62
H. Rubin et al.
1-Cb
(
)
- - - = exp - K fLit! ,
1-C bO
(14)
where Cbo is the initial concentration of the fluid particle.
Referring to an elementary volume of the permeable block material, the
conservation of mass yields:
aS n
ac;
tPbPn-. +qb-.-=O,
(15)
at
ax
where Pn is the NAPL density.
By introducing the dimensionless quantities ofEq. (5) into Eq. (15), we obtain:
aSn + C aC b =0.
(16)
at nv ax
Here, Cnv is the volumetric equilibrium concentration ofNAPL, given by:
c·
C nv = _ S
Pn
(17)
Variation of the value of Sn leads to changes in the value of Kfas shown by Eq.
(11).
The flux average concentration of the dissolved solute in the water phase in a
cross-section perpendicular to the flow direction is calculated as:
•
1
[
*
Bsin8. *]
Cay =
. QfC +qb f Cbdy
Qf +qb Bsm8
0
(18)
By introducing the dimensionless quantities of Eq. (5) into Eq. (18), the
expression for the normalized average flux concentration is obtained:
Cay = 1 [C+NMfCbdY]
(19)
l+NM
0
4
The Simulation Method
A finite difference approach is used to solve the basic dimensionless equations
developed in the preceding section. Discretization of the permeable block domain
uses small squares as shown in Fig. 3. The fracture orientation obtained in that
grid is 45°. Therefore, in the dimensionless domain of x-y, the finite difference
grid easily assimilates the difference intervals of the permeable blocks and those
of the fracture network. As implied by the study of Birkholzer et al. (1993b) it is
convenient to use Ax = ~y = ~t = MI' Referring to the symbols given in Figs. 2
and 3, the simulated domain incorporates nc sections contaminated with entrapped
NAPL.
Solute transport downstream of the contaminated sections entails
advection of the dissolved solute within the permeable blocks and fracture, as well
as mixing between these two types of flow. Solute transport processes under these
conditions were investigated by Birkholzer et al. (1993a,b) and Rubin et al. (1997)
H. Rubin et al.
1-Cb
(
)
- - - = exp - K fLit! ,
1-C bO
(14)
where Cbo is the initial concentration of the fluid particle.
Referring to an elementary volume of the permeable block material, the
conservation of mass yields:
aS n
ac;
tPbPn-. +qb-.-=O,
(15)
at
ax
where Pn is the NAPL density.
By introducing the dimensionless quantities ofEq. (5) into Eq. (15), we obtain:
aSn + C aC b =0.
(16)
at nv ax
Here, Cnv is the volumetric equilibrium concentration ofNAPL, given by:
c·
C nv = _ S
Pn
(17)
Variation of the value of Sn leads to changes in the value of Kfas shown by Eq.
(11).
The flux average concentration of the dissolved solute in the water phase in a
cross-section perpendicular to the flow direction is calculated as:
•
1
[
*
Bsin8. *]
Cay =
. QfC +qb f Cbdy
Qf +qb Bsm8
0
(18)
By introducing the dimensionless quantities of Eq. (5) into Eq. (18), the
expression for the normalized average flux concentration is obtained:
Cay = 1 [C+NMfCbdY]
(19)
l+NM
0
4
The Simulation Method
A finite difference approach is used to solve the basic dimensionless equations
developed in the preceding section. Discretization of the permeable block domain
uses small squares as shown in Fig. 3. The fracture orientation obtained in that
grid is 45°. Therefore, in the dimensionless domain of x-y, the finite difference
grid easily assimilates the difference intervals of the permeable blocks and those
of the fracture network. As implied by the study of Birkholzer et al. (1993b) it is
convenient to use Ax = ~y = ~t = MI' Referring to the symbols given in Figs. 2
and 3, the simulated domain incorporates nc sections contaminated with entrapped
NAPL.
Solute transport downstream of the contaminated sections entails
advection of the dissolved solute within the permeable blocks and fracture, as well
as mixing between these two types of flow. Solute transport processes under these
conditions were investigated by Birkholzer et al. (1993a,b) and Rubin et al. (1997)