Ind. Eng. Chem. Res. 1998, 37, 1679-1684
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Sulfur Solubility in Sour Gas: Predictions with an Equation of State Model Kunal Karan, Robert A. Heidemann,* and Leo A. Behie Department of Chemical and Petroleum Engineering, The University of Calgary, 2500 University Drive, N.W., Calgary, Alberta, Canada T2N 1N4
The Peng-Robinson equation has been used to describe the phase behavior of elemental sulfur and the solubility of sulfur in natural gas mixtures. The sulfur is modeled as S8 in all phases with b ) 0.131 22 m3/kmol and a(T) ) 6.1051 + 2568.1/T MPa (m3/kmol)2. Vapor pressures varying by 5 orders of magnitude are reproduced with a maximum error of 11% over a temperature range from 120 to 640 °C, and the calculated saturated liquid density is within 1% of the data up to 320 °C and within 3.6% at all temperatures. Calculated vapor densities are inaccurate because of the dissociation of S8 at low pressure or high temperature. The fugacity for pure solid sulfur is found from a separate model. A calculated phase diagram for sulfurhydrogen sulfide matches three-phase lines and the solid-liquid-liquid-vapor quadruple point. Solubilities calculated from the proposed model show all the qualitative behaviors in the data and agree very well with experimental data at higher pressures in gases covering a broad range of compositions. Introduction Sulfur is produced in Western Canada and elsewhere from partial oxidation of hydrogen sulfide in variations on the Claus process. The hydrogen sulfide occurs in natural gases with a broad range of compositions, some analyzing more than 90% H2S. Further, the high H2S content gases may contain elemental sulfur in solution. Production of these “sour” natural gases can become complicated by precipitation of the sulfur as a solid in the formation, in well bores, and in associated aboveground equipment (Hyne, 1983). During various stages of the Claus process, mixed gases are in equilibrium with liquid or solid sulfur. In this study, a thermodynamic model was developed for predicting sulfur solubility in sour gas mixtures at natural gas reservoir conditions. The Peng-Robinson equation of state was used to model the liquid and the vapor phases, and a separate model was used for solid sulfur. The only truly predictive model for sulfur solubility in sour gases was reported by Tomcej et al. (1988), who also used the Peng-Robinson equation of state to model liquid and vapor phases. However, numerical values of the parameters they used for sulfur and its interactions with other gas components were not published. Hence, reproduction of their work is impossible. Sulfur has a complex chemistry; it may exist as a number of polymeric species ranging up to S8 in the vapor and combines with other gases to produce polysulfides or sulfanes such as H2S9 (Hyne et al., 1966). In the liquid, polymerization is responsible for a dramatic increase in viscosity with increasing temperature above 433 K (Poulis et al., 1962; Wiewiorowski and Touro, 1966; Touro and Wiewiorowski, 1966; Meyer et al., 1971). In a recent study, Descoˆtes et al. (1993) measured the equilibrium polymerization of sulfur using * To whom correspondence should be addressed. E-mail:
[email protected]. Telephone: (403) 220-8755. Fax: (403) 284-4852.
neutron scattering. Their experimental results confirmed that sulfur is a molecular liquid between 386 and 433 K, made up almost wholly of S8 rings, but, above 433 K, the S8 rings open to polymerize into very long S8 chains. Swift et al. (1976) developed a reaction equilibrium model to interpret and extrapolate sulfur solubility data. In this paper, we have treated sulfur as if it were the single molecule S8 under all conditions, with molar mass 256.32 g/mol. Preliminary calculations of reaction equilibrium in typical vapors treated as ideal gases showed that S8 was the dominant vapor species at all moderate temperatures and the liquid, as noted above, is generally regarded as being primarily S8. We wished to explore to what extent a simple equation of state model, based on the Peng-Robinson equation, could succeed in correlating a wide variety of data for pure sulfur and for sulfur in mixed gases. In a subsequent paper, a correlation will be presented that fully takes into account the chemical associations among the various sulfur species. Modeling Approach The Peng-Robinson equation, as noted, was used for all vapor and liquid phases:
P)
a(T) RT v - b v2 + 2bv - b2
(1)
For the pure components, with the exception of sulfur, the ai and bi parameters were evaluated from acentric factors and critical data in Reid et al. (1987). For sulfur, ai and bi were regressed to fit selected data. The conventional mixing rules were used; i.e.,
b)
∑i xibi
and a )
∑j ∑i xixj(aiaj)0.5(1 - kij)
(2)
Pure Sulfur Vapor and Liquid Sulfur. The critical point of sulfur is far from petroleum reservoir conditions and is
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1680 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 Table 1. Comparison of the Predicted Vapor Pressure of Sulfur with Data (The Sulfur Data Book, 1954): Peng-Robinson b ) 0.131 22 m3/kmol P-R a, MPa (m3/kmol)2 T, K 393.15 413.15 433.15 473.15 513.15 553.15 593.15 633.15 673.15 713.15 753.15 793.15 833.15 873.15 913.15
vapor pressure, bar
exact Psat
correlated
calculated
data
diff., %
12.502 12.234 11.988 11.546 11.161 10.818 10.508 10.227 9.969 9.732 9.514 9.312 9.128
12.638 12.322 12.035 11.533 11.110 10.748 10.435 10.161 9.920 9.706 9.515 9.343 9.187
3.60 × 10-5 1.32 × 10-4 4.10 × 10-4 2.72 × 10-3 0.0122 0.0416 0.1142 0.2658 0.5445 1.0079 1.7210 2.7523 4.1718 6.0488 8.4512
4.10 × 10-5 1.42 × 10-4 4.46 × 10-4 2.83 × 10-3 0.0123 0.0402 0.1070 0.2472 0.5066 0.9494 1.6516 2.7155 4.3022 6.5253 9.5417
11.17 7.04 8.03 3.74 -0.92 -3.57 -6.36 -7.53 -7.47 -6.16 -4.20 -1.36 3.03 7.30 11.4
also highly uncertain. Rau et al. (1973) note reported critical temperatures as low as 1209 K. The critical pressure has been estimated at 11.75 MPa (West, 1950) and 18.2 MPa (Rau et al., 1973). Reid et al. (1987) tabulate the sulfur critical data as 1314 K and 20.7 MPa. For these reasons and because of the chemical complexity of sulfur, the Peng-Robinson parameters were not evaluated from sulfur critical properties. We first found a and b parameters that give precisely the sulfur liquid density and vapor pressure at 413.15 K (140 °C) using a technique similar to that proposed by Panagiotopoulos and Kumar (1985). The b parameter was then treated as temperature independent. The a parameter was evaluated (with b fixed) in order to match sulfur vapor pressures at a number of temperatures. As mentioned, sulfur was treated as S8. The liquid density and vapor pressure data that were fitted were those that are tabulated in The Sulfur Data Book (Tuller, 1954). The original source of the vapor pressure data was West and Menzies (1929), who made measurements in the temperature range of 373-823 K, and the later extrapolation by West (1950) to 919 K. Tabulated liquid densities appear to be the measurements of Kellas (1918). Rau et al. (1973) extended the range of measured vapor pressures and densities of coexisting phases to conditions near the critical point of sulfur, but these higher temperature measurements were not fitted by us in this study. The recent correlations of physical properties of sulfur by Shuai and Meisen (1995) apply to the vapor pressure up to 850 K and saturated liquid density up to 718 K, but we used the Tuller (1954) tabulation rather than the Shuai and Meisen (1995) correlation. Table 1 presents the values of the Peng-Robinson parameters that were obtained from matching the liquid density at 413.15 K and the vapor pressure exactly at the indicated temperatures. The b parameter was fixed at 0.131 22 m3/kmol. The temperature dependence of the a parameter is not especially strong and, to simplify the presentation, a linear least-squares fitting was performed to yield the following expression that applies in the temperature range 393.15 K to 793.15 K: 3
2
a(T) ) 6.1051 + 2568.1/T MPa (m /kmol)
(3)
This correlation results in some error in the calculated
Table 2. Saturated Liquid and Vapor Specific Volumes of Sulfur Calculations and Data (The Sulfur Data Book, 1954) temp, K
vapor volume, m3/kg model data diff., %
393.15 3537.5 3239.1 413.15 1018.2 979.2 433.15 342.9 329.5 473.15 56.46 57.2 513.15 13.57 17.4 553.15 4.303 5.036 593.15 1.678 2.033 633.15 0.766 0.938 673.15 0.395 0.504 713.15 0.223 0.292 753.15 0.136 0.180 793.15 0.088 0.121 833.15 0.059 0.084 873.15 0.042 0.062 913.15 0.031 0.044
-9.21 -3.98 -4.06 1.38 22.03 14.55 17.44 18.36 21.55 23.42 24.28 27.13 28.63 32.17 30.49
liquid volume, (m3/kg) × 103 model data diff., % 0.5529 0.5571 0.5605 0.5687 0.5778 0.5875 0.5983 0.6099 0.6228 0.6192 0.6526 0.6701 0.6896 0.7117 0.7368
0.5533 0.5571 0.5620 0.5682 0.5769 0.5844 0.5931 0.6018 0.6117 0.6369 0.6341 0.6465 0.6776 0.7087 0.7522
0.06 0.00 0.26 0.09 0.14 0.54 0.87 1.35 1.81 2.86 2.91 3.63 1.76 0.41 2.05
vapor pressures as shown in Table 1, but the errors remain within 11% over the whole temperature range from 393 to 913 K, over which the vapor pressure varies by more than 5 orders of magnitude. Vapor and liquid experimental and calculated volumes are shown in Table 2. The calculated liquid specific volume is surprisingly close to the data over a 540 K temperature range. The indicated errors in the saturated vapor volume at the lowest temperatures are traceable to the vapor pressure errors. At the higher temperatures, the calculated vapor volume is 30% smaller than the experimental value, and these errors are undoubtedly due to the dissociation of S8, which is not accounted for in the model. We have also calculated the heat of vaporization of sulfur. The value is the difference between the enthalpies of the saturated vapor and the saturated liquid as computed from the Peng-Robinson equation using standard expressions (Walas, 1985). The values for the heat of vaporization that are tabulated in The Sulfur Data Book (Tuller, 1954) were calculated by West and Menzies (1929) and West (1950) from vapor pressure and coexisting volume data, using the Clausius-Clapeyron equation. West and Menzies found a remarkable minimum in the heat of vaporization, with a value of 281 kJ/kg at a temperature around 640 K, which must be due to the endothermic dissociation of S8. Our calculated heat of vaporization is 252 kJ/kg at 640 K and decreases as temperature increases, while the West and Menzies value increases as temperature increases beyond this point. At 400 K, our calculated heat of vaporization is 323 kJ/kg, which compares reasonably with the West and Menzies value of around 348 kJ/kg. Solid Sulfur. Sulfur liquid solidifies (at equilibrium and at moderate pressures) into a monoclinic structure, and the equilibrium solid transforms into a rhombic crystalline structure at lower temperatures. Both crystalline forms sublime directly to vapor, and there is a triple point consisting of the two solid forms in equilibrium with a vapor at 94.4 °C. We did not attempt to reflect the full complexity of this behavior. In our approach, the sulfur fugacity was computed using an equation of the form:
ln fS ) A/T + B + PvS/RT
(4)
The first two terms can be thought of as giving the fugacity of the sulfur at its sublimation pressure (es-
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1681
sentially, the very low sublimation pressure is equal to the fugacity), and the third term is the Poynting correction for higher pressures. The volume vS is for the solid sulfur and is assumed to be independent of pressure. Since the equation of state model gives somewhat inaccurate vapor pressures at the lower temperatures and since three-phase behavior is highly dependent on the value used for the solid volume, we have treated A, B, and vS in eq 4 as empirical parameters available for fitting data. The values we obtained give
ln (fS, MPa) ) 22.83572 - 13846.797/T + 0.122479P/RT (5) The molar volume of the solid in this equation, vS ) 0.122 479 m3/kmol of S8, corresponds to a solid density of 2094.3 kg/m3, which compares with experimental values of 2070 and 1960 kg/m3 for the rhombic and monoclinic forms (Tuller, 1954). The implied sublimation pressure at the vapor-solid-liquid triple point (238.1 °F or 385.6 K) is 0.019 mmHg, as opposed to an accepted value of 0.018 mmHg (Tuller, 1954). The parameters were obtained, however, not from these data but from two hydrogen sulfide-sulfur three-phase points and one data point of Roof (1971) on solid sulfur solubility in hydrogen sulfide. Sulfur in Natural Gases The binary interaction parameters, kij, between sulfur and other gas components and the molar volume of solid sulfur are the only parameters available for fitting mixture data. A brief description of the principal sources of data follows. Kennedy and Wieland (1960) measured the equilibrium sulfur content in pure methane, carbon dioxide, hydrogen sulfide, and mixtures of these gases at temperatures of 339, 367, and 394 K and in the pressure range of 6.9-41.3 MPa. Roof (1971) measured solubility of sulfur in hydrogen sulfide in the range of temperature between 317 and 394 K and at pressures up to 31 MPa. These results differed significantly from those of Kennedy and Wieland (1960). Swift et al. (1976) reported the solubility of sulfur in hydrogen sulfide at pressures of 35-140 MPa and in a temperature range of 390-450 K, conditions that may be encountered in high-pressure natural gas reservoirs. Brunner and Woll (1980) measured the sulfur solubility in pure hydrogen sulfide and in four gas mixtures composed of H2S, CO2, CH4, and N2 in a temperature range of 373.15-433.15 K and at pressures up to 60 MPa. Their solubility data in hydrogen sulfide were in good agreement with those reported by Swift et al. (1976) and by Roof (1971). Later, Brunner et al. (1988) measured the sulfur solubility in sour gas mixtures of various compositions at pressures up to 155 MPa and in the temperature range of 394486 K. One of their objectives was to study the effect of alkanes up to carbon number six. Woll (1983) examined the effect of hydrogen sulfide on the depression of the freezing point of sulfur. Davis et al. (1992) of Alberta Sulfur Research Limited (ASRL) have reported solubility data in sour gases of high hydrogen sulfide content (up to 90%) at four temperatures of 333.15, 363.15, 393.15, and 423.15 K and over a pressure range of 5-55 MPa. Model Parameters. The binary interaction parameter for S8-H2S was fixed at kij ) 0.083 by matching
data from Brunner and Woll (1980) at a temperature of 393.15 K and a pressure of 40 MPa. The isotherms cross at around 40 MPa, and this pressure was chosen as a fitting point for that reason. Binary interaction parameters for S8-CH4 and S8CO2 were determined as kij ) 0.110 and kij ) 0.140, respectively, by matching solubility data of Kennedy and Wieland (1960), at 394 K and 35 MPa in both cases. The accuracy of the Kennedy and Wieland data for the sulfur-hydrogen sulfide system has been questioned, but their measurements on sulfur with methane and carbon dioxide are the only comprehensive data available. The computed sulfur solubilities in the pure gases are quite sensitive to the numerical values used for the interaction parameters. A model with zero interaction parameters gives results entirely different from the data. There are insufficient data to extract interaction parameters for sulfur with other gas components. In the calculations performed, we used kij ) 0.100 for S8N2, S8-C2H6, and S8-C4H10, a number on the same order as that for S8-CH4. Results Phase Diagram for H2S-Sulfur. Brunner et al. (1988) reported a P-T projection of solid-liquidliquid-gas equilibrium for the H2S-sulfur system. The data of Woll (1983) on the depression of the sulfur melting point by dissolved hydrogen sulfide under threephase equilibrium were utilized in construction of the diagram. Hydrogen sulfide and sulfur have limited miscibility as liquids. The liquid-liquid separation, plus the presence of a solid phase, results in three-phase equilibria of several different types: (i) solid, a H2S-rich liquid, and a vapor (S-L-G); (ii) solid, a sulfur-rich liquid, and a vapor (S-LS-G); (iii) solid, a H2S-rich liquid, and a sulfur-rich liquid (S-L-LS); and (iv) two liquids and a vapor (L-LS-G). Each of the three-phase equilibria appears as a line on the P-T phase diagram. The four three-phase lines intersect at the quadruple point. Calculations were performed to evaluate the threephase pressure or temperature in a method similar to that used by Evelein et al. (1976). To obtain the threephase temperature at a fixed pressure for, say, S-L-G equilibria, flash calculations were carried out for S-G equilbrium and S-L equilibrium at the selected pressure over a range of temperature. The Gibbs free energy for each equilibrium was evaluated. The temperature at which the Gibbs free energy was the same for both S-G and S-L equilibrium is the three-phase temperature. Temperatures from 340 to 400 K and pressures up to 30 MPa were examined, so that all regions of the S-LSL-G system would be covered. The four three-phase lines and the vapor pressure curve for hydrogen sulfide are plotted in Figure 1. The three-phase lines intersect at a quadruple point which is computed from our model to be at 364.17 K and 7.663 MPa. Brunner et al. (1988) estimate the value of this quadruple point to be 361.9 K and 7.32 MPa, but the data of Woll (1983), shown in the figure, would support an estimate at a slightly higher temperature. The vapor pressure line of hydrogen sulfide is slightly above the three-phase S-G-L line (see inset) but nearly coincides with it. The calculated
1682 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
Figure 1. P-T phase diagram for sulfur-hydrogen sulfide.
S-LS-L line is an excellent representation of the data reported by Woll (1983). The S-LS-G line intersects the Woll (1983) data. The calculated line ends near the reported triple point of sulfur, 385.6 K (The Sulfur Data Book); however, the Woll (1983) data extend to a slightly higher temperature. The model also locates a critical end point on the liquid-liquid-vapor line at 373.8 K and 9.01 MPa, which can be compared to the critical point of hydrogen sulfide at 373.2 K and 8.94 MPa. We believe that the phase diagram resulting from the model is in excellent agreement with the data. Particularly, placing the quadruple point temperature within 3 K of the Brunner et al. (1988) estimate would seem to demonstrate an underlying validity of the modeling approach. Solubility Calculations. The solubilites involved with sulfur and one other substance were obtained by performing flash calculations. Strictly, to compare predictions from the model with solubility data for sulfur in mixed gases, a dew-point calculation must be carried out. Our results were obtained through flash calculations with feed compositions selected so that the fraction in the vapor was greater than 0.98. Additionally, we verified that the vapor phase compositions represented the original mixed gas. Sulfur-H2S System. The solubility of liquid sulfur in hydrogen sulfide is presented in Figure 2, where the model calculations are compared with the data of Brunner and Woll (1980). The predictions from the model are in reasonable agreement with the data for all three temperatures of 393.15, 413.15, and 433.15 K. At lower pressures, the predicted sulfur solubility is lower than that shown by the data. A peculiar feature of the data is that the solubility increases with decreasing temperature below 30 MPa and increases with an increase in temperature above the pressure of 40 MPa. This behavior is predicted by the model, with the crossover taking place at a pressure of 40 MPa. The behavior is attributed by Brunner and Woll (1988) to the changing density of hydrogen sulfide. The solid sulfur-liquid H2S region can be determined from the phase diagram in Figure 1. Experimental data in this region have been presented by Roof (1971). A comparison of the model prediction with the experimental data of Roof at temperatures of 316, 339, and 366 K is illustrated in Figure 3. The model provides a reasonable match of data and accounts for the effect of
Figure 2. Solubility of a liquid sulfur in hydrogen sulfide comparison with data of Brunner and Woll (1980).
Figure 3. Solubility of a solid sulfur in hydrogen sulfide comparison of the model with data.
increasing pressure, especially at 339 K where the data were used to obtain a value for the solid S8 molar volume. In general, the calculated solubilities are closer to the data at higher pressures which is parallel to the results shown in Figure 2. In the model calculations, the sulfur-rich equilibrium phase at the lower pressure points on the 366 K isotherm is the liquid. The threephase line is crossed and solid sulfur is the equilibrium phase at the 30.7 MPa point shown in the figure. In the transition across the three-phase line, there is no discontinuity or sharp change in slope in the solubility of sulfur in the hydrogen sulfide phase. Sulfur-Sour Gas Systems. Data on the sulfursour gas system have been contributed by Brunner and co-workers (Brunner and Woll, 1980; Brunner et al., 1988) and Davis et al. (1992) of Alberta Sulfur Research Ltd (ASRL). The experiments were carried out with gases of different compositions, which complicates comparison. Model results are compared with the data provided by Brunner’s group in Figures 4-6. Figure 4 demonstrates the effect of temperature on the equilibrium sulfur content of a gas mixture that is 81% methane, 6% hydrogen sulfide, 9% carbon dioxide, and 4% nitro-
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1683
Figure 4. Sulfur solubility in a methane-rich sour gas; temperature effect.
Figure 6. Effect of the alkane content on sulfur solubility, 398 K.
mixing rules could be adjusted to better match the data.) Conclusions
Figure 5. Sulfur solubility in gases of varying composition.
gen. The calculations from the Peng-Robinson model are in excellent agreement with the data of Brunner and Woll (1980) over a wide range of temperature and pressure. The strong effect of hydrogen sulfide content on sulfur solubility is elucidated in Figure 5. The model predictions are compared with data of Brunner et al. (1988) for mixtures with compositions of 35% H2S (8% CO2, 57% CH4) at 398 and 458 K and 84% H2S (9% CO2, 7% CH4) at 398 K and with the Brunner and Woll (1980) data for 100% hydrogen sulfide at 393.15 K. The effect of H2S content is quite significant in comparison with the effect of temperature. The model calculations, which are predictive in this case, agree very well with the data. Figure 6 shows the effects of hydrocarbon type and content. Brunner et al. (1988) measured the sulfur solubility in three gas mixtures with a total hydrocarbon percentage of 57%, with the balance made up by 35% hydrogen sulfide and 8% carbon dioxide. The three gas mixtures had compositions of 57% CH4, 45% CH4 + 12% C2H6, and 45% CH4 + 12% C4H10. Solubility data at 398.15 K are reproduced by the model calculations, as is shown in the figure. (Note that the sulfur-ethane and sulfur-n-butane interaction parameters in the
The model developed for sulfur was successfully tested over a wide range of temperature, pressure, and gas composition. The limitations of this simple equation of state model are made clear by the failure to predict the vapor density and the heat of vaporization of sulfur at higher temperatures, although excellent liquid volumes and vapor pressures were obtained. The phase diagram for the H2S-sulfur system generated by the model mirrors the data, even without any effort to build into the model the crucial liquid-liquid separation between sulfur and hydrogen sulfide. The solid model was tested only with a small set of data, nonetheless, predictions were satisfactory. Good agreement was obtained with experimental data for gases with a broad range of compositions and covering a wide range of temperatures and pressures. The results can be compared with the calculations reported by Tomcej et al. (1988). Figures in their paper indicate a better fit of sulfur solubility at lower pressures than we report. Their figures do not extend to the higher pressures, where the model in this paper matches the data very well. Tomcej et al. (1988) used an empirical correlation to determine whether the equilibrium sulfur phase was liquid or vapor. In contrast, our procedure permits a smooth transition across multiphase lines by satisfying all the equilibrium criteria. We were able to compute all the three-phase lines in the sulfur-hydrogen sulfide system with apparently very good accuracy. We believe that these results demonstrate again the value of the Peng-Robinson equation in correlating a broad range of physical phenomena. Further work is under way to account for the actual sulfur species expected in the vapor at higher temperatures. Acknowledgment This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
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Literature Cited Brunner, E.; Woll, W. Solubility of Sulfur in Hydrogen Sulfide and Sour Gases. Soc. Pet. Eng. J. 1980, 20, 377. Brunner, E.; Place, M. C., Jr.; Woll, W. H. Sulfur Solubility in Sour Gas. J. Pet. Technol. 1988, 40, 1587. Davis, P. M.; Lau, C. S. C.; Hyne, J. B. Data on the Solubility of Sulfur in Sour Gases. Alberta Sulphur Res. Ltd. Q. Bull. 199293, XXIX, 1. Descoˆtes, L.; Bellisent, R.; Pfeuty, P.; Dianoux, A. J. Dynamics of Liquid Sulphur around the Equilibrium Polymerization Transition. Physica A 1993, 201, 381. Evelein, K. A.; Moore, R. G.; Heidemann, R. A. Correlation of the Phase Behavior in the Systems Hydrogen Sulfide-Water and Carbon Dioxide-Water. Ind. Eng. Chem. Process Des. Dev. 1976, 15, 423. Hyne, J. B. Controlling Sulfur Deposition in Sour Gas Wells. World Oil 1983, 35. Hyne, J. B.; Muller, E.; Wiewiorowski, T. K. Nuclear Magnetic Resonance of Hydrogen Polysulfide in Molten Sulfur. J. Phys. Chem. 1966, 11, 3733. Kellas, A. M. The Determination of the Molecular Complexity of Liquid Sulphur. J. Chem. Soc. 1918, 113, 903. Kennedy, H. T.; Wieland, D. R. Equilibrium in the MethaneCarbon Dioxide-Hydrogen Sulfide-Sulfur System. Pet. Trans. AIME 1960, 219, 166. Meyer, B.; Oomen, T. V.; Jensen, D. The Color of Liquid Sulfur. J. Phys. Chem., 1971, 75, 912. Panagiotopoulos, A. Z.; Kumar, S. K. A Generalized Technique to Obtain Pure Component Parameters for Two-Parameter Equations of State. Fluid Phase Equilib. 1985, 22, 77. Poulis, J. A.; Massen, C. H.; v. d. Leeden, P. Magnetic Susceptibility of Liquid Sulphur. Trans. Faraday Soc. 1962, 58, 474. Rau, H.; Kutty, T. R. N.; Guedes De Carvalho, J. R. F. HighTemperature Saturated Vapor Pressure of Sulphur and the Estimation of its Critical Quantities. J. Chem. Thermodyn. 1973, 5, 291.
Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987. Roof, J. G. Solubility of Sulfur in Hydrogen Sulfide and in Carbon Disulfide at Elevated Temperature and Pressure. Soc. Pet. Eng. J. 1971, 11, 272. Shuai, X.; Meisen, A. New Correlations Predict Physical Properties of Elemental Sulfur. Oil Gas J. 1995, Oct 16, 50. Swift, S. C.; Manning, F. C.; Thompson, R. E. Sulfur Bearing Capacity of Hydrogen Sulfide Gas. Soc. Pet. Eng. J. 1976, 16, 57. Tomcej, R. A.; Kalra, H.; Hunter, B. E. Prediction of Sulphur Solubility in Sour Gas Mixtures. Presented at the 39th Annual Technical Meeting of the Petroleum Society of CIM, Calgary, Alberta, June 12, 1988; Paper No. 88-39-14. Touro, F. J.; Wiewiorowski, T. K. Viscosity-Chain Length Relationship in Molten Sulfur Systems. J. Phys. Chem. 1966, 70, 239. Tuller, W. N. The Sulphur Data Book; McGraw-Hill: New York, 1954. Walas, S. M. Phase Equilibria in Chemical Engineering; Butterworth: Boston, 1985. West, J. R. Thermodynamic Properties of Sulfur. Ind. Eng. Chem. 1950, 42, 713. West, W. A.; Menzies, A. W. C. The Vapor Pressures of Sulfur between 100° and 550° with Related Thermal Data. J. Phys. Chem. 1929, 33, 1880. Wiewiorowski, T. K.; Touro, F. J. The Sulfur-Hydrogen Sulfide System. J. Phys. Chem. 1966, 70, 234. Woll, W. The Influence of Sour Gases Upon the Melting Curve of Sulfur. Erdoe-Erdgas-Z. 1983, 99, 297.
Received for review September 10, 1997 Revised manuscript received February 12, 1998 Accepted February 12, 1998 IE970650K
