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

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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

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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

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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:

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100-sphere random packing with distribution of sphere sizes. Porosity = 35%

Approach:

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12

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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:

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ONE MORE PIC

HERE

Y

X

Case Problem I:

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Case Problem I:

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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 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

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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

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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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