Gas rate decline analysis for boundary-dominated flow with fractal reservoir properties under constant/variable bottom-hole pressure conditions

Current gas rate decline analysis methods in boundary-dominated flow (BDF) are mainly based on Arps' empirical decline models, or the liquid-based analytical models associating with pseudo-variables. Recently, Stumpf and Ayala (2016), and Wang and Ayala (2020) demonstrated that the decline exponents (b) used in Arps' hyperbolic model can be rigorously estimated in advance for both constant and variable conditions regardless of reservoir properties and before collecting any production data. In this paper, we further investigate the gas rate flow behavior for heterogeneous reservoir, which is characterized by fractal properties. The decline exponents (b) are thus re-derived based on the gas flow rate equation in BDF, and it is shown that the expression of decline exponents can be written in the same format with homogeneous reservoir by defining new productivity indexes. This allows for the application of the step-by-step explicit original-gas-in-place (OGIP) determination methods proposed by Stumpf and Ayala (2016), and Wang and Ayala (2020) in fractal radial flow. However, due to the heavily pressure depletion before BDF for linear flow, the average value of decline exponent (donated as bi) is not available any more. Therefore, our explicit OGIP determination method CANNOT be directly applied, which would lead to the underestimation of the true value if it is blindly used. Finally, several simulated cases are discussed to validate the capabilities of the methodology. The finding of this study can help for better understanding of the gas rate decline behavior in heterogeneous reservoirs.