72
H. Rubin et al.
Simulation results with a large mass transfer coefficient, KjO = 10, are presented
in Figs. 4 - 7, plots c and d. Results in Figs. 4c and 5c show that when rate of
dissolution is not controlled by mass transfer limitations, and the mobility number
is small, NM = 0.5, predicted distributions of Sn and Cb are non-uniform in the
cross sections perpendicular to the flow direction.
Correspondingly, the
longitudinal profiles of Snav and Cay (Figs. 6c and 7c) exhibit spatial oscillations.
This oscillatory behavior is due to the greater flow through the fracture network
combined with mixing between the permeable block and fracture flows. When the
mobility number is large, NM = 5, the permeable block flow is greater than the
fracture flow, and since NAPL dissolution occurs only in the permeable blocks,
mixing between the two flows does not lead to significant spatial variability in the
saturation and solute concentration distributions.
Simulation results with the large mass transfer coefficient indicate that in the
absence of mass transfer limitations, equilibrium solute concentrations are attained
over relatively short travel distances. During the early stages, NAPL dissolution is
concentrated in the front portion of the domain, producing sharper profiles of Snav
and Cay at the front portion of the domain, as shown in Figs. 6c,d, and 7c,d.
Correspondingly curves of Snav and Cay are convex at early time periods. Over
time, dissolution gradually reduces the value of K J at the front portion of the
domain. Then the value of K J increases with x, leading to concave profiles of Cay'
As a result of the increased mass transfer rates and larger effluent concentrations,
Figs 6c,d and 7c, 7d show that the total time required for complete NAPL removal
is smaller than the time needed when KjO = 0.1. However, the time required for
complete reclamation of the formation with NM = 0.5 is about one half that for
formation with NM = 5. Mixing with the additional flow in the fracture network,
apparently enhances NAPL dissolution by the permeable block flow. The greater
fracture flow behaves as a conduit for transport of NAPL solute downgradient, as
well as providing a source of additional water with low solute concentration that
can further drive dissolution. Note, however, that the overall quantity of water to
be treated is almost identical in formations with N M = 0.5 - 5.
5.3 Influence of the Flow Rate
For comparative purposes, a constant permeable block discharge was used in all
simulations presented in the previous section. Simulation results suggested that in
some scenarios, changes in the system pumping rate could lead to improved
removal efficiency in terms of a reduced treatment horizon and/or reduced
pumping volume. Changes in the total pump-and-treat discharge lead to
proportional changes in the permeable block flow and the system dimensionless
interphase mass transfer coefficient. These issues are analyzed in the following
paragraphs. It should, however, be noted that rates of pumping are subject to
constraints of the aquifer, which are not considered in the calculations presented in
following paragraphs.
Analyses in the preceding section were based on identical values of Qb.
Therefore, without loss of generality, the examples above may be treated in terms
H. Rubin et al.
Simulation results with a large mass transfer coefficient, KjO = 10, are presented
in Figs. 4 - 7, plots c and d. Results in Figs. 4c and 5c show that when rate of
dissolution is not controlled by mass transfer limitations, and the mobility number
is small, NM = 0.5, predicted distributions of Sn and Cb are non-uniform in the
cross sections perpendicular to the flow direction.
Correspondingly, the
longitudinal profiles of Snav and Cay (Figs. 6c and 7c) exhibit spatial oscillations.
This oscillatory behavior is due to the greater flow through the fracture network
combined with mixing between the permeable block and fracture flows. When the
mobility number is large, NM = 5, the permeable block flow is greater than the
fracture flow, and since NAPL dissolution occurs only in the permeable blocks,
mixing between the two flows does not lead to significant spatial variability in the
saturation and solute concentration distributions.
Simulation results with the large mass transfer coefficient indicate that in the
absence of mass transfer limitations, equilibrium solute concentrations are attained
over relatively short travel distances. During the early stages, NAPL dissolution is
concentrated in the front portion of the domain, producing sharper profiles of Snav
and Cay at the front portion of the domain, as shown in Figs. 6c,d, and 7c,d.
Correspondingly curves of Snav and Cay are convex at early time periods. Over
time, dissolution gradually reduces the value of K J at the front portion of the
domain. Then the value of K J increases with x, leading to concave profiles of Cay'
As a result of the increased mass transfer rates and larger effluent concentrations,
Figs 6c,d and 7c, 7d show that the total time required for complete NAPL removal
is smaller than the time needed when KjO = 0.1. However, the time required for
complete reclamation of the formation with NM = 0.5 is about one half that for
formation with NM = 5. Mixing with the additional flow in the fracture network,
apparently enhances NAPL dissolution by the permeable block flow. The greater
fracture flow behaves as a conduit for transport of NAPL solute downgradient, as
well as providing a source of additional water with low solute concentration that
can further drive dissolution. Note, however, that the overall quantity of water to
be treated is almost identical in formations with N M = 0.5 - 5.
5.3 Influence of the Flow Rate
For comparative purposes, a constant permeable block discharge was used in all
simulations presented in the previous section. Simulation results suggested that in
some scenarios, changes in the system pumping rate could lead to improved
removal efficiency in terms of a reduced treatment horizon and/or reduced
pumping volume. Changes in the total pump-and-treat discharge lead to
proportional changes in the permeable block flow and the system dimensionless
interphase mass transfer coefficient. These issues are analyzed in the following
paragraphs. It should, however, be noted that rates of pumping are subject to
constraints of the aquifer, which are not considered in the calculations presented in
following paragraphs.
Analyses in the preceding section were based on identical values of Qb.
Therefore, without loss of generality, the examples above may be treated in terms