Prediction of thermodynamic properties of oil and gas condensate

Jul 19, 1990 - Prediction of Thermodynamic Properties of Oil and Gas Condensate. Mixtures. Kim Aasberg-Petersen and Erling Stenby*. Instituí for Kemi...
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I n d . Eng. Chem. Res. 1991, 30, 248-254

Critical Temperature of Water. J. Phys. Chem. 1969, 73,81-90. Zemaitis, J. F., Jr.; Clark, D. M.; Mal,M.; Scrivner, N. C. Handbook of Aqueous Electrolyte Thermodynamics; DIPP, Sponsored by AIChE: New York, 1986. Zen, E.-An. Solubility Measurements in the System CaSO4-NaC1-

H20 a t 35O, 50°,and 7OoC and One Atmosphere Pressure. J. Petrol. 1965, 6, 124-164. Received for reuiew February 12, 1990 Accepted July 19, 1990

Prediction of Thermodynamic Properties of Oil and Gas Condensate Mixtures Kim Aasberg-Petersen and Erling Stenby* Institut for Kemiteknik, Building 229, Danmarks Tekniske H@jskole,2800 Lyngby, Denmark

This paper presents a new method for the prediction of phase behavior in reservoir fluids using a four-parameter cubic equation of state. T h e parameters in the employed C7+-characterization procedure are calculated directly from measured molecular weight and specific gravity data for the hydrocarbon fractions. I t is shown that PVT properties (e.g., liquid dropout) and phase equilibria can be accurately predicted even in the near-critical region by using the new method. Saturation points for a number of fluids containing significant amounts of non-hydrocarbons (COPor N,) are calculated. The predicted saturation points agree well with experimental data. Finally, it is shown that the new model is able to accurately predict liquid volumes of mixtures including those with a considerable content of N2.

Introduction Accurate determination of phase behavior is essential in reservoir simulation and in design of transport and separator equipment. As the need for enhanced oil recovery methods such as gas injection is increasing, the demand for accurate phase behavior predictions is growing. The phase behavior model must take into account not only the effects caused by the complicated composition of the reservoir fluids but also the effects caused by the presence of injection gases such as COPor N z in significant amounts. Much effort has been given to develop models suitable for the prediction of phase behavior in oil and gas condensate mixtures. However, most models in the literature are not preaictive, as experimental phase equilibrium data are needed to tune one or more parameters in the model. Recently, Pedersen et al. (1988) developed a characterization procedure for the SRK equation of state coupled with the volume correction term of Peneloux et al. (1982). This procedure does not need experimental data and generally gives good predictions of saturation points and vapor-liquid equilibria. However, the model frequently calculates a too large liquid precipitation for gas condensates when simulating constant composition expansion experiments. In addition, predicted liquid density values are sometimes inaccurate. It is the purpose of this paper to describe a new model that preserves the good qualities of the model of Pedersen et al. with respect to phase equilibrium predictions and at the same time improves liquid dropout and liquid density calculations. The model should also be able to accurately predict the phase behavior of fluids with a considerable content of COPor N2. This is of special importance in the simulation of miscible or immiscible gas injection processes. The Model Models for the prediction of the phase behavior of reservoir fluids are extensively used in compositional reservoir simulation studies. It seems natural to choose a cubic equation of state (EOS) as the thermodynamic basis for the model to be developed, since cubic EOS's are simple and fast models and easy to implement in any reservoir

simulation program. Jensen (1987) found the ALS EOS (Adachi et al., 1983) to be the most accurate for prediction of the phase behavior of well-defined hydrocarbon mixtures with and without a considerable content of C 0 2 or N z . The ALS EOS is given below:

For pure components, the four parameters are calculated as follows:

a ( T ) = (1 + m(1 - ( T / T c ) 1 / 2 ) ) 2 @k

=

RbkRTc 7

k = 1, 2, 3

(3) (4)

Expressions for the calculation of Q,, Qbi, and m are given in the Appendix. The expressions for Qb2 and Qb3 are derived such that the critical point criteria are satisfied. The ALS EOS seems to be well suited for calculation of the phase equilibria of reservoir fluids but often proves to give inaccurate predictions of the densities of hydrocarbon mixtures (Aasberg-Petersen, 1989). It was therefore decided to incorporate the volume translation principle of Peneloux et al. (1982) into the ALS equation, resulting in the following new equation of state: (5)

The b parameters are calculated as follows: (6) bl = @1 - C bz = 62 - C (7) (8) b3 = 03 + C For each component, the Peneloux-type parameter, C, is in this work determined such that the equation of state gives the correct value of the liquid density at atmospheric pressure and at a temperature where the component is a liquid. The C parameters of the C7+fractions are deter-

0888-5885/91/2630-0248$02.50/00 1991 American Chemical Society

Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 249 Table 11. Optimum Values of dl-dlz with 5% Confidence Limits coeff value dl 190.8 f 37

Table I. Binary Interaction Coefficients COZ 0.000 -0.017 0.092 0.130 0.130 0.138 0.128 0.125 0.127 0.098 0.095

coz N2 C1 c2

c3

i-C, c4

i-C5 c5 c6

Cl+

N2 -0.017 0.000 0.033 0.051 0.081 0.102 0.062 0.093 0.086 0.140 0.070

mined by matching the equation of state to measured specific gravity data at 288.15 K and 1 atm. For mixtures, the following classical mixing rules are employed: N N

u = Ez(uiuj)14ixj(l- k,j) i l

(9)

Table 111. Composition of Mixture 1" component N2 COP

c1

N

bk = CXibk,i

87.70 f 3.1 0.6387 f 0.087 -5247.7 f 2830 -0.5836 f 0.097 2.3211 f 0.23 282.2 f 24 -4484.9 f 2100 2.829 X f 6.4 X 4.248 x 10-3 f 4.7 x 10-4 1.156 X f 3.0 X -4.069 X 10" f 7.5 X lo-''

k = 1, 2, 3

( 10)

I

The interaction coefficients ( k i j )are assumed to be zero between all hydrocarbon components and non-zero between hydrocarbons and non-hydrocarbons and between pairs of non-hydrocarbons. The optimal values of the non-zero interaction coefficients were obtained by minimizing the difference between calculated values of liquidand vapor-phase fugacities using the binary experimental data from Knapp et al. (1982). The resulting values are given in Table I. The molar composition of the plus fraction of a reservoir fluid is not known. In this work, the procedure suggested by Pedersen et al. (1985) to estimate the composition is used: In zi = A l + A,CNi (11) where zi and CNi are respectively the mole fraction and the carbon number of component (or fraction) i. A, and A2 are constants specific to the actual mixture determined from the measured weight fraction and molecular weight of the total plus fraction. All components with a mole fraction less than 10" or a carbon number greater than 80 are neglected. The molecular weight of a given carbon number fraction is determined from the equation MWi = 14CNi - 4 (12) The densities of the subfractions of the plus fraction at atmospheric conditions are calculated from SGi = B1+ B, In CNi (13) where B1and B2 are determined from the measured densities of the total plus fraction and of the last defined (true boiling point) fraction. Further details of this procedure are given by Pedersen et al. (1985, 1988). For a given plus fraction, the extrapolation procedure described by eqs 11-13 ensures that the distributions of mole fractions, molecular weights, and densities are consistent with the measured data for the plus fraction. The number of components and C7+fractions in the final distribution may be more than 80. This number can be reduced as described by Pedersen et al. (1985). The individual hydrocarbon fractions are lumped into a number of groups where the weight fractions of all groups are approximately equal. In this work, 20 hydrocarbon groups are used to represent the hydrocarbon part of a reservoir fluid.

C2

c3 i-C4 n-C4 i-C5 n-C5 c6 c7

C8 C9

Go+

mol 7%

MW

density (g/cm3) at 15 OC, 1 atm

0.71 8.64 70.85 8.53 4.95 0.75 1.26 0.41 0.40 0.46 0.61 0.71 0.39 1.33

91 105 120 222

0.820 0.777 0.803 0.853

OSource: Pedersen et al. (1988).

T,, P,, and w , which are necessary input parameters for equation of state calculations, are not known for the C7+ fractions. In this work, these parameters are calculated by using the following functions: T, = dlSG + d2 In MW + d3MW + d,/MW (14) In P, = d5 + d6SG + d7/MW o = d9

+ d8/MW2

+ dloMW + dllSG + dI2MW2

(15) (16)

The functional form of the equations for the calculation of T,and P, is the same as those used by Pedersen et al. (1988). The optimum values of the 12 constants in eqs 14-16 have been determined. The parameter estimation was based on the following experimental data for North Sea fluids: (a) dew points and liquid volumes in the two-phase region relative to dew point volumes for seven gas condensates including mixture 1 (the compositions and sources of experimental data of all numbered mixtures are given in Tables 111-IX); (b) dew and bubble points and liquid volumes in the two-phase region relative to saturation point volumes for two near critical fluids including mixture 2; (c) the bubble point pressure a t reservoir temperature for eight oil mixtures. The optimum values of the 12 constants are given in Table I1 along with 5% confidence limits. When using the values in Table I1 with eqs 14 and 15, the value of T,is obtained in K and P, in atm. Figures 1-3 show typical plots of T,, P,, and w versus molecular weight.

Results Calculated and experimental results for a number of different reservoir fluids are shown in Figures 4-13 and in Tables X and XI. The relative average deviation of the 22 dew and bubble points which were included in the parameter estimation was 4.58%. The correspondingvalue

250 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 Table VIII. Composition of Mixture C

Table IV. Composition of Mixture 2' component

N2 COP

c,

c2 c3

i-C4 n-C4 i-C5 n-CS c6

c7 C8

C9

GO+

mol % 0.46 3.36 62.23 8.88 5.30 0.91 2.07 0.73 0.85 1.04 1.84 1.73 1.39 9.21

MW

density (g/cm3) a t 15 "C, 1 atm

component N2

COP Cl CZ c3

1-c4 c4

1-c5 c5 c6

95 107 121 241

0.7325 0.7561 0.7722 0.8604

Cl+

'Source:

N2

co2 Ci CP

c,

i-C, n-C4 i-Cs n-C5 C6 c7+

density (g/cm3) a t 15 "C, 1 atm

177.1

0.8002

Donohue and Buchanan (1981).

component Cl

Table V. Composition of Mixture 3' mol % 0.23 2.12 73.15 9.39 4.86 1.02 1.78 0.60 0.49 0.93 5.43

MW

Table IX. Composition of Mixture 7'

'Source: Pedersen e t al. (1988).

component

mol % 0.37 0.57 59.39 13.78 7.58 0.79 3.28 0.84 1.31 1.80 10.29

MW

density (g/cm3) a t 15 OC, 1 atm

mol % 47.47 6.51 4.89 6.61 6.87 7.59 20.06

c2 c3 c4

c5 c6

Cl+

MW

density (g/cm3) a t 15 "C, 1 atm

181.0

0.8259

'source: Wiespape et al. (1977).

162

0.7957

"Source: Vogel and Yarborough (1980).

Table VI. Composition of Mixture 4' component C,

c,

c3

i-C, n-C4 i-C5 n-C5 c6

c7

c,

C9

Go+

mol % 52.00 3.81 2.37 0.76 0.96 0.69 0.51 2.06 2.63 2.34 2.35 29.52

MW

density (g/cm3) a t 15 "C, 1 atm

500

0

99 110 121 221

0.749 0.758 0.779 0.852

1

1

1

1

J

200

400

800

800

1000 MU lg/Ino 111

Figure 1. Critical temperature versus moIecular weight.

'Source: Hoffmann et al. (1953),

Table VII. Composition of Mixture 5' MW mol 90 91.35 Cl 4.03 c2 c3 1.53 i-C, 0.39 n-C4 0.43 i-C6 0.15 n-C5 0.19 C6 0.39 Cl 0.361 100 c, 0.285 114 C9 0.222 128 GO+ 0.672 179 "Source: Hoffmann et al. (1953). component

density (g/cm3) a t 15 "C, 1 atm

0.745 0.753 0.773 0.814

when using the three-parameter Peneloux-SRK (P-SRK) equation of state of Pedersen et al. (1988) is 4.94%. Figure 4 shows the calculated and experimental liquid dropout curves at T = 392.1 K for mixture 1. Also shown

0

200

400

800

800

1000 MN 11/1101*1

Figure 2. Critical pressure versus molecular weight.

is the liquid dropout curve calculated by the P-SRK model. As can be seen, the new model is superior to the P-SRK method at all pressures. This is, to a certain extent, due to the difference in the calculated saturation point pressures.

Ind. Eng. Chem. Res., Vol. 30,No. 1, 1991 251 Table X. Experimental (PE) and Predicted (Pp)Saturation Pressures for a Number of Fluids" mixture LOC type T,K %COz % Nz PE,MPa A syn 322 40 0 12.14 322 60 0 11.93 B SYn GC 0.2 2.0 30.7 381 us. C GC 30 1.4 55.8b 381 D us. 42.8b GC 10 1.9 381 E us. 29.2 GC 1.7 20 401 F North Sea 28.1 0 2.4 356 GC Iran G 0.9 34.3 351 0.3 GC China H 0.4 30.2 0.6 GC 363 6 us. 27.5 oil 0.8 0.3 366 I North Sea 32.8 444 3.6 0.3 oil J us. 0 32.0 oil 380 K 0 us. 0.2 21.26 oil 20 397 L us.

Pp,MPa 11.12 11.41 33.6 60.4 44.4 30.5 29.8 34.3 29.5 25.6 31.9 32.3 22.3

"Sources of experimental data: mixture A-B, Turek e t al. (1984). Mixture C-E, Vogel and Yarborough (1980). Mixture F, Thomassen (1989). Mixture G, Firoozabadi e t al. (1978). Mixture H, Guo (1988). Mixture I, Pedersen e t al. (1989). Mixture J-K, Firoozabadi and Aziz (1986). Mixture L, Simon et al. (1978). Mixture 6,see Table VIII. bDetermined from graphs.

Table XI. Measured and Predicted Liquid- and Vapor-Phase Compositions of Mixture 7 at T = 394 K and P = 12.4 MPa" vaDor Dhase liquid phase exptl SRK new component exptl SRK new c1 0.2885 0.3138 0.3001 0.7771 0.7812 0.7688 CZ 0.0570 0.0598 0.0581 0.0737 0.0753 0.0769 0.0532 0.0529 0.0523 0.0446 0.0413 0.0433 C3 n-C4 0.0833 0.0803 0.0804 0.0385 0.0390 0.0419 n-C6 0.0919 0.0900 0.0912 0.0283 0.0281 0.0308 c6 0.1087 0.1045 0.1068 0.0211 0.0214 0.0238 C,+ 0.3174 0.2987 0.3111 0.0167 0.0138 0.0145

-

-

100-

E

B

eo

I

I

I

-

0

"Total vapor mole fraction: experimental 0.38,SRK 0.344,new, 0.373. 0

10

20

30

50

40

P 1HP.I

Figure 5. Liquid dropout curves for mixture 2 at T = 424.0 K. Experimental points. (-) P-SRK model. (- - -) New Model.

i

0 O

I

I

I

I

200

400

000

BOO

I

I

I

I

10

20

30

40

(0)

I

1000 MU

I#/mol.l

Figure 3. Acentric factor versus molecular weight. 0

50 P IMP*I

Figure 6. Liquid dropout curves for mixture 2 at T = 436.0 K. Experimental points. (-) P-SRK model. (- - -) New model.

0 0

I

I

I

10

20

30

40

IO P Inpal

Figure 4. Liquid dropout curves for mixture 1 at T = 392.1 K. (0) Experimental points. (--) P-SRK model. (- - -) New model.

(0)

In some North Sea reservoirs, the fluids exhibit near critical behavior. The PVT properties of such fluids are very difficult to predict because small variations in pressure may result in large changes of the system properties. An example of such a fluid is mixture 2. In Figures 5 and 6, calculated and experimental liquid dropout curves for mixture 2 are shown a t T = 422 and 434 K, respectively. The figures show that the new model is able to calculate liquid dropout curves in the near vicinity and on both sides of the critical temperature. The critical point of the mixture has been experimentally determined to be T,= 426 K and P, = 38.8 MPa. The liquid dropout curves are somewhat better calculated when using the new model

252 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991

-

I

I5

I

I

I

I

I

I

I

I

.a

0

10

5

21

20

18

0

I

I

I

I

I

I

I

10

20

30

40

50

BO

70

P 1MPd

Figure 7. Predicted and experimental liquid mole fractions for Experimental points. (-) P-SRK model. (-- -) New mixture 4. (0) model.

-

,

I5

I

I

I

I

I

I

I

Figure 10. Experimental and predicted liquid volumes for 70% mixture 3 and 30% N2 at T = 381 K. (0) Experimental values. (- - -) New model. ,

d

BO

P IMP.1

15

1

I

I

I

I

*

I

I

"

-

10

-

-

0

0

-- -- --

0

0

I

I

I

10

20

30

I

I

I

I

40

50

60

70

- \

BO

--.

0

I

0

-.._

a

,,n-

0

-

_ - - - -- _ _ -_ _

.-;___--.*be

5 -

I

I

1

1

I

I

P MP.1

Figure 8. Experimental and predicted relative liquid volumes for Experimental values. (- - -1 New model. mixture 3 a t T = 381 K. (0)

-

,

15

I

I

I

I

I

I

I

I

J

m

*

I

I

I

I

5

10

15

20

10

5

0 0

10

20

BO

40

50

BO

EO

70

P 1HP.I

Figure 9. Experimental and predicted liquid volumes for 90% mixture 3 and 10% N2a t T = 381 K. (0) Experimental values. (- -) New model.

-

than when using the P-SRK method. In this case, the improvement is not due to the calculated location of the saturation points, since the calculated values when using the two models are almost identical. The results that have been described up to now are all for mixtures which were used in estimating the parameters in eqs 14-16. In order to test the predictive capabilities of the model, various properties were calculated for fluids not included in the parameter estimation. Table X shows predicted and experimental saturation points for a number

0

25 P lMP.1

Figure 12. Predicted and experimental liquid densities for mixture 5. (0) Experimental points. (-) P-SRK model. (- -) New model.

-

of fluids, including some with a considerable content of COz or N2. No tuning has been performed, and the only data used to calculate the saturation points given in Table X were the composition of the fluid and the measured molecular weights and densities of the C7+fraction($. Figure 7 shows experimental and predicted liquid mole fractions of mixture 4 (Texas oil). The predicted results are in good agreement with experimental data, and the relative mean deviation is 1.3% when using the new model

Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 253 and 2.5% when using the SRK-based method. Table XI shows experimental and predicted gas- and liquid-phase compositions for mixture 7 (US.fluid). The predictions are generally good and slightly better than when using the P-SRK EOS. Experimental and predicted relative liquid volumes in the two-phase region are shown in Figures 8-11 for mixture 3 mixed with various concentrations of N2from 0 to 50 mol 90.Although the calculated liquid volumes are slightly too high, the predicted results seem to be in good agreement with the experimental data. Figure 12 shows predicted and experimental liquid densities for mixture 5 (Texas gas condensate). Agreement with experiment is good, and the new model improves liquid density predictions considerably when compared with the P-SRK model. Experimental and predicted liquid dropout curves for mixture 6 are given in Figure 13. The predicted results are in good agreement with experimental data although the maximum retrograde condensation is calculated somewhat too high.

Discussion Accurate predictions of phase equilibria and related properties for oil and gas condensate mixtures have been the main objective for developing the new model described in this paper. No attempt has been made to calculate physical properties of the individual C7+components. The functions for the calculation of T,, P,, and w (eqs 14-16) should therefore not be used for quantitative conclusions regarding the phase behavior of oil fractions. The qualitative behavior of T, and P, versus molecular weight shown in Figures 1 and 2 seems reasonable. No physical explanation can be given for the development of w versus molecular weight for the high molecular weights shown in Figure 3. However, other authors (Pedersen et al., 1988; Metcalfe and Raby, 1986) have also observed small values of the acentric factor for heavy fractions, when the acentric factor is used as a correlation parameter. One of the most difficult tasks for any phase behavior model is the prediction of liquid dropout curves. This is because precise liquid dropout calculations require that the model is able to accurately determine both phase compositions and phase densities simultaneously. The new model presented in this paper has improved liquid density determinations considerably without loss of accuracy in the calculation of phase compositions. This results in the very fine liquid dropout curves shown in Figures 4-6. Special attention should be given to Figure 13. This good prediction of liquid dropout for the near critical mixture 6 has, as all other calculations in this work, been done without tuning of any kind. In principle, perfect agreement with an experimental liquid dropout curve can be achieved even though both phase compositions and phase densities are wrong. This is the case when the inaccuracies of the calculated densities and phase compositions cancel. This is not the case when using the new model. As shown in Figure 12, the predicted liquid densities are in good agreement with the experimental values for mixture 5. The mean deviation of the predicted liquid mole fractions of mixture 4 shown in Figure 7 using the new model is only half when compared with the P-SRK EOS. It should also be noted that the predicted vapor fraction of mixture 7 (see Table XI) is considerably better when using the new model than when using the P-SRK method. It can therefore be concluded that the new model has significantly improved the accuracy of predictions of vapor or liquid mole fractions.

There is no great difference between the two models in the predicted phase compositions of mixture 7 shown in Table XI. The liquid-phase composition is predicted with greater accuracy by using the new model, while the gasphase composition is predicted slightly better by using the P-SRK EOS. Aasberg-Petersen (1989) has made a more thorough comparison between the two models with experimental data for a number of fluids. He concludes that the two models are of comparable quality regarding the prediction of phase compositions. The calculated critical temperature of mixture 2 is 426 K. When comparing this with the experimental value of 424 K, it could be concluded that the new model can be used to predict critical points of reservoir mixtures. This is not generally the case. The molecular weight of the plus fraction is usually not determined with an accuracy greater than 10% (Pedersen et al., 1989). Small variations in this molecular weight can, however, result in a considerable change in the value of the calculated critical temperature. The saturation points given in Table X for a number of different fluids are all predicted with reasonable accuracy with the possible exception of mixture C. Mixture C is the only fluid that needs an adjustment of the molecular weight of the plus fraction of more than 10% to obtain agreement with the experimentally determined saturation point. Generally the saturation points for the mixtures with a large content of non-hydrocarbons (mixtures A, B, D-F, and L) seem to be predicted with the same accuracy as saturation points for mixtures that almost only consist of hydrocarbons. The predicted liquid volumes for the mixtures with a considerable content of N2 (Figures 9-11) should also be noted. Considering the large concentrations of N2 and that no tuning has been performed, the predicted values are in very good agreement with the experimental data. In spite of the fact that the parameter estimation was performed with experimental data for fluids from the North Sea only, the accuracy of the predictions is not influenced by the geographical location of the reservoir. Even though the model presented in this paper gives good predictions of PVT properties, tuning may in some cases be necessary to obtain the desired accuracy. The parameter that is best suited for tuning in the model is the molecular weight of the plus fraction. Maintaining constant weight fractions, an adjustment of usually only a few percent is necessary to obtain agreement with a measured saturation point. This adjustment is physically justified because, as mentioned above, the accuracy of the experimental determination of the molecular weight of the plus fraction is not greater than 10% (Pedersen et al., 1989).

Conclusions This paper presents a new model for the calculation of the phase behavior of oil and gas condensate mixtures. The thermodynamic framework is a four-parameter cubic equation of state. The necessary parameters in the employed C7+-characterizationprocedure are calculated with only measured molecular weights and specific gravities. The model has been used for prediction of a number of different PVT properties for a wide variety of reservoir fluids ranging from light gas condensates and near critical mixtures to heavy oils. The model is able to predict simultaneously phase compositions and phase densities. Phase mole fractions and liquid densities are predicted with greater accuracy with the new model than with the P-SRK equation of state. This results in very accurate liquid dropout predictions even in the near critical region. The liquid dropout curves are predicted with the same or greater

254 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991

1

Y

.,I

f

The value of m as function of w was obtained by fitting to pure component vapor pressures:

m = 0.4070 + 1.3787~- 0 . 2 9 3 3 ~ ~ (A3) Using the experimentally observed critical point criteria ( P / 6 V ) , = (SZP/SV2), = 0 Jensen (1987) derived the following expressions for !4,2 and Ob3:

c

QO

+ !&,I) - 3na'/3 + (4na- 3R2,2/3)'/2] (A4) fib3 = 0.5[-2(1 + !&I) + 3na'l3 + (4Ra - 3R,2/3)1/2] (A5)

f&,2

0 0

I

I

10

20

I 30

40

Registry No. COP,124-38-9;N,7727-37-9. 50

P IMPS1

Figure 13. Experimental (-) curves for mixture 6.

= 0.5[2(1

and predicted (- - -1 liquid dropout

accuracy than when using the P-SRK equation of state. The new model has also been applied for the prediction of phase behavior for a number of mixtures with a significant content of COz or Nz. Predicted saturation points agree well with experimental data, and the new model is able to accurately predict liquid volumes of mixtures with a considerable content of N,. Acknowledgment We thank Professor Aa. Fredenslund of the Department of Chemical Engineering a t the Technical University of Denmark for his many valuable contributions to this work. We are grateful to the Norwegian Oil Company Norsk Hydro for financial support of this project. Nomenclature A,, A2: constants in eq 11 a ( T ) : EOS parameter (eq 2) B,, B2: constants in eq 12 6;: EOS parameters (eqs 6-8) C: molar volume correction parameter CNi: hydrocarbon fraction number di: constants in eqs 14-16 kij: binary interaction parameter between components i and j

m: EOS parameter (eq A3) MW: molecular weight, g/mol N: number of components P: pressure P,: critical pressure R: universal gas constant SG: specific gravity at T = 288.15 K and P = 0.101 325 MPa T: temperature T,: critical temperature u: molar volume x i , zi: mole fraction of component i Greek Symbols

EOS parameter (eq 3) EOS parameters (eq 4) 0: EOS parameters (eqs A l , A2, A4, and A5) W: acentric factor a: /3:

Literature Cited AasbergPetersen, K. Bulkphase Properties and Phase Equilibria for Miscible and Immiscible Oil Displacement Processes. Ph.D. Thesis Progress Report, Department of Chemical Engineering, The Technical University of Denmark, Denmark, 1989. Adachi, Y.; Lu, B. C.-Y.; Sugie, H. A Four-Parameter Equation of State. Fluid Phase Equilib. 1983, 11, 29. Donohue, C. W.; Buchanan, R. D. Economic Evaluation of Cycling Gas-Condensate Reservoirs With Nitrogen. J. Pet. Technol. 1981, 263.

Firoozabadi, A,; Aziz, K. Analysis and Correlation of Nitrogen and Lean-gas Miscibility Pressure. SPE Reservoir Eng. 1986, 575. Firoozabadi, A.; Hekim, Y. Katz, D. L. Reservoir Depletion Calculations for Gas Condensates Using Extended Analysis in The Peng-Robinson Equation of State. Can. J. Chem. Eng. 1978,56, 610.

Guo, T.-M. Properties of Selected Chinese Gas Condensates and Crude Oils (Experimental Data Collection). Beijing Graduate School of Petroleum University, China, 1988. Hoffmann, A. E.; Crump, J. S.; Hocott, C. R. Equilibrium Constants for a Gas-Condensate System. Pet. Trans. AIME 1953, 198, 1. Jensen, B. H. Densities, Viscosities and Phase Equilibria in Enhanced Oil Recovery. Ph.D. Thesis, Department of Chemical Engineering, The Technical University of Denmark, Denmark, 1987.

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Appendix The following expressions for calculation of R, and were obtained by Adachi et al. (1983) by fitting to pure component properties along the critical isotherm:

+ 0.04024~+ 0 . 0 1 1 1 1 ~-~0 . 0 0 5 7 6 ~ ~( A l ) Rbl = 0.08974 - 0.03452~+ 0 . 0 0 3 3 ~ ~ (A2)

R, = 0.44869

Vogel, J. L.; Yarborough, L. The Effect of Nitrogen on the Phase Behaviour and Phvsical Prooerties of Reservoir Fluids. SPE Daper 8815, 1980. Wiesoaoe. C. F.. Kennedv. H. T.: Crawford. P. B. A Crude OilNatural Gas System Vapor-Liquid Equilibrium Ratios. J . Chem. Eng. Data 1977,22, 260.

Receiued for reoiew February 15, 1990 Accepted July 5, 1990