The Effect of Fractures on the Reclamation ofNAPL
67
numerical simulations, KjO = 0.1 - 10. These values roughly correspond to a range
in mass transfer coefficients from 10-6 - 10-4 m/s (Rubin et al. 1997), based on the
survey of Powers et al. (1991).
Simulations with the low and high values of the mobility number are
representative of formations with different values of hydraulic conductivity,
fracture aperture and orientation, and permeable block size. It is convenient,
however, to facilitate comparisons between simulations by assuming that
dimensionless space and time variables x and t are identical for the lower and
upper range values of NM. Therefore, from Eq. (5), Vb, B, and q,b are assumed
identical in all formations. According to Eq. (1 b), the total discharge conveyed
through the domain of Fig. 2b is given by:
Qt = ( 1 + N~ fb.
(28)
Therefore, under the conditions assumed in this level, the domain subject to NM
= 0.5 conveys a discharge of water that is 2.5 times the discharge in the domain
subjectto NM = 5.
Parameter values listed in Table 2 can be used to develop characteristics of a
representative aquifer. Such an aquifer is composed of sandstone with a block
conductivity of Kb = 10- 5 m S-l and a porosity of 1Pb = 0.1. The fracture spacing is
assumed to be about 0.5 m, and the orientation angle is (J = 45°. If the imposed
hydraulic gradient in the pump-and-treat project is 0.01 m m- l , then the permeable
block specific discharge is qb == 10- 7 m sol. Under these conditions, one
dimensionless time unit of the variable t represents 3.5 x 105 s, or about 4.1 days.
5.2 Characteristics of Aquifer Remediation
Simulation results are presented in Figs. 4 and 5, which show the predicted spatial
distribution of Sn and Cb at specific times representing 30 - 40% of the domain
reclamation. Figures 6 and 7 present time varying longitudinal profiles of the
average saturation of the entrapped NAPL, Snav, and the flux average
concentration of the dissolved constituents, Cay.
The influence of rate-limited NAPL dissolution was investigated with a small
mass transfer coefficient, KjO = 0.1. Under rate-limited conditions, simulation
results in Figs. 4a and b show that NAPL dissolution occurs over the entire
contaminated region, and Figs. 5a and b show that the concentration of the
dissolved constituents in the permeable block flow is below the equilibrium
concentration throughout the domain. Predicted NAPL saturation profiles at
selected times are shown in Figs. 6a and b. Here, rate limitations are reflected by
the relatively flat saturation profiles throughout the pump-and-treat operation.
Correspondingly, profiles of the predicted flux average concentration, plotted in
Figs. 7a and b, show that the solute concentration increases linearly throughout the
domain, but that the domain is not sufficiently long to reach equilibrium
concentration at the downstream end. It should be noted that curves of Cav versus
67
numerical simulations, KjO = 0.1 - 10. These values roughly correspond to a range
in mass transfer coefficients from 10-6 - 10-4 m/s (Rubin et al. 1997), based on the
survey of Powers et al. (1991).
Simulations with the low and high values of the mobility number are
representative of formations with different values of hydraulic conductivity,
fracture aperture and orientation, and permeable block size. It is convenient,
however, to facilitate comparisons between simulations by assuming that
dimensionless space and time variables x and t are identical for the lower and
upper range values of NM. Therefore, from Eq. (5), Vb, B, and q,b are assumed
identical in all formations. According to Eq. (1 b), the total discharge conveyed
through the domain of Fig. 2b is given by:
Qt = ( 1 + N~ fb.
(28)
Therefore, under the conditions assumed in this level, the domain subject to NM
= 0.5 conveys a discharge of water that is 2.5 times the discharge in the domain
subjectto NM = 5.
Parameter values listed in Table 2 can be used to develop characteristics of a
representative aquifer. Such an aquifer is composed of sandstone with a block
conductivity of Kb = 10- 5 m S-l and a porosity of 1Pb = 0.1. The fracture spacing is
assumed to be about 0.5 m, and the orientation angle is (J = 45°. If the imposed
hydraulic gradient in the pump-and-treat project is 0.01 m m- l , then the permeable
block specific discharge is qb == 10- 7 m sol. Under these conditions, one
dimensionless time unit of the variable t represents 3.5 x 105 s, or about 4.1 days.
5.2 Characteristics of Aquifer Remediation
Simulation results are presented in Figs. 4 and 5, which show the predicted spatial
distribution of Sn and Cb at specific times representing 30 - 40% of the domain
reclamation. Figures 6 and 7 present time varying longitudinal profiles of the
average saturation of the entrapped NAPL, Snav, and the flux average
concentration of the dissolved constituents, Cay.
The influence of rate-limited NAPL dissolution was investigated with a small
mass transfer coefficient, KjO = 0.1. Under rate-limited conditions, simulation
results in Figs. 4a and b show that NAPL dissolution occurs over the entire
contaminated region, and Figs. 5a and b show that the concentration of the
dissolved constituents in the permeable block flow is below the equilibrium
concentration throughout the domain. Predicted NAPL saturation profiles at
selected times are shown in Figs. 6a and b. Here, rate limitations are reflected by
the relatively flat saturation profiles throughout the pump-and-treat operation.
Correspondingly, profiles of the predicted flux average concentration, plotted in
Figs. 7a and b, show that the solute concentration increases linearly throughout the
domain, but that the domain is not sufficiently long to reach equilibrium
concentration at the downstream end. It should be noted that curves of Cav versus