Perturbative-Integro-Differential Solution for Permeability Hysteresis Modeling with Transient Compaction Effects Caused by Pores Collapse and Reservoir Depletion

Abstract

Abstract The impact of the mechanical formation damage in the production curve caused by the unsteady-state permeability hysteresis in pressure-sensitive reservoirs has an important role in oilfield developments. Hence, the petroleum industry has continuously sought new analytical approaches to provide adequate well-reservoir performance management and surveillance. This work proposes a new unsteady-state two-dimensional (2-D) analytical solution for modeling the oil flow in a permeability hysteretic pressure-dependent reservoir during alternating loading/unloading cycles. The nonlinear hydraulic diffusivity equation (NHDE) is perturbed through a first-order asymptotic series expansion. The reservoir engineering literature shows that this first-order expansion represents satisfactory the magnitude of the nonlinear phenomena regarding pressure-sensitive rock and fluid properties. A new hysteretic deviation factor is presented for flow (drawdown) and buildup periods. The model calibration is performed by a porous media numerical oil flow simulator named CMG IMEX, which is broadly used in formation evaluation and reservoir engineering literature. The results presented high accuracy for the drawdown and buildup of hysteretic and non-hysteretic cases. The practical uses of the model developed in this work are related to identifying flow regimes and hysteresis responses in pressure-sensitive reservoirs, estimating buildup pressure, and oil flow rates specification to prevent severe hysteretic behavior and history matching during reservoir surveillance.