New Method of Solving the Seepage Model for the Multilayer Composite Reservoir with the Double Porosity

Qiang Wang^1, , Shunchu Li¹, Mei Luo¹ and Dongdong Gui²

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

²Beijing Dong run ke Petroleum Technology Co,Ltd, Beijing, China

Cite this paper:
Qiang Wang, Shunchu Li, Mei Luo and Dongdong Gui. New Method of Solving the Seepage Model for the Multilayer Composite Reservoir with the Double Porosity. American Journal of Energy Research. 2015; 3(1):8-12. doi: 10.12691/ajer-3-1-2

Abstract

Aimed at multilayer composite reservoir with the double porosity, meanwhile considering the influence of well bore storage and skin effect, the seepage model for multilayer composite reservoir with the double porosity which the flow was steady from pore to crack was established in different outer boundary (infinite; closed; constant pressure) conditions; the exact solution of reservoir pressure drop and bottom hole pressure drop were obtained by Laplace transform in the Laplace space; the unified expression of solution was obtained by constructing similar kernel functions in different outer boundary conditions, therefore new method which solving this class of reservoir model is put forward, namely similar construction method. This method plays an important guiding role in exploring seepage law of oil and gas reservoir.

Keywords:
double porosity multilayer composite reservoir similar construction method similar 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]	Shunchu Li, Bingguang Huang. Laplace transform and Bessel functions and the theoretical basis of well test analysis. Beijing: Petroleum Industry Press, 2000.
[2]	Kuchuk F J, Ayestaran L et al. Application of Multilayer Testing and Analysis: A Field Case. Paper SPE15419 presented at 61 Annual Technical Conference and Exhibition in New Orieans,LA October 5-8,1986.
[3]	Xianzhi Xu, Guohua Kuang, Fenglei Chen, etc. Method of well test for multilayer commingled producing (in Chinese). Acta Petrolei Sinica,1999,20(5):43-47.
[4]	Shunchu Li, Puzai Zhang, Bingguang Huang, etc. General solution of the pressure distribution in multilayer reservoir (in Chinese). Journal of Southwest Petroleum Institute, 2002, 24(4):28-29.
[5]	Liehui Zhang, Haitao Wang, Yonglu Jia,etc. Model of two-layered reservoir with crossflow and dual porosity media (in Chinese). Journal of Southwest Petroleum Institute, 2009, 31(5):178--184.
[6]	Jingjing Guo, Liehui Zhang, Haitao Wang. Productivity analysis on commingled production wells in layered dual porosity reservoirs(in Chinese). Journal of Hydrodynamics, 2011, 26(6):704-712.
[7]	Quanyong Li, Shunchu Li, Wei Li, etc. Solution to Base on the Similar Structure of the Double Porosity-Multilayer Reservoir(in Chinese). College Mathematics, 2013, 29(1): 56-60.
[8]	Shunchu Li, Minhui Jia. The formal similarity of solutions on the class of differential equation(in Chinese). Journal of UEST of China, 2004, 33(Supp.):95-98.
[9]	Lijie Guo, Shunchu Li, Cuicui Sheng. Similar structure of solutions for radial flow of fractal reservoir(in Chinese). Fault-Block Oil & Gas Field, 2012, 19(1): 114-116.
[10]	Shunchu Li, Junchao Wang, Li Xu. The Similar Structure of Solutions to the Spherical Fluids Flow Problems for a Composite Reservoir(in Chinese). Journal of Mathematics in Practice and Theory, 2014,44(3):122-127.
[11]	Liya Chen, Shunchu Li, Xia Lai.Solution analysis of bottom hole pressure distribution in the dual porosity composite reservoir(in Chinese). Drilling & Production Technology, 2010, 33(5): 52-54(to61).
[12]	Ying Chi, Shunchu Li, Quanyong Li. Nonlinear flow solution of fractal composite reservoir model based on similar structure(in Chinese). Drilling & Production Technology, 2011, 34(2):46-48(to108).
[13]	Junchao Wang, Shunchu Li, Li Xu. Spherical fluids flow models in composite reservoir based on similar structure of solution (in Chinese). Journal of Guilin University of Technology, 2012, 32(4): 624-627.
[14]	Xuxia Xiao, Shunchu Li. The similar structure of solutions for the boundary value problem of Euler’s hypergeometric differential equation(in Chinese). Journal of Inner Mongolia Normal University (Natural Science Edition), 2012, 41(6): 597-600(-603).
[15]	Furong Wang, Shunchu Li, Dongxu Xu. The similarity construction method of a kind of boundary value problem of airy equation(in Chinese). Journal of Hubei Normal University (Natural Science), 2013, 33(1):79-85.
[16]	Cuicui Sheng, Jinzhou Zhao, Yong-Ming Li, Shunchu Li, Hu Jia. Similar construction method of solution for solving the mathematical model of fractal reservoir with spherical flow. Journal of Applied Mathematics, vol. 2013, Article ID 219218, 8 pages, 2013.
[17]	Yong Wang, Xitao Bao, Shunchu Li. Similar constructive method for solving a non-linearly spherical percolation model. Telkomnika Indonesian Journal of Electrical Engineering, Vol. 11, No.3, pp.1393-1402, 2013.
[18]	Li Xu, Xiangjun Liu, Lixi Liang, Shunchu Li, and Longtao Zhou. The similar structure method for solving the model of fractal dual-porosity reservoir. Mathematical Problems in Engineering, Volume 2013, Article ID 954106, 9 pages.
[19]	Pengshe Zheng, Shunchu Li, Lihui Leng, Dongdong Gui. Similar construction method of boundary value problems of a nonlinear composite modified bessel equations(in Chinese). Journal of Xinyang Normal University (Natural Science Edition), 2014, Vol.27 (4): 490-492(-504).
[20]	Kamke E. The manual of Ordinary differential equation. Beijing: Science Press, 1977.