(560g) A Nonsmooth Approach to Multicomponent Mass and Water Integration

Mass 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 material in a system to minimize both mass waste and supply as well as solvent requirements. They are also applicable to a wide range of system types and materials, including many water integration problems. However, most of these methods can only consider a single stream property, and therefore often provide infeasible results for real systems in which mass reuse is limited by the presence of multiple materials. Solving these problems efficiently is inherently challenging because they require nonsmooth operations, both to determine the limiting component in each mass transfer unit and also to sort streams into intervals based on these limiting concentrations. As a result, the existing approaches to solving multicomponent 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 previously developed a new approach to solving the multicomponent mass integration problem that takes advantage of its nonsmooth structure by using compact, explicitly nonsmooth expressions. [1] However, this approach assumes that there is only a single lean solvent or freshwater stream in the system. While this assumption still allows us to design feasible reuse networks, the inability to consider other solvent streams for mass removal means that our original approach may not be able to identify networks with more potential savings. Therefore, in this talk, we share an extension to our previous multicomponent mass integration approach that can incorporate multiple lean streams.

As in the initial formulation, we use a nonsmooth system of two equations to select streams by concentration interval and describe the optimality conditions for pinch-constrained resource transfer. [1,2] To consider multiple components, we adapt the nonsmooth concentration scalings proposed by Alva-Argaez et al. in their superstructure approach [3]. These scalings describe the interrelated mass transfer between components and use max expressions to ensure that one component is always at its limit. However, when deriving the mass transfer relations that determine the concentration scalings, our new approach assumes that the lean stream concentrations are negligible compared to those in the rich streams. This assumption, which is common in mass integration systems and approaches, allows us to include mass transfer with multiple lean streams without having to consider specific lean and rich stream pairings. Therefore, we can directly incorporate any number of lean streams into our pinch analysis approach, and the resulting equation system can be combined with a process model and solved using new advances in nonsmooth equation solving to simulate the multicomponent system. [4]

In this presentation, we will use example systems to highlight the unique benefits of our approach. We will demonstrate our formulation’s ability to solve for optimal resource targets and for process variables and that it remains only two equations regardless of both the number of solvent streams and the number of components in the system. We will also show the significant utility savings that can result from the potential to incorporate additional lean and fresh streams in our formulation. As a result, we have developed an adaptable approach to improving resource use in mass and water networks that can provide computationally tractable solutions to a wide variety of large-scale, multicomponent integration problems.

[1] C. J. Nielsen and P. I. Barton. Comput. Chem. Eng. 48: pp. 253-258, 2020.

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

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

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