Analytical Solution of Equations for Chemical Transport with Adsorption, Longitudinal Diffusion, Zeroth-Order Production, and First-Order Decay

This Demonstration examines one-dimensional chemical transport in a porous medium as influenced by simultaneous adsorption, zeroth-order production, and first-order decay. The corresponding equation is [1]:



2

∂

c

∂

2

x

-v

∂c

∂x

-R

∂c

∂t

=μc-γ

,

where



is the effective dispersion coefficient,

c

is the fluid phase concentration,

x

is distance,

t

is time,

v

is the interstitial fluid velocity,

R

is a retardation factor defined as

R=1+ρk/θ

,

μ

is a general decay constant defined as

μ=α+βρk/θ

, and

γ

is the zeroth-order fluid phase source term. Here

ρ

is the porous medium bulk density,

k

is the ratio of adsorbed to fluid phase concentration,

θ

is the volumetric moisture content,

α

is a first-order liquid phase decay constant, and

β

is the first-order solid phase decay constant.

The transport equation is solved subject to the following initial and boundary conditions:

c(x,0)=

C

i

,

-

∂c(0,t)

∂x

+vc(0,t)=

v C 0	0≤t≤ t 0
0	t> t 0

,

and

∂(∞,t)

∂x

=0

, where

C

i

and

C

0

are the constant initial fluid and surface boundary concentrations, taken here as

(

C

i

,

C

0

)=(0,1)

.