Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells

doi:10.1007/s10483-018-2292-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (2): 181-192.doi: https://doi.org/10.1007/s10483-018-2292-6

Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells

Jiaxuan LIU¹, Xinchun SHANG^1,2, Weiyao ZHU²

1. Department of Applied Mechanics, University of Science and Technology Beijing, Beijing 100083, China;
2. Institute of Applied Mechanics, University of Science and Technology Beijing, Beijing 100083, China

收稿日期:2017-01-22 修回日期:2017-06-22 出版日期:2018-02-01 发布日期:2018-02-01
通讯作者: Xinchun SHANG E-mail:shangxc@ustb.edu.cn
基金资助:
Project supported by the National Basic Research Program of China (973 Program) (No. 2013CB228002)

Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells

Jiaxuan LIU¹, Xinchun SHANG^1,2, Weiyao ZHU²

1. Department of Applied Mechanics, University of Science and Technology Beijing, Beijing 100083, China;
2. Institute of Applied Mechanics, University of Science and Technology Beijing, Beijing 100083, China

Received:2017-01-22 Revised:2017-06-22 Online:2018-02-01 Published:2018-02-01
Contact: Xinchun SHANG E-mail:shangxc@ustb.edu.cn
Supported by:
Project supported by the National Basic Research Program of China (973 Program) (No. 2013CB228002)

摘要/Abstract

摘要： A unified mathematical model is established to simulate the nonlinear unsteady percolation of shale gas with the consideration of the nonlinear multi-scale effects such as slippage, diffusion, and desorption. The continuous inhomogeneous models of equivalent porosity and permeability are proposed for the whole shale gas reservoir including the hydraulic fracture, the micro-fracture, and the matrix regions. The corresponding semi-analytical method is developed by transforming the nonlinear partial differential governing equation into the integral equation and the numerical discretization. The nonlinear multi-scale effects of slippage and diffusion and the pressure dependent effect of desorption on the shale gas production are investigated.

关键词: shale gas, complementarity problems, variational inequality, duality theory, elastoplastic beam, contact problem, multi-scale percolation, inhomogeneous permeability, nonlinear effect, integral equation

Abstract: A unified mathematical model is established to simulate the nonlinear unsteady percolation of shale gas with the consideration of the nonlinear multi-scale effects such as slippage, diffusion, and desorption. The continuous inhomogeneous models of equivalent porosity and permeability are proposed for the whole shale gas reservoir including the hydraulic fracture, the micro-fracture, and the matrix regions. The corresponding semi-analytical method is developed by transforming the nonlinear partial differential governing equation into the integral equation and the numerical discretization. The nonlinear multi-scale effects of slippage and diffusion and the pressure dependent effect of desorption on the shale gas production are investigated.

Key words: complementarity problems, variational inequality, duality theory, elastoplastic beam, contact problem, multi-scale percolation, nonlinear effect, inhomogeneous permeability, shale gas, integral equation

中图分类号:

76S05

Jiaxuan LIU, Xinchun SHANG, Weiyao ZHU. Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(2): 181-192.

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Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells

Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells

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