed as
2 ** 6 6 3 3
( ) (2 )
me w o me w w s
s w o s w s s
V V V V
A A A A
. (5.11)
Since the average curvature of the type III microemulsion is always constrained to be
equal to the inverse of ξ*, from Eq. (3.16) and Eq. (5.11),
*
1 1 2
o w . (5.12)
.
Equation (5.12) hence shows that the solubilization ratios in the type III microemulsion are
always constrained by the optimum solubilization ratio, a key screening factor in phase behavior
113
studies. In order to determine the values of the oil and water solubilization ratios, Eq. (5.2) and
Eq. (5.12) are solved simultaneously. Therefore in a type III microemulsion,
*
1 3 1
2o
IHLD
, (5.13)
and,
*
1 3 1
2w
IHLD
. (5.14)
.
Specifically for a salinity scan,
* *
1 3 1ln
2o
I S
S
, (5.15)
and,
* *
1 3 1ln
2w
I S
S
. (5.16)
Here again we see a linear correlation between the inverse of solubilization ratios and logarithm
of salinity in a typical salinity scan. The inverse of the solubilization ratios will also vary linearly
as a function of other HLD factors like EACN, T and P. However, the slope of the linear
relationship (1.5I) is half of that in the two-phase regions (3I). Figure 5-3 shows evidence of a
linear relationship between solubilization ratios (from experiments) and HLD in the type III
region. Experimental data used here was reported by Sheng (2010).
114
5.3. Two-phase Limits and Stability Criteria for Dimensionless Equations
Chapter 2 discussed the stability criteria used in HLD-NAC. Similar criteria applicable to
dimensionless equations can be developed. At the lower HLD limit (HLDL), both Eq. (5.5) and
Eq. (5.12) need to be satisfied. Therefore,
0 *
1 1 23 L
w w
IHLD
. (5.17)
However, σw = σ0w in type II- microemulsions. Hence,
0 *
2 1 1
3L
w
HLDI
(5.18)
Similarly, for the upper HLD limit (HLDU),
* 0
2 1 1
3U
o
HLDI
. (5.19)
Equations (5.18) and (5.19) both show that a decrease in interfacial volume ratio (I) increases the
upper and lower HLD limits. The width of the three-phase region expressed in terms of HLD for a
constant overall composition can be expressed as,
0 0 * 0 * 0
* 0 0 * 0 0
22 2 1 1 2
3 3
o w w o
o w o w
HLDI I
. (5.20)
115
At the invariant point representing the type III microemulsion composition, the width of the
three-phase zone is zero. The invariant composition is also the point of transition between type III
and type IV microemulsions. Hence, from Eq. (5.20) at the invariant point,
0 0 * 0 * 02 0o w w o , (5.21)
or,
* 2
( )
w o
s w o
V V
V V V
. (5.22)
Equation (5.22) expressed in terms of component volume fractions in the microemulsion
becomes,
* 2
( )
w o
s w o
. (5.23)
Equation (5.23) represents the locus of the invariant point of the tie-triangle in the compositional
space (ϕo, ϕw, ϕs). We define a new parameter χ, which determines the presence of a three-phase
region as,
2( )
w o
s w o
. (5.24)
The lower HLD limit HLDL, as defined in Eq. (5.18) marks the transition from type II- to
type III microemulsion for a particular overall composition constrained by σ0w. Thus, HLDL gives
the point of transition between the two-phase lobe (type II-) and the tie triangle (type III region).
116
However, a critical lower HLD limit (HLDL*) exists below which a type III microemulsion cannot
exist. The model assumes excess phases to be pure. The critical lower HLD limit (HLDL*) is
obtained by finding HLDL as the overall surfactant concentration goes to zero. Therefore HLDL*
is obtained when the inverse of σ0w is set to zero. Hence, from Eq. (5.18),
*
*
2 1
3LHLD
I
(5.25)
Similarly, a critical upper HLD limit (HLDU*) exists above which, a type III
microemulsion cannot exist. HLDU* is obtained by setting the inverse of σ0
w to zero. Hence.
From Eq. (5.19),
*
*
2 1
3UHLD
I
(5.26)
The limits and the transition zones can be described using fish plots as shown later in
section 5.4.2.2. Based on the upper and lower limits of HLD, the modified stability criteria are as
follows.
Case 1: If HLD < HLDL* , type III and type II+ microemulsions cannot exist.
HLD ≥ HLDU , a type IV microemulsion exists (single phase microemulsion).
HLD < HLDU , a type II- microemulsion exists (two-phase system).
Case 2: If HLD > HLDU* , type III and type II- microemulsions cannot exist.
HLD ≤ HLDL , a type IV microemulsion exists (single phase microemulsion).
HLD > HLDL , a type II+ microemulsion exists (two-phase system).
Case 3: If HLDL* ≤ HLD ≤ HLDU
* and,
if χ ≥ σ* ,
117
o HLD < HLDL , a type II- microemulsion exists (two-phase system).
o HLD > HLDU , a type II+ microemulsion exists (two-phase system).
o HLDL ≤ HLD ≤ HLDU a type III microemulsion exists (three-phase system).
If χ ≤ σ*,
o HLD > HLDL , a type II+ microemulsion exists (two-phase system).
o HLD < HLDU , a type II- microemulsion exists (two-phase system).
o HLDL ≥ HLD ≥ HLDU, a type IV microemulsion exists (single phase system).
5.4. Results
This section discusses key outcomes of the dimensionless equations developed applicable to
microemulsions across both two and three-phase regions. This dissertation is the first to clearly
define a robust way to calculate optimum solubilization ratios and optimum salinities. Chapter 3
and Chapter 4 uses the area term (as) as a tuning parameter after empirically estimating the length
term L. The dimensionless solutions eliminate the need to treat both as and L separately. Instead,
we use the interfacial volume ratio (I) as the single tuning variable. Figure 5-4 shows an example
(WOR=1, σ* = 13.5 cc/cc and I = 0.129) of the linear relationship between the inverse of
solubilization ratios and the HLD in the two-phase and three-phase regions.
5.4.1. Interpretation of Phase Behavior Experiments
Salinity scan experiments were conducted using sodium dodecyl benzenesulfonate (SDBS) and
sodium dodecyl sulfate (SDS) as surfactants. Iso-butyl alcohol (IBA) was used as a co-solvent.
The oils used were pure hydrocarbons (heptane and dodecane). Experiments were done at a
constant temperature of 40 °C. The experimental procedure is described in Appendix C.
118
Salinity scans reported by Aarra et al. (1999) have been used in this section. They
investigated the effect of different monovalent and divalent cations on microemulsion phase
behavior. The scans were done using NaCl, KCl, CaCl2 and MgCl2 as salts. Two different
surfactant systems were considered, one with sodium dodecyl sulfate (SDS) and the other with a
blend of an alkyl aryl sulfonate and dodecyl ethoxy sulfonate (AAS). The experiments were
conducted at different temperatures.
5.4.1.1. Prediction of Optimum Solubilization Ratios
Equation (5.12) suggests that the optimum solubilization ratio σ* is always equal to the harmonic
mean of the oil and water solubilization ratios (σo and σw) in a type III microemulsion. Therefore,
the optimum solubilization ratio can be estimated from a single pipette in a scan with a type III
microemulsion, irrespective of that pipette being at optimum salinity. Traditionally, optimum
solubilization ratios are obtained by manually finding the intersection of the oil and water
solubilization ratios. Alternatively, the harmonic mean approach is far more robust. If more than
one type III microemulsion data is available for a particular scan, the harmonic means of the
solubilization ratios could be averaged.
5.4.1.2. Prediction of Optimum Salinities
Equations (5.15) and (5.16) suggest that the inverse of optimum solubilization ratios vary linearly
with the logarithm of salinity. Therefore, using experimental data in the type III region, a linear
regression is done for lnS plotted against 1/σo and 1/σw. The intersection of the lines occurs at
lnS*. This is again a systematic way to predict the optimum salinity. The HLD is then calculated
from the optimum salinity using Eq. (3.4).
119
5.4.1.3. Tuning the Interfacial Volume ratio (I) to Match Phase Behavior Data
With the optima known, iteration is done on the interfacial volume ratio (I) to match
experimentally obtained solubilization ratios at different salinities. Therefore for every salinity, a
tuned interfacial volume ratio (I) is obtained. However, due to experimental uncertainties,
multiple values of interfacial volume ratios are obtained at various salinities. An average
interfacial volume ratio (I) that satisfies all data points reasonably is then calculated by
eliminating outliers (outside the range from 0 to 1). Data within the physical range of 0 to 1 was
considered, while the others were discarded in estimating the average tuned interfacial volume
ratios.
Table 5-1 and Table 5-2 shows a summary of the optima and the average tuned interfacial
volume ratios for different salinity scans. The σ* predicted for 24 salinity scans using the
harmonic mean approach had an average relative error of 2.18% and 2.7% as compared to the
optima reported by Aarra et al. (1999). This shows that the harmonic mean approach is highly
reliable. Furthermore, the optimum salinities calculated using the intersection method is also in
very good agreement with the reported values with the average relative error being less than
1.5%. The tuned interfacial volume ratios have also been reported.
Figure 5-5 and Figure 5-6 show the tuning results for the experiments described in
Appendix C. Figure 5-7 to Figure 5-30 show the tuning results for all 24 salinity scans reported
by Aarra et al. (1999). The results indicate that the dimensionless solutions are reliable and can
easily be used to match phase behavior data. Figure 5-31 and Figure 5-32 show the summary of
average interfacial volume ratios for all reported salinity scans. From the figures, it can also be
concluded that the type of salt does not significantly affect the interfacial volume ratio.
120
5.4.2. Analysis
This section qualitatively explains the effect of each dimensionless group on the phase behavior.
Key formulation design criteria are presented.
5.4.2.1. Design Criteria for a Wide Three-phase Region
Equation (5.20) shows that the width of the three-phase region is a function of the overall
composition, the optimum solubilization ratio and the interfacial volume ratio (I). Figure 5-33
shows that smaller interfacial volume ratios (I) gave a thicker width of the three-phase zone.
However, the width of the three-phase zone also decreases with increasing σ*. For good oil
recovery, high solubilizations and a wide three-phase region is desirable. Hence, EOR
formulations must be designed to have low interfacial volume ratios (I) with high σ*.
5.4.2.2. Modified Fish Diagrams Using χ
As shown in Chapter 4, fish diagrams are traditionally represented at a water-oil ratio of one
(fixed overall composition). The three-phase limits are then expressed as a function of the total
surfactant content in the system. χ as shown in Eq. (5.24) considers compositional effects of
both WOR and surfactant volume. Hence, the new parameter χ is a more appropriate variable to
represent fish plots. Figure 5-34 shows an example of a fish plot with an interfacial volume ratio
(I) of 0.2 and σ* equal to 10 cc/cc. The composition at which χ becomes equal to σ* is the
invariant point of the three-phase region. In chemical engineering applications, this point is
marks the beginning of the “fish-tail.” The invariant point marks the beginning of the type IV
region. Therefore, three-phase systems cannot exist when χ is less than σ*. This is an important
121
result from this research. The figure also clearly shows the critical upper HLD limit (HLDU*) and
critical lower HLD limit (HLDL*). A type III microemulsion can only exist when conditions for
both χ and HLD are satisfied. It is also important to note that the HLDU and HLDL curves
intersect and flip (HLDU becomes less than HLDL) when χ is less than σ*. The various limits and
regions in the fish plot corresponds to the stability criteria discussed in section 5.3.
5.4.2.3. The Tie-Triangle Locus
The model developed assumes excess phases to be pure. Hence in a ternary diagram, the base of
the tie triangle in a three-phase system is always fixed with vertices at excess phase compositions
representing pure oil and water components. Under the constraints of these assumptions, the tie
triangle evolves from the base of the ternary diagram with type III microemulsion composition
beginning at the excess brine phase and ending at the excess oil phase as the HLD increases.
Equation (5.23) can be used to find a locus of the invariant point representing the microemulsion
composition. The locus is solely a function of the optimum solubilization ratio σ*. Figure 5-35 to
Figure 5-37 show the locus for three different values of σ*, 3 cc/cc, 10 cc/cc and 30 cc/cc. The
height of the locus decreases with increasing σ*. Physically, such a result is true because
solubilization ratio is inversely proportional to the volume of surfactant in the microemulsion.
Hence the height of the locus (which is directly proportional to the surfactant concentration)
decreases.
5.4.3. Dimensionless Solutions Applied to Temperature and Pressure Scans
The inverse of solubilization ratios varies linearly with the HLD of the system. HLD, as
explained in Chapter 3, varies linearly with temperature and pressure depending on the value of α
122
and β respectively. Data from Austad and Strand (1996) was used in Chapter 3 to match pressure
and temperature scans for dead and live oil. The same dataset can be used to show that the
inverse of solubilization ratios is a linear function of temperature and pressure. Austad and
Strand (1996) reported temperature and pressure scan data for type III microemulsions.
Therefore, for a pressure scan of a type III microemulsion,
*
3 ( )1 1
2
ref
o
I P P
, (5.27)
and,
*
3 ( )1 1
2
ref
w
I P P
. (5.28)
.
Hence, the slope of 1/σ vs pressure line is dependent on the product Iβ. Similarly, for a
temperature scan (type III),
*
3 ( )1 1
2
ref
o
I T T
, (5.29)
and,
*
3 ( )1 1
2
ref
w
I T T
. (5.30)
The slope of 1/ σ vs temperature is dependent on Iα. Thus, the slopes are scaled by either α or β.
123
Figure 5-38 to Figure 5-41 show the linear dependence of 1/ σ on pressure for both dead
and live oil systems. Figure 5-42 to Figure 5-45 show the linear dependence of 1/σ on
temperature. A summary of the slopes obtained and the interfacial volume ratios obtained are
presented in Table 5-3 and Table 5-4. The mean interfacial volume ratio was 0.25. Table 5-5
shows that the interfacial volume ratio can be considered to be constant with temperature and
pressure.
5.4.4. Interfacial Volume Ratio for Surfactant Mixtures
As discussed in Chapter 4, the total volume of surfactant pseudocomponent, L and as is dependent
on the mole fractions of the surfactants present in the mixture. Therefore, the interfacial volume
ratio is also dependent on the surfactant mole fraction. For a surfactant pseudocomponent, from
Eq. (5.3),
s
s a s
MWI
LN a (5.31)
where, MWs is the molecular weight of the surfactant pseudocomponent, ρs is the surfactant
pseudocomponent density (which is traditionally taken to be equal to density of water) and Na is
Avogadro’s number. Equation (5.31) applied to a surfactant mixture with n number of surfactant
components becomes,
1
1 1
ni
i si
n n
a i i i i
i i
X
I
N X L X a
. (5.32)
124
where �̅�si is the molar density of the surfactant i .
Figure 5-46 shows I for a mixture consisting of two surfactants, sodium oleate and
sodium laurate. The dependence of I on the mole fraction of sodium laurate in a mixture with
sodium oleate is shown as an example. The molecular weights, L and as for soaps were
calculated using the equations discussed in Chapter 4. The alkali phase behavior data used in
Chapter 4 was then used in order to obtain the average tuned interfacial volume ratios. Figure
5-47 and Figure 5-48 show the tuned interfacial volume ratio as a function of the soap mole
fractions.
Therefore, to use dimensionless solutions developed in this chapter, the following key
relationships are needed:
1. Equation (4.15), which accounts for the changes in lnS* due to Xsoap.
2. Equation (4.16), which accounts for the changes in 1/σ* due to Xsoap.
3. Equation (5.32), which accounts for the changes in the interfacial volume ratio as a
function of Xsoap.
The soap formation model described in Chapter 4, along with these three equations can then be
used in the dimensionless equations.
5.5. Conclusions
Dimensionless solutions to represent microemulsion phase behavior were established. The
following conclusions can be made:
1. Inverse of oil and water solubilization ratios vary linearly with HLD and hence, lnS.
2. The slopes of the linear relationships are determined by the interfacial volume ratio (I).
The slope in the two-phase regions are twice that of the slopes in the three-phase region.
125
3. The optimum solubilization ratio σ* is the harmonic mean of σo and σw in the type III
microemulsion. This property should be used to infer optima from phase behavior
experiments.
4. The intersection of the linear trends of lnS as a function of 1/σw and lnS as a function of
1/σo gives an accurate estimate of the optimum salinity.
5. The type III microemulsion window is dependent on the upper and lower HLD limits and
the value of the χ factor.
6. The χ factor represents fish diagrams better as opposed to considering the effects of
WOR and Vs separately.
7. Based on the data available to date, the type of cations do not affect the interfacial
volume ratio (I) significantly. However, salinities should be expressed in terms of
equivalents and not in terms of weight %.
8. The locus of the type III microemulsion composition is represented by χ = σ*.
9. The interfacial volume ratio is independent of temperature and pressure.
10. For surfactant mixtures, the interfacial volume ratio is dependent on the individual
surfactant mole fraction ratios.
126
Table 5-1: Summary of optima and tuned interfacial volume ratio (I) for experiments using
SDS surfactant reported by Aarra et al. (1999)
Salt Temperature
in °C
S* in
meq/ml
Reported
by Aarra
et al.
(1999)
S* in
meq/ml
Predicted
from
Eqs.(5.15)
and (5.16)
σ*
in cc/cc
Reported
by Aarra et
al. (1999)
σ*
in cc/cc
Predicted
from
Eq.(5.12)
% relative
error in
S*
%
relative
error in
σ*
Average
Tuned
I
NaCl 20.00 1.55 1.53 6.20 6.18 1.07 0.28 0.20 35.00 1.57 1.56 6.00 5.91 0.77 1.52 0.28 50.00 1.69 1.68 5.80 5.73 0.56 1.23 0.28 KCl 20.00 1.09 1.09 6.00 6.23 0.15 3.87 0.21 35.00 1.17 1.16 5.80 5.94 0.76 2.46 0.22 50.00 1.33 1.32 5.70 5.85 0.76 2.68 0.23 CaCl2 20.00 0.97 0.93 4.70 4.88 3.78 3.78 0.10 35.00 0.95 0.90 4.80 4.93 4.71 2.68 0.10 50.00 0.97 0.97 4.80 4.82 0.15 0.45 0.12 MgCl2 20.00 1.29 1.26 5.00 5.19 2.26 3.82 0.12 35.00 1.29 1.27 5.00 5.14 2.03 2.79 0.13 50.00 1.39 1.38 5.00 5.03 0.82 0.62 0.15
Average 1.49% 2.18%
0.18
±0.02 (std.
error)
127
Table 5-2: Summary of optima and tuned interfacial volume ratio (I) for experiments using
AAS surfactant reported by Aarra et al. (1999)
Salt Temperatur
e in °C
S* in
meq/ml
Reporte
d by
Aarra et
al.
(1999)
S* in
meq/ml
Predicted
from
Eqs.(5.15)
and (5.16)
σ*
in cc/cc
Reported
by Aarra
et al.
(1999)
σ*
in
cc/cc
Predicte
d
from
Eq.(5.12)
%
relative
error in
S*
%
relative
error
in σ*
Average
Tuned
I
NaCl 20.00 0.358 0.355 8.10 7.90 0.79 2.49 0.20 50.00 0.444 0.428 7.00 7.13 3.64 1.82 0.17 90.00 0.564 0.560 5.00 5.03 0.77 0.66 0.26 KCl 20.00 0.240 0.242 8.30 7.93 0.54 4.51 0.28 50.00 0.327 0.323 7.30 7.43 1.17 1.75 0.19 90.00 0.491 0.481 5.30 4.93 2.06 7.02 0.28 CaCl2 20.00 0.070 0.070 12.10 11.89 0.53 1.77 0.41 50.00 0.077 0.077 9.30 9.16 0.13 1.46 0.33 90.00 0.086 0.086 7.10 6.65 0.11 6.36 0.49 MgCl2 20.00 0.092 0.092 9.60 9.64 0.43 0.47 0.27 50.00 0.102 0.102 8.60 8.39 0.03 2.48 0.29 90.00 0.117 0.117 5.70 5.79 0.03 1.62 0.26
Average 0.85% 2.7%
0.29
±0.03
(std.
error)
128
Table 5-3: Summary of interfacial volume ratio at different temperatures from analysis of
pressure scans reported by Austad and Strand (1996).
Temperature in
°C
Oil type β from
Table 3-5 and
Table 3-6
Tuned βI Interfacial
volume ratio I
55
60
65
70
75
80
85
70
75
80
85
90
Dead
Dead
Dead
Dead
Dead
Dead
Dead
Live
Live
Live
Live
Live
7.70E-04
7.60E-04
7.30E-04
7.10E-04
8.30E-04
9.80E-04
1.00E-03
2.50E-04
3.80E-04
3.00E-04
3.70E-04
2.90E-04
2.48E-04
2.60E-04
2.65E-04
2.90E-04
2.82E-04
2.89E-04
2.96E-04
1.18E-04
1.26E-04
1.23E-04
1.29E-04
1.15E-04
0.21
0.23
0.24
0.27
0.23
0.20
0.20
0.31
0.22
0.27
0.23
0.26
Average 6.14E-04 2.12E-04 0.24
Table 5-4: Summary of interfacial volume ratio at different pressures from analysis of
temperature scans reported by Austad and Strand (1996).
Pressure in bars Oil type α from
Table 3-7 and
Table 3-8
Tuned αI Interfacial
volume ratio I
50
100
150
200
250
300
600
500
450
400
300
250
200
100
Dead
Dead
Dead
Dead
Dead
Dead
Live
Live
Live
Live
Live
Live
Live
Live
8.90E-03
8.30E-03
7.70E-03
6.40E-03
5.90E-03
5.00E-03
3.20E-03
5.10E-03
4.20E-03
4.40E-03
6.40E-03
5.40E-03
7.30E-03
8.40E-03
3.55E-03
3.19E-03
2.97E-03
2.60E-03
2.39E-03
2.33E-03
1.62E-03
1.49E-03
1.66E-03
1.72E-03
2.00E-03
2.00E-03
2.75E-03
2.69E-03
0.266
0.256
0.257
0.271
0.270
0.311
0.338
0.195
0.264
0.260
0.208
0.247
0.251
0.214
Average 5.91E-03 2.29E-03 0.262
129
Table 5-5: Statistical summary of interfacial volume ratio data obtained from pressure and
temperature scans reported by Austad and Strand (1996).
Statistic Interfacial volume ratio I
Mean
Standard Error
Standard Deviation
Sample Variance
Minimum
Maximum
0.250
0.007
0.037
0.001
0.195
0.338
130
Figure 5-1: An example showing the linear
relationship between the inverse of oil
solubilization ratios and HLD for type II-
microemulsions. Data obtained from Sheng (2010).
Figure 5-2: An example showing the linear
relationship between the inverse of water
solubilization ratios and HLD for type II+
microemulsions. Data obtained from Sheng (2010).
Figure 5-3: An example showing the linear relationship between the inverse of solubilization ratios (red
for oil, blue for water) and HLD for type III microemulsions. Data obtained from Sheng (2010).
y = -0.49x - 0.02 R² = 0.94
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-1.5 -1 -0.5 0
1/σ
o
HLD
y = 0.47x + 0.03 R² = 0.95
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.2 0.4 0.6
1/σ
w
HLD
y = 0.18x + 0.059 R² = 0.99
y = -0.21x + 0.06 R² = 0.96
0
0.02
0.04
0.06
0.08
0.1
0.12
-0.2 -0.1 0 0.1
1/σ
HLD
131
Figure 5-4: An example showing the linear
relationship between the inverse of solubilization
ratios and HLD. Red represents inverse of oil
solubilization ratios. Blue represents inverse of
water solubilization ratios. (WOR=1, σ* = 13.5
cc/cc and I-ratio = 0.129).
Figure 5-5: Tuned phase behavior (solid lines)
compared to data (circles) for experiments with
NaCl and SDS+SDBS+IBA surfactant mixture at
40 °C. Red represents oil solubilization ratios. Blue
represents water solubilization ratios. I-ratio =
0.21, σ* = 7.35 cc/cc and S*= 1.47 meq/ml. Oil used
was heptane.
Figure 5-6: Tuned phase behavior (solid lines) compared to data (circles) for experiments with NaCl and
SDS+SDBS+IBA surfactant mixture at 40 °C. Red represents oil solubilization ratios. Blue represents
water solubilization ratios. I-ratio = 0.34, σ* = 4.56 cc/cc and S*= 2.52 meq/ml. Oil used was dodecane.
0.8 1 1.2 1.4 1.6 1.8 2 2.20
5
10
15
20
NaCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
1 1.5 2 2.5 3 3.50
5
10
15
20
NaCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
132
Figure 5-7: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with NaCl and SDS surfactant at 20 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-8: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with KCl and SDS surfactant at 20 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-9: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with CaCl2 and SDS surfactant at 20 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-10: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with MgCl2 and SDS surfactant at 20 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
1 1.2 1.4 1.6 1.8 20
5
10
15
20
NaCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.7 0.8 0.9 1 1.1 1.2 1.3 1.40
5
10
15
20
KCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
5
10
15
20
CaCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.8 1 1.2 1.4 1.6 1.8 20
5
10
15
20
MgCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
133
Figure 5-11: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with NaCl and SDS surfactant at 35 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-12: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with KCl and SDS surfactant at 35 °C. Blue
represents water solubilization ratios. Data from
(Aarra et al., 1999)
Figure 5-13: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with CaCl2 and SDS surfactant at 35 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-14: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with MgCl2 and SDS surfactant at 35 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
0.8 1 1.2 1.4 1.6 1.8 2 2.20
5
10
15
20
NaCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.8 1 1.2 1.4 1.6 1.8 20
5
10
15
20
KCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
5
10
15
20
CaCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.5 1 1.5 20
5
10
15
20
MgCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
134
Figure 5-15: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with NaCl and SDS surfactant at 50 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-16: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with KCl and SDS surfactant at 50 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-17: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with CaCl2, and SDS surfactant at 50 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-18: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with MgCl2, and SDS surfactant at 50 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.40
5
10
15
20
NaCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.8 1 1.2 1.4 1.6 1.8 20
5
10
15
20
KCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
5
10
15
20
CaCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.5 1 1.5 20
5
10
15
20
MgCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
135
Figure 5-19: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with NaCl and AAS surfactant at 20 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-20: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with KCl and AAS surfactant at 20 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-21: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with CaCl2, and AAS surfactant at 20 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-22: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with MgCl2, and AAS surfactant at 20 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
5
10
15
20
NaCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
5
10
15
20
KCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.06 0.065 0.07 0.075 0.08 0.0850
5
10
15
20
25
30
CaCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.08 0.09 0.1 0.11 0.12 0.130
5
10
15
20
25
30
MgCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
136
Figure 5-23: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with NaCl and AAS surfactant at 50 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-24: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with KCl and AAS surfactant at 50 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-25: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with CaCl2, and AAS surfactant at 50 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-26: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with MgCl2, and AAS surfactant at 50 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
5
10
15
20
NaCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.25 0.3 0.35 0.40
5
10
15
20
25
30
KCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.065 0.07 0.075 0.08 0.085 0.09 0.0950
5
10
15
20
25
30
CaCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.08 0.09 0.1 0.11 0.12 0.130
5
10
15
20
25
30
MgCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
137
Figure 5-27: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with NaCl and AAS surfactant at 90 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-28: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with KCl and AAS surfactant at 90 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-29: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with CaCl2, and AAS surfactant at 90 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
Figure 5-30: Tuned phase behavior (solid lines)
compared reported data (circles) for experiments
with MgCl2, and AAS surfactant at 90 °C. Red
represents oil solubilization ratios. Blue represents
water solubilization ratios. Data from (Aarra et
al., 1999)
0.4 0.5 0.6 0.7 0.80
5
10
15
20
25
30
NaCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.650
5
10
15
20
25
30
KCl concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.1150
5
10
15
20
25
30
CaCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.170
5
10
15
20
25
30
MgCl2 concentration in meq/ml
So
lub
iliz
ati
on
rati
os (
cc/c
c)
138
Figure 5-31: Average tuned interfacial volume
ratios for experiments using SDS surfactant at
20°C (Blue), 35°C (Red), 50°C (Green). Black lines
represent average interfacial volume ratios for
each salt.
Figure 5-32: Average tuned interfacial volume
ratios for experiments using AAS surfactant at
20°C (Blue), 50°C (Red), 90°C (Green). Black lines
represent average interfacial volume ratios for
each salt.
Figure 5-33: Width of the three-phase region as a
function of the optimum solubilization ratio and
the interfacial volume ratio (I) for a fixed overall
concentration of ϕo=0.495, ϕw=0.495 and ϕs=0.01.
Figure 5-34: Example of a modified fish diagram
(interfacial volume ratio (I)=0.2). Red shows the
upper salinity limit and blue the lower salinity
limit. Type III microemulsions can only exist when
χ is larger than σ* and, HLD is within the upper
and lower critical limits HLDU*
and HLDL* .
0.00
0.10
0.20
0.30
0.40
0.50
0.60
SodiumChloride
PotassiumChloride
CalciumChloride
MagnesiumChloride
Tu
ned
I-R
ati
o
0.00
0.05
0.10
0.15
0.20
0.25
0.30
SodiumChloride
PotassiumChloride
CalciumChloride
MagnesiumChloride
Tu
ned
I-R
ati
o
0.5
1 1020
30
0
1
2
3
4
5
*
I-ratio
H
LD
HLDU*
HLDL
*
σ *
139
Figure 5-35: Locus of the invariant type III
microemulsion composition in a ternary space.
(σ*= 3 cc/cc)
Figure 5-36: Locus of the invariant type III
microemulsion composition in a ternary space.
(σ*= 10 cc/cc)
Figure 5-37: Locus of invariant type III microemulsion composition in a ternary space (σ*= 30 cc/cc).
0
20
40
60
80
0 20 40 60 80
0
20
40
60
80
Oil
Surfactant
Brine 0
20
40
60
80
0 20 40 60 80
0
20
40
60
80
Oil
Surfactant
Brine
0
20
40
60
80
0 20 40 60 80
0
20
40
60
80
Oil
Surfactant
Brine
140
Figure 5-38: Inverse of oil solubilization ratios as a
function of pressure at different constant
temperatures using dead oil. Data from Austad
and Strand (1996)
Figure 5-39: Inverse of water solubilization ratios
as a function of pressure at different constant
temperatures using dead oil. Data from Austad
and Strand (1996)
Figure 5-40: Inverse of oil solubilization ratios as a
function of pressure at different constant
temperatures using live oil. Data from Austad and
Strand (1996)
Figure 5-41: Inverse of water solubilization ratios
as a function of pressure at different constant
temperatures using live oil. Data from Austad and
Strand (1996)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 100 200 300 400
1/σ
o
Pressure in Bars
55 °C
60 °C
65 °C
70 °C
75 °C
80 °C
85 °C
90 °C0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 100 200 300 400
1/σ
w
Pressure in Bars
55 °C
60 °C
65 °C
70 °C
75 °C
80 °C
85 °C
90 °C
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
50 250 450 650
1/σ
o
Pressure in Bars
70 °C
75 °C
80 °C
85 °C
90 °C
95 °C
100 °C
110 °C
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
50 250 450 650
1/σ
w
Pressure in Bars
70 °C
75 °C
80 °C
85 °C
90 °C
95 °C
100 °C
110 °C
141
Figure 5-42: Inverse of oil solubilization ratios as a
function of temperature at different constant
pressures using dead oil. Data from Austad and
Strand (1996).
Figure 5-43: Inverse of water solubilization ratios
as a function of temperature at different constant
pressures using dead oil. Data from Austad and
Strand (1996).
Figure 5-44: Inverse of oil solubilization ratios as a
function of temperature at different constant
pressures using live oil. Data from Austad and
Strand (1996).
Figure 5-45: Inverse of water solubilization ratios
as a function of temperature at different constant
pressures using live oil. Data from Austad and
Strand (1996).
0.04
0.06
0.08
0.1
0.12
0.14
0.16
50 70 90
1/σ
o
Temperature in °C
300 bars
250 bars
200 bars
150 bars
100 bars
50 bars
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
50 70 90
1/σ
w
Temperature in °C
300 bars
250 bars
200 bars
150 bars
100 bars
50 bars
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
65 85 105
1/σ
o
Temperature in °C
600 bars
500 bars
450 bars
400 bars
300 bars
250 bars
200 bars
100 bars0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
65 85 105
1/σ
w
Temperature in °C
600 bars
500 bars
450 bars
400 bars
300 bars
250 bars
200 bars
100 bars
142
Figure 5-46: Interfacial volume ratio for a
surfactant mixture (sodium laurate and sodium
oleate) as a function of laurate soap mole fraction
using Eq. (5.32).
Figure 5-47: Inverse of water solubilization ratios
as a function of temperature at different constant
pressures using dead oil. Data from Austad and
Strand (1996).
Figure 5-48: Inverse of oil solubilization ratios as a
function of temperature at different constant
pressures using live oil. Data from Austad and
Strand (1996).
0.23
0.24
0.24
0.25
0.25
0.26
0.26
0.27
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Inte
rfacia
l V
olu
me R
ati
o
Xlaurate
0
0.05
0.1
0.15
0.2
0.25
0 0.2 0.4 0.6 0.8
Tu
ned
I-R
ati
o
Xsoap
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
Tu
ned
I-R
ati
o
Xsoap
143
Chapter 6
Conclusions and Recommendations
6.1. Conclusions
The effects of solution gas, pressure, temperature and alkali on the phase behavior of systems
consisting of surfactant, brine and crude oil have been examined. For the first time, a new HLD-
NAC based EOS model for microemulsion phase behavior was developed that can account for
changes in different formulation variables. This research has shown how to estimate the optimum
salinity and solubilization ratio under most conditions. We demonstrate that simple PVT data of
such systems eliminate the need to perform salinity scans at high pressures and temperatures. The
following conclusions are made:
1. Microemulsion phase behavior depends on pressure changes. The logarithm of optimum
salinity varies linearly with pressure. The existing HLD equation was updated to include
a new β factor to account for the change in HLD due to pressure.
2. The optimum solubilization ratio depends inversely on the width of the three-phase
window expressed in HLD units. This dependence can be used to obtain a relationship
between optimum salinities and solubilization ratios. Based on salinity scans using
different pure alkanes, these relationships can be easily determined and used for
prediction.
3. The modified HLD-NAC developed in this dissertation is the first phase behavior model
that was successfully used to interpret temperature and pressure scans.
4. PVT experiments like those reported by Austad and Strand (1996) are critical in
understanding the effect of pressure and temperature on phase behavior. They provide a
144
quick and easy way to obtain phase behavior data, specifically α and β in the HLD
equation, over a wide range of temperature and pressure. In comparison, salinity scans at
high pressures give limited information and are more cumbersome and expensive.
5. Pressure and solution gas both affect phase behavior and in a compensating manner.
Therefore ignoring either one of them can lead to errors. We do not recommend the use
of surrogate oils (using toluene to mimic live oil composition) or forcing the EACN of
methane to be values other than 1.0.
We then extended the modified HLD-NAC equation of state to model and predict
microemulsion phase behavior applicable to alkali-surfactant EOR. The approach was validated
by using available published data. The following conclusions are made:
1. The soap formed under in-situ conditions is dependent on the alkyl carbon number and
molecular weight of the petroleum acid pseudocomponent. The alkyl carbon number of
the acid can be used to estimate distribution coefficients, soap tail length, and soap mole
fractions thereby reducing the number of input/tuning variables.
2. The inverse of optimum solubilization ratio (1/σ*) is a linear function of the soap mole
fraction (Xsoap). This empirical relationship is new to this research. The relationship
between inverse of optimum solubilization ratio, lnS*, and mole fraction of soap formed
can be represented by a plane in three-dimensional coordinates. This relationship to
predict optima can be used to constrain the soap model and determine an effective alkyl
carbon number for the acid pseudocomponent.
3. Flash calculations using the modified HLD-NAC model are non-iterative, fast, and
robust. Flash calculations were extended to model soap as a second component lumped in
the surfactant pseudocomponent. Additional synthetic surfactants can also be added.
4. Only two tuning parameters are required (n and asurf) to model alkali-surfactant-oil-brine
phase behavior. In comparison, the Hand’s model approach has seven input parameters
145
(five if excess phases are assumed to be pure) that require tuning (Sheng, 2010). The new
model predictions are in good agreement with un-tuned experimental data.
5. Activity maps can be predicted easily by our model without the need to fit three-phase
windows from experiments as done in UTCHEM.
6. Fish diagrams for alkali-surfactant system are asymmetric, which is in agreement with
published literature.
Dimensionless solutions to represent microemulsion phase behavior were then established by
correcting the average curvature equation. The NAC equations were made dimensionless in order
to identify key dimensionless groups that govern microemulsion phase behavior. The following
conclusions can be made:
1. Inverse of oil and water solubilization ratios vary linearly with HLD and hence, lnS. The
slopes of the linear relationships are determined by the interfacial volume ratio (I). The
slope in the two-phase regions are twice that of the slopes in the three-phase region.
2. The optimum solubilization ratio σ* is the harmonic mean of σo and σw in the type III
microemulsion. This property should be used to infer optima from phase behavior
experiments. The intersection of the linear trends in the type III region gives an accurate
estimate of the optimum salinity.
3. The type III microemulsion window is dependent on the upper and lower HLD limits and
the value of the χ factor. The χ factor scales fish diagrams better as opposed to
considering the effects of WOR and Vs separately.
4. The type of cations do not affect the interfacial volume ratio (I) significantly. However,
salinities should be expressed in terms of equivalents and not in terms of weight %.
5. The locus of the type III microemulsion composition (invariant point) is a function of σ*
alone.
146
6.2. Recommendations for Future Research
In this section, we present recommendations that can help to better understand the phase
behavior of microemulsion and its impact on oil recovery in chemical EOR floods. We
recommend the following tasks:
1. PVT experiments similar to the ones analyzed in this dissertation can be done for
alkali-surfactant-oil-brine systems. The modified HLD-NAC model explained in
Chapters 3 and 4 is fully capable of capturing the effects of different formulation
variables like alkali, pressure and temperature. Such experimental data do not
exist in the published literature and are therefore, highly desirable.
2. Bourrel and Schechter (2010) showed that the constants in the linear relationship
between the width of the three-phase region and the optimum solubilization ratio
are unique for each type of surfactant. Therefore, the constants for lnS* vs 1/σ
*
relationship can be made a function of the surfactant structure properties like alkyl
chain length, number of ethoxy units, number of propoxy units and type of head
group. Hammond and Acosta (2012) showed that the Cc parameter in the HLD
equation is a function of the surfactant structure. Combining HLD and the
optimum solubilization ratio equations, a robust screening model can be
developed where surfactants with different structures can be screened to cater to
phase behavior requirements for a particular crude oil.
3. A complex geochemical model can be integrated with the modified HLD-NAC in
Chapter 4. This would allow simulators to capture phase behavior changes as a
function of rock-fluid interactions.
147
4. The model developed here assumes that the solubilized micelles are spherical in
shape. However, Acosta et al. (2003) showed that such an assumption is a
simplification. In reality, the shape of micelles are spherical in the two-phase
regions, but they transition to rod-like micelles near the two-phase and three-
phase boundaries. The bi-continuous type III microemulsion often consists of
lamellar structures with alternating layers of solubilized oil and water. A shape
factor can be introduced in the definition of the curvature in the NAC equations to
see how the shape factor changes as a function of HLD.
5. Integration of the models discussed in this dissertation with a reservoir simulator
is highly desirable. Different flood scenarios can be investigated and oil recovery
can be analyzed. Current simulators are not equipped to deal with the changes in
formulation variables other than WOR and salinity. Pressure and temperature
variations across a reservoir during an EOR flood impacts oil recovery.
148
Appendix A
Effect of Pressure on the Surfactant Affinity Difference and the
Hydrophilic-Lipophilic Difference
In this appendix, we show the thermodynamic premise behind the inclusion of the β factor in the
HLD equation by first elaborating on the concept of the surfactant affinity difference (SAD),
followed the description of the method by Salager (1988).
Consider the chemical potential of the surfactant in phase j to be µsj where j may be either
oil or water. Now, consider these chemical potentials at some reference state to be µsj*. The
equations for chemical potentials of the surfactant component in the water and oil phases can
therefore be expressed as
* ln( )sw sw sw swRT x a (A-1)
and,
* ln( )so so so soRT x a . (A-2)
where xso and xsw represent relative concentrations of the surfactant in oil and water, respectively.
Activity coefficients of the surfactant in oil and water phases are represented by aso and asw
respectively. At equilibrium, the chemical potentials of the surfactant component are equal to
each other. The difference between the reference state chemical potentials of the surfactant in the
149
water and the oil phase is the surfactant affinity difference. The dimensionless form of the SAD is
the hydrophilic lipophilic difference. Therefore,
* * ln( / )sw so so so sw swSAD RT x a x a , (A-3)
and,
SADHLD
RT . (A-4)
For high quality formulations, the concentration of the surfactant in the excess oil and
water phases is very small. This implies that the activity coefficients are equal to 1.0 in those
phases. Therefore, activities can be replaced by concentrations in the SAD equation. Furthermore,
at optimum salinity, the concentrations of surfactant in the excess oil and water phases are equal.
Hence the SAD (and the HLD) at optimum condition is zero.
When pressure and salinity are changed in the system, the change in reference state
chemical potentials cause the SAD and the HLD to change. Therefore, we form the following
differential equations similar to those derived by Salager (1988) for changes in EACN and lnS*:
* *
* *
*ln
ln
so so
sod dP d SP S
, (A-5)
and,
* *
* *
*ln
ln
sw sw
swd dP d SP S
. (A-6)
150
Now, salinity causes changes in µsw* alone (Salager, 1988) and does not affect µso
*.
Therefore,
*
* so
sod dPP
. (A-7)
Additionally, the change in µsw* is dominated by the change in salinity. Therefore, the
effect of pressure on µsw* can be assumed to be weak as compared to the strong influence of
salinity. Neglecting the pressure effect in Eq. (A-6) yields,
*
* *
*ln
ln
sw
swd d SS
. (A-8)
As shown empirically in this dissertation, the logarithm of optimum salinity and pressure
are linearly dependent. Therefore,
*ln S P C , (A-9)
where C is a constant. Thus,
*lnd S dP . (A-10)
151
At optimum conditions, SAD is always zero. This means the changes in µsw* and µso
* due
to changes in formulation variables must compensate each other at optimum conditions.
Therefore, dµsw* and dµso
* are equal. Hence combining (A-7), (A-8) and (A-9),
* *
*ln
so sw
P S
. (A-11)
This result is analogous to the one expressed by Salager (1988) for compensating changes
in EACN and lnS*. Furthermore, SAD is a function of formulation variables that are independent.
This is shown as follows. Since µsw* and µso
* are functions of different variables, the partial
derivatives must be constant. That is,
* *
1 2* and
ln
so swb bP S
, (A-12)
where, b1 and b2 are constants. Therefore by generalizing this result for other HLD variables,
*
*d ( d ) ( d )sj
sj i i i
i
X b XX
, (A-13)
where, every Xi is a HLD variable with bi as a relevant constant (the partial derivative). Linear
expressions of µw* and µo
* can be obtained by integration. The difference between µw* and µo
*
then forms a linear expression for SAD. That is,
* * ( )sw so i iSAD b X . (A-14)
152
Hence pressure, just like the other variables considered by Salager (1988), should also
form a linear (and independent) term in the SAD equation. In this dissertation, we show the
similarity between the pressure and temperature effects. Hence we adopted a linear term for
pressure that has a similar functional form to the term for temperature, which was already present
in the equation. We updated the SAD and HLD equations to include the pressure effects as
follows:
ln ( ) ( )ref ref
SADHLD S K EACN f A T T P P Cc
RT . (A-15)
153
Appendix B
Alkalinity of Aqueous Sodium Carbonate Solution
This section describes in more detail, the reactions and equilibrium constants used in this
dissertation to calculate the pH of sodium carbonate solutions. Aqueous sodium carbonate
solutions are alkaline in nature. Sodium and carbonate ions are formed as a result of dissolution.
The carbonate ion reacts with water to form bicarbonate and hydroxyl ions such that,
3
23
2
3 2 3 1andHCO OH
CO
C CCO H O HCO OH K
C
(B-1)
However, the molar concentrations of bicarbonate and the hydroxide ions are equal.
Hence,
23 3
1
1OH HCO COC C K C , (B-2)
where, C1OH- is the hydroxyl ion concentration from Eq. (B-1). The bicarbonate ion is also in
equilibrium with water, carbonic acid and hydroxyl ion,
2 3
3
3 2 2 3 2and H CO OH
HCO
C CHCO H O H CO OH K
C
. (B-3)
Again, since concentrations of carbonic acid, and hydroxyl ions are equal,
154
3
2
2OH HCOC K C . (B-4)
where C2OH- is the hydroxyl ion concentration from Eq. (B-3). Therefore, the total concentration
of hydroxyl ions will be,
2 23 3
1 2 1/4
1 2 1( )OH OH OH CO CO
C C C K C K K C . (B-5)
In this dissertation, we considered K1 to be 2.08×10-4 M and K2 to be 2.22×10-8 M (Lister,
2000). We then used the total hydroxyl ion concentration COH- in Eq. (3) to calculate the soap
content as a function of sodium carbonate concentration. The concentration of hydroxyl ions is
used to calculate pH and pOH.
155
Appendix C
Salinity Scan Experiments at Atmospheric Pressure
This section describes the procedure to conduct salinity scans at atmospheric pressure. Salinity
scans are typically done by mixing surfactant-oil-brine mixtures in sealed graduated pipettes in a
controlled environment (constant temperature oven). The pure oils used in the experiments were
heptane and dodecane. Surfactants used were sodium dodecyl benzenesulfonate (SDBS) and
sodium dodecyl sulfate (SDS). Iso-butyl alcohol (IBA) was used as a cosolvent. The procedure is
as follows:
1. Borosilicate pipettes were prepared by sealing the narrow end with a MAP gas flame
torch.
2. A salt stock solution (NaCl) was then prepared by adding salt to DI water. The
concentration of the stock solution needs to be high in order to obtain the desired range
and resolution in a salinity scan. A magnetic stirrer was used to dissolve the salt into DI
water. The salt solution is prepared on weight basis such that,
Weight of salt( )Salt Concentration( %) 100
Weight of salt( ) Weight of water( )
gwt
g g
. (C-1)
3. A surfactant stock solution was prepared by mixing equal amounts of SDS and SDBS.
The aqueous surfactant solution in each pipette contained 1 wt.% SDS, 1wt% SDBS and 3
wt.% of IBA. The concentrations of SDS, SDBS and IBA in the stock solution were four
times that of the desired aqueous surfactant solution concentration. The dilution of the
surfactant stock with the brine solution would eventually give the desired surfactant
concentrations in the pipettes.
156
4. The desired amounts (by weight) of surfactants and co-solvent (IBA) were added to DI
water to prepare the surfactant stock solution such that,
Weight of surfactant( )Surfactant Concentration( %) 100
Weight of surfactant( ) Weight of water( )
gwt
g g
.
(C-2)
A magnetic stirrer was used to dissolve the chemicals in DI water.
5. An array of pipettes was then prepared to create a salinity gradient. Each pipette was
labelled to show the salt content and the chemicals used.
6. Correct proportions of brine, surfactant solution and DI water were sequentially added to
each pipette to obtain the desired salinity and surfactant concentration. The resultant
solution in the pipette constitutes the aqueous volume. For our experiments the aqueous
volume was 2 ml.
7. Oil was then added to the pipette (the oil was dyed with a red dye). In the experiments
described here, 2 ml of oil was added.
8. An Argon stream was used to strip out the air from top of the pipette. This helps to
minimize the impact of gas on the phase behavior and also creates an inert environment
in the pipette addressing a potential fire hazard.
9. The top end of each pipette were then sealed using a flame torch.
10. The fluids were then mixed. Each pipette was checked for leaks.
11. All pipettes were then allowed to equilibrate for one day at 40 °C in a constant
temperature oven.
12. The fluids were then mixed at the desired temperature and allowed to settle for one day.
13. Readings of the interfaces formed in each pipette were measured and recorded every
three days (See Figure C-1). The final readings were obtained after two weeks.
157
14. Oil and water solubilization ratios are then calculated by measuring the volume of oil and
water solubilized in the microemulsion.
15. A list of experimental observations and calculations has been included in
158
Table C-1: Summary of observations and calculations in a salinity scan. Total volume
capacity of each pipette is 5 ml.
Variable name Quantity measured with units Calculation / Observation
A Salinity
(meq/ml) Salinity of pipettes prepared
B Initial aqueous level
(ml) See Figure C-1
C Initial oil level
(ml) See Figure C-1
D Top of microemulsion phase
(ml) See Figure C-1
E Bottom of microemulsion phase
(ml) See Figure C-1
F
Volume of surfactant in the
system
(ml)
(5-B) × (aqueous surfactant
concentration in wt. %)
Surfactant density is assumed to be
equal to water. Hence, volume % is
equal to weight %.
G Solubilized oil
(ml) G = B – D
H Solubilized water
(ml) H = E – B
I Oil solubilization ratio
(dimensionless) I = G / F
J Water solubilization ratio
(dimensionless) J = H / F
K
Volume fraction of excess oil
phase
(dimensionless)
K = (D – C) / (5 – C)
L
Volume fraction of
microemulsion
(dimensionless)
L = (5 – D) / (5 – C) for type II-
L = (E – D) / (5 – C) for type III
L = (E – C) / (5 – C) for type II+
M
Volume fraction of excess water
phase
(dimensionless)
M = 1– K – L
159
Figure C-1: Schematic of readings measured from a phase behavior pipette scan. O: oil, W:
water and ME: microemulsion. Total volume capacity of each pipette is 5 ml.
O
W
O
ME
O
W
ME
W
ME
Tota
l V
olu
me
= 5 -
Oil
L
evel
Argon
/ Air
Argon
/ Air
Argon
/ Air
Argon
/ Air R
ead
ings
incr
ease
0 t
o 5
ml
Oil level (C)
Aqueous
level (B)
Top of ME
Bottom
of ME
Oil
Solubilized
Water Solubilized
Initial Type II- Type III Type II+
160
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VITA
Soumyadeep Ghosh was born in Ramachandrapuram, India on 6th May 1989. He holds a
Bachelor of Technology degree in Oil, Oleochemical and Surfactant Technology from the
Institute of Chemical Technology, Mumbai, India (2011). He earned his PhD student in Energy
and Mineral Engineering (Petroleum and Natural Gas Engineering option) at The Pennsylvania
State University. His research interests include enhanced oil recovery, surfactant science,
thermodynamics, fluid phase behavior and reservoir engineering. He is currently working for
Chevron Corporation as a Reservoir Simulation Engineer in the improved oil recovery/enhanced
oil recovery (IOR/EOR) unit in Chevron Energy Technology Company.