Depletion Performance of Volumetric High-Pressured Gas Reservoirs

Abstract

Summary A method to predict the percent recovery of volumetric, high-pressured gas reservoirs from the initial pressure to the abandonment pressure with only initial reservoir data is presented. This method can also be used with early-life production data to predict the initial gas in place. The method is based on an incremental solution to the general material-balance equation. All parameters in the material balance are pressure-dependent and are recalculated for every 100-psi [690-kPa] drop in reservoir pressure. Procedures were developed to calculate these parameters with correlations and data available in the literature. PV compressibilities, formation-water compressibilities, and gas compressibility factors were determined for temperatures and pressures ranging up to 400 degrees F and 20,000 psia [204 degrees C and 137.9 MPa], respectively. The pressure dependency of the PV compressibility and the formation-water compressibility is a unique feature of this model. The reservoir depletion model presented here was applied to a field example, as were three published techniques for determining reserves in abnormally pressured reservoirs. When predictions of initial gas in place were compared, the reservoir depletion model yielded a more accurate value than the other techniques. Introduction An accurate assessment of initial gas in place for a volumetric gas reservoir, made early in its production life, is crucial in making economic decisions regarding the reservoir's development. The most generally accepted method for the prediction of initial gas in place for volumetric gas reservoirs is a plot of the ratio of average reservoir pressure to the gas compressibility factor at that pressure, p/z, vs. the cumulative gas production, Gp. The plot is used to determine the initial gas in place by making a straight-line extrapolation to zero pressure. This method is derived from a material balance with the implied assumption that the gas compressibility is the sole drive mechanism of the reservoir. Initial-gas-in-place estimates determined from making a straightline extrapolation of early-life p/z-vs.-Gp data are generally not reliable for high-pressured reservoirs. A curved line rather than a straight line is usually seen on a p/z-vs.-Gp plot for a high-pressured reservoir. The curvature is thought to be caused by formation compaction, grain expansion, shale-water influx, and formation-water expansion. At high pressures, these mechanisms contribute significantly to gas production in addition to the gas compressibility. Linear extrapolation of the data during the early life of the reservoir yields an apparent initial gas in place that is much higher than the actual gas in place. At lower pressures, the gas compressibility becomes large enough to make the other mechanism mentioned above insignificant. Hence, an extrapolation of the late- life p/z-vs.-Gp data usually yields an accurate estimate of the initial gas in place. Several methods have been proposed to estimate the initial gas in place for abnormally pressured reservoirs. These methods do not neglect PV and formation-water compressibilities as the conventional p/z-vs.-Gp plot does; however, they do not account for the pressure dependence of these parameters over the producing life of the reservoir. The effect of shale-water influx is not considered in these methods, nor is it considered in the method presented in this paper. The technique presented in this work differs from previous methods by allowing the PV and formation-water compressibilities to be pressure-dependent. The computer program developed in this study calculates an estimate of the initial gas in place for each production data point. The program can also be used to generate profile of the percent recovery as a function of reservoir pressure. Reservoir Depletion Model The reservoir depletion model presented in this paper is based on the following equation, which is derived in the Appendix: .................. (1) Three assumptions are inherent in Eq. 1:a volumetric, single-phase gas reservoir;no interstitial water production; andthe PV compressibility, cf, remains constant over the pressure drop (pi - p). The formation-water two-phase FVF, Btw, is analogous to the oil two-phase FVF and can be computed with Eq. 3. Implicit in the change of Btw with pressure is the formation-water compressibility, cw. All terms in Eq. 1 are pressure-dependent. To allow for the pressure dependence of the PV compressibility in the application of Eq. 1, an incremental solution technique was developed in which very small, 100-psi [690-kPa], pressure decrements were used. The derivations of the equations used in the reservoir depletion model and a brief description of the computational procedure are given in the Appendix. Correlations and Data Used To Determine Parameters Pressure-dependent parameters for high-pressured gas reservoirs must be evaluated at temperatures up to 400 degrees F [204 degrees C] and pressures up to 20,000 psia [137.9 MPa]. Data and correlations from the literature were used to evaluate these parameters. Some of the data and correlations had to be extrapolated and/or interpolated to reach the desired pressures and/or temperatures. Gas FVF. The gas FVF can be computed by ......................(2) The technique proposed by Dranchuk et al. was used to determine the compressibility factor (z factor). They fitted the Benedict-Webb-Rubin equation of state to the z-factor surface defined by the Standing-Katz z-factor correlation. The nonlinear equation thus obtained is solved for the z factor as a function of reduced temperature and pressure by Newton-Raphson iteration. The range of validity for this technique is for reduced temperatures between 1.05 and 3.0 and for reduced pressures between 0.2 and 30. Formation-Water Two-Phase FVF. The formation-water two-phase FVF is determined with the expression ........................(3) Several steps are required to determine the solution gas/water ratio, Rsw. The Culberson-McKetta data for the solubility of methane in pure water are used for two pressure/temperature ranges:temperatures less than 160 degrees F [less than 71 degrees C] and pressures from 200 to 10,000 psia [1.4 to 68.9 MPa] andpressures less than 3,500 psia [less than 24.1 MPa] and temperatures from 100 to 340 degrees F [38 to 171 degrees C]. The data obtained by Eichelberger and Michels et al. are used to correct the solubility in pure water to that in brine for the above pressure/temperature ranges. A correlation by Blount and Prices is used to determine solubilities for pressures from 3,500 to 20,000 psia [24.1 to 137.9 MPa] and temperatures above 160 degrees F [71 degrees C]. SPERE P. 279^