Log-Log Analysis for Compaction Damage Evaluation Caused by Pores Collapse in Depletion-Dependent Oil Reservoirs

The impact of the mechanical formation damage in the production curve caused by the transient 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 anew transient 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 technique. The reservoir engineering literature shows that this first-order expansion represents 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. This deviation factor represents the permeability deviation during the drawdown and its partial restoration in the buildup period. A set of pressure and permeability field data is used as input to the computational code. The model calibration is performed by a porous media numerical oil flow simulator named CMG IMEX®, 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. 1 INTRODUCTION The mathematical modeling of the production loss caused by the reservoir compaction damage is essential to prevent premature well abandonment and field disinvestment (Fernandes, 2022; Fernandes and Braga, 2023). The Hydraulic Diffusivity Equation (HDE) models the isothermal, single, and multi-phase flow in porous media. It is derived from the coupling of Darcy's law, continuity equation, and porous media constitutive equations for rock and fluid properties (Matthews and Russell, 1967). Often in the petroleum engineering and dynamics of fluids in porous media scientific literature, the Linear Hydraulic Diffusivity Equation (LHDE) is solved through Laplace and Fourier transform or Boltzmann transformation, (Everdingen and Hurst, 1949; Matthews and Russell, 1967; Peres et al., 1989). In order to achieve cost savings and accurate model demand, analytical solutions for the Nonlinear Hydraulic Diffusivity Equation (NHDE) have been studied for many years by geoscientists, well-testing, and reservoir engineers.