Two-Phase Compressibility Factors for Retrograde Gases

Abstract

Summary The two-phase compressibility factor should he used in material-balancecalculations for rich-gas-condensate systems. This paper presents a correlationfor estimating this factor from field data. The correlation, which is based on67 fluid-depletion studies with C concentrations 4 mol% also applies to richgases with large amounts of CO, H S, and N. The correlation gives an averageerror of 3.66% but may result in larger errors for some rich gases. Introduction The Standing and Katz correlation for the gas compressibility factor isvalid only for dry-gas systems. Retrograde gas-condensate reservoirs experienceliquid fallout during depletion below the dewpoint. The two-phasecompressibility factor accounts for the formation of a liquid phase. Compressibility factors are used in material-balance equations to estimateinitial gas in place and reserves. Gas compressibility factors normally areused when a reservoir fluid-depletion study is not available. This practice isacceptable for retrograde gases if the gas condensate is lean; however, if thegas is rich, the reserves may he seriously underestimated if the two-phasecompressibility factor is not used. Fig. 1 shows the relationship of the compressibility factors of a rich gascondensate as a function of pressure. In this system, the two-phasecompressibility factor is uniformly less than the gas compressibility factor, and the two compressibility factors diverge as the pressure depletes. Systemsthat exist at higher pressures and temperatures may display a differentbehavior near the dewpoint. High-pressure regions have been observed in whichthe two-phase compressibility factor is greater than the gas compressibilityfactor. At low pressures, however, the two-phase compressibility factor is lessthan the gas compressibility factor and both diverge as the pressure decreases. For the case in Fig. 1, failure to use the pressure decreases. For the case in Fig. 1, failure to use the two-phase compressibility factor will cause p/z tobe too low, underestimating the initial gas in place and the reserves. This paper presents correlations that aid in determining when a two-phasecompressibility factor should be used and how to calculate this factor fromfield data. The correlation for the two-phase compressibility factor is basedon the pseudoreduced properties of the produced gas that can be calculated fromthe well-stream gas composition or the primary-separator gas specific gravitycorrected to well stream. The pseudoreduced pressure and pseudoreducedtemperature were calculated with the methods presented by Sutton. These methodsinclude correlations for calculating the pseudocritical properties of theheptane-plus fraction, adjustment of the pseudocritical properties of theheptane-plus fraction, adjustment of the pseudocritical properties forimpurities, and use of the pseudocritical properties for impurities, and use ofthe modified Stewart-Burlthardt-Voo mixing rules. Sutton also gives acorrelation for calculating pseudoreduced pressure and temperature from thewell-stream gas specific gravity. The correlation for determining when to usethe two-phase compressibility factor is based on the initial well-stream gasspecific gravity that can be calculated from surface separation data ifwell-stream-composition data are not available. The correlations were verifiedwith simulated production data. production data. Theory The material-balance equation for volumetric performance of a retrograde gasreservoir is derived easily from the real gas law. Initially the reservoircontains moles of gas: (1) Assuming that only gas is produced, a liquid phase condenses in thereservoir as the pressure depletes below the dewpoint, leaving moles of gas andliquid remaining in the reservoir: (2) Because the compressibility factor in Eq. 2 now applies to both gas andliquid, it is a two-phase compressibility factor. Dividing Eq. 2 by Eq. 1 gives, after substitution of Gp/G for andrearrangement, (3) a form of the material-balance equation similar to that given by Dake. Rearrangement and expansion of Eq. 2 to account for the volumes occupied bythe gas and liquid remaining in the reservoir give a relationship between thetwo-phase compressibility factor and the compressibility factors of theequilibrium gas and liquid, (4) Eq. 4, recently given by Vo et al, indicates that the two-phasecompressibility factor is a weighted average of the liquid and gascompressibility factors and a function of pressure, temperature, composition, and the amount of liquid remaining in the reservoir. Development of Correlations Our correlations were developed with data from 131 constant-volume depletionstudies performed on retrograde gas samples collected worldwide. Table I showsthe range of the data at dewpoint conditions. The data was partitioned on thebases of C concentrations and impurities (Table 2). A sensitivity study wasperformed with the final correlations that supported these partitions. The two-phase compressibility factor was correlated with pseudo-reducedpressure and pseudoreduced temperature. The pseudo-reduced pressure andpseudoreduced temperature. The compositions of the produced gas from each stepof the constant-volume depletion studies were used to calculate both thepseudoreduced pressure and temperature with the methods presented by Sutton. Fig. pressure and temperature with the methods presented by Sutton. Fig. 2shows the laboratory-determined two-phase compressibility factor for the entiredata set as a function of pseudoreduced pressure. Although the data spreads atlow pseudoreduced pressures, a general linear trend is apparent. Figs. 3 through 6 show similar plots for Data Sets 1 through 4. Thesefigures indicate that the data have two different trends as a result of CConcentration. The two-phase compressibility factor for the rich gases (Figs. 3and 5) shows a general linear trend with pseudoreduced pressure, while thetwo-phase compressibility factor for the lean gases (Figs. 4 and 6) shows acurvature similar to that of a single-phase gas. While not indicated in Figs. 2through 6, the two-phase compressibility factor was found to be a linearfunction of the inverse of pseudoreduced temperature. In fact, the variation inpseudoreduced temperature partially accounts for the spreading of data noted atlow values of pseudoreduced pressure. SPEFE P. 87