Approaching the Groundwater Remediation Problem ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Approaching the Groundwater Remediation Problem Using Multifidelity Optmization
Paper
Author:Kathleen Fowler <kfowler@clarkson.edu> (Clarkson University)
Genetha Gray <gagray@sandia.gov> (Sandia National Lab)
Presenter:Genetha Gray <gagray@sandia.gov> (Sandia National Lab)
Date: 2006-06-18     Track: Special Sessions     Session: Groundwater Optimal Management Session
DOI:10.4122/1.1000000723
DOI:10.4122/1.1000000724

The objective of the hydraulic capture method for optimal groundwater remediation design is containment of a contaminant plume using barrier wells to reverse the direction of groundwater flow. Finding a solution involves applying optimization algorithms in conjunction with simulators for groundwater flow and possibly for contaminant transport. The formulation of the objective function and its corresponding constraints dictates which optimization algorithms are appropriate and usually eliminates gradient based approaches from consideration. In addition, objective functions and constraints can be nonlinear, non-convex, non- differentiable, or even discontinuous, and the simulations involved can be computationally expensive. Both computational efficiency and accuracy are important, and this further influences the choice of solution method. With the advent and increasing availability of massively parallel computers, computational speed has increased tremendously. Unfortunately, the numerical and model complexities of problems like groundwater remediation still demand significant computational resources. Moreover, these expenses can be a limiting factor of optimization since obtaining solutions often requires the completion of numerous computationally intensive jobs. Therefore, we propose an algorithm designed to improve the computational efficiency of an optimization method for a wide range of applications and apply it to groundwater remediation. Our approach takes advantage of the interactions between multifidelity models and is applicable to problems for which models of varying fidelity are available. The method can be described as follows: First, a direct search method is applied to the high fidelity model over a reduced design space. In conjunction with this search, a specialized oracle is employed to map the design space of this high fidelity model to that of a computationally cheaper low fidelity model using space mapping techniques. Then, in the low fidelity space, an optimum is obtained using gradient based optimization, and it is mapped back to the high fidelity space. To motivate this work, we consider a hydraulic capture problem proposed in the literature for benchmarking purposes. The problem is to minimize the cost to install and operate a set of wells subject to constraints on the concentration of a contaminant at specified locations in the physical domain. We solve the problem by applying the multifidelity approach described above using only flow information for the low fidelity model and using concentration based constraints for the high fidelity model. We present some promising results for this preliminary problem, and explain how we plan to extend our study by considering more representative physical models, simulators, objective function formulations, and by incorporating real-site data.