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Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (1): 102-109.

• 论文 • 上一篇    下一篇

EXACT SOLUTIONS FOR NONLINEAR TRANSIENT FLOW MODEL INCLUDING A QUADRATIC GRADIENT TERM

曹绪龙1,2, 同登科3, 王瑞和3   

  1. 1. Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, P. R. China;
    2. Geological Science Research Institute, Shengli Oilfield Co.Ltd, Dongying, Shandong 257000, P. R. China;
    3. Department of Applied Mathematics, University of Petroleum, Dongying, Shandong 257061, P. R. China
  • 收稿日期:2002-08-29 修回日期:2003-08-02 出版日期:2004-01-18 发布日期:2004-01-18
  • 通讯作者: TONG Deng-ke(Corresponding author)(Tel: 86-0564-8393487; Fax: 86-0546-8396065; E-mail: tongdk@mail.hdpu.edu.cn) E-mail:tongdk@mail.hdpu.edu.cn
  • 基金资助:

    973 Program Foundation of China(2002 CB211708)

EXACT SOLUTIONS FOR NONLINEAR TRANSIENT FLOW MODEL INCLUDING A QUADRATIC GRADIENT TERM

CAO Xu-long1,2, TONG Deng-ke3, WANG Rui-he3   

  1. 1. Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, P. R. China;
    2. Geological Science Research Institute, Shengli Oilfield Co.Ltd, Dongying, Shandong 257000, P. R. China;
    3. Department of Applied Mathematics, University of Petroleum, Dongying, Shandong 257061, P. R. China
  • Received:2002-08-29 Revised:2003-08-02 Online:2004-01-18 Published:2004-01-18
  • Supported by:

    973 Program Foundation of China(2002 CB211708)

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摘要： The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform. Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.

Abstract: The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform. Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.

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