(297d) Retrofitting of Municipal Wastewater Treatment Plants for Maximizing Resilience Under Cost Limitations: Graph-Theoretic Approach

According to the United Nations (UN), the world population will surpass 9.5 billion people by 2050 (UN, 2022). One of the most serious consequences of the fast population growth is the increase in water pollution. Every year, more than 300 km³ of municipal wastewater are treated globally (Mateo-Sagasta et al., 2015), and it is expected that this figure will increase alongside with the population. Hence, the capacity of numerous wastewater treatment plants (WWTPs) has been exceeded, especially during rainy seasons when the volume of water to be treated may be significantly enlarged, and high volumes of water remain untreated. Because of this, analysis and retrofitting of WWTP has emerged as a key area in wastewater treatment engineering, and have attracted attention of numerous stakeholders (Bozkurt et al., 2016).

Process Network Synthesis (PNS) refers to the task of defining the structure of a process from a set of plausible building blocks, i.e., defining the basic units comprising the transformation process and their connectivity. The algorithmic approach to PNS has been deployed before for the synthesis of wastewater treatment plants, as it endows the designer with the capacity to explore numerous alternatives (Galan and Grossmann, 1998; Grossmann et al., 2014). Similarly, the task of retrofitting WWTPs can be regarded as a PNS problem where the best improvements to the current structure needs to be determined; such a problem can also be addressed algorithmically by resorting to optimization methods. Previous contributions have addressed this problem of finding the best retrofitting based on cost optimization (Bozkurt et al., 2016); however, determination of the best retrofit should not be based exclusively on economic criteria and additional sustainability metrics should be involved. An especially significant property for this kind of system is its resilience, which accounts for its capacity to recover from failures. However, the comparison of resilience for assorted designs requires a method to account for the effects of both expected and unexpected failures simultaneously. The consideration of unexpected failures is a daunting task, as it requires the enumeration of possible consequences for all possible failures in the process units (Orosz et al., 2022); such an enumeration can be performed by considering the properties of the process structure itself.

The P-graph framework is a graph-theoretic approach for process synthesis that is based on an unambiguous graphical representation and a set of combinatorial axioms and algorithms (Friedler et al., 1992). These elements are employed to exploit the properties of a synthesis problem’s structure to enhance its solution, which endows numerous traits for the designers. On one hand, the graphical representation permits a user-friendly depiction of the changes in the process and its manipulation during the solution procedure. On the other hand, the combinatorial algorithms permit the algorithmic construction of a rigorous superstructure and the enumeration of the feasible processes that comprise it. Moreover, they handle the design decisions structurally, thus, numerous infeasibilities can be removed from the outset and no binary decision variables need to be included in the problem (Friedler et al., 1996); hence, the risk of convergence to local optima related to the structure is reduced. Because the optimization is enhanced and the search space is drastically reduced, the framework can efficiently deliver not only the best solution but also the set of n-best alternative designs. Such a set of solutions provides the designers with insightful information concerning the process and may be analyzed to determine the best alternative in light of criteria that are not considered in the model.

In this work, the P-graph framework (Friedler et al., 2022) is employed as a synthesis tool for retrofitting WWTPs that considers sustainability, resilience, and economic indicators. For this, the structure of the existing process is extended with plausible operation alternatives, as shown in Figure 1. Then the optimization is performed to determine the new connections is most suitable for resilience enhancement. For this, combinatorial algorithms are used for the rigorous examination of all possible retrofitting options and the exhaustive enumeration of failure cases in the extended process structure. The examination renders the n-best alternatives for retrofitting that maximize the resilience of WWTP under a limited budget, from which the designers may select the most suitable alternative, thereby yielding insightful information for the decision-makers.

References

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