Unsteady-State Mechanical Formation Damage Modeling in Pressure-Sensitive Oil Reservoirs Near No-Flow Boundaries Using a Coupled-Integro-Differential-Perturbation Method

Identification of no-flow zones and mechanical formation damage management are essential for a successful exploratory and production campaign during the development of an oil field. This work develops a new unsteady-state two-dimensional (2-D) integro-differential solution for permeability loss monitoring in a well near an infinite sealing fault. The model presented in this study allows solving the nonlinear hydraulic diffusivity equation (NHDE) with the oil source term. The proper Green's Function (GF) for an infinite sealed barrier represents the well's instantaneous oil point-source/sink effect. Based on image method (IM), the pressure field for the constant permeability solution is given by the sum of two exponential integral functions Ei(tD). However, this solution does not consider the nonlinear effect caused by pressure-sensitive permeability loss. A new deviation factor ξ(p) is derived and coupled to an asymptotic first-order series expansion to deal with this phenomenon. The model also allows for evaluating the oil flow rate influence on the permeability loss during the well-reservoir production curve. Sensitivity analysis investigates the parameters that highly influence the diffusivity deviation factor. Pressure and permeability input data were obtained through a uni-axial test performed in two sandstone layers of the same reservoir rock in an offshore field in Brazil. The analytical solution addressed in this paper was calibrated by a porous media oil flow simulator named IMEX®, broadly used in reservoir engineering works, and the results were accurate. The results present the instantaneous permeability decay effect by a deviation compared to the linear solution in a semi-log plot. The main advantages of the proposed solution are the accuracy, availability of a comprehensive table of the GFs, ease of implementation, and computational cost savings. It constitutes a valuable and attractive mathematical tool to calibrate new models and support well-reservoir performance management.