Combined Heat and Mass Exchange Networks Synthesis Using a Hybrid Trust-Region Optimization Approach Including Optimal Detailed Unit Design

Mass exchanger network synthesis and heat exchanger network synthesis are important process integration tasks for designing optimal flowsheets that minimize costs and emissions to the environment. The two network synthesis problems are often performed separately, with much progress having been made, particularly in the case of heat exchanger network optimization. It is especially challenging, but also important, to perform these two tasks simultaneously as mass transfer coefficients relate to temperature and velocities, forming a highly interdependent system of variables. In order to model these systems, simplified, mostly convex, representations of unit operations are used at the network topology step in order to be able to solve the resulting mixed-integer nonlinear programming (MINLP) formulation. There are many important applications for solving these problems including water networks, pollutant recovery systems, and optimal separation networks. However, since these units contain complex mass and heat transfer operations, the simplified unit representations used in the MINLP do not necessarily model the real system accurately. For this reason, many of these process integration tools have not found significant industrial application.

In this talk we present a newly developed algorithm that solves a sequence of optimization problems to solve for the optimal combined heat and mass exchanger network (CHAMEN), including detailed representations of the units. In the first step an initialization strategy is employed, whereby the HENS and MENS problems are solved separately. A subsequent step combines the initialized models to form a large MINLP problem, where simplified representations, based on those found in Yee and Grossmann (1990) and Szitkai et al. (2006) models are solved simultaneously. This MINLP contains parameters that ensure the objective function is underestimated and thus provides a lower bound for the overall problem.

After solving this model, an NLP representation of the found network topology is formulated. This NLP formulation uses a combination of modelling strategies, including directly incorporating detailed unit optimisation models for the mass exchangers as well as using surrogate representations of heat exchangers. The detailed unit models are based on recent work by Kazi et al. (submitted) and Short et al. (2018). Packed columns are represented by the models of Short et al. (2018), where detailed differential-algebraic equations (DAEs) are used to obtain the optimal diameters and packing sizes for the columns. These require no binary decisions to be made and can therefore be directly incorporated into the NLP flowsheet. In Kazi et al. (submitted), shell-and-tube heat exchangers are also represented as DAEs, resulting from discretization based on a topology obtained from enumeration with the Bell-Delaware method. This enumeration finds the optimal combination of shells, tube passes, etc., but are difficult to incorporate directly into the NLP. We therefore include these models via a trust-region optimization strategy. The trust-region optimization strategy embeds reduced order-models into the NLP that are directly linked to the detailed heat exchanger models. Through updating the reduced-order models with new models, including gradients, at each iteration of the trust region algorithm, optimality of both the detailed model and overall network is guaranteed. Upon convergence of the trust region algorithm, this NLP solution is assumed to provide an upper bound for the overall problem.

A binary cut is then added to exclude this network topology from subsequent MINLP runs, and the upper bound, from the NLP objective value, is enforced as a constraint. The MINLP is rerun to generate new topologies, followed by the NLP trust-region optimization, until there exists no feasible solution to the MINLP step. The new optimization strategy does not increase the computational effort of solving the original non-convex MINLP problem, but also allows for detailed unit designs to be included while designing the integrated process flowsheets. In addition, we not only obtain an optimal network design, but also a detailed optimization-based simulation of the final flowsheet. This method is the first to explore detailed unit designs within the CHAMEN synthesis problem and shows the need to include detailed unit modelling considerations for this problem. The algorithm is tested on several case studies and compared to results found in literature.

REFERENCES:

Kazi, S. R., Short, M., Biegler, L. T., submitted, Heat Exchanger Network Synthesis With Detailed Exchanger Designs - 1. A Discretized Differential Algebraic Equation(DAE) Model for Shell and Tube Heat Exchanger Design.

Short, M., Isafiade, A. J., Fraser, D., Kravanja, Z., 2016, Two-step hybrid approach for the synthesis of multi- period heat exchanger networks with detailed exchanger design. Appl. Therm. Eng. 105, 807-821.

Short, M., Isafiade, A., Biegler, L.T., Kravanja, Z., 2018, Synthesis of mass exchanger networks in a two-step hybrid optimization strategy. Chem. Eng. Sci., 178, 118-135.

Szitkai, Z., Farkas, T., Lelkes, Z., Rev, E., Fonyo, Z., Kravanja, Z., 2006, Fairly linear mixed integer nonlinear programming model for the synthesis of mass exchange networks. Ind. Eng. Chem. Res., 45(1), 236–244.

Yee, T. F., Grossmann, I. E., 1990, Simultaneous Optimization Models for Heat Integration - II. Heat Exchanger Network Synthesis. Comput. Chem. Eng., 14, 1165-1184.