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Energies 2018, 11(12), 3422; https://doi.org/10.3390/en11123422

An Analytical Flow Model for Heterogeneous Multi-Fractured Systems in Shale Gas Reservoirs

1,2,3,* , 1
,
1,* , 1
,
4
and
1,*
1
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China
2
John and Willie Leone Family Department of Energy and Mineral Engineering, The Pennsylvania State University, University Park, PA 16802, USA
3
Key Laboratory of Shale Gas Exploration, Ministry of Land and Resources Engineering, Chongqing 400042, China
4
Petro China West Pipeline Company, Urumqi 830013, China
*
Authors to whom correspondence should be addressed.
Received: 14 October 2018 / Revised: 2 December 2018 / Accepted: 4 December 2018 / Published: 6 December 2018
(This article belongs to the Special Issue Flow and Transport Properties of Unconventional Reservoirs 2018)
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Abstract

The use of multiple hydraulically fractured horizontal wells has been proven to be an efficient and effective way to enable shale gas production. Meanwhile, analytical models represent a rapid evaluation method that has been developed to investigate the pressure-transient behaviors in shale gas reservoirs. Furthermore, fractal-anomalous diffusion, which describes a sub-diffusion process by a non-linear relationship with time and cannot be represented by Darcy’s law, has been noticed in heterogeneous porous media. In order to describe the pressure-transient behaviors in shale gas reservoirs more accurately, an improved analytical model based on the fractal-anomalous diffusion is established. Various diffusions in the shale matrix, pressure-dependent permeability, fractal geometry features, and anomalous diffusion in the stimulated reservoir volume region are considered. Type curves of pressure and pressure derivatives are plotted, and the effects of anomalous diffusion and mass fractal dimension are investigated in a sensitivity analysis. The impact of anomalous diffusion is recognized as two opposite aspects in the early linear flow regime and after that period, when it changes from 1 to 0.75. The smaller mass fractal dimension, which changes from 2 to 1.8, results in more pressure and a drop in the pressure derivative. View Full-Text
Keywords: fractional diffusion; fractal geometry; analytical model; shale gas reservoir fractional diffusion; fractal geometry; analytical model; shale gas reservoir
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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 (CC BY 4.0).
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Tao, H.; Zhang, L.; Liu, Q.; Deng, Q.; Luo, M.; Zhao, Y. An Analytical Flow Model for Heterogeneous Multi-Fractured Systems in Shale Gas Reservoirs. Energies 2018, 11, 3422.

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