Summary
A fully coupled geomechanics and single-phase, fluid-flow model is developed to evaluate the combined effects of stress, fluid flow, and reservoir property changes on well responses in stress-sensitive reservoirs. In particular, we pay attention to the interpretation of pressure buildup tests and to changes in the production characteristics of wells. In general, for weak hydrocarbon reservoirs that exhibit nonlinear, elastic and plastic constitutive behaviors, and stress-dependent properties such as permeability and porosity, the physical effect contributed from geomechanics may not be ignored in well test analysis. The coupled interaction between geomechanics and reservoir fluid production markedly affects the stress state and reservoir properties. Because we are using a coupled, numerical model, we evaluate the consequences of using simplified relationships (e.g., permeability as a function of pressure). Numerical analyses are performed to quantitatively assess the impact of reservoir stress sensitivity on practical well test problems. The key variables investigated in the study, that are important in evaluating stress-sensitive reservoirs, include permeability, porosity, and constitutive behaviors of reservoir rock including hysteresis and loading conditions. The development of high-stress regions around wellbores and its consequences on well performance are considered. The numerical results from the study indicate that for analyzing highly stress-sensitive reservoirs, a fully coupled geomechanics and fluid-flow modeling approach is necessary and the developed model employed in this study provides such a tool.
Introduction
Conventional treatments of pressure-transient analysis of stress-sensitive reservoirs are based on either Biot's formulation or by a simple decoupling of the fluid-flow and geomechanical considerations by the pore-volume compressibility. Regardless of the approach taken, the final step involves the solution of a nonlinear differential equation with permeability and compressibility dependent on pressure. This step permits us to draw on analogous problems in linear thermoelasticity to obtain solutions for the pressure distribution. Implicit in all of these works is the assumption of a linear-elastic medium with no hysteresis. What is not recognized is that pure compaction and stress sensitivity may follow different constitutive relationships and further loading and unloading conditions dictate the manner in which pore volume and permeability changes occur. In situations where fluid-flow and geomechanical processes are decoupled, the consequences of decoupling and conditions under which it appears that decoupling is appropriate are never mentioned. Intuitively, the decoupling would not be appropriate if the assumption of a linear-elastic medium does not hold.
It is the objective of this paper to use a fully coupled geomechanical model to evaluate the interaction of the stress state and fluid flow on pressure behavior. This model permits us to address the issues we have raised in a comprehensive manner and thus presents a basis for the study of pressure-transient analysis in stress-sensitive reservoirs.
This paper is divided into four sections. First, we briefly outline the coupled field equations, discuss stress-strain relationships for linear-elastic and elastoplastic systems and describe numerical procedures for obtaining solutions of each system. Second, we examine the effect of rock compaction on well responses in reservoirs with constant permeability. Third, we discuss characterization of pressure tests for linear-elastic and elastoplastic systems. Various dependencies of permeability as a consequence of compaction noted in the literature are examined and analyzed. Fourth, we present a method to determine initial permeability from pressure data even though the permeability around the sandface may not recover as a consequence of hysteresis in stress-sensitive reservoirs. Fifth, we compare responses for coupled and uncoupled systems under the assumption that the rock obeys linear-elastic behaviors. The discussion that follows should serve as an underpinning for further studies.
The Model
A numerical model based on a finite-element method was developed for analyzing the coupled problem of isothermal, single-phase flow in a deformable porous medium. In the following subsections, the mathematical formulation, stress-strain relations, and the numerical procedure used for the model are briefly described. The detailed description of the developed model and its validation was presented in Ref. 1.
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