262
8. Applications of Groundwater Quality Models
crossing over the fractures. Then, the transmissivity T between nodes i, p and
i, q becomes IXT, while between nodes i, j, i, k and i, I becomes ßT. IX = 1 and
ß = 1 indicate no modification is necessary; IX > 1 means the conductivity
increases along the fracture; and ß < 1 means that water flow is obstructed
by the fracture when crossing it. The modification factors IX and ß can be
obtained by solving the inverse problem. Different fractures, or different
sections of the same fracture, may have different modification factors. The
locations of fractures can also be identified through the calibration of the
modification factors.
The discrete fracture model mayaIso be used for solving water quality
problems. Because the transmissivities are modified, the flow velocities in
the exclusive subdomain of node i will also change, which, in turn, causes
the corresponding changes in the hydrodynamic dispersion coefficients. No
matter how the coefficients change, the integrated mass conservation equation is still valid. Therefore, we can still establish a mass conservation equati on for the exclusive subdomain of node i, just as we did before, and take it
as the discrete equation for this node.
The discrete fracture method can truly reflect the actual condition, provided that the geometric shapes and physical properties of the fractures are
known. Unfortunately, these requirements are rarely satisfied in practice.
Tsang (1987) and Tsang and Tsang (1987) proposed several channel models
for studying various coupled processes in fractured media. They conducted
laboratory, modeling and field studies on solute and heat transport in fractures. Johns and Roberts (1991) considered the effects of adsorption and
diffusion in channels. Numerical solutions of discrete fracture models were
further studied by Germain and Frind (1989), Rasmussen and Evans (1989),
and Sudicky and McLaren (1992). In Sudicky and McLaren (1992), the
Laplace transform Galerkin (LTG) method (Sudicky, 1989) was adopted
because it can avoid time stepping and permit the use of a relatively coarse
grid. Thus, it is well-suited for solving large scale and long-term contaminant
transport problems. Bear et al. (1993) presented a comprehensive review of
the state of the art of flow and concentration transport in fractured rocks,
from theories, numerical methods to field tests.
8.2 Seawater Intrusion
8.2.1 The Problem of Seawater Intrusion
In coastal areas, groundwater usually flows into the sea. As the specific
gravity of seawater is larger than that of fresh water, the seawater rests under
the fresh water like a wedge, as shown in Figure 8.6.
If the fresh water in a confined or unconfined aquifer is overpumped, the
hydraulic head of the fresh water may be dropped drastically. As a result, a
8. Applications of Groundwater Quality Models
crossing over the fractures. Then, the transmissivity T between nodes i, p and
i, q becomes IXT, while between nodes i, j, i, k and i, I becomes ßT. IX = 1 and
ß = 1 indicate no modification is necessary; IX > 1 means the conductivity
increases along the fracture; and ß < 1 means that water flow is obstructed
by the fracture when crossing it. The modification factors IX and ß can be
obtained by solving the inverse problem. Different fractures, or different
sections of the same fracture, may have different modification factors. The
locations of fractures can also be identified through the calibration of the
modification factors.
The discrete fracture model mayaIso be used for solving water quality
problems. Because the transmissivities are modified, the flow velocities in
the exclusive subdomain of node i will also change, which, in turn, causes
the corresponding changes in the hydrodynamic dispersion coefficients. No
matter how the coefficients change, the integrated mass conservation equation is still valid. Therefore, we can still establish a mass conservation equati on for the exclusive subdomain of node i, just as we did before, and take it
as the discrete equation for this node.
The discrete fracture method can truly reflect the actual condition, provided that the geometric shapes and physical properties of the fractures are
known. Unfortunately, these requirements are rarely satisfied in practice.
Tsang (1987) and Tsang and Tsang (1987) proposed several channel models
for studying various coupled processes in fractured media. They conducted
laboratory, modeling and field studies on solute and heat transport in fractures. Johns and Roberts (1991) considered the effects of adsorption and
diffusion in channels. Numerical solutions of discrete fracture models were
further studied by Germain and Frind (1989), Rasmussen and Evans (1989),
and Sudicky and McLaren (1992). In Sudicky and McLaren (1992), the
Laplace transform Galerkin (LTG) method (Sudicky, 1989) was adopted
because it can avoid time stepping and permit the use of a relatively coarse
grid. Thus, it is well-suited for solving large scale and long-term contaminant
transport problems. Bear et al. (1993) presented a comprehensive review of
the state of the art of flow and concentration transport in fractured rocks,
from theories, numerical methods to field tests.
8.2 Seawater Intrusion
8.2.1 The Problem of Seawater Intrusion
In coastal areas, groundwater usually flows into the sea. As the specific
gravity of seawater is larger than that of fresh water, the seawater rests under
the fresh water like a wedge, as shown in Figure 8.6.
If the fresh water in a confined or unconfined aquifer is overpumped, the
hydraulic head of the fresh water may be dropped drastically. As a result, a