Porosity distributions in a fluidized bed with an immersed obstacle

Bouillard, Jacques; Lyczkowski, Robert W.; Gidaspow, Dimitri

doi:10.1002/aic.690350604

Cited by 228 publications

(96 citation statements)

References 24 publications

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“…Discussion regarding the modeling of this term may be found in [8,9]. These same papers discussed the modeling of the solids compaction stress rc.…”

Section: Re 5 1000mentioning

confidence: 99%

NMR imaging and hydrodynamic analysis of neutrally buoyant non-Newtonian slurry flows

Bouillard

1994

Powder Technology

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“…Discussion regarding the modeling of this term may be found in [8,9]. These same papers discussed the modeling of the solids compaction stress rc.…”

Section: Re 5 1000mentioning

confidence: 99%

NMR imaging and hydrodynamic analysis of neutrally buoyant non-Newtonian slurry flows

Bouillard

1994

Powder Technology

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“…The effect of solid phase on fluid flow is modeled in a simplified manner as an average effect over many particles, instead of modeling the details of fluid flow between the particles. The effects of solid particles in the fluid flow are introduced to the numerical solution of Navier-Stokes equations in terms of porosity and coupling force (Bouillard et al 1989). For porosities e \ 0.8, the following fluid flow equation is implemented in PFC 2D (Bouillard et al 1989):…”

Section: Dem-cfd Model With Improved Contact Lubrication Modelmentioning

confidence: 99%

“…The effects of solid particles in the fluid flow are introduced to the numerical solution of Navier-Stokes equations in terms of porosity and coupling force (Bouillard et al 1989). For porosities e \ 0.8, the following fluid flow equation is implemented in PFC 2D (Bouillard et al 1989):…”

Section: Dem-cfd Model With Improved Contact Lubrication Modelmentioning

confidence: 99%

Micromechanics of proppant agglomeration during settling in hydraulic fractures

Tomac

Gutierrez

2015

J Petrol Explor Prod Technol

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The micromechanics of proppant settling in quiescent fluid in a rough and relatively narrow rock fracture is investigated. The study focuses on particleparticle and particle-wall interactions in a dense-phase particle settling. The study used a coupled discrete element method and computational fluid dynamics (DEM-CFD) code because DEM-CFD is the most suitable computational method for modeling the frequent interactions of dense assembly of rigid particles and enables modeling of two-way solid-fluid interactions. Due to frequent particleparticle interactions of grains submerged in fluids, the particle interaction model in DEM is improved by the incorporation of the effects of lubrication due to a layer of fluid surrounding particles. Results of the numerical study are compared to previous experimental and theoretical relationships. The findings of the study highlight conditions that lead to proppant aggregation due to the fluid viscosity and fracture width in relation to particle diameter ratio. In the light of the DEM-CFD results, it was found that published relationships are inadequate in describing the settling rates for proppant in a rough and narrow hydraulic fracture and high fluid viscosity. Micromechanical particle interactions during settling and erratic upward and fluid counter-flow may cause proppant trajectories that are not always in the direction of gravity in a rough fracture resulting in clogging of the fracture or forming faster settling particle agglomerates. The maximum packing density 0.3-0.4 (3.9-5.9 lbs/gal) of proppant in a narrow and rough hydraulic fracture was obtained in this study, which is lower than the usually assumed one of 0.5 (9.8 lbs/gal) for any given fracture roughness.Keywords DEM-CFD Á Lubrication Á Fluid-solid coupling Á Dense-phase flow Á Proppant settling Á Hydraulic fracture List of symbols

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“…Based on the prescribed hydraulic conditions, base soil particles may be either retained within the filter at various depths or washed out of the system. To consider the principles of hydrodynamics within the system, the Navier-Stokes equation for porous media was used (Bouillard et al 1989) r w ∂ð2 uÞ ∂t þ r w u ∂ð2 uÞ…”

Section: Mathematical Descriptionmentioning

confidence: 99%

Analytical Solutions for Filtration Process Based on the Constriction Size Concept

Indraratna

Rujikiatkamjorn

Nguyen

et al. 2014

Geo-Congress 2014 Technical Papers

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An analytical model is proposed to describe the filtration process applicable to a base soil-filter system. The Navier-Stokes equations for porous media are used to capture the hydrodynamic behavior, whereas, numerically, a new algorithm is proposed to solve the Navier-Stokes equation in a nonlinear form. The various mixtures of base soil particles eroded and water flow within the system are computed using the workenergy principle incorporating the constriction size of the filter.The model can assess the filtration process through the flowrate and the accumulation and redistribution of fine particles within the filter. By discretizing the base soil and filter domains into discrete elements, the model can predict the time-dependent particle gradation of the filter for each element. Laboratory tests reported in other studies and those conducted by the authors validate the model in relation to other available models. Abstract: An analytical model is proposed to describe the filtration process applicable to a base soil-filter system. The Navier-Stokes equations for porous media are used to capture the hydrodynamic behavior, whereas, numerically, a new algorithm is proposed to solve the Navier-Stokes equation in a nonlinear form. The various mixtures of base soil particles eroded and water flow within the system are computed using the workenergy principle incorporating the constriction size of the filter. The model can assess the filtration process through the flow rate and the accumulation and redistribution of fine particles within the filter. By discretizing the base soil and filter domains into discrete elements, the model can predict the time-dependent particle gradation of the filter for each element. Laboratory tests reported in other studies and those conducted by the authors validate the model in relation to other available models.

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Porosity distributions in a fluidized bed with an immersed obstacle

Cited by 228 publications

References 24 publications

NMR imaging and hydrodynamic analysis of neutrally buoyant non-Newtonian slurry flows

NMR imaging and hydrodynamic analysis of neutrally buoyant non-Newtonian slurry flows

Micromechanics of proppant agglomeration during settling in hydraulic fractures

Analytical Solutions for Filtration Process Based on the Constriction Size Concept

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