We propose a mathematical model and a discretization strategy for the simulation of pressurized fractures in porous media accounting for the poroelastic effects due to the interaction of pressure and flow with rock deformations. The aim of the work is to develop a numerical scheme suitable to model the interplay among several fractures subject to fluid injection in different geometric configurations, in view of the application of this technique to hydraulic fracturing. The eXtended Finite Element Method, here employed for both the mechanical and fluid-dynamic problems, is particularly useful to analyze different configurations without remeshing. In particular, we adopt an ad hoc enrichment for the displacement at the fracture tip and a hybrid dimensional approach for the fluid. After the presentation of the model and discretization details we discuss some test cases to assess the impact of fracture spacing on aperture during injection.

Unfitted FEM for Modelling the Interaction of Multiple Fractures in a Poroelastic Medium

Bianca Giovanardi;Luca Formaggia;Anna Scotti;Paolo Zunino
2017-01-01

Abstract

 We propose a mathematical model and a discretization strategy for the simulation of pressurized fractures in porous media accounting for the poroelastic effects due to the interaction of pressure and flow with rock deformations. The aim of the work is to develop a numerical scheme suitable to model the interplay among several fractures subject to fluid injection in different geometric configurations, in view of the application of this technique to hydraulic fracturing. The eXtended Finite Element Method, here employed for both the mechanical and fluid-dynamic problems, is particularly useful to analyze different configurations without remeshing. In particular, we adopt an ad hoc enrichment for the displacement at the fracture tip and a hybrid dimensional approach for the fluid. After the presentation of the model and discretization details we discuss some test cases to assess the impact of fracture spacing on aperture during injection.
2017
Geometrically Unfitted Finite Element Methods and Applications
978-3-319-71430-1
File in questo prodotto:
File Dimensione Formato  
GFSZ_CutFEM_LNCSE_rev.pdf

Accesso riservato

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 1.75 MB
Formato Adobe PDF
1.75 MB Adobe PDF   Visualizza/Apri
Zunino_et_al_Geometrically_unfitted_FEM_and_applications.pdf

Accesso riservato

: Publisher’s version
Dimensione 610.59 kB
Formato Adobe PDF
610.59 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1038616
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 12
social impact