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Transport in Porous Media

, Volume 75, Issue 2, pp 227–247 | Cite as

Effect of Slow and Fast Moving Liquid Zones on Solute Transport in Porous Media

  • Suresh A. KarthaEmail author
  • Rajesh Srivastava
Article
  • 165 Downloads

Abstract

A conceptual model is developed in this article that accounts for the effect of slow and fast moving liquid zones on solute transport in porous media. The liquid phase within the porous media is divided into three zones—immobile, slow moving, and fast moving. Slow moving liquids surround the solid particles in thin layers and have lower velocity in flow. Fast moving liquids have higher velocity and are not in contact with the solid particles. Solute mass transfer occurs between the slow and fast liquids, and the slow and immobile liquids. The immobile and slow moving liquids interact with the solid matrix in the media through the mechanism of sorption and desorption. Implicit finite-difference methods are used to solve the partial differential equations that describe the slow and fast movement of solute in the porous medium. The model was validated for a laboratory column experimental data. Sensitivity analyses were conducted to ascertain the effects of the model parameters on solute movement. The effect of each parameter on retardation of the solute movement was analyzed. It was observed that the maximum retardation of solute occurs when there is high adsorption coefficient, high mass transfer rates, and high volume of slow moving liquid in the porous media.

Keywords

Darcy discharge Immobile liquid Multi-process non-equilibrium SFT Retardation Breakthrough curves Non-ideal transport 

Notations

Ω

Volume of an individual finite-difference cell, M0L3T0

αim

Solute mass transfer rate between slow and immobile liquid, M0L0T−1

αsf

Solute mass transfer rate between slow and fast liquid, M0L0T−1

α*

van-Genuchten’s parameter for liquid pressure computation, M0L−1 T0

ε

Porosity of the media, M0L0T0

λ

van-Genuchten’s parameter in computing permeability, M0L0T0

μ

Kinematic viscosity of the liquid, ML−1T−1

Δx

Spatial step size for finite-difference scheme, M0L1T0

Δt

Temporal step size for finite-difference scheme, ML−1T−1

ρb

Bulk density of the porous medium, ML−3T0

ρl

Density of liquid, ML−3T0

σfs

Saturation of the fast moving liquid, M0L0T0

σl

Total liquid saturation in the porous medium, M0L0T0

σim

Immobile liquid saturation in the porous medium, M0L0T0

σle

Effective liquid saturation in the porous medium, M0L0T0

σr

Irreducible liquid saturation in the porous medium, M0L0T0

σsl

Saturation of the slow moving liquid, M0L0T0

σsle

Effective slow liquid saturation in the porous medium, M0L0T0

A

Area of cross section used in divergence theorem for integration, M0L2T0

Cfs

Solute concentration in fast moving liquid (g/g), M0L0T0

Cim

Solute concentration in immobile liquid (g/g), M0L0T0

Cm

Solute concentration in slow moving liquid (g/g), M0L0T0

C0

Solute concentration in the inflow liquid (g/g), M0L0T0

\({D_{f}^{\ast}}\)

Dispersion coefficient in fast liquid, M0L2T

\({D_{\rm sl}^{\ast}}\)

Dispersion coefficient in slow liquid, M0L2T

Fim

Instantaneous sorption fraction in immobile zone, M0L0T0

Fsl

Instantaneous sorption fraction in slow liquid, M0L0T0

Kim

Immobile equilibrium adsorption coefficient, M−1L3T0

Ksl

Equilibrium adsorption coefficient in the slow liquid, M−1L3T0

L

Length of column, M0L1T0

Pl

Liquid pressure in the column, ML−1T−2

PV

Pore volume, M0L0T0

\({\dot {S}_{\rm fs}}\)

Liquid source term in the fast zone, ML−3T−1

\({\dot {S}_{\rm sl}}\)

Liquid source term in the slow zone, ML−3T−1

Sim1

Instantaneously sorbed solute concentration from immobile liquid (g/g), M0L0T0

Sim2

Rate-limited sorbed solute concentration from immobile liquid (g/g), M0L0T0

Ssl1

Instantaneously sorbed solute concentration from slow liquid (g/g), M0L0T0

Ssl2

Rate-limited sorbed solute concentration from slow liquid (g/g), M0L0T0

d

Dispersivity, M0LT0

f

Fraction of sorption site available for slow moving liquid, M0L0T0

ĝ

Acceleration due to gravity vector, M0LT−2

krls

Relative permeability for slow liquid, M0L0T0

kim

Sorption rate in the immobile liquid, M0L0T−1

ksl

Sorption rate in the slow liquid , M0L0T−1

kps

Intrinsic permeability in the slow liquid zone, M0L2T0

ksat

Saturated intrinsic permeability, M0L2T0

\({\vec {u}_{\rm l}}\)

Darcy Discharge or Darcy Velocity, M0LT−1

\({\vec {u}_{\rm fs}}\)

Fast component of Darcy discharge, M0LT−1

\({\vec {u}_{\rm sl}}\)

Slow component of Darcy discharge, M0LT−1

t

Time variable, M0L0T

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Civil EngineeringIndian Institute of Technology GuwahatiGuwahatiIndia
  2. 2.Department of Civil EngineeringIndian Institute of Technology KanpurKanpurIndia

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