Optimal Design of Hybrid Membrane Networks for Wastewater Treatment
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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.