MODELING OF HYDRAULIC
FRACTURES
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HYDRAULIC FRACTURES
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Hydraulic fracturing can be broadly
defined as the process by which a
fracture initiates and propagates due to
hydraulic loading (i.e., pressure)
applied by a fluid inside the fracture.
Hydraulic fracturing is a complicated
process to model, as it involves the
coupling of at least three processes:
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(i) the mechanical deformation induced
by the fluid pressure on the fracture
surfaces;
(ii) the flow of fluid within the fracture;
(iii) the fracture propagation.
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HYDRAULIC FRACTURES
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creation of an initial path for the fracture (‘‘perforation’’ - specially
designed shaped-charges are blasted on the wellbore walls with
given orientations, perforating the casing and creating finger-like
holes or weak points in the hydrocarbon-laden formation)
a viscous fluid is pumped inside the wellbore, inducing a steep
rise in the pressure which eventually leads to the initiation of a
fracture at the perforated interval.
a ‘‘pad’’ of clean fluid is usually pumped first, to provide sufficient
fracture width for the proppant that follows.
proppant is injected at a later stage as a suspension or slurry.
at the end of the treatment, when pumping stops, leak-off of the
residual fracturing fluid into the porous reservoir allows the
fracture surfaces to close onto the proppant pack under the action
of the far-field compressive stresses.
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POSSIBLE PROBLEMS
prediction of fracture geometry
 effective prevention of crack closure
 optimal choice of fracturing fluid
 fluid leak-off
 avoid screenouts caused by proppant a
bridging and holdup
 proppant flowback
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MODEL ASSUMPTIONS
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the material of the reservoir is considered to be linearly elastic
 in the case of layered reservoir layers are parallel and perfectly paired
 the fracture occurs in the same vertical plane
 accepted model of Newtonian fluid
One don’t need to take into account
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inelastic (plastic) behavior of the breed
 non-parallelism and imperfect conjugation of surface layers
 the real geometry of the crack
 natural fracturing
 the initial inhomogeneous stress fields caused, in particular, porosity
patterns
 compressibility, plasticity, viscoelasticity of the fluid
 the impact of leakage on the pressure inside the cracks
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KGD Model
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For the horizontal plane strain
geometry, the fracture zone
should deform independently of
the upper and lower layers. This
would occur for free slippage on
these layers, or approximately
represent a fracture with a
horizontal penetration much
smaller than the vertical one. The
fracture shape should not depend
on the vertical position. Such a
geometry is shown in Fig. 3-5; it
has a constant and uniform height
and a rectangular cross section
(Khristianovic and Zheltov, 1955;
Geema and de Klerk, 1969-KGD
Model).
Crack opening is solved in the
horizontal plane.
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PKN Model
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A second situation exists when
there is a large confinement,
hence the fracture is limited to a
given zone. Perkins and Kern
(1961) and Nordgren (1972)
considered the plane strain
assumption in vertical planes, so
each vertical cross section
deforms independently of the
others (PKN Model). However, the
fracture widths in vertical planes
are coupled through the fluid-flow
and continuity equations. Since
there is no vertical extension (or
fluid flow) in each vertical section,
the pressure is uniform.This case
would approximate a fracture with
a horizontal penetration much
larger than the vertical
penetration.
Crack opening is solved in the
vertical plane.
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REFERENCES
Adachi J., Siebrits E., Peirce A.,
Desroches J. Computer simulation of
hydraulic fractures // Int. J. of Rock
Mechanics & Mining Sciences, 44, 2007
 Michael. J. Economides, Kenneth G.
Nolte Reservoir Stimulation
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Thank you for your attention!
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