Alternative Mixed-Integer Linear Programming Formulations for Shell and Tube Heat Exchanger Optimal Design

Gonçalves, Caroline de O.; Costa, André L.H.; Bagajewicz, Miguel J.

doi:10.1021/acs.iecr.6b04950

Cited by 25 publications

(33 citation statements)

References 16 publications

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“…Table displays a comparison of the application of the proposed approach with the results present in Gonçalves et al for 10 heat exchanger design problems. Both approaches are based on linear formulations; in our case, we used the Bell–Delaware method, and in the case of Gonçalves et al, the Kern method was employed.…”

Section: Comparison With Results Using the Kern Methodsmentioning

confidence: 99%

“…To obtain an MILP formulation, we use the relations between the discrete variables and the corresponding binary variables as in previous work . Instead of representing each discrete alternative of each variable by an individual index, a single index, srow , is associated to each set of discrete values which compose a candidate solution.…”

Section: Development Of the Milp Formulationmentioning

confidence: 99%

“…The next step consists of a reformulation . Thus, an expression as

p^{n 1} q^{n 2} \dots z^{nm} = {[\sum_{italicsrow} {\overset{pd}{true}}_{italicsrow} {italicyrow}_{italicsrow}]}^{n 1} {[\sum_{italicsrow} {\overset{qd}{true}}_{italicsrow} {italicyrow}_{italicsrow}]}^{n 2} {[\sum_{italicsrow} {\overset{zd}{true}}_{italicsrow} {italicyrow}_{italicsrow}]}^{nm}

is reorganized to:

p^{n 1} q^{n 2} \dots z^{nm} = \sum_{srow} {({\overset{true^}{italicpd}}_{srow})}^{n 1} {({\overset{true^}{italicqd}}_{srow})}^{n 2} \dots . . {({\overset{true^}{italiczd}}_{srow})}^{nm} {yrow}_{srow}

We then linearize products of binaries as in previous work …”

Section: Development Of the Milp Formulationmentioning

confidence: 99%

“…In addition, Gonçalves et al showed that the nonlinear equations of the heat exchanger model based on the Kern method can be reformulated as a mixed‐integer linear programming problem (MILP), whose solution is therefore global. They also proposed a more efficient integer linear programming problem formulation …”

Section: Introductionmentioning

confidence: 99%

“…The central aspect in this article is to show that the mathematical techniques developed by Gonçalves et al to transform nonlinear (and nonconvex) equipment models to linear ones can also be employed when several disjunctions for laminar and turbulent flow for tube‐side and shell‐side flows are needed (e.g., as it occurs in the Bell–Delaware method).…”

Section: Introductionmentioning

confidence: 99%

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Linear method for the design of shell and tube heat exchangers using the Bell–Delaware method

2019

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In this article, we present a rigorous reformulation of the Bell–Delaware model for the design optimization of shell and tube heat exchanger to obtain a linear model. We extend a previously presented methodology1,2 of rigorously reformulate the mixed‐integer nonlinear programing Kern model and we add disjunctions to automatically choose the different correlations to calculate heat transfer coefficients and pressure drop under different flow regimes. The linear character of the formulation allows the identification of the global optimum, even using conventional optimization algorithms. The proposed mixed‐integer linear programming formulation with the Bell–Delaware method is able to identify feasible solutions for the design of heat exchangers at a lower cost than those obtained through conventional design formulations in the literature. Comparisons with the Kern method also indicate an average 22% difference (usually lower) in area.

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Section: Comparison With Results Using the Kern Methodsmentioning

confidence: 99%

Section: Development Of the Milp Formulationmentioning

confidence: 99%

“…The next step consists of a reformulation . Thus, an expression as

p^{n 1} q^{n 2} \dots z^{nm} = {[\sum_{italicsrow} {\overset{pd}{true}}_{italicsrow} {italicyrow}_{italicsrow}]}^{n 1} {[\sum_{italicsrow} {\overset{qd}{true}}_{italicsrow} {italicyrow}_{italicsrow}]}^{n 2} {[\sum_{italicsrow} {\overset{zd}{true}}_{italicsrow} {italicyrow}_{italicsrow}]}^{nm}

is reorganized to:

p^{n 1} q^{n 2} \dots z^{nm} = \sum_{srow} {({\overset{true^}{italicpd}}_{srow})}^{n 1} {({\overset{true^}{italicqd}}_{srow})}^{n 2} \dots . . {({\overset{true^}{italiczd}}_{srow})}^{nm} {yrow}_{srow}

We then linearize products of binaries as in previous work …”

Section: Development Of the Milp Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Linear method for the design of shell and tube heat exchangers using the Bell–Delaware method

2019

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Globally optimal linear approach for the design of process equipment: The case of air coolers

2017

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In a recent article, Gonçalves et al., introduced a linear and rigorous methodology for equipment design, in particular shell‐and‐tube heat exchanger. Here, we explore its application to air coolers, a problem that we solve globally for the first time. Because the approach is linear, results are globally optimal. The objective function is the total annualized cost. The constraints include the thermal and hydraulic modeling of the process stream flow in the tube bundle and the air flow through the finned surface. In addition, we worked on reducing computing time, through an analysis of different alternatives for the description of the original discrete variables organized in sets of binary variables. The performance of the proposed approach is illustrated through its comparison with an air cooler described in the literature. © 2017 American Institute of Chemical Engineers AIChE J, 64: 886–903, 2018

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Globally optimal linear approach to the design of heat exchangers using threshold fouling modeling

2018

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This article presents a method for the mathematical optimization of the design of heat exchangers including fouling rate modeling for the tube-side. The description of the fouling rate in crude preheat trains of petroleum distillation units is commonly based on threshold models (Ebert-Panchal model and its variants). Our formulation of the design problem employs a mixed-integer linear programing approach; therefore the solution is the global optimum and common nonconvergence drawbacks of mixed-integer nonlinear programming models are totally avoided. Three different examples are employed to compare the proposed approach with an optimization procedure using fixed fouling resistances. The results indicate that in two problems was possible to obtain design solutions associated to smaller heat exchangers. Additionally, three case studies are also explored to discuss how fouling is related to crude types, pressure drop manipulation, and energy integration.In heat exchanger design, it is common to consider some constraints regarding relations between geometric variables. The baffle spacing must be limited between 20 and 100% of the shell diameter 22 and also the ratio between the tube length and shell diameter must be between 3 and 15 23

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Alternative Mixed-Integer Linear Programming Formulations for Shell and Tube Heat Exchanger Optimal Design

Cited by 25 publications

References 16 publications

Linear method for the design of shell and tube heat exchangers using the Bell–Delaware method

Linear method for the design of shell and tube heat exchangers using the Bell–Delaware method

Globally optimal linear approach for the design of process equipment: The case of air coolers

Globally optimal linear approach to the design of heat exchangers using threshold fouling modeling

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