Mechanical formation damage management and sealed boundaries identification in pressure-sensitive oil reservoirs with source effects

Abstract

Sealed zones identification is essential for a successful exploratory and production campaign during the development of an oil field. This work develops a new unsteady two-dimensional (2-D) integro-differential solution for permeability loss monitoring in a well near a sealant fault. The model presented in this study allows solving the nonlinear hydraulic diffusivity equation (NHDE) with an oil source term. The appropriate Green’s Function (GF) for a sealed barrier represents the instantaneous oil point-source in the well. Based on the well-known image method, the pressure field for the constant permeability solution is given by the sum of two exponential integral functions Ei(tD). Although, this solution does not consider the nonlinear effect caused by the permeability loss. Therewith, a new deviation factor is derived and coupled to a first-order series expansion to approach this phenomenon. The calibration of the proposed solution was carried out by a finite-difference-based simulator named IMEX® broadly used in the reservoir engineering works, and the results were accurate. The results clearly present the instantaneous permeability decay effect by a deviation when compared to the linear solution in a semi-log plot. The main advantages of the proposed solution are the accuracy, availability of a wide table of the GFs, ease of implementation, and computational cost savings. It constitutes a useful and attractive mathematical tool to calibrate new models and support the well-reservoir performance management.