Time-varying optimal control of groundwater remediation in unconfined aquifers

• Main Author: Mansfield, Christopher Martin
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-1997
• Subjects: Environmental engineering; Environmental science; Systems design; Systems science
• ISBN: 9780591240016; 0591240017

An optimal control method for computing time varying groundwater pumping rates for cleanup of contaminated unconfined aquifers is developed. The analytical derivatives of the matrix equations solved by a two dimensional finite element simulation model are presented. These derivative equations are used by the optimal control model to compute optimal pumping rates. This approach differs significantly from previous work because the flow dynamics for unconfined aquifers are nonlinear, which introduces an element of state dependence to the derivative calculations not present in the confined aquifer case. The computation of derivative terms is computationally demanding and can require large computer resources. Several algorithmic enhancements are presented, which reduce computational demands. A quasi linearization of the derivatives is performed, and a steady flow derivative approximation is presented. The quasi linearization procedure allows partial derivatives of simulation model coefficient matrices to be neglected from the derivatives. The steady flow approximation allows all of the derivatives of the flow equation to be dropped from the optimization. Finite element simulation model sparsity is employed in all applicable optimization computations. The algorithm is applied to a field site. Optimixed pumping policies for the containment or removal of material from the site are computed. The simulation data is taken from reports on the site hydrogeology; this data is used with the optimization to compute the policies. This paper shows that the SALQR optimal control algorithm can be employed to compute optimal pumping rates for remediation of field sites in unconfined aquifers. Optimization runs are completed for cases in which there are 1506 state variables and up to 108 control variables and 50 decision periods, although this problem does not represent a limit on the size of problems solvable.