The Similar Structure Method for Solving the Radial Seepage Model of Fractal Composite Reservoir with Double-porosity

Wen-wen Xia¹, Shun-chu Li^1, and Dong-dong Gui²

¹Institute of Applied Mathematics of XiHua University, Chengdu, China

²Beijing Dongrunke Petroleum Technology Co.,Ltd., Beijing, China

Cite this paper:
Wen-wen Xia, Shun-chu Li and Dong-dong Gui. The Similar Structure Method for Solving the Radial Seepage Model of Fractal Composite Reservoir with Double-porosity. American Journal of Applied Mathematics and Statistics. 2015; 3(2):80-85. doi: 10.12691/ajams-3-2-7

Abstract

This paper introduces the fractal theory into composite reservoir with double-porosity, and establishes the radial seepage model of fractal composite reservoir with double-porosity. Based on the similar structure theory of solutions for the boundary value problem of differential equation, the similar structure expression of solutions can be obtained in Laplace space. The similar structure theory of solution which avoids the complex calculation is used to solve the model, meanwhile, the similar structure expression of solution reflects the influence of different parameters for the bottom pressure.

Keywords:
radial seepage composite reservoir with double-porosity laplace transformation similarity kernel function similar structure

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Xiang-yan Kong. Higher seepage mechanics [M]. Hefei: China University of Science and Technology Press, 1999.
[2]	Shun-chu Li. A solution of fractal dual porosity reservoir model in well testing analysis (in Chinese)[J]. Progress in Exploration Geophysics, vol.25(5), p.60-62, 2002.
[3]	Shun-chu Li.Well test model for fractal dual porosity closed reservoir (in Chinese)[J].Xinjiang Petroleum Geology, vol.24(2), p. 149-151, 2003.
[4]	Shun-chu Li. A model solution of testing analysis in fractal dual porosity reservoirs with constant pressure outer boundary (in Chinese) [J]. Petroleum Drilling Techniques, vol.31(1), p.51-52,2003.
[5]	Shun-chu Li, Tian-pu Zheng. A model solution of testing analysis in fractal composite reservoir (in Chinese)[J]. Journal of Jilin University (Engineering and Technology Edition), vol.34, p.104-107, 2004.
[6]	Xue-ru Deng, Shun-chu Li. Solution to the well testing model for fractal composite reservoirs (in Chinese)[J]. Journal of Xihua University (Natural Science Edition), vol. 24(2), p.4-7, 2005.
[7]	Tian-pu Zheng, Shun-chu Li, Ying Xu. A model solution of testing analysis in fractal composite reservoir with constant pressure outer boundary (in Chinese)[J]. Journal of Northeast Normal University (Natural Science Edition), vol.35(Supp.), p.46-49(to13), 2003.
[8]	Shun-chu Li. The Similarity Structuring Method of Boundary Value Problems of the Composite Differential Equations (in Chinese) [J]. Journal of Xihua University (Natural Science Edition),vol.32(4), p. 27-31,2013.
[9]	Cui-Cui Sheng, Jin-Zhou Zhao, Yong-Ming Li, Shun-Chu Li and Hu Jia. Similar construction method of solution for solving the mathematical model of fractal reservoir with spherical flow[J]. Journal of Applied Mathematics, vol. 2013, Article ID 219218, 8 pages, 2013.
[10]	Shun-chu Li, Bing-guang Huang. Laplace transform and Bessel functions and the theoretical basis of well test analysis [M].Beijing: Petroleum Industry Press, 2000.
[11]	Li-ya Chen, Shun-chu Li, Xia Lai. Solution analysis of bottom hole pressure distribution in the dual porosity composite reservoir (in Chinese)[J]. Drilling & Production Technology, vol.33(5), p. 52-54(to61), 2010.
[12]	Wei Li, Xiao-ping Li, Shun-chu Li, Quan-yong Li.The Similar structure of solutions in fractal multilayer reservoir including a quadratic gradient term [J]. Journal of Hydrodynamics, vol. 24(3), p. 332-338, 2012.
[13]	Xiao-xu Dong, Shun-chu Li, Dong-dong Gui, Jun Pu, Hui-chun Li. Similar constructing method for solving the boundary value problem of the composite first Weber system[J]. American Journal of Applied Mathematics and Statistics, vol.1(4), p.76-82, 2013.
[14]	Cong-yin Fan, Shun-chu Li, Dong-dong Gui, Ming Hu, Hui-chun LI. Similar constructing method for solving the model of the plane radial flow of dual permeability reservoir [J]. Applied Mechanics and Materials, vol. 419, p.43-50, 2013.