A fully coupled geomechanics and fluid-flow model is developed to analyze pressure-transient problems in stress-sensitive reservoirs with nonlinear elastic and plastic constitutive behavior. For hydrocarbon reservoirs with stress-dependent permeability (stress-sensitive reservoirs), the coupled interaction between geomechanics and fluid production may significantly influence both the stress state and the fluid flow in the reservoir. Therefore, in general the coupling effect cannot be ignored when analyzing stress-sensitive reservoir problems. Detailed model formulations and the numerical implementation are presented. Practical applications illustrating various aspects of well behavior of stress-sensitive reservoirs are also demonstrated in this article.
Fluid production of a hydrocarbon reservoir generally results in a decrease of fluid pressure and an increase in effective overburden load on porous reservoir rock. As fluid production proceeds, the progressive increase in effective overburden load will in turn compact the reservoir rock and change the stress state in the reservoir. For reservoir rocks that are mechanically competent with fluid-flow properties such as permeability that are not influenced by effective stress changes or are solely dependent upon fluid pressure change under a constant overburden load, pressure transient problems can be properly analyzed by conventional methods (e.g., see Ref. 1). Reservoir rocks with fluid-flow characteristics (permeability) that are highly sensitive to effective stress changes and/or if they are of weak mechanical strength, giving rise to large rock deformation, are considered to be stress sensitive. In stress-sensitive reservoirs, interaction between reservoir effective stress change and fluid pressure change is significant. Consequently, coupling of geomechanics and fluid flow to analyze pressure transient problems for stress-sensitive reservoirs may be necessary.
Advances in digital computer technology have made the numerical analysis of fully coupled geomechanics and fluid flow problems fairly straightforward and economically attractive. In this article, a general numerical procedure for solving the coupled equations that govern isothermal single-phase fluid flow in a deformable porous medium is proposed. The permeability tensor used in the procedure may have any form of stress dependence. Similarly, the constitutive model used in the procedure for simulating the compaction behavior of the deformable porous medium may be any nonlinear elastic model and any elastoplastic model based on plasticity theory. The developed procedure can handle general two- and three-dimensional problems in both geometry and stress-strain conditions. The capability and accuracy of the procedure are verified by a number of problems with known analytical solutions.
Exact analytical solutions for nonlinear, coupled geomechanics and single-phase, fluid-flow problems in stress-sensitive reservoirs are in general not available, whereas a numerical procedure has the advantage of solving complex, coupled field problems in well test analysis with no difficulty. It is the objective of this study, using the numerical procedure developed, to investigate pressure transient problems in stress-sensitive reservoirs. Based on laboratory data and reservoir properties as input, a number of numerical well tests were performed for both high- and low-permeability stress-sensitive reservoirs under a wide range of operating conditions. These simulation results illustrate the effect of stress sensitivity on well-test curves. Based on the cases studied, quantitative relationships between reservoir characteristics and operating conditions and the severity of reservoir stress-sensitivity are established. The capability of the proposed procedure for analyzing stress-sensitive reservoirs is clearly demonstrated by these applications.
Virtually all studies concerning flow to a well (production/injection through a wellbore), particularly pressure-transient analysis, assume that it is sufficient to concentrate on pressure dependent properties (permeability, porosity, compressibility) to evaluate stress-sensitive reservoirs. Others usually invoke the linear theories of Biot and draw upon the solutions in linear coupled thermal elasticity to study problems in flow through porous media. But this recourse exists only if coupling terms are discarded and it is not clear when such terms may be discarded. Furthermore, important issues such as hysteresis, elastoplastic behavior, and the like remain to be addressed and under such circumstances it may not be appropriate to ignore coupling terms. The key difference between our work and that of others is that not only do we present a formulation to the problem under consideration but also present detailed calculations. It is emphasized that the observations we make in this regard concern the specific subject at hand and are not intended to cover issues beyond the scope of this study, for example, wellbore stability, drilling operations, hydraulic fracturing, etc.
Before presenting the details of our work, we present some clarifications so that the context of our work is understood, because we recognize that the subject of geomechanics encompasses a number of scales in both space and time. First, by "fully coupled" we imply that the numerical procedure outlined in this work is capable of solving a system of coupled equations simultaneously (equations of equilibrium and fluid flow) that are based on a Lagrangian description with a deformed mesh configuration that changes with time. It is not intended to imply Biot's formulation and the consequences that follow there from. Also, because of the scale of the problem (the area drained by a well and the duration of pressure tests), we do not examine nonreservoir regions (the overburden, sideburden, and underburden) in these simulations, although the formulation proposed is flexible enough to incorporate such regions when such domains are specified. We do, however, presume that the experimental data we need do take into account such effects. If we have to solve for pressure/stress distributions on the reservoir scale, nonreservoir regions would have to be included. Again, for the same reason, we begin with conditions that assume the reservoir is homogeneous and that uniform conditions prevail (stress and pressure distributions) at time equal to zero. If we are to look at heterogeneous systems (e.g., fractured reservoirs), our formulation is capable of incorporating such effects, provided that appropriate measurements are made. Our emphasis is on the influence of stress sensitivity on permeability and resulting consequences on well productivity—the issue most pertinent to reservoir engineers.