《《Finite element modeling of hydraulic fracturing in 3D》.pdf

Comput Geosci (2013) 17:647–659 DOI 10.1007/s10596-013-9346-2 ORIGINAL PAPER Finite element modeling of hydraulic fracturing in 3D Magnus Wangen Received: 23 April 2012 / Accepted: 28 February 2013 / Published online: 22 March 2013 © Springer Science+Business Media Dordrecht 2013 Abstract A procedure based on the finite element Keywords Hydraulic fracturing · 3D · method is suggested for modeling of 3D hydraulic Finite elements formulation fracturing in the subsurface. The proposed formulation partitions the stress field into the initial stress state and an additional stress state caused by pressure buildup. 1 Introduction The additional stress is obtained as a solution of the Biot equations for coupled fluid flow and deformations Hydraulic fracturing is the coupled dynamics of frac- in the rock. The fluid flow in the fracture is represented ture and fluid flow, where the rock fractures because of on a regular finite element grid by means of “fracture” an increasing pore fluid pressure [17]. It is a process that porosity, which is the volume fraction of the fracture. is commonly used by the petroleum industry to enhance The use of the fracture porosity allows for a uniform the flow properties of the near-well region [13]. The finite element formulation for the fracture and the rock, injection fluid often contains proppants that props up both with respect to fluid pressure and displacement. It the fractures after the injection has stopped. Hydraulic is demonstrated how the fracture aperture is obtained fracturing is necessary in the production of the gas from the displacement field. The model has a fracture from low-permeability shales [6]. Another example is criterion by means of a strain limit in each element. the use of hydraulic fract