The mathematical model of gravity drainage in naturally fractured reservoirs and singular perturbation analyses are presented which explore the effect of capillary, gravity, and wettability on oil saturation distribution and oil recovery in reimbibition. This study shows that wettability capillary end effect and fracture transmissibility appear to be most important factors in oil recovery. Numerical results are also presented which summarize and compare the effective saturation in nonequilibrium state with the actual saturation in equilibrium state. Based on this work, we believe reimbibition or capillary continuity in a stack of matrix blocks can not provide higher oil recovery than in continuity core.
Introduction
In recent years, growing attention has been focused on reimbibition and capillary continuity in gravity drainage. Reimbibition process is closely related to various forces (gravity, capillary, viscous, diffusive and relaxation). However, the experimental and theoretical research on gravity drainage mechanism in naturally fractured reservoirs is limited. Bogomolova and Glazova (1970) have observed the end effects and saturation discontinuities on the boundaries of unconsolidated porous media with some different permeability. Hagoort (1980) used the classical Buckley-Leverett theory to study the gravity drainage in homogeneous media, and indicated that oil relative permeability is a key factor in the gravity-drainage process. Barenblatt's work investigated the end effects in heterogeneous media.
Recent experiments and observations by Firoozabadi and his co-worker (l992), Catalan and Dullien (1992) prompted us to reexamine the gravity drainage mechanism. This study has tried to examine from both a mathematical and a physical viewpoint the key features of gravity drainage in a stack of matrix blocks.
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