Compressibility Factors for Lean Natural Gas-Carbon Dioxide Mixtures at High Pressure

PAN AMERICAN PETROLEUM CORP. THOMASS.BUXTON TULSA, OKLA. JOHN M. CAMPBELL THE U. OF OKLAHOMA MEMBERS AIME NORMAN, OKLA. Downloaded from http://onepetro.org/spejournal/article-pdf/7/01/80/2152684/spe-1590-pa.pdf/1 by guest on 30 September 2021 ABSTRACT the principle of corresponding states (PCS) are presently available for reliably predicting the The most widely used methods of predicting the compressibility factor of lean natural gas, i.e., volumetric properties of gas are based on the natural gas with low concentrations of hydrocarbons principle of corresponding states, which asserts heavier than methane. When these same correlations that the compressibility factor is a universal are used for mixtures of natural gas and carbon function of reduced temperature and pressure. dioxide, large deviations between actual and Previous studies have shown that the acentric predicted compressibility factors are observed. factor, as proposed by Pitzer, 1 is an important This study was undertaken to provide a means for addition to reduced pressure and reduced temper­ accurately predicting the compressibility factor ature as factors affecting the compressibility for such mixtures. factor. Results of this study indicate that, if the In the past, two avenues of approach have been pseudocritical temperature and pressure used to employed to extend the applicability of the PCS. determine the reduced conditions are adequately The first has been to introduce additional param­ predicted, characterization of natural gas-carbon eters. The second has been to develop combination dioxide mixtures with the acentric factor will rules for predicting pseudocritical constants allow reliable determination of the compressibility which do not suffer from the limitations of the factor. commonly used molal average constants. In this Comparisons of predicted and experimental study, both of these approaches have been con­ compressibility factors have shown that the pseudo­ sidered and employed to arri ve at a method for critical constant rules of Stewart, Burkhardt and predicting the compressibility factor of mixtures Voo 2 are satisfactory for hydrocarbon mixtures. of hydrocarbons and carbon dioxide. However, these rules fail to predict the pseduo­ critical constants for hydrocarbon-carbon dioxide SELECTION OF A TIIIRD PARAMETER mixtures. Based on graphically determined Failure of the original PCS to predict the pseudocritical temperatures for binary hydrocarbon­ compressibility factor for all pure gases, regard­ carbon dioxide mixtures, a correlation which gives less of their mass, shape or polar moment, has the required correction to the Stewart, Burkhardt led to the introduction of additional parameters and Voo rules was prepared and a compressibility into the PCS. Parameters have been introduced factor prediction technique was proposed. To test to correct for quantum deviations, 3-5 non-spherical the proposed technique,' compressibility factors or globular shapes 6-9 and for polar moments. 8 - 12 for five mixtures of methane, carbon dioxide and In addition to these parameters which are based either et hane or propane were experimentally on some microscopic property and intended to determined at 100, 130 and 160F and pressures up correct for some specific cause of deviation, to 7,026 psia. The predicted and experimental more general parameters based on some bulk compressibility factors for these five mixtures property have also been introduced. 1, 13-16 To had an average absolute deviation of 0.55 percent. use additional parameters to correct for each of the possible causes of deviation among the INTRODUCTION individual constituents of a gas mixture would Two-parameter generalized correlations based on require a rather complex form of the PCS. To maintain the PCS in as simple a form as possible, Original manuscript received in Society of Petroleum it is more desirable to ha ve a single third parameter Engineers office Aug. 8, 1966. Revised manuscript received Feb. 16, 1967. Paper (SPE 1590) was presented at SPE 41st which is based on some bulk property influenced Annual Fall Meeting held in Dallas, Tex., Oct. 2-5, 1966. by several of the factors causing deviations. © Copyright 1967 American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. The third parameter selected for use in this lReferences given at end of paper. study is a factor originally proposed by Pitzer. 9

80 SOCIETY OF PETROLEUM ENGINEERS JOURNAL Pitzer has stated that the effect of non-spherical, used to combine the pure component intermolecular globular or polar molecules on the forces existing parameters to obtain the parameters for the between molecules are evidenced in the slope of mixtures. Sarem 14 showed that, by varying the the vapor pressure vs temperature curve. For rules for combining the intermolecular parameters, this reason, Pitzer used the increase in slope over differen t pseudocritical constan t prediction rules that of a simple fluid (the inert gases krypton may be obtained. As in the case of the pseudo­ and xenon) to obtain a third parameter UJ which critical rules obtained from two parameter he called the acentric factor. equations-of-state, it is impossible to choose one Prausnitz and Gunn (7 and Satter 18 used a molal of these sets of rules over another on a theoretical average acentric factor UJ' for mixtures. The basis. compressibility factor was computed with UJ' by Stewart, Burkhardt and Voo (SBV), using the means of pseudocritical compressibility factor as a third parameter and 21 diffe.ren t combination rules for z :zo+W'z' ...... (1) predicting pseudocritical constants, tested 23 different binary systems. They concluded the where z 0 and z' are each functions of Tr and Pro most satisfactory pseudocriticals are given by

Charts of zO and z' were prepared by Pitzer. 19 Downloaded from http://onepetro.org/spejournal/article-pdf/7/01/80/2152684/spe-1590-pa.pdf/1 by guest on 30 September 2021 These charts were extended by Satter for values of Tr = 1.0 to 2.0 from the termination of Pitzer's charts at P = 9.0 to a P of 14.0. The values of Tpc I Tc 2 Tc 1;:]2 2 r r J=-' :-~Yi - .+-~Yi -, .. (2) the acentric factor and the ,critical temperatures Ppc 3 I ()Pc I 3 I (Pel ) and pressures of the principle constituents of ~ natural gas are given in Ref. 18.

PSEUDOCRITICAL CONSTANTS ... (3) EXISTING COMBINATION RULES To obtain the pseudoreduced temperature and K2 pressure to be used for a particular ga s mixture, Tpc:' J' ...... (4) it is necessary to predict the pseudo critical temperature and pressure of the mixture. The best known pseudocritical constant prediction rules Tpc are those proposed by Kay.20 With Kay's rules, Ppc:'J ...... (5) the pseudocritical constants for a mixture are the molal average of the critical constants for the components in the mixture. From an investigation They also found that deviations from experimental of his pseudocritical rules, Kay concluded that compressibility data are larger for those mixtures they are sufficiently accurate for the light hydro­ containing carbon dioxide or hydrogen sulfide. carbons for most engineering calculations. Satter compared 740 experimental compressibility However, he warned that, for mixtures whose factors with factors computed wi th the acen tric constituents differ greatly, values of the pseudo­ factors and four different sets of pseudocritical critical constants calculated in a similar manner rules. He found that the most satisfactory rules are likely to be in error. Considerable effort has for hydrocarbon binaries were those given by the been directed toward development of combination SBV rules. He also found that none of the methods rules which do not suffer from the limitations of he tested adequately predicted the pseudocritical the molal average rules of Kay. The most notable constants for hydrocarbon-carbon dioxide mixtures. combination rules developed have been based on The choice of the best pseudocritical constant either two constant equations-of-state or the virial rules must be based on comparison with experi­ approach to mixtures. mental data. No such comparisons have established The basic difference between the pseudocritical pseudocritical rules for hydrocarbon-carbon combination rules obtained from two constant dioxide mixtures. equations-of-state lies in the different assumptions used to combine the pure component constants to GRAPHICALLY DETERMINED obtain the constants for the mixture. This is evident PSEUDOCRITICALS from the work of Joffe 21 who developed two To determine the effect of different components different sets of combining rules from the van der and component concentration on the pseudocritical Waals equation-of-state simply by changing the constants, an empirical method of determining method of calculating one of the constants for the pseudocritical constants was employed. The mixture. An analogous situation exists when procedure used was slightly different than that pseudocritical constant-prediction rules are of Kay, but the basic concept was the same. The developed from the virial approach to mixtures. pseudocri tical temperature controls the location of Development of pseudocritical constant rules using an isotherm on a z vs Ppr plot in a vertical direction, the virial approach is dependent upon methods and the pseudo critical pressure controls its spread

MARCH, 1967 81 in a horizontal direction. If a pseudocritical corresponding to the other values of Pr and plot temperature can be obtained which allows a pre­ the compressibility factors for these pressures. dicted minimum z value to match the experimental If they do not agree with the experimental curve, minimum z for a given isotherm, then the isotherm adjust the pseudocritical pressure to obtain the should be located in a vertical direction. If the best agreement for all of the points. high pressure part of this predicted isotherm can Pseudocritical constants were determined for be made to match experimental data by proper four binary hydrocarbon-carbon dioxide mixtures selection of the pseudocritical pressure, then the using the experimental CH4-C02 data of Reamer, proper horizontal spread should be established. Olds, Sage and Lacey22 and the C 2H 6-C02, C3H S­ The net result should be a good fit between the CO 2 and C4H lO-C02 data of Sage and Lacey.23 predicted and experimental isotherm in both The results are tabulated in Table 1 along with directions. The procedure finally developed to the pseudo critical constants predicted by Kay's determine the pseudocritical constants may be rules and the SBV rules. The graphically determined summarized as follows. pseudocritical constants always fall below those calculated with Kay's or the SBV rules. Pseudocritical Temperature 1. Calculate a mixture acentric factor from PROPOSED COMPRESSIBILITY FACTOR PREDICTION METHOD Downloaded from http://onepetro.org/spejournal/article-pdf/7/01/80/2152684/spe-1590-pa.pdf/1 by guest on 30 September 2021 Wi=- 2:y'W' . (6) . I I A basic requirement of any combination rule is I that it must be able to account for not only the 2. Read the minimum value of z 0 for each Tr in forces operating between similar molecules but Pitzer's acentric factor charts. also those between dissimilar molecules. The fact 3. Read a value of z ' at the Tr and Pr correspond- that some of the mixing rules are satisfactory for ing to the minimum zO values. the prediction of the pseudocritical constants for 4. Calculate a z minimum from Eq. 1. hydrocarbon binaries is indicati ve that the methods of combining the pure component properties satis­ 5. Plot z min vs the corresponding Tr • 6. Read the minimum value of z for the mixture factorily account for the forces between dissimilar being studied for several isotherms of the experi­ hydrocarbon molecules. Between hydrocarbon mental data. molecules dispersion forces predominate, but 7. For each isotherm, locate the experimental between two carbon dioxide molecules the quad­ minimum z value on the plot discussed in Step 5. ruple force must also be considered. Between a Record the corresponding T r value. hydrocarbon and a carbon dioxide molecule, this S. By knowing the temperature of the experimental quadruple force is not present. The failure of the isotherm and the reduced temperature at which the mixing rules to predict the pseudocritical constants minimum z was found, the pseudocritical temper­ ature may be calculated from TABLE 1-PSEUDOCRITICAL CONSTANTS-BINARY MIXTURES Graphically T Determined Kay's Rules SBV Rules Tpc (7) =-Tr' ...... Mole Froc. Tpc Ppc Tpc Ppc Tpc Ppc Binary 1st Camp. ("F) (psia) (OF) (psia) CF) (psia) 900.0 CH4·C02 0.2035 500.4 965.0 506.0 502.0 982.7 P seudocritical Pressure 0.4055 455.5 882.7 464.8 909.6 459.0 898.7 0.6050 413.7 807.3 424.0 830.2 417.5 819.0 1. Plot the experimental compressibility factors, 0.8469 369.9 721.6 374.6 733.9 371.5 728.0 for an isotherm of the mixture being studied, vs C2H6·C02 0.1 541.0 pressure. 0.2 535.0 936.0 548.0 998.0 546.7 974.0 0.3 530.5 2. With the graphically determined pseudocritical 0.4 528.0 temperature, calculate a reduced temperature for 0.5 527.0 811.0 548.7 890.0 546.8 855.0 0.6 528.5 the isotherm. 0.7 532.0 3. Using w' of the mixture, the calculated reduced 0.8 537.0 739.0 549.3 781.0 548.2 761.0 temperature and Pitzer's charts, calculate a com­ 0.9 543.0 pressibility factor for several of the larger values C3Hg.C02 0.1 549.0 0.2 553.3 869.0 571.3 980.0 572.7 933.0 of Pr compatible with the experimental data. 0.3 561.0 4. Locate the compressibility factor for the 0.4 571.5 largest value of on the plot discussed in Step 0.5 584.5 722.0 606.7 844.0 609.3 783.0 Pr 0.6 598.5 1 and record the corresponding pressure. 0.7 615.0 5. With the value of Pr and the pressure read 0.8 632.0 648.0 642.1 708.0 643.9 675.0 0.9 649.0 from the plot, a value of the pseudocritical pressure nC4 H lO ·C02 0.1 559.5 may be calculated from 0.2 575.0 831.0 591.2 '167.0 596.8 899.0 0.3 593.0 0.4 614.0 P ...... (S) 0.5 637.5 664.0 656.5 811.0 665.5 727.9 Ppc =p; 0.6 661.0 0.7 686.0 0.8 711.0 584.0 721.7 655.0 727.4 611.0 6. Using this value of Ppc ' calculate the pressure 0.9 738.0

82 SOCIETY OF PETROLEUM ENGINEERS JOURNAL for hydrocarbon-carbon dioxide binaries is indicati ve factor for the SBV pseudocritical temperature by that the methods of combining the pure component treating the multi component mixture of hydrocarbons properties do not allow for the alteration in the and carbon dioxide as a binary of one hydrocarbon intermolecular forces for this type of system. and carbon dioxide. This requires characterization One possible method for developing a pseudo­ of the hydrocarbons present so that an appropriate critical combination rule satisfactory for binary may be used to obtain the adjusting factor. hydrocarbon-carbon dioxide systems would be to In extending the use of the acentric factor to alter the rules for combining pure component multicomponent mixtures, it was assumed that the constants to obtain constants for the mixtures. mixture may be characterized by a mixture acentric From our present state of knowledge, this would of factor determined from Eq. 6. Since this extension necessity have to be done empirically. Rather than worked well for hydrocarbon mixtures, it should be alter the basic rule for each system, the authors possible to characterize the hydrocarbons in the have chosen a somewhat different approach in this mixtures of hydrocarbons and carbon dioxide by a study. The following discusses how the mixture acentric factor. pseudocritical constants, obtained from a The deviation between the pseudocritical combination rule which satisfactorily predicts the temperatures determined from the SBV rules and constants for the ordinary system, may be modified those graphically determined is a result of the Downloaded from http://onepetro.org/spejournal/article-pdf/7/01/80/2152684/spe-1590-pa.pdf/1 by guest on 30 September 2021 to account for the presence of a diluent such as method used to combine pure component constants carbon dioxide. which failed to properly account for the variation Satter found that the SBV rules satisfactorily of the multipole component of the attractive forces. predicted the pseudocritical constants for This difference will hereafter be referred to as the hydrocarbon binaries, but failed to adequately multipole factor T. When T of Fig. 1 is cross-plotted predict them for hydrocarbon· carbon dioxide vs the hydrocarbon acentric factor with the binaries. This suggests that the SBV rules, along percentage carbon dioxide as a parameter, Figs. 2 with the acentric factor, may be used to predict the and 3 result. These figures may be used for compressibility factor for natural gases containing multicomponent mixtures by calculating the hydro­ only hydrocarbons, but that the rules would have carbon mixture acentric factor wh and reading T for to be modified in some way to be used for natural the appropriate percentage of carbon dioxide. The gases containing carbon dioxide. In Fig. 1, the difference between the SBV PER CENT pseudocritical temperatures and those graphically CARBON DIOXI DE .--r--,---,---,--.,---,----r-r---,----, determined is plotted vs the mole fraction of carbon + I- 30 t---t---t--j----t---t----i--+-+_---i---j 50 dioxide in the mixture. It may be seen that this difference is dependent upon the percentage carbon a::------40 dioxide and what hydrocarbons are in the mixture. ~ 30 ~ 20 25 With Fig. 1, a reliable prediction of the compressi­ .... 20 bility factor for hydrocarbon-carbon dioxide binaries w could be made. The pseudocritical temperature <5 15 ~ 10 10 could be calculated with the SBV rules and then ~ adjusted by subtracting the difference between the i 5 calculated and graphically determined pseudocritical O~~~~~--~~--~~--~-L~ temperatures for the appropriate binary. Since the .0 0.1 0.2 ACENTRIC FACTOR, W pseudocritical pressure is calculated from the pseudocritical temperature, an adjusted pseudo­ FIG. 2 - MULTIPOLE FACTOR VS HYDROCARBON critical pressure could also be obtained. While ACENTRIC FACTOR FOR PERCENTAGES OF this scheme is possible for binaries of carbon CARBON DIOXIDE UP TO 50 PERCENT. dioxide with methane, ethane, propane or n-butane, it would not be possibl,e for mixtures containing more than one hydrocarbon since the graphically determined pseudocritical constants would not be 30 --t-+---f---,--I 60 available. It is possible to obtain the adjusting I­ 70 a: o 80 t; 20 _-1-_...... "---1 ~ L> 30 ...."- w 25 o-' 90 ~ 20 ~ 10~-+-_h~t7~~~--+_---i~~~+____t w f­ '-'z 15 -' w :::> a: :;: w 10 .... 5 OL-~ __L-_L __ ~~ __~~ __~--' __~ 0 o 0.1 0.2 ACENTRIC FACTOR, W 10 30 40 50 60 70 80 90 100 PERCENT CARBON DIOXIDE FIG. 3 - MULTIPOLE FACTOR VS HYDROCARBON FIG. 1 - SBV T pc MINUS THE GRAPHICALLY ACENTRIC FACTOR FOR PERCENTAGES OF DETERMINED Tpc VS PERCENT CARBON DIOXIDE. CARBON DIOXIDE OVER 50 PERCENT.

MARCH, 1967 83 recommended procedure for predicting the The experimental equipment consisted of a compressibility factor for natural gases containing high - pressure section consisting of a variable carbon dioxide is then as follows. volume cell, mercury pump and constant-temperature 1. Calculate Tpc and Ppc from Eqs. 2 through 5. bath. The low-pressure section was comprised of 2. Determine tbe hydrocarbon mixture acentric the basic components of a standard Bean unit. The factor from high-pressure section was used to determine the pressure, volume and temperature relationship for Ly· W. a given sample. The sample was then expanded Wh = j J J,...... (9) into the low-pressure section where the number of L: Yj moles could be measured. This equipment and the j operating procedure used are detailed in Ref. 24. To check the accuracy of the experimental where the summations are for all hydrocarbon equipment, methane compressibility factors were constituents. measured for five isotherms and pres sures from 3. Read T from Fig. 2 for the appropriate hydro­ 1,026 to 7,026 psia. A comparison between these carbon acentric factor and percentage carbon values and compressibili ty factors obtained by dioxide. in terpolation of the methane data of Sage and Downloaded from http://onepetro.org/spejournal/article-pdf/7/01/80/2152684/spe-1590-pa.pdf/1 by guest on 30 September 2021 4. Calculate the adjusted pseudocritical con­ Lacey23 showed only two points deviating by more stants from than 0.5 percent (both occurred at 1,026 psia). These deviations were 0.55 and 0.65 percent. An (10) Tpc' =Tpc -T. error analysis made on the equipment indicates that a maximum error of 1.265 percent could be , T pc' (ll) P pc =Ppe X - • obtained for the compressibility factor at 1,026 T pc psia. The analysis showed that the error for the 5. Find the total mixture acentric factor from rest of the points should be less than 1.0 percent. Comparison of determined compressibility factors Eq. 6 where the summation is now taken over all with published data and the error analysis indicate components. that the equipment used might not be sufficiently 6. For the temperature and pressure of the accurate for a basic study of molecular in terac­ system, calculate reduced constants from tions, but is sufficiently accurate for the determination of useful volumetric data. T (12) Tpr = Tpc' . TABLE 3 - EXPERIMENTAL COMPRESSIBILITY FACTORS P (13) Mixture 1 Mixture 2 Ppr -p" = pr Pressure 100F 130F 160F 100F 130F 160F (psia) Z Z Z Z Z Z

7. With the reduced pseudocritical constants and 1,026 0.881 0.904 0.925 0.881 0.904 0.923 the mixture acentric factor, values of zO and z' may 1,526 0.844 0.875 0.899 0.838 0.872 0.899 2,026 0.818 0.855 0.885 0.812 0.850 0.882 be read from Pitzer's graphs or tables and the 2,526 0.811 0.851 0.879 0.804 0.844 0.877 compressibility factor calculated from Eq. 1. 3,026 0.822 0.857 0.885 0.815 0.851 0.883 3,526 0.846 0.877 0.901 0.838 0.870 0.899 4,026 0.878 0.904 0.923 0.871 0.897 0.921 EXPERIMENTAL DETERMINATION OF 4,526 0.917 0.937 0.954 0.910 0.930 0.949 COMPRESSIBILITY FACTORS 5,026 0.959 0.974 0.988 0.952 0.969 0.983 6,026 1.050 1.056 1.064 1.045 1.052 1.058 To provide experimental data for testing the 7,026 1.146 1.143 1. 143 1.140 1.139 1.139 ideas presented in the previous section, compres­ Mixture 3 Mixture 4 sibility factors were determined for five mixtures 1,026 0.865 0.889 0.910 0.813 0.851 0.874 1,526 0.814 0.852 0.882 0.750 0.799 0.834 of methane, carbon dioxide and ethane or propane 2,026 0.778 0.825 0.860 0.714 0.770 0.810 at 100, 130 and 160F and pressures up to 7,026 2,526 0.768 0.814 0.850 0.714 0.763 0.804 3,026 0.778 0.820 0.855 0.737 0.778 0.813 psia. Table 2 shows the chromatographic analysis 3,526 0.804 0.839 0.870 0.775 0.808 0.836 of these mixtures. The experimentally determined 4,026 0.838 0.867 0.893 0.821 0.845 0.867 compressibility factors are given in Table 3. 4,526 0.879 0.902 0.924 0.871 0.889 0.903 5,026 0.923 0.941 0.956 0.923 0.936 0.945 6,026 1.018 1.026 1.034 1.031 1.035 1.036 7,026 1.116 1.116 1.115 1.141 1.136 1.128

Mixture 5 1,026 0.793 0.830 0.861 TABLE 2 _ COMPOSITION OF EXPERIMENTAL MIXTURES IN 1,526 0.715 0.772 0.813 THIS STUDY (EXPRESSED AS MOLE FRACTION) 2,026 0.676 0.736 0.783 Components Mixture 1 Mixture 2 Mixture 3 Mixture 4 Mixture 5 2,526 0.678 0.730 0.775 0.748 0.786 CH 0.8977 0.8520 0.7458 0.7593 0.5841 3,026 0.708 4 3,526 0.751 0.782 0.881 0.0410 0.0474 0.2867 C2H6 0.0464 4,026 0.801 0.824 0.847 0.1316 4,526 0.855 0.871 0.889 C3HS 5,026 0.910 0.921 0.933 0.0053 0.0057 0.0052 N2 6,026 1.024 1.025 1.029 0.1091 0.1292 CO2 0.0506 0.1013 0.2016 7,026 1.138 1.131 1.127

84 SOCIETY OF PETROLEUM ENGINEERS JOURNAL COMPARISON OF EXPERIMENTAL AND develop a multi pole factor that provides a simple PREDICTED COMPRESSIBILITY FACTORS means of better characterizing the behavior of lean natural gas-carbon dioxide mixtures. The following By using the acentric factor as a third parameter was also concluded. and pseudocritical constants predicted with the 1. The third parameter proposed by Pitzer (the SBV rules, it was possible to predict the acentric factor) is a suitable third parameter for compressibili ty factor of the hydrocarbon-carbon hydrocarbon - carbon dioxide mixtures. If the dioxide systems experimentally determined with an pseudocritical constants are adequately predicted, average absolute deviation of 0.92 percent and a the acentric factor correlations will provide a maximum deviation of - 3.62 percent. The results reliable prediction of the compressibility factor. of comparing experimental and predicted 2. When the pseudo critical constants are deter­ compressibility factors indicate that carbon dioxide mined with the rules of Stewart, Burkhardt and Voo, will not cause large deviations when the the deviations which may be expected between the concentration of ethane and heavier hydrocarbons experimental and predicted compressibility factors is low and the carbon dioxide content is less than for hydrocarbon - carbon dioxide sy stems are 20 percent. Mixture 3 containing 20.16 percent dependent on both the carbon dioxide content and carbon dioxide and 4.74 percent ethane showed an

what hydrocarbons are in the mixture. Downloaded from http://onepetro.org/spejournal/article-pdf/7/01/80/2152684/spe-1590-pa.pdf/1 by guest on 30 September 2021 average absolute deviation of 1.22 percent. With 3. When the pseudocritical constants of Stewart, comparable ethane contents but lower carbon Burkhardt and Voo are adjusted with the multi pole dioxide contents, the deviations for Mixtures 1 and factor determined in this study, improved compres­ 2 were considerably lower. Mixture 4, with a carbon sibility factors for hydrocarbon -carbon dioxide dioxide content comparable to that of Mixture 2 but mixtures are obtained. For the five mixtures with the hydrocarbons heavier than methane considered in this study the average absolute increased to 13.16 percent, showed a slightly larger deviation was 0.55 percent. deviation. Mixture 5, containing 28.67 percent ethane and 12.92 percent carbon dioxide, showed NOMENCLATURE the largest deviation of any of the mixtures. The a verage absolute deviation in this case was 1.83 subscript denoting ith component percent with a maximum deviation of -3.62 percent. ] Tpc/ppc The compressibility factors for the hydrocarbon­ carbon dioxide mixtures of this study were also K Tpc/(ppc) 1/2 predicted using the SBV pseudocritical constants Pc critical pressure adjusted with the multi pole factor. Using T, the Ppc pseudocritical pressure average absolute deviation was reduced to 0.55 Ppr pseudoreduced pressure percent and the maximum deviation was reduced to P, reduced pressure -2.27 percent. The multipole factor for all the P ' = corrected pseudocritical pressure systems of this study was small. The maximum T pc for the fi ve mixtures wa s 4.0° for Mixture 5. Tc critical temperature Because of the small T corrections, the compressi­ Tpc pseudocritical temperature bility factors predicted with and without the Tpr ps eudoreduced temperature multipole factor were comparable. Except for Tr reduced temperature Mixture 1 where both methods satisfactorily T pc' = corrected pseudocritical temperature predicted the compressibility factor, the use of the multi pole factor alway s improved the compres sib iIi ty y mole fraction factor prediction. A summary of the results of z compressibility factor comparing predicted and experimental compres­ zO compressibility factor of a substance with sibilities is presented in Table 4 and example zero acentric factor calculations are in the Appendix. z' = slope of compressibility factor vs acentric factor curve at a given reduced tempera­ CONCLUSIONS ture and pressure As a result of this study, it was possible to w = Pitzer's acentric factor for a pure gas w acentric factor for a mixture wh = acentric factor for the hydrocarbons in a TABLE 4 _ COMPARISON OF DEVIATIONS OF PREDICTED mIxture COMPR ESSIBILITY F ACTORS FROM EXP ERIMENTAL VAL U ES T multi pole factor Temperature range for all mixtures was 100 to 160F. Pressure range for all mixtures was 1,026 to 7,026 psia. Average Absolute Deviation Max imum Devi at ion REFERENCES Prediction Method Prediction Method Number of SBV Rules SBV Rules 1. Pitzer, K. S.: J. Chem. Phys. (1939) Vol. 7, 583. Mixture Points SBV Rules with T SBV Rules with T 2. Stewart, W. F., Burkhardt, S. F. and Voo, D.: "Pre­ 1 33 0.46 0.67 + 1.08 + 1.32 2 33 0.46 0.17 - 0.85 - 0.42 diction of Pseudocritical Parameters for Mixtures", 3 33 1.22 0.49 - 1.98 - 0.95 Paper presented at the AIChE Meeting, Kansas City, 4 33 0.65 0.50 - 1.86 c 1.60 Mo. (1959). 5 33 1.83 0.91 - 3.62 - 2.27

MARCH, 1967 85 3. DeBoer, J. and Michels, A.: Physics (1938) Vol. 5, W'=0.0668 945. 4. Hirschfelder, J. 0., Curtiss, C. F. and Bird, R. B.: J::. Tc To 2 Molecular Theory Gases and Liquids, John Wiley .!. 2: . + ~ L -=. )'I.J2 0/ 3 i Y, ()Pc i 3 [ i Yj ( Pc i and Sons, Inc., New York (1954). 5. Leland, T. W., Kobayashi, Riki and Mueller, W. H.: AIChE J. (1961) Vol. 7, No.4, 535. 6. Kihara, T.: Rev. Mod. Phys. (1953) Vol. 25, 83l. 7. Corner, J.: Proc., Royal Society (1948) A192, 275. 8. Lyderson, A. L., Greenhorn, R. A. and Hougen, O. A.: "Generalized Thermodynamics Properties of Pure Fluids", U. of Wisconsin Eng. Exper. Station, Report No.4, Madison, Wise. (1955). Tpc 9. Pitzer, K. S.: J. Am. Chem. Soc. (1955) Vol. 77, 3427. Ppc=-J-= 736.2 PSIA 10. Rowlinson, J. S.: Liquids and Liquid Mixtures, Butterworth Scientific Publications, London (1959). 11. Hall, N. A. and Ibele, W. E.: Trans., ASME (1955) T :L=589.6= 1.374 1003. pr Tpc 429.1

12. Pople, J. A.: Proc., Royal Society (1954) A22l, 508. Downloaded from http://onepetro.org/spejournal/article-pdf/7/01/80/2152684/spe-1590-pa.pdf/1 by guest on 30 September 2021 13. Meissner, H. P. and Sefferian, R.: Chem. Eng. Prog. P 5026 (1951) Vol. 47, 579. Ppr = Ppc = 736.2= 6.827 14. Sarem, A. M.: "Investigation of the Densities of Coexisting Liquid and Vapor for Light Hydrocarbons From Pitzer's acentric factor charts: and Their Mixtures Near the Critical Region", PhD Dissertation, The U. of Oklahoma, Norman (1964). zo=0.9041 15. Cook, D. and Rowlinson, J. S.: Proc., Royal Society (1953) A2l9, 405. z'::.0.040 16. Riedel, L.: Chem. Ing. Tech. (1954) Vol. 26, 83. 17. Prausnitz, J. M. and Gunn, R. D.: AIChE J. (1958) Z =z.O+W'Z ' Vol. 4, No.4, 430. 18. Satter, Abdus and Campbell, J. M.: "Non-Ideal z =0.9067 Behavior of Gases and Their Mixtures", Soc. Pet. Eng. J. (Dec., 1963) 333-347. Calculation of z using T tel correct for CO 2: 19. Pitzer, K. S., Lippman, D. Z., Curl, R. F., Jr., Huggins, C. M. and Peterson, D. E.: J. Am. Chem. ?YjWj Soc. (1955) Vol. 77, 3433. Wh:~ 20. Kay, W. B.: Ind. Eng. Chem. (1936) Vol. 28, No.9, ~ Yj 1014. J 21. Joffe, J.: Ind. Eng. Chem. (1947) Vol. 39, No.7, 837. W 0.0433 22. Reamer, H. H., Olds, R. H., Sage, B. H. and Lacey, h = W. N.: Ind. Eng. Chem. (1944) Vol. 36, No.1, 88. From Fig. 2: 23. Sage, B. H. and Lacey, W. N.: Some Properties 0/ the Lighter Hydrocarbons, Hydrogen Sui/ide, and Carbon Dioxide, API, New York (1955).

24. Buxton, T. S.: "The Prediction of the Compressi­ Tpc'TO =. pc -4.0 = 425.1 R bility Factor for Lean Natural Gas-Carbon Dioxide Mixtures at High Pressures", PhD Dissertation, The Tpc' U. of Oklahoma, Norman (1965). Ppc': P x- =729.3 PSIA pc T pc APPENDIX 589.6 SAMPLE CALCULA nON USING THE Tpr: 425.1 = 1.387 PROPOSED PROCEDURE FOR PREDICTING COMPRESSIBILITY FACTORS 5026 Ppr = 723.3 = 6.892 MIXTURE 5 Mole Acentric ComQonent Fraction Factor {w) Tc (OR) Pc (psia) From Pitzer's acentric factor charts: CH 4 0.5841 0.013 343.3 673 Zo::' .9110 C 2H6 0.2867 0.105 549.7 708 CO 0.1292 0.225 547.6 1,073 2 z' =0.040 Pressure = 5,026 psia, temperature = 130F, experi­ mental z = 0.9209. z::.zo+W'z' Calculation of z without correcting for CO2: z = 0.9137 Wi =2: Y·Wj i ' *** 86 SOCIETY OF PETROLEUM ENGINEERS JOURNAL