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《《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
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