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Upscaling polydispersed particle transport in porous media using pore network model

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Abstract

Understanding particle transport in porous media is critical in the sustainability of many geotechnical and geoenvironmental infrastructure. To date, the determination of the first-order rate coefficients in the advection–dispersion equation for simulating attachment and detachment of particles in saturated porous media typically has been relied on the result of laboratory-scale experiments. However, to determine attachment and detachment coefficients under varied hydraulic and geochemical variables, this method requires a large experimental matrix because each test provides only one set of attachment and detachment coefficients. The work performed in this study developed a framework to upscale the results obtained in pore-scale modeling to the continuum scale through the use of a pore network model. The developed pore network model incorporated variables of mean particle size, the standard deviation of particle size distribution, and interparticle forces between particles and sand grains. The obtained retention profiles using the pore network model were converted into attachment coefficients in the advection–dispersion equation for long-term and large-scale simulation. Additionally, by tracking individual particles during and after the simulation, the pore network model introduced in this study can also be employed for modeling the clogging phenomenon, as well as fundamental investigation of the impact of particle size distribution on particle retention in the sand medium.

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Abbreviations

A (M L2 T−1):

Hamaker constant

C 0, C (M L−3):

Inlet concentration and particle concentration

d 50 (L):

Median grain size of sand

D ij (L):

The Euclidean distance between centers of pore i and j

d p, d t (L):

Diameter of the pore and throats

g t, g p (M−1 L4 T):

Hydraulic conductances of throats and the half of pores

h 0 (L):

Minimum separation distance

i,j :

Pore index

J T (M L−3 T−1):

Total particle flux

k (L T−1):

Hydraulic conductivity

k att, k det (T−1):

First-order coefficients for attachment and detachment

K 1 :

Pore wall correction factor

L ij (L):

The length of the throat between pore i and pore j

L ref (L):

Reference length

M ij (M):

Transferred mass of particles from pore i to pore j

n :

Porosity

N c :

Total number of sampled particles

P (M L T−2):

Pressures at pores

p cap :

Capture probability

p m :

Cumulative probability of mth interval

Q ij (L3 T−1):

The flow rate between pore i and j

r c , r t (L):

Radius of particle and throat

r new (L):

Updated effective throat radius

r p (L):

Radius of pores

S att, S max (M M−1):

Solid phase attached particles and attachment capacity

t, Δt (T):

Time and time for one time step

U (L T−1):

Centerline velocity of throats

v, v c (L T−1):

Velocity of water and critical velocity

V inlet (L3):

Total volume of inlet pores

ΔP p, ΔP total (M L T−2):

Pressure drop at a throat and total pressure drop

θ, θ 0 :

Lumped parameter and interparticle force parameter

Μ (M L− 1 T− 1):

Viscosity of water

μ c, σ c :

Mean and standard deviation of particle size distribution

ρ s, ρ b (M L−3):

Density of particle and bulk density of sand

ψ att :

Attachment function

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Acknowledgements

This material is based upon work supported by the Georgia Department of Transportation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the writers and do not necessarily reflect the views of the Georgia Department of Transportation. Special thanks are given to Mr. J.D. Griffith, P.E., P.G. (deceased) for his support of this research project.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Ulsan, Daehak-ro 93, Nam-gu, Ulsan, 680-749, South Korea

    Jongmuk Won

  2. School of Civil and Environmental Engineering, Georgia Institute of Technology, 790 Atlantic Drive, N.W., Atlanta, GA, 30332-0355, USA

    Junghwoon Lee & Susan E. Burns

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  1. Jongmuk Won
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Correspondence to Jongmuk Won.

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Won, J., Lee, J. & Burns, S.E. Upscaling polydispersed particle transport in porous media using pore network model. Acta Geotech. 16, 421–432 (2021). https://doi.org/10.1007/s11440-020-01038-z

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