Optimization of water network synthesis
Creators: name: Khor, Cheng Seong
Publisher: name: Imperial College London
Year: 2012

description: Water is a key component in most industries. It has become a crucial resource today particularly in the process and allied industries due to increasingly higher demand for water use, scarcities in water resources, and ever more stringent regulations on wastewater discharges. Hence, this thesis addresses water network synthesis with the goal of developing a systematic approach for optimizing water recovery through regeneration-reuse and regeneration-recycle schemes. A water network super structure is first develop ed that consists of three elements similar to a pooling problem formulation: sources for reuse/recycle, regenerators for contaminants removal, and sinks for acceptance of water for reuse/recycle. The superstructure encompasses membrane separation-based technologies for water regeneration, particularly ultrafiltration and reverse osmosis, which are gaining widespread industrial applications. For the membrane regenerators, we formulate simplified linear models that admit a more general concentration expression as functions of both the liquid phase recovery factors and contaminant removal ratios. The overall superstructure leads to a mixed-integer nonlinear programming (MINLP) optimization model formulation, with continuous variables on water flowrates and contaminant concentrations while binary 0–1 variables are used for selection of piping interconnections. The resultant model is nonconvex particularly in bilinear terms due to contaminant mixing in the regenerators. Realizing the important influence of the physical parameters of a membrane regenerator, the network design is refined by proposing the use of a more detailed nonlinear preliminary design model of this regenerator type that also accounts for various cost elements of the associated equipment components. The more detailed model is applied to a single-stage reverse osmosis network that is incorporated within an overall water network MINLP. To address uncertainty in the formulation, this work develops a recourse-based two-stage stochastic programming framework by using multiple discrete scenarios to approximate the underlying probability distribution of the uncertain parameters. The model is extended with risk management considerations by using the conditional value-at-risk (CVaR) metric. However, a large number of scenarios are often required to capture the uncertainty meaningfully, causing the model to suffer from the curse of dimensionality. Hence, a stepwise solution strategy is propose d to reduce the computational load. This framework is appl ied to reformulate the original deterministic water network synthesis model as a multiscenario stochastic MINLP consisting of a first -stage network design and a second-stage operation as recourse. The thesis handles these challenging nonconvex formulations, which can result in multiple local optimal solutions, by employing global optimization techniques to ensure reliable solutions. To enhance convergence, a solution strategy is presented that incorporates additional constraints into the model in the form of logic-based linear inequalities by exploiting the physics of the underpinning problem. These logical constraints enforce certain design and structural specifications that consequently reduce the solution time. The proposed modeling and solution strategy is implemented on industrial-size case studies of the water systems in an actual operating petroleum refinery in Malaysia and obtained promising results by employing a state-of-the-art general purpose global solver GAMS/BARON. For the stochastic model formulation, computational comparisons are also conducted with the performance of a recently available global solver, GloMIQO. Finally, the main contributions of this thesis are consolidated and perspectives for future work are offered.