A numerical study on hydraulic fracturing problems via the proper generalized decomposition method

The hydraulic fracturing is a nonlinear, fluid-solid coupling and transient problem, in most cases it is always time-consuming to simulate this process numerically. In recent years, although many numerical methods were proposed to settle this problem, most of them still require a large amount of com...

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Detalles Bibliográficos
Autores: Wang, Daobing, Zlotnik, Sergio|||0000-0001-9674-8950, Díez, Pedro|||0000-0001-6464-6407
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/184842
Acceso en línea:https://hdl.handle.net/2117/184842
https://dx.doi.org/10.32604/cmes.2020.08033
Access Level:acceso abierto
Palabra clave:Hydrodynamics
Hydraulic fracturing
proper generalized decomposition
reduced order modeling
numerical simulation
Hidrodinàmica
Classificació AMS::76 Fluid mechanics::76E Hydrodynamic stability
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Simulació
Descripción
Sumario:The hydraulic fracturing is a nonlinear, fluid-solid coupling and transient problem, in most cases it is always time-consuming to simulate this process numerically. In recent years, although many numerical methods were proposed to settle this problem, most of them still require a large amount of computer resources. Thus it is a high demand to develop more effificient numerical approaches to achieve the real-time monitoring of the fracture geometry during the hydraulic fracturing treatment. In this study, a reduced order modeling technique namely Proper Generalized Decomposition (PGD), is applied to accelerate the simulations of the transient, non-linear coupled system of hydraulic fracturing problem, to match this extremely tight response time constraint. The separability of the solution in space and time dimensions is studied for a simplifified model problem. The solid and flfluid equations are coupled explicitly by inverting the solid discrete problem, and a simple iterative procedure to handle the non-linear characteristic of the hydraulic fracturing problem is proposed in this work. Numeral validation illustrates that the results of PGD match well with these of standard fifinite element method in terms of fracture opening and fluid pressure in the hydro-fracture. Moreover, after the off-line calculations, the numerical results can be obtained in real time.