Water consumption and wastewater generation depletes water resources and has a destructive impact on the environment. Recent attention has aimed at preserving water resources and preventing pollution through several routes. Restrictions on wastewater discharge into the environment, recycling, reuse and regeneration of wastewater streams are now common practices toward achieving these objectives. Membrane and integrated membrane processes have been shown to be effective at reducing water usage and recovering valuable compounds. This thesis focuses on topics related to the optimal synthesis of wastewater treatment networks by hybrid membrane systems. The use of superstructures has been a useful tool to synthesize chemical engineering process flowsheets. The approach postulates all possible alternatives of a potential treatment network. Within the representation, an optimal solution is assumed to be hidden in the given superstructure. State space is a framework to process synthesis problems which involves heat and mass exchange. In this representation, unit operations, utility units and utility streams can be embedded in such a way that all the process synthesis alternatives can be realized. Such a framework can be applied for water and wastewater synthesis problems. Several research optimization studies presented membrane and hybrid membrane process synthesis problems for wastewater treatment. Nonetheless, the problems in fact can be represented in several ways. Therefore, the mathematical programs are expected to be different for every postulated representation. Comparison between different representations and their mathematical programs are analyzed to highlight the relationship between the superstructure representation and their mathematical programming formulations. Possible improvement of these superstructures is addressed. Also, a generic representation is provided to give a systematic and clear description for assembling hybrid membrane system superstructures via the state space approach. The synthesis of reverse osmosis networks (RON) for water and wastewater treatment network is presented as a superstructure problem. The mathematical programming model describes the RON through a nonconvex mixed integer nonlinear program (MINLP). A mixed integer linear program (MILP) is derived based on the convex relaxation of the nonconvex terms in the MINLP to bound the global optimum. The MILP models are solved iteratively to supply different initial guesses for the nonconvex MINLP model. It is found that such a procedure is effective in finding local optimum solutions in reasonable time. Water desalination and treatment of aqueous wastes from the pulp and paper industry are considered as case studies to illustrate the solution strategy. The RON mathematical program is a nonconvex MINLP which contains several local optima. A deterministic branch and bound (B&B) algorithm to determine the global optimum for the RON synthesis problem has also been developed. A piecewise MILP is derived based on the convex relaxation of the nonconvex terms present in the MINLP formulation to approximate the original nonconvex program and to obtain a valid lower bound on the global optimum. The MILP model is solved at every node in the branch and bound tree to verify the global optimality of the treatment network within a pre-specified gap tolerance. Several constraints are developed to simultaneously screen the treatment network alternatives during the search, tighten the variable bounds and consequently accelerate algorithm convergence. Water desalination is considered as a case study to illustrate this approach for global optimization of the RO network. Wastewater and groundwater streams contaminated with volatile organic compounds (VOCs) require proper treatment to comply with discharge standards or drinking requirement restrictions. Air stripping and pervaporation are two common treatment technologies for water streams contaminated with VOCs. The combination of these technologies for water treatment which are representative of hybrid membrane systems may offer advantages over stand-alone treatments. Superstructure optimization uses the framework of hybridization to determine the optimal treatment network and the optimal operational requirements for the treatment units to achieve desired water qualities. Two case studies are presented to illustrate the proposed approach and sensitivity of the optimal solutions to given perturbations is analyzed.

Water consumption and wastewater generation depletes water resources and has a destructive impact on the environment. Recent attention has aimed at preserving water resources and preventing pollution through several routes. Restrictions on wastewater discharge into the environment, recycling, reuse and regeneration of wastewater streams are now common practices toward achieving these objectives. Membrane and integrated membrane processes have been shown to be effective at reducing water usage and recovering valuable compounds. This thesis focuses on topics related to the optimal synthesis of wastewater treatment networks by hybrid membrane systems. The use of superstructures has been a useful tool to synthesize chemical engineering process flowsheets. The approach postulates all possible alternatives of a potential treatment network. Within the representation, an optimal solution is assumed to be hidden in the given superstructure. State space is a framework to process synthesis problems which involves heat and mass exchange. In this representation, unit operations, utility units and utility streams can be embedded in such a way that all the process synthesis alternatives can be realized. Such a framework can be applied for water and wastewater synthesis problems. Several research optimization studies presented membrane and hybrid membrane process synthesis problems for wastewater treatment. Nonetheless, the problems in fact can be represented in several ways. Therefore, the mathematical programs are expected to be different for every postulated representation. Comparison between different representations and their mathematical programs are analyzed to highlight the relationship between the superstructure representation and their mathematical programming formulations. Possible improvement of these superstructures is addressed. Also, a generic representation is provided to give a systematic and clear description for assembling hybrid membrane system superstructures via the state space approach. The synthesis of reverse osmosis networks (RON) for water and wastewater treatment network is presented as a superstructure problem. The mathematical programming model describes the RON through a nonconvex mixed integer nonlinear program (MINLP). A mixed integer linear program (MILP) is derived based on the convex relaxation of the nonconvex terms in the MINLP to bound the global optimum. The MILP models are solved iteratively to supply different initial guesses for the nonconvex MINLP model. It is found that such a procedure is effective in finding local optimum solutions in reasonable time. Water desalination and treatment of aqueous wastes from the pulp and paper industry are considered as case studies to illustrate the solution strategy. The RON mathematical program is a nonconvex MINLP which contains several local optima. A deterministic branch and bound (B&B) algorithm to determine the global optimum for the RON synthesis problem has also been developed. A piecewise MILP is derived based on the convex relaxation of the nonconvex terms present in the MINLP formulation to approximate the original nonconvex program and to obtain a valid lower bound on the global optimum. The MILP model is solved at every node in the branch and bound tree to verify the global optimality of the treatment network within a pre-specified gap tolerance. Several constraints are developed to simultaneously screen the treatment network alternatives during the search, tighten the variable bounds and consequently accelerate algorithm convergence. Water desalination is considered as a case study to illustrate this approach for global optimization of the RO network. Wastewater and groundwater streams contaminated with volatile organic compounds (VOCs) require proper treatment to comply with discharge standards or drinking requirement restrictions. Air stripping and pervaporation are two common treatment technologies for water streams contaminated with VOCs. The combination of these technologies for water treatment which are representative of hybrid membrane systems may offer advantages over stand-alone treatments. Superstructure optimization uses the framework of hybridization to determine the optimal treatment network and the optimal operational requirements for the treatment units to achieve desired water qualities. Two case studies are presented to illustrate the proposed approach and sensitivity of the optimal solutions to given perturbations is analyzed.

This work introduces a systematic seawater reverse osmosis (SWRO) membrane network synthesis approach, based on the coordinated use of process superstructure representations and global optimization. The approach makes use of superstructure formulations that are capable of extracting a globally optimal design as a performance target, by taking into consideration desired process conditions and constraints that are typically associated with reverse osmosis systems. Thermodynamic insights are employed to develop lean network representations so that any underperforming solutions can be eliminated a priori. This essentially results in considerable improvement of the overall search speed, compared to previously reported attempts. In addition, the approach enables the extraction of structurally different design alternatives. In doing so, distinct membrane network design classes were established by partitioning the search space, based on network size and connectivity. As a result, corresponding lean superstructures were then systematically generated, which capture all structural and operational variants within each design class. The overall purpose is thus to enable the extraction of multiple distinct optimal designs, through global optimization. This mainly helps provide design engineers with a better understanding of the design space and trade-offs between performance and complexity. The approach is illustrated by means of a numerical example, and the results obtained were compared to previously related work. As anticipated, the proposed approach consistently delivered the globally optimal solutions, as well as alternative efficient design candidates attributed to different design classes, with reduced CPU times. This work further capitalizes on the developed representation, by accounting for detailed water quality information, within the SWRO desalination network optimization problem. The superstructures were modified to incorporate models that capture the performance of common membrane elements, as predicted by commercially available simulator tools, e.g. ROSA (Dow) and IMSDesign (Hydranautics). These models allow tracing of individual components throughout the system. Design decisions that are supported by superstructure optimization include network size and connectivity, flow rates, pressures, and post treatment requirements. Moreover, a detailed economic assessment capturing all the significant capital and operating costs associated in SWRO processes, including intake, pre and post treatment has also been accounted for. These modifications were then illustrated using a case study involving four seawater qualities, with salinities ranging from 35 to 45 ppt. The results highlight the dependency of optimal designs on the feed water quality involved, as well as on specified permeate requirements.