caa a22 4500 463163494 CHVBK 20180406164754.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s11242-006-9038-7 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9038-7 On the problem of fluid leakoff during hydraulic fracturing [Elektronische Daten] [Michael Economides, Dmitry Mikhailov, Victor Nikolaevskiy] 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. Springer Science+Business Media B.V., 2006 Hydraulic fracture nationallicence Pressure diffusion nationallicence Mass transport nationallicence Porous media nationallicence Leakage nationallicence Integral transform nationallicence Non-steady fluid flows nationallicence Special boundary condition nationallicence Heat conductivity nationallicence Economides Michael University of Houston, Houston, TX, USA aut Mikhailov Dmitry Institute of Earth Physics, Russian Academy of Sciences, Bolshaya Gruzinskaya 10, 123995, Moscow, Russian Federation aut Nikolaevskiy Victor Institute of Earth Physics, Russian Academy of Sciences, Bolshaya Gruzinskaya 10, 123995, Moscow, Russian Federation aut Transport in Porous Media Kluwer Academic Publishers 67/3(2007-04-01), 487-499 0169-3913 67:3<487 2007 67 11242 https://doi.org/10.1007/s11242-006-9038-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9038-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Economides Michael University of Houston, Houston, TX, USA aut NATIONALLICENCE 700 1- Mikhailov Dmitry Institute of Earth Physics, Russian Academy of Sciences, Bolshaya Gruzinskaya 10, 123995, Moscow, Russian Federation aut NATIONALLICENCE 700 1- Nikolaevskiy Victor Institute of Earth Physics, Russian Academy of Sciences, Bolshaya Gruzinskaya 10, 123995, Moscow, Russian Federation aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/3(2007-04-01), 487-499 0169-3913 67:3<487 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer