Pressure Transient Analysis for Wellbore Mechanical Formation Damage Control Near No-Flow Boundaries Using an Asymptotic-Perturbation Method

Abstract

ABSTRACT Identifying no-flow boundary areas 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 sealing fault. The model presented in this study allows for solving the nonlinear hydraulic diffusivity equation (NHDE) with an oil source term. To approach this phenomenon, a new deviation factor is derived and coupled to a first-order series expansion. The proposed solution was calibrated by a finite-difference-based simulator named IMEX® broadly used in 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. Hence, the modeling developed in this paper becomes a useful and attractive tool for predicting and monitoring permeability loss, oil flow rate specification, reservoir history matching and calibrating new models. INTRODUCTION The nonlinear oil flow through porous media near sealed boundaries has a vital role in reservoir damage evaluation and engineering because various oil and gas pressure-sensitive formations are located near sealed zones world-wide (Fernandes, 2022; Fernandes et al., 2022a,b,c). Sealing faults may significantly impact the fluid flow patterns within a petroleum reservoir, (Kuchuk and Kabir, 1988; Kuchuk, 2009). Thereby, the knowledge of fault zones is essential for the economic viability analysis of exploration projects to prevent early depletion during the well-reservoir performance management, (Knipe et al., 1998; Nurafiqah et al., 2020). The mathematical modeling of the permeability pressure-dependent effect through the nonlinear hydraulic diffusivity equation (NHDE) with source term is still challenging in the petroleum industry. Therefore, accurate analytical models for the nonlinear source term have been extensively researched to save computational resources and calibrate new reservoir models. Image data (ID) and pressure transient analysis (PTA) constitute useful, practical tools to identify sealed zones, (Bengtson, 1981, 1982; Goetz, 1993; Adams and Dart, 1998). Therefore, new advances in seismic inversion algorithms and analytical models are sought for no-flow boundary region identification to provide adequate oilfield development, (Schuller and Vogele, 2019).