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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 726910, 11 pages
http://dx.doi.org/10.1155/2015/726910
Research Article

An Analytical Solution of Partially Penetrating Hydraulic Fractures in a Box-Shaped Reservoir

1School of Energy Resources, China University of Geosciences, Beijing 100083, China
2Beijing Key Laboratory of Unconventional Natural Gas Geology Evaluation and Development Engineering, Beijing 100083, China

Received 19 August 2014; Revised 8 December 2014; Accepted 8 December 2014

Academic Editor: Shaofan Li

Copyright © 2015 He Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a new method to give an analytical solution in Laplace domain directly that is used to describe pressure transient behavior of partially penetrating hydraulic fractures in a box-shaped reservoir with closed boundaries. The basic building block of the method is to solve diffusivity equation with the integration of Dirac function over the distance that is presented for the first time. Different from the traditional method of using the source solution and Green’s function presented by Gringarten and Ramey, this paper uses Laplace transform and Fourier transform to solve the diffusivity equation and the analytical solution obtained is accurate and simple. The effects of parameters including fracture height, fracture length, the position of the fracture, and reservoir width on the pressure and pressure derivative are fully investigated. The advantage of the analytical solution is easy to incorporate storage coefficient and skin factor. It can also reduce the amount of computation and compute efficiently and quickly.