The synthesis of cost optimal heat exchanger networks

The synthesis of cost optimal heat exchanger networks

Comput. &em. Eiagng, Vol. 12, No. 6, pp. 503430. 1988 Printed in Great Britain. All rights merwd 0098~1354/88 $3.00 + 0.00 Copyright 0 1988 Pqamon Pm...

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Comput. &em. Eiagng, Vol. 12, No. 6, pp. 503430. 1988 Printed in Great Britain. All rights merwd

0098~1354/88 $3.00 + 0.00 Copyright 0 1988 Pqamon Pma plc










a.s Research

(Received 22 September


N-3901 Porgrunn,

1987; received f&publication


5 October 1987)

Abstract-The industrial heat exchanger network synthesis (HENS) problem is very complex and involves combinatorial problems in the “matching” between hot and cold streams to enhance heat recovery, temperature dependent physical and transport properties, the choice of flow configuration and materials of construction for the heat exchangers, the combination of “hard” and “soft” problem data (some target temperatures must be met, while others may be varied within limits if this is of advantage for the total process economy), various kinds of constraints (forbidden and compulsory matches) and different types of streams (liquid, vapour and mixed phase). Pressure drop limitations and the cost of piping are also important. The design objective includes a quantitative part (cost of heat exchange equipment and Cxtemal utili!ies) and a qualitative part (safety, operability, flexibility and controllability). This makes it difficuJt to eslabhsh a single objective function to evaluate the design. Due to topological effects (services are added or removed), the investment cost function exhibits discontinuities since there is a unit cost involved in the equipment. Some of the qualitative aspects mentioned above cannot easily be formulated ahead of time. The cost of flexibility can be calculated, but only for given situations (networks). The global optimum is thus hard to guarantee and the engineer has,. to resort to simplifications of the model and some heuristic rules that will lead towards a near optimal solution. Research is progressing along three different lines which are the use of thermodynurhic concepts. mathematical methods and the use of knowledge based systems for process design. In order to solve real life industrial problems, the engineer should take advantage of all these disciplines. However, the skill and experience of the engineer himself will remain of vital importance. &o-This paper presents the state of the art of HENS methods together with some applications to previous literature problems. An evaluation of the various methods is performed from an [email protected] poipt of view. There is also a brief discussion of some of the software tools available to solve such problems. The presentation will emphasize on the design of the heat exchanger network itself although interactions with the rest of the process and the utility system inevitably will be discussed. The aspects of flexibility and operability will also be briefly mentioned. HENS is the most mature field of process synthesis when it comes to systematic methods. The increase of energy prices during the 70s and early 80s has been the major driving force. As things have been developed, however, the emphasis has changed from energy optimal (minimal) structures to cost optimal networks. The latest developed methods can tind the proper trade-off between investment cost and operating cost for any price scenario (including regional factors such as the cooling water temperature etc.) ahead ofdesign. Nevertheless, all problems have not yet been solved, and important research is still being conducted addressing all three areas of HENS, which are targeting, synthesis and optimization. Industry spends a significant amount of money to carry out energy analysis of new and existing plants, to support academia in their research and to deirelop and acquire accurate and efficient computer tools. It is the involvement of our company in these areas that has given us the opportunity, on an industrial basis, to review the field. In the past there have been two schools of HENS. One relies on thermodynamic principles and a few heuristic rules, where the designer manually (or interactively if software is available) synthesizes the network. The other, more automatic, approach relics on mathematical methods like linear and nonlinear programming. The relative merits of these schools will be discussed with reference to case studies. There will also be a short presentation of the historical development within these schools.

INTRODUCnON The process design exercise involves several interacting activities, and Linnhoff (1983) illustrated this by the “onion diagram”. The heat exchanger network synthesis (HENS) problem has been viewed as a

subproblem of process synthesis, but the interactions with the process itself and the utility system must be taken into consideration. Even in the case of a frozen

process and utility system, problem is very complex.

the industrial


The combinatorial problem when matching streams and sequencing heat exchangers has been reported for the classical literature problems with less than ten streams. A typical industrialprocess contains 3&80 streams that need heating or cooling. These streams may change phase and the physical and transport properties of relevance to the HENS prob503




and L. NAESS

lem will change with temperature. The heat transfer process design situations, including HENS, refrigconditions will be very different in a gas-gas ex- eration systems and total process systems. changer, in a liquid-liquid exchanger or in a steam Norsk Hydro a.s has been active in prototyping boiler. There are many choices with respect to flow software (Naess and Gundersen, 1984) and has access configuration and materials of construction for the to several computer tools and the latest methods by heat exchangers. Due to the interaction between the supporting research at UMIST in Manchester, CMU heat exchanger network and the rest of the process, in Pittsburgh and NTH in Trondheim. There has it is important to be aware of the fact that some also been brief contact with the group at CALTECH stream parameters are “hard” and some are “soft”. in Los Angeles. This knowledge has been used in Some target temperatures must be met from process process synthesis studies, within the company on requirements, while others may be changed within existing and new processes, and motivated the preplimits; if this is of advantage for the heat recovery and aration of this review paper. thus the overall process economy. Finally, there will Initially, reducing the energy consumption was the be qualitative aspects of operability, flexibility, safety objective of the research and methods available. This and controllability. In many cases this means that resulted in the discovery of important and fundanonthermodynamic constraints will be imposed on mental concepts like the /zeat recouery pinch as a the model in the form of forbidden, restricted o’r bottleneck for reduced energy consumption. The required matches. latest methods put emphasis on* the total cost of The work of Westbrook (1961) on the use of energy and equipment and aspects of flexibility ‘and dynamic programming and Hwa (1965) on the use of operability are addressed during design rather than as separable programming and a superstructure includan add on activity. Although retrofit projects are ing promising configurations are among the first harder to find in periods with low energy prices (such reported attempts to systematically solve the HENS as in 1986), methods are now available for new problem. The real pioneers in this area were Rudd designs that find the correct trade-off between inand coworkers at the University of Wisconsin (Lee et vestment and operating cost for any price scenario. al., 1970; Masso and Rudd, 1969; Rudd, 1968) and Hohmann and Lockhart at the University of Southem California (Hohmann, 1971; Hohmann and THE HISTORY OF HENS Lockhart, 1976) around 1970. Since then, about 200 papers have been published, out of which more than When trying to solve the HENS problem systemthe half are from the last 4 yr. atically, the problem was initially transformed to a mathematical model and solved by numerical methThe area has been previously reviewed several ods. The complexity of the industrial HENS problem times, either stand-alone or as a part of overall process synthesis. Hendry et al. (1973) viewed the mentioned above made several simplifications necesHENS problem as a homogeneous subproblem in sary to make these mathematical models manageable. process synthesis, where the main difficulty involved First of all, one could question the industrial useis the combinatorial matching and sequencing probfulness of these simplified models. Secondly, even if accepting these models, the size of the problems that lem. Siirola (1974) classified the methods presented so could be solved due to the inherent combinatorial far and proposed new branching rules to reduce the problem size. He was also among the first to point out nature was less than 10 streams, which in itself is a that methods should relax the constraint that utilities severe limitation in industrial applications. A brief review of the first attempts to solve the are handled last and thus placed at extreme temperatures. Rathore and Powers (1975) and Nishida HENS problem is given below to aid the subsequent et al. (1977) compared their own methods with presentation of newer methods. A more thorough previous work in a tabular review, and Hlavacek description of these works are given in earlier review (1975, 1978) has reviewed the area as part of the papers mentioned above. overall process design activity including both simuTo meet the requirements of a review paper while lation and synthesis of steady state and dynamic remaining useful for the industry, some methods have processes. been included purely for completeness, other methThe latest complete review is the excellent work of ods for emphasis. Nishida et al. (1981) where HENS is one of several Assignment probIem of LP process synthesis areas. Since then, Hohmann (1984) presented HENS as a multitier problem and reviewed Kesler and Parker (1969) divided each stream into the latest achievements in using thermodynamic small heat duty elements (“exchangelets”) of equal methods. Westerberg and Grossmann (1985) gave a size and posed the matching between hot and cold nice and pedagogic introduction to overall process elements as an assignment problem. This approach synthesis with emphasis on heat exchanger nethas been improved by Kobayashi et al. (1971) who works and application of mathematical methods. used the heat content diagram to allow for stream Grossmann (1985a) has reviewed the application of splits and cyclic matches. Nishida et al. (1971) intromixed integer linear programming (MILP) in various duced matching rules for minimizing total area

The synthesis of cost optimal heat exchanger networks and Cena et al. (1977) allowed for constraints and multiple utilities. Another attempt to solve the matching problem by simultaneous methods is the already mentioned work of Hwa (1965) on separable programming of a superstructure. Methods that decide one match at a time have been named sequential methods, and include tree searching and heuristic methods. These strategies may or may not utilize mathematical methods. Decomposition

or tree search

Several early methods were published within the decomposition or tree searching group. Lee er al. (1970) introduced a branch and bound method, but the combinatorial problems were still severe; Siirola (1974) introduced new rules for branching. Pho and Lapidus (1973) used partial enumeration and their “synthesis matrix” was used by Kelahan and Gaddy (1977) who used adaptive random search. The disadvantage of this matrix is the exclusion of cyclic matches and stream splits. Greenkorn er al. (1978) relaxed this constraint and introduced a heat availability function (HAF, actually a grand composite curve) to assure good initial solutions. Rathore and Powers (1975) used forward branching to avoid the generation and evaluation of infeasible solutions. Grossmann and Sargent (1978a) combined implicit enumeration with heuristic estimates to solve the configuration problem allowing for constraints on the matches. Finally, Menzies and Johnson (1972) used branch and bound for the synthesis of optimal energy recovery networks including mechanical energy. Heuristic


The heuristic approach was introduced by Masso and Rudd (1969) who weighted a set of rules according to the adaptive learning during design. Ponton and Donaldson (1974) suggested to match the hot stream with the highest supply temperature with the cold stream with the highest target temperature, an approach that was followed by numerous researchers later. Wells and Hodgkinson (1977) presented an extensive list of heurstic rules for general process synthesis considerations, targets and stream matching. Thermodynamic


Today, it is amazing how little recognition the work of Hohmann (1971) seemed to get among the researchers in the early 1970s. The explanation often given that the work was little published [only as a Ph.D. extract by Hohmann and Lockhart (197611 is only part of the story. Attempts to publish the work were actually turned down twice, and the only reason we can see is a very strong confidence in those days that the HENS problem could be automated and solved by mathematical methods. The work of Hohmann had little contribution to the mathematical approach of that time, but the significance to the solution of industrial HENS problems is paramount.


This fact has slowly been recognized in parallel with the failure of the pure mathematical methods.. Hohmann’s feasibility table was the first rigorous way to establish the minimum utility target ahead of design. The famous (N - 1) rule gives,a close target to the minimum number of exchangers in a network, and even though Linhoff et al. (1979) later pointed out that there are cases where this target cannot be reached, Hohmann actually discussed the effect of loops and subgraphs. The minimum heat transfer area target was also addressed in a TQ-diagram by the temperature contention concept, which gave guidance to the splitting of streams to reach the target. If cost data are available, it is possible to determine the optimum utility rates and corresponding minimum temperature of approach ahead of design. A very important part of Hohmann’s work is the feasible network solution space demonstrated by the area vs energy diagram in Fig. 1. The curve connecting the A,, and the Emintarget for various values of AT,,,, divides the “space” in feasible and infeasible solutions. Hohmann pointed out that this line actually defines an effective maximum number of units necessary to reach the area target. The same diagram was also used to discuss the threshold situation. When decreasing the value of AT,,,, the energy consumption decreases while required heat transfer area increases (A/E trade-off). For some stream systems, there is a limiting value of AT, where energy remains constant, and the curve turns vertical as indicated in Fig. 1. Following the line further increases area and reduces the number of heat exchange units (A/U trade-off). Today we know that this trade-off is more complex, since reduced driving forces have the unfortunate side effect of increasing the number of shells. In his design procedure, Hohmann pointed out that networks with more units than the minimum target include heat load loops which represent degrees of freedom that should be used to minimize area. In this optimization, one should keep in mind the possibility of loop breaking that would reduce the number of units by one and thus harvest a step reduction in the overall cost. Finally, sensitivity fac-


Ed” Energy Fig. 1. Hohmann’s feasible network solution space. Thnrhold


T. GUNDERSEN and L. Nrsss

tors were calculated and used to replace rigorous simulation in operability considerations. The additivity of simultaneous changes in inlet temperatures and flowrates was also discussed. The hear recovery pinch Towards the end of the 197Os, the discovery of the heat recovery pinch as a bottleneck for energy savings resulted in increased efforts in academia and industry in developing and applying systematic methods in retrofit and new designs. Umeda er al. (1978, 1979a,b) draw their composite lines in the available energy diagram in such a way that the curves touched at one point (temperature). This point, which forms a bottleneck that prevents further heat integration and thus energy savings, was named the pinch, Huang and Elshout (1976) presented similar ideas using the TQ diagram The fundamental understanding of the heat recovery pinch, including the &composition effect was presented by Linnhoff ei al. (1979). Linnhoff and coworkers further related excess utility consumption to cross pinch heat flow with contributions from process to process heat exchange, heating below and cooling above the pinch. Then came the appropriate pkacemenr concept for correct integration of turbines, heat pumps and distillation columns into overall processes, and finally the more general plus/minus principle, that suggests which (and how) process modifications should be made to increase the heat recovery. Since then, Linnhoff and coworkers, first within ICI and later at UMIST have developed the pinch concept into a complete methodology named pinch technology, addressing several aspects of process design that will be discussed in a later section. DESIGN OF HEAT EXCHANGER

NETWORKS In this section, the various contributions will be classified in subsections for: (1) important concepts; (2) targets; (3) synthesis methods; (4) optimization; and briefly (5) flexibility. By concepts we mean both fundamental physical insight and representations that enhance the analysis and understanding. Targets have already been discussed and involve estimates of the theoretically best performance of a heat exchanger network. Synthesis methods include the matching of hot and cold streams and the sequencing of the resulting heat exchangers. Optimization involves both topological and parameter improvements that reduce the total annual cost. Finally flexibility is the ability of a heat exchanger network to cope with operating conditions different from design case. Important concepts The temperature/enthalpy (TQ) diagram has been adopted by several researchers. What is new in heat exchanger network design, is the merging of all hot

streams into a composite heat source curve and all cold streams into a composite heat sink curve. The composite curves were first used by Huang and Elshout (1976). A similar concept is the composite line in the available energy diagram applied by Umeda et al. (1978). The composite curve is an important concept in the work of Linnhoff and coworkers. In the “User Guide” by Linnhoff et al. (1982), the grand composite curve (CCC) is introduced and explained on the basis of the heat cascade. The applications involve multiple utility targeting, flue gas optimization, utility pinches, and to some extent, process modifications. Itoh et al. (1982) at the same time introduced the heat demand and supply (HDS) diagram, which is equivalent to the Grand Composite. The application was to find load and level for the utilities, to observe options for steam generation and how to integrate different processes on a site (relative position of the individual pinches). Two perhaps less known but early variants of the GCC are the heat surplus diagram introduced by Flower and Linnhoff (1977) to indicate opportunities for using heat pumps or utility generation (waste heat boilers) and the heat availability fiction (HAF) introduced by Greenkom er al. (1978). Its application was to graphically find minimum utility targets and the lowest hot utility temperature level. This work is based on fundamental results obtained by Raghavan (1977). As an aid to make decisions about matching hot and cold streams, Kobayashi er al. (1971) and Nishida et al. (1971) introduced the heat content diagram, which is a heat capacity flowrate vs temperature diagram. The duty of each stream is represented by boxes in the diagram, and one can allow for temperature dependent heat capacities. By dividing the box for a stream horizontally or vertically, one can represent multiple matches and stream splits. A similar representation is the heat spectrum diagram used by Nishimura (1980). Linnhoff (1979) introduced two concepts that have proven to be of advantage for HENS, the heat cascade diagram and the stream grid. The heat cascade illustrates the basic idea behind the problem table algorithm (PTA) and gives rise to the GCC. The stream grid is a clever way to represent hot and cold streams, the process and utility pinches, and most important, the heat exchanger network. The representation makes it easy to redraw other sequences, illustrate head load loops and paths, stream splitting and mixing and has thus been adopted by many other researchers. Another network representation is the match matrix of Pho and Lapidus (1973), with the inherent disadvantage of not allowing for stream splitting and cyclic matches, a severe limitation to industrial applications. The single most important concept for HENS is the heat recoverypinch that was discovered independently by Umeda et al. (1978) and Linnhoff et al. (1979). The pinch point was also mentioned but not explained by

The synthesis of cost optimal heat exchanger networks Elshout and Hohmann (1979). The same applies to Huang and Elshout (1976) who moved their composite curves towards each other until they touch at one point, and the hot composite being above the cold composite at all other places. This position was said to define maximum heat that may be recovered with a corresponding infinite area. The heat recovery pinch forms the basis for a complete methodology namedpinch fechnology developed by Linnhoff and coworkers. The recent progress in the use of automatic and mathematical methods (will be discussed in detail later) is caused by taking the pinch decomposition into consideration. The reason why methods like the one presented by Ponton and Donaldson (1974) may perform poorly on some problems but yield very good solutions in other cases, is the fact that some problems are pinched (even down to AT,, = 0), while others are threshold problems, which means that for approach temperatures below a certain threshold, only one type of utility (hot or cold) is needed, and that the utility consumption is insensitive to the value of Ai”,, [see Linnhoff et al. (197911. Design should always start where the process is most constrained, and for threshold problems with heat surplus, this is at the hot end. Closely linked to the heat recovery pinch is the L’plus/minus” principle, which was defined by Linnhoff and Parker (1984) and by Linnhoff and Vredeveld (1984) but had been previously used by Umeda et al. (1979a,b). The idea is to modify the process in such a way, that heat is added to the heat sink above pinch and removed from the heat source below pinch. The appropriate placement concept uses the + / - principle to give rules for the integration of heat pumps and turbines (Townsend and Linnhoff 1983a,b; Linnhoff and Townsend, 1982) and distillation columns (Linnhoff et al., 1983) in overall processes. A tool for energy management, is the heat path diagram proposed by Westerberg (1983). The utility system and various processes operating on a site are drawn and positioned according to their relative temperatures. Each process is divided by its pinch temperature (if not a threshold problem) into a sink and source part. The relative position of these pinches is important for the possible integration between the processes. The idea to embed several promising networks into one large flowsheet, or superstructure, that was used for the first time by Hwa (1965) has been extended to powerful process synthesis tools during the last years. Papoulias and Grossmann (1983) used MILP to model and solve superstructures for heat exchanger networks as well as overall processes. The invention of the stream superstructure by Floudas et al. (1986) made automatic network generation and optimization possible from the heat load sets given by the MILP solution. Wilcox (1985) also contributed to the automation of the network synthesis by a split-mix-bypass technique.


Targets Upper and lower hounds were introduced to reduce the combinatorial problem limiting some of the first methods. These bounds were later developed further into more or less rigorous targets for energy, heat transfer area, number of heat exchange units and finally total annual cost. 1. Energy consumption. Minimum utility targets proposed by Rathore and Powers (1975), Nishida er al. (1977) and Grossmann and Sargent (1978a) are correct for threshold problems, but are too optimistic in pinched situations. These targets were basically used as lower bounds to reduce the search, and as such they were reasonable. Correct energy target has been established for the unconstrained case by several researchers. Hohmann (1971) used the feasibility table, Linnhoff and Flower (1978a) developed the PTA, Umeda et al. (1978) read the utility targets off the TQ diagram and a graphical procedure was also proposed by Greenkom et al. (1978), who used the HAF (i.e. the grand composite). In constrained situations (forbidden, restricted or required matches) rigorous targets were formulated as an LP transportation problem by Cerda et al. (1983) and as an LP transshipment problem with reduced size by Papoulias and Grossmann (1983). Recently, Viswanathan and Evans (1987) presented the dual stream approach to reduce the energy penalty often related to constraints. A hot stream may be heated (then it becomes a cold stream by definition) by the hot part of a forbidden pair, and then substitute the forbidden hot stream to heat up the cold part of the forbidden pair. The problem is formulated as a modified transshipment model and then solved as a network flow problem by the out-of-kilter algorithm. The resulting energy target will then be in the region between the constrained and the unconstrained target, depending on the specific stream data. Both the PTA and LP models may allow for individual stream contributions AT, to the approach temperature to reflect differences in the heat transfer conditions. Various LP models suggested by Saboo et al. (1986a,b) allow for individual stream contributions, and one may also obtain an energy target for a given structure or a specified total area, a feature that is interesting in retrofit cases. Finally, Doldan et al. (1985), when retrofitting a process with a given utility system for heat and power introduced a secondary bottleneck often encountered in energy studies. This means that there is little incentive for reducing the hot utility consumption below the amount available from back pressure turbines, unless the power system is modified. A small nonlinear program (NLP) is used to obtain this retrofit energy target. 2. Heat transfer area. When it wmes to heat transfer area, one should make the distinction between minimum area procedures which include stra-




tegies for the network development that minimizes total area, and algorithms for calculating a minimum area target ahead of design. Network generating procedures have been presented by Hohmann (1971) (TQ diagram with temperature and stream contention) and Nishida et al. (1971) who addressed the minimum area task in the heat content diagram matching streams in the order of decreasing inlet temperatures. Nishida et al. (1977) refined this approach by including the utilities in the minimum area algorithm. In this way, utilities are not necessarily placed at extreme temperatures, but located in an “optimal” way in the network. Finally, Umeda et al. (1978) discussed how differences in heat transfer coefficients and unit costs for area could be handled by changing temperatures in the splitting and mixing points in the network. Nishida ef al. (1981) in their review paper summarized the work so far on minimum heat transfer area. When all heat transfer coefficients are equal and vertical, counter-current heat transfer is assumed, the following equation for calculating the area target was presented:






u’(Th - T.1

With piecewise linear composite curves as indicated in Fig. 2, this equation can be transformed into a summation:

Townsend and Linnhoff (1984) introduced a new target for area taking into account the individual film transfer coefficients for the streams. The assumption of an average overall U is too crude to be used in cost estimates ahead of design, and equation (3) is thus an important contribution to both area and cost targeting: (3) The new area target is exact only if all film transfer coefficients are equal and that heat exchange is strictly vertical, but gives good approximations in other situations. The vertical requirement means that all streams, k, in each interval, i in Fig. 2 have to be split and matched according to the total heat capacity flowrate ratio given by the composite curves. The Atin network may therefore involve a large number of splits and heat exchangers, and has been named spaghetti design by Linnhoff and coworkers. A rigorous target for heat transfer area, even in the case of different film transfer coefficients, can be found by the LP transportation model put forward by Saboo er al. (1986b). Although vertical heat transfer usually leads to minimum total area, there are cases of significant differences in film transfer coefficients where one could gain from deliberately

and L. Nm

Tl Hot streoms





Fig. 2. Enthalpy intervals for area calculation. criss crossing as explained by Ahmad (I 985) and Tjoe and Linnhoff (1986) and illustrated in Fig. 3. The approach taken by Saboo et al. (1986b) is to start with temperature intervals according to the “kinks” on the composite curves and gradually decrease these intervals until either the area target obtained by solving the LP converges, or the size of the LP becomes prohibitively large. 3. Number of units. The (N - 1) rule where N is the total number of hot and cold streams including utilities proposed by Hohmann (1971), has been widely used to set target for the minimum number of units in a heat exchanger network. Boland and Linnhoff (1979) extended this rule by Euler’s theorem from graph theory to (N - S + L) to account for the number of subsystems (S) and the number of loops (L). This discussion was repeated by Linnhoff et al. (1979), who also presented a counter example to Hohmann’s claim that an (N - 1) network could be found for any stream system. The observation made by Linnhoff et al. is correct, but unfortunately the problem they presented (Fig. 4) is not a true counter example. This was shown by Wood ;r al. (1985), who discussed the application of splitting, mixing and bypassing, iticluding nonisothermal mixing to reduce the number of units. Figure 5 shows how the posed “counter example” actually meets the units target of two units (no utilities needed). In an earlier work, Linnhoff (1979) also discussed unit reduction by a combination of splitting, mixing and bypassing.


Fig. 3. Vertical vs “criss-crossed” heat transfer (Ahmad, 1985).

The synthesis of cost optimal heat exchanger networks



m - 352*





Fig. 4. Proposed counter example to the (N - 1) rule (Linnhoff et al., 1979). An important aspect of the heat recovery pinch is the decomposition of the problem into separate subnetworks, one completely above and one completely below the pinch temperatures. Linnhoff and Turner (1981) introduced the maximum energy recooery (MER) target for number of units. V,,,,,, by applying the (N - 1) rule above and below pinch. Grimes et al. (1982) introduced a formula that accounts for streams existing in more than one subnetwork (crossing the pinch), which in essence is the same target as the one presented by Linnhoff and Turner. Cerda and Westerberg (1983) formulated an MILP model for the target which was transformed to an LP transportation problem by relaxation in order to avoid solving the original MILP problem. A similar approach was taken by Papoulias and Grossmann (1983) who formulated and solved an MILP model given the constrained utility target from an LP transshipment model. The advantage of using linear programming is that constraints and multiple utilities can be handled, and that necessary loops in the network to achieve MER as well as the existence of subnetworks is detected ahead of design. Figure 6 shows a four stream problem with no need for utilities, where the minimum number of units target of 3 cannot be reached. Cold stream 3 must be matched with both hot streams 1 and 2, to reach the target temperature of 350°C for the hot streams. This gives two exchangers, but since stream 3 is too small in load to completely cool any of the hot streams, they both need another match, and four units is the true minimum. Hohmann’s (N - 1) rule and the extension by Linnhoff and coworkers (that lJmin+,sR is achieved by applying the (N - 1) rule for each subnetwork) consider both temperatures and enthalpies, but enthalpy

Fig. 5. Network that achieves the units target (Wood et al., 1985).

Fig. 6. A true counter example to the (N - 1) rule (Grossmann, 1985b). only on a “composite” basis in the calculation of Quti. and Q,,,, The reason why the MILP model gives a rigorous target is that individual stream enthalpies and temperatures are considered. Jones and Rippin (1985) used LP to find all heat load distributions (HLD) with the global (disregarding the pinch) minimum number of units, but still achieve MER. This is possible if streams are split in such a way that hot and cold streams being matched in the pinch region have identical heat capacity flowrates. Some exchangers thus operate across the pinch, but without transferring heat across the pinch which would have resulted in a utility penalty. The price for achieving this is a constant approach temperature equal to AT’,‘,, throughout the exchanger, with a corresponding large heat transfer area. In cases where networks (or HLDs) with U,, (global) cannot be found, one may relax the number of units, AT,, or the MER constraint. Colbert (1982) argued that Uminis a bad target for networks with shell and tube heat exchangers. Rather than counting the number of units, one should count the minimum number ofshells. Heggs (1985) pointed out that when using the pinch design method, the exchangers operating in the vicinity of the pinch often would have to be strict counter-current units in order to handle the expected duties with the given inlet and outlet temperatures. A graphical stage by stage procedure for estimating the number of shells from the composite curves was proposed by Shiroko and Umeda (1983). Liu et al. (1985) proposed to increase the number of shells by one until the &-factor for the exchanger reaches an acceptable value. Their experience, however, was that the question of single or multi-shell is not important for the network top,ology. As one of the latest developments in pinch technology (will be discussed in a separate section), Ahmad (1985), Ahmad et al. (1988) also include target for the minimum number of shells as part of the annual cost target. 4. Toral annual cost. Having targets available ahead of design obviously was a major step forward. The targets can be used as a motivation or to give the designer confidence that a network is close to “optimal”. The design procedure for heat exchanger networks after the discovery of the heat recovery pinch and by using targets is summarized in Fig. 7. The



Fig. 7. Design procedure based on targets.

synthesis method used is the pinch design method (PDM) presented by Linnhoff and Hindmarsh (1983). Other synthesis methods aim for area, and in that case the area target must be included in the targeting box. The minimum allowed approach temperature is obtained from experience, but if the elaborate trading off area, energy and units in the optimization box indicates that the chosen AT,, was inadequate, an outer loop must be performed. A new minimum approach temperature is then applied at the targeting and the synthesis stage. The pinch point may change in the process, resulting in a possibly very different network. Even with experience in designing a certain type of process, the chosen value of AT,, may not be optimal, since the value of the minimum approach temperature that properly trades off the cost factors involved depends on the following three aspects: (1) relative prices for energy and equipment; (2) shape of the composite curves (parallel or wide open); and (3) good or bad heat transfer conditions in the pinch region. The need for a tool to assist the engineer’s “experience” was certainly needed, and the answer is cost targeting, where a total annual cost is obtained by adding the contributions from the targets for energy, area and units. By calculating the total annual cost for various values of AT,,, Abmad (1985), Ahmad and Linnhoff (1984, 1986), Linnhoff and Abmad (1986a,b) can predict an optimal value of the ap proach temperature which will lead to near-minimum cost networks. The final piece of this “puzzle” was the area target from Townsend and Linnhoff (1984). As discussed in a previous section this target is not rigorous, but since some assumptions must be made about the area distribution in the network that is not yet designed, it can be questioned whether one really should go for the rigorous target obtained by the LP model put forward by Saboo er al. (1986b). This does not prevent that such a target may find its applica-

tions, but when it comes to cost targeting and design initialization, AT,, is the crucial parameter. If errors in area target and distribution counteract (experience shows that this in fact is the case) to make a close cost target, we are willing to sacrifice science for industrial applicability. By introducing cost data earlier in the design procedure and applying the total annual cost target to find the optimum AT,, ahead of design (referred to as “supertargeting”; Linnhoff and Ahmad 1986a,b; Naess and Gundersen, 1984), Fig. 8 is obtained which indicates a significant reduction in the design work, especially during optimization. The way targets for energy, area and units play together to obtain the total annual cost target is shown in Fig. 9, where the discontinuities are caused by the kinks on the composite curves. When targeting for total annual cost ahead of design, the investment or capital cost is much harder to predict than the operating cost, since investment is more dependent on the network structure. Energy can be targeted for in a rigorous manner, and experience shows that designs meeting this target are nearoptimal also in total cost. The idea of preoptimization or trading off energy and capital ahead of design has recently been discussed in a few other works, apparently without the necessary rigor in their capital cost targets. Rev and Fonyo (1983) give sparse information about how the capital cost is obtained. Li and Motard (1986) proposed’ an interesting analytical approach to the preoptimizatibn, but ,their method relies on the limiting assumption of an average heat transfer coefficient U for all exchangers. A small error is also introduced, since the utility exchangers are not included in the total area calculation. A more promising approach is taken by Akselvoll and Lnrken (1987) who allows, for temperaturedependent individual film transfer coefficients 1for the streams. Vertical heat transfer is assumed, but a heat transfer utilization factor may be specified by the engineer to cope with the ideal counter-current assumption.

Fig. 8. New design procedure with cost targets.

The synthesis of cost optimal heat exchanger networks




* AT,,,

Fig. 9. The four targets as a function of T,,,i,.

Several contributions have been made to add rigor to the capital cost target. In the previous section on target for minimum number of heat exchange units, the shell vs unit aspect was discussed. Other aspects that might be considered are pumping and piping costs. Finally, some works on exchanger type and materials of construction will be mentioned. Hall (1985) and Ahmad (1985) both discuss how to incorporate exchanger type and materials of construction into the capital cost target. Their suggestion is to adjust the film heat transfer coefficients to account for exotic materials of construction and exchanger configurations different from l-2 shell and tube. Detailed algorithms are given in these works. The most extensive work on capital cost targeting and also on how to design for this capital cost has been given by Ahmad (1985). One of the important conclusions in this work is that if capital cost is wrong, it does not matter as long as the slope (sensitivity) is nearly correct. In that case the predesign trade-off between capital and energy is correct resulting in a correct ATti, and thus a proper initialization of the design. After all, this is more important than the target for capital cost itself. This also means that it is only in extreme cases that exchanger type and materials of construction play a significant role. A rule of thumb is that the manipulated film coefficients will have to differ by an order of magnitude from the original ones. Synthesis In this section we will briefly discuss methods proposed for establishing the heat exchanger network. The presentation will attempt to give a complete picture, while the most interesting methods from an industrial point of view will be presented in a later section on Advances in HENS Methods. Some of the early methods were discussed in a previous section and will be omitted here, like the assignment methods (Cena et al., 1977; Kesler and Parker, 1969; Kobayashi et al., 1971; Nishida et al., 1971), the tree searching methods (Greenkom et al., 1978; Grossmann and Sargent, 1978a; Kelahan and Gaddy, 1977; Lee et al., 1970; Menzies and Johnson, 1972; Pho and Lapidus, 1973; Rathore and Powell, 1975; Siirola, 1974) and the heuristic methods (Mass0 and


Rudd, 1969; Ponton and Donaldson, 1974; Wells and Hodgkinson, 1977). Most of the early methods used minimum area as the design criterion and the guide for selecting matches. Due to increased energy prices, development of rigorous utility targets and the discovery of the heat recovery pinch, the methods developed towards the end of the 70s and beginning of the 80s were geared towards maximum energy recovery (MER). The heuristic rule accepted and used by most methods today is that networks achieving MER in the fewest number of units are near-optimal, and that area minimization within such a structure is applied as the second step. While total cost considerations earlier were handled in an optimization step following the synthesis, the ability to target for capital cost and thus trade-off energy and capital, triggered the development of methods to design for capital as well as energy. Finally, some methods are aimed at reducing the number of units, some methods’ are exergy, based and some methods are in effect multi-objective. 1. Design for area. Minimum area synthesis methods were presented by Nishida et al. (1971), Hohmann (1971), Nishida et&. (1977) and Umeda et al. (1978). The fast heuristic method ,suggested by Ponton and Donaldson (1974) also makes sure that driving forces are used properly resulting in low area requirements. In addition, the method will lead to low utility requirements at least for threshold problems. Improvements of Ponton and Donaldson’s rules have been presented in Zachoval and Konecny (1982), Zachoval et al. (1984) to handle cross-flow exchangers. Rev and Fonyo (1983) combined the pinch design method with a modification of Ponton and Donaldson’s fast method to automate the design. Hama and Matsumura (1982) presented a five-stage procedure for designing heat exchanger networks, where the engineer is allowed to interact between the stages. The synthesis task was performed by dynamic programming to reduce the area to a minimum. As already discussed, area should not be the first objective in the network generation. Later Hama (1984) extended this method to automatic or interactive synthesis, forbidden or imposed matches and minimum allowed exchanger size. A limitation with this method is that utilities are placed last, thus at extreme temperatures. A very interesting approach that simultaneously addresses the task of reducing area and number of units is the “compound” structure (a combination of series and parallel matching) put forward by Rev and Fonyo (1982). Again, since the method does not take the pinch decomposition into account, it will work best in threshold cases, especially those with one large hot (cold) stream and several cold (hot) streams. In Fig. 10, one cold stream is heated by several hot streams. The approach is to split the cold stream in two branches, find one long range stream (LRS),



and L. NAESS


C 3 = Heat

Fig. IO. The compound structure proposed Fonyo (1982).

by Rev and

meaning a stream with a large AT between the supply and target temperature, and classify the remaining hot streams in a low temperature group (LTG) and a high temperature group (HTG). This procedure may be applied recursively to LTG and HTG. 2. Design for units. One of the problems often encountered when designing for area only is that the number of units tend to be large. This is due to the inherent feature of the HENS problem that minimum area requires an effective maximum number of units (“spaghetti” &sign). Figure 11 shows a five-unit network resulting from Rev and Fonyo’s method which is cheaper in total annual cost than a ten-unit solution from Ponton and Donaldson (1974) and a six-unit network from Nishida et al. (1977). The minimum number of units for the problem is four, since it is of the threshold type. When solving this problem with the combined efforts of Papoulias and Grossmann (1983) (MILP model) and Floudas et al. (1986) (stream superstructure and minimum investment cost), a four-unit network (Fig. 12) may be found. With the cost data used by Rev and Fonyo, this network is only marginally cheaper (2.4%) than Rev and Fonyo’s five-unit network. The advantage of saving one unit has been reduced by an increase in total heat transfer area. Jones and Rippin (1985) found all heat load distributions satisfying the global minimum number of units without energy relaxation by an LP model. Since Umin,ueRnormally is greater than U,, in pinched cases, heat load loops exist. The traditional approach is to break these loops and pay a penalty in energy (to reestablish AT,,) or area (keeping the reduced AT,,,,,). An alternative is to split streams passing through the pinch in such a way that hot and cold stream branches matched in an exchanger have identical heat capacity flowrates. Two exchangers on each side of the pinch may be merged into one, thus operating across pinch but without transferring heat across the pinch. This approach may find its applications, but should be used with care. The merged pinch heat exchangers will operate at a constant approach temperature equal to AT,, and thus need large heat transfer area. With almost parallel composite curves,


Fig. 11. Rev and Fonyo’s solution 19.847 $ yr-’


with a total cost of

the driving forces are limited anyway, and the approach may find cost effective networks that would be very hard to discover by hand. If, however,, the composite curves are opening up away from the pinch temperature, the resulting use of driving forces lead to a total area in excess of what is necessary, and may completely reduce the saving of one or more units. Figure 13 shows an MER design developed by the pinch design method with six units, which is one less than the K,m.MERtarget, since there is an ideal match above pinch between stream 1 and 4. This example was discussed by Jones and Rippin (1985) and the stream data were taken from the User Guide (Linnhoff et al., 1982). The dashed line indicates the heat recovery pinch. Jones and Rippin demonstrated that a U,,,, solution of five units can be found by a special split stream arrangement as shown in Fig. 14. It is also possible to start with the design in Fig. 13 and use the concept of loops and paths (Linnhoff et al., 1982) to reduce the number of units without increasing energy consumption, but at the expense of a reduced value for AT,,,, . The result is the network shown in Fig. 15, and it is easy to add up the necessary U. A for the exchangers and compare the two alternative ways to reach U,,. The three networks have the following total U ‘A, when utility exchangers are ignored (they carry the same load and operate at identical temperatures for the three cases): PDM solution 6 units (U.A)=24.751 Jones and Rippin 5 units (LI. A) = 29.342 Evolved PDM 5 units (U A) = 25.660 500* c13.21


1 -Heat




Fig. 12. Network from automatic synthesis (MILP) with a total cost of 19.366 S yr-‘.

The synthesis

Fig. 13. PDM

solution for a 4-stream “User Guide”.

of cost optimal




It should be obvious that the network in Fig. 15 is the best solution, since the area is significantly less than for the network in Fig. 14, and actually only 3.6% more than the six-unit network in Fig. 13. Usually a larger increase in area will be experienced, but in this case the match between stream 1 and 3 is favoured by the merging of the two exchangers between stream 2 and 3. Finally, it should be noted that the composite curves in this case are moderately parallel, which should favour Jones and Rippin’s approach. It should be noted that allowing a smaller value of AT,, in Fig. 15 adds degrees of freedom to the problem as far as network topology is concerned. It has been shown, by using the MAGNETS computer program (MILP and NLP models), that when the approach temperature is allowed to drop to AT,, = 5°C while keeping the energy consumption unchanged from Fig. 13, one of the configurations that can be found is the network of Fig. 15. The same thing would be true for Jones and Rippin’s approach. The concept of loops and paths gives, however, the engineer easy guidance in the optimization from the MER design into the non-MER design. A variant of Ponton and Donaldson’s rule aimed at units rather than area was presented by Rathore (1982), who ranked the hot and cold streams according to their heat capacity flowrate before matching, in order to reduce the number of heat exchange units. Mocsny and Govind (1984) used a decomposition strategy, looking for approximate subsets in the problem, which will reduce the number of units towards the global minimum. A similar approach was presented by Li and Motard (1986), where ATpi,,+,was adjusted until subsystems were obtained resulting in reduced number of units. 3. Design for shells. The difference between exchanger units and actual number of shells has been SO.





_ T




1 240


14. Jones


Rippin’s minimum solution.


of units

heat exchanger


15. Evolved


network from breaking.




by loop

reported by Mitson (1984) in some cases to have a significant effect on capital cost. Kardos and Strelow (1983) pointed out that a network solution of the synthesis problem based on purely countercurrent heat exchangers only will remain optimal in practice if each unit can be realized by one exchanger. This is the exception rather than the rule. A two-unit example was presented, where the optimal network used sequential matching. Given the fact that each of these units actually required four shells, a different network structure would have been optimal, indicating that one should consider shells rather than units at the synthesis stage. The topic of shells vs units was treated under targeting and will be further discussed in the section on designing for capital cost. 4. Designfor energy. The first systematic approach to obtaining MER designs is the temperature interval (TI) method of Linnhoff and Flower (1978a). Matching hot and cold streams within temperature intervals, the pinch decomposition is obeyed, since the pinch will coincide with one of the interval temperatures. Linnhoff and Flower (1978b) also proposed an evolutionary development (ED) method as a second step to reduce the number of units. Since stream splitting during the TI method will distort the ED stage, it is recommended not to split streams unless necessary to avoid very complex networks. Even though cyclic matches and stream splitting may substitute each other to obey AT,, and reduce area requirement, there are cases where streams have to be split to obtain MER. Thus, the nonsplit TI method cannot guarantee MER. A method with some similarities to the TI method was presented by Naka and Takamatsu (1982). Rather than dividing into temperature intervals, they divided the problem at the kinks of the composite curves into enthalpy intervals. An explicit pinch decomposition was made, grouping the intervals above and below pinch. Using enthalpy rather than temperature intervals has the advantage of vertical heat transfer and no heaters and coolers inside the network that must be shifted towards the end or combined to heat exchangers as the case is with the TI/ED method. With the discovery and full understanding of the heat recovery pinch, it became clear that the design exercise should start where the problem is most constrained. For pinched problems, this is at some



intermediate pinch temperature, and for threshold problems it is at the highest (heat surplus) or lowest (heat deficit) temperature. An outline of the PDM is given in Linnhoff and Turner (1981) and in the User Guide (Linnhoff et al., (1982). The comprehensive description is by Linnhoff and Hindmarsh (1983). The PDM gives guidelines for matching streams as well as when and how to split streams in order to achieve MER. In order to reduce the number of units to the fewest possible, each exchanger is made as large as possible, hopefully to satisfy either the hot or the cold stream with respect to enthalpy change. This heuristic rule is referred to as tick-ofi The stream termination concept was also used in previous methods, but since these methods did not obey the pinch decomposition, the rule sometimes worked across the pinch, thus resulting in utility penalties. Grimes er al. (1982) also decomposed the problem at the pinch in a method intended for application by hand. The method follows some of the ideas presented by Greenkorn et al. (1978), like the “tickoff” heuristic. Reducing units while having a high degree of heat recovery is the main objective of their method, which also can handle multiple utilities and constraints on the matches. When designing for energy, the PDM makes sure that no heat is transferred across the pinch and that proper matches are chosen in the thermodynamically most constrained part of the process. However, a more general statement can be made about exchanging heat in various temperature regions of the process. Ahmad (1985) pointed out that the energy target will be violated if matches occur that transfer more heat across an interval temperature than cascaded by the PTA. The heat recovery pinch is the most constrained interval temperature, where no heat is allowed to be transferred. A similar statement was made by Rev and Fonyo (1986), who encountered hidden or pseudo-pinches when designing away from the pinch. The tick-off rule was constrained by the total allowable heat load assigned to a match based on the available heat flow in the cascade. Having established that MER designs are nearoptimal in total cost, especially if the heat recovery level is achieved in the fewest number of units, it is also important to be aware of the fact that a large number of MER designs exist for each stream data set. These designs have different structures and may thus have very different operability and flexibility characteristics. They also have different scope for reducing the number of units by energy (nonMER) or area relaxation (AT < A Tmi.). Flower and Linnhoff (1980) approached the HENS problem in a combinatorial manner, but using thermodynamic criteria and topological arguments to reduce the problem size. For classical literature examples like 6SP1, the number of possible networks is approximately 3.6 x lo5 [(nh.n,)!]. There will be 924

Uti networks and no more than 6 feasible designs which achieve MER with the minimum number of units. The reduction in number of possible solutions is enormous, and makes it possible to list, evaluate and rank all networks. The TC (thermodynamic combinatorial) method does, however, not allow for stream splits. A similar approach is presented by Govind et al. (1986). An automated approach is also described by Akselvofl and Leken (1987) which is based on the PDM and presents a predefined number of promising networks. The level of energy recovery is found at the targeting stage, trading-off energy and capital. With the corresponding value of AT,,, networks are created and ranked according to their investment cost. The method allows for temperature dependent physical properties, constraints and different cost equations depending on materials of construction. A partial enumeration of the tree of all possible stream matchings is performed, bounded by the investment cost multiplied with a factor, in order to find a set of near-optimum solutions. The authors also claim that the strategy for stream splitting guarantees minimum number of splits, however, without documentation or presentation of their algorithm. The problem of finding the minimum number of stream splits to obtain MER designs have been solved as an MILP problem by Hanson and Comish (1984), who included constraints on the matches and the number of split branches. Thermodynamic considerations about the heat recovery pinch is built into the model. Saboo ef al. (1986a) allowed the engineer to put constraints on the number and position of stream splits, as well as the number of heat exchangers on a a specific stream. 5. Design for capital cost. A new and important guiding device for the PDM in order to consider area and thus capital is the driving force plot (DFP) presented by Linnhoff and Vredeveld (1984), where each exchanger can be evaluated according to its use of temperature driving forces. In order to reduce total area, it is important that each exchanger uses exactly the amount of driving forces which are available in that temperature region of the process. Compromises must often be made between the DFP and the tick-off rule, since the minimum number of units is not compatible with the minimum total area. The driving force plot may also recommend the splitting of streams in cases to save area, even though not strictly required to achieve MER. The most comprehensive work on designing for capital (as well as energy) was presented by Ahmad (1985). The objective of that research was to add capital cost guidance to the PDM which steers the designer towards MER in the fewest number of units. With the ability to target for capital cost, two new methods were introduced in order to try to meet this target. In addition to the above mentioned DFP, Ahmad (1985) introduced the remaining problem


The synthesis of cost optimal heat exchanger networks analysis (RPA) for energy and area. Ahmad also applied the energy/area target plot, which is similar to Hohmann’s feasible solution space (Fig. l), as a map for designs. A network on the target line is optimal with respect to area and energy, but may have a nonoptimal trade-off (wrong AT,,). The pinch concept requires no heat transfer across the pinch (vertical heat transfer) and limited heat transfer across other interval temperatures (some criss-crossing is allowed). The total heat transfer area will be most sensitive to the heat transfer taking place in the most constrained part of the process, the pinch region. In most cases, minimum area is achieved by vertical heat transfer, which means that the pinch concept and the c&s-cross idea actually merge in the pinch region. Away from pinch some amount of nonvertical heat transfer is allowed. The RPA is used to check whether a proposed match will be in conflict with the targeted energy or area. Another important contribution from Ahmad’s work is the treatment of near-pinches as regular pinches when the composite curves are narrow. An outline of the design procedure ,is given in Fig. 16. 6. Design for exergy. Reducing the exergy loss in a process has always been a sound strategy for design. Linnhoff (1979) concluded, however, that second law analysis in the context of chemical process design is both difficult to produce and difficult to interpret. The literature on heat exchanger networks show that simplified thermodynamic methods have replaced entropy or exergy functions. A few approaches will be mentioned that use second law analysis to study some aspects of designing heat exchanger networks. Schmidt (1984) used exergy considerations to determine the optimal approach temperature for a single heat exchanger, trading off the cost of exergy loss and the cost of equipment. Exergy was evaluated by using the electricity price. The conclusion drawn that was illustrated by a case study is that the optimal approach temperature depends on the actual temperature level. The two established techniques of either using a single value of AT,, for all exchangers or using a single value for the exergetic efficiency were both shown to be wrong. Irazoqui (1986) used entropy to simultaneously study the ability of the process to generate heat and shaft power, giving the heat recovery from hot to cold streams highest priority. Problem independent charts of optimal operating lines were used to derive the network. Liu (1982) and Pehler and Liu (1983) approached the HENS problem as a multiobjective problem (exergy and capital) and used a multistep evolutionary method. Their thermoeconomic concept made it possible during synthesis to evaluate the designs without cost calculations. The important observation that the loss of available energy actually is independent of the heat exchanger network with fixed utility consumption, was made by Umeda et al. (1977). Exergy loss in heat

Optimum energy target Optimum units torget Optimum orea target Optimum+ tat01 cost torget + Composite curv**

Very little evdutian


Fig. 16.

Noniterotive: Design

match placement

for energy and capital (Ahmad, 1985).

exchangers is linked to heat transfer with driving forces larger than zero. The trade-off between exergy loss and area was the basis for a method of Nishitani et nl. (1982). Vinograd er al. (1983) improved Umeda et al.% method to handle multiple utilities in an exergy driven method. The matching is performed by graphical tools and dividing the problem into zones by the various utility temperatures. Some of the problems with traditional 2nd law analysis was discussed by Linnhoff and Carpenter (1981), the most important one being to distinguish between inevitable and avoidable losses. In a nitric acid plant, for instance, the converter accounts for more than half of the exergy loss in the process, but most of it is inevitable. Other problems exist when designing heat exchanger networks. Linnhoff (1986b) pointed out that 2nd law analysis is unit operation oriented, which means that network interactions are lost. Linnhoff actually showed that pinch technology (PT) is firmly based on the 2nd law of thermodynamics. The advantage with PT is that it performs true synthesis, no base case design is needed as in 2nd law analysis. Linnhoff (1986b) also showed that, the inevitable exergy loss can be found (approx.) from the composite curves with AT,, = 0. Alternatively, a practical and economic exergy loss can be established from the composite curves and the optimum value of AT,, (supertargeting). Finally, Jakob er al. (1986) discussed the practical aspects of 2nd law analysis, and presented a com-


puter, program FLEXER reason for exergy losses.


to find the location


Automatic synthesis Since the first formulation of the HENS problem, researchers have tried to automate the design stage. While the majority of these methods used some kind of mathematical programming, a few methods will be mentioned first that try to automate methods based on thermodynamics and heuristic rules on a computer. Rev and Fonyo (1983, 1986) combined the strict rules of the PDM in the pinch region with modifications of the fast method of Ponton and Donaldson (1974) to automate the synthesis of the network away from the pinch. Another automated approach is described by Akselvoll and Leken (1987) and by Govind et af. (1986). When it comes to mathematical methods to automate the synthesis stage, one of the most popular approaches has been to formulate the matching problem as an assignment task of LP. Some of these methods were discussed under the historical section. More recently, the assignment algorithm approach has been used and improved by Jezowski (1982b) who increased the engineer’s involvement and applied heuristic rules based on thermodynamics. Jezowski (1982a) also approached the inherent problem with the assignment algorithm that a large number of small exchangers are created. By introducing preferred matches as those who create neighbours, the evolution phase was simplified by the merging of such units. Later Jezowski and Halat (1986) incorporated the PTA into the optimal assignment problem which was solved repeatedly to avoid excess utility consumption. The solution of the HENS problem by the assignment algorithm has also been reported by Ivakhnenko et al. (1982) Kafarov et al. (1982a,b,c) Kafarov and Schmidt (1982) and Ostrovsky et aI. (1985). A number of contributions have been given to the solution of the automatic synthesis problem with more potential for industrial use than the above mentioned mathematical methods. Fundamental to the success of this approach is the use of MILP and taking basic thermodynamic concepts like the heat recovery pinch into consideration. Papouiias and Grossmann (1983) first solved the minimum utility cost problem [optimizing the selection among utilities) by an LP transshipment model, and then posed the minimum number of units problem as an MILP model. The resulting heat load sets (or distributions) can be used to derive the network by hand, but for problems of industrial size, this has been reported by Hartmann (1984) to be very difficult even with good knowledge of the actual process. The stream superstructure introduced by Floudas et al. (1986) automates the network generation given the heat load sets, and at the same time minimizes the

investment cost for the given utility consumption and number of units. Cerda and Westerberg (1983) also contributed to the solution of the automated network generation. The minimum utility problem was solved by the LP transportation model presented by Cerda et al. (1983) and the minimum number of units by an MILP model that was transformed and solved repeatedly as an LP problem. The basic difference from the ap preach taken by Papoulias and Grossmann is that transportation models are used rather than transshipment, the latter being significantly smaller in size. Optimization The example discussed through Figs 13-15, leads naturally into the optimization section. Optimizing the network involves both topology and parameter changes of the initially synthesized design in order to minimize the total annual cost. Several methods presented in the 70s have been named evolutionary and may qualify as optimization methods (Linnhoff and Flower, 1978b; McGalliard and Westerberg, 1982; Nishida et al., 1977; Shah and Westerberg, 1975; Umeda ei al., 1978). The PDM as presented by Linnhoff and Hindmarsh (1983) describes how MER networks can be evolved towards non-MER designs with increased energy consumption, but reduced number of exchangers. This is achieved by sequentially breaking loops and reestablishing the driving forces by increasing utility consumption through a “path” in the network. The new concept of supertargeting actually means optimizing the heat recovery level ahead of design by trading off capital cost and operating cost using predesign targets. Naka and Takamatsu (1982) evolved their network established by the El method by three basic operations (rearrange, merge and shift). Muraki and Hayakawa (1982) introduced evolutionary rules for reducing the number of units from a good initial network obtained by pinch decomposition, the engineer’s judgement to split streams, and a new matching rule. Another interesting feature is that available utilities are treated as streams which means that utility placement may be optimized. Shiroko and Umeda (1983) used evolution to simplify complex minimum area networks and finally Pehler and Liu (1984) applied thermoeconomic evolution. By the term thermoeconomic the authors mean that thermodynamic considerations like available energy is used to replace traditional economic calculations, during network evolution. The target for their evolutionary approach is to simultaneously reduce the number of units and loss of available energy. Evolution was also used by Grimes et al. (J982) who first generate a network through a procedure with several similarities to the PDM (targeting, pinch decomposition and tick-off rule to reduce the number of units). Stream splits are introduced only if both Q H,~~”and umin.MER are “threatened”. An interesting

The synthesis of cost optimal heat exchanger networks feature of their evolutionary approach is that loops are not only broken to reduce units, but sometimes created by adding infinitely small exchangers and then shifting load to search through different topologies. Su and Motard (1984) presented a loop breaking procedure for evolving networks from MER designs established by the TI method towards optimum or near-optimum networks with close to the minimum number of units (without increasing utility consumption). A primary level did not allow for stream splits, which was introduced at the second level if Kin.Mea could not be reached in a split-free design. Basically, this is an automated routine which goal is the same as the manual PDM. The networks established with the TI method are complex, and there will be many possible ways to break loops to reach minimum number of units. The approach gives no guidance as to which loop to break apart from the requirement of thermodynamic feasibility. Finally, Saboo et al. (1986a,b) introduced an MILP with constraints on the number and location of stream splits and exchangers. In retrofit cases, the engineer can incrementally add these constraints to the MILP to semi-automatically evolve a network structure more compatible with the existing network. The previous discussion has mainly been concerned with topological optimization, although the concept of loops and paths in the PDM simultaneously addresses network configuration and parameters like duties, areas and temperatures. The optimization of the parameters in a heat exchanger network with a given structure will not be discussed any further, but many of the computer programs mentioned in a later section have facilities for such optimization. Flexibility

Various terms have been used in the literature to describe other features of a heat exchanger network than the steady state operation with given flowrates, supply and target temperatures. Operability normally includes flexibility, controllability, reliability and safety, while Jlexibility is limited to the steady-state feasible (thermodynamic) operation of the HEN for different operating modes. Another frequently used term is resilience, with a similar meaning as operability, and which has been divided into dynamic and steady state resilience. In this paper, emphasis will be on flexibility aspects. It is of course desirable that the entire process is as operable or resilient as possible, but Colberg and Morari (1988) stated that in a tightly energyintegrated plant it is especially important that the heat exchanger network is resilient. Nash et al. (1978) pointed out the feature of HENS that several nearminimum cost topologies exist. When choosing among these, flexibility and operability should be emphasized. Early works addressing flexibility of heat exchanger networks introduced the concept of sensiC.A.C.E. w--B


tivity analysis (Hohmann, 1971; and Takamatsu, et al., 1970). In the latter work, sensitivity tables were used to determine the overdesign factors for each exchanger rather than adding an equal contingency to all units. Grossmann and Sargent (1978b) introduced probability distribution functions to replace empirical overdesign factors. Finally, Bingzhen et al. (1982), applied sensitivity analysis to check the flexibility of the network in retrofit situations. After reporting failures of existing synthesis techniques with respect to handling process uncertainties and variations, Marselle et al. (1982) defined the resilient HENS problem. In addition to traditional economic requirements, like maximum energy recovery and minimum number of units, qualitative aspects of flexibility, operability, controllability and safety (named resilience) should be taken into account. Properties of resilience and some advances towards systematic methods were made. Four “worst cases” were designed separately and combined into a design with the flexibility of handling all these situations. I. Analysis. The corner-point theorem was introduced by Saboo and Morari (1984). It claims that a network which is feasible for the corner points (boundary values of the disturbance range for the parameters) will operate for any intermediate situation. Unfortunately, this is only true for a limited class of problems, and Saboo and Morari discussed what has been referred to as the problem of nonconvexity. The reasons for nonconvexity have also been discussed by Colberg and Morari (1988) and by Calandranis and Stephanopoulos (1986), and involve change of pinchpoint in the process, flowrate variations, stream splits, temperature dependent heat capacities and phase changes. Saboo et al. (1985) introduced the resilience index (RI) as a measure for the flexibility of heat exchanger networks. This index is obtained through simple physical considerations or a rigorous numerical algorithm, and its application is to detect bottlenecks in existing networks or to guide the selection between alternatives in new design. The key issue is to determine which exchanger that limits, the RI by its load or driving force. In their approach, simplifying assumptions were made that reduce the industrial applicability (no boiling or condensing streams, constant heat capacities, no mass flowrate variatiqns and no stream splits). These assumptiops are addressed in current research at CALTECH where some of the results are in the process of publication (Saboo et ul., 1987a,b). Swaney and Grossmann (1985a,b) introduced a different resilience measure called the flexibility index (FI). While the RI is the largest total disturbance load a network is able to handle, the FI determines the largest variation of one parameter independent of other disturbances. 2. Design. The importance of the structure as opposed to the unit operations themselves has been



increasingly appreciated during the last few years when it comes to economy, exergy, controllability and also flexibility. Townsend and Morari (1984), among others, have stated that oversizing is an unreliable approach to resilience. The need to consider the aspect of network flexibility at the synthesis stage is thus obvious. Townsend and Morari (1984) introduced a target for the RI to guide the synthesis. They also found that increased network resilience is compatible with minimum heat transfer area for a specific value of AT,,,,. Since minimum area requires more than the minimum number of units (actually an effective maximum), there is a trade-off between resilience and number of units. While moderate nonvertical heat transfer in most cases has marginal effect on the total area, it may have a significant effect on the resilience of the network. Colberg er al. (1986) later introduced a similar FI target for heat exchanger networks. Parkinson et al. (1982) applied results from Raghavan (1977). using the heat availability function. Their synthesis procedure for resilient HENS was based on the “worst average” HAF and flexibility tests for energy and temperature. A more mathematical approach was taken by Beautyman and Comish (1984) who designed flexible heat exchanger networks based on computer simulation and optimization. Floudas and Grossmann (1986) managed to extend the MILP models of Papoulias and Grossmann (1983) to handle the multiperiod situation, which is another aspect of the network flexibility problem. In this case, a predefined number of periods with given duration and process conditions are known, and the “optimal” network is found by taking into consideration equipment cost and utility costs for all periods. The approach is able to handle pinch changes from one period to another, and the automatic network generation is obtained by extending the techniques (NLP formulation based on the stream superstructure) from single-period problems (Floudas and Grossmann, 1987a). Later Floudas and Grossmann (1987b) showed how the MILP and NLP models from previous works could be effectively coupled with flexibility analysis. Specified uncertainties in flowrates and inlet temperatures are handled in a two-stage design procedure. A quite differet approach is taken by Linnhoff and Kotjabasakis (1984) who discussed operability considerations by using the stream grid diagram. Using concepts like downstreum paths (the propagation of a “disturbance” through the heat exchanger network to a “controlled” target temperature) it is possible at the design stage to take operability considerations into account. When breaking a loop in order to reduce the number of units, an additional effect can be that a disturbance path is broken. Another aspect is the placement of utility heaters and coolers and bypasses on heat exchangers. Linnhoff and Smith (1985) stated

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that the flexibility problem is economically undefined, and that rigorous techniques like the RI concept is of little help in the design process. An extended path analysis is proposed to handle disturbance propagations not only within the heat exchanger network, but through the overall process. Linnhoff and Kotjabasakis (1986) relined these ideas (Kotjabasakis and Linnhoff, 1986; Linnhoff and Kotjabasakis, 1986) into a methodology that makes it possible to simultaneously study the three-way trade-off between energy, capital cost and flexibility. The use of sensitivity tables replaces rigorous simulation to study the passive response of internal network temperatures and target temperatures to changes in supply temperatures, heat capacity flowrates and effective (U. A) values for the heat exchangers. A three-stage procedure is suggested in their works. By the concept of downstream paths one can analyze. whether a modified flowrate or inlet temperature will affect a specific target temperature. If it will, the stream grid is applied to Ford possible topological modifications to either break the downstream path or to introduce means to reestablish the target temperature. Finally, the question of how much flexibility and which action to choose can be considered. Kotjabasakis and Linnhoff (1986) have pointed out that the relative cost-effectiveness of alternative design options depends on the degree of flexibility required. This is illustrated in their work by a graph which indicates the investment of each contingency action as a function of the new target temperature. Backing off on a target temperature to save capital may in some cases also involve choosing another network manipulation. In more complex networks, combined actions can be considered using the sensitivity tables. An interactive approach using object-oriented concepts derived within AI was taken by Calandranis and Stephanopoulos (1985, 1986). They psed a similar approach as the research at UMIST referred to above, with the stream grid as an excellent tool to study structural aspects of operability and flexibility. Two important concepts in their work are the disturbance propagation network and the freedom of each exchanger, defined by the ability to tolerate a load shift. This concept was used for the first time in HENS by Linnhoff and Flower (1978b). Calandranis and Stephanopoulos (1986) also contributed to the physical understanding of the operability problem, and the reasons for nonconvexities were grouped into intrinsic and pinch associated mechanisms. ADVANCES IN HENS METHODS

In this section, we will present the advances that have been made along three lines of research that we consider to be of importance for the solution of industrial HENS problems today and in the future.

The synthesis of cost optimal heat exchanger networks

These lines will be referred to as pinch technology (based on thermodynamic concepts), mathematical programming (trying to automate subtasks of the design) and knowledge based systems using AI techniques. Pinch technology Linnhoff and Vredeveld (1984) stated that pinch technology “has come of age”, referring to a complete methodology for the design of heat exchanger networks, utility systems, heat and power systems and integration of distillation columns with the background process. They also pointed out the importance of considering process modifications to improve heat recovery before the heat exchanger network problem is addressed. The best introduction to pinch technology is given by Linnhoff et al. (1979), Linnhoff and Turner (1981), Linnhoff et a[. (1982) and Linnhoff and Hindmarsh (1983). A new view on energy savings in distillation is given by Linnhoff et al. (1983) and the integration and appropriate placement of heat pumps and turbines is given by Townsend and Linnhoff (1983a,b). 1. Applications. There is little doubt that so far, pinch technology has had a lead among the three mentioned research lines when it comes to industrial applications. Linnhoff and Turner (1980) reported applications within ICI and concluded that three beliefs often encountered in industry when it comes to heat integration are quite unfounded: (1) to design better processes, one needs more design time: (2) process integration for energy conservation leads to control problems; and (3) energy conservation always costs money (area vs energy trade-off). Most processes -are highly integrated, and pinch technology is only a tool to make sure that this integration is done properly. Dyson and Kenny (1982) reported how the PDM has been used within Davy McKee, with special emphasis on crude preheat trains. Some interesting practical aspects of using such systematic methods are given. Industrial applications are also reported by Boland (1983), Boland and Hindmarsh (1984) and Linnhoff and Vredeveld (1984) together with some considerations on technology transfer within large companies like ICI and Union Carbide. Steinmetz and Chaney (1985) discussed total site energy integration by using pinch technology and Westerberg’s heat path diagram. The importance of the relative positions of the single process pinch points for the total plant integration was discussed. Hindmarsh et al. (1985) described how the “Tensa” Group in ICI addresses the integration of diesel engines, turbines and refrigeration systems into the overall process. Heat load and level information from the GCC is used to exploit heat interactions between a process and a power system to maximize cogenerated power. Finally, G’Reilly (1986) reported experiences with the pinch technology by warning against the indis-


criminate use of systematic methods. He stated that design constraints will be encountered and must be properly dealt with. Since 1984, important new developments have taken place within pinch technology. The specific areas are capital cost targeting and design, retrofit targeting and design, flexibility considerations at the design stage and finally total site heat and power integration. 2. Capital. The ability to target and design for capital cost as well as for energy has added a new dimension to pinch technology. Even though MER designs in the fewest number of units by experience are near-optimal in total cost, there are obviously cases where total area can be improved to reduce the investment. In cases where no significant improvement in total annual cost is observed, targeting and design for capital and energy will at least reduce the time consuming optimization (A/E and V/E trade-offs) and also give the engineer confidence that, the design is near-optimal. - A spin-off from this researcn has been increased understanding of the mechanisms in HEN design. This includes concepts like topology traps and crisscrossing, which will be briefly discussedin the following. The area target based on individual film beat transfer coefficients from Townsend and Linnhoff (1984) is fundamental to this progress. Ahmad and Linnhoff (1984) reported how targets can be obtained for total annual cost. This made it possible ,to obtain a near optimal value of AT,, ahead of design, which reduced downstream optimization. Later Ahmad (1985) introduced a new method for targeting the number of shells as opposed to units. The last contribution along this line is the concept of topdogy traps by Linnhoff and Ahmad (1986a,b). When choosing a certain AT,,, one also indirectly makes topological decisions. In a design optimization there may be idiosyncrasies in the topology that make evolution from an initial network to the global optimum impossible. With price differences or local specialities like cooling water temperature, the optimum AT,, will be different, possibly leading to different topologies rather than one “world-wide” optimum design. With the driving force plot and the remaining problem analysis, Ahmad (1985) showed how the PDM can be extended to simultaneously design for energy and capital. While the cross pinch concept relates to energy, &s-crossing is linked to heat transfer area. These two mechanisms converge in the most constrained part of the process. 3. Retro_fit. Tjoe and Linnhoff (1984) defined the retrofit HENS problem. In this case, the optimal minimum approach temperature is a function of the energy/capital trade-off and in addition the existing structure of the network and the expected payback time. They outlined a retrofit procedure where heat




exchangers transferring heat across the pinch are removed and that compatibility with the existing network is searched by manipulating heat load loops and paths. Linnhoff and Tjoe (1985) presented a procedure for retrofit targeting based on the idea that new exchangers or shells installed will be utilized with the same area efficiency. They presented a graph relating investment cost and utility savings. Depending on expected payback times or an upper limit on the investment, one may obtain an estimate for AT,,, to be used in the network manipulation together with target for energy reductions. Tjoe and Linnhoff (1986) presented a complete methodology for retrofit targeting and design. An existing network is usually nonoptimal in both structure and area/energy tradeoff. They pointed out that the smallest approach temperature only indicates wrong use of driving forces, and that this value should not be used in the retrofit design procedure. An in depth treatment of this topic, including industrial case studies, is given by Tjoe (1986). Linnhoff and Witherell(1986) reported application of these latest developments when retrofitting parts of an ethylene plant. The importance of correct data extraction was emphasized. 4. Flexibility. With the work of Kotjabasakis and Linnhoff (1986), Linnhoff and Kotjabasakis (1984, 1986) pinch technology is able to address flexibility considerations at the design stage. The concepts of downstream paths and sensitivity tables applied in the stream grid give the engineer a “bird’s eye view” when designing cost optimal networks that also are flexible. 5. Total site. Morton and Linnhoff (1984) discussed total site integration by using the GCC and the relative location of the individual process pinches. Linnhoff (1986a) introduced the balanced composite curves to handle the situation where the use of intermediate level utilities may introduce new pinch points called utility pinches. The paper discussed the process/utility interface, and the relative merits of the CC and the GCC are explained. These principles were further discussed by Linnhoff and Ahmad (1986b). Current research in pinch technology is progressing along several lines and Linnhoff (1985) introduced a variant of the “Rubic Cube” to describe three basic dimensions of the development. From heat exchanger networks, the technology has been extended to handle heat and power networks, total processes and overall plants. After starting with energy, capital has been taken into consideration and by the work of Kotjabasakis and Linnhoff (1986), Linnhoff and Kotjabasakis (1984, 1986) operability is handled at the design stage. The next step will be raw materials utilization. Finally, the last dimension of the picture is the development from new designs to also handling retrofit cases. The techniques have also been briefly applied to batch processes. Linnhoff (1985) gave this overview as a reply to O’Reilly (1985) who suggested

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that the pinch concept had been developed beyond its capabilities. Although this section has been devoted to the research at UMIST in Manchester (Linnhoff and coworkers), the contribution of Hohmann and Lockart and the Japanese researchers, first of all Umeda and coworkers, have been of paramount importance in the development of the thermodynamic approach as a whole. Mathematical programming In this section, we will describe the latest developments of the various approaches that apply mathematical methods in order to make parts of, or the whole design exercise automatic: 1The considerable efforts in this area during the 70s did not result in many applications in the industry. There has, however, been a considerable progress in the last few years, when some basic thermodynamic concepts like the heat recovery pinch have been included in the models. The activity on using various LP models (including MILP) is fundamental in this picture, and important contributions have been given by Westerberg, Grossmann and coworkers at CMU in Pittsburgh and Morari and coworkers at CALTECH Pasadena. In addition, the works of Su and Motard (1984) who automated the PDM, and the minimum number of units approach of Jones and Rippin (1985) should be mentioned. Rigorous targets can be found for the minimum utility cost; allowing for multiple utilities, all kinds of constrained matching and stream individual contributions to the minimum approach temperature. A rigorous alternative to the (N - 1) rule as target for the minimum number of units, again allowing for constraints, can be found by MILP transshipment models. A rigorous area target has also been proposed, although one may question its importance. Automatic and semi-automatic network generation have been reported based on the heat load distributions that obey the targets. This allows for area or cost optimization, by finding optimal values of stream splits and bypass streams. The networks in Figs 6 and 12 illustrate the power of MILP models and automatic synthesis. First, the true minimum number of units can be obtained ahead of design, but more important is the automatic discovery and optimization (investment cost) of networks achieving this target. The MILP approach also has the advantage that the model for the heat exchanger network easily can be incorporated in an MILP model for the overall process. A mathematical approach to the simultaneously optimization and heat integration of chemical processes was presented by Duran and Grossmann (1986) who reported considerable savings when compared with the sequential approach. A new pinch location method was developed to cope


The synthesis of cost optimal heat exchanger networks with the situation of not having preestablished temperature intervals. This is the case because the temperatures of the hot and cold streams are among the parameters that are allowed to vary in the optimization. Finally, the latest developments in using various LP models to handle interesting aspects of the retrofit situation should be mentioned. Saboo et al. (1986a,b) described procedures for finding the most economic way to add area to installed exchangers. A new trade-off introduced is the number of exchangers to be modified vs the total additional area. The existing utility consumption can be evaluated, not only against the traditional minimum target for a given AT,, and all structures, but also against a new target for the given structure and AT,,= 0. The latter situation is interesting, since adding area to an exchanger is fairly simple and may be done during normal plant down time. Knowledge based systems Recently there has been a very rapid growth in the application of knowledge based systems (KBS), or expert systems (ES), in many areas. This has not yet, however, had any profound effect on the activity related to HENS. When Niida et af. (1986) described experiences in using expert systems in process systems engineering within a major Japanese engineering/ construction company, there is typically very few applications reported in heat exchanger network design, and more use in for instance separation systems. Jezowski and Kuciel(lY79) approached the HENS problem by generating a search tree of various structures. Jezowski (1981) then applied AI techniques like ordered search to find the best network, and this work is continued by Jezowski et al. (1983) and Jezowski (1983). Hartmann et al. (1986) pointed out that a large number of feasible structures exist for the HENS problem, and with multiple criteria. Since some of these evaluation criteria to some extent are “fuzzy”, they devised a simple interactive expert system combing heuristic rules and fuzzytheory. This approach is also described in two other papers from the same research group (Zeising et al., 1985; Zheljev et al., 1985). Unfortunately, both the works of Jezowski and coworkers and Hartmann and coworkers have the disadvantage that the pinch decomposition is not included, i.e. more “knowledge” is needed. Grimes et al. (1982) presented the HEATEX program which synthesized heat exchanger networks with minimum utility requirements. A heuristic ap preach was used, and the rules were represented as a set of 115 production rules. By using 0PS3 RX, an early version of the today well known OPSS knowledge engineering tool, the performance of HEATEX was too slow to be really useful (Chowdhury, 1985). Interestingly, by formulating the knowledge base for HEATEX, a more detailed insight in the HENS problem was obtained and formed the basis for a new

algorithm to solve the HENS problem Grimes et al., 1982; Banares-Alcantara et al., 1985). Calandranis and Stephanopoulos (1985) used a Symbolics 3640 computer with the Flavors erivironment for the operability anafy&s of MER heat exchanger networks. After the decision on the range of operating parameter variations for a given network is made, the program reduces the problem space by employing the underlying stream structure to assess the number of varying parameters. The possible nonconvexity of the network is investigated using several theorems that are actually production rules of a KBS. A set of eight base cases is used for the analysis of the network. The base cases depend upon pinch point changes (“swaps”), the number of disturbances to the network and flowrate variations. The program does not only tell whether the network is operable, but also which heat exchanger that’ should be further investigated together with proper guidance for retrofit action. The program is based on object oriented concepts that enable a transparent, graphics-based, interaction with the designer. By using the proposed theorems, the problem under consideration can be broken down into simpler problems and solved. Strictly speaking, the theorems presented are not rigorous insights, but used in connection with the chosen inference mechanism, a practical result is obtained within the given domain. This approach shows that it is possible to reduce the problem space and that big combinatorial problems may be solved to a “sufiicient” degree. Note that optimality still is the designer’s responsibility. Finally, in order to combine several techniques for the synthesis of heat exchanger networks, Viswanathan and Evans (1986,1987) used an expert system to generate and control the various modules involved in HENS. They used a modified transshipment model for the minimum utility consumption, a modified transportation model for the minimum number of units and a new transshipment model using the flexible “out-of-kilter” algorithm for the forbidden match problem. The expert system controls the interaction between the various problem aspects and generates the models to be solved. The apparent advantage of using knowledge based techniques in this manner is the flexibility in applying, or to combine, several methods for subproblems within HENS. It is easy to modify or improve the capabilities of the system by expanding the contents of the knowledge base. COMPUTER


Norsk Hydro as has access to the following computer programs for designing heat-exchanger networks: ADVENT, HEXTRAN, INTERHEAT, MAGNETS, RESHEX and SUPERTARGET, the last one only as an early prototype version. We have also tried a copy of HENSYN from Rev and Fonyo (1984), available in universities from the EURECHA




committee. These programs will be briefly discussed together with other commercial or research type programs referenced in the literature. Two programs included in this review are based on the use of LP techniques to handle several aspects of HENS. Both RESHEX and MAGNETS are university developed, prototype software aimed at research studies, but with significant potential for future industrial applications. HEXTRAN obviously has some nice features for rigorous simulation, optimization and monitoring of heat exchanger networks, and is used worldwide in a large number of industrial companies. When it comes to synthesis, however, our company has decided to use ADVENT with its user-friendly, colour graphics, workstation-based approach as the primary tool. The core of this program is based upon the latest results in pinch technology. HEXTRAN Being introduced in 1980, and described by Challand and O’Reilly (1981) HEXTRAN from Simulation Sciences Inc. was for a long time the only commercially available computer program addressing the design of heat exchanger networks on a general basis. This batch-oriented proram handles .targeting, synthesis, optimization and rigorous simtilation and rating of the network. The targeting and synthesis part is based on the work of Linnhoff and Flower (1978a), with the loop breaking algorithm of Su and Motard (1984) to reduce the number of heat exchangers while achieving MER. Challand et al. (1981) and Colbert (1982) introduced the idea of a double temperature approach (DTA), where the heat recovery approach temperature (HRAT) determines the relative position of the composite curves and thus the level of heat integration, while the exchanger minimum approach temperature (EMAT) is allowed to have values below HRAT, however, without changing the utility consumption. O’Reilly (1985) suggested that this was contradictory to the pinch principle which says that whenever heat is transferred across the pinch, there will be a double penalty on the utility side. What really happens in HEXTRAN is that an equal amount of heat is transferred from above to below pinch (with AT > AT,,,,) and from below to above (AT -c AT,,). In pinch technology, this has been named c&s-crossing (Ahmad, 1985), and may be used to optimize the total heat transfer area without changing the utility consumption. Another approach to this situation which actually describes the industrial fact that streams may have quite different heat transfer conditions, is the concept of individual stream contributions to AT,, . Applications of HEXTRAN were reported by Kleinschrodt and Hammer (1983) who used the DTA approach to handle multishell situations in crude preheat trains. Recently, Jones et al. (1986) described how the program can handle retrofit situations in-

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eluding targeting for payback time and synthesis through constraints to evolve the network for compatibility. A major advantage with HEXTRAti is a rigorous handling of streams (compositional) and their physical properties (data base) as well as the heat-exchanger calculations. AD VENT An interactive, pinch technology based, tool was introduced commercially by Union Carbide Corp. in 1985. ADVENT operates in a workstation environment using colour graphics, multiple windows, full-screen panels and mouse to enhance the man-machine interface. Gautam and Linnhoff (1985) emphasized that the very nature of process synthesis requires interactive and flexible tools to give the engineer full control of the network development. Gautam and Smith (1985) presented the modules of ADVENT, which include HENS, process modification, optimization, heat and power, separation synthesis, operability/flexibility and furnaces. The program also has certain simulation capabilities, first of all meant to supply the synthesis activities, but also for detailed heat exchanger calculations. Running on a Unix-based process engineering workstation (Dickert et al., 1985; Smith, 1986), Gautam and Smith claimed that ADVENT combines state-ofthe-art in computing technology and process synthesis. The program certainly has an edge when it comes to user interface and the application of pinch technology. First, the user can address the aspects of process modification, utility allocation and finding the optimal level of heat recovery by graphical aids like the composite and grand composite curves and an implementation of the “supertargeting” features described in the section on pinch technology. Then the network can be interactively generated in the stream grid environment, with additional tools like the driving force plot to evaluate each heat exchanger thermodynamically. An automatic synthesis algorithm based on the TI method with a subsequent unit reduction is also available, or the program may “fill in the rest” after the engineer has decided the crucial near-pinch matches. Finally network evolution includes graphical and calculational tools for loop and path manipulations. INTERHEA T As the name suggests, this program is basically interactive, but with some automated features for network generation and parameter optimization. The program was initially developed by professor Lerken at the Norwegian Institute of Technology in Trondheim, but an extension to the program, marketed under the name of HEATNET, has been developed in cooperation with National Engineering Laboratory (NEL) in the U.K. This also includes links to the PPDS physical property data base and

The synthesis of cost optimal heat exchanger networks


to detailed heat exchanger calculations by HTFS software. The features of the program including temperature dependent physical properties (enthalpy and heat transfer coefficients), parameter variations, multivariable optimization (up to 9 parameters) and heat pump and turbine models are described in Loken, (1984, 1985, 1986). Akselvoll and L&en (1987) describe the most recent enhancements of the program on automatic network generation, where a number of near-optimal solutions are listed by treating the problem in a combinatorial way, obeying the pinch decomposition and introducing the minimum number of split streams that is necessary to obtain MER.

the traditional energy target obtained by PTA or LP models, which gives the minimum utility consumption for a specified value of AT,, and all possible structures. RESHEX calculates the minimum energy requirements given the existing structure and AT,, = 0. This may help in deciding between repiping and area addition to the existing structure. In the latter case, the program finds the minimum additional area necessary in order to achieve a certain reduction of the energy bill. The new trade-off between the number of exchangers to be modified and the corresponding total additional area can be addressed by penalizing area addition on selected heat exchangers.


The activity at Carnegie-Mellon University in Professor Grossmann’s group on heat exchanger network synthesis and the application of MILP models has been implemented in an automatic synthesis program named MAGNETS (Grossmann, 1985b). The LP and MILP transshipment models of Papoulias and Grossmann (1983) give rigorous constrained targets for energy and minimum number of units. The constraints take the form of forbidden, required or restricted matches. The automatic network generation was made possible by the clever stream superstructure described by Floudas et al. (1986). Based on MER heat load distributions for the minimum number of units, the optimal match sequence and stream split ratios are found which minimizes the investment cost through the solution of a NLP problem. One advantage of the program is that heat transfer coefficients and heatexchanger cost data are specified at a stage of development where the matches are known, but the network topology and stream structure still free to be optimized. Good or bad heat transfer conditions as well as the possible need for exclusive materials of construction can thus be accounted for. When the minimum utility cost problem has been solved by the LP transshipment model, the user has the option to obey or disregard one or more of the possible pinch points in the process, which means that designs with units in the range between U,,,,, and U,, can be studied. An outer (at present) manual iteration loop is necessary to address the problem of cost-optimal AT,,,,. A limitation with the current approach is that nonlinear heat capacities cannot be handled, but this is subject to further research at CMU. In pinch technology one obvious problem is that there are many MER networks that can be developed by PDM. When optimizing these initial networks by loop-breaking and path manipulation, each network will follow different patterns, and an exhaustive search is necessary to guarantee the global “optimum”. A similar situation arises when using MILP models. There will be many possible HLDs resulting in the minimum number of units, and each of these


Linnhoff March, process integration consultants, have marketed a pure targeting program named TARGET II, based on university software developed in professor Linnhoff’s group at UMIST, Manchester (see Linnhoff and Senior, 1983). The program can handle constrained targeting to find the energy penalty of a forbidden match, and results are given graphically (composite and GCCs, energy target plot and stream grid with stream population above and below pinch). The idea of establishing the optimum value of AT,, ahead of design presented by Ahmad and Linnhoff, (1984, 1986), Ahmad (1985) and Linnhoff and Ahmad (1986a,b) forms the basis of a new program named SUPERTARGET. In addition to these extended targets for heat exchanger networks, the program gives the user some guidance in the ’ match selection when establishing the network. Important tools are the CP-table and the DFP. The philosophy taken is that the initialization through annual cost targeting to find a close to optimal AT,, is the crucial task. The network development may then be done by hand. RESHEX RESHEX was initially developed to aid the research on resilience of heat exchanger networks in Professor Morari’s group at the University of Wisconsin and later CALTECH (see Saboo and Morari, 1984). The latest developments of the program have been described by Saboo et al. (1986a,b). RESHEX can give rigorous constrained energy and area targets allowing for individual stream contributions to AT,,. The resilience of a network structure can be tested for a specified disturbance range, or the resilience index can be computed. Automatic network generation is based on a modification of the MILP model of Papoulias and Grossmann (1983), where the MER requirement can be relaxed in order to reduce the number of units. Some features are included in the program that are of special interest in retrofit situations. In addition to




will lead to different splits.




and stream

Other programs A number of computer tools have been briefly described in the literature, but without enough information to make a proper review possible. The majority of these programs have been developed to support research in the HENS field. EAPEX, which was presented by Ono et al. (1982), is a large computer package involving both process simulation and heat integration, where the modules of the program communicate through files. The heat integration part is based on the approach of Naka and Takamatsu (1982). HENSYN is one half of the program SYNSET developed to aid teaching of process synthesis, which is available for universities through the EURECHA committee. HENSYN is developed by Rev and Fonyo (1984) and combines the PDM and a modification of the fast matching algorithm of Ponton and Donaldson (1974) to develop nearoptimal initial MER networks with the fewest possible number of units. The modification from Ponton and Donaldson is simply that the minimum utility target for the remaining problem is calculated after each match to check whether MER is prevented by the last match. HENS from the Research Institue of Chemical Equipment in Bmo, Czechoslovakia, is also based on a combination of methods from Linnhoff and coworkers and Ponton and Donaldson’s matching rule. Since this procedure is very fast, one can afford to obtain networks for several values of AZ’,, and thus find the optimum trade-off between capital and energy. The features of the program are described by Klemes and Ptacnik (1984, 1985) and include a link to the simulation program SIPRO. Later, Ptacnik and Klemes (1987) introduced HENS-II to handle multipass exchangers. The pinch decomposition is included and an inverse Ponton and Donaldson rule is applied below pinch, meaning that the design starts from the cold end. A microcomputer implementation of a synthesis algorithm based on the thermodynamic combinatorial method of Flower and Linnhoff (1980) has been presented by Govind et al. (1986). The simplifications involved in this approach reduce industrial applicability, but this does not prevent its usefulness as a teaching program. Jabali (1984) implemented and evaluated several thermodynamic based methods in prototype software including the aspect of resilience and flexibility. Jezowski et al. (1983) developed computer programs for both tree-search and assignment task algorithms. Depth-first search was applied for small-scale and ordered search for large-scale problems: The assignment algorithm was implemented such that some of the inherent drawbacks were removed.


Finally, a tailor made program for crude oil preheat trains, named EXTRAIN, has been marketed by Pace Consultants in Houston, Texas (member of the Jacobs Engineering Group). The program handles heat exchanger rating and preheat train optimization. Simulation programs Some of the programs mentioned above have simulation capabilities ranging from rigorous calculations to shortcut methods aimed at supporting the synthesis activity. In addition, there are several general-purpose simulation and design programs available on the market that will not be mentioned here. Rather, we will refer to a few contributions that attempt to exploit the special characteristics of heat exchanger networks in the simulation procedure. While, for example, EAPEX is a sequential modular program, Shindo et al. (1982) argued that the integrated nature of heat exchanger networks will lead to a high number of information recycle loops. The special purpose simulation, rating and design program for heat exchanger networks, HENS, that was presented in their work thus uses the equationbased solution strategy. Another equation-based program is the EROS flowsheeting package for evaluation and optimization of heat exchanger networks including mixers and splitters, presented by Shah and Westerberg (1980). Even though Simulation Sciences Inc. uses sequential modular techniques in their general-purpose flowsheeting program, PROCESS, they have chosen to use matrix methods in HEXTRAN. Klemcs and Vasek (1983) suggested that in order to handle industrial heat exchanger systems as opposed to ideal counter current formulations, integrated software for the synthesis and simulation is required. Their HENS synthesis program is thus integrated with the SIPRO simulation program, which uses an equation-based solution approach. Finally, Asbjemsen and Haug (1985) discussed the choice of variables and approximations in the optimization of heat exchanger networks. RECOMMENDATIONS


Systematic methods and computer tools are available today which can be used to address and solve the industrial heat exchanger network synthesis problem. The proper solution of the various trade-offs involved in heat integration has significant impact on the process economy. Large energy savings with short payback times that meet todays short-term based economic reality have been reported. In some cases, proper integration can reduce both energy consumption and capital investment and even produce more operable processes. To remain competitive, industry will have to take advantage of the blend of methods presented in this review&i So far, pinch technology has produced the most extensive list of good projects in industry for im-

The synthesis of cost optimal heat exchanger networks

proved heat integration. However, fundamental to pinch technology, mathematical methods and knowledge based systems is the skill and experience of the engineer himself. Industrial companies should therefore put emphasis on technology transfer to increase the understanding of the technical and economical mechanisms involved. Universities should reduce their emphasis on unit operations when teaching process design and put more emphasis on the network structure and related important trade-offs in economy, operability, controllability, safety and flexibility. Process synthesis with its blend of heuristic and systematic methods is fundamental in this respect. New “revolutions” in the design of heat exchanger networks, resulting from discoveries like predesign targets for best performance and the heat recovery pinch, are not expected. The use of thermodynumic principles in other areas of process synthesis, however, is still to be explored. Linnhoff uses the picture of the Onion Diagram and the Rubic Cube to describe the extensions and new areas for research within pinch technology. There is still significant scope for improvements in the mathematical methods that have been employed to automate the design of heat-exchanger networks, both in solution techniques, in added realism of the models to satisfy industrial needs, and in flexibility to make sure that the process synthesis activity remains designer driven. The use of sophisticated hardware and software will be of importance for future development of HENS tools. The requirement for some high level software to integrate the various approaches to HENS is one incentive, another is the need to accommodate design engineers with tools that support the design activity, are user-friendly and have fast response. The use of knowledge based techniques in some high-level environment seems inevitable in this respect, and will be of advantage in several areas. Pinch technology could gain from “intelligent” programs which behave differently according to the nature of the stream data and the environment of the heat exchanger network. Mathematical techniques that use some kind of superstructure will benefit from sophisticated software which ensure that the optimum solution is contained within the superstructure, while excluding unnecessary possibilities, thus reducing the problem space. Some of the qualitative considerations included in the optimization (safety, environmental aspects, company policy etc.) can be programmed using knowledge based techniques. Finally, we will bring across some of the ideas presented by Stephanopoulos (1986) on expert SYSterns and computing environments for process design activities. Today’s programming tools like FORTRAN do not have the flexibility to meet tomorrow’s needs. However, the advanced and flexible tools for program development now available within AI, are too slow for engineering applications. It is thus expected that design tools are developed on one


machine, but used in applications in a faster environment on another machine. The strong argument is made that the culture of personal computers has misdirected the capabilities in computer aided engineering. Stephanopoulos (1986) further suggested that the expert systems built for computer aided process design should take the form of an expert assistant or consultant rather than the expert solver. Acknowledgements-The authors are grateful to Norsk Hydro a.s, for the opportunity to explore this industrially important area, and for supporting this publication. We also wish to express our thanks and admiration to the research groups that we have been in contact with during the last few years.

NOMENCLATURE A = Heat transfer area A,, = AI = C = DFP = DTA = E = ED = EMAT = Em, = ES = FI = Fr = GCC = h = H = HAF = HDS = HENS = HLD = HRAT = HTG = HTS = KBS = L = LP = LRS = LTG = LTS =

Minimum heat transfer area Artificial intelligence Cooler (Figs 13-15) Driving force plot Double temperature approach Energy Evolutionary development method Exchanger min approach temperature Minimum energy consumption Expert system Flexibility index Heat exchanger configuration factor Grand composite curve Film heat transfer coefficient Enthalnv or heater (Fies 13-15) Heat akilability fur&n ’ Heat demand and supply diagram Heat exchanger network synthesis Heat load distribution Heat recovery approach temperature High temperature group (Fig. 10) High temperature streams (Fig. 10) Knowledge based system Number of heat load loops Linear programming Long range stream (Fig. 10) Low temperature group (Fig. 103 Low temperature streams (Fig. 10) m .cg = Heat capacity flowrate j MER = Maximum energy recovery MILP = Mixed integer linear programming nh = Number of hot streams ne = Number of cold streams N = Number of streams and utilities NLP = Nonlinear programming, PDM = Pinch design method PT = Pinch technology PTA = Problem table algorithm Q = Enthalpy AQ = Enthalpy change Q. = Hot utility consumpiton Q a,,; = Minimum hot utility Q, = Cold utility consumpiton Q Crmn= Minimum cold utility RI = Resilience index RPA = Remaining problem analysis S = Number of subsystems ST = Steam (Fig. 11) T = Temperature T, = Temperature of a cold stream Th = Temperature of a hot stream

526 T. = T, = TC = TI = TQ = AT = ATi = AT,, = AT,, = AT.,, = ATpinch= U = CJ = (I,. = &+i”,MER=

T. GUNDW~EN and L. NAF_SS Supply (start) temperature Target (end) temperature Thermodynamic combinatorial method Temperature interval method Temperature enthalpy Temperature difference Stream contribution to AT,, Log mean temperature difference Minimum approach temperature Optimum temperature difference (Fig. 16) Approach temperature at the pinch Heat transfer coefficient Number of units Minimum number of units (global) Minimum number of units (MER)

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