Analytical Solution of Equations for Chemical Transport with Adsorption, Longitudinal Diffusion, ZerothOrder Production, and FirstOrder Decay
Analytical Solution of Equations for Chemical Transport with Adsorption, Longitudinal Diffusion, ZerothOrder Production, and FirstOrder Decay
This Demonstration examines onedimensional chemical transport in a porous medium as influenced by simultaneous adsorption, zerothorder production, and firstorder decay. The corresponding equation is [1]:
cvR=μcγ
2
∂
∂
2
x
∂c
∂x
∂c
∂t
where is the effective dispersion coefficient, is the fluid phase concentration, is distance, is time, is the interstitial fluid velocity, is a retardation factor defined as , is a general decay constant defined as , and is the zerothorder fluid phase source term. Here is the porous medium bulk density, is the ratio of adsorbed to fluid phase concentration, is the volumetric moisture content, is a firstorder liquid phase decay constant, and is the firstorder solid phase decay constant.
c
x
t
v
R
R=1+ρk/θ
μ
μ=α+βρk/θ
γ
ρ
k
θ
α
β
The transport equation is solved subject to the following initial and boundary conditions:
c(x,0)=
C
i
+vc(0,t)=
∂c(0,t)
∂x

and
∂(∞,t)
∂x
C
i
C
0
(,)=(0,1)
C
i
C
0