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
NotationsVolume of an individual finite-difference cell, M 0 L 3 T 0 α im Solute mass transfer rate between slow and immobile liquid, M 0 L 0 T −1 α sf Solute mass transfer rate between slow and fast liquid, M 0 L 0 T −1 's parameter for liquid pressure computation, M 0 L −1 T 0 ε Porosity of the media, M 0 L 0 T 0 λ van-Genuchten's parameter in computing permeability, M 0 L 0 T 0 µ Kinematic viscosity of the liquid, ML −1 T −1 x Spatial step size for finite-difference scheme, M 0 L 1 T 0 t Temporal step size for finite-difference scheme, ML −1 T −1 ρ b Bulk density of the porous medium, ML −3 T 0 ρ l Density of liquid, ML −3 T 0 σ fs Saturation of the fast moving liquid, M 0 L 0 T 0 σ l Total liquid saturation in the porous medium, M 0 L 0 T 0 σ im Immobile liquid saturation in the porous medium, M 0 L 0 T 0 σ le Effective liquid saturation in the porous medium, M 0 L 0 T 0 σ r Irreducible liquid saturation in the porous medium, M 0 L 0 T 0 σ sl Saturation of the slow moving liquid, M 0 L 0 T 0 σ sle Effective slow liquid saturation in the porous medium, M 0 L 0 T 0 A Area of cross section used in divergence theorem for integration, M 0 L 2 T 0 C fs Solute concentration in fast moving liquid (g/g), M 0 L 0 T 0 C im Solute concentration in immobile liquid (g/g), M 0 L 0 T 0 C m Solute concentration in slow moving liquid (g/g), M 0 L 0 T 0 C 0 Solute concentration in the inflow liquid (g/g), M 0 L 0 T 0 D * f Dispersion coefficient in fast liquid, M 0 L 2 T D * sl Dispersion coefficient in slow liquid, M 0 L 2 T F im Instantaneous sorption fraction in immobile zone, M 0 L 0 T 0 F sl Instantaneous sorption fraction in slow l...