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

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Compressibility Factors for Lean Natural Gas-Carbon Dioxide Mixtures at High Pressure 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. ABSTRACT the principle of corresponding states (PCS) are Downloaded from http://onepetro.org/spejournal/article-pdf/7/01/80/2152684/spe-1590-pa.pdf by guest on 03 October 2021 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 by guest on 03 October 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
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