�
2
∂
∂
∂
c
c
c
+
D
−
k
= −v
2
∂
t
∂
∂
x
x
c x = L)
⎛
⎞
(
L
= exp ⎜ −k� ⎟
⎝
⎠
c
v
0
65
Groundwater Modeling Involving PRBs
in Chapters 2 and 3. The implementation stages of PRB technology include
the initial feasibility assessment, laboratory treatability studies (including
column studies), estimation of PRB design parameters, and development of a
long-term monitoring network for the performance evaluation of the barrier.
This chapter provides a general overview of mathematical models used for
implementing the PRB technologies.
4.2 Design of PRBs
The most important parameter in designing the PRB is the thickness of barrier, which is a function of both hydrogeological and contaminant parameters. The contaminant concentration entering the barrier and its spatial
distribution is the key for the design purposes. Since the contaminant transport depends on various hydrogeological and chemical properties it is critical to estimate the hydraulic conductivity (K), dispersion coefficient (D) of
the subsurface environment and the first-order decay coefficient of the contaminant. Estimates of various parameters for designing the PRB are provided in the following sections.
A simple mathematical model (Rabideau et al., 2005) governing the transport process through the reactive barrier is represented by a one-dimensional
advective–dispersive–reactive equation (ADRE). The governing equation for
the single decay ADRE assuming a homogenous subsurface medium is as
follows:
where
c = aqueous phase contaminant concentration (M/L3)
t = time (T)
x = distance from the entrance of the PRB (L)
v = interstitial fluid velocity (L/T)
D = dispersion coefficient (L2/T)
k = first-order decay constant (l/T)
Application of the above equation to a PRB setting is commonly accomplished by neglecting the dispersion term and treating the PRB as an ideal
plug flow reactor, which leads to the following simple design equation (e.g.,
Gavaskar et al., 1998; USEPA, 1998):
2
∂
∂
∂
c
c
c
+
D
−
k
= −v
2
∂
t
∂
∂
x
x
c x = L)
⎛
⎞
(
L
= exp ⎜ −k� ⎟
⎝
⎠
c
v
0
65
Groundwater Modeling Involving PRBs
in Chapters 2 and 3. The implementation stages of PRB technology include
the initial feasibility assessment, laboratory treatability studies (including
column studies), estimation of PRB design parameters, and development of a
long-term monitoring network for the performance evaluation of the barrier.
This chapter provides a general overview of mathematical models used for
implementing the PRB technologies.
4.2 Design of PRBs
The most important parameter in designing the PRB is the thickness of barrier, which is a function of both hydrogeological and contaminant parameters. The contaminant concentration entering the barrier and its spatial
distribution is the key for the design purposes. Since the contaminant transport depends on various hydrogeological and chemical properties it is critical to estimate the hydraulic conductivity (K), dispersion coefficient (D) of
the subsurface environment and the first-order decay coefficient of the contaminant. Estimates of various parameters for designing the PRB are provided in the following sections.
A simple mathematical model (Rabideau et al., 2005) governing the transport process through the reactive barrier is represented by a one-dimensional
advective–dispersive–reactive equation (ADRE). The governing equation for
the single decay ADRE assuming a homogenous subsurface medium is as
follows:
where
c = aqueous phase contaminant concentration (M/L3)
t = time (T)
x = distance from the entrance of the PRB (L)
v = interstitial fluid velocity (L/T)
D = dispersion coefficient (L2/T)
k = first-order decay constant (l/T)
Application of the above equation to a PRB setting is commonly accomplished by neglecting the dispersion term and treating the PRB as an ideal
plug flow reactor, which leads to the following simple design equation (e.g.,
Gavaskar et al., 1998; USEPA, 1998):