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dc.contributor.authorWang, Daobing
dc.contributor.authorZlotnik, Sergio
dc.contributor.authorDíez, Pedro
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.identifier.citationWang, D.; Zlotnik, S.; Diez, P. A numerical study on hydraulic fracturing problems via the proper generalized decomposition method. "CMES: computer modeling in engineering and sciences", 1 Febrer 2020, vol. 122, núm. 2, p. 703-720.
dc.description.abstractThe 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.
dc.description.sponsorshipThis work is financially supported by the National Science Foundation of China (Grant Nos. 51804033 and 51936001), China Postdoctoral Science and Foundation (Grant No. 2018M641254), Beijing Postdoctoral Research Foundation (2018- ZZ-045), the Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality (Grant No. IDHT20170507) and Program of Great Wall Scholar (Grant No. CIT&TCD20180313) and Jointly Projects of Beijing Natural Science Foundation and Beijing Municipal Education Commission (Grant No. KZ201810017023).
dc.format.extent18 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Simulació
dc.subject.otherHydraulic fracturing
dc.subject.otherproper generalized decomposition
dc.subject.otherreduced order modeling
dc.subject.othernumerical simulation
dc.titleA numerical study on hydraulic fracturing problems via the proper generalized decomposition method
dc.contributor.groupUniversitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::76 Fluid mechanics::76E Hydrodynamic stability
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
local.citation.authorWang, D.; Zlotnik, S.; Diez, P.
local.citation.publicationNameCMES: computer modeling in engineering and sciences

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