Coupling Fluid-Flow and Geomechanics in Dual-Porosity Modeling of Naturally Fractured Reservoirs
- Her-Yuan Chen (New Mexico Institute of Mining and Technology) | Lawrence W. Teufel (New Mexico Institute of Mining and Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Annual Technical Conference and Exhibition, 5-8 October, San Antonio, Texas
- Publication Date
- Document Type
- Conference Paper
- 1997. Society of Petroleum Engineers
- 1.2.3 Rock properties, 1.2.2 Geomechanics, 5.8.6 Naturally Fractured Reservoir, 5.3.4 Integration of geomechanics in models
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The purpose of this study is to formulate a coupled fluid-flow/geomechanics model of a naturally fractured reservoir. Fluid flow is modeled within the context of dual-porosity (more generally, overlapping-continuum) concept while geomechanics is modeled following Biot's isothermal, linear poroelastic theory. The development follows along the line of the conventional and existing porous fluid-flow modeling. The commonly used systematic fluid-flow modeling is therefore preserved. We show how the conventional fluid-flow dual-porosity formulations are extended to a coupled fluid flow/geomechanics model. Interpretation of the pore volumetric changes of the dual continua, fractures and matrix-blocks, and the associated effective stress laws are the most difficult and critical coupling considerations. New relations describing the dual rock volumetric changes are presented. These relations allow a smooth and consistent transition between single-porosity and dual-porosity concepts and are in terms of measurable quantities. Reduction to the single-porosity is presented to demonstrate the conceptual consistency of the proposed model.
Geomechanics is particularly important in petroleum reservoir management of naturally fractured reservoirs [Teufel et al., 1993]. Economical petroleum production from most naturally fractured reservoirs relies on the fracture permeability (including magnitude and orientation of an isotropy). Natural fractures basically are the product of evolving rock stress state. Therefore any disturbance of the stress field, such as due to fluid production/injection, can affect the existing fractures (e.g., opening, closure, reorientation) and the associated reservoir performance. A coupled fluid-flow/geomechanics model thus provides a rational tool for a better understanding and management of a naturally fractured reservoir.
The theory describing fluid-solid coupling was first presented by Biot [1941, 1955, 1956] in which mechanical issues were emphasized over the fluid flow issues. Because of this, Biot's theory is less compatible with the conventional fluid-flow models (without geomechanics considerations) in terms of concept understanding, physical interpretation of parameters involved (e.g., rock compressibilities), and computer code upgrading. These issues, however, can be resolved if Biot's theory is reinterpreted and reformulated along the line of conventional fluid-flow modeling as done by Geertsma  and Vermijt , and recently by Chen et al. . In essence, these reformulations provide better "compatibility" and "expandability" to the existing fluid-flow knowledge and models.
The original Biot's theory is a single-fluid/single-solid model, i.e., a single-porosity type of model from a fluid-flow point of view. Naturally fractured reservoirs are often modeled by the dual-porosity (overlapping continuum) type of concept developed by Barenblatt et al.  (also Warren and Root ). Models incorporating both Biot's poroelastic theory and Barenblatt et al's dual-porosity concept have been studied by several authors. These models can be classified into two types based on the approach taken.
The first approach is based on mixture theory and was adopted by Wilson and Aifantis , Beskos and Aifantis , and Bai et al.'s . Two related features of the resulting formulations are: (i) all the fluid-flow equations in a "mixture" have the same functional form as that of a single- porosity if the fluid exchange term is dropped, and (ii) phenomenological coefficients are proposed firstly and their physical interpretations are deduced, if necessary, after the completion of the formulation. Item (i) implies that the stress- dependent rock properties in one continuum are independent of the other mixing continua. This in turn may cause difficulty for the later physical interpretation (i.e., item (ii)) and even inconsistency with the geomechanical equations adopted.
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