Poroelasticity in Hydraulic Fracturing Simulators

Abstract

Summary This paper describes a 2D hydraulic fracturing simulator that relies on Blot's theory of poroelasticity. The simulator is based on a poroelastic extension of the displacement-discontinuity (DD) method: it uses time and space distributions of impulse-point DD's and impulse-point sources. Because both solutions satisfy Blot's equations, the model fully accounts for the coupling between fluid diffusion and rock deformation. Thus, this model yields a rigorous determination of the influences of fluid leakoff on fracture width and of opening distribution on reservoir pore pressures. Some preliminary results relevant to hydraulic fracturing are then presented. Introduction Models for predicting fluid leakoff, width, and length of hydraulic fractures can be divided into three classes, depending on the complexity of the interaction between diffusion of reservoir/fracturing fluids and deformation of the rock. Class 1-Uncoupled Models. In most hydraulic fracturing models, the stress/ displacement analysis of the reservoir rock is based on the assumption that the rock is elastic. The fracture aperture can be computed from the elastic constants of the rock, in-situ stresses, and pressure distribution inside the fracture. Calculation of the fluid loss to the formation is generally based on Carter's ID diffusion solution, which predicts an instantaneous leakage inversely proportional to the square root of the wetting time. There is no direct interaction between the diffusion and deformation processes, except for a leakoff term in the mass-conservation equations of the fluid-flow analysis inside the fracture. Class 2-Partially Coupled Models. In these models, the stress/displacement analysis is still based on the assumptions of elasticity. The fluid loss is calculated exactly, within the framework of the linear diffusion law, by distributing fluid sources along the fracture. The effect of pore-pressure gradient (caused by leakoff) on rock deformation and therefore on fracture width is accounted for with the concept of back stress. Class 3-Fully Coupled Models. These models include the full range of coupled diffusion/deformation effects predicted by Biot's theory of poroelasticity: sensitivity of the volumetric response of the rock to the rate of loading, pore-pressure change induced by the variation of mean stress, and back-stress effects already accounted for in the Class 2 models. This paper presents the first phase of the implementation of an in-plane, 2D, fully coupled, poroelastic model that uses the boundary-element approach. The general problem is reduced to the investigation of a line fracture along which displacements and fluid flows are discontinuous. These discontinuities are modeled with impulse DD's and source discontinuities, respectively. The interest of the frilly coupled approach resides in the inclusion of the effects of the DD's (fracture aperture) on the stresses and fluid flow in the formation and the effect of the source discontinuities (fluid loss) on the fracture pressure and aperture profiles.