Abstract

Simulation of naturally fractured reservoirs has been one of the topical research subjects and several methods have been proposed as results of these research efforts. Since a fine grid model of an actual reservoir would be impossible to run even with today's advanced computers, all these methods employ dual porosity or dual porosity-dual permeability representations of fractured reservoirs. They differ in the treatment of fracture/ matrix fluid transfer. None of them, needless to say, is omnipotent and new approaches continue to appear in the literature.

The new gravity model that the authors and coworkers have developed is one of such approaches. The vertical equilibrium is assumed to define the transition zone in the matrix block in order to better express the transient saturation profile, which is the manifestation of the combined effects of viscous, capillary, and gravity forces. The fracture/matrix fluid exchanges in the lateral and vertical directions are calculated separately using, with some modifications, the Kazemi type shape factor, o.

This paper reports the results calculated by this new gravity model for the two imbibition cases of advancing water levels in fractures. These calculation results are compared with those obtained from the experiments or fine grid simulations. Physical meanings of the shape factor, a, Physical meanings of the shape factor, a, are discussed on the basis of this comparison.

Introduction

Naturally fractured reservoirs are composed of high flow capacity-low storage fractures and high storage-low flow capacity matrix blocks. These reservoirs are generally represented as two overlapping continua, one for fractures and the other for matrix blocks, and the mathematical governing equations for these continua are coupled through fluid flow between fracture and matrix. When these equations are discretized, each grid cell has two porosity values (or two pairs of porosity and permeability), thus, the porosity and permeability), thus, the resulting model is referred to as dual porosity (or dual porosity-dual porosity (or dual porosity-dual permeability) model. permeability) model. The fracture/matrix interaction greatly influences production behavior and hence recovery factor of fractured reservoirs. It is, therefore, of primary importance to accurately express the interaction in a numerical model. Various methods to handle the interaction have been proposed to this date and new approaches continue to appear in the literature.

The first mathematical representation of microscopically heterogeneous structure of a fractured reservoir was presented by Warren and Root. It was a systematic array of rectangular parallelepipeds that simulate matrix blocks, and based on this representation, they derived an analytical solution for single phase flow in a fractured reservoir.

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