Analysis for pressure transient of coalbed methane reservoir based on Laplace transform finite difference method

Abstract

Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare with the results from the analytical method, the result from Laplace transform finite difference method turns out to be accurate. The influence factors are analyzed, including fractal dimension, fractal index, skin factor, well bore storage coefficient, energy storage ratio, interporosity flow coefficient and the adsorption factor. The calculating error of Laplace transform difference method is small. Laplace transform difference method has advantages in well-test application since any moment simulation does not rely on other moment results and space grid.

Keywords

Coalbed methane / Pressure performance / Fractal medium / Laplace transform finite difference method

Acknowledgment

This research was Supported by the Scientific Research Project of the Heilongjiang Education Department (Grant No: 12521044).

References

[1] Zhao Aihong, Liao Yi, Tang Xiuyi, Quantitative analysis of pore structure by fractal analysis, J. China Coal Soc. 23 (4) (1998) 439-442.

[2] Qin Yueping, Fu Gui, Study on fractal characteristic of pore in coal and dmoisture-absorbing property of coal, J. China Coal Soc. 25 (1) (2000) 55-59.

[3] F.U. Xuehai, Q.I.N. Yong, Xue Xiuqian, Li Guizhong, Wang Wengfeng, Research on fractals of pore and fracture-structure of coal reservoirs, J. China Univ. Min. Technol. 30 (3) (2001) 225-228.

[4] J. Chang, Y.C. Yortsos, Pressure transient analysis of fractal reservoirs, SPEFE 5 (1990) 31-38.

[5] R.A. ABeier, Pressure-transient model for a vertically fractured well in a fractal reservoir, SPEFE 7 (1994) 122-128.

[6] J.A. Acuna, I. Ershaghi, Y.C. Yortsos, Practical application of fractal pressuretransient analysis in naturally fractured reservoirs, SPEFE 9 (1995) 173-179.

[7] J.S. Olarewaju, Modeling Fractured Reservoirs with Stochastic Fractals[C], 1996, pp. 352-367. SPE36207.

[8] He Yingfu, Yang Zhengming, Sun Ping, Li Anqi, Analysis of pressure performance of coalbed methane through deformable fractal medium [A], Theor. Technol. Coalbed Methane Explor. 5 (2007) 261-265.

[9] Gao Huimei, He Yingfu, Cao Lili, Jiang Hanqiao, Chen Minfeng, Analysis of pressure performance of coal-bed methane through deformable medium, Special Oil Gas Reservoirs 01 (2007) 66-68.

[10] Zhang Xianmin, Tong Dengke, Analysis for pressure transient of coal bed methane reservoir, Well Test. 17 (6) (2008) 1-4.

[11] Liu Hong, Wang Xinhai, Zhang Fuxiang, Niu Xinnian, Laplace transform finite difference method for well-test problem with one-dimensional seepage flow, Chin. J. Comput. Phys. 02 (2012) 245-249.

[12] H. Stehfest, Numerical invesion of laplace transforms communications of the ACM, vol. 13(1), 1970, pp. 47-49.