TY - JOUR

T1 - Behavior of Viscoplastic Rocks near Fractures

T2 - Mathematical Modeling

AU - Shelukhin, V. V.

AU - Kontorovich, A. E.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - On the basis of the laws of conservation and the principles of thermodynamics, a mathematical model of the flow of a two-phase granular fluid is proposed. One of the phases is the viscoplastic granular Bingham fluid; the other phase is a viscous Newtonian fluid. The equations for flows in the Hele–Shaw cell are analyzed asymptotically, i.e., when the flat-channel width is much less than its length. The correlations between the phase flow rates and the pressure gradient leading to equations of filtration for a two-phase granular viscoplastic fluid are constructed. The criterion is found for the initiation of motion of a granular phase in a porous medium. It is established that, depending on the shear-yield stress, such a phase does not flow if either the pressure gradient or the channel thickness is small. The phase flow rates are analyzed numerically at various input parameters such as the phase viscosities, phase resistivities, ultimate shear stress, etc. The factors slowing down the penetrating motion of the solid phase into the porous medium are revealed.

AB - On the basis of the laws of conservation and the principles of thermodynamics, a mathematical model of the flow of a two-phase granular fluid is proposed. One of the phases is the viscoplastic granular Bingham fluid; the other phase is a viscous Newtonian fluid. The equations for flows in the Hele–Shaw cell are analyzed asymptotically, i.e., when the flat-channel width is much less than its length. The correlations between the phase flow rates and the pressure gradient leading to equations of filtration for a two-phase granular viscoplastic fluid are constructed. The criterion is found for the initiation of motion of a granular phase in a porous medium. It is established that, depending on the shear-yield stress, such a phase does not flow if either the pressure gradient or the channel thickness is small. The phase flow rates are analyzed numerically at various input parameters such as the phase viscosities, phase resistivities, ultimate shear stress, etc. The factors slowing down the penetrating motion of the solid phase into the porous medium are revealed.

UR - http://www.scopus.com/inward/record.url?scp=85081026308&partnerID=8YFLogxK

U2 - 10.1134/S1028335819120036

DO - 10.1134/S1028335819120036

M3 - Article

AN - SCOPUS:85081026308

VL - 64

SP - 461

EP - 465

JO - Doklady Physics

JF - Doklady Physics

SN - 1028-3358

IS - 12

ER -