ABSTRACT:

This paper presents the mathematical formulation and numerical results of two-phase fluid flow and rock deformations in fractured hydrocarbon reservoirs using the dual-porosity poroelastic approach. Deviating from traditional single-phase models, the wetting and nonwetting fluids, typically water and oil, are considered as immiscible liquids resident in the interacting fractures and matrix blocks of deformable formations. In addition, the developed governing equations follow rigorous volume fraction basis, instead of being proposed via phenomenological intuitions adopted in many existing dual-porosity models. The significance of this approach rests on its ability to include additional components of fluids as well as solids, as they may be needed in the actual reservoir simulation.

INTRODUCTION

To a certain degree, all hydrocarbon reservoirs contain natural fractures. The study of two-phase fluid flow through fractured and deformable porous media is, therefore, an important issue directly associated with the quality of energy resources recovery (petroleum, natural gas, geothermal water and steam) and environmental protection (chemical contamination in groundwater aquifers, and in partially saturated vadose zones). For the former field, attention focuses on identifying the fluid displacement between the wetting and nonwetting phases. For example, in the case that water is a wetting fluid, imbibition becomes a more crucial process to flush the residual oil trapped in the porous matrix. For the fractured reservoirs, the imbibition is reduced significantly by the presence of natural fractures which dominate the drainage process. As a result, the fracture-matrix interaction cannot be neglected due to its substantial impact on production (Barenblatt, et al., 1960; Warren and Root, 1963).

Traditional views about fluid flow in porous media often neglects other factors, such as thermal, or chemical mechanisms. Even though they may not be dominant driving forces for hydrocarbon recovery, omitting them frequently results in costly planning and prediction errors. In petroleum engineering, the flow-deformation coupling has revealed phenomena more complex than reservoir compaction, and has proved to have considerable impact on production (Lewis and Sukirman, 1993a; Finol and Ali, 1975). These phenomena are attributed to the well-known poroelastic effect (Blot, 1941).

The coupled poroelastic effects for homogeneous (single-porosity) and heterogeneous media (dualporosity) have been investigated extensively during the past; however, primary focus has been in the areas related to single-phase fluid (Noorishad, et al., 1982; Khaled et al., 1984; Elsworth and Bai; 1992; Ghafouri and Lewis, 1996, Bai and Abousleiman, 1997). Since two-phase, or multiphase fluids are common in practical situations, more recent efforts are shifting to examine the coupled phenomena involving two or multiple immiscible fluids in deformable and/or fractured reservoirs (Li, et al., 1990; Schrefier and Zhang, 1993; Lewis and Sukirman, 1993b).

A literature search on the state of the art in modeling two-phase fluid flow in deformable fractured porous media using the concept of two-phase dual-porosity poroelasticity reveals that only one relevant paper appears to be available (Lewis and Ghafouri, 1997). However, Lewis and Ghafouri (1997)'s approach was based on physical intuition, rather than theoretical derivation. On the other hand, the single-porosity model for two-phase flow in deformable porous media by Liet al. (1990) was derived from fundamental conservations of mass and momentum. Extension os this theoretical model to the dual-porosity media is feasible.

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