8.3. Groundwater Quality Management Models
285
tions of pumping wells and determine the pumping schedule that can minimize the drawdowns of the wells, while satisfying the water demand. Also, in
order to reduce the cost of recharge and sewage treatment, we may wish to
choose the locations of artificial recharge wells and the recharge schedules to
minimize the pressure in the recharge wells. Obviously, designing a good plan
before regional development will bring more benefit in the future. Management models for these purposes are more complicated than pollution management models mentioned before.
Assurne that the whole management procedure is divided into several time
intervals and it is required to determine the values of decision variables for
each interval. For instance, in the kth interval, the decision variables of a
project model may include: (1) extraction rate Q7 for node i; (2) injection rates
- Q7 for node j; (3) solute concentrations of injection wells Cf. The state
variables may consist of: (1) hydraulic heads hf; and (2) concentrations Cf.
During the simulation, one management interval needs to be divided into
several time steps. The concentrations corresponding to different time steps
in the kth interval are denoted by Cf', where I indicates the lth time step.
The relationship between state variables and decision variables can be
determined by the water flow and water quality models. Using FEM or
FDM, the models may be expressed in the following discrete forms:
dh
[E]h + [G] dt + F = 0,
(8.3.25)
dC
[A]C + [B]Tt + H = 0,
(8.3.26)
where hand C are vectors of state variables. Vectors of decision variables, Q
and C, are included in the source and sink vectors, Fand H. In order to
clearly express the dependence relationships between state and decision variables, Eqs. (8.3.25) and (8.3.26) in the kth management interval may be written as
Pk(h\ Qk) = 0,
Rk(C\ Q\ (:k) = O.
(8.3.27)
(8.3.28)
After the time derivatives in Eqs. (8.3.25) and (8.3.26) are approximated by
finite difference, both P k and R k are algebraic operators.
The objectives of groundwater hydraulic and water quality management
usually contain:
(1)
Zl = max min hf, i E 'TC,
k
i
(8.3.29)
where 'TC is a set of pumping wells. This objective is to reduce the cost of
pumping as much as possible, and meanwhile to prevent the harmful consequences, such as poor quality water intrusion and land subsidence, from
occurring.
285
tions of pumping wells and determine the pumping schedule that can minimize the drawdowns of the wells, while satisfying the water demand. Also, in
order to reduce the cost of recharge and sewage treatment, we may wish to
choose the locations of artificial recharge wells and the recharge schedules to
minimize the pressure in the recharge wells. Obviously, designing a good plan
before regional development will bring more benefit in the future. Management models for these purposes are more complicated than pollution management models mentioned before.
Assurne that the whole management procedure is divided into several time
intervals and it is required to determine the values of decision variables for
each interval. For instance, in the kth interval, the decision variables of a
project model may include: (1) extraction rate Q7 for node i; (2) injection rates
- Q7 for node j; (3) solute concentrations of injection wells Cf. The state
variables may consist of: (1) hydraulic heads hf; and (2) concentrations Cf.
During the simulation, one management interval needs to be divided into
several time steps. The concentrations corresponding to different time steps
in the kth interval are denoted by Cf', where I indicates the lth time step.
The relationship between state variables and decision variables can be
determined by the water flow and water quality models. Using FEM or
FDM, the models may be expressed in the following discrete forms:
dh
[E]h + [G] dt + F = 0,
(8.3.25)
dC
[A]C + [B]Tt + H = 0,
(8.3.26)
where hand C are vectors of state variables. Vectors of decision variables, Q
and C, are included in the source and sink vectors, Fand H. In order to
clearly express the dependence relationships between state and decision variables, Eqs. (8.3.25) and (8.3.26) in the kth management interval may be written as
Pk(h\ Qk) = 0,
Rk(C\ Q\ (:k) = O.
(8.3.27)
(8.3.28)
After the time derivatives in Eqs. (8.3.25) and (8.3.26) are approximated by
finite difference, both P k and R k are algebraic operators.
The objectives of groundwater hydraulic and water quality management
usually contain:
(1)
Zl = max min hf, i E 'TC,
k
i
(8.3.29)
where 'TC is a set of pumping wells. This objective is to reduce the cost of
pumping as much as possible, and meanwhile to prevent the harmful consequences, such as poor quality water intrusion and land subsidence, from
occurring.