Abstract

A new analytical pressure transient solution (constant rate) for a well containing multiple arbitrarily-oriented uniform-flux, infinite-conductivity, or finite-conductivity fractures in an infinite-slab reservoir is presented. The multiple-fracture solution is derived using a new uniform-flux solution for a single arbitrarily-oriented fracture in an anisotropic reservoir. The variables in this solution are: fracture half-length, fracture conductivity, and fracture angle of rotation for each fracture relative to the primary fracture. Example constant-rate type curves are provided for two intersecting fractures - cruciform or oblique - and three intersecting fractures - trifracture.

Introduction

Fracture imaging has changed the concept of a well producing from an infinite-slab through a single planar fracture. Microseismic fracture imaging strongly suggests complex fracture patterns can develop during primary fracture treatments,[1–2] and fracture imaging during subsequent refracturing treatments demonstrates that secondary fractures are oriented in a plane(s) other than the primary fracture.[3]

An analytical solution for a well producing from an infinite-slab reservoir through multiple arbitrarily-oriented finite- or infinite-conductivity fractures is presented that was developed as part of a new pressure-transient test for refracture-candidate assessment.[4] Obviously, this solution is also applicable when interpreting conventional pressure transient tests in reservoirs with multiple arbitrarily-oriented fractures.

The purpose of this paper is to derive the new analytical solution; evaluate a pressure-averaging infinite-conductivity solution versus a semianalytical solution; illustrate the solutions by generating type curves for typical configurations of two intersecting - cruciform or oblique - fractures and three intersecting - star-shaped - tri-fractures; and present a model and type curves for a pressure-transient test in a formation exhibiting complex fracturing patterns.

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