Tese: Integro-Differential Solutions for Formation Mechanical Damage Control during Oil Flow in Permeability-Pressure-Sensitive Reservoirs
Aluno(a) : Fernando Bastos FernandesOrientador(a): Arthur Braga
Área de Concentração: Termociências
Data: 17/11/2021
Link para tese/dissertação: https://doi.org/10.17771/PUCRio.acad.57287
Resumo: The Nonlinear Hydraulic Diffusivity Equation (NHDE) models the single-phase flow of fluids in porous media considering the variation in the properties of the rock and the fluid present inside its pores. Often, the dimensionless linear solution for the flow of oil is computed using the Laplace and Fourier transform or Boltzmann transformation and provides the unsteady pressure field in Cartesian coordinates given by complementary error function erfc(xD, yD, tD) and in cylindrical coordinates described by the exponential integral function Ei(rD, tD). This work develops a new analytical model based on an integro-differential solution to predict the formation mechanical damage caused by the permeability loss during the well-reservoir life-cycle for several oil flow problems. The appropriate Green’s function (GF) to solve NHDE for each well-reservoir setting approached in this thesis is used. The general solution is implemented in the Matlab® and the mathematical model calibration will be carried out by comparing the solution obtained in this work to the porous media finite difference oil flow simulator named IMEX®. The general solution of the NHDE is computed by the sum of the linear solution (constant permeability) and the first order term of the asymptotic series expansion, composed of the nonlinearities present in the hydraulic diffusivity function η(p). The second term of asymptotic series expansion is obtained by solving a Volterra’s second kind integro- differential equation in Matlab® and the permeability functions for some types of reservoir rock will be obtained through laboratory correlations, generated from field data. The instantaneous permeability loss effect is clearly noticed in the diagnostic and specialized plots.