Доклады Академии наукДоклады Академии наук0869-5652The Russian Academy of Sciences1868610.31857/S0869-56524894362-367Research ArticleBehavior of viscoplastic rocks near fractures: mathematical modellingShelukhinV. V.shelukhin@hydro.nsc.ruKontorovichA. E.<p>Academician of the Russian Academy of Sciences</p>KontorovichAE@ipgg.sbras.ruLavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of SciencesNovosibirsk State UniversityTrofimuk Institute of Petroleum Geology and Geophysics Sibirian Branch of the Russian Academy of Sciences1012201948943623671512201915122019Copyright © 2019, Russian academy of sciences2019<p>Starting from conservation laws and basic thermodynamic principles, we derive equations for a two-phase granular fluid. The first phase is the granular viscoplastic Bingham fluid and the second phase is the viscous Newtonian fluid. We perform an asymptotic analysis of the equations for the flows in the Hele-Show cell when the channel width is well much below its length. While calculating the fluid fluxes-pressure gradient relationship, we derive laws of flow of the two-phase granular viscoplastic fluid through porous media. A criterium is formulated for the start up of the granular phase flow through a porous medium. Given a yield stress, we prove that such a phase does not flow if either or both pressure gradient and channel width are small. We calculated phase flows varying phase viscosities, phase resistivities and yield stress. We reveal reasons which slow down particle intrusion into a porous medium.</p>two-phase granular fluidsviscoplasticityyield stressflows in porous mediaдвухфазные гранулированные жидкостивязкопластичностьпредельное напряжение сдвигафильтрация[Chateau X., Ovarlez G., Trung K.L. Homogenization Approach to the Behavior of Suspensions of Noncolloidal Particles in Yield Stress Fluids // J. Rheol. 2008. V. 52. P. 489-506.][Eringen A.C. Microcontinuum field theories. N.Y.: Springer-Verlag, 1999.][Mewis J., Wagner N. Colloidal Suspension Rheology. Cambridge: Cambridge University, 2012.][Shelukhin V.V. Thermodynamics of Two-Phase Granular Fluids // J. Non-Newtonian Fluid Mechanics. In press. https://doi.org/10.1016/j.jnnfm.2018.02.004][Shelukhin V.V. Bingham Viscoplastic as a Limit of Non-Newtonian Fluids // J. Mathematical Fluid Mechanics. 2002. V. 4. P. 109-127.][Shelukhin V.V., Růžička M. On Cosserat-Bingham Fluids // Z. angew. Math. Mech. 2013. Bd 93. № 1. S. 57-72.][Конторович А.Э., Родякин С.В., Бурштейн Л.М., Костырева Е.А., Рожкова С.В., Ян П.А. Пористость и ненасыщенность баженовской свиты // Геология нефти и газа. 2018. № 3. С. 61-73.]