Prediction of Phase Equilibria and Volumetric Behavior of Fluids with High Concentration of Hydrogen Sulfide

Prediction of Phase Equilibria and Volumetric Behavior of Fluids with High Concentration of Hydrogen Sulfide — A systematic study of the properties of hydrogen sulfide and its mixtures with hydrocarbons is presented, using the modified and volume translated (t-mPR) as well as the Jhaveri and Youngren volume translated (J-PR) Peng-Robinson equation of state (EoS). Hydrogen sulfide vapor pressure and saturated liquid volume predictions are presented with both EoS. Volumetric predictions with the J-PR EoS are improved when a shift parameter for H2S is incorporated. A simple generalized correlation of the interaction parameters of H2S/n-alkane binary mixtures as a function of the hydrocarbon acentric factor is proposed. The correlation can also be applied to i-alkanes and provides good extrapolation capability to larger alkanes. Interaction parameters for H2S with other hydrocarbons are also given. Application to synthetic multicomponent mixtures and to reservoir oils with high content of H2S gives very satisfactory results.


INTRODUCTION
Processing of natural fluids with significant amount of hydrogen sulfide is continuously increasing since energy shortage problems impose an integrated and more effective use of energy resources.Some of the following practical problems indicate this upcoming interest: -the processing of sour natural gas, particularly at low temperatures, to enhance the recovery of ethane and propane; -the sweetening of the liquefied petroleum gases (LPG) often contaminated with hydrogen sulfide and/or carbon dioxide (acid gas components must be removed from LPG before any other treatment); -the recent (renewed) interest in developing oil and gas reserves that have been bypassed in earlier times because of their carbon dioxide and hydrogen sulfide content; -the number of rich H 2 S sour natural gas or oil fields that have been discovered around the world (North China, Canada, Greece, Italy, etc.) and some of them are already under production.
In addition, Swain (1993) underlines the problem of the USA refiners which already face the declining crude oil quality as they will have to process feedstocks that become heavier and sourer than in the past.
The design of any of the above processes is governed by the presence of hydrogen sulfide, which becomes one of the major components of these fluids.It is, therefore, necessary to pay particular attention to the influence of H 2 S on mixture behavior.Furthermore, literature data on hydrogen sulfide/ hydrocarbon systems are rather limited, since up-to-date research is mainly focused on other non-hydrocarbon/ hydrocarbon mixtures such as carbon dioxide or nitrogen.
The purpose of this work is the thorough study of the properties of H 2 S and its mixtures with hydrocarbons aiming to provide all the relevant parameters for the existing thermodynamic models in order to enhance their capability in the prediction of vapor-liquid equilibria (VLE) and thermophysical properties with emphasis on high-H 2 S-content hydrocarbon mixtures.
The methodology followed includes: -prediction of the thermodynamic properties of pure H 2 S; -use of all the binary VLE data in evaluating the interaction parameters for hydrogen sulfide/hydrocarbon mixtures and in developing generalized correlations for them; -use of conventional thermodynamic models, cubic equation of state (EoS), to predict the phase behavior and the volumetric properties of synthetic mixtures and natural fluids with high content of hydrogen sulfide.

PREDICTION OF VAPOR PRESSURES AND SATURATED LIQUID VOLUMES OF HYDROGEN SULFIDE
Experimental vapor pressures (P s ) and saturated liquid volumes (V l s ) were available from Clarke and Glew (1970).Similar information was available from the correlation of experimental data of Daubert andDanner (1985, 1989).The comparison of the experimental data with those of the correlation of Daubert and Danner showed a deviation of 2.1 and 0.4% in P s and V l s respectively, values within the uncertainty range of Daubert and Danner equations.The experimental data of Clarke and Glew were adopted for all the following calculations.
The original Peng-Robinson (PR) (Peng and Robinson, 1976), the modified and volume translated PR (t-mPR) of Magoulas and Tassios (1990) and the volume translated PR EoS (J-PR) of Jhaveri and Youngren (1984) were utilized for the prediction of the vapor pressures and saturated liquid volumes of hydrogen sulfide.The t-mPR and J-PR equations used are presented in Appendix.
The results of the prediction of the vapor pressures are shown in Figure 1 and Table 1.There is a slight overall advantage of the t-mPR, with an average deviation of 3.4%, over the PR, with 5.1%.We must note the better performance of the t-mPR at low temperatures.
The J-PR EoS was selected because of its wide application in petroleum industry.The volumetric predictive capability of the J-PR EoS is based on the incorporation of the compound shift parameter (s) that represents the saturated volume correction at T r = 0.7 in the b term of the PR EoS.Authors presented numerical values of the shift parameter for  For H 2 S, the corresponding shift parameter was not available and its evaluation was, therefore, considered worthwhile.The method followed was similar to that suggested by Jhaveri and Youngren in their relevant study (Eqs.(1) to (3)): (1) where: The obtained value was s = -0.10356.The negative value of the shift parameter indicates the underprediction of the liquid density from the EoS.Table 1 and Figure 2 present the performance of all the EoS in the prediction of the saturated liquid volumes.The volumetric deficiency of the PR equation is obvious when compared with the translated ones; it gives an average absolute deviation of 6.5% while the other ones have equivalent performance with an average deviation of 0.7%.The difference between the temperature-dependent and temperature-independent types of the translation factor t is demonstrated through the t-mPR and the J-PR EoS for a reduced temperature, T r > 0.8.As expected, a higher deviation is observed for the J-PR.Although this statement has no influence on the following applications, since our volumetric data are not in this temperature range, it must be taken into account for general practical applications.

INTERACTION PARAMETERS OF H S/HYDROCARBON BINARY SYSTEMS
There are literature references to several attempts for the prediction of interaction parameters of H 2 S/hydrocarbon mixtures: - Moysan et al. (1986) presented the first generalized expression for k ij as a function of the acentric factor.They propose a linear function for paraffins and naphthenes and a second-order polynomial for aromatics.Since their database is limited to paraffins up to a carbon number (CN) of ten and four aromatic binary systems, the extrapolation capability of their correlation is questionable; - Valderrama et al. (1987) presented another generalized expression for the k ij of H 2 S/n-alkanes as a function of the acentric factor (second-order polynomial) and the reduced temperature of the hydrocarbon component.Their correlation is applicable to systems with hydrocarbons with CN > 5, while for the lighter ones regressed values are suggested.Their limited database (up to nC 9 ) does not justify the complexity of the correlation and does not provide any extrapolation capability; - Nishiumi et al. (1988), using the same as the above limited database, presented a correlation in terms of the ratio of critical molar volumes; - Carroll and Mather (1995) presented a more comprehensive study for the k ij of H 2 S/n-alkanes using an extended database up to nC 20 plus i-butane, i-pentane and neopentane.They propose two simple correlations: one in terms of the carbon number of the paraffin and the other as a quadratic function of the normal boiling point of the paraffin.
Table 2 includes all the experimental VLE data available in the literature for H 2 S/hydrocarbon binary systems.It is notable that all the data for hydrocarbons with a carbon number greater than ten (CN > 10) are very recent (after 1992), indicating the recent interest in systems containing H 2 S. The system with the heaviest hydrocarbon is that of nC 20 .
The optimum value of the interaction parameter for each binary pair was derived from the correlation of all the system VLE data by minimizing the percent average absolute deviation (% AAD) in bubble-point pressure using the t-mPR EoS.These values are presented in Table 2 along with the resulting % AAD in pressure and are plotted versus the acentric factor (ω) of the hydrocarbon in Figure 3.A decrease of the k ij value is observed as the size of the hydrocarbon increases.
Finally, preliminary calculations showed an insignificant dependence of the k ij value on temperature.In addition, the examination of the dependence on pressure was meaningless because of the very low-pressure range of the available VLE data.To extend the table of interaction parameters to n-alkanes with CN > 20, VLE data for H 2 S/nC 26 , nC 32 and nC 40 have been "generated" through the predictive equation of state/ excess Gibbs energy (EoS/G E ) model, LCVM (Boukouvalas et al., 1994).The LCVM model uses the t-mPR EoS coupled with the original UNIFAC G E model and introduces a new mixing rule, a linear combination of the Vidal and Michelsen ones, for parameter a in the attractive term of the EoS.The original UNIFAC interaction parameter table used with LCVM has been enhanced to include gas/gas, gas/CH 2 , gas/ACH and gas/ACCH 2 parameters for the gases CO 2 , CH 2 , C 2 H 6 , N 2 and H 2 S. The use of the LCVM model for this purpose is justified by its successful performance in the VLE prediction for asymmetric systems (Apostolou et al., 1995;Spiliotis et al., 1994aSpiliotis et al., , 1994b;;Voutsas et al., 1996;Yakoumis et al., 1996).
The k ij values obtained for these larger n-alkanes are included in Table 2 and are shown graphically in Figure 3.Note that they follow the trend established by the k ij values for CN < 20; they are also close to those predicted by the Carroll and Mather correlation (1995) shown in Figure 3. T c , P c and ω values for the n-alkanes up to CN = 20 were obtained from Magoulas and Tassios (1990); for alkanes with CN > 20 values predicted from the same source were used.T c , P c and ω values for the rest of the hydrocarbons were obtained from Daubert andDanner (1985, 1989).
A least-squares regression of the optimum k ij values for H 2 S/n-alkanes yields the following generalized expression for k ij as a function of the hydrocarbon acentric factor: The same correlation can be used for the isomers included in the database.For the remaining systems, no trend can be established, as shown in Figure 3, and the suggested values given in Table 2 should be used.
Prediction results for the bubble-point pressure of the systems used in developing the above equation are given in Table 2.They are very good and fairly close to those found using the optimum values of k ij .The typical results shown in Table 2 with the PR EoS indicate that the proposed correlation and the recommended k ij values can be used with the PR EoS as well.
The results presented in Figure 3 suggest that the proposed correlation and that of Carroll and Mather (1995) have fairly similar performances.Using the LCVM model to generate VLE data for highly asymmetric H 2 S/n-alkane systems and to evaluate the change of interaction parameters as the acentric factor increases enhances the extrapolation reliability of the proposed correlation over the one of Carroll and Mather (1995).
The correlation of Nishiumi et al. (1988) is not included because experimental V c values for large n-alkanes are not available.The correlation of Valderrama et al. (1987) must be considered unreliable for CN > 10.

PREDICTION OF PHASE EQUILIBRIA AND VOLUMETRIC BEHAVIOR OF MULTICOMPONENT MIXTURES
3.1 Ternary Mixture of H 2 S/nC 6 /nC 15 (Laugier and Richon, 1995) Bubble-point pressures at temperature T = 424.5K for several liquid compositions with H 2 S ranging from 10 up to 64 mol% and the corresponding equilibrium vapor phase compositions were available.
Prediction results with the t-mPR are illustrated in Figure 4.The % AAD in bubble-point pressure is 3.6% with a maximum absolute deviation of 5.6% observed in the first point.The prediction of the vapor phase compositions is also very satisfactory.Laugier and Richon (1995) presented correlation results using the Redlish-Kwong-Soave and PR EoS with different mixing and combining rules.In the case of combining rules k ij or k ij plus l ij appear in the a or a and b parameter of the EoS respectively, the interaction parameters have been fitted to binary VLE experimental data.Their results show that the correlation of bubble-point pressure is slightly better represented when k ij plus l ij adjustable interaction parameters are used with the PR EoS (3.8% in bubble point and 2% in H 2 S vapor phase composition).
The prediction results of this study (3.6% in bubble-point pressure and 1.35% in H 2 S vapor phase composition) using the t-mPR EoS and k ij values for H 2 S/nC 6 and H 2 S/nC 15 derived from the generalized expression (Eq.( 4)) are equivalent to the correlated ones presented by Laugier and Richon (1995).Moysan et al., 1986  Carroll and Mather, 1995  Non-alkanes  This work  This observation supports the good predictive performance of the proposed correlation for k ij .In this case the results may also be affected by the use of the t-mPR EoS which provides better vapor pressure predictions due to the modification in the expression of m of the parameter a of the EoS.

Ternary
Mixture of H 2 S/nC 16 /nC 20 (Feng et al., 1995) Feng et al. (1995) presented experimental data for the solubility of H 2 S in mixtures with nC 16 and nC 20 at 323.2 K and pressures 1, 2 and 3 MPa.As shown in Figure 5 the prediction of these data using the t-mPR EoS with binary interaction coefficients derived from the proposed correlation gives an overall absolute percent error in pressure of 6%, similar to the one obtained by using the Carroll and Mather correlation (1995).The LCVM model provides somewhat better results (5%).

"Prinos" Reservoir Oil
The "Prinos" case was of special interest since the H 2 S content in this reservoir oil was about 42% (mole The following volumetric parameters have been considered: -oil formation volume factor (Bo), defined as the volume (in barrels) occupied in the reservoir, at the prevailing pressure and temperature, by one stock tank barrel (standard conditions) of oil plus its dissolved gas; -solution gas/oil ratio (Rs), defined as the number of standard cubic feet of gas dissolved in one stock tank barrel of oil when both are taken to the prevailing reservoir conditions.In addition, reservoir oil densities and gas phase compositions are also available.The compositional analysis of the reservoir oil up to C 7+ and the properties-molecular weight (MW) and specific gravity (SG)-of the heavy fraction C 7+ are presented in Table 3.
Because of the substantial number of uncertainties involved in natural fluids modeling, the prediction of the PVT behavior of the reservoir oil was based on the following considerations: -interaction parameters for all non-hydrocarbon/ hydrocarbon pairs plus those of methane/hydrocarbons have been calculated through the correlations developed in this laboratory (Avlonitis et al., 1994;Kordas et al., 1994Kordas et al., , 1995)).For the k ij of H 2 S/hydrocarbons the proposed correlation, Equation (4), was used; -the heavy fraction was treated as: • one pseudocomponent.This is a reasonable assumption since Prinos oil is not a very volatile one.The critical temperature and the critical pressure of the C 7+ 517 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0  (Carroll and Mather, 1995) Exp.Pts (30 bar) LCVM x (nC 16 ) x (H 2 S) Prediction of the phase envelope for the ternary system H 2 S/nC 6 /nC 15 (Laugier and Richon, 1995), with the t-mPR EoS.
Figure 5 Prediction results for the ternary system H 2 S/nC 16 /nC 20 (Feng et al., 1995), with the t-mPR EoS and the LCVM model.
pseudocomponent have been estimated from the correlation of Twu (1984) and the acentric factor from that of Kesler and Lee (1976).They are given in Table 3; • three pseudocomponents.Splitting of the C 7+ in three fractions was made by the method of Whitson (1980) and the properties of the resulting pseudocomponents have been estimated as above (Table 3).Although no significant improvement is expected through this heavy end treatment due to the low oil volatility, splitting of the C 7+ was considered useful in testing the performance of the proposed k ij correlation when applied to higher molecular weight hydrocarbons as Table 3 indicates for the three pseudocomponents.It is well known that the treatment of PVT data of reservoir fluids should follow a deeper investigation of the heavy end characterization and of the methods for estimating the thermophysical properties of the heavy fractions.Additionally, tuning of the EoS parameters is an acceptable procedure to match experimental data and should be applied with conscious to avoid unphysical predictions.Such a thorough analysis of Prinos oil reservoir fluid was considered out of the scope of this study.Therefore, no tuning was applied and straight prediction of all the experimental data was made.The main objective was to test the predictive capability of the EoS models enhanced by the incorporation of the specific parameters for pure H 2 S and for H 2 S/hydrocarbon systems developed in this work.
Both t-mPR and J-PR EoS have been used.In the case of the J-PR the shift parameter for the volume correction of H 2 S developed in this study has been used.
Prediction results are satisfactory as shown in Figures 6  to 8.There is a very slight overall improvement when C 7+ is treated as three pseudocomponents.This observation is in agreement with that of Coats and Smart (1986) who studied the effect of heavy end splitting to phase equilibria and volumetric predictions for several reservoir oils with different volatilities.For one of the oil mixtures included in their study, fairly close to the Prinos one in terms of volatility, they concluded that splitting the C 7+ resulted in insignificant improvement in the predicted values.Their prediction results for Bo and Rs are equivalent to those obtained here.This is an interesting point, which indicates that although we have an oil mixture where methane is essentially substituted by H 2 S, the obtained results are of the same quality as those for a typical oil with the same volatility.
Both EoS perform very well.The prediction of the volumetric parameters, Bo and Rs, is very satisfactory considering that no adjustment of any parameter has been performed and that the calculations cover a wide pressure range (6000 psig up to atmospheric pressure).Figures 6 and  7 show that the maximum absolute average deviation in Bo and Rs prediction is 8 and 11% respectively.The same is valid for the prediction of the oil density in the same pressure range, where the percent absolute deviation does not exceed the value of ten.
There is a small overall advantage of the J-PR EoS with a % AAD of 0.1% in Bo prediction and 6.7% in Rs when the heavy end is treated as three subfractions.It should be mentioned that the volumetric prediction performance of the J-PR EoS is improved by a factor of two when the shift parameter for H 2 S is incorporated.Calculations using the 518 J-PR EoS with no shift parameter for H 2 S give a % AAD of 6.2% in oil density prediction, while in the opposite case the % AAD in oil density prediction is 3.7%, as Figure 8 indicates.However, these prediction results can be further improved if other schemes for the estimation of the critical characteristics of the heavy fractions are tested.
These results suggest that the proposed correlation for the k ij of H 2 S/hydrocarbon systems appears to be very satisfactory for a molecular weight range significantly greater than that of the binary VLE database; and for oil whose heavy end is highly aromatic as indicated by its MW and SG values.

CONCLUSIONS
Very satisfactory results were obtained with the t-mPR and J-PR EoS for predicting the vapor pressures and saturated liquid volumes of hydrogen sulfide.The J-PR approach provides results equivalent to the t-mPR results for the saturated liquid volumes when the H 2 S shift parameter for the volume correction, developed in this study, is incorporated.
The proposed generalized correlation for the interaction parameters of H 2 S/n-alkanes and their isomers gives very good results, fairly close to those obtained by fitting T-P-x VLE data.The correlation of Carroll and Mather (1995) is also recommended for it gives similar results to that developed here.The use of the LCVM model proved very helpful in overcoming the lack of binary VLE for higher hydrocarbon systems.The "generated" VLE data for H 2 S/large n-alkanes enhance the extrapolation capability of the proposed correlation to highly asymmetric systems.
Application to multicomponent synthetic mixtures and to natural fluids gives satisfactory results both for phase equilibria and for volumetric predictions using the t-mPR or the J-PR EoS.Furthermore, a comparison of the obtained results with those for conventional (no H 2 S) oils suggests that the methodology presented in this study should be applicable to any reservoir oil with high concentration of hydrogen sulfide.Figure 7 Prediction of the solution gas/oil ratio (Rs) for Prinos oil.

APPENDIX The t-mPR
The t-mPR EoS has the following form: (1) where the expressions for the calculation of its parameter values are: (2) m = 0.384401 + 1.522760ω -0.213808ω 2 + 0.034616ω 3 -0.001976ω 4 (3) (4) (5) ß = -10.2447-28.6312ω The EoS has a cubic form with respect to the compressibility factor as follows: For the calculation of the critical compressibility factor Z c the following expression has been assumed (Czerwienski et al., 1988): Z c = 0.289 -0.0701ω -0.0207ω 2 For the calculation of the parameters a m , b m and the translation factor t m of the t-mPR EoS for binary mixtures, the following mixing rules have been assumed: -for the a m parameter: where a 1 and a 2 are the pure component "energy parameters" of the t-mPR EoS and a 12 is defined through the following expression: (11) where k 12 is the binary interaction coefficient; -for the b m parameter the following linear expression is used: A similar linear expression is also used for the translation factor of the binary mixture, t m : The Volume Translation of Jhaveri-PR Jhaveri and Yougren (1984), based on the PR EoS, suggested a dimensionless correcting factor s that is dependent on the component of interest.This factor is determined as S = t / b, where b is the covolume parameter of the EoS and t is the correction of the volume that is given by the EoS (V=V EoS -t).
The s values up to nC 6 are obtained by matching the experimental molar volumes at T r = 0.7 of the pure compound and they are presented in Table 1.For larger hydrocarbons, the following expression is used: (14 where MW is the molecular weight.Values for d, e are given in Table 2.
Figure 1Prediction of the vapor pressure of pure H 2 S.

Figure 2
Figure 2Prediction of the saturated liquid volume of pure H 2 S.
Figure 6Prediction of the oil formation volume factor (Bo) for Prinos oil.

TABLE 1
Prediction results for the vapor pressures and the saturated liquid volumes of H 2 S with the t-mPR, PR and J-PR EoS

TABLE 2
Correlation and prediction results of VLE for binary systems included in the database