The poromechanics of naturally fractured rock formations: A finite element approach.

Abstract

The mathematical models have been cast into finite element form and verified against analytical solutions for one-dimensional consolidation and an inclined wellbore in a fully saturated single-porosity formation subjected to pore pressure and thermal gradients. The displacements, pressures in the two media and the temperature (in the non-isothermal case) are the primary unknowns in the finite element model. The saturations and capillary pressures are the secondary unknowns obtained from saturation-capillary pressure-temperature (in the non-isothermal case) relations. Also, the relative permeabilities, formation volume factors, gas-solubility ratios and oil volatility ratios are auxiliary unknowns estimated from relations involving the saturations and individual phase pressures. The resulting system of non-linear equations is solved using a direct solver and the stability is checked within each time-step. The finite element model has been extensively applied to the problem of an inclined wellbore and the sensitivity analyses carried out in this dissertation focus on the effect of thermal loading, heat transport by conduction and convection, secondary medium (representing the fractures) characteristics and, phase saturations on the pore pressures and effective stress distributions near the wellbore.

Land subsidence and fluctuation of water-table levels in the vicinity of a vertical well penetrating an aquifer have been studied employing a three-dimensional finite element model based on the mathematical equations developed herein. Two cases, one in which the aquifer is assumed to be fully saturated and, the other in which the aquifer is assumed to be unsaturated, are considered. The two-phase dual-porosity poroelastic model developed incorporating the black-oil model, has been modified in order to be applied to the unsaturated case. The effect of compliance and permeability of the secondary medium on the vertical displacements and water-table levels has been studied. (Abstract shortened by UMI.)

In this dissertation, an attempt has been made to develop a theoretically consistent model for fully-coupled multiphase flow in a fractured rock formation under non-isothermal conditions. The model has been systematically developed following a dual-porosity poromechanics approach wherein a fractured porous medium is envisaged as being composed of two distinct but overlapping media. The first medium represents the matrix and void spaces corresponding to matrix pores (primary porosity) whereas the second medium represents the fractures (secondary porosity), and a complementary solid part. Thus, the fluid flow and solid domains are both represented by two distinct but overlapping continua in this model with Barenblatt's original concept of two fluid pressures at a point and Aifantis's extension of Blot's poroelastic theory serving as basis. The intensity of interaction between the two media is controlled by fluid mass exchange rates, assumed to be proportional to the permeability of the primary medium and a quasi-steady pressure differential between the two media. Thermo-hydro-mechanical coupling has been incorporated by adopting the "single-temperature" approach wherein a single representative thermodynamic continuum is assumed to be sufficient to describe the temperature dependent response of a fractured formation. Further, the black-oil and limited compositional models have been incorporated to simulate fully-coupled oil and gas flow in a fractured formation under isothermal and non-isothermal conditions, respectively.