Coupled Integro-Differential-Assymptotic Solution for Permeabiliy Loss/Restoration Monitoring in Pressure-Sensitive Oil Reservoirs

Abstract

AbstractThe Nonlinear Hydraulic Diffusivity Equation (NHDE) models the isothermal single-phase Darcian flow through porous media considering the variation in the properties of the rock and the fluid present inside its pores. Typically, the dimensionless solution of the Linear Hydraulic Diffusivity Equation (LHDE) pD(rD, tD) for constant permeability oil flow in porous media is computed through Laplace and Fourier transform or Boltzmann transformation. For the constant permeability approach, the dimensionless general solution in cylindrical coordinates is expressed by the transcendental function exponential integral Ei(rD,tD). This work develops analytically a new coupled perturbative-integro-differential model to solve the NHDE for oil flow in a permeability-pressure-sensitive reservoir with source. The general solution is computed combining a first order asymptotic series expansion, Green's functions (GF's) and a Volterra's second kind integro-differential formulation. A set of pore pressure and permeability values from two sandstones samples of an offshore reservoir from Brazil is obtained experimentally using the geomechanical elastic parameters e.g. the Young's modulus and Poisson's ratio, and uni-axial cell data. These data are used as an input in the computational code to run the proposed model and evaluate the reservoir permeability change. After these data input, the model runs and allowing to compute the instantaneous reservoir permeability values over the well-reservoir life cycle. The model calibration is performed using a porous media oil flow simulator and the results are accurate.