Pollution of Water Resources from Agricultural Fields and Its Control - Practices of Irrigation and On-farm Water Management - page 254

7.4.3 Convection-Dispersion Equation

The movement of solute in porous media is commonly described by the convection-
dispersion equation (CDE) (Bear, 1972 ) . For a steady state, one-dimensional
transport of a reactive solute through a uniform soil, the CDE can be written as

2 C
∂

D ∂ θ ∂

C
∂

v ∂

C
∂ t =

R − (7.6)

z 2

z

where
R = retardation factor (dimensionless)

hydrodynamic dispersion coefficient (m 2 /s)

D =

C = solute concentration (mol/s)

θ = water content (volumetric)

v = pore water velocity (m/s)

=

z depth (m)

The dispersion coefficient D is often assumed to be linearly related to the pore
water velocity, D is the dispersivity (m).

The CDE describes solute transport as the sum of the average convection with
flow, and the hydrodynamic dispersion.

= λ v , where λ

7.4.3.1 Assumptions in CDE

The CDE is based on three basic assumptions:

- Continuous porous media
- Average flow velocity
- Fick's first law for solute dispersion

7.4.3.2 Drawbacks of CDE

The most important drawbacks of CDE when it is used to simulate transport, can
be attributed to non-Fickian behavior of dispersive transport as well as the apparent
scale dependence of the dispersivity.

The solute dynamics in the root zone profile can be described by different
mathematical equations under different situations.

7.4.4 Governing Equation for Solute Transport Through
Homogeneous Media

7.4.4.1 Two-Dimensional Equation

The partial differential equations governing two-dimensional nonequilibrium chem-
ical transport of solutes involved in a sequential first-order decay chain during