Improved sequential strategy for the synthesis of near-optimal heat exchanger networks (original) (raw)
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Computer Aided Chemical Engineering, 2006
A Sequential Framework for Heat Exchanger Network Synthesis (HENS) is presented and the philosophy of this iterative methodology is explained. There are two main advantages of the proposed methodology. First, the design procedure is, to a large extent, automated while keeping significant user interaction. Second, the subtasks of the framework (MILP and NLP problems) are much easier to solve numerically than the MINLP models that have been suggested for HENS. The limiting factors of the methodology are the NLP and MILP models where enhanced convex estimators are required to reach global optimum in the former while significant improvements are required to prevent combinatorial explosion in the latter. This paper makes an attempt to address a few of the limiting elements of the framework.
Computers & Chemical Engineering, 2015
Determining the minimum number of units is an important step in heat exchanger network synthesis (HENS). The MILP transshipment model (Papoulias and Grossmann, 1983) and transportation model (Cerda and Westerberg, 1983b) were developed for this purpose. However, they are computationally expensive when solving for large-scale problems. Several approaches are studied in this paper to enable the fast solution of large-scale MILP transshipment models. Model reformulation techniques are developed for tighter formulations with reduced LP relaxation gaps. Solution strategies are also proposed for improving the efficiency of the branch and bound method. Both approaches aim at finding the exact global optimal solution with reduced solution times. Several approximation approaches are also developed for finding good approximate solutions in relatively short times. Case study results show that the MILP transshipment model can be solved for relatively large-scale problems in reasonable times by applying the approaches proposed in this paper.
A Novel Sequential Approach for the Design of Heat Exchanger Networks
Frontiers in Chemical Engineering, 2021
This paper presents a new algorithm for the design of heat exchanger networks (HEN) that tries to take advantage of the strengths of the sequential and simultaneous approaches. It is divided into two sequential parts. The first one is an adaptation of the transportation model (TransHEN). It maintains the concept of temperature intervals and considers the possibility of heat transfer between all the hot and cold streams inside those intervals, and at the same time it allows the a priori calculation of the logarithmic mean temperature difference between all possible heat exchanges, and therefore it maintains the area estimation linear in the model. The second step (HENDesign model), uses a superstructure that contains all the possible alternatives in which the matches predicted by the first stage model can exchange heat to design the final heat exchanger network. Unlike the sequential approach, in this model, all heat flows, temperatures, areas, etc. are reoptimized maintaining the se...
Optimal synthesis of multiperiod heat exchanger networks: A sequential approach
2017
Heat exchanger network (HEN) synthesis is an important research field in industrial processes. It is possible to minimize utilities usage as well as pollutant emissions by an optimal HEN synthesis. In multiperiod HENs, the same heat transfer devices must be able to operate under different operating conditions. The synthesis of multiperiod HEN can be formulated as an optimization problem. In the present paper it is used a sequential approach to solve the problem of synthesizing multiperiod HEN, considering heat capacities and stream temperatures variations into different operation periods. In this approach, multiperiod HEN synthesis is decomposed into three sequential steps, considering three optimization models. The novelties of the proposed approach are a modification in a well-known superstructure from the literature, with the inclusion of new by-pass streams, and an improvement in the NLP model of the third step. Two benchmark literature examples are studied and the obtained resu...
Industrial & Engineering Chemistry Research, 2003
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.
The synthesis of heat exchanger networks (HENs) has mainly been done through the use of approximate models for each of the individual heat exchangers that comprises the network. These approximate models do not adequately take into account key parameters such as the overall heat transfer coefficient , TEMA standards, pressure drops, FT correction factors, and multiple shells. These factors can significantly alter the cost of the network. This paper presents a new methodology for the synthesis of heat exchanger networks using detailed heat exchanger design models that takes into account the aforementioned design parameters. The newly developed method involves the following steps. First, a SYNHEAT (Yee and Grossmann, 1990) MINLP model is solved. The individual exchangers for the resulting network are then designed using heuristics, TEMA standards and the Bell-Delaware method. From the designs obtained for these individual exchangers, correction factors are inserted into the SYNHEAT model that account for changes in overall heat transfer coefficient, TEMA choices, pressure drops, Ft correction factors and the effect of multiple shell passes. The SYNEAT model is then rerun and individual exchangers redesigned and the procedure repeated until convergence is achieved. For each iteration the change in each correction factor is limited to avoid the omission of certain solutions. While the methodology cannot guarantee global optimality it can ensure that the synthesised processes are physically achievable and has also been shown to converge on physically meaningful parameters without the explicit formulation of complicated non-linear equations in the MINLP formulation.
This article describes a study in which the various stagewise and interval-based superstructures for the mixed integer non-linear programming (MINLP) optimisation of heat exchanger networks were systematically compared, using exactly the same basis. The effect of using different logarithmic mean temperature difference (LMTD) approximations on the Total Annual Cost of the network and the network structure were examined. The accuracy of the approximations was also analyzed over a wide range of temperature difference ratios. It is concluded that the best approximation, which is the Underwood-Chen approximation, should be used in future mathematical optimisation of Heat Exchanger Network Synthesis problems.
New rigorous one-step MILP formulation for heat exchanger network synthesis
Computers & Chemical Engineering, 2005
In this paper, a rigorous MILP formulation for grass-root design of heat exchanger networks is developed. The methodology does not rely on traditional supertargeting followed by network design steps typical of the Pinch Design Method, nor is a non-linear model based on superstructures, but rather gives cost-optimal solutions in one step. Unlike most models, it considers splitting, non-isothermal mixing and it counts shells/units. The model relies on transportation/transshipment concepts that are complemented with constraints that allow keeping track of flow rate consistency when splitting takes place and with mechanisms to count heat exchanger shells and units. Several examples from the literature were tested, finding that the model usually obtains better solutions. In some cases, the model produced unknown solutions that were not found using superstructure optimization methods, even when the same pattern of matches is used.
Chemical Engineering Science, 2016
This study makes use of a novel methodology for the synthesis of heat exchanger networks, which is aimed at overcoming the shortcomings associated with the use of shortcut models to represent individual exchangers in the synthesis network. The new approach entails the use of a number of correction factors to get networks which are based on the use of shortcut models, such as the mixed integer non-linear programming (MINLP) stage-wise superstructure (SWS) of Yee and Grossmann (1990) to more closely represent physically achievable heat exchangers and ensure that the MINLP network topology optimisation step of these models converge on a real design, rather than an approximated one. In this paper, the SWS formulation is used for the generation of an initial network after which its objective function is modified to include the correction factors that force its objective function towards the cost of a network whose individual exchangers are designed using methods such as Bell-Delaware and heuristics. The modified objective function includes parameters that modify the areas obtained by the shortcut based MINLP model so as to more closely represent the areas obtained by the detailed models and also includes a novel method for including the number of shells required for each exchanger duty. The correction factors account for pressure drops, F t correction factors, number of shells, TEMA considerations, and changes to the overall heat transfer coefficient of each stream match. The methodology is applied to two examples and the solutions are comparable with other solutions obtained in literature and were shown to produce good solutions. The reason that the method is effective is because many potential networks are evaluated during the iterative procedure and the best network, based on the detailed exchanger designs, is chosen. In this way it is possible to use the detailed exchanger designs to "guide" the MINLP optimisation towards more realistic networks and also to generate many different potential networks.
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