Abstract

This paper reviews the role of coupled diffusion/ deformation phenomena in the various facets associated with hydraulic fracturing: breakdown, propagation and closure, and the assessment of these effects by means of Blot's linear theory of poroelasticity.

The poroelastic concepts are first recalled and emphasis is placed on the fundamental parameters needed. The importance of the coupling terms in the elasticity and diffusion equations is also stressed. The general equations are then simplified for two particular applications: one-dimensional column and particular applications: one-dimensional column and radial symmetry.

It is then shown that the reservoir history as well as the percolation occurring prior to hydraulic fracture initiation affects the breakdown pressure value. Poroelastic models also explain the decrease of propagation pressure with pore pressure, as has been often reported in the field. Finally, the fracture closure is considered and the coupling mechanisms clearly demonstrate the width decrease as well as the increase of shut-in pressure with time.

Introduction

There is growing evidence that coupled diffusion/ deformation phenomena play a significant role in hydraulic fracturing operations. Field evidence includes the variation of the breakdown pressure with pumping rate and/or fluid characteristics, influence pumping rate and/or fluid characteristics, influence of reservoir pressure on propagation pressure and the increase of the shut-in pressure during multiple pressurization cycles. pressurization cycles. The simplest consistent theory to account for coupled diffusion/deformation processes is the linear theory of poroelasticity introduced by Biot in 1941. To this date, however, and with due acknowlegment to the pioneering contribution of Geerstma and later of Cleary, the role of poroelasticity in hydraulic fracturing simulation and prediction is still in its infancy. Indeed, none of the simulators presently used by the Industry properly accounts for presently used by the Industry properly accounts for poroelastic effects; with little exception, poroelastic effects; with little exception, poroelastic effects have only been assessed by means of poroelastic effects have only been assessed by means of onedimensional models which, because of their character, do not display the full flavor of Blot's theory.

The goal of this paper is two-fold:

  1. provide an overall review of practically important conclusions that have been reached from the perspective of poroelasticity, and

  2. indicate possible weaknesses in poroelasticity, and

  3. indicate possible weaknesses in the models used and the need of more rigorous analyses.

An outline of the theory is presented, stressing in particular the fundamental material parameters needed. Poroelastic effects on the magnitude of breakdown, propagation and closure pressures are analyzed.

LINEAR POROELASTIC THEORY
Introduction

The presence of a freely moving fluid in a porous rock introduces a time-dependent character to the mechanical response of a rock which, for all practical purposes, does not show any sensitivity to the rate of purposes, does not show any sensitivity to the rate of loading. In others words, the rock will respond in a softer or a stiffer manner, depending on whether the rate of loading is slow or fast compared to the characteristic time that governs the processus of porepressure diffusion. The problem is further porepressure diffusion. The problem is further complicated by the fact that this diffusion is itself partially controlled by the deformation of the rock. partially controlled by the deformation of the rock. P. 629

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