Analytical Solution of Equations for Chemical Transport with Adsorption, Longitudinal Diffusion, Zeroth-Order Production, and First-Order Decay
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]:
c-v-R=μc-γ
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 zeroth-order 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 first-order liquid phase decay constant, and is the first-order 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