Analytical Model for Multifractured Systems in Liquid-Rich Shales with Pressure-Dependent Properties

摘要

One of today's challenges in reservoir management of liquid-rich shales is to accurately forecast production performance based on pressure/rate transient analyses. The need for large pressure gradients to produce from shale reservoirs through multifractured horizontal wells (MFHWs) may induce considerable changes in rock and fluid properties that can largely affect transient bottom-hole pressure response which can result in inaccurate predictions for well performance. Therefore, the assumption of constant properties in shale reservoirs may not be safe when modeling MFHW performance. This paper presents a nonlinear analytical MFHW performance model for single-phase systems based on the five-region model (Stalgorova and Mattar in SPE Reserv Eval Eng 16(03):246-256, 2013) that accounts for pressure-dependent rock and fluid properties in liquid-rich shales. Properties are assumed to vary exponentially with pressure. Because of this, the resulting nonlinear diffusivity equation is linearized by means of an exponential transformation. The nonlinear MFHW performance model is benchmarked against numerical simulation data for a number of case studies. The proposed analytical solution is able to accurately capture transient bottom-hole pressure response while delivering a highly accurate estimation of depletion time. In this study, it was found that nonlinear diffusion processes in liquid-rich shales, under the assumption of exponential changes in properties with pressure, are fully described by the porous medium equation (PME). The PME is presented along with a straightforward application to identify and forecast flow regimes in the reservoir (fast, normal or slow diffusion). Finally, a brief review on diagnostic plots for systems with pressure-dependent properties concludes this work.