Fractal Analytical Solutions for Nonlinear Two-Phase Flow in Discontinuous Shale Gas Reservoir

Xiaoji Shang, Zhizhen Zhang (), Zetian Zhang (), J. G. Wang, Yuejin Zhou and Weihao Yang
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Xiaoji Shang: State Key Laboratory of Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
Zhizhen Zhang: State Key Laboratory of Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
Zetian Zhang: Key Laboratory of Deep Earth Science and Engineering (Sichuan University), Ministry of Education, Chengdu 610065, China
J. G. Wang: State Key Laboratory of Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
Yuejin Zhou: State Key Laboratory of Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
Weihao Yang: State Key Laboratory of Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China

Mathematics, 2022, vol. 10, issue 22, 1-14

Abstract: The paths of a two-phase flow are usually non-linear and discontinuous in the production of shale gas development. To research the influence mechanism between shale gas and water, several integer two-phase flow models have been studied but few analytical solutions have been obtained on shale gas and water pressure. This study first developed a local fractional mathematical model for gas and water two-phase flow in shale gas production. The model thus created considers the effects of capillary pressure, the fractal dimension of the flow pipe, and the discontinuity of the flow path. Second, the local fractional traveling wave method and variational iteration method were applied to this model for the development of iterative analytical solutions. Both shale gas and water pressure were analytically derived. Third, the depressurization process of the shale gas and water was analyzed, and a parametric study was conducted to explore the impacts of fractional dimension, entry capillary pressure, and travel wave velocity on shale gas pressure. Finally, our conclusions are drawn, based on the results of these studies.

Keywords: two-phase flow; capillary pressure; fractal dimension; fractional model; analytical solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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