Global Optimization of Heat Exchanger Networks. Part 1: Stages/Substages Superstructure

Abstract

We solve globally an extension of the isothermal mixing stages model (Synheat) proposed by Yee and Grossmann, later extended to nonisothermal mixing by Bjork and Weterlund and solved globally by Faria et al. This new extension of that model was recently presented in a conference proceedings. The model allows specific structures that are more commonly accepted in industry than generalized complex structures that suffer from somewhat disorganized branched and sub-branches which present several practical challenges. This stages/substages superstructure has limited branching and several matches in series in each branch. Our industrial experience shows us that these are acceptable in practice. The novel contribution of this article is then solving such a model globally, adding the control of temperature differences upon mixing

Globally optimal synthesis of heat exchanger networks. Part I: Minimal networks

“…For example, if the generalized superstructure by Floudas et al 3 is used, then even assuming isothermal mixing can be used in models PSTR and PLB (a LB model proposed by Kim and Bagajewicz), as well as PESTR . Other extensions of the Synheat model, interesting for industry, like the stages/Substages model, may require some changes in the PSTR and PESTR models, while a linear LB model was already developed . Generating new constraints to avoid repeated structures is also ongoing work.…”

“…Kim and Bagajewicz developed a new generalized superstructure for HEN synthesis and solved it globally. Later, Kim et al presented a new substage superstructure for HEN synthesis that is also solved globally. Finally, Beck and Hofmann proposed solving several MILP and NLP subproblems iteratively that allow to solve small‐scale problems to global optimality, but the algorithms are not efficient for large‐scale problems.…”

“…4 The former was further generalized by Kim and Bagajewicz, 5 while the latter, more appealing to practitioners in industry and widely preferred in academia, was expanded to consider nonisothermal mixing by Björkand and Westerlund 6 and Huang et al 7 In addition, Huang and Karimi 8,9 proposed extensions of the stagewise superstructure that include recycles inside each stage as well as partial bypasses of the stages. Finally, regarding staged superstructures, another extension to consider substages and nonisothermal mixing was proposed by Jongsuwat et al 10 and solved globally by Kim et al 11 Bypasses and recycles, as well as several exchangers in series on each branch, were also considered by Barbaro and Bagajewicz 12 who proposed a superstructure that uses transshipment-type equations to obtain a rigorous linear model.…”

Globally optimal synthesis of heat exchanger networks. Part III: Non‐isothermal mixing in minimal and non‐minimal networks

“…The authors proposed a useful bound contraction procedure (RYSIA) to globally solve HEN models without using BB steps. Kim et al 30 constructed a stages/substages superstructure to synthesize HENs with non‐isothermal mixing. Their model allowed more commonly acceptable networks than the topology configurations of the generalized superstructures featuring disorganized branches and presenting challenges in practice.…”

Synthesis of stream‐split heat exchanger networks using non‐structural model considering serial equipment in stream branches and submixing of substreams

“…To relax the assumptions, some subsequent studies have allowed non‐isothermal mixing of substreams. [ 13–16 ] Kim et al [ 17 ] and Kim and Bagajewicz [ 18 ] have done away with restricting one heat exchanger per stream branch and introduced substages in SWS‐based superstructures to allow several stream matches in series in a substream. Also, using the SWS idea with substages, Pavão et al [ 11,12 ] have considered series connection of heat exchangers in individual stream branches.…”