Wellbore Solution for Mechanical Formation Damage Control During Oil Flow Through Infinite Permeability-Pressure-Sensitive Reservoirs

Abstract

ABSTRACT: Analytical solutions for the nonlinear hydraulic diffusivity equation (NHDE) to model the oil flow through permeability pressure-sensitive reservoirs still constitutes a challenge for formation evaluation engineers and geoscientists. This work develops analytically a new integro-differential solution for the NHDE for oil flow in permeability-pressure-sensitive reservoirs with instantaneous point-source. A set of pore pressure and permeability values for two sandstones samples in an offshore reservoir from Brazil is obtained experimentally using the geomechanical elastic parameters e.g. the Young’s modulus and Poisson’s ratio in addition to an uni-axial cell. These data are used as input in the computational code to run the analytical model and evaluate the reservoir permeability change. After these data input, the model runs and it allows users to compute the instantaneous reservoir permeability values over the well-reservoir life-cycle. The model calibration is performed with a numerical porous media oil flow simulator which is widely used in the reservoir engineering and formation evaluation literature. The accuracy, easy implementation and the low computational costs constitute the main advantages related to the developed model. Therewith it may be a useful and attractive mathematical tool to support the well-reservoir performance management. 1 INTRODUCTION Pressure transient analysis (PTA) has an important role in oil industry to provide several well-reservoir information, e.g., formation damage, permeability change, reservoir characterization and management, flow regimes identification, flow potential forecast and reservoir extension. In this context, 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. Several analytical solutions for the hydraulic diffusivity equation (HDE) in poro-elastic reservoirs with constant permeability are available in the petroleum engineering literature (Peres et al., 1989; Chin et al., 1998). Although, there are many lacks in the scientific literature to deal with the source term solution in the right hand side of the NHDE. Often, the classical solutions for these cases are developed through Fourier and Laplace transform or Boltzmann transformation (Fernandes, 2021a,b; Fernandes et al., 2021; Fernandes, 2022; Fernandes et al., 2022). Green’s functions (GF’s) are widely used in to solve partial differential equations related to transient phenomena related to heat transfer and flow through porous media problems.