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Importance of the C7+ fraction in phase

behavior calculations

Maria A. Barrufet Petroleum Engineering Department Texas A&M University – College Station Tx 77843-3136

Physical properties of pure components essential for EOS calculations are the

critical pressure (Pc), the critical temperature (Tc), and the acentric factor (ω)

Many of these properties have been measured and compiled over the years.

Petroleum engineers are usually interested in the behavior of hydrocarbon

mixtures rather than pure components. However, as seen in the first article of this

series, to predict the behavior of fluid mixtures, equations of state require critical

properties and acentric factors of pure components which are used with

appropriate mixing rules.

Problems arise when working with any type of reservoir oil which may consist of

thousands of different molecular species, most of them nearly impossible to

quantify accurately using any analytical technique. A common approach is to

characterize this oil mixture as made up of well-defined components (C1, CO2,

C2,.. etc.) plus a heavy fraction. Defined components may be quantitatively

identified using a gas chromatographic analysis. The undefined fraction, usually

known as the C7+ fraction, contains hydrocarbon compounds heavier than

heptane. Depending upon the cases studied, this fraction may be extended up to

C10+ or C20

+, or split into a larger number of fractions.

To be able to use the EOS for any physical property prediction of reservoir fluids,

the C7+ fraction must be identified by assigning �virtual� critical properties and an

acentric factor to it. However, by using the plus fraction as a single component,

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fluid property predictions using an EOS can be erroneous and invalid conclusions

may result. In these cases, correct results can be obtained when the heavy

fraction is subsequently broken down into a manageable number of

pseudocomponents for EOS computations. The number of pseudocomponents

may range between 2 and an upper limit often constrained by computational load

and degree of accuracy required. An apparent constraint in defining these groups

is to ensure that the molecular weight and specific gravity of the mixture must be

equal to the measured properties for the C7+ fraction.

There are numerous correlations for estimating critical properties and acentric

factors of a heavy fraction. Most of these use specific gravity and normal boiling

point as correlating parameters; others use the molecular weight and the specific

gravity. Frequently, these are the only measured properties of the fraction.

The objectives of this article are not to discuss the advantages or disadvantages

of the different ways to handle the C7+ fraction by splitting or not, or to discuss

the different correlations to allocate critical properties and acentric factors.

These are case-dependent decisions, which will depend upon the type of

reservoir fluid, degree of accuracy required, time and economic constraints.

The objectives of this article are to present some numerical examples that

indicate the magnitude of changes in the physical properties obtained by

perturbing the molecular weight of the C7+ and by splitting this fraction. A

hypothetical volatile/condensate fluid, A, and a black oil fluid, B, are considered

in this analysis.

Among the properties analyzed are the effect of the C7+ fraction molecular weight

in the evaluation of formation volume factors (Bo’s) and of solution gas oil ratios

(Rs�s) for a black oil. The effect of splitting upon saturation pressures and the

prediction of wax deposition will also be briefly presented. The SRK EOS is used

for all computations.

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Volatile/Condensate Fluid A A synthetic fluid which may classify as a volatile oil or a gas condensate1,2 was

selected for the first example. This hypothetical oil contains about 75% methane

and 13% C7+ (composition indicated in Table 1). The molecular weight of this

fraction was allowed to change between 107 and 251.

Figure 1 shows the pairs used for molecular weights and densities for the C7+

fraction as obtained from a typical chromatographic analysis.3 Densities for

higher molecular weights have been smoothed.

0.76

0.78

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

Den

sity

/ g/

cm3

100 200 300 400 500 600Molecular Weight of C7+

Figure 1. Relationship between molecular weight of the hydrocarbon fraction and

density at standard conditions.

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Figure 2 illustrates the effect of the C7+ in the evaluation of phase envelopes for

Fluid A. It can be seen that at a reservoir temperature of 250oF the fluid classifies

as a gas condensate for the lower molecular weight, while it is a volatile oil for

higher molecular weights.

0

1000

2000

3000

4000

5000

6000

7000

Pres

sure

/psi

a

-100 0 100 200 300 400 500 600 700Temperature / F

Critical Points

Increasing Mw C7+

TR

Figure 2. Phase envelopes for fluid B with composition indicated in Table 1 and

molecular weight of the C7+ fraction changing from 107 to 251.

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Table 1. Molar Composition of Reservoir Fluid A

Component Name

Component Identification

Mole % Molecular Weight (lb / lb mole)

Density (g/cm3)

Nitrogen N2 0.121 28.014

Carbon Dioxide CO2 0.605 44.010

Methane C1 74.864

16.043

Ethane C2 3.885 30.070

Propane C3 2.416 44.097

n-Butane n-C4 0.971 58.124

i-Butane i-C4 0.966 58.124

n-Pentane n-C5 0.503 72.151

i-Pentane i-C5 1.208 72.151

Hexanes C6 1.505 86.178

Heavy Fraction C7+ 12.955

189.800 0.84

Figure 3 indicates the effect of splitting the C7+ fraction. All envelopes

correspond to Oil A with composition and molecular weight for the C7+ fraction as

indicated in Table 1. The difference among the predictions is due to the splitting.

The cases included are:

(1) No plus fraction � indicated by considering that C7+ is only one component

with the critical properties evaluated from Pedersen et al. 4 correlations using

the provided density and molecular weight.

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(2) One plus fraction � in this case the molecular weight and density provided are

assumed that belongs to a mixture of components from C7 to C80.

(3) Two or more plus fractions � here several cuts are defined according to

Pedersen et al. 5 scheme.

0

1000

2000

3000

4000

5000

6000

7000

8000

Pres

sure

/psi

a

-100 0 100 200 300 400 500 600 700 800Temperature / F

Critical PointsIncreasing Splitting of (C7+) fraction

TR No Plus

2 41 8

Figure 3. Phase envelope shifts due to splitting the C7

+ fraction in Fluid B with

composition indicated in Table 1.

Increasing the number of splits in Fluid A causes the EOS to predict lower critical

temperatures and higher critical pressures. Therefore, by proper selection of the

C7+ splitting, a fluid can be modeled either as a gas condensate, exhibiting a

dew-point at reservoir temperature, or as a volatile oil, exhibiting a bubble-point.

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The predicted physical properties depend upon the number of splits as indicated

in the previous figure, but after a certain number � which is case-dependent � the

predicted physical properties reach a plateau, or cease changing with the

number of splits.

Figure 4 illustrates the variation in the predicted saturation pressure at T = 250oF

for Fluid A with compositions given in Table 1, and with varying molecular

weights for the C7+ fraction. Three different cases are presented: (a) without

considering a plus fraction, (b) with 2 pseudocomponent groups and (c) with 4

pseudocomponent groups. It is apparent that the 2 and 4 pseudocomponent

scheme give nearly identical results, but the computational load is much bigger

for the latter case. This, however, cannot be generalized since at another

temperatures, saturation pressures change substantially with the number of

splittings as seen in Figure 3.

3000

4000

5000

6000

7000

8000

9000

Satu

ratio

n Pr

essu

re /

psia

100 120 140 160 180 200 220 240 260Molecular Weight of C7+

No Plus42

T = 250 F

Splitting Groups

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Figure 4. Effect of splitting the C7+ fraction in the saturation pressure at 250oF.

Fluid B has composition indicated in Table 1.

Black Oil Fluid properties such as Rs and Bo, can be systematically and easily evaluated

from an EOS as a function of pressure, temperature and compositions as

indicated in the second article of this series. The molecular weight of the C7+

fraction also affects the values of these properties for a black oil.

Figure 5 shows the changes in Bo due to changes in the molecular weight of the

C7+ fraction for a typical west Texas black oil (Fluid B) with about 38% C7

+ and

50% C1. The molecular weights here were changed between 237 (equivalent to

C17) and 345 (equivalent to C25).

It can be observed that higher molecular weights increase the bubble point

pressures while they lower the Bo. All calculations were done at 120oF.

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1.0

1.1

1.2

1.3Bo

0 1000 2000 3000 4000 5000Pressure /psia

345305278237

Molecular Weight C7+ T = 120 F

Figure 5. Effect of the molecular weight of the C7

+ fraction in the formation

volume factor of black oil B. Fluid B has 38 mole % of C7+.

Figure 6 illustrates the effect of changes in the molecular weight upon Rs. As

expected, the solution gas/oil ratio decreases as the molecular weight of the

heavy fraction increases.

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0

100

200

300

400

500

600R

s

0 1000 2000 3000 4000 5000Pressure /psia

345305278237

Molecular Weight C7+ T = 120 F

Figure 6. Effect of the molecular weight of the C7

+ fraction in the solution gas-oil-

ratio of black oil B. Fluid B has 38 mole % of C7+.

These changes, however, are not as important as for volatile oils. Uncertainties

in the experimental determination of this Mw can be about + 10%, and a 10%

change is translated into about a 5% change in the bubble point and in Rs, and

less than 2% in Bo.

Splitting the C7+ in black oil B did not introduce any significant changes in the

prediction of these properties.

The Wax Deposition Problem A major problem confronting the petroleum industry is the untimely deposition of

heavy organic compounds present in the oil. The production, transportation and

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processing of petroleum, bitumen, and other heavy-organic-containing

hydrocarbons could be significantly affected by deposition of solids

(asphalthenes, paraffin/wax , diamondoid, organo-metallics, etc.) in the reservoir

rock, oil well, pumps, storage vessels, and transportation pipelines, with

devastating economic consequences.

Paraffin/wax deposition around the wellbore causes plugging of the pore space

and permeability reduction. This leads to higher production costs, low production,

and premature abandonment of wells.

As the crude flows through a cold pipe or conduit (with a wall temperature below

the cloud point of the crude) crystals of wax form and grow on the inner wall. As

the wax thickness increases, the pressure drop across the pipe needs to be

increased to maintain a constant flow rate. As a result, the power requirement to

transport the crude will increase. The blockage problems in these crudes can be

efficiently controlled by insulation and heating of the pipe to a temperature above

their cloud point.

The kind and amount of depositions of heavy organics from petroleum fluids vary

depending on the hydrocarbons present in oil and the relative amounts of each

family of heavy organics.

One question of interest in the oil industry is �when� and �how much� heavy

organics will precipitate out under certain conditions. Here, EOS�s again help in

predicting the solubility of �waxes� in oil and the onset of solid deposition as a

function of temperature, pressure, and oil composition.

Vapor-Liquid-Wax Phase Equilibria At thermodynamic equilibrium between a vapor (gas), liquid (oil) and a solid

(wax) phase, the fugacity of component i in the liquid phase equals the fugacity

of component i in the solid phase, and the fugacity of component i in the gas

phase.

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s

il

ig

i fff ˆˆˆ == . (1)

As indicated in part two of this series, when a cubic equation of state is used for

the liquid phase and the gas phase, it is practical to express the fugacities in

terms of fugacity coefficients. Thus eq. (1) can be expressed as:

s

ilii

vii fPxPy ˆˆˆ == φφ . (2)

In this expression yi and xi are the gas and the liquid phase mole fraction of

component i. For an ideal solid phase mixture, the solid phase fugacity of

component i can be expressed in terms of the fugacity coefficient of component i

in the liquid phase as follows.

−

∆−= f

i

fil

isi

si T

TRT

HPxf 1expˆ φ , (3)

where six is the solid phase mole fraction of component i, and f

iH∆ is the

enthalpy of fusion of component i at the normal melting point Tf. The liquid

fugacity coefficient of pure i is found from the EOS at the temperature and

pressure of the system. Correlations or data may be used for the enthalpy of

fusion and the melting temperature. Here the correlations proposed by Wong6

were used.

Wax Deposition as a Function of Molecular Weight of the C7+

fraction Reservoir Fluid B, was used to predict different wax-forming conditions as a

function of temperature, pressure, and molecular weight of the C7+ fraction.

The range in molecular weights analyzed was from 237 to 345, still not an

extremely heavy oil. The composition of most paraffin solids usually consists of a

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mixture of hydrocarbons ranging from C18 to C70 with molecular weights up to

7007.

Figure 7 indicates the percent of wax deposited at a fixed temperature of 90oF

and different pressures. This shape, similar to the shape of viscosity, shows a

minimum weight percent of wax deposition around the bubble-point pressure.

The higher percentages below the bubble-point are because the solubility of

waxes decreases as gas is lost from solution.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Wax

Wei

ght %

0 1000 2000 3000 4000 5000 6000 7000 8000Pressure /psia

237278305345

Molecular Weight C7+ T = 90 F

Figure 7. Effect of the molecular weight of the C7

+ fraction in the precipitation of

waxes at constant temperature for black oil B. Fluid B has 38 mole % of C7+.

Figure 8 shows the weight percent deposition of wax as a function of

temperature for a fixed pressure. The circle in the curve for Mw = 305 indicates a

transition from liquid-solid equilibrium, to vapor-liquid-solid equilibrium. As

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expected, wax deposition increases as the molecular weight of the C7+ increases.

The deposition temperature also increases with the molecular weight of the C7+.

For example, at 100oF no wax will precipitate at 2000 psia for molecular weights

oft 237, and 278, while precipitates will form for higher molecular weights.

0

1

2

3

Wax

Wei

ght %

60 70 80 90 100 110 120Temperature / F

345305278237

Molecular Weight C7+

Pressure = 2000 psia

L-S

S-L-V

L-S

S-L-V

L-S

Figure 8. Effect of the molecular weight of the C7

+ fraction in the precipitation of

waxes at constant pressure for black oil B. Fluid B has 38 mole % of C7+.

The next article in the series will discuss another solid-vapor equilibrium problem

presented by gas hydrates.

References 1. McCain, W. D., Jr.:, �Chemical Composition Determines Behavior of

Reservoir Fluids� , Petroleum Engineer International (October 1993) 18-25.

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2. McCain, W. D., Jr.:, �Revised Gas-Oil Ratio Criteria Key Indicators of

Reservoir Fluid Type�, Petroleum Engineer International (April 1994) 57-60.

3. Osjord, E. H., RØnnigsen, H. P., and Tau, L.l �Distribution of Weight, Density,

and Molecular Weight in Crude Oil Derived from Computarized Capillary GC

Analysis,� Journal of High Res. Chrom. & Chrom. Comm., 8, (1985), pp-. 683-

690.

4. Pedersen K. S. , Fredenslund Aa., and Thomassen P.:, Properties of Oils and

Natural Gases. Vol. 5, Gulf Publishing Co., Houston, TX, (1989).

5. Pedersen K. S., Thomassen P., and Fredenslund Aa.,: �Thermodynamics of

Petroleum Mixtures Containing Heavy Hydrocarbons. 3. Efficient Flash

Calculation Procedures using the SRK Equation of State:, Ind. Eng. Chem.

Process Des. Dev., 24, (1985), pp-948-954.

6. Won, K. W.:, �Thermodynamics for Solid Solution � Liquid � Vapor Equilibria:

Wax Phase Formation from Heavy Hydrocarbon Mixtures. Fluid Phase

Equilibria, (1986) 30, pp. 265-279.

Additional Course References

• McCain, W. D. Jr. The Properties of Petroleum Fluids, 2nd Edition � Penn Well Books (1990).

• McCain, W. D. Jr. �Calculation of Fluid Properties from Black Oil PVT Reports Revisited� SPE 36017 (1996).

• Barrufet, M.A., Habiballah, W. A., Liu K., and Startzman, R., �A Warning on the Use of Composition Independent K-Value Correlations to Solve Reservoir Engineering Problems.� J. of Petroleum Science and Engineering 14, (1995), pp. 25-34.

• Kartoadmodjo, T. and Schmidt, Z., �Large Data Bank Improves Crude Physical Property Correlations�, Oil and Gas Journal (July 1994), 51-55.

• Walsh P. M., �New Improved Equation Solves for Volatile, Condensate Reserves�. Oil and Gas Journal, Aug. 22, 1994, pp. 72-76.

• Walsh P. M., �New Improved Equation Solves for Volatile, Condensate Reserves. Oil and Gas journal, Aug. 22, 1994, pp. 72-76

Reference Material – Fluid Series – M.A. Barrufet 16/16

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• Havlena, D., and Odeh A. S., �The Material Balance as an Equation for a Straight Line�, JPT, August 1963, pp. 896-900.

• Spivak, A., and Dixon, T. N. �Simulation of Gas Condensate Reservoirs�, SPE 4271, 1973, SPE Symposium of Reservoir Simulation, Houston, Jan. 10-12, 1973.

• McCain W. D., �The Properties of Petroleum Fluids�. PennWell Books. (1990).

• �Thermodynamics of Hydrocarbon Reservoirs� Abbas Firoozabadi. McGraw Hill 1. (1999).

• "The Collected Works of J. Willard Gibbs," Vol. I- Thermodynamics, Yale University Press, New Haven, 1957.

• Kingston, P.E., and Niko, H.: "Development Planning of the Brent Field," JPT (Oct. 1975) 1190-98.

• Creek, J.L., and Schrader, M.L.: "East Painter Reservoir: An Example of a Compositional Gradient from a Gravitational Field," SPE 14411, paper presented at the 60e Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Las Vegas, Nevada, Sept. 22-25, 1985.

• Tribune, F.A., and Zadora, G.I.: "Experimental Study of the Effect of a Porous Media on Phase Changes in Gas Condensate Systems," Neft'i Gaz (1968) Vol. 81, No. 8,37-41.

• Tint, R., and Raynal, M.: "Are Test-Cell Saturation Pressures Accurate Enough?" The Oil and Gas Journal (Dec. 1966) 128-139.

• Sigmund, P.M., e a.: "Retrograde Condensation in Porous Media," SPEJ (April 1973) 93-104.

• Stegemeier, G.L., e a.," Interfacial Tension of the Methane-Normal Decane System," SPEJ (Sept. 1962) 257-260.

7.