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

Abstract

ABSTRACT: Several analytical solutions for the hydraulic diffusivity equation (HDE) in poro-elastic reservoirs with constant permeability are available in the petroleum engineering literature. Although, the mathematical modeling of the permeability pressure-sensitive effect through the nonlinear hydraulic diffusivity equation (NHDE) still constitutes a challenge in the petroleum industry. 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 factors are presented for drawdown and build-up periods in order to represent the permeability deviation during the drawdown and its partial restoration in the build-up period. When the well is open to flow, the results show clearly the permeability deviation compared to the linear solution (constant permeability), as well as, when the well is shut, the hysteresis-response is also noticed on the diagnostic plots. The model calibration is performed by a numerical oil flow simulator, widely used in the reservoir engineering literature. The accuracy, ease implementation and the low computational costs constitute the main advantages related to the developed model. Therewith it may be a useful and attractive mathematical tool to support the well-reservoir performance management. 1 INTRODUCTION Minimizing the economic impairments caused by the permeability-hysteresis effect in pore pressure-dependent porous media during the alternating oil loading/unloading cycles is essential to prevent premature wells abandonment and field disinvestments. Extensive analytical solutions for the hydraulic diffusivity equation (HDE) in poro-elastic reservoirs with constant permeability are available in the literature, (Peres et al., 1989; Chin et al., 1998). Commonly the solutions developed for these cases are developed through Fourier and Laplace transform or Boltzmann transformation, (Fernandes, 2021a,b; Fernandes et al., 2021a; Fernandes, 2022; Fernandes et al., 2022). However, the mathematical modeling of the permeability pressure-dependent effect through the nonlinear hydraulic diffusivity equation (NHDE) with source term still constitutes a challenge for geoscientists, formation evaluation and reservoir engineers.