Mechanical formation damage control in permeability Biot’s effective stress-sensitive oil reservoirs with source/sink term

Geomechanical effects monitoring on reservoir rock and fluid properties response during the oil production curve are essential to improve oil recovery in a petroleum field. 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. In this context, mechanical formation damage control plays a key role in preventing early-permeability loss that may result in reservoir compaction and oil field disinvestments. This work develops a new analytical solution for the nonlinear hydraulic diffusivity equation (NHDE) with instantaneous point-source/sink effects in permeability 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.