A new bounding strategy for synthesizing distillation schemes with energy integration

Abstract

An efficient method is developed for synthesizing distillation systems with energy integration. In order to reduce the search space a predictor-based ordered-search technique is used. The main feature of the two-level method is the utilization of the heat-cascade theory by setting up lower bounds for all feasible energy-integrated separation sequences. A separation structure can be built up from individual columns, two-column matches and higher-order integrated matches as well. The objective function of the optimal separation system is the total annual cost, which is a combination of capital and operating expenses. For comparison with previous works, in this study the pressures and reflux ratios of distillation columns are selected as design variables. The effectiveness of the synthesis method is demonstrated on the five-component example of Heaven. The algorithm, utilizing the heat-cascade theory, can be simply implemented on computer. Scope—Chemical processes frequently apply distillation systems for separating multicomponent mixture into products with relatively pure species. The task of synthesizing optimal (or a small number of near-optimal) separation sequences with heat integrations often represents a huge combinatorial problem. The number of feasible separation schemes increases rapidly as the number of components to be separated increases. Because the computation time and cost for the analysis of separation processes are not negligible, it is desirable to have procedures for determining the optimal (or a small number of near-optimal) separation structures without examining all the possible schemes. In order to reduce the search space of the synthesis problem several systematic procedures have been developed. Unlike previous methods, the predictor-based ordered-search method proposed here utilizes the heat-cascade theory [1, 2]. By applying the heat-cascade theory a minimum value can be predicted for the total annual cost of all heat-integrated sequences without detailed evaluation of all possible heat matches. The predicted minimum cost can be used as lower bounds for the objective function. The lower bounds are computed as the sum of the actual total annual cost of the unintegrated substructure and a prediction of the minimum cost for that part of the remaining substructure to be integrated. The structures are ordered according to the lower bounds and the heat matches are optimized starting with the structure of the lowest lower-bounding value. The optimized total annual cost of the best sequence is used as a continuously renewed upper bound. The search for a better candidate is complete when the lower bound of the forthcoming structure in the order exceeds the upper bound. In this manner, the predictor-based ordered-search strategy proposed here is capable of omitting a large number of feasible separation schemes and heat matches, and can save considerable computer time. Conclusions and Significance—The method reported here for synthesizing heat-integrated distillation systems applies a predictor-based ordered-search technique. Using the heat-cascade theory a minimum value for the total annual cost of all the separation structures can be estimated. These minimum values are assigned to the corresponding structures and used as lower bounds of the objective function. The important feature of the method is that mathematical guarantees on the elimination of uneconomical solutions are maintained, hence the optimal solution for heat-integrated distillation schemes is not eliminated by the search reduction. The new bounding strategy could be combined, to include that integration, with the method proposed by Gomez and Seader [3]. The effectiveness of the method is demonstrated on a five-component hydrocarbon mixture where only 20% of the feasible separation structures had to be examined.