Mathematical programming model for heat exchanger design through optimization of partial objectives

Abstract

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell-Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied.The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

Numerical investigation on baffle configuration improvement of the heat exchanger with helical baffles

“…But this type of heat exchanger has some inherent drawbacks, such as a large pressure drop in the shell side and a dead zone in the back of the segmental baffles, and leading to a serious fouling and high risk of vibration failure on tube bundles [2][3][4][5][6]. A number of new methods were proposed to overcome the above-mentioned drawbacks in shell-and-tube heat exchangers with segmental baffle [7][8][9][10][11][12][13]. STHX with helical baffles (STHXsHB) was firstly proposed by Lutcha and Nemcansky [14].…”

Simultaneous synthesis of work exchange networks with heat integration

“…The optimization of heat recovery is critical to solve the problem of the efficient use of energy and, consequently, to promote the reduction of gaseous emissions and consumption of oil and natural gas, since the reduction of energy consumption is closely linked to improvement of heat transfer (Cheng and Liang, 2012a;Kaluri and Basak, 2011;Onishi et al, 2013a;Wang et al, 2011). Thereby, harnessing energy from process streams through thermal integration between heat exchangers and cooling and/or heating systems is one of the most effective ways to reduce costs.…”

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

“…Example 1, originally proposed by Shenoy, is based on the minimization of heat transfer area, and Example 2, originally presented by Mizutani et al, involves the minimization of the total annualized cost. Both examples were solved by Ravagnani and Caballero and Onishi et al using an MINLP formulation. The comparison of our results and Ravagnani and Caballero and Onishi et al must consider some differences: The tube‐side correlations in our model are different from the correlations used by Ravagnani and Caballero and Onishi et al Our model for the evaluation of the tube‐side convective heat transfer coefficient encompasses all flow regimes.…”

“…Among different alternatives using mathematical programming, Jegede and Polley presented a nonlinear programming model where the independent variables are the tube‐side and shell‐side heat transfer coefficients (or a convective heath transfer coefficient and the area). In turn, Mizutani et al, Ravagnani and Caballero, and Onishi et al considered some optimization variables to be discrete, which yielded nonconvex mixed‐integer nonlinear programing (MINLP) problems. 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.…”