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Brazilian Journal of Chemical Engineering

Print version ISSN 0104-6632On-line version ISSN 1678-4383

Braz. J. Chem. Eng. vol.17 n.4-7 São Paulo Dec. 2000 



F.S. Liporace1, F.L.P. Pessoa1 and E.M. Queiroz1
1 Departamento de Engenharia Química , Escola de Química, Universidade Federal do Rio de Janeiro,
Centro de Tecnologia, Bloco E, Sala 209, CEP 21949-900, Cidade Universitária, Rio de Janeiro - RJ
Brazil, Phone: 55 (0) 21 590-3192, Fax: 55 (0) 21 590-4991
E-mail: -


(Received: August 25, 1999 ; Accepted: April 6, 2000)


Abstract - Heat exchanger network (HEN) synthesis has been traditionally performed without accounting for a more detailed unit design, which is important since the final HEN may require unfeasible units. Recently, publications on this matter have appeared, as well as softwares that simultaneously perform synthesis and units design. However, these publications do not clearly show the influence of the new added features on the final HEN. Hence, this work aims at showing that units' design can strongly affect the final HEN. Improvements on heat transfer area and total annual cost estimations, which influence the HEN structural evolution, are the main responsible for that. It is also shown the influence of some design bounds settings, which can indicate an unfeasible unit design and, therefore, the need for a new match search or the maintenance of a loop. An example reported in the literature is used to illustrate the discussion.
Keywords: heat exchanger network, automatic synthesis and evolution, simultaneous synthesis and design, influence of detailed heat exchanger design.




The area of heat exchanger network (HEN) synthesis has a significant evolution since the 1980's. Nowadays, there are two kinds of approach to solve the synthesis problem: the thermodynamic approach, as in the Pinch Design Method, PDM (Linnhoff and Hindmarsh, 1983), and the mathematical programming approach (Zhu,X.X. et al., 1995, Victorov, 1995, Gundersen et al., 1996). However, few publications in the literature deal with the influence of heat exchanger design on the HEN synthesis. It is usual to find proposed HEN's containing some units of unfeasible design. This fact points out to the importance of performing, simultaneously, unit design and HEN synthesis. In this case, a fast and detailed unit design procedure should be used, since there is an increase on the problem complexity and computing time. In addition, this kind of approach should include a strategy to be used when a match, not recommended because of an unfeasible design, is identified.

The heat exchanger design is accomplished from the knowledge of the streams' mass flowrates, inlet and outlet temperatures and thermophysical properties. The tube side flow modeling is well known. On the other hand, the shell side model is more complex due to many possible flow paths along the shell. The kind of baffles, shell geometry and mechanical construction restrictions directly affect the heat transfer coefficient and head loss estimations. Kern (1950) proposed a method based on the specification of a first heat transfer geometry and on the performance of successive simulations until reaching convergence between the calculated and specified outlet conditions. Bell (1981) proposed a new correlation for the shell side, identifying regions and defining several flow paths. The heat transfer coefficient and head loss calculations are performed assuming that the shell side stream only flows through the main stream path on a crossflow ideal configuration. Correction factors are then used to account for the other stream paths and some heat exchanger geometric features. Again, it is required the knowledge of the shell side operational conditions, the stream's thermophysical properties and detailed geometric bundle data. In this sense, the use of this method is similar to that of Kern. Jegede and Polley (1992) rearranged pertinent thermofluidynamic correlations and geometric relations making it possible to calculate the tube side and shell side heat transfer coefficients from the knowledge of the streams' total pressure drops. This kind of approach is different from the previous ones since it does not need, a priori, data on heat exchanger geometry and, then, there is no need for successive simulations. The geometric variables are directly calculated.

This work aims at showing that, in the context of the PDM, the heat exchanger design can strongly influence the synthesis of the initial HEN structure with minima consumption of utilities (MCU), as well as its structural optimization. The synthesis of the initial HEN is based on an algorithm proposed by Liporace et al. (1997), which uses a modified PDM rule to synthesize the HEN near to the pinch point (PP) and a heuristic rule (Ponton and Donaldson, 1974) to perform the synthesis away from the PP. The loop identification is based on the determination of the rank of the Incidence Matrix (Pethe et al., 1989). For the loop-breaking procedure, it is used the Simulation Matrix (Liporace et al., 1999a), which is an array that represents the HEN with its process-process heat exchangers, heaters, coolers, mixers and splitters. The Simulation Matrix allows a steady state simulation of the HEN every time a loop is broken in order to restore the minimum temperature difference (MTD), if it has been violated, and/or to check if all streams reach their target temperatures on the new HEN structure. The advantage of this procedure over the traditional one is that a path between a heater and a cooler, passing through the heat exchanger where the MTD violation is occurring (Linnhoff et al., 1982), has no longer to be found.

As the units' design is performed after each match selection in the initial HEN synthesis stage, setting design criteria to identify unfeasible unit design leads to the need for a new match search. During the structural evolution stage, an unfeasible unit design also indicates that a loop should not be broken. A classical example from the literature is used to show that the procedures accounting, and not, for unit's design can lead to quite different HEN structures. First, it is shown that, when using the detailed heat exchanger design procedure, there are improvements on the heat transfer coefficients results over the ones obtained by the traditional procedure, where the stream's film coefficients are specified and kept constant in all the units this stream passes. These improvements have effect on the heat transfer area, on the capital cost and, hence, on the Total Annual Cost, which is the parameter used to guide the loop-breaking procedure and the loop identification order. Therefore, different HEN topologies are obtained. After that, it is also shown that, even when a detailed heat exchanger design procedure is used, there may appear units with design parameters far away from their practical bounds, meaning that they cannot be built. Therefore, these bounds are used as design restrictions during the HEN synthesis and evolution and the results obtained are quite different from the ones before.

In the HEN synthesis and evolution stages, the software AtHENS (Automatic Heat Exchanger Network Synthesis), developed at the Departamento de Engenharia Química, Escola de Química/Universidade Federal do Rio de Janeiro (DEQ/EQ/UFRJ) is used. AtHENS works on a Windows-Matlab-Fortran environment.



Jegede and Polley (1992) presented a way to calculate the tube side and shell side heat transfer coefficients from the knowledge of streams' total pressure drops, as shown in Equations (1) and (2),




where DPt is the tube side pressure drop, ht is the tube side heat transfer coefficient, DPs is the shell side pressure drop, hs is the shell side heat transfer coefficient and A is the heat transfer area. Kpt and Kps are constants which are functions of tube inner and outer diameters, bundle pitch ratio and arrangement, number of tube passes and streams' thermophysical properties and flowrates, as shown in Equations (3) to (10). In this set, Equations (6) and (8) assume a triangular tube bundle arrangement:
















where r is the density, m is the viscosity, k is the thermal conductivity, Pr is the Prandtl Number, Di is the tube inner diameter, Do is the tube outer diameter, Vi is the tube side volumetric flowrate, De is the equivalent diameter for the shell flow, proposed by Kern (1950), Pt is the tube pitch (1.25.Do) and Vo is shell side volumetric flowrate. Equations (3) to (5) use the tube side stream's thermopysical properties, while Equations (6) to 10 use the shell side ones. If a square tube bundle arrangement is used, Equations (6) and (8) must be changed accordingly. Details about these equations can be obtained in Jegede and Polley (1992).

Turbulent flow is assumed for both tube and shell sides. The development of the shell side correlations was based on the work of Kern (1950). Although the results obtained using these correlations may have an unsatisfactory tolerance, they are well suited to the direct design procedure and can be used to show trends of the more sophisticated ones. The description of the shell side flow by the Bell correlations would be better, but it would also bring a great increase on the algorithm complexity and computing time. The Bell correlations are well suited to successive simulations procedures.

In order to improve the results, Oliveira et al. (1996) used the following equation, proposed by Sinnott (1993), to calculate the shell diameter accounting for some shell clearances:


where Dlmt is the tube bundle diameter, N is the total number of tubes and K1 and n1 are constants that depend on the tube bundle arrangement and number of tube passes. In a first approximation, Dlmt can be taken equal to the shell diameter (Ds). Therefore:


Due to this change, the constant Kc2 becomes dependent on Ds and tube bundle arrangement, as shown in Equation (13):


This new form for Kc2 imposes a simple iterative procedure into the unit design algorithm, which was not accomplished before.

These equations, along with the new form for Kc2, the rate equation and some other geometric correlations, are used for the heat exchanger design. As mentioned before, the design is performed simultaneously with the synthesis, immediately indicating the feasibility, or not, of the heat exchanger demanded by the match. This approach allows the designer to forbid a match, and return to the synthesis step at once looking for another match. Hence, the time to complete the synthesis and generate an HEN that would be unattainable is not wasted. This feature is very important, especially for large problems, which is often the case in industrial plants. The heat exchanger design can also influence the HEN evolution. After a loop is broken, some units have their heat load and temperature conditions modified and so, their design, which can become unfeasible, indicating that this loop should not be eliminated from the HEN.

The AtHENS algorithm is presented in Figure 1. Differently from other loop-breaking heuristic procedures reported in the literature (Trivedi et al., 1990; Zhu,X.X. et al., 1993; Zhu,J. et al., 1996 and Zhu,J.Y. et al., 1999), which are concerned only on the lowest energy penalty incurred by the loop-breaking and do not account for the total annual cost (TAC) of the new HEN structure, AtHENS breaks a loop only if the TAC is reduced (Liporace et al., 1999b).



The unit design subroutine, which uses the described procedures, begins with an attempt to design an exchanger with 1 shell and 1 tube pass (ST - 1:1). If any design parameter (tube length, tube side mean fluid velocity, L/Ds relation, for instance) exceeds their upper bounds, the tube outer diameter is increased until the maximum value recommended by TEMA (2 in - 5.08 cm) is reached. When this happens, the procedure attempts to design a ST - 1:N (N pair). If there is a large temperature crossing, indicated by a value of the log mean correction factor (F) lower than 0.75, the design goes to the ST - M:N design, where the shell is split so that equal heat transfer areas are obtained (Oliveira and Queiroz, 1998). In the ST - 1:N design procedure, before increasing the tube outer diameter, there is an increase on the number of tube passes (npt) until a specified upper bound is reached, in order to adapt the geometric parameters to their respective bounds.



The examples usually reported in the literature only account for the traditional unit design. Therefore they do not supply streams' thermopysical properties, which must be known in order to perform the heat exchanger design. Then, in the Case Study here presented, it will be assumed that all streams are oil engine with constant properties, whose values are estimated at the arithmetic mean temperature of the stream (between supply and target temperatures). The total pressure drops are estimated as a function of the stream viscosity (Sinnott, 1993).

The example used in this work is the Aromatic Plant studied by Linnhoff and Ahmad (1990). Table 1 presents the streams' data, their thermophysical properties and operational and capital costs data, while Table 2 shows the PP temperature and utilities targets.



In order to show how the detailed unit design can influence the HEN synthesis, the results reported by Linnhoff and Ahmad (1990) will be considered first. Figure 2 and Table 3 present the initial HEN with minima consumption of utilities obtained by the previous authors. The heat transfer area and the capital cost on Table 3 were calculated using two different methods. The first one only accounts for the traditional design (A), i.e., it was assumed countercurrent arrangement with specified heat transfer coefficients (Linnhoff and Ahmad, 1990), while the second one accounts for the detailed heat exchanger design (Ad), which was obtained according to the design procedure previously presented. The Ad value would be the heat transfer area if a detailed heat exchanger design was performed for a specified match. Table 4 shows some data on the detailed unit design for the HEN presented in Figure 2.



The final HEN reported by Linnhoff and Ahmad (1990) is presented in Figure 3 and Table 5. The heat transfer areas (A and Ad) were calculated as before. Some data on the detailed unit design are shown in Table 6.



For all units in Figures 2 and 3, the tube outer diameter (Do) is 1.905 cm, the tube inner diameter (Di) is 1.4833 cm (results from the design procedure), the pitch is 1.25.Do and the

tube bundle arrangement is triangular. The tube side fluid is the stream (process or utility) with the highest fouling factor. When they are equal, the tube side fluid is the hot stream.

It is worth to say that Linnhoff and Ahmad (1990) did not supply information on the outlet temperatures of the hot utility in the heaters and of the cold utility in the coolers. Therefore, the present work was not able to reproduce their initial and final TAC (considering the traditional design). The values presented in Tables 3 and 5, for the traditional design, as well as for the detailed design, were obtained assuming that the utilities undergo the maximum possible DT (refer to Table 1), i.e., their outlet temperatures do not violate the MTD.

The first influence of the detailed unit design appears when the TACs of the initial (with minima consumption of utilities) and final HEN obtained with traditional and detailed design are compared. As stated earlier, in our point of view, a loop should only be broken if the TAC is reduced. However, for this example, the final TAC is lower than the initial one with traditional design and, on the other hand, the final TAC is higher than the initial one using the detailed design. This fact indicates that, during the second structural optimization, some loops that caused an increase on the TAC of the resulting network were broken. This happens due to a better heat transfer area, and so better capital cost and TAC, estimations. These improved values changed a "reducing TAC loop-breaking" into an "increasing TAC loop-breaking". As the HEN synthesis and unit design were not performed simultaneously, this change on the loop characteristic could not be identified and a final TAC higher than an initial one was obtained. So, in this example, the final HEN structure should be different from the one reported by Linnhoff and Ahmad (1990) when the detailed unit design is accounted for.

Comparing these two results, another important fact should be noted. The initial and final TACs with traditional unit design are different from those with detailed unit design, although the HEN structures are the same. This happens due to differences on the heat transfer coefficient for each stream on each match, which change the calculated heat transfer area. Nevertheless, a more complete comparison can not be done since the heat transfer coefficients reported in Linnhoff and Ahmad (1990), used in the traditional design, were not estimated according to the assumed streams' thermophysical properties, and therefore they have no relation with those calculated by the detailed unit design procedure here proposed.

It is worth mentioning that the match between the final TACs with traditional and detailed designs, i.e., the match between both capital costs, is a coincidence. Actually, it is important to note the differences among the heat transfer areas for the matches in each design case.

Let us now better illustrate the change on the loop-breaking behavior according to the unit design procedure used. Figure 4 and Table 7 present the initial HEN (with minima consumption of utilities) obtained with the traditional design, in which the heat transfer coefficients reported by Linnhoff and Ahmad (1990) are used, and with the detailed unit design here proposed. Table 8 shows some unit design parameters. For both cases, the initial HEN structure, obtained by AtHENS, is the same because the match selection still does not feel the influence of the heat exchanger design, which will be performed latter. The presence of splitters is due to the application of the modified PDM rule on the heat capacity flowrate used by AtHENS to perform the synthesis near to the PP (Liporace et al., 1997). This rule states that, if the heat capacity flowrate of the incoming stream is lower than the heat capacity flowrate of the outgoing stream, the latter should be split. This rule allowed the automation of the HEN synthesis.



The way the unit design is performed can influence the capital cost, hence the TAC, the loop-breaking order and the final HEN structure. Figure 5 and Table 9 present the final structure with traditional design, while Figure 6 and Tables 10 and 11 show the final HEN with detailed design. It is important to note that, differently from the traditional structural evolution procedures, the existing by-passes are not eliminated from the HEN during its evolution (refer to Figures 2 and 3), which can increase the possibility of control strategies (Oliveira et al., 1999).




Table 12 shows a comparison among some parameters of the initial and final HEN using both design cases, where the influence of the detailed unit design on the loop-breaking order and final structure can be noted. The final HEN presented in Figure 5 (with traditional design) has 14 units (4 loops were broken) and a consumption of utilities higher than the target, while the final HEN presented in Figure 6 (with detailed unit design) has 15 units (3 different loops were broken) and minima consumption of utilities. Another important fact is that the loop identification order depends on whether the loop identified previously was broken or not. As the loop-breaking order is different for both design cases, so is the loop identification order and, hence, the final HEN structure.



Note also that, when the detailed unit design was accounted for during the structural optimization, the final HEN TAC proposed by AtHENS is lower than the initial one, differently from the results obtained for the HENs proposed by Linnhoff and Ahmad (1990).

It is worthwhile to note the differences on the initial and final HENs with traditional design obtained by AtHENS and by Linnhoff and Ahmad (1990) (both using the same heat transfer coefficients). These differences are due to different match selection and rules used to synthesize the HEN near to and away from the PP. Although the TAC of the initial HEN proposed by AtHENS is higher than the one of Linnhoff and Ahmad (1990), the final TACs are closer. The advantage of the structure proposed by AtHENS is a high probability of control strategies due to a high number of variables to be manipulated (Oliveira et al., 1999).

Until now, any criteria to indicate unfeasibility of an unit design were used. Therefore we are still obtaining heat exchangers with almost 10.0 m for tube length, heat transfer area of about 10.0 m2 among areas of about 3,200.0 m2, high L/Ds relation etc. According to engineering practice in heat exchanger design (Hewitt et al., 1994), some design parameters must be bounded. For liquid streams, which is the case in this example, these bounds are: - 1 m/s £ vt £ 4 m/s ; L £ 6 m; npt £ 10; 5 £ L/Ds £ 10

If these bounds were accounted for, many of the matches from the initial and final HENs, proposed by AtHENS and by Linnhoff and Ahmad (1990), would generate unfeasible units (refer to Tables 4, 6, 8 and 11). This indicates that none of the earlier HEN structures could really operate. In order to avoid such results, these bounds must be accounted for during the HEN synthesis and evolution, and more, the unit design must be performed simultaneously with the match selection and loop-breaking stages, as we propose, so a match can be immediately forbidden and a loop not broken if the unit design indicates so. Due to these restrictions, the goal of the initial HEN synthesis is no longer to design a structure that accomplishes the MCU, but to design a structure with feasible units, no matter if the utilities consumption stays above the target.

Figure 7 and Tables 13 and 14 present the initial HEN with bounded detailed unit design, proposed by AtHENS, while Figure 8 and Tables 15 and 16 present the final HEN.




The first thing to be noted are the differences between the initial HEN structure with unbounded detailed unit design (Figure 4) and the one with bounded detailed unit design (Figure 7). The matches [hot stream 1, cold stream 9], [hot stream 2, cold stream 7] and [hot stream 4A, cold stream 7] above the PP and [hot stream 4C, cold stream 7] below the PP were discarded since, even with the possibility of increasing the tube outer diameter until it reaches its upper bound (2" according to TEMA), no feasible design could be obtained. Furthermore, none of the streams were used on other matches, hence hot stream 4 bellow the PP was not split. A similar fact occurred with the match [hot stream 4B, cold stream 6] above the PP, but, this time, the hot stream 4B was matched with another cold stream (cold stream 7), generating a feasible unit design, and so the cold stream 6 was not split. Due to all of these structural modifications and match restrictions, which were possible because the unit design and HEN synthesis, were performed simultaneously, the utility targets were not accomplished (note the presence of coolers above the PP and heaters below the PP) and the TAC increased from $2.81 x 106/year (unbounded design) to $3.52 x 106/year (bounded design).

Another fact should be discussed. The presence of two coolers in series on hot stream 4 is due to the fact that the regions above and below the PP must be energetic balanced. Because of the structure modifications, the hot stream 4 above the PP did not reach its target temperature (PP temperature) and a cooler was added. This also happens in the region below the PP for the same stream. Besides, the second cooler is, in fact, representing 4 units in parallel, each one with 502.2 m2 and the same unit design (the detailed unit design presented in Table 16 refers to one of these 4 units). This is due to the assumption that coolers, and heaters as well, should always generate feasible units, which can be accomplished with equal splits of the process stream until a feasible design is obtained. As the initial HEN structure will be evolved, it is expected that this utility-loop will be eliminated.

As the initial HEN structures with unbounded and bounded detailed unit design are different, it is expected that the loop-breaking order, the final HEN structures and their TAC would also be different from one case to another. In fact, this was observed. When the initial and final HENs with bounded detailed unit design are compared, the latter, although presenting the same utilities consumption, has a lower TAC due to the elimination of some heaters and changes on the operational conditions (inlet and outlet temperatures and heat load) for some units, which modified their heat transfer area and design. The elimination of the utility-loop on hot stream 4, which was expected, did not occur because the changes on the operational conditions for the remaining cooler would lead to an infinite split of the process stream in order to obtain a feasible design. This is an example of how the bounded detailed unit design can interfere on the loop-breaking procedure.

When all the final HENs (traditional design, unbounded detailed unit design and bounded detailed unit design) proposed by AtHENS are compared, the influence of the heat exchanger unit design becomes clear due to the differences on the structures and TACs, as shown in Table 17. The final HEN presented in Figure 8 (bounded detailed unit design) would be the proposed one, since all its units have feasible designs.

For all heat exchangers, the tube outer diameter (Do) is 1.905 cm, the tube inner diameter (Di) is 1.4833 cm, the pitch is 1.25.Do and the tube bundle arrangement is triangular. The tube side fluid is the stream (process or utility) with the highest fouling factor. When they are equal, the tube side fluid is the hot stream. The header pressure drop was not considered in this work and when the unit design demands more than 1 shell, the results presented are relative to one shell (the others are similar).

Even when design procedures were added, with the possibility of defining matches restrictions during the synthesis stage, it took AtHENS an average of less than one minute of computing time (Pentium 166 MHz and 32 MB RAM) to complete the HENs synthesis and evolution. In the same conditions, the average computing time to perform the HEN synthesis and evolution with traditional design is less than 15 seconds (Liporace et al., 1999a).



This work shows the large influence of the heat exchanger design on the HEN synthesis and evolution, which can only be observed because the unit design and HEN synthesis are performed simultaneously. Using a Case Study (a classical example from the literature), it is shown that setting some design criteria to indicate an unfeasible unit design during the synthesis and evolution stages can lead to quite different structures and TACs than those obtained when these bounds are not accounted for and when the unit design is the traditional one.

This large influence is also observed in the generation of the initial HEN with MCU. The unfeasibility of some units demanded by the matches can make impossible the synthesis of a HEN with consumption of utilities equal to the targets, as shown in the Case Study here presented.

The design criteria used in this work to indicate unfeasible design can still be extended. Situations in which the heat transfer areas are too small or the influence of the header pressure drop, for instance, were not analyzed yet.



The authors would like to acknowledge the financial support from Coordenadoria de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and from Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ).



A heat transfer area, m2
Ad heat transfer area with detailed design, m2
Ad* heat transfer area with bounded detailed design, m2
Cp specific heat at constant pressure, kJ/kg ºC
cu cold utility
Di tube inner diameter, m
Do tube outer diameter, m
Ds shell diameter, m
hs shell side heat transfer coefficient, kW/m2 ºC
ht tube side heat transfer coefficient, kW/m2 ºC
hu hot utility
ITC inlet temperature of cold stream, ºC
ITH inlet temperature of hot stream, ºC
L tube length, m
M mass flow rate, kg/s
M.Cp heat flow capacity rate, kW
MTD minimum temperature difference, ºC
N total number of tubes
npt number of tube passes
Ns number of shells
OTC outlet temperature of cold stream, ºC
OTH outlet temperature of hot stream, ºC
PP pinch point, ºC
Pt pitch, m
Q heat load, MW
Rf fouling factor, m2 ºC/W
TAC total annual cost, $/year
Ti inlet temperature, ºC
To outlet temperature, ºC
vt tube side mean fluid velocity, m/s

Greek Letters

r density, kg/m3
k thermal conductivity, W/m ºC
m viscosity, N s/m2
DPtotal total pressure drop, kN/m2



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