Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime  

作　　者：Cexuan Liu Emmanuel Detournay Fengshou Zhang 

机构地区：[1]Department of Geotechnical Engineering,Tongji University,Shanghai,200092,China [2]Key Laboratory of Geotechnical&Underground Engineering of Ministry of Education,Tongji University,Shanghai,200092,China [3]Department of Civil,Environmental,and Geo-Engineering,University of Minnesota,Minneapolis,55455,MN,USA

出　　处：《Rock Mechanics Bulletin》2024年第1期55-63,共9页岩石力学通报（英文）

基　　金：support from the International Exchange Program for Graduate Students,Tongji University(NO.2023020010).

摘　　要：This paper describes a numerical algorithm for solving the classic problem of a plane strain(KGD)fracture propagating in an impermeable elastic medium with zero toughness.The method,which takes advantage of the self-similar nature of the solution,combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation.This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects,noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method.To enhance the efficiency and accuracy of the numerical scheme,the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening,while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation.The proposed technique yields results that closely match the analytical solution,even with a coarse mesh.This approach offers potential for addressing more complex hydraulic fracturing problems in the future.

关 键 词：Hydraulic fracturing Numerical simulation Domain-based method Far-field asymptotic boundary Tip asymptote 

分 类 号：TE377[石油与天然气工程—油气田开发工程]