Scaling Parameters for Characterizing Gravity Drainage in Naturally Fractured Reservoirs
Authors: Miguel-H N. , Miller M.A. , Sepehrnoori K. 
Published: December 2007

Abstract
Numerical models for naturally fractured reservoirs are generally divided into two types. The first is the double-porosity, single-permeability (dual porosity) model. The second is the double-porosity, double-permeability (dual permeability) model. The difference between the two models is basically that the second type considers matrix block-to-block flow while the first does not. The present work is focused on the dual porosity model, which also requires a transfer function calculation between matrix and fracture. Therefore, proper calculation of mass transfer from matrix to fracture plays an important role in generating good simulation results. In a gas-oil system when the gas with low viscosity and nonwetting characteristics reaches the fractures, it moves rapidly, leaving the wetting fluid (oil) preferentially in the matrix.
This paper determines methods of scaling dimensionless variables to simplify the analysis and thus identify the main parameters controlling the gas-oil gravity drainage process in naturally fractured reservoirs. This work is based on a simplified model matched to published lab data and information of a fractured reservoir. The differences between this paper and others are the following:an analysis to simplify a complex problem by neglecting gas viscous pressure drop,a comparison of oil transfer function models from matrix to fracture flow represented in a simple integral equation,an analysis of matrix-fracture flow in all directions with gravity drainage using fine grid simulation, andnumerical simulation of a stack of matrix blocks separated by fractures which compares gas-oil gravity drainage in matrix to fracture flow.
The information in this paper has time saving application in history matching and stochastic simulation. Considering gas-oil systems with gravity drainage in stacked matrix blocks, the main technical contributions of this paper are as follows:flow is only in the vertical direction and there is minimal or no flow to lateral fractures;there is maximum oil flux from matrix to fracture which is a function of matrix permeability, oil relative permeability, oil viscosity, and difference of density between oil and gas phases; andthe detailed comparison of dual porosity models.

Introduction
In naturally fractured reservoirs, as in non-fractured reservoirs, when multiple fluids exist, gravity segregation is present to some degree. Segregation is driven by the difference in density between fluids. The larger the difference in density, the more important is gravity segregation.
This paper first presents a literature review, covering important topics in fractured reservoirs and a review of matrix-fracture transfer functions used in numerical simulators; a model is then developed to simulate gravity-capillary phenomena in the vertical direction. This paper also discusses gravity drainage with no capillary pressure and a procedure to generate pseudo oil relative permeability with gravity drainage. A comparison of different transfer functions for dual porosity models is done to determine the differences between them. This work also addresses a methodology to generate pseudo capillary pressure with gravity drainage. Then, this paper reviews 3D flow from matrix to fracture to determine the effects with lateral flow and no liquid saturation in the fracture. Finally a procedure is established to represent matrix-fracture transfer with gravity drainage, which also presents a comparative case between a dual porosity model in a commercial simulator with gravity drainage and a gridded system of a stack of matrix blocks separated by fractures.