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

作　　者：Jiaxuan LIU Xinchun SHANG Weiyao ZHU 

机构地区：[1]Department of Applied Mechanics, University of Science and Technology Beijing [2]Institute of Applied Mechanics, University of Science and Technology Beijing

出　　处：《Applied Mathematics and Mechanics(English Edition)》2018年第2期181-192,共12页应用数学和力学（英文版）

基　　金：supported by the National Basic Research Program of China(973 Program)(No.2013CB228002)

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 includ- ing 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.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 includ- ing 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 nonlinear effect multi-scale percolation inhomogeneous perme ability integral equation 

分 类 号：O1[理学—数学]