(583f) Compact, Nonsmooth Operators for Single-Component Mass and Water Integration

Focus in modern plant retrofit, expansion, and design has shifted towards the use of intensification techniques to implement processes that are both sustainable and economically competitive. By calculating the minimum resource usage required for a process with optimal reuse, process integration methods can be used to identify targets where there is significant scope for intensification and motivate the design of novel technologies, such as multistream heat exchangers for optimal heat recovery. Therefore, process integration can be used both to intensify existing plants where a fundamental redesign of the process is infeasible and also to ensure that proposed intensified processes operate optimally. To further decrease resource use, these integration methods have expanded beyond integrating individual processes to sharing resources between plants in the form of eco-industrial parks. However, as process integration is applied to increasingly complex problems, improved numerical methods are required to efficiently consider resource usage and constraints.

Current methods for solving process integration problems fall into two general categories: pinch analysis or superstructure approaches. Pinch analysis methods are physically intuitive and relatively easy to implement; however, current techniques are often heuristic and limited to a small class of problems. Even algorithmic pinch point approaches are typically mathematical programming problems with numbers of constraints that increase significantly with the number of sources and sinks. In the context of fixed-flow rate water allocation problems, these approaches are also unable to solve for concentration process variables and cannot be used for simultaneous process integration and optimization. On the other hand, superstructure techniques are adaptable to many different integration problems. However, these formulations are mixed-integer programming problems that often involve nonconvex functions, are difficult to solve, and whose complexity increases rapidly with problem size.

To address these limitations, we have developed compact, nonsmooth operators for both single-contaminant mass and water integration problems. These operators extend the work of Watson et al., who simulated multistream heat exchangers using a nonsmooth system of equations adapted from a mathematical programming pinch analysis approach proposed by Duran and Grossmann [1,2]. Our formulation consists of systems of only two equations: an overall resource balance for the process and a single nonsmooth equation describing the resource balance below potential pinch points. Automatic lexicographic-directional differentiation is used to calculate exact generalized derivative elements for the nonsmooth equation system [3]. These elements are used in a suitable method, such as Semismooth or Linear Programming Newton, to solve the system without requiring smoothing approximations or additional variables.

We will present these novel operators and their solution methods and demonstrate how they can be used both to solve for optimal resource targets and for process parameters given resource constraints, including source and sink concentrations in water allocation problems. In addition, we will show other unique benefits of this approach, including the ability to simulate both pinch and threshold problems using a single model. Overall, our results will highlight how these nonsmooth operators significantly reduce problem complexity compared to optimization approaches and can provide computationally tractable solutions to large-scale interplant integration problems.

References

[1] H .A. J. Watson, K. A. Khan, and P.I. Barton. Multistream Heat Exchanger Modeling and Design. AIChE Journal, 61(10):3390-3403, 2015.

[2] M.A. Duran and I.E. Grossmann. Simultaneous Optimization and Heat Integration of Chemical Processes. AIChE Journal, 32(1):123-138, 1986.

[3] K. A. Khan and P. I. Barton. A vector forward mode of automatic differentiation for generalized derivative evaluation. Optimization Methods and Software, 30(6):1185-1212, 2015.