Heuristic pressure profiles in hydraulic fracturing. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Schätzer, Markus; Fries, Thomas‐Peter
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800068
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: In hydraulic fracturing, the pressure exerted by the fracking fluid onto the surrounding solid, is typically obtained from solving the Reynolds equation. This is not always robust and leads to a complex behaviour at the crack front (toughness or viscous regimes). In the presented work, the Reynolds equation is replaced by a simplified fluid model, where pre‐defined pressure distributions are assumed which lead to a simpler and robust coupled problem. The mapping of dimensionless prescribed pressure distributions onto the physical crack surface of the mesh is discussed based on a dimensionless distance function. This function is obtained by solving the Laplace‐Beltrami operator on the explicit representation of the manifold, i.e., the surface mesh, where distances are evaluated along streamlines which represent the fluid flow of the fracking fluid within the fracture.