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Mathematical Problems in Engineering
Volume 2018, Article ID 4570539, 10 pages
https://doi.org/10.1155/2018/4570539
Research Article

A New Way to Calculate Flow Pressure for Low Permeability Oil Well with Partially Penetrating Fracture

1College of Earth Sciences, Yangtze University, Wuhan 430100, China
2College of Engineering and Technology, Yangtze University, Jingzhou 434020, China
3China Petrochemical Exploration and Development Research Institute, Beijing 100083, China
4Key Laboratory of Marine Oil & Gas Reservoirs Production, Sinopec, Beijing 100083, China
5Department of Geosciences, The University of Tulsa, Tulsa, OK 74104, USA

Correspondence should be addressed to Liu Hailong; moc.qq@806772874

Received 25 May 2017; Revised 29 August 2017; Accepted 21 March 2018; Published 30 May 2018

Academic Editor: Luca Heltai

Copyright © 2018 Xiong Ping 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

In order to improve the validity of the previous models on calculating flow pressure for oil well with partially perforating fracture, a new physical model that obeys the actual heterogeneous reservoir characteristics was built. Different conditions, including reservoir with impermeable top and bottom borders or the reservoir top which has constant pressure, were considered. Through dimensionless transformation, Laplace transformation, Fourier cosine transformation, separation of variables, and other mathematical methods, the analytical solution of Laplace domain was obtained. By using Stephenson numerical methods, the numerical solution pressure in a real domain was obtained. The results of this method agree with the numerical simulations, suggesting that this new method is reliable. The following sensitivity analysis showed that the pressure dynamic linear flow curve can be divided into four flow streams of early linear flow, midradial flow, advanced spherical flow, and border controlling flow. Fracture length controls the early linear flow. Permeability anisotropy significantly affects the midradial flow. The degree of penetration and fracture orientation dominantly affect the late spherical flow. The boundary conditions and reservoir boundary width mainly affect the border controlling flow. The method can be used to determine the optimal degree of opening shot, vertical permeability, and other useful parameters, providing theoretical guidance for reservoir engineering analysis.