An Enhanced Nonlinear Analytical Model for Unconventional Multifractured Systems

Abstract One of today's challenges in reservoir management of liquid-rich shales is to forecast production performance based on rate/pressure transient analysis. The need of large pressure gradients to produce from shale reservoirs through multifractured horizontal wells (MFHW) can induce considerable changes in rock and fluid properties that can largely affect the bottom-hole pressure behavior with time and consequently the accuracy in the prediction of well performance. Therefore, the assumption of constant properties in shale reservoirs may not be safe when modeling MFHWs performance. This paper presents an analytical model for MFHW that accounts for pressure-dependent rock and fluid properties by the application of a modified pressure to the five-region model (Stalgorova and Mattar, 2013) which can be easily inverted to get an analytical solution to the nonlinear problem in terms of pressure. The validity of the proposed MFHW performance model is compared against data obtained from numerical simulation for several case studies. We observe that our analytical solution accurately captures bottom-hole pressure behavior and gives an excellent estimation of depletion time under a certain restriction. Furthermore, we find that nonlinear diffusion processes in liquid-rich shales, for which pressure-dependent rock and fluid properties are given in exponential form, can be fully described by using the Porous Medium Equation (PME). We present a straightforward application of the PME to predict flow regimes (fast diffusion, normal diffusion or slow diffusion) and the excess energy gained or required to keep a constant production rate in MFHW undergoing nonlinear diffusion; however, the application of the PME to the five-region model is not forthright and remains a matter of future development.