On the problem of fluid leakoff during hydraulic fracturing |
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Authors: | Michael J Economides Dmitry N Mikhailov Victor N Nikolaevskiy |
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Institution: | (1) University of Houston, Houston, TX, USA;(2) Institute of Earth Physics, Russian Academy of Sciences, Bolshaya Gruzinskaya 10, Moscow, 123995, Russian Federation |
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Abstract: | While a hydraulic fracture is propagating, fluid flow and associated pressure drops must be accounted for both along the fracture
path and perpendicularly, into the formation that is fractured, because of fluid leakoff. The accounting for the leakoff shows
that it is the main factor that determines the crack length. The solved problem is useful for the technology of hydraulic
fracturing and a good example of mass transport in a porous medium. To find an effective approach for the solution, the thin
crack is represented here as the boundary condition for pore pressure spreading in the formation. Earlier such model was used
for heat conduction into a rock massif from a seam under injection of hot water. Of course, the equations have other physical
sense and mathematically they are somewhat different. The new plane solution is developed for a linearized form that permits
the application of the integral transform. The linearization itself is analogous to the linearization of the natural gas equation
using the real gas pseudo-pressure function and where the flux rates are held constant and approximations are introduced only
into the time derivatives. The resulting analytical solution includes some integrals that can be calculated numerically. This
provides rigorous tracking of the created fracture volume, leakoff volume and increasing fracture width. The solutions are
an advance over existing discreet formulations and allow ready calculations of the resulting fracture dimensions during the
injection of the fracturing fluid. |
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Keywords: | Hydraulic fracture Pressure diffusion Mass transport Porous media Leakage Integral transform Non-steady fluid flows Special boundary condition Heat conductivity |
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