THE ACCURACY OF PREDICTING COMPRESSIBILITY FACTOR FOR SOUR NATURAL GASES

Transcription

1 PETROLEUM SCIENCE AND TECHNOLOGY, 19(5&6), (2001) THE ACCURACY OF PREDICTING COMPRESSIBILITY FACTOR FOR SOUR NATURAL GASES Adel M. Elsharkawy* and AliElkamel College of Engineering and Petroleum Kuwait University, P.O. Box 5969, Safat 13060, Kuwait ABSTRACT This paper presents the initial stage of an effort aimed at developing a new correlation to estimate pseudo critical properties for sour gas when the exact composition is not known. Several mixing rules and gas gravity correlations available in the literature are first evaluated and compared. The evaluation is performed on a large database consisting of more than 2106 samples of sour gas compositions collected worldwide. Several evaluation criteria are used including the average absolute deviation (AAD), the standard deviation (SD), the coefficient of correlation, R, and cross plots and error histograms. The mixing rules include: Kay s mixing rule combined with Wichert Aziz correlation for the presence of non-hydrocarbons, SSBV mixing rule with Wichert and Aziz, Corredor et al. mixing rule, and Piper et al. mixing rule. These methods, in one form or another, use information on gas *Corresponding author. Fax: (965) ; asharkawy@kuc01.kuniv. edu.kw 711 Copyright ß 2001 by Marcel Dekker, Inc.

2 712 ELSHARKAWY AND ELKAMEL composition. Three different other methods that are based on gas gravity alone were also analyzed. These are: Standing, Sutton, and Elsharkawy et al. gas gravity correlations. While the methods based on knowledge of composition showed reasonable accuracy, those based on gas gravity alone showed weak accuracy with low correlation coefficients. A new gas gravity correlation that is based on the fraction of nonhydrocarbons present in the sour gas was proposed. Preliminary results indicate that a good improvement over past gravity correlations was achieved. The compositional correlations, still show, however, better accuracy. Research is still going on to come up with more accurate correlations that are based on only readily available descriptors. INTRODUCTION Gas compressibility factor is involved in calculating gas properties such as formation volume factor, density, compressibility, and viscosity. All these properties are necessary in the oil and gas industry for evaluating newly discovered gas reservoirs, calculating initial and gas reserves, predicting future gas production, and designing production tubing and pipelines. The industry standard is to measure gas properties, Pressure Volume Temperature (PVT), in laboratory using reservoir samples (Standing, 1981). The draw back is that these isothermally measured PVT data is applicable at measured pressures and reservoir temperature. Calculation methods such as correlations and equations of state are used to predict properties at other pressures and temperatures. Also, laboratory analyses for PVT behavior are sometimes expensive and time consuming. Correlations, which are used to predict gas compressibility factor, are much easier and faster than equations of state. Sometimes these correlations have comparable accuracy to equations of state. Predicting compressibility factor for sour gases is much more difficult than that of sweet gases. Therefore, several attempts have been made to predict compressibility factor for sweet gases (Kay, 1936; Stewart et al., 1959; Sutton, 1985). Wichert and Aziz (1972) presented corrections for the presence of hydrogen sulfide and carbon dioxide for determining compressibility factor of sour gases. Because there is no exact method for predicting the PVT behavior of natural gases several approximations have been proposed. The most common method is to use one of the forms of the principle of corresponding states (Mac Cain, 1990; Ahmed, 1989). In this form, gas compressibility factor is expressed as a function of pseudo reduced

3 PREDICTING COMPRESSIBILITY FACTOR 713 pressure and temperature (P pr, T pr ). Standing and Katz (1942) presented a chart for determining gas compressibility factor based on the principle of corresponding states. Standing and Katz will be referred to as (SK). The SK chart was prepared for binary mixtures of low molecular weight sweet gases. Several mathematical expressions fitting the SK chart, have been proposed to calculate the gas compressibility factor (Papy, 1968; Hall and Yarborough, 1973; Yarborough and Hall, 1974; Dranchuk and Abou Kassem, 1975; Dranchk et al., 1974; Hankinson et al., 1969; Brill and Beggs, 1974). Evaluation of these methods by Takacs (1976) and Elsharkawy et al. (2000) concluded that Dranchuk Abou-Kassem (DK) correlation is the most accurate representation of SK chart. When dealing with gas mixtures, the mixture critical pressure (P pc ) and temperature (T pc ) are required. Critical properties of natural gas are calculated from either gas composition or gas gravity. Several mixing rules have been proposed to calculate mixture critical properties of natural gases. Among these methods, Kay s (1936) mixing rule and Stewart Burkhardt Voo (1959) are the most widely used. Kay s mixing rule is simple and provides an accurate determination of gas compressibility factor for sweet gases of low molecular weight. Satter and Campbell (1963) evaluated several mixing rules for calculating properties of natural gases. They concluded that Stewart Burkhardt Voo rule known as SBV provided the most satisfactory results, especially for gases of high molecular weight. Sutton (1985) studied the performance of several mixing rule for calculating compressibility factor for gas condensates that contain a large amount of heptane plus fraction. He modified SBV mixing rule to account for the presence of heptane plus in the natural gases. Standard laboratory analysis gives composition of natural gases through hexane and lump components heavier than hexane in a heptane plus fraction known as C 7+. Critical properties of pure components are well documents, Table 1. The critical properties of the C 7+ fraction are, however, calculated from correlations using molecular weight and specific gravity of the heptane plus (Win, 1957; Keseler and Lee, 1976; Sim et al., 1980; Lin and Chao, 1984; Watansiri et al., 1985; Pedersen et al., 1989). Whitson (1983) and Elsharkawy et al. (2000) reviewed several methods for calculating pseudo critical properties of the heptane plus fraction. Whitson (1983) recommended that Kesler Lee (1976) correlation to be used to estimate critical properties of C 7+. However, Elsharkawy et al. (2000) found that Lin Choa (1984) and Kesler Lee (1976), respectively, with SSBV mixing rule and DK correlation are the best combination to determine gas compressibility factor for gas condensate reservoirs.

4 714 ELSHARKAWY AND ELKAMEL Table 1. Physical Properties of Defined Components Critical Pressure Critical Temperature Component Molecular Weight psi R H 2 S CO N C C C i-c n-c i-c n-c C Composition of natural gases, from which pseudo critical properties are computed, is not always available. Therefore, correlations relating pseudo critical pressure and temperature to gas gravity are used. Standing (1981) presented correlation of pseudo critical properties to gas gravity based on low molecular weight California natural gases. His correlation has the following form: P pc ¼ :7 g g 11:1 g 2 g T pc ¼ 187 þ 330 g g 71:5 g 2 g ð1þ ð2þ Standing indicated that his correlation works only when there is no non-hydrocarbon gases present in the natural gas. Sutton (1985), working with PVT reports of high molecular weight gases which are rich in heptane plus, developed the following correlation: P pc ¼ 756:8 131:0 g g 3:6 g 2 g T pc ¼ 169:2 þ 349:5 g g 74:0 g 2 g ð3þ ð4þ The gases that were used to develop Sutton s gas gravity correlation are mostly sweet gases. These gases have minor amount of carbon dioxide and nitrogen, and no hydrogen sulfide. Using a large data bank of retrograde gases, Elsharkawy et al. (2000) presented another correlation for gas condensates. The latter correlation covers heavier gases than that used in

5 PREDICTING COMPRESSIBILITY FACTOR 715 Sutton s and have a minor amount of hydrogen sulfide. Elsharkawy et al., gas gravity correlation has the following form: P pc ¼ 787:06 147:34 g g 7:916 g 2 g T pc ¼ 149:18 þ 358:14g g 66:976g 2 g ð5þ ð6þ Thus there is a need for correlation relating gas gravity to pseudo critical properties for sour gases. This study has two objectives. The first objective is to evaluate the previously published methods of calculating gas compressibility factor for sour gases. The second objective is to develop a correlation to estimate pseudo critical properties from gas gravity for sour gas when detailed composition is not available. GAS DATA BANK One of the main objectives of the current work is to evaluate the previously published methods of calculating gas compressibility factors of sour gases using either gas composition or gas gravity. The best test to evaluate such methods is the accuracy with which these methods approximate reliable experimental data. The data bank used in this study comprises measurements of two thousand and one hundred and sixgas compressibility factor for sour gases. Some of these data have been collected from the literature (Whitson, 1985; Simon et al., 1964; Robinson et al., 1965; Buxton and Campbell, 1967; McLeod, 1968; Wichert and Aziz, 1970; Elsharkawy and Foda, 1988). These measurements cover a pressure range from 90 psi to 12,000 psi, a temperature range from 40 to 327 F, and a wide range of molecular weights from 16.4 to 55 (gas gravity from to 1.895). A complete description of the data bank is reported in Table 2. Calculating Gas Compressibility Factor When Composition Is Known When gas composition is available, pseudo critical properties are calculated using a given mixing rule. In order to calculate the pseudo-critical properties of natural gas mixtures, critical properties of the heptane plus fraction must be computed. In this study, Kesler Lee (1976) method, Eqs. (7) and (8), are used to calculate critical properties of the C 7+.

6 716 ELSHARKAWY AND ELKAMEL Table 2. Properties of Sour Gas Data Used in the Study Min. Ave. Max. Pressure, psi ,000 Reservoir temperature, F Composition mole % Methane Ethane Propane Iso-Butane N-Butane Iso-Pentane n-pentane Hexane Heptane plus M w C g C Z-factor Gas gravity (air ¼ 1) Hydrogen sulfide Carbon dioxide Nitrogen P c ¼ exp 8:3634 0:0566=g ð0:24244 þ 2:2898=gþ0:11857=g 2 Þ10 3 T b þð1:4685 þ 3:648=gþ0:47227=g 2 Þ10 7 T 2 b ð0:42019 þ 1:6977=g 2 Þ10 10 T 3 b ð7þ T c ¼ 341:7 þ 811:g þð0:4244 þ 0:1174:gÞT b þð0:4669 3:2623:gÞ10 5 =T b ð8þ The KL method correlates critical properties as a function of boiling point and specific gravity. However, laboratory reports normally provide only the specific gravity and molecular weight of the heptane plus fraction. Whitson (1983) has presented an equation for estimating boiling point (T b ) from molecular weight (M ) and specific gravity (g) of the heptane plus fraction. T b ¼ 4:5579 M 0:15178 g 0: ð9þ

7 PREDICTING COMPRESSIBILITY FACTOR 717 In this study, Kay s mixing rule, Stewart-Burkhardt-Voo (SBV) mixing rule as modified by Sutton (SSBV) are considered. Kay s (1936) mixing rule, based on molar weighted average critical properties, has the following form: P pc ¼ X y i P ci T pc ¼ X y i T ci ð10þ ð11þ Stewart Burkhardt Voo (1959) (SBV) proposed the following mixing rule for high molecular weight gases. J ¼ 1 hx i yi ðt 3 c =P c Þ i þ 2 hx i 2 yi ðt 3 c =P c Þ 0:5 i ð12þ K ¼ X y i ðt c =P 0:5 c T pc ¼ K 2 =J P pc ¼ T pc =J Þ i ð13þ ð14þ ð15þ If the natural gas contains heptane plus fraction, Sutton (1985) modification of SBV (SSBV) is used. F j ¼ 1 3 yðt c=p c Þ C 7þ þ 2 3 y iðt c =P c Þ 0:5 i 2 C 7þ E j ¼ 0:6081F j þ 1:1325F 2 j 14:004F j y C7þ þ 64:434F j y 2 C 7þ h i E k ¼ðT c =P 0:5 c Þ C7þ 0:3129y C7þ 4:8156y 2 C 7þ þ 27:3751y 3 C 7þ J 0 ¼ J E j K 0 ¼ K E k T pc ¼ K 02 =J 0 P pc ¼ T pc =J 0 ð16þ ð17þ ð18þ ð19þ ð20þ ð21þ ð22þ Eqs. (10) and (11) or (12) through (22) provide critical properties for sweet natural gas systems. For sour gases, these equations must be corrected for the presence of non-hydrocarbon components. The method proposed by

8 718 ELSHARKAWY AND ELKAMEL Wichert and Aziz (1972) is used to correct the pseudo critical properties of natural gases to the presence of these non-hydrocarbon components. The correction factor is given below: ¼ 120ðA 0:9 A 1:6 Þþ1:5ðB 0:5 B 4 Þ ð23þ Where the coefficient A is the sum of the mole fraction of H 2 SandCO 2 and B is the mole fraction of H 2 Sin the gas mixture. The corrected pseudo critical properties P 0 pc and T 0 pc are: T 0 pc ¼ T pc ð24þ P 0 pc ¼ P pct 0 pc =½T pc þ Bð1 BÞŠ ð25þ Reduced pressure (P pr ) and reduced temperature (T pr ) are calculate from pressure (P) and temperature (T ) of interest and critical properties of the natural gas (P 0 pc, T pc 0 ) by the following relationship: P pr ¼ P=P 0 pc ð26þ T pr ¼ T=T 0 pc ð27þ Recently, Corredor et al. (1992), and Piper et al. (1993) proposed a mixing rule similar to SBV rule, Eqs. (12) and (13). However, they treated the non-hydrocarbons and the C 7+ plus fraction differently. Their mixing rule has the following form: J ¼ a 0 þ X X hx i 2 a i y i ðt c =P c Þ i þ a 4 yj ðt c =P c Þ j þ a 5 yi ðt c =P c Þ i þ a 6 ð y C7þ M C7þ Þþa 7 ð y C7þ M C7þ Þ 2 ð28þ K ¼ b 0 þ X b i y i þ T c =P 0:5 c i þ b 4 X yj T c =P 0:5 c j þ b 5 hx yj T c =P 0:5 i 2 c j þ b 6 ð y C7þ M C7þ Þþb 7 ð y C7þ M C7þ Þ 2 ð29þ Where y i [ f y H2 S; y CO2 ; y N2 g and y j [ f y C1 ; y C2 ;...; y C6 g and a and b are constants. The difference between Corredor et al. method and Piper et al., method is that each method has different values for a and b. To calculate the pseudo critical properties of the gas condensate, Corredor et al. and Piper et al., used the weight fraction of the C 7+ rather than the critical properties. Thus, they eliminate the need to characterize the heptane plus fraction. They also eliminated the corrections needed for presence of acid gases, Eq. (23) through (25).

9 PREDICTING COMPRESSIBILITY FACTOR 719 The gas compressibility factor (Z) is computed from DK correlation using reduced pressure (P r ) and reduced temperature (T r ) as follows: Z ¼ 1 þ A 1 þ A 2 =Tr þ A 3 =Tr 3 þ A 4 =Tr 4 þ A 5 =Tr 5 rr þ A 6 þ A 7 =Tr þ A g =Tr 2 r 2 r A 9 A 7 =Tr þ A g =Tr 2 r 5 r þ A 10 1 þ A 11 r 2 r r 2 r =Tr 3 exp A11 r 2 r ð30þ Where r r ¼ 0:27 ½P r =ZT r Š ð31þ The constants A 1 through A 11 in Eq. (30) are as follows: A 1 ¼ A 2 ¼ A 3 ¼ A 4 ¼ A 5 ¼ A 6 ¼ A 7 ¼ A 8 ¼ A 9 ¼ A 10 ¼ A 11 ¼ Because the gas compressibility factor appears on both sides of DK s correlation, Eq. (30), an iteration solution is necessary. Newton Raphson method is used which has the following iteration formula: Z nþ1 ¼ Z n ðf z =f 0 z Þ ð32þ Where Z n+1 and Z n are the new and old values of gas compressibility factors, f z is the function described in Eq. (30), and fz 0 is its derivative. Calculating Gas Compressibility Factor When Composition Is Unknown When gas composition is not available, the compressibility factor is computed via estimating the critical properties from gravity correlations. In this section, the accuracy with which gas gravity correlations, Eq. (1) through (6), reproduced the pseudo critical properties is evaluated. Although Standing s gas gravity correlations, Eqs. (1) and (2) were prepared to estimate critical properties of sweet low molecular gases, it is important to know the magnitude of the error that results from using that correlation. The accuracy of the gas gravity correlations developed by Sutton, Eqs. (3) and (4), and Elsharkawy et al. given in Eqs. (5) and (6) is also studied in this section.

10 720 ELSHARKAWY AND ELKAMEL RESULTS AND DISCUSSION The accuracy of four different methods for the calculation of gas compressibility factor for sour gases is discussed in this section. The first method is Kay s mixing rule with Wichert Aziz correction for the presence of non-hydrocarbons. The second is SSBV-Wichert and Aziz. The third is Corredor et al. method. The last method is Piper et al. Table 3 shows the accuracy of these methods. Piper et al. and Corridor et al. have the best accuracy. Both of these methods account for the presence of heptane plus and non-hydrocarbons. Piper et al. methods has average absolute deviation (AAD) of 1.21% and standard deviation (SD) of 1.92% and coefficient of correlation (R) of 99.10%. SSBV-Whichert and Aziz shows the highest errors and the lowest correlation coefficient. Figure 1 through 4 show the error distribution for the four methods considered in this study. Kay Wichert and Aziz method, Figure 1, Table 3. Data Accuracy of Calculating Z-factor for Sour Gases Using Compositional Method ARE AAD SD R Kay-Wichert and Aziz SSVB-Wichert and Aziz Corredor et al Piper et al Figure 1. Histogram of Er% with normal curve (Kay-WA).

11 PREDICTING COMPRESSIBILITY FACTOR 721 Figure 2. Histogram of Er% with normal curve (SBV-KA). Figure 3. Histogram of Er% with normal curve (Piper). Corredor et al. method, Figure 2, and Piper et al. methods, Figure 4 have comparable error distribution. However, Piper et al. method has the smallest error range and the highest frequency of zero error. SSBV-Wichert and Aziz method, Figure 2 has a wider error range and smaller frequency of error distribution around zero error line comparing to the other methods. The accuracy of calculating gas compressibility factor for sour gases using gas gravity when gas composition is unknown is shown in Table 4. Standing gas gravity correlation, Eqs. (1) and (2) has an average absolute deviation (AAD) of 3.50% and standard deviation (SD) of 6.78%. Sutton gas gravity correlation, Eqs. (3) and (4), has AAD of 3.47% and SD of Elsharkawy et al. gas gravity correlation, Eqs. (5) and (6) shows AAD

12 722 ELSHARKAWY AND ELKAMEL Figure 4. Histogram of error with normal curve (corredore). Table 4. Equation Accuracy of Calculating Z-Factor for Sour Gases Using Gas Gravity Method ARE AAD SD R Standing Sutton Elsharkawy et al Current study ARE: Average relative error %. AAD: Average absolute deviation %. SD: Standard deviation %. R: Coefficient of correlation. of 3.48% and SD of 7.30%. All of these gas gravity correlations have similar correlation coefficients. The reason for the low accuracy of these correlations is that Standing s gas gravity correlation was prepared for sweet gases. Sutton gas gravity correlation was prepared for heavy gases rich in C 7+ with minor amounts of hydrocarbons. The latter gas gravity correlation is applicable for gases that have no hydrogen sulfide and with a nitrogen content less than 12% and a CO 2 content less than 3% (Lee and Wattenberger, 1996). Elsharkawy et al. gas gravity correlation was prepared from data on gas condensate that has a significant portion of hydrogen sulfide and carbon dioxide, however, the concentration of the acid gases is not comparable with the sour gases used in this paper.

13 PREDICTING COMPRESSIBILITY FACTOR 723 New Gas Gravity Correlation One of the objectives of this study is to start the development of a new correlation to estimate pseudo critical properties from gas gravity for sour gas when composition is not available. Using large data bank of sour gas system, inferred pseudo critical pressures and temperatures are calculated from experimentally measured gas compressibility factors using DK equations. The first attempt was to correlate these inferred pseudo critical values to gas gravity for sour gases. Figure 5 shows that pseudo-critical pressures of sour gases are not strongly correlated to total gas gravity. In order to improve the correlations it was attempt to study the effect of non-hydrocarbon component on pseudo-critical properties. Figure 6 shows that pseudo-critical pressures are highly correlated to the percentage of non-hydrocarbon gases. The percentage of non-hydrocarbon component is expressed as molecular weight of non-hydrocarbon components divided by the total molecular weight of the gas. This percentage can also be related to non-hydrocarbon gas gravity (g 2 ) divided by total gas gravity (g g ). Pseudo critical temperature, however, is strongly dependent on total gas gravity, Figure 7. Therefore, it was found that best correlation of pseudo-critical properties to gas gravity can be achieved by considering both the hydrocarbon and non-hydrocarbon portions of gas gravity as follows: Pc ¼ 193: :347 g g þ 217:144 g 1 =g g þ 1060:349 g 2 =g g þ 344:573 ðg 1 =g g Þ 2 60:591 ðg 2 =g g Þ 2 ð33þ Figure 5. Pseudo-critical pressure as a function of total gas gravity for sour gases.

14 724 ELSHARKAWY AND ELKAMEL Figure 6. Pseudo-critical pressure as a function of non-hydrocarbon to total gas gravity for sour gases. Figure 7. Pseudo-critical temperature as a function of total sour gas gravity. Tc ¼ 195: :121 g g þ 25:855 g 1 =g g 6:421 g 2 =g g þ 9:022 ðg 1 =g g Þ 2 þ 163:247 ðg 2 =g g Þ 2 ð34þ The new gas gravity correlation presented in this study has smaller error range than the other correlations. Correlating critical properties to the amount of hydrocarbon and non-hydrocarbon gases, Eqs. (33) and (34), improves the accuracy of the proposed correlation. Among the gas gravity correlations considered in this study, the new correlation shows the smallest

15 PREDICTING COMPRESSIBILITY FACTOR 725 AAD (1.69%), the least SD (3.22%), and the highest correlation coefficient (97.66%). However, the standard deviation is still high. Figures 8 10 show the absolute error percentage in estimating gas compressibility factor from gas gravity correlations is highly dependent on the amount of CO 2 and H 2 Spresent in the sour gas. An error as high as 50% in gas compressibility factor occurs if these gas gravity correlations are used to estimate the gas compressibility for sour gases. Figure 11 shows first smaller error level in calculating gas compressibility factor using the new gas gravity correlation than the other correlations. Second, the error is not dependent on the amount of CO 2 and H 2 Spresent in the sour gas. Figure 12 shows a crossplot of measured and calculated gas compressibility factor Figure 8. Error % in z-factor using Standing gas gravity equation. Figure 9. Error % in z-factor using Sutton gas gravity equation.

16 726 ELSHARKAWY AND ELKAMEL Figure 10. Error % in z-factor using Elsharkawy et al. gas gravity equation. Figure 11. Error % in z-factor using new gas gravity equation. using the new gas gravity correlation for the sour gases used in this study. The figure illustrates that most of the data fall on the 45 parity line. Therefore, calculating the gas compressibility factor for sour gases from pseudo-critical pressure and temperature estimated from total gas gravity correlations has some limitations. The major limitation is in the process of correlating gas gravity to pseudo critical properties. For any gas, there could be an infinite number of hydrocarbon and other non-hydrocarbon combination. Each hydrocarbon and non-hydrocarbon component has a unique pseudo critical property. However, different mixtures can have different pseudo-critical properties and the same gas gravity. This is the reason why calculating gas compressibility factor using gas gravity is not as

17 PREDICTING COMPRESSIBILITY FACTOR 727 Figure 12. equation. Crossplot of measured and calculated z-factor using new gas gravity much accurate as calculating gas compressibility factor from composition. Correlating pseudo critical properties to hydrocarbon portion of gas gravity and non-hydrocarbon portion have resulted in little improvement of gas compressibility calculations. CONCLUSIONS In this paper, several methods of calculating sour gas compressibility factors were compared. Two classes of methods were considered: methods that are based on composition and those that are based on gas gravity alone. From the methods based on composition, Piper et al. (1992) and Corridor et al. (1993) showed the best accuracy and correlation coefficient. These methods account for the presence of heptane plus and non-hydrocarbons. Of the methods based on gas gravity Sutton and Elsharkawy et al., methods were the most accurate. The accuracy of these methods was, however, poorer than those methods based on composition. It was decided therefore to study the effect of the presence of non-hydrocarbons on accuracy. A plot of pseudo-critical pressure with both gas gravity and non-hydrocarbon gas gravity was evaluated. It was found that while the correlation with gas gravity is weak, that with the non-hydrocarbon gas gravity is strong with a correlation coefficient more that The correlation of pseudo-critical temperature was rather indifferent to the presence of non-hydrocarbons. A new correlation was then proposed to account for the presence of

18 728 ELSHARKAWY AND ELKAMEL non-hydrocarbons without knowing the compositional details. This correlation is based on two descriptors: gravity of the gas and gravity of the non-hydrocarbon portion in the gas. The new correlation provided a good improvement over past gas gravity methods. Research is still going on to develop more improvement strategies. r r NOMENCLATURE Reduced density Wichert and Aziz pseudo-critical g g gas specific gravity, (air ¼ 1) g 1 Hydrocarbon gas specific gravity, (air ¼ 1) g 2 Non-hydrocarbon gas specific gravity, (air ¼ 1) A mole fraction (CO 2 +H 2 S) B mole fraction H 2 S AAPD Average absolute error E J Sutton SBV parameter, R/psia E K Sutton SBV parameter, R/psia 0.5 ARE Average relative error F J Sutton adjustment parameter temperature adjustment parameter, R J SBV parameter, R/psia J 0 Sutton parameter, R/psia J inf Inferred value of J parameter, R/psia K SBV parameter, R/psia 0.5 K 0 Sutton parameter, R/psia 0.5 K inf Inferred value of K parameter, R/psia 0.5 M Molecular weight, lb-mole M C7þ molar mass of heptane plus fraction, lb-mole P pressure, psia p c critical pressure, psia P pc pseudo-critical pressure, psia P pr pseudo-reduced pressure R correlation coefficient SD standard deviation T temperature, R T b normal boiling point temperature, R T c critical temperature, R T pc pseudo-critical temperature, R T pr pseudo-reduced temperature y C7þ mole fraction of heptane plus fraction y i mole fraction of component, i

19 PREDICTING COMPRESSIBILITY FACTOR 729 y i Z mole fraction of the ith component gas compressibility factor ACKNOWLEDGMENT The first author thanks the Kuwait Foundation for the Advancement of Science (KFAS) for providing financial support for this study, research grant No REFERENCES Ahmed, T Hydrocarbon Phase Behavior, Gulf publishing Co. Brill, J.P. and Beggs, H.D Two-phase flow in pipes, INTERCOMP Course, The Huge. Buxton, T.S. and Campbell, J.M Compressibility factors for lean natural gas carbon dioxide mixtures at high pressures, SPEJ, March, Corredor, J.H., Piper, L.D. and McCain, W.D., Jr Compressibility Factors for Naturally Occurring Petroleum Gases, Paper SPE presented at the SPE Annual Technical Meeting and Exhibition, Washington D.C., Oct Dranchk, P.M. and Abou-Kasem, J.H Calculation of Z Factors for Natural Gases Using Equations of State. J. Cdn. Pet. Tech. (July Sept.), Dranchk, P.M., Purvis, R.A. and Robinson, D.B Computer Calculation of Natural Gas compressibility Factors Using the Standing and Katz correlations, Institute of Petroleum Technical Series, No. IP74-008, Elsharkawy, A.M. and Foda, S.G EOS simulation and GRNN modeling of the constant volume depletion behavior of gas condensate reservoirs. Energy and Fuels 12: Elsharkawy, A.M., Hashem, Y.Kh. and Alikhan, A.A Compressibility factor for gas condensate reservoirs, Paper SPE presented at the SPE 2000 Permian Basin Oil and Gas Recover Conference held in Midland, TX, March. Hall, K.R. and Yaborough, L A New Equation of State for Z-Factor Calculations. Oil and Gas J. (June 18) 82 85, 90, 92. Hankinson, R.W., Thomas, L.K. and Philips, K.A Predict Natural Gas Properties. Hydrocarbon Processing, April,

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