a study of drag forces on attached colloidal particles in a packed bed using multiscale numerical...
DESCRIPTION
"A STUDY OF DRAG FORCES ON ATTACHED COLLOIDAL PARTICLES IN A PACKED BED USING MULTISCALE NUMERICAL MODELING" ; Slides of my presentation in the American Geophysical Union's Fall Meeting in 2013, San Francisco, USA.TRANSCRIPT
A STUDY OF DRAG FORCES ON ATTACHED
COLLOIDAL PARTICLES IN A PACKED BED USING
MULTISCALE NUMERICAL MODELING
Amin Mirsaeidi* and Karsten E. Thompson*,**
*Cain Department of Chemical Engineering **Craft & Hawkins Department of Petroleum Engineering
Louisiana State University — Baton Rouge, LA, USA
December 3, 2012
AGU Fall Meeting
San Francisco, USA 1
Size of Colloidal Particles :
Usually smaller than 1 µm in size
and greater than 1 nm.
Wide Range of Application:
Filtration Processes: Mineral Industry, Pharmaceutical Industry,
etc.
Colloidal Fouling: Particulate Fouling by Solid Particles,
Biological Fouling
Medicine: Blood Vessel Clogging
Coating Processes
Transport of Colloidal containments such as Bacteria and Viruses
in Ground Water
Introduction
SEM images of a mixture of 3.8 µm particles
together with the bulk colloid of 0.33 µm
PMMA spheres. Source: blogs.nasa.gov
2
Modeling Colloid Transport at Multiple Scales
10−9m 10−5m 10−1 m 102 m
Streamline
Scale
Pore
Scale
Continuum
Scale
Macroscopic
Scale
𝜌𝜕𝒖
𝜕𝑡+ 𝒖. 𝛁𝒖 = 𝜌𝒈 + 𝛁. 𝝈
𝛁. 𝒖 = 𝟎
𝑽 = 1
𝜇 𝑲. 𝛁𝑃
𝜵. 𝑽 = 0
3
Physics Built into Transport Models
• van der Waals Attraction
• Double Layer Interaction
• Surface Heterogeneity
• Gravity
• Hydrodynamic Interactions
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• van der Waals Attraction
• Double Layer Interaction
• Surface Heterogeneity
• Gravity
• Hydrodynamic Interactions:
• Happel Cell model (1)
• Brinkman model (1)
• Constricted Tube Model (1)
• Effective Medium Approximation (2)
(1) Tien, C. and Ramarao, B. V. Granular Filtration of Aerosols and Hydrosols; Elsevier: Oxford, U.K., 2007.
(2) Yongcheng Li, C.-W. Park Effective medium approximation and deposition of colloidal particles in fibrous
and granular media Advances in Colloid and Interface Science, Volume 87, Issue 1, 29 September 2000,
Pages 1–74
Physics Built into Transport Models
5
Hydrodynamic Modeling in Realistic Materials
Problem
Traditional models do not capture the variety of
hydrodynamics seen in realistic, heterogeneous materials.
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1,000-sphere random packing with distribution of sphere sizes. Porosity = 37%
Periodic packing of 1507 cylinders. Porosity=63%.
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Image of a Dolomite Rock Porosity = 13.18% 420x420x790 Voxels, Resolution = 3.9 micron
1,000-sphere random packing with distribution of sphere sizes. Porosity = 37%
Synthetic sandstone Porosity=16.98%
Periodic packing of 1507 cylinders. Porosity=63%.
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Hydrodynamic Modeling in Realistic Materials
Problem
Traditional models to not capture the variety of
hydrodynamics seen in realistic, heterogeneous materials.
Objective
Investigate forces on small particles attached to
heterogeneous porous media using computational
modeling.
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Approach:
10
100-sphere random packing with distribution of sphere sizes. Porosity = 35%
Approach:
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12
13
Validation: Analytic Versus Numerical Computation of
Hydrodynamic Forces
Colloid Particle Radius = R/100
Filter Particle
Radius = R
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This particular formulation taken from
Huilian Ma and William P. Johnson
Langmuir 2010 26 (3), 1680-1687
Analytic Computation: Generic Sphere in Cell Model
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Numerical Computation: Generic Sphere in Cell Model
1. Multiscale meshing with
colloidal particles embedded
in the porous medium.
(Algorithm designed for
arbitrarily complex pore
structures.)
2. FEM simulation of low-
Reynolds number flow
3. Nodal computational of
forces on attached particles
(both viscous and pressure
forces).
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Validation
Particle Magnitude of Drag Force Value
1 0.0135
2 0.0120
3 0.0147
4 0.0026
5 0.0135
Particle Magnitude of Drag Force Value
1 0.0105
2 0.0100
3 0.0105
4 0.0062
5 0.0100
Numerical Computation: Cubic packing separated to 70% porosity
Analytic Formula: sphere in cell model
Order of magnitude agreement between analytic and numerically computed drag
forces.
• The two problems are not identical
• Numerical answers can be improved with mesh refinement.
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Case Problem I:
Random-Pack consisted of 120 spherical Grains of Uniform Diameter
5 Colloidal Particles 100 times smaller than the average Grain Demeter.
Porosity = %33.78
Schematic of a Random Pack
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Case Problem I:
Pressure Field Velocity Field
Y
X 19
ONE MORE PIC
HERE
Pressure Field Velocity Field
Y
X
Case Problem I:
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ONE MORE PIC
HERE
Y
X
Case Problem I:
21
ONE MORE PIC
HERE
Y
X
Case Problem I:
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Case Problem I:
23
Case Problem I:
Random-Pack consisted of 120 spherical Grains of Uniform Diameter
5 Colloidal Particles 100 times smaller than the average Grain Demeter.
Porosity = 0.3378
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
1 2 3 4 5
Normalized Drag Force Values using Analytical Formulae (Case I)
NormalizedDrag ForceValues usingAnalytical…
Analytical Solution
0.0E+00
5.0E-01
1.0E+00
1.5E+00
2.0E+00
2.5E+00
1 2 3 4 5
Normalized Magnitude of Drag Force Values(Case I)
NormalizedMagnitude ofDrag ForceValues
Numerical Solution
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Case Problem I:
Random-Pack consisted of 120 spherical Grains of Uniform Diameter
5 Colloidal Particles 100 times smaller than the average Grain Demeter.
Porosity = 0.3378
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
1 2 3 4 5
Normalized Magnitude of Drag Force Values
NormalizedDrag ForceValues usingAnalytical…
Analytical Solution
0.0E+00
5.0E-01
1.0E+00
1.5E+00
2.0E+00
2.5E+00
1 2 3 4 5
Normalized Magnitude of Drag Force Values
NormalizedMagnitude ofDrag ForceValues
Numerical Solution
25
Case Problem I:
Particle 3
Particle 4
Particle 5
Particle 1 Particle 2
0.0E+00
5.0E-01
1.0E+00
1.5E+00
2.0E+00
2.5E+00
1 2 3 4 5
Normalized Magnitude of Drag Force Values
Normalized Magnitudeof Drag Force Values
26
Case Problem I:
Particle 3
Particle 4
Particle 5
Particle 1 Particle 2
0.00E+00
5.00E-08
1.00E-07
1.50E-07
2.00E-07
2.50E-07
1 2 3 4 5
Magnitude of Drag ForceValues (Due to Pressure)
Magnitude of Drag ForceValues ( due to ViscousStress)
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Case Problem II:
Particle 4
Particle 5
Particle 1
Particle 2
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Particle 4
Particle 5
Particle 1
Particle 2
Particle 3
Particle 1
Particle 4
Particle 2
Particle 5
0.00E+00
5.00E-01
1.00E+00
1.50E+00
2.00E+00
2.50E+00
1 2 3 4 5
Normalized Magnitude of Drag Force Values (Case II)
Normalized Magnitudeof Drag Force Values
0.0E+00
5.0E-01
1.0E+00
1.5E+00
2.0E+00
2.5E+00
1 2 3 4 5
Normalized Magnitude of Drag Force Values(Case I)
Normalized Magnitude ofDrag Force Values
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Conclusion
• Complex Geometry of a Porous Material Significantly influences the Flow Fields
• Flow Channeling, Unexpected Stagnation
Regions, etc., occur. • Direct Numerical Simulations Provide
Detailed Insight into Flow Behavior in Complex Geometries: Random Packs, Real Porous Media
• Colloidal Retention, Blockage Effect, etc., can be Observed and Explained at Streamline-Scale Level.
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Acknowledgment
Dr.Nathan Lane for help with the finite-element Stokes Solver Timothy W. Thibodeaux for assistance with the Visualization Graduate School of LSU For Partial Funding
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Thank You!
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