Abstract

New analytical pressure-transient solutions for a horizontal well intersecting multiple random discrete fractures in both an infinite and a bounded reservoir are presented. The horizontal well is assumed to penetrate multiple randomly distributed vertical fractures. The infinite reservoir Containing the horizontal well is bounded at the top and at the bottom. For the case of a bounded reservoir, all exterior boundaries are non-flow boundaries. New source functions for a random vertical fracture are first derived. The pressure-transient solutions are then obtained using the derived source functions, as well as superposition principles. A uniform flux is assumed along all fracture faces. An averaging technique is used to approximate the wellbore pressure.

The new solutions provide a theoretical basis for the analysis of the pressure transient behavior of a horizontal well intersecting multiple random discrete fractures. Different flow regimes are identified. The effects of fracture characteristics, such as fracture orientation and length, on the pressure transient behavior of a horizontal well are investigated. New evaluation techniques using the derived pressure-transient solutions can be developed to determine reservoir properties and fracture characteristics from horizontal well test data.

Introduction

Characterization of discrete natural fracture systems presents a challenging task in the production modeling of naturally fractured reservoirs because important fracture data (orientation, length, aperture, and spacing) are rarely available. The chance for a vertical well to intersect a discrete natural fracture is extremely small, since most natural fractures in oil-bearing formations tend to be vertical. The use of horizontal well drilling in developing naturally fractured reservoirs, however, provides a practical means for actual measurements of discrete fracture characteristics. It is reported that new well logging tools such as Formation MicroScanner and Borehole Televiewer can be used to identify the location, orientation, and possibly aperture of fractures along a wellbore. Fracture length, however, has to be determined from well testing analyses. The limited fracture information from well logging and well testing can then be used to condition the statistical distributions of fracture characteristics obtained from other sources, such as outcrop studies. The objective of this paper is to present new analytical pressure-transient solutions for a horizontal well intersecting multiple random discrete fractures in both an infinite and a bounded reservoir.

The pressure transient analysis and well testing interpretation techniques for a single vertical hydraulic fracture are well documented in the literature. The pressure transient behavior for a horizontal well in a dual-porosity type of naturally fractured reservoir has been investigated by various researchers. The pressure transient solutions for a horizontal well intersecting multiple uniform (parallel and identical) discrete fractures have also been presented recently. This paper focuses on the case of a horizontal well intersecting multiple natural fractures whose orientation, length, and aperture are randomly distributed.

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