ABSTRACT ABSTRACT
The stability of a hemispherical cavity, intended to model a perforation opening in the vicinity of a borehole, is analyzed for the case of poroelastic-plastic material behavior. Two plasticity models of differing complexity are considered, with the emphasis in either model being the use of strain softening to calculate inelastic stiffness. Sample results illustrate the effect of steady fluid flow on the response, and possible collapse, of the near perforation region.
INTRODUCTION
Analysis of the stability of subsurface formations in the vicinity of a borehole is a problem of continuing interest to the petroleum industry. With regard to such problems as the production of formation solids accompanying exploitation of a hydrocarbon reservoir, accurate prediction of the response of a formation to the local pore pressure/stress environment is a prerequisite to proper anticipation and/or prevention of costly downhole remedial actions. A knowledge of the local in-situ conditions promoting excessive formation deformation cannot only reduce the expense of subsequent production operations, but can also minimize the possibility of failure of any tubulars adjacent to the subject rock. The problem of near wellbore stability has been addressed by a number of authors using a variety of constitutive models to determine formation response and failure (Nordgren, 1977; Nguyen and Berest, 1977; Bratli and Risnes, 1981; Farenthold, 1984; Pattillo and Smith, 1985). The purpose of the current paper is to emphasize the use of strain softening considerations in such an analysis (Nguyen and Berest, 1977). Two poroelastic-plastic models are considered in this study. The models employ classical plasticity theory, with both associated and nonassociated flow rules, and are differentiated by the fact that one model is based on a Kohr-Coulomb criterion for the boundary between elastic and inelastic behavior and the other uses a quadratic yield surface (Smith and Cheatham, 1980; Smith and Pattillo, 1983), so as to account for material yield under near hydrostatic loadings. Following exposition of the models, the behavior of a strain softening material under pore pressure gradients in the vicinity of a perforation (modeled as a hemispherical cavity) is analyzed. Analysis of the nature of the inelastic region near the cavity provides a clear differentiation between the various hardness models, and may also be used to study the integrity of the cavity under variations in key parameters, in particular rock constitution and pore pressure.
PROBLEM STATEMENT
Consider a porous rock whose stress-strain behavior in an unconfined compression test may be approximated by the curves shown in Figure 1.
Fig. I - Idealized Stress-Strain Curves for Unconfined Compression(available in full paper)
Response of the specimen is characterized by three regions: (1) an elastic region; (2) a plastic region where the slope of the stress- strain curve may be positive (strain hardening) or negative (strain softening); and (3) a plastic region where the slope of the stress strain curve is zero (perfect plasticity). Nith particular regard to the strain softening portion of the material response curve, it is desired to investigate the effect of this type of material behavior on formation integrity in the vicinity of a perforation.