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Nonlinear Robust Optimal Design and Operation of Effluent Treatment Systems
- Author / Creator
- Kammammettu, Sanjula
The optimal design and operation of effluent treatment system networks poses a significantcant challenge in the present time, with the imposition of stricter environmental regulations and an increased demand for resources exacerbated by a diminishing resource pool. In practice, this problem presents an additional layer of complexity owing to the presence of uncertainty in the operation of the system. This uncertainty may come from a variety of sources, such as effluent flow rate, contaminant concentration, and treatment unit removal efficiency. Therefore, the need to focus on developing a stochastic optimization framework for the optimal design and operation of effluent treatment systems has been well-recognized.
Robust and stochastic optimization techniques have been explored in the literature for water network optimization under uncertainty. Robust optimization solves for the worst case of uncertainty realized and presents a conservative solution to the problem that would be valid for any realization of uncertainty it was solved for. In contrast, stochastic optimization deals with uncertainty in an optimization problem by assuming that the probability distribution of the uncertainty is known and seeks to address the uncertainty through different techniques. Uncertainty in optimization
problems can be dealt with using a variety of techniques, such as scenario-based programming, chance constrained programming, and the decision rule approach. This thesis presents a study of the applicability of the decision rule approach - specifically, the affine decision rule - in dealing with uncertainty in the optimal design and operation of effluent treatment systems. The main aim of this thesis was to obtain i)
robust process design, and ii) robust operational policies, that is, a set of decision rules for the operation of the effluent treatment system, which are easily applicable for any realization of uncertainty that the problem has been modeled to handle.
The thesis compared three approaches to modeling the nonlinear effluent treatment system network under uncertainty. The first approach involved the use of McCormick
envelopes in developing a linear framework to which the affine decision rule formulation was applied. The second approach employed first order Taylor series approximation around the nominal process network to linearize the system, and the affine decision rule was applied to this approximated model. The third approach used two-stage nonlinear robust optimization of the model linearized around uncertainty, in
which the affine decision rule formulation was applied to the control variables. The formerly intractable model was transformed into its tractable form using the affine
decision rule, and the finite, robust counterpart of the problem was modeled using the property of strong duality in linear programming problems, for a defined uncertainty
set. The thesis applied these three approaches to the operation of a small water treatment model. The performance, advantages, and limitations of each approach were then analyzed and contrasted. The two-stage nonlinear robust optimization approach using the affine decision rule was found to offer superior performance over the other approaches, and this approach was chosen to tackle a larger optimization problem - the optimal design and operation of the effluent treatment and steam generation system network for a SAGD reservoir.
- Graduation date
- Fall 2019
- Type of Item
- Master of Science
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