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Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas
Processing
Measurement and Modelling of Absorption of Carbon Dioxide into Methyldiethanolamine Solutions at High Pressures
Ph.D Dissertation Even Solbraa14.February 2003
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
What has been done ?
• A high pressure experimental equipment has been built and new high pressure experimental data are presented
• Equilibrium and kinetic limitations related to CO2 removal at high pressures in MDEA solutions are identified
• NeqSim - a general simulation program for natural gas processing operations has been developed. It is based on equilibrium and non-equilibrium models developed in this work. Many types of processes can now be solved effectively using a general non- equilibrium two-fluid model
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
How are the results used today?
• Capacity and kinetic limits of high pressure absorption processes of CO2 in MDEA-solutions are estimated
• The simulation program developed is used to solve and teach thermodynamics and mass transfer processes
• High pressure equilibrium (e.g. dew point) and non-equilibrium (e.g. drying) processes are solved in an effective way
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
1. Introduction to Natural Gas Processing and Transport
2. Equilibrium and Non-Equilibrium Model Development
3. Presentation of the Simulation Program Developed
4. Modelling and Regression to Experimental Data
5. Experimental Work and Results
6. Conclusions
Outline
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
The Natural Gas Chain
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Natural Gas Processing
Natural Gas + CO2
Natural Gas
Lean Amine
Rich Amine
CO2 Gas
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Lean Amine Solution
Rich Amine Solution
Acid Natural Gas
Sweet Gas
Random and structured packings:
Film Flow
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
CO2 removal with physical and chemical solvents
PCO2
xCO2
Physical
Solvents
Chemica
l
Solvents
CO2
Water+CO2
Physical Solvent (water):
CO2
Water
Chemical Solvent(MDEA):
MDEA
CO2HCO3
-
CO32-
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Two Illustrative and Case Studies
Problem to reach design specification in high pressure (100 bar) CO2 absorption plant operating at 70-80°C using MDEA
Condensation of Liquid Water in Sub Sea Dry Gas Pipeline operating between 100-200 bar
1. Erroneous predictions of water dew-point with standard equations of state in high pressure natural gas systems
1. Almost all models developed are low pressure models (GE-models).
2. High pressure equilibrium and mass transfer data not available
2. Non-equilibrium models for two-phase pipe flow not available
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
1. Introduction to Natural Gas Processing and Transport
2. Equilibrium and Non-Equilibrium Model Development
3. Presentation of the Simulation Program Developed
4. Modelling and Regression to Experimental Data
5. Experimental Work and Results
6. Conclusions
Outline
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
The Non-Equilibrium Two Fluid Model
The Non-Equilibrium Two Fluid Model
Closure Relations
Thermodynamic Models
Mass Transfer / Kinetic Models
Physical Property Models
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Weak Electrolyte Calculation Procedure
2 2 3MDEA H O CO HCO MDEA
Reactive/Non-reactive TP-flash algorithm
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Thermodynamic Modelling of Amine Thermodynamic Modelling of Amine SolutionsSolutions
Polynoms(Kent and Eisenberg, 1976)
Electrolyte GE-modelsAustgen (1989), Li and Mather (1994)
State of the Art
Future
Electrolyte Equations of StateFurst and Renon (1993), this work
+ Easy and fast- Too simple, no physics
+ Relatively easy and fast- Problematic to add supercritical components- Low pressure model
+ Generally applicable
- Computational demanding
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Thermodynamic ModelsThermodynamic Models
Type of FluidType of Fluid
ElectrolyteElectrolyteNon-PolarNon-Polar PolarPolar PolymersPolymers
GE-ModelsGE-Models19501950
19801980
EoS-ModelsEoS-Models
EoS-ModelsEoS-Models
19901990
GE-ModelsGE-Models
Debye-Debye-HuckelHuckel
EoS-ModelsEoS-Models EoS-ModelsEoS-Models
EoS-ModelsEoS-Models
20002000
EoS-ModelsEoS-Models
Empirical Empirical modelsmodels
Empirical Empirical modelsmodels
otherother
EoS-ModelsEoS-Models EoS-ModelsEoS-Models EoS-ModelsEoS-Models EoS-ModelsEoS-Models
YearYear
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Definition and Calculation of Thermodynamic Equilibrium
Equation of Statesi i i ix P y P
Parameters:
• Critical Temperature and Pressure
• Accentric Factor
GE-models ,
, xpi sat i
i i sat i i i
v P Px P e y P
RT
Molecular Parameters:
• Vapour Pressure of Pure Components
• Molar Volumes in solution
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Development of Two New Electrolyte Equations of State
BORNLRSRSRRFRT
AA
RT
AA
RT
AA
RT
AA
RT
AA
RT
AA
00
2
0
1
000
,
, ,r
T P
A T V nRTP
V V
nGeneral Equation of State
Contributions to the Helmholtz Energy
The Modelling Procedure
Find Best Molecular EoS
Find Best Electrolyte Terms
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Development of Two New Electrolyte Equations of State
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Equations of State Considered
• RK (Redlich Kwong, 1949)
• SRK (Soave, 1971)
• PR (Peng and Robinson, 1979)
• ScRK (Scwartzentruber and Renon, 1989)
• CPA (Kontegorgios, 1999)
Equations of State Mixing Rules
• no
• Classic (Van der Waals, 1905)
• Huron Vidal (Huron-Vidal, 1979)
• Wong-Sandler (Wong and Sandler, 1993)
Electrolyte Extensions
• Debye-Huckel (Debye-Huckel, 1952)
• MSA (Blum and Høye, 1982)
• Furst and Renon (Furst and Renon, 1993)
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Molecular Terms of Electrolyte Equations of State
Absolute average relative deviation1) [%] between experimental and calculated vapour pressures and densities with different equation of states
Component RK SRK PR ScRK2) CPA3) Experimental Data Methane vapour pressure: liquid density: gas density:
15.6 5.8 17.7
2.8 6.5 3.9
0.9 8.1 1.5
2.8 6.5 4.6
- - -
Perry (1998), Borgnakke et. al (1997)
Nitrogen vapour pressure: liquid density: gas density:
10.1 4.5 11.8
1.7 4.2 3.3
0.5 4.5 2.3
2.2 4.1 3.8
- - -
Perry (1998), Borgnakke et. al (1997)
CO2 vapour pressure: liquid density: gas density:
21.4 14.9 24.9
0.3
11.6 3.2
0.8 4.0 2.5
0.2
11.5 3.5
2.2 1.9 1.9
Perry (1998), Borgnakke et. al (1997)
MDEA vapour pressure: liquid density: gas density:
>>100 20.8
-
83.3 13.3
-
67.2 3.16
-
5.1
14.4 -
4.2 1.1 -
Noll et.al. (1998)
Water vapour pressure: liquid density: gas density:
>>100 30.7
>>100
11.5 27.8 15.5
6.9
18.8 10.6
0.3
27.8 5.9
1.2 1.1 1.7
Perry (1998), Borgnakke et. al (1997)
1) Deviation (%) = 100 x (experimental-calculated)/experimental 2) The polar coefficients in the ScRK-EOS coefficients were fitted for water, CO2 and MDEA 3) The coefficients in the CPA-EOS were fitted to experimental data
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Mixing Rules for Molecular Terms
Absolute average deviations (%) between experimental data and different models for the calculation of solubility of gasses in water and water in gas.
Gas No.points used for fitting1)
SRK + classic
SRK- HV2)
ScRK-HV
PR-HV
SRK-WS
CPA + classic
Number of Fitted Parameters
1 4 4 4 5 1
Nitrogen nitrogen in water water in nitrogen
13 78
>>100 32.2
3.0 8.1
7.1
17.6
4.3 10.0
8.7
11.6
29.7 28.2
CO2 CO2 in water water in CO2
43 57
>>100 45.0
6.0
13.5
6.1
10.6
5.8 11.8
7.6
15.4
12.0 22.5
Methane methane in water water in methane
176 215
>>100 52.2
6.4
13.1
5.5
10.6
5.9 10.1
7.6
10.4
31.8 14.1
1) See chapter 8 for references to the actual experimental data used in the fitting 2) The parameter in the Huron Vidal and Wong Sandler mixing rule was not fitted
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Electrolyte Terms
0
321k l kl
k lSR
A A n nW
RT V
i i
iiLR
LRN
VZn
RT
AA
314
3220
20 2
*0
11
4i i
is iBORN
n ZA A Ne
RT RT D
Osmotic coefficients of salt solutions calculated using the electrolyte ScRK-EOS
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Evaluation of Electrolyte Terms
Evaluation of different electrolyte models for the calculation osmotic coefficient and mean ionic coefficient for 28 halide salt solutions1)
Model No. of experimental points used in fitting
Osmotic coefficient abs.avg.rel.dev [%]
Mean ionic activity abs.avg.rel.dev [%]
Experimental data
Electrolyte ScRK-EOS
230 2.1 5.5 Robinson (1952)
Electrolyte CPA-EOS
230 2.3 4.9 Robinson (1952)
1) Salt concentrations: 0.1-6.0 molal. Salt solutions: NH4Cl, LiCl, LiBr, LiI, NaCl, NaBr, NaI, KCl, KBr, KI, KBr, KI, RbCl, RbBr, RbI, CsCl, CsBr, CsI, MgCl2, MgBr2, MgI2, CaCl2, CaBr2, MgI2, CaCl2, CaBr2, CaI2, SrCl2, SrBr2, SrI2, BaCl2, BaBr2, BaI2
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Predictions With the Electrolyte Model
Calculated and experimental density of an aqueous NaCl solution
Calculation of mean ionic activity coefficients of salt solutions using the electrolyte ScRK-EOS.
Density of Ionic Solution Mean Ionic Activity Coefficient
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Non-Equilibrium Modelling
1900:
1920:
1950:
1970:
1980:
1990:
2000:
Fick’s law for diffusion
Fourier law of heat transfer
Kinetic Theory of Gasses
Multicomponent Mass Transfer
Non-Equilibrium Thermodynamics
Molecular Simulation
Resistance at Interface
Scientific Work Simulation Tools
Equilibrium Models
Stage Efficiencies
Simple Maxwell Stefan
General Maxwell Stefan
OLGA
Software
HYSYS
ASPEN PLUS
Fick’s law
Simple Maxwell Stefan
General Maxwell StefanThis work
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Generalized Maxwell Stefan Equations
,1
n
t k k T P k k k k jj
c RTd c P
k jF F
1
tJ c B d
1`
1 1, 1,2,..., 1
ni k
iikin iki k
ij iij in
x xB
D D
B x i j and i j nD D
Multicomponent Maxwell Stefan Equation:
Generalized Driving Force:
+ General model
- Relatively complicated- Need thermodynamic model
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
The Enhancement Factor
CO2 Water
xCO2
yCO2
CO2Water MDEACO2
HCO3-
MDEA+xCO2
yCO2
2 2 3MDEA H O CO HCO MDEA
,
,
i reactivei
i non reactive
JE
J
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Calculation of the Enhancement Factor
Two Ways to Estimate the Enhancement Factor:
• Analytical Expressions (for simple reactions, e.g reversible first order reactions)
• Numerical Solutions of Film (for coupled and reversible reactions)
This work:
2
2
2
2 ,
2,
1t CO eff
COCO eff
k MDEA DE
k analytical
2 2
* *, ,( )t CO i CO bJ c E k x x
2
*,CO bx CO2 fraction at chemical equilibrium in liquid bulk
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
The Generalized Non-Equilibrium Two Fluid Model
• Conservation of total mass
• Conservation of components
• Conservation of momentum
• Conservation of energy
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
1. Introduction to Natural Gas Processing and Transport
2. Equilibrium and Non-Equilibrium Model Development
3. Presentation of the Simulation Program Developed
4. Modelling and Regression to Experimental Data
5. Experimental Work and Results
6. Conclusions
Outline
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
NeqSim – a General Non-Equilibrium Simulator
• General modelling tool for non-equilibrium and equilibrium processes
• Based on rigorous thermodynamic models
• Fluid mechanics based the on the one- or two fluid model
• Implemented in an object oriented language (Java/Python object oriented design where everything is an object)
• Suitable for being used as a modelling tool (general parameter fitting routines implemented)
• Validated against experimental data (equilibrium/non-equilibrium)
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
NeqSim – a General Non-Equilibrium Simulator
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
NeqSim - Examples of use
• Multiphase flash calculation
• Construction of phase envelopes
• Weak electrolyte calculations
• Process plant simulation
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Parameter Fitting Routines
2
2
1
;( )
Ni i
i i
y y x
aa
Shi-Square Fitting
Minimized using the Levenberg- Marquardt Method
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
1. Introduction to Natural Gas Processing and Transport
2. Equilibrium and Non-Equilibrium Model Development
3. Presentation of the Simulation Program Developed
4. Modelling and Regression to Experimental Data
5. Experimental Work and Results
6. Conclusions
Outline
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Thermodynamic Properties of Mixtures
ScRK-EOS + Huron Vidal CPA-EOS + ClassicMutual solubility of Water+CO2:
Freezing points of MDEA+Water: Mutual solubility of Methane+Water:
Mutual solubility of Water+CO2:
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Solubility of CO2 in water+MDEA solutions
Electrolyte ScRK-EoS
20.5 wt % MDEA : 50 wt% MDEA
Ref. MDEA (wt%) Temperature (K) Loading range (mol CO2/mol
amine)
Number of points
AAD (%)
Jou et.al. (1993) 35 313, 373 0.005-0.795 35 26.5
Jou et.al. (1982) 23.448.9
298,313,343,373,393298,313,343,373,393
0.0009-1.8330.0001-1.381
5455
29.628.4
Austgen et.al. (1991)
23.448.9
313313
0.006-0.8420.04-0.671
95
21.021.0
Chakma and Meisen (1987)
19.8, 48.9 373 0.04-1.304 17 18.8
Bahiri (1984) 20.0 311, 339 0.157-1.336 44 12.8
Kuranov (1996) 18.8-19.232.1
313, 333, 373, 393313, 333, 373, 393
0.209-1.3160.195-1.157
3334
16.323.2
Rho et.al. (1997) 5.020.5
323, 348, 373323, 348, 373
0.03-0.6840.026-0.847
1931
16.411.3
Mac Gregor and Mather (1991)
23.4 313 0.124-1.203 5 31.4
Average Deviation
26%
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
High pressure solubility of CO2 and methane in water+MDEA solutions
Electrolyte ScRK-EoSEstimated bubble point pressure30 wt % MDEA
Estimated PCO2:30 wt% MDEA
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
High pressure solubility of methane in CO2+water+MDEA solutions
Electrolyte ScRK-EoSEstimated methane solubility30 wt % MDEA
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Capacity Loss of Amine Solution at 100 bar and 70C
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
1. Introduction to Natural Gas Processing and Transport
2. Equilibrium and Non-Equilibrium Model Development
3. Presentation of the Simulation Program Developed
4. Modelling and Regression to Experimental Data
5. Experimental Work and Results
6. Conclusions
Outline
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
The High-Pressure Wetted Wall Column
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Experiments Done in This Work
Experiment Type
Number of Experiments
Comments Temperature [ C]
Pressure [bar]
Purpose
Water-CO2-nitrogen
12 Low pressure experiments
25, 40 20 Study physical mass transfer – compare to exciting low pressure data
Water-CO2-nitrogen
35 High pressure experiments
25, 40 50, 100,150
Measure new high pressure data
MDEA-water-CO2-nitrogen
48 High pressure experiments
25, 40 50, 100,150
High pressure absorption data of CO2 in MDEA solutions
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Experimental Results – Reference Data CO2 +Water
Reference Reynolds Number K a b Abs.rel.dev. [%]
Yih et.al. (1982) 300<Re<1600 2.99510-2 0.2134 0.50 13.0 This work 230<Re<1750 3.10110-2 0.2201 0.50 10.5
1/32* Rea bLL
kk K Sc
D g
Reference Reynolds Number K a b Abs.rel.dev. [%]
Yih et.al. (1982) 300<Re<1600 2.99510-2 0.2134 0.50 13.0 This work 230<Re<1750 3.10110-2 0.2201 0.50 10.5
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Experimental Results – Reference Data CO2, MDEA and water
2
2
2
2 ,
2,
1 t CO eff
COCO eff
k MDEA DE
k 2 2 313
1 1exp
313a
t t T K
Ek k
R T K
0
50
100
150
200
250
300
270 290 310 330 350 370 390
Temperature [K]
k2 [
m/k
mo
l sec]
Pacheco (1998) -low pressure
This work - highpressure
3
2 313.15 6.45 /
50.0
t T K
a
k m kmol s
kJE mol
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Conclusions
A high pressure wetted wall column was designed and constructed New mass transfer data were obtained for absorption of CO2 into MDEA-solutions at
pressures between 50 and 150 bar An electrolyte EOS (electrolyte ScRK-EOS) was used to model the thermodynamics
of the CO2-MDEA-water systems The electrolyte EOS was able to represent the experimental data for the systems CH4-
CO2-MDEA-water with good accuracy A general non-equilibrium mass transfer model was developed A non-equilibrium simulator – NeqSim – was implemented in a Java code Examples of how to do non-equilibrium process simulations were presented The non-equilibrium model developed is able to represent the experimental mass
transfer data of this work with a good precision.
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Conclusions
For a given partial pressure CO2, the capacity of MDEA solutions is lowered at increasing pressures. The capacity can be reduced up to 40% at 200 bar total pressure (inert gas methane)
For a specified natural gas, the capacity of MDEA solutions will increase with increasing gas stream pressures. This increase is not as high as we would expect from only consideration of the increased partial pressure of CO2
The reaction kinetics is not considerable affected by the total pressure (up to 150 bar with nitrogen as inert gas)
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Operation Chart 100 bar, 70-80C
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0 0.2 0.4 0.6 0.8 1
Loading
CO
2 P
art
ial P
res
su
re
Hysys
Operationline
Ideal Electrolyte EOS
Real Electrolyte EOS
Case 1: Case 2: Condensation of Liquid Water in Sub Sea Dry Gas Pipeline operating between 100-200 bar
Case 1: Problem to reach design specification in high pressure (100 bar) CO2 absorption plant operating at 70-80°C using MDEA
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Case 2: Case 2: Condensation of Liquid Water in Sub Sea Dry Gas Pipeline operating between 100-200 bar
Solubility of water in methane:
Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing
Thanks
• Institute for Energy- and Process Technology
• Statoil
• Norwegian Research Council