(461g) A Nonsmooth Approach to Multicontaminant Water Integration

Water integration methods have been widely proposed and utilized to improve sustainability both in well-established chemical processes and in new designs. These approaches can significantly reduce environmental impact by optimally reusing water to minimize fresh and wastewater utilities. However, most of these methods can only consider a single stream property, and therefore often provide infeasible results for real systems in which water reuse is limited by the presence of multiple contaminants. Solving these problems efficiently is inherently challenging because they require nonsmooth operations, both to determine the limiting contaminant in each water-using unit and also to sort streams into intervals based on these limiting concentrations. As a result, the existing approaches to solving multicontaminant problems are primarily limited to superstructures that scale exponentially with the number of resource streams and are not well-equipped to handle large-scale problems or to be embedded in programs for simultaneous process optimization.

To improve scaling and decrease complexity, we present a new approach to solving the multicontaminant water integration problem that takes advantage of its nonsmooth structure by using compact, explicitly nonsmooth expressions. To select streams by concentration interval, we have extended our previous work on the nonsmooth integration operator, which uses a system of two nonsmooth equations to both partition streams and describe optimality conditions for pinch-constrained resource transfer [1]. Our extended formulation considers multiple contaminants by incorporating the nonsmooth concentration scalings proposed by Alva-Argaez et al. in their superstructure approach [2]. These scalings describe the interrelated mass transfer between components and use max expressions to ensure that one component is always at its limit. When included in the nonsmooth integration operator, the resulting equation system can be combined with a process model and solved using new advances in nonsmooth equation solving [3] to simulate fixed-load, multicontaminant systems.

Using example systems, we will demonstrate that this approach uniquely enables us to solve both for optimal resource targets and for process parameters, including the contaminant concentrations present in the nonsmooth scalings. In addition, unlike other approaches, the resulting formulation requires only equation-solving methods and retains a compact system of only two equations regardless of the number of water streams. As a result, we have developed a readily adaptable approach that significantly reduces problem complexity and can provide computationally tractable solutions to a wide variety of large-scale, multicontaminant integration problems.

[1] C. J. Nielsen and P. I. Barton. Ind. Eng. Chem. Res. 59(1): 253-264, 2020.

[2] A. Alva-Argaez, A. Vallaintos, and A. Kokossis. Comput. Chem. Eng. 23: 1439-1453, 1999.

[3] K. A. Khan and P. I. Barton. Optim. Methods and Softw., 30(6): 1185-1212, 2015.