Optimal remediation of unconfined aquifers: Numerical applications and derivative calculations

Abstract

Abstract. This paper extends earlier work on derivative-based optimization for costeffective remediation to unconfined aquifers, which have more complex, nonlinear flow dynamics than confined aquifers. Most previous derivative-based optimization of contaminant removal has been limited to consideration of confined aquifers; however, contamination is more common in unconfined aquifers. Exact derivative equations are presented, and two computationally efficient approximations, the quasi-confined (QC) and head independent from previous (HIP) unconfined-aquifer finite element equation derivative approximations, are presented and demonstrated to be highly accurate. The derivative approximations can be used with any nonlinear optimization method requiring derivatives for computation of either time-invariant or time-varying pumping rates. The QC and HIP approximations are combined with the nonlinear optimal control algorithm SALQR into the unconfined-aquifer algorithm, which is shown to compute solutions for unconfined aquifers in CPU times that were not significantly longer than those required by the confined-aquifer optimization model. Two of the three example unconfined-aquifer cases considered obtained pumping policies with substantially lower objective function values with the unconfined model than were obtained with the confined-aquifer optimization, even though the mean differences in hydraulic heads predicted by the unconfined-and confined-aquifer models were small (less than 0.1%). We suggest a possible geophysical index based on differences in drawdown predictions between unconfined-and confined-aquifer models to estimate which aquifers require unconfinedaquifer optimization and which can be adequately approximated by the simpler confinedaquifer analysis.

Simulation and optimization technologies for petroleum waste management and remediation process control

“…Mansfield et al (1998) proposed a method for exploiting the sparsity of a finite element model within an optimization model using the SALQR approach, in an attempt to reduce the computational effort. Mansfield and Shoemaker (1999) extended their earlier work on derivative-based optimization for cost-effective remediation to unconfined aquifers, which had more complex, non-linear flow dynamics than confined aquifers. Exact derivative equations were presented, and two computationally efficient approximations, the quasi-confined (QC) and head independent from previous (HIP) unconfined-aquifer finite element equation derivative approximations, were presented and demonstrated to be highly accurate.…”

Optimal planning of a dynamic pump-treat-inject groundwater remediation system

“…(10)-(12) contains the operation cost and constraints and is a continuous nonlinear dynamic optimization problem. A CDDP algorithm (Chang and Shoemaker, 1992;Shoemaker, 1992, 1993;Mansfield et al, 1998;Mansfield and Shoemaker, 1999) is suitable to solve the sub-problem because the functions are separable in time. In principle, the sub-problem can also be calculated by GA but this will dramatically increase the required computational resources.…”

Optimizing Remediation of an Unconfined Aquifer Using a Hybrid Algorithm

“… Mansfield and Shoemaker (1999, p. 1457) completely detailed the matrix terms in Equations , which contain information on the spatial distribution of the physical parameters that relate to flow and transport in the aquifer. Here, the unconfined aquifer simulator is modified from the ISOQUA (Pinder 1978), a two‐dimensional confined aquifer simulator, using the Picard method.…”

“…This limitation probably follows from the fact that the flow equation for an unconfined aquifer is nonlinear and is more complex than that for a confined aquifer. Recently, Mansfield and Shoemaker (1999) implemented a successive approximation linear quadratic regulator algorithm (SALQR, Chang et al 1992) to obtain least‐cost pump‐and‐treat remediation policies for cleaning up unconfined aquifers. Their study derived and computed the analytic derivatives of the nonlinear unconfined aquifer flow and transport equations.…”