Theory of sand transport in thin fluids - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 1985

Theory of sand transport in thin fluids

W.L. Medlin
  • Fonction : Auteur

Résumé

We present a comprehensive theory of sand transport in thin fluid slot flow. Equations of motion are developed for each of the transport mechanisms observed in slot flow experiments: viscous drag, turbulence, and bed load transport. Viscous drag and turbulence are treated together by deriving a differential field equation for sand distribution in the slot. The terminal fall velocity and a turbulent diffusion coefficient appear as parameters. The field equation is simplified by transformation to a system of curvilinear coordinates. The coordinate lines are streamlines of sand particles in the absence of diffusion. Turbulent transport is accounted for by the diffusion of a square wave distribution at the slot entrance. The diffusion length associated with this process is a measure of the concentration of sand process is a measure of the concentration of sand transported by turbulence. We consider both natural turbulence and stimulated turbulence generated at the slot entrance. Our theoretical results show that natural turbulence produces little sand transport. Stimulated turbulence is more important, but it dies out quickly with distance. Bed load transport is treated by using a principle of virtual dissipation. We consider two kinds of dissipation in the fluidized layer. One is associated with motion of sand particles relative to the fluid. The other is due to an increase in viscosity with increasing sand concentration. We derive equations of motion for sand particles in the fluidized layer. An important result is that sand transport in the bed load does not scale up with fracture height as long as the flow velocity and the entrance concentration remain the same. This leads to the conclusion that bed load transport is a significant factor in laboratory-scale experiments, but not on a scale of field treatments. Therefore, of the three transport mechanisms observed in slot flow experiments, only viscous drag is important under hydraulic fracturing conditions. We discuss application of the complete theory to sand transport in fracturing treatments.
Fichier non déposé

Dates et versions

hal-01371501 , version 1 (26-09-2016)

Identifiants

Citer

Maurice A. Biot, W.L. Medlin. Theory of sand transport in thin fluids . SPE Annual Technical Conference and Exhibition, 1985, Las vegas, Nevada, United States. ⟨10.2118/14468-MS⟩. ⟨hal-01371501⟩
9 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More