Optimal remediation of unconfined aquifers: Numerical applications and derivative calculations

This paper extends earlier work on derivative-based optimization for cost-e ffective remediation to unconfined aquifers, which have more complex, nonli near Row dynamics than confined aquifers. Most previous derivative-based op timization of contaminant removal has been limited to consideration of conf ined aquifers; however, contamination is more common in unconfined aquifers . Exact derivative equations are presented, and two computationally efficie nt approximations, the quasi-confined (QC) and head independent from previo us (HIP) unconfined-aquifer finite element equation derivative approximatio ns, are presented and demonstrated to be highly accurate. The derivative ap proximations can be used with any nonlinear optimization method requiring d erivatives for computation of either time-invariant or time-varying pumping rates. The QC and HIP approximations are combined with the nonlinear optim al control algorithm SALQR into the unconfined-aquifer algorithm, which is shown to compute solutions for unconfined aquifers in CPU times that were n ot significantly longer than those required by the confined-aquifer optimiz ation model. Two of the three example unconfined-aquifer cases considered o btained pumping policies with substantially lower objective function Values with the unconfined model than were obtained with the confined-aquifer opt imization, even though the mean differences in hydraulic heads predicted by the unconfined- and confined-aquifer models were small (less than 0.1%). W e suggest a possible geophysical index based on differences in drawdown pre dictions between unconfined- and confined-aquifer models to estimate which aquifers require unconfined-aquifer optimization and which can be adequatel y approximated by the simpler confined-aquifer analysis.