52nd U.S. Rock Mechanics/Geomechanics Symposium,
2018. American Rock Mechanics Association
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ABSTRACT: Understanding subsurface stress modifications and the resulting permeability evolution in unconventional reservoirs, both functions of effective stress, is valuable when evaluating their technical and economic feasibility. As a part of this study, the variation of anisotropic Biot's coefficient under different boundary conditions was established, based on the assumption that different boundary conditions lead to different stress paths with reservoir depletion. First, unconstrained shrinkage/swelling experiment and pressure-dependent-permeability (PdK) experiments were carried out on San Juan coals under two boundary conditions, uniaxial strain and constant triaxial effective stress, where stresses and strain in vertical and horizontal directions were monitored with continued depletion. The experimental results were used to model the Biot's coefficient in vertical and horizontal directions. The two were found to be different. Furthermore, they varied differently for the two boundary conditions, clearly demonstrating the dependence of the depletion stress path on boundary condition selected. Hence, the results and analysis presented improve the capability of modeling work that requires information about the variation of effective stresses in reservoirs, such as, pressure-/stress-dependent permeability, hydro-/re- fracturing and failure analysis.
1. INTRODUCTION AND BACKGROUND
Predicting subsurface stress modification in reservoirs with gas depletion, injection and hydrofracturing is critical for production and failure modeling. Effective stress is central to the concept of flow, geomechanical and production modeling in both conventional and unconventional reservoirs. The earliest inception of the concept was by Terzaghi (1943) in his study of soil compaction. Since then, the concept has seen several key modifications and changes, from being a simple arithmetic difference between total stress and pore pressure (Terzaghi, 1943) (Eq. 1) to difference of total stress and some multiple of pore pressure (Biot, 1941) (Eq. 2), as shown below:
where, (inline equation) is the effective stress tensor, σij is the total stress tensor, p is the pore pressure, δij is the Kronecker delta symbol and α is the Biot's coefficient. After Biot (1941), most studies have concentrated on the definition of effective stress provided by Biot and establishing the nature of variation of the coefficient. Some of the notable ones are by Geertsma (1957), Nur and Byerlee (1971) (Eq. 3), Skempton (1961) (Eq. 4) and Suklje (1969) (Eq. 5), summarized as:
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