Analytical Model for Mechanical Formation Damage Control in Permeability-Hysteretic Oil Reservoirs

Abstract

Several analytical solutions for the hydraulic diffusivity equation (HDE) in poroelastic reservoirs with constantpermeability are available in the petroleum engineering literature. Although, the mathematical modeling of the permeabilitypressure-sensitive effect through the nonlinear hydraulic diffusivity equation (NHDE) still constitutes a challenge in the petroleumindustry. This work presents a new transient two-dimensional (2-D) analytical model for oil flow in an infinite permeability-hysteretic pressure-sensitive reservoir during alternating loading/unloading cycles. Two new hydraulic diffusivity deviator factorsare presented for drawdown and build-up periods in order to represent the permeability deviation during the drawdown and itspartial restoration in the build-up period. When the well is open to flow, the results show clearly the permeability deviationcompared to the linear solution (constant permeability), as well as, when the well is shut, the hysteresis-response is also noticedon the diagnostic plots. The model calibration is performed by a numerical oil flow simulator, widely used in the reservoirengineering literature. The accuracy, ease of implementation, and low computational costs constitute the main advantages relatedto the developed model. Therewith it may be a useful and attractive mathematical tool to support the well-reservoir performancemanagement.