Geomechanical-Integro-Differential Solution for Biot's Effective Stress-Sensitive Permeability Monitoring During the Well-Reservoir Drawdown

Abstract

ABSTRACT Incorporating geomechanics to flow models become the mathematical formulation regarding well-test and reservoir engineering more realistic because geomechanical parameters, e.g., in situ and overburden stress, as well as Biot's coefficient, play a fundamental role in pressure response. Hence, permeability stress-sensitive oil reservoirs are the scope of various research in the petroleum industry for minimizing formation damage during drilling, completion, and stimulation operations. This work develops a new analytical solution for the nonlinear hydraulic diffusivity equation (NHDE) with instantaneous point-source/sink effects in Biot's effective stress-sensitive oil reservoirs. The proposed model considers Biot's effective stress change in the permeability response, and a new deviation factor is derived from comparing the nonlinear effect concerning the constant permeability classical solution and a decoupled case available in the literature. The calibration methodology is performed using a numerical simulator named IMEX®, widely used in formation evaluation works, and the results presented high convergence. The findings of this study allowed us to notice the role of overburden stress, oil flow rate, deviation factor, and Biot's coefficient in permeability change during production in the diagnostic plots. Thereby, the modeling developed in this paper becomes a useful and attractive tool for predicting and monitoring permeability loss, oil flow rate specification, and reservoir history matching. INTRODUCTION Coupling geomechanics to pressure transient analysis (PTA) has been an important challenge for oil industry. This coupling allows providing the role of geomechanical parameters e.g., overburden stress and Biot's coefficient in permeability loss management. PTA is used for obtaining several well-reservoir information, e.g., formation damage, permeability change, reservoir characterization and management, flow regimes identification, flow potential forecast, and reservoir extension. Hence, minimizing the economic impairments caused by the permeability loss effect during the well-reservoir life-cycle is essential to prevent premature wells abandonment and field disinvestments (Fernandes, 2021a,b). In various formation evaluation and reservoir engineering works, analytical solutions for linear hydraulic diffusivity equation (LHE) using Boltzmann transformation, Laplace and Fourier transform have been extensively applied (Everdingen and Hurst, 1949). Nevertheless, solutions for nonlinear hydraulic diffusivity equation (NHDE) remain a challenge for scientists and engineers, mostly when it involves a source term modeling (Fernandes et al., 2021; Fernandes, 2022; Fernandes et al., 2022a,b,c,d,e).