Solute Transport Equation

Advection-Dispersion Equation

θ	water content
c	solute concentration [M/L3]
t	time [T]
x	spatial coordinate [L]
Dw	dispersion coefficient [L2/T]
q	volumetric flux density [L/T]

Advection-Dispersion-Reaction Equation

Equilibrium and non-equilibrium (non)linear sorption, linear equilibrium between aqueous and aqueous phase, first-order sequential (unidirectional) or decay rate reactions, and zero-order rate reactions are included in the advection-dispersion equation for solutes in the aqueous, solid and gaseous phase. The equation is:

θ	water content
c	solute concentration in liquid phase [M/L3]
s	solute concentration in solid phase [M/M] described by a (non)linear (non) equilibrium adsorption isotherms.
t	time [T]
x	spatial coordinate [L]
Dw	dispersion coefficient [L2/T]
q	volumetric flux density [L/T]

Advection-Dispersion Equation with equilibrium gas exchange

θ	water content
av	gas content
c	solute concentration [M/L3]
g	gas concentration [M/L3] described by a linear equilibrium model
t	time [T]
x	spatial coordinate [L]
Dw	dispersion coefficient in liquid phase [L2/T]
Dg	gas diffusion coefficient [L²/T]
q	volumetric flux density [L/T]
γw	zero-order rate constant for the liquid phase [M/L³T]
γa	zero-order rate constant for the gas phase [M/L³T]

Dual-porosity non-equilibrium advection-dispersion equation [Simunek and van Genuchten, 2008]

θm	water content in mobile region
θim	water content in immobile region
cm	solute concentration in mobile region [M/L3]
cim	solute concentration in immobile region [M/L3]
t	time [T]
x	spatial coordinate [L]
Dwm	dispersion coefficient in liquid phase (mobile region) [L2/T]
q	volumetric flux density [L/T]
Γs	mass transfer term between mobile and immobile region [M/L3T]
ω	mass transfer coefficient [1/T]
Γw	water transfer term between mobile and immobile region [M/L3T]
c*	equal to cm if Γw>0 equal to cim if Γw<0