Development of Two-Phase Compressibility Factor Correlations Using a Stochastic and Robust Gradient-Based Optimization Algorithm.

Abstract

Abstract Accurate estimation of two-phase compressibility factor is of great importance in predicting the performance of a gas condensate reservoir using the material balance approach. Over the years, several correlations for estimating gas compressibility factor have been developed. Some of these correlations are; the Standing and Katz, Rayes etal, Dranchuk and Abou-Kassem, Brill and Beggs’ and Hall-Yarborough’s correlations. However, these correlations have not been so successful in predicting the compressibility factor of gas reservoir fluids in the two-phase region (below dew point pressure) and this explains why the industry still relies on the expensive and time-consuming constant volume depletion (CVD) approach. Therefore, this paper presents two different correlations for estimating two-phase compressibility factor using stochastic and robust gradient-based Newton-Raphson optimization algorithm. The first correlation presents the two-phase Z-factor as a function of pseudo-reduced pressure, pseudo-reduced temperature and the specific gravity. The second correlation on the other hand presents the two-phase Z-factor as a function of the single-phase Z-factor (obtained using Standing and Katz approach). Both correlations were developed using over 50 constant volume depletion (CVD) data of reservoir fluid samples obtained from gas condensate reservoirs around the world. Furthermore, in order to develop these correlations, two different models were proposed and the heptane-plus (C7+) and acid gas fractions were accounted for using the Sutton’s and Lee Kesler correlations respectively. Moreover, using the expected values of the pseudo-reduced pressure, pseudo-reduced temperature, specific gravity and single-phase Z-factor (all obtained using appropriate probability distributions) as the input variables, the optimum values of the models’ fitting parameters that minimize the sum of squares of the errors (SSE) were obtained using the stochastic and robust optimization algorithm(an algorithm obtained from Taylor series expansion of the error function and implemented on Octave programming language for the purpose of this study). Finally, having developed the correlations using 70% of the available data, the performances of these correlations were evaluated using 30% of the available data and the results obtained shows that these correlations outperform other pre-existing correlations.