288
8. Applications of Groundwater Quality Models
ing a reliable model for solving the proposed management problem. In the
planning model, two recharge locations were designed for storing imported
water and reclaimed water in wet seasons, and blocking the high TDS water
flowing into the basin through its boundary. The optimal solution of the
management model can provide arecharge schedule for the planning period
and determine the amounts of recharge water coming from different sources.
8.3.5 Remediation oi Polluted Aquifers
The self-purification ofpoIluted aquifers usuaIly requires a very long time. To
speed up purification, we can pump out the poIluted water and inject clean
water, or use some chemical or biological methods to remediate the poIluted
aquifers. Optimal remediation design includes two contradictory objectives:
one is to achieve the optimal remediation results, and the other is to minimize
the cost. Therefore, we may have the foIlowing management problems:
(1) Under the condition of a fixed remediation budget (remediation capability), look for a plan (decision) that can produce the best remediation
results.
(2) Under the condition that certain remediation results should be
achieved, seek the minimum cost alternative.
The mathematical statements of the two problems are given below. Assume that the domain of the aquifer (Q) is divided into M elements. Let
M
Zl= L WmOmVmCm,
(8.3.36)
m;l
where W m is the weighting coefficient, Om the porosity, Vm the volume of
element m, and C m the contaminant concentration of element m after the
remediation is finished. If aIl W m = 1, Zl will be the total content of contaminants in the domain (Q) when the remediation is ended. The cost of operating
this remedial plan can be expressed as
I
J
Z2 = L (Xiqi + L ßjqj,
(8.3.37)
i;l
j;l
where land J are the numbers of the potential injection and extraction weIls,
respectively, qi the injection rate of injection weIl i, (Xi the cost of injecting
a unit volume of water, qj the pumping rate of extraction weIl j, and ßj is the
cost of pumping a unit volume of water. If the cost of weIl construction is
neglected, Z2 may be used to represent the total cost of the remediation.
When the decision variables of the remediation problem are expressed by
vectors:
q+ = (qi,qi,···,qj) and q- = (qlA;,··.,qj),
(8.3.38)
the problem of minimizing the remaining contaminant subject to a cost
constraint may be stated as
(8.3.39)
8. Applications of Groundwater Quality Models
ing a reliable model for solving the proposed management problem. In the
planning model, two recharge locations were designed for storing imported
water and reclaimed water in wet seasons, and blocking the high TDS water
flowing into the basin through its boundary. The optimal solution of the
management model can provide arecharge schedule for the planning period
and determine the amounts of recharge water coming from different sources.
8.3.5 Remediation oi Polluted Aquifers
The self-purification ofpoIluted aquifers usuaIly requires a very long time. To
speed up purification, we can pump out the poIluted water and inject clean
water, or use some chemical or biological methods to remediate the poIluted
aquifers. Optimal remediation design includes two contradictory objectives:
one is to achieve the optimal remediation results, and the other is to minimize
the cost. Therefore, we may have the foIlowing management problems:
(1) Under the condition of a fixed remediation budget (remediation capability), look for a plan (decision) that can produce the best remediation
results.
(2) Under the condition that certain remediation results should be
achieved, seek the minimum cost alternative.
The mathematical statements of the two problems are given below. Assume that the domain of the aquifer (Q) is divided into M elements. Let
M
Zl= L WmOmVmCm,
(8.3.36)
m;l
where W m is the weighting coefficient, Om the porosity, Vm the volume of
element m, and C m the contaminant concentration of element m after the
remediation is finished. If aIl W m = 1, Zl will be the total content of contaminants in the domain (Q) when the remediation is ended. The cost of operating
this remedial plan can be expressed as
I
J
Z2 = L (Xiqi + L ßjqj,
(8.3.37)
i;l
j;l
where land J are the numbers of the potential injection and extraction weIls,
respectively, qi the injection rate of injection weIl i, (Xi the cost of injecting
a unit volume of water, qj the pumping rate of extraction weIl j, and ßj is the
cost of pumping a unit volume of water. If the cost of weIl construction is
neglected, Z2 may be used to represent the total cost of the remediation.
When the decision variables of the remediation problem are expressed by
vectors:
q+ = (qi,qi,···,qj) and q- = (qlA;,··.,qj),
(8.3.38)
the problem of minimizing the remaining contaminant subject to a cost
constraint may be stated as
(8.3.39)