A hydraulic capture application for optimal remediation design

Abstract

The goal of a hydraulic capture model for remediation purposes is to design a well field so that the direction of groundwater flow is altered, thereby halting or reversing the migration of a contaminant plume. Management strategies typically require a well design that will contain or shrink a plume at minimum cost. Objective functions and constraints can be nonlinear, non-convex, non-differentiable, or even discontinuous. The solution uses optimization algorithms with groundwater flow and possibly transport simulators. The formulation of the objective function dictates possible optimization algorithms that can be used. For example, a gradient based method is likely to fail on a discontinuous objective function or gradient information may not be available. Computational efficiency as well as accuracy is desirable and often influences the choice of solution method. In this paper we present two hydraulic capture models. Our motivation is a hydraulic capture application proposed in the literature for benchmarking purposes. We present numerical results for the three models using the implicit filtering algorithm.

Developing a computationally efficient dynamic multilevel hybrid optimization scheme using multifidelity model interactions.

“…Although the test problems were developed after an extensive literature search and are indicative of real world problems, the domain is still relatively simple. For this simple, homogeneous case considered in this work, the FBHC model is sufficient and computationally cost-effective [11]. However, the introduction of heterogeneities or other complexities will likely require the TBCC or other models in which the plume boundary is precisely defined.…”

A mixed-integer simulation-based optimization approach with surrogate functions in water resources management

“…The hydrological setting for the hydraulic capture problem is the same homogeneous, unconfined aquifer used in the well-field problem. A detailed description about the groundwater flow model and hydrological settings can be found in (Mayer et al 2002b;Fowler et al 2004aFowler et al , 2004bFowler et al , 2007.…”

“…Such approaches were earlier proposed in the context of subsurface flow problems by (Ritzel et al 1994;Watkins 1998;Mayer et al 2002a). For the sake of comparability to earlier work on the community problems, we use the notation proposed by Mayer et al (2002a) and also applied by Fowler et al (2004aFowler et al ( , 2004b.…”

“…The decision variables are given by the vector of the control parameters w, but in a slightly different way than they are used in the reference approach from (Fowler et al 2004a). The position of each installed well is given by its x and y position on the domain, the operating rate of each well is given by Q, and the total number of wells in the system is n. In the reference formulation, the number of potential wells in the design is fixed and the decision of which wells are installed or de-installed is directly connected to the operation rate Q of each well.…”

“…We will give more details about the reference approach in the subsequent sections. To conform to the numerical experiments that are made not only in (Fowler et al 2004a) but also in (Fowler et al 2004b) we introduce a switching vector s, with s ∈ {0, 1} n , that controls whether or a not a well is installed and ultimately included in the simulation.…”