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

doi:10.1007/s10483-018-2292-6

Abstract

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

2010 MSC Number:

76S05

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

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