Nonlinear optimization model for CSO control facilities planning

Storage is considered a necessary combined sewer overflow (CSO) pollution control measure because it can respond cost-efficiently to the intermittent and very often large volumes associated with stormwater and induced CSOs. However, CSO storage facilities are conventionally sized on the individual basis, but not in concert with other CSO control measures such as the provision of alternative CSO treatment technologies (screening, high-rate primary treatment, swirl or helical bad concentrators), and the addition of more transport or/and treatment capacities to the existing combined sewer system (CSS) with the downstream wastewater treatment plant (WWTP) included. This common practice can lead to sub-optimal results in both economic and environmental senses, because inherent interactions and economic trade-offs among these CSO control devices are not taken into account. A general optimization framework for the planning of CSO storage, conveyance and treatment capacities in addition to the existing CSS is developed which incorporates the stochastic aspect of the wet-weather inflows, the maximum usage of the available wet-weather capacities, the sizing of each CSO control facility in combination with the others, as well as appealing optimization features of decision models. Derived probability distribution approach is employed to develop a set of new closed form analytical expressions to describe the general layout and performance of the characteristics of the potential CSO pollution control components at the subcatchment level. Combining these expressions with appropriate flow conservation equations, a system-wide economic optimization model is formulated that primarily establishes minimum cost tradeoffs between the economics of scale involved in the provision of on-site CSO storage and high-rate treatment (SHRT) facilities, and the cost of additional transport capacities and ultimate treatment at the WWTP. The basic system-wide CSO control facilities planning model is manipulated into a mixed-integer non-linear programming model, the CSO-CFP-MINLP model that is implemented in high-level language for solution using an outer-approximation decomposition procedure for solution. At first, a simple application provides move insights about the outer-approximation procedure. Then, a more complex CSO pollution control problem is considered to investigate the usefulness and computational attributes of the CSO-CFP-MINLP model in evaluating very large number of system-wide CSO control alternative plans.