Slurry flow, gravitational settling and a proppant transport model for hydraulic fractures

Journal of Fluid Mechanics

Volumn 760, Issue 1, 2014, Pages 567-590

  Dontsov, E V ^a   Peirce, A P ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

particle fluid flows; suspensions

Indexed keywords

BOUNDARY LAYERS; FRACTURE; INTEGRAL EQUATIONS; NEWTONIAN LIQUIDS; PIPE FLOW; PROPPANTS; SUSPENSIONS (FLUIDS); VELOCITY CONTROL;

APPROXIMATE SOLUTION; GRAVITATIONAL SETTLINGS; PARTICLE CONCENTRATIONS; PARTICLE VELOCITIES; PARTICLE/FLUID FLOWS; PROPPANT CONCENTRATIONS; PROPPANT TRANSPORTS; TWO-DIMENSIONAL FLOW;

TRANSPORT PROPERTIES;

BOUNDARY LAYER; CONTINUUM MECHANICS; DARCY LAW; FLOW MODELING; HYDRAULIC FRACTURE; PARTICLE MOTION; PARTICLE SETTLING; SLURRY; TWO-DIMENSIONAL FLOW;

EID: 84961289291     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2014.606     Document Type: Article

References (21)

1. ADACHI, J. I., DETOURNAY, E. & PEIRCE, A. P. 2010 An analysis of classical pseudo-3D model for hydraulic fracture with equilibrium height growth across stress barriers. Intl J. Rock Mech. Min. Sci. 47, 625-639.
2. ADACHI, J., SIEBRITS, E., PEIRCE, A. & DESROCHES, J. 2007 Computer simulation of hydraulic fractures. Intl J. Rock Mech. Min. Sci. 44, 739-757.
3. BATCHELOR, G. & GREEN, J. 1972 The determination of the bulk stress in a suspension of spherical particles to order c2. J. Fluid Mech. 56, 401-427.
4. BOYER, F. 2011 Suspensions concentreés: expériences originales de rheólogie. PhD thesis, Aix-Marseille Université, France.
5. BOYER, F., GUAZZELLI, E. & POULIQUEN, O. 2011 Unifying suspension and granular rheology. Phys. Rev. Lett. 107, 188301.
6. BRADY, J. F. & MORRIS, J. F. 1997 Microstructure of strongly sheared suspensions and its impact on rheology and diffusion. J. Fluid Mech. 348, 103-139.
7. DAVIS, R. H. & ACRIVOS, A. 1985 Sedimentation of noncolloidal particles at low Reynolds numbers. Annu. Rev. Fluid Mech. 17, 91-118.
8. ECONOMIDES, M. J. & NOLTE, K. G. (Eds) 2000 Reservoir Stimulation, 3rd edn. Wiley.
9. EINSTEIN, A. 1906 A new determination of molecular dimensions. Ann. Phys. 4, 289-306.
10. ESKIN, D. & MILLER, M. J. 2008 A model of non-Newtonian slurry flow in a fracture. Powder Technol. 182, 313-322.
11. GARSIDE, J. & AL-DIBOUNI, M. R. 1977 Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems. Ind. Eng. Chem. Process Des. Dev. 16, 206-214.
12. LECAMPION, B. & GARAGASH, D. 2014 Confined flow of suspensions modelled by a frictional rheology. J. Fluid Mech. 759, 197-235.
13. LEIGHTON, D. & ACRIVOS, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415-439.
14. LHUILLIER, D. 2009 Migration of rigid particles in non-Brownian viscous suspensions. Phys. Fluids 21, 023302.
15. LISTER, J. R. 1990 Buoyancy-driven fluid fracture: the effects of material toughness and of lowviscosity precursors. J. Fluid Mech. 210, 263-280.
16. MATAS, J.-P., MORRIS, J. F. & GUAZZELLI, E. 2004 Inertial migration of rigid spherical particles in Poiseuille flow. J. Fluid Mech. 515, 171-195.
17. MORRIS, J. F. & BOULAY, F. 1999 Microstructure of strongly sheared suspensions and its impact on rheology and diffusion. J. Rheol. 43, 1213-1237.
18. NOTT, P. R. & BRADY, J. F. 1994 Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275, 157-199.
19. OURIEMI, M., AUSSILLOUS, P. & GUAZZELLI, E. 2009 Sediment dynamics. Part 1. Bed-load transport by laminar shearing flows. J. Fluid Mech. 636, 295-319.
20. SEGRE, G. & SILBERBERG, A. 1961 Radial particle displacements in Poiseuille flow of suspensions. Nature 189, 209-210.
21. STICKEL, J. J. & POWELL, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129-149.