A Novel Visualization Tool for Heat Exchanger Network Retrofit

Ind. Eng. Chem. Res. 1996, 35, 4507-4522

4507

PROCESS DESIGN AND CONTROL A Novel Visualization Tool for Heat Exchanger Network Retrofit Ramachandran Lakshmanan* and Rene´ Ban ˜ ares-Alca´ ntara Department of Chemical Engineering, University of Edinburgh, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JL, United Kingdom

Research into heat exchanger network (HEN) retrofit has focused on either complete automation or evolutionary, thermodynamic approaches. The former involves the solution of mixed-integer, nonlinear programs, with the advantage of rigor, but suffering from exorbitant computational overheads. On the other hand, existing thermodynamic approaches, though useful in greenfield design, are inadequate for retrofit problems. Using a visualization tool that makes graphically explicit both the loads and the driving forces in a heat exchanger network-providing a succinct, graphical description of the first and second laws of thermodynamics applied to the systemswe present design guidelines which facilitate rapid evolution of good retrofit solutions by inspection. The method is elucidated using case studies, the retrofits proposed are comparable or superior to existing solutions and are more rapidly obtained, and the rationale behind the proposed modifications is easily documented. This final feature greatly enhances the industrial acceptability of the approach. 1. Motivation 1.1. The Economic Importance of HEN Retrofit. Heat exchanger network (HEN) design is unquestionably the area of process synthesis that has received the most attention in the academic literature. It is also, in many respects, the area in which the most significant advances have been made. Research in this area has been continuously fueled over the last two decades by dramatic increases of energy costs in most parts of the world. By 1982, for example, utility costs accounted for more than 20% of plant operating costs, up from just 5% in 1973 (Korich, 1982). Although energy costs have decreased somewhat in recent years, they still constitute a significant fraction of plant operating costs. Application of systematic design approaches, such as Pinch technology, has yielded anywhere between 15 and 90% energy savings and reduction of capital outlay by as much as 25% (Linnhoff-March, 1992). Clearly, the grass-roots design of efficient HENs is an important process engineering problem. In industrial practice, however, the majority of the HEN problems encountered do not concern new designs. Existing plants typically have an energy integration scheme already in place, and these systems are often suboptimal; large shifts in energy vs capital costs, significant changes in process operating conditions, or simply misguided initial design can lead to situations where a retrofit of the existing HEN is economically attractive. In fact, experience has shown that over 70% of real, industrial problems call for retrofit solutions rather than grass-roots design (Shokoya, 1992). 1.2. Previous Research. The research into methodologies for HEN retrofit has proceeded in two main streams: (a) mathematical programming approaches and (b) those methods based on applied thermodynamics. Each of these has its advantages and limitations, * Author to whom correspondence should be addressed. Tel, +44-131-650-4862; Fax, +44-131-650-6551; email, rama@ chemeng.ed.ac.uk.

S0888-5885(96)00372-7 CCC: $12.00

but neither has provided a technology that is applicable over a wide range of problems. A third approach, namely retrofit by inspection, has been mentioned in passing (Tjoe, 1986) and has been advocated in conjunction with the use of the composite curves (van Reisen et al., 1995) but has generally been neglected by academia. The first two approaches are reviewed below, while the presentation of a graphical visualization aid, along with guidelines for carrying out HEN retrofit by inspection, is the subject of this paper. 1.2.1. Mathematical Programming Approaches. Although there have been several mathematical programming formulations proposed for the HEN retrofit problem, the majority of them are either aimed solely at targeting or solve simplifications of the most general problem (Ciric and Floudas, 1989; Saboo et al., 1986a,b; Yee and Grossmann, 1987). The current state-of-theart in HEN retrofit using the mathematical programming approach is represented by the work of two groups of researchers. Ciric and Floudas (1990) propose an MINLP formulation which selects the optimal structural modifications (stream matches and repipes) simultaneously with load reassignments. No attempt is made to determine targets ahead of design, and this can result in inefficiency of the algorithm. Yee and Grossmann (1991) use a combined targeting and synthesis approach, which is aimed at improving the efficiency of the problem formulation. However, computation costs reported appear to grow exponentially with the number of exchangers, making it impossible to solve, in a reasonable amount of time, problems involving more than a handful of units. Mathematical programming approaches typically operate as “black boxes”, and as such they suffer from an additional limitation that the rationale behind the designs they produce is not made explicit, and thus, in the presence of multiple objectives, modeling inaccuracies, and nonconvexity, it is difficult to assess the true quality of a solution produced by these methods. This © 1996 American Chemical Society

4508 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996

failure to explain the reasoning behind the design choices made by the program has severely restricted the industrial applicability of such tools. An additional limitation is that, at the time of problem formulation, a decision must be made as to how many new exchangers are to be used, and this may not always be obvious a priori. 1.2.2. Applied Thermodynamic Approaches. With the success of Pinch targeting and design techniques for the grass-roots design of HENs, it is natural to consider the extension of these ideas to the retrofit situation. Unfortunately, the current state-of-the-art in Pinch retrofit technology is unable to provide the clear guidelines that the grass-roots methods offer. The definition and use of the composite curves for grass-roots design is based on the available energy sources or sinks in the “temperature intervals” created by the supply and target temperatures of the process streams. Assuming we are able to determine the minimum temperature approach that represents the optimal trade-off between energy recovery and capital expendituresand experience would appear to indicate that this is usually possible by supertargeting (Linnhoff and Ahmed, 1990)sthen rigorous energy targets and good area targets can be obtained. Furthermore, the so-called ∆Tmin, or minimum temperature approach, in conjunction with the composite curves, gives valuable rigorous insight into the design of grass-roots HENs, decomposing the design into above- and below-Pinch subsystems and discouraging energy transfer across the Pinch. In a retrofit problem, there is not this clear definition of the available heating or cooling load on a stream. These loads have already been assigned to existing exchangers and utilities, although possibly suboptimally. The existing exchangers may be relocated within the network, should this be beneficial, but they must be moved in discrete “chunks” and not in infinitesimally small quantities, which is an implicit assumption in grass-roots targeting; it is this assumption, which does not apply to retrofit situations, which enables the use of a ∆Tmin to determine energy-area trade-offs and facilitates design by providing a criterion for decomposition of the network. It is not clear, therefore, that results derived from analysis of the grass-roots problem have any bearing on HEN retrofit. Nevertheless, attempts have been made to devise empirical retrofit targeting methods using the notion of a Pinch (Silangwa, 1986; Tjoe, 1986), and interactive methodologies have been proposed for performing HEN retrofit (Shokoya, 1992; Tjoe, 1986). Attempts at developing a Pinch retrofit energy target assume that the “line of best retrofit” (on a graph of energy requirement vs capital expenditure) is a smooth curve. This assumption has been shown to be erroneous, as rigorous targeting yields a discontinuous curve (Yee and Grossmann, 1991). Furthermore, Pinch targeting is based on the entirely empirical “area efficiency” concept which can lead to overly conservative targets, as is demonstrated later in this paper. In addition to the inaccuracy of the Pinch energy targets, there is no convincing theoretical foundation for the use of a ∆Tmin for retrofit. In the grass-roots case, this quantity is used to constrain the design as it can be rigorously shown that cross-pinch heat exchange will result in an inability to meet energy targets; no such theory is known to exist for retrofit problems.

A final disadvantage of the approach is that the overall methodology involves a convoluted process of determining a pinch, removing cross-pinch heat exchangers, repairing the damage, and finally evolving to a “reasonable” solution. This process can take hours, and the smallest temperature approach that is found in the proposed solution can be quite different from the one that was used to start the evolutionary process (see section 2.5). Since the main reason for performing the targeting analysis is precisely to determine the correct ∆Tmin so as to decompose the problem into above- and below-pinch regions, the applicability of the approach to retrofit is questionable. 2. The Retrofit Thermodynamic Diagram (RTD) An important contribution of research into grass-roots Pinch design has been the development of excellent visualization tools and targeting procedures: the composite curves, the driving force plots, maximum energy recovery targets, minimum area and number of units targets, and the grid diagram. However, with the exception of the driving force plot, these tools give limited, and sometimes even misleading (section 2.5), insight into the network retrofit problem. In this section, a new visualization tool, the retrofit thermodynamic diagram, is introduced, and its application to a well-known case study from the literature is described. The rest of the paper will focus on outlining a methodology by which the diagram may be used to systematically and rapidly arrive at good retrofit solutions. 2.1. Case Study 1: The Aromatics Plant. The first case study examined in this paper appears in Tjoe (1986) and represents a simplified aromatics plant. Although the actual design modifications proposed in this section are simple, the analysis illustrates some of the interesting features of the retrofit thermodynamic diagram, without introducing unnecessary complications. No attempt at using stream splits or complicated repiping configuration is made at present; we focus here on giving insight into the utility of the new diagram. Later sections of the paper discuss the contexts in which stream splitting and exchanger relocation are likely to be advantageous, and in section 4.3 we see that the solution presented here can be improved even further. The original HEN for the aromatics plant consists of a system of nine process streamssfour hot and five coldsfive process heat exchangers, three cold utilities, and two heaters. The conventional grid diagram for the network is shown in Figure 1, and the stream data for the problem are given in Table 1. Using the Pinch retrofit targeting procedure and a payback period of 2 years, a ∆Tmin of 26 °C was chosen, and at the end of the evolutionary Pinch retrofit methodology, the design shown in Figure 2 was proposed in Tjoe (1986). (Filled-in circles on an exchanger imply that it has been added as part of the retrofit solution.) The energy savings are £210 000, with a 1.8 year payback period, and although the authors do not indicate the time taken to arrive at the solution, such analyses typically take several hours to complete. We shall now see that, with the aid of the new visualization tool, a superior solution can be obtained in a matter of minutes. 2.2. Definition of the Retrofit Thermodynamic Diagram. The conventional grid diagram has a major limitation with regard to its use in retrofit problems. This is the fact that information pertaining to driving

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Figure 1. Conventional grid diagram for the simplified aromatics plant.

Figure 2. Retrofit solution developed using Pinch technology. Table 1. Stream Data for the Aromatics Plant stream name

MCp (kW/°C)

H1 H2 H3 H4 C1 C2 C3 C4 C5

100 160 60 200 100 70 175 60 200

temperature (°C) supply target 327 220 220 160 100 35 80 60 140

30 160 60 45 300 164 125 170 300

h (kW/(m2‚°C)) 0.8 0.5 2.0 0.4 5.0 1.0 0.5 0.2 0.8

forces within exchangers is not explicitly displayed, making it impossible to assess the degree of “crisscross” (a major cause of area inefficiencies) in a network. Furthermore, with regard to new exchanger placement, it is not clear where the additional matches may feasibly be made. A secondary limitation of the grid diagram is that it does not visually highlight those streams with particularly large utility loads. Occasionally, this information is displayed in numerical form, but this does not give the same impact as the visualization that is described here. In order to alleviate some of these limitations, we have developed the retrofit thermodynamic diagram, a modification of the conventional grid diagram, which makes graphically explicit both loads and driving forces in an existing HEN. The grid diagram is used to display the HEN topology and, in the software prototype

Figure 3. Retrofit thermodynamic diagram for the aromatics plant.

described in the appendix, for editing the structure graphically. The definition of the RTD is very simple: streams are drawn as rectangles (as opposed to arrows) in the same order as they appear in the grid diagram (see Figure 3). The thickness (height) of a given stream rectangle is proportional to its MCp, and its end points are located on a temperature scale increasing from right to left (to follow the same convention as is used in the grid diagram). This construction results in a stream representation in which the total heating or cooling requirement of a stream is proportional to the area of the rectangle which represents it. Utilities are also drawn as rectangles on top of the streams which pass through them. Again, with the thickness of a utility as a measure of the MCp of its process stream, and with its width proportional to the temperature drop across it, the area of a utility “box” is proportional to its load. Heat exchangers, in a similar manner to the conventional grid diagram, are represented by a hot side and a cold side connected by a bar. Unlike the conventional grid, however, the bars are not vertical and always have a negative slope. The absolute value of the slope is inversely related (though not necessarily proportional) to the driving force in a given exchanger. Loosely speaking, an exchanger that is closer to the limit of thermodynamic feasibility has a bar which is “more vertical” than one that has a larger driving force, although comparisons are exact only between exchangers whose streams are the same distance apart on the diagram. The RTD for the aromatics process is shown in Figure 3. 2.3. Physical Significance of the Diagram. Retrofit of a heat exchanger network involves the reallocation of loads wthin existing units and structural modifications to the system. The physical laws which place restrictions on feasible changes to the HEN are simply the first and second laws of thermodynamics: energy balances are to be satisfied (first law), and nonpositive driving forces are not allowed (second law). As pointed out above, the RTD is drawn so that the areas of exchangers and streams represent the load on them; this is the information the designer requires in order to satisfy the energy balances implied by the first law of thermodynamics. In addition, and perhaps more importantly, driving force information is also provided in the diagram, implicit in the slope of the exchanger


bars; this may be used to direct the designer toward only those modifications which would not lead to second law violations. Thus, despite its simplicity, the RTD makes graphically explicit the most important information required by the designer making a retrofit study, providing a succinct, visual summary of the physical laws which apply to the problem. 2.4. Introduction to the Use of the RTD. Having defined the retrofit thermodynamic diagram, we will now look at a simple example of how it may be used to arrive at a good engineering design. At this point, no attempt will be made to present a comprehensive methodology for retrofitsthis issue is addressed later in the paper. Furthermore, we restrict our attention here to modifications involving addition of exchangers and load shifts alone, so as to avoid making this introductory case study overly complex. Later, in section 4.3, we show how even greater economic benefits may be obtained. The following cost functions reported in Tjoe (1986) are used, and an upper limit of 2 years is assumed for the payback period.

hot utility cost ) 2(£/GJ)

(1)

capital cost )

{

8600 + 670A0.83 (£); 10 < A < 300 m2 (2) 252A (£); A > 300 m2

To begin with, we shall investigate, by trial and error, the economic benefits, if any, of shifting a portion of the utility loads from utilities 1 and 4 onto exchangers 1 and 5, as these units comprise a “path” already existing in the network (UTIL-1 f HEX-5 f HEX-1 f UTIL4). This is easily done using the prototype software package ećlair (Appendix A), either by editing the values of the loads in a spreadsheet-like interface or by sliding the boundaries of the exchangers/utilities with the mouse. The software includes a constraint propagation tool (Lakshmanan and Banãres-Alcańtara, 1996) based on the one described in Forbus and de Kleer (1993), which dynamically updates the state of the system as well as the costs, with a minimum of recomputation. Thus the user is provided with immediate feedback regarding the economic attractiveness of proposed changes. E Ä clair also provides the facility for the user to request an optimum load assignment for a given topology. The problem is formulated as a nonlinear program, with a constraint on the maximum payback period (supplied by the user). The optimization package used is described in Zoppke-Donaldson (1995) and is particularly efficient for sparse problems such as this one. However, due to the problem of possible nonconvexities, it is necessary to perform some initial trial-and-error calculations in order to determine a good initial guess for the optimizer. By shifting loads incrementally off utility 1, it is determined that, given the upper bound of 2 years on payback period, it is uneconomical to shift loads along this path. This is primarily because exchanger 5 has a relatively low thermal driving force, and so further reduction of the temperature approach (which is a consequence of shifting additional load onto the exchanger) is paid for with a relatively large additional area requirement. For this reason, we eliminate utility 1 from the set of utilities whose loads we are trying to

Figure 4. First modification (zero load on HEX-6).

reduce. (In ećlair, this is done by constraining the value of the temperature approach on exchanger 5.) We now need to investigate the possibility of improving energy recovery in the HEN by adding exchangers at strategic locations. The addition of these exchangers can be viewed as the creation of new paths between pairs of hot and cold utilities so as to reduce the utility load at the expense of additional exchanger area. It is difficult to determine, from the conventional grid digram, the locations where a new exchanger may feasibly be placed, even if temperature information is displayed numerically on the diagram. On the RTD, however, potential for adding exchangers is graphically explicit: clearly, the only matches that would be thermodynamically feasible are between streams which have a horizontal “overlap”; furthermore, the degree of overlap (multiplied by the MCp of the smaller of the two streams) is an indication of the size of the load that can be placed on the new exchanger before it becomes “vertical” (and hence infeasible). Examining the RTD and bearing in mind that we have excluded utility 1 from the set whose loads are to be reduced, we identify the possible feasible matches: 1. H3 and C1 2. H3 and C5 3. H4 and C1 4. H4 and C5 From the RTD, it is clear that the largest utility loads are on utilities 3 and 5. It may be tempting, therefore, to choose the last of the above matches, in the hope that the maximum reduction of utility load may be achieved. Closer examination reveals, however, that the overlap between streams H4 and C5 is not great, which means (a) that adding an exchanger between them will be relatively expensive due to the low driving force on it and (b) even if we are willing to bear this expense, the actual load that can be absorbed by this exchanger before it becomes infeasible (vertical) is small. As a result, we exclude choice 4 from our initial considerations. The most promising match appears to be the penultimate one: utility 3 has a large load, and the overlap between the two streams is quite sizeable. This means that if a new exchanger is placed linking the two streams, shifting load onto it will be relatively inexpensive. It also presents an opportunity to shift a relatively large load off the utilities onto the process exchangers. Thus a choice is made to add a new exchanger (HEX-6) as shown in Figure 4.


Figure 5. Retrofit thermodynamic diagram with shifted loads.

Figure 6. Second proposed modification.

Once this exchanger has been added, we can shift a load onto it, and as before this is done by trial and error until a solution with an acceptable payback period is found. The corresponding RTD is shown in Figure 5. Comparison of this design with the one in Figure 1 reveals that we have arrived at precisely the same design proposed by the Pinch approach, but with significantly less effort. The obvious question to be asked at this point is, “Can we do better?” Looking back at the list of possible matches for new exchanger placement and consulting the RTD again, we see that there is still the possibility of matching streams H3 and C5 and absorbing some of the load off utilies 2 and 5. Again, this match would have a large negative slope, but whether or not it is economical can only be determined by trial and error or by solving a nonlinear program. Using the software, we propose this additional modification by adding exchanger 7 in the location shown in Figure 6. Using ećlair, this is accomplished by simply “drawing” it onto the grid diagram with the mouse, as described in section A.1.1. We then shift loads onto the new exchanger, as before, and by trial and error we find a solution which does, indeed, satisfy our upper bound on payback period, but which offers significantly greater energy savings than the Pinch solution (£343 000/year) (see Figure 7). 2.5. Comparison with the Pinch Solution. The case study above allows us to draw some illuminating comparisons between the method presented here and the Pinch targeting approach. The most obvious is that

the design by inspection affords greater energy savings than the Pinch solution. Figure 8 shows the target envelope defined by the Pinch area-efficiency method, on a plot of energy savings vs capital expenditure. With these axes, the 2-year payback period constraint is a straight line as shown. Pinch targeting predicts that the best energy savings that can be achieved in a retrofit of this network is in the region of £210 000. However, the design produced using the RTD lies well above the Pinch target, giving an energy saving 63% greater than predicted. It is well-known that the Pinch target is conservative (Shokoya, 1992; Silangwa, 1986; Tjoe, 1986), but an error this large is clearly unacceptable. Pinch retrofit theory predicts that an energy savings of £210 000 will be achieved using a ∆Tmin of 26 °C. It furthermore predicts that, using a value of 10 °C, the shortest payback period that can be expected is 4 years. Close examination of the solution presented in Tjoe (1986) reveals that the smallest temperature approach is actually 10 °C, not 26 °C. Since the payback period for this Pinch design is only 1.8 years, the target of 4 years is clearly erroneous. In grass-roots HEN design, the correlation between ∆Tmin and the energy target is clear and rigorous: an increase in the one leads to a linear increase of the other (within a supertarget range). The analysis above shows conclusively that for HEN retrofit this one-to-one correspondence is lost. The most critical limitation of the Pinch approach, however, is not simply that the design it produced is less attractive than the one developed using ećlair. Area efficiency targeting purports to do two things: (a) provide a good, if not rigorous, target for energy recovery and (b) identify the best ∆Tmin for the retrofit. It is the second of these goals that is crucial to the success of the methodology, since it serves as the basis for decomposition of the system prior to design. Consequently, an improper choice of ∆Tmin will usually result in very poor solutions. It is interesting to note that had the true ∆Tmin of 10 °C been used to “seed” the evolutionary pinch retrofit method instead of the value of 26 °C, the solution presented in Tjoe (1986) would not have been found! Thus the failure of the Pinch retrofit approach is on several levels: 1. It is unable to reliably predict the energy targets for retrofit problems. 2. There appears to be no relationship between the ∆Tmin recommended by the targeting procedure and the actual ∆Tmin that obtains in the best designs. 3. Using the Pinch approach, it is sometimes impossible to find the best solution if we begin with the “real” ∆Tmin; instead an artificial ∆Tmin must be used to seed the design process, followed by laborious evolution to the correct value. It is clear, therefore, that although Pinch technology provides valuable design tools for the grass-roots design of HENs, its application to retrofit lacks sound theoretical basis. 3. Guidelines for HEN Retrofit by Inspection The thesis of this paper is that good solutions to HEN retrofit problems may be quickly obtained simply by applying engineering intuition, provided the appropriate visualization tools are available to the designer. This approach, referred to as retrofit by inspection (Tjoe and Linnhoff, 1986), has not been strongly advocated in the


Figure 7. Final design.

Figure 8. Example showing that Pinch targets can be misleading.

literature in the past, and no satisfactory methodology has yet been presented for the task. The most complete attempt to define such a method appears in van Reisen et al. (1995); however, since this approach still relies on retrofit Pinch targets, it suffers from the same limitations as the Pinch method of Tjoe (1986). Having defined the retrofit thermodynamic diagram, we now proceed to further demonstrate its utility by supplying a set of guidelines for its practical use in arriving at good HEN retrofit solutions. Clearly, no guarantee of optimality can be made, but our initial experience has shown that systematic use of the diagram leads to retrofit solutions that are either comparable to or better than those presented in the literature. The main advantages of the approach by inspection are that (a) the results are often obtained much faster and (b) it is easier to explain (and thus record) the rationale behind the design decisions that are made. The latter feature is extremely important for the industrial acceptance of proposed modifications to an existing plant. 3.1. Assumptions of the Approach. Although the use of the diagram is not limited to cases where stream parameters are fixed, in this paper we shall limit our comments (and, indeed, the facilities offered by the software prototype described in Appendix A) to problems where the flow rates, specific heat capacities, and supply and target temperatures are fixed for a given problem. Future work will address the graphical interface and computational issues involved in removing these restrictions.

Furthermore, we shall assume that the heat transfer coefficient of a given stream is fixed, although this is clearly not the case: in reality, values are a function of pressure drop, flow rate and temperature, exchanger type and material of construction, and the physical properties of the fluid. However, the assumption of constant stream transfer coefficients is commonly made in the literature, and we adopt this approach here as well. 3.2. Combining Engineering Intuition with Heuristics. The proposed approach involves providing the designer with the visual information contained in both the grid and retrofit thermodynamic diagrams and guiding the evolution of solutions based on the user’s engineering judgement and special understanding of process-specific costs and constraints. Capital and operating costs (and payback period) are updated dynamically by the software every time a modification is made. The following set of guidelines is intended to assist the designer in determining which modifications are likely to be most beneficial. 3.2.1. Load Shifting. The first and most obvious way of reducing utility loads is to identify an existing path in the HEN leading from a hot utility to a cold one and to shift a portion of the utility load onto the exchangers which lie along the path. (Although not implemented in the current version of ećlair, the process of finding such paths could be easily automated, and so the burden of identifying them need not be on the designer.) Shifting a load onto a path implies an equal reduction of duty on both the hot and cold utilities and a corresponding increase in the load on the exchangers along the path. In most cases (case study 3, described in section 4.2, is a notable exception), driving forces will be reduced in all these exchangers, requiring the addition of area. 1. The cost of additional area is usually nonlinear and will typically include some fixed installation cost. For this reason, it is recommended that paths with the fewest exchangers are investigated first, as they will require the smallest number of additional units to be added.


2. Clearly, paths where the largest existing utility loads are present should be investigated first, as these represent the maximum potential for shifting a large load off the utilities, provided other exchangers along the paths are not already close to the limit of thermodynamic feasibility. This information is readily apparent in the retrofit diagram. 3. In cases where existing paths involve relatively small utility loads, it is sometimes beneficial to defer load shifting along these paths until the possibility of creating new paths along which to shift larger loads has been investigated. Due to the typical installation costs accompanying modification of a network, it is unlikely that simple load shifting will be economically attractive unless the initial design of the HEN was particularly poor or energy costs have dramatically increased since the HEN was designed. The major savings in energy during a HEN retrofit usually come as a result of topological modifications, the most common of which involves the creation of a new path in the network. 3.2.2. Path Creation with Load Shifting. Path creation with load shifting involves the addition of an exchanger between the two streams which are to be linked, as well as the cost of adding area to existing units in the HEN which happen to lie along the newly created path. The RTD provides the necessary visual information to determine the points in the HEN at which the addition of an exchanger will create a path onto which load shifting is likely to be both feasible and economically attractive. The following considerations must be taken into account: 1. The path must be thermodynamically feasible, which means there must be an overlap between the hot and cold streams at the point where the new exchanger is to be placed. 2. All other things being equal, favor creating a path which includes at least one sizeable utility. If both utilities are large, then there is potential to save a large amount of energy on each of them. If, on the other hand, one of them is significantly smaller than the other, it may be beneficial to eliminate the smaller utility entirely and use the utility exchanger for process/ process exchange elsewhere in the network. 3. Avoid creating paths which traverse exchangers that are relatively vertical and hence close to the limit of thermodynamic feasibility: these units can only accommodate a small additional load and usually involve larger than average additional area requirements. 4. Once a pair of streams is chosen for potential path creation, place the linking exchanger in the position which would result in the least amount of crisscross in the network: unless there is considerable variation in individual stream heat-transfer coefficients, a HEN in which all of the exchangers have similar driving forces (slopes) is likely to require less area overall than one in which there is a wide disparity in the driving forces on the exchangers. Using the simple guidelines above, a large number of HEN retrofit problems can be successfully addressed. More subtle modifications can also be made by either splitting the load on a stream between two or more exchangers in parallel or actually relocating an exchanger within the HEN. The remainder of this section describes how to identify situations in which these modifications are likely to be economically attractive.

Figure 9. Case for exchanger relocation/repiping.

3.2.3. Stream Splitting. Stream splitting is done to reduce the crisscross in a HEN. In practice, such modifications are to be avoided unless they provide significant economic benefits, as a HEN with split streams is considerably more complex to operate than one without. In situations where a pair of exchangers in the HEN are placed in series on a given stream (either hot or cold) while their opposite ends lie one below the other on the RTD, it is possible that splitting this stream would be beneficial. (The degree of crosscross is reduced.) The guideline on stream splitting will become clearer when it is applied to case study 2 (section 4.1) later in the paper. 3.2.4. Exchanger Relocation. A final option is to relocate exchangers. There are several reasons why this may be economically attractive. Relocation To Reduce Crisscross. One reason why exchanger relocation might be attractive is the presence of significant crisscross in the original network. This can very often be reduced by reconfiguring the HEN. The advantage of doing this is that the overall area required to meet the existing load on the network is reduced; this “area excess” can then be used to absorb additional load from the utilities. An example of a situation in which relocation will reduce crisscross is depicted in Figure 9. The modifications that are suggested here are: 1. Move the cold side of HEX-2 to the position where HEX-1 is currently. 2. Move the cold side of HEX-1 to where HEX-4 is now. 3. Move the cold side of HEX-4 to the point where HEX-2 was in the original HEN. The rationale behind these relocations is simply to rearrange the units so that the visual degree of crisscross in the RTD is minimized and all exchangers have similar slopes. Relocation To Reuse Freed Area. In certain situations, it is possible to completely eliminate one or more utility exchangers from the network. Reducing the load on the utility will, of course, reduce the operating costs. However, if the unit can be eliminated, then it could potentially be used elsewhere in the HEN where additional area is required due to load shifting. In situations where a relatively small utility load appears in the RTD, investigate the possibility of eliminating it entirely and using the exchanger elsewhere. (In the case of retrofit using ećlair, the ad-


Figure 11. Summary of exchanger relocation guidelines.

Figure 10. Summary of load-shifting guidelines.

ditional area requirements are dynamically displayed in the spreadsheet interface, so locations where the free area may be effectively used should be evident.) Obviously, when determining whether relocation is possible, the materials of construction of the utility exchanger must be compatible with the handling requirements of the process stream on which it is to be placed. Relocation To Exploit the Form of the Cost Function. The exchanger area cost function is usually nonlinear, at least in part of the range. Typically, there are fairly significant installation costs, which render uneconomical those design modifications which use a large number of small exchangers. In such cases, it may be expedient to shift exchangers around in order to reduce the capital cost. These modifications involve exploitation of the special form of the cost function, and the RTD cannot provide any insight in such cases. An example of a situation where relocation can be done to exploit the special nature of the cost function is encountered in case study 3 (section 4.2). 3.3. Summary of the Guidelines. Generally speaking, there are two classes of modification that are made during HEN retrofit. The most common of these is aimed at reducing the loads on the utilities by shifting a portion onto other exchangers in the network or onto new exchangers added at strategic locations. Use of the RTD to identify situations in which load shifting is likely to be economic is summarized in Figure 10. Another way of improving the efficiency of the HEN is to repipe the exchangers so that the overall degree of crisscross is reduced. This has the effect of reducing the area required to achieve a given level of energy recovery, and this additional area can then be used to shift a portion of the duty off the utilities onto the process exchangers. The RTD may be consulted to identify some of these situations, as shown in Figure 11. 4. Application of the Retrofit Guidelines We have already seen a simple example of how the RTD can assist us in creating paths for load shifting, dramatically improving the effectiveness of a heat exchanger network. This section describes the application of the guidelines presented above to two case

Figure 12. Grid diagram for case study 2. Table 2. Stream Data for Case Study 2 stream name

MCp (kW/°C)

H1 H2 H3 C1 C2

228.5 20.4 53.8 93.3 196.1

temperature (°C) supply target 159 267 343 26 118

77 88 90 127 265

h (kW/(m2‚°C)) 0.4 0.3 0.25 0.15 0.5

studies from the literature: one which was originally addressed using the Pinch approach and the other which was solved by formulation as an MINLP. In addition, we revisit the aromatics plant retrofit and determine that even greater energy savings may be obtained (within the 2-year payback period) by eliminating one of the utilities and reusing this area elsewhere in the HEN. 4.1. Case Study 2: A More Interesting Example. Case study 2 is taken from Tjoe and Linnhoff (1986). The grid diagram is shown in Figure 12, while the stream data appear in Table 2. 4.1.1. Creating New Paths. In Tjoe and Linnhoff (1986), this example is used by the authors to claim that retrofit by inspection yields substandard solutions. Using the grid diagram, they propose a retrofit solution that they believe is most “obvious”. This is shown in Figure 13. As the authors correctly point out, this modification is uneconomical. However, their claim that this proves


Figure 13. Modification proposed by inspection by Tjoe and Linnhoff.

Figure 15. RTD for case study 2.

Figure 16. More logical modification. Figure 14. RTD for Tjoe-Linnhoff modification by inspection.

the inefficacy of retrofit by inspection is fallacious: it is simply a demonstration that the grid diagram is not an effective visualization tool for identifying attractive retrofit modifications. Consider the RTD representing the modification (by inspection) suggested by Tjoe and Linnhoff (1986) (Figure 14). Clearly, the exchanger they have chosen to add has a very poor driving force (it is near-vertical), the load that can be feasibly shifted onto it is quite small (again, as a result of its vertical orientation), and it introduces crisscross into the HEN. Studying the RTD for the original HEN (Figure 15), however, we see that there is a more logical place to add a new exchanger (Figure 16), and shifting load onto it we arrive at Figure 17. Placing this new exchanger on the original grid diagram involves “straddling” exchangers 2, 3, and 4 and is not likely to be considered without the assistance of the RTD. 4.1.2. Load Shifting. We can also exploit the potential for a second load shift along the existing path between utilities 2 and 3 via exchanger 4. This option was deferred until now since utility 2 is relatively small. However, there is an additional economic benefit in carrying out this modification. The final solution, presented in Figure 17, yields an annual energy saving of £310 000, just 3% lower than the maximum of any known solution. It has the great advantage of being simple to implement, and the reason behind each modification can be clearly explained and justified.

4.1.3. Stream Splitting. In industrial practice, it is uncommon to choose to split a process stream simply to improve energy recovery. This is particularly true of retrofit, where such modifications incur large indirect costs in retraining plant personnel and reassessing plant safety and operability. However, in some situations, where significant energy savings result, stream splitting may be considered. The RTD is a useful tool for identifying situations where stream splitting might be beneficial. In Figure 17, we see that the hot sides of exchangers 2 and 3 lie directly below one another, while their cold sides, on the other hand, are placed in series on stream C1. Clearly, this introduces a degree of crisscross in the HEN. The overall effect of this is that the exchanger area required here, compared to a situation in which both exchangers have similar driving forces, is greater. In situations such as this, splitting the stream on which the exchangers lie in series allows them to be linked in parallel, reducing the overall degree of crisscross and consequently the area required. Again, it is clear how the RTD provides the visual information which prompts such design decisions. The designer now has a choice. If it is felt that the process operation will not be significantly comprised by adding a stream split on stream C1, then the final design proposed in Figure 18 would be the optimal one. This decision is often subjective and requires plant specific knowledge that is not easily introduced into an MINLP formulation. In this particular case, it is unlikely that the additional £10 000 per year saving in


Figure 17. Most logical modification, with a load shift.

Figure 18. Design involving a stream split.

energy will justify the cost of the split, and the solution presented in Figure 17 is likely to be the most economic option. 4.1.4. Comparison with the Pinch Solution. The stream-split design proposed above is, in fact, the solution reported in Tjoe (1986) and Tjoe and Linnhoff (1986) using the Pinch approach. The main difference here is that, using the approach by inspection, the designer would usually arrive at the solution within minutes, while the evolutionary Pinch approach, even for a skilled designer, typically takes hours. Although this design does afford the maximum energy savings of any solution reported in the literature, from an industrial standpoint it is unlikely that it would be considered superior to the design without the split, for the reasons mentioned in section 4.1.3. It should be noted that two other design modifications were examined using ećlair, but neither of them was more attractive than the ones presented here. The total time taken to analyze all solutions was less than 30 min. 4.2. Case Study 3: Comparison with MINLP Formulation. Having compared the performance of the approach by inspection with Pinch technology, it would be interesting to see how it performs relative to the more rigorous optimization methods. We consider here an example presented in Yee and Grossmann (1991), represented by the grid diagram in Figure 19. The RTD for this problem is shown in Figure 20, and the stream data are given in Table 3. 4.2.1. Load Shifting. Initially, it seems that load may conveniently be shifted from utilities 1 and 2 onto

Figure 19. Grid diagram for case study 3.

Figure 20. RTD for case study 3.

the other exchangers, as there is, indeed, already a path in the existing network. However, closer examination reveals that this will actually reduce the area required in HEX-2, and while it is possible to achieve this, physically, using a bypass, it represents a waste of existing heat exchange area. As a result, it is unlikely that this modification will be among the best solutions.

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4517 Table 3. Stream Data for Case Study 3 stream name

MCp (kW/°C)

H1 H2 C1 C2

30 15 20 40

temperature (°C) supply target 443 423 293 353

333 303 408 413

h (kW/(m2‚°C)) 1.6 1.6 1.6 1.6

Figure 23. Utility 3 eliminated.

Figure 21. Grid diagram showing the first modification.

Figure 24. RTD after load shifting.

Figure 22. RTD for the first modification.

4.2.2. Exchanger Relocation. Further study of the diagram, however, leads us to consider exchanger relocation. if HEX-3 is used as the only link between the utilities, then load can be shifted onto it without affecting the other two exchangers. It seems logical, therefore, to exchange the cold sides of HEX-1 and HEX-3. This modification does require the addition of a new utility on stream C1 in order to take up the excess load on this stream (Figures 21 and 22), but by shifting load onto HEX-3, it is possible to eliminate utility 3 entirely, so this unit is free to be used to take up the heating load on stream C1. (See Figures 23 and 24.) 4.2.3. Creating New Paths. Further examination of Figure 24 reveals that there is potential for even greater utility load reduction by adding a new exchanger to link streams H1 and C1. The location for this exchanger is chosen as shown in Figures 25 and 26 since this results in a situation where the degree of crisscross is minimized, requiring the smallest amount of overall additional area.

Figure 25. Addition of a new exchanger.

4.2.4. Comparison with the Solution of Yee and Grossmann. The retrofit solution obtained using ećlair has similar load saving and additional area requirements to the solution presented in Yee and Grossmann (1991). The only structural difference between the two solutions is that the locations of exchangers 3 and 4 are switched. If there are significant installation costs, as is often the case, then the solution using the MINLP approach is superior. In that case, additional area is installed only in two places: on HEX-1 and in the form of a new exchanger (HEX-4). By contrast, the solution presented in this paper, although it requires the same


Figure 26. Final retrofit design.

Figure 27. Case study 1 revisited.

overall additional area, apportions it into three small places (HEX-4 and additional area on HEX-1 and HEX3). So this design will incur higher installation cost than the solution proposed in Yee and Grossmann (1991). The astute designer, however, may realize that the situation above presents an opportunity to improve the HEN by exploiting the nature of the area cost function. Given the final design obtained using ećlair, he or she might consider switching HEX-4 and HEX-3, thus effectively requiring only two new installations instead of three. Currently, such decisions depend completely on the ingenuity of the designer; however, future versions of the software will incorporate heuristics to detect such potential for improved savings and present these suggestions to the user. Although the mathematical programming approach yielded a solution which is better than the solution obtained using ećlair, it should be noted that the latter was obtained in a matter of minutes, whereas the MINLP solver took between 1 and 3 h to converge, depending on the algorithm used. Most importantly, the rationale behind the modifications proposed in this paper can be easily explained and justified, while the MINLP solver, operating as a black box, is unable to document the reasoning behind its solution. In many cases, clear reporting of the rationale of a design modification is crucial to its acceptance by plant management. 4.3. Case Study 1 Revisited. In Section 2.1, the first case study was presented and the use of the RTD

illustrated. The emphasis was on presenting as simple a solution to the problem as possible, and so exchanger relocation and stream splitting were not considered at the time. Let us now take a second look at the design proposed earlier (Figure 7) to see whether any significant improvements may be made by applying the guidelines just presented. From the RTD we notice that the load on utility 4 is quite small, and it would be (at least from a thermodynamic viewpoint) feasible to shift the rest of this load onto exchangers 1, 6, and 3 (Figure 27). This would free up the utility exchanger which could then, conceivably, be used elsewhere. Let us assume that hot oil was used as the heating utility between 250 and 300 °C, with an oil-side coefficient of 900 W/(m2‚°C) and an LMTD of 12 °C; the original area of utility exchanger 4 would then be 516 m2. The spreadsheet interface (Figure 28) displays the additional area required on each exchanger, and we notice that ∆A for HEX-3 is particularly large. The form of the cost function is such that additional exchangers larger than 300 m2 are costed linearly and are much less expensive than small ones. If we relocated UTIL-4 and used it to supply a portion of the additional area required on HEX-3, then the deficit (977 m2) is still in the linear region. Thus, this is likely to be the most promising location for the utility exchanger. The total energy saving (still within a 2-year payback period) that this design represents is £390 000 per year, which is 86% higher than that predicted by the Pinch targeting approach. It also represents a 14% improvement on the design proposed earlier in this paper. Note, however, that the expense of repiping was not considered in the computation of payback period, and so whether or not this solution is superior would depend on how significant these costs are and on the suitability of the material of construction of UTIL-4 for matching streams H4 and C3. 5. Conclusions In this paper we argue that heat exchanger network retrofit can be successfully addressed simply by combining engineering intuition with the appropriate visualization tools. One such tool, the retrofit thermodynamic diagram, is defined, its utility in solving diverse retrofit problems illustrated, and a software package which may be used to rapidly obtain retrofit solutions described (Appendix A). For the case studies considered in this paper, typical times taken to completely evaluate a potential solution were on the order of 5-10 min. The rationale behind the proposals could be clearly documented, and the trade-offs between various design choices more clearly assessed than is possible using a mathematical programming approach. As such, it is likely that designs produced using the software will receive greater industrial acceptance than black-box MINLP solutions. The approach has not yet been applied to significantly larger problems, and it is likely that in these cases it will become more difficult for the designer to keep track of the alternatives. However, it is believed that, with a more flexible interface, which would include a rationalemaintenance tool such as the one provided by KBDS (a decision-support system for conceptual design (BanãresAlcańtara and King, 1996)), retrofit studies could still be done rapidly using the RTD.


Figure 28. Additional area displayed in the spreadsheet.

The RTD provides excellent insight into the effectiveness of a HEN design. Although this paper has focused on the benefits of using the diagram as an aid to retrofit, the visualization tool has also been used a posteriori to rapidly assess the quality of grass-roots designs, and is particularly useful for identifying crisscross. Clearly, for the HEN retrofit problem, whether or not one chooses to use a mathematical programming approach, the RTD provides valuable insight into the problem. The diagram has also allowed us to obtain an improved understanding of the HEN retrofit problem itself. Our experience with various case studies indicates that the actual number of modifications that are logical in any given retrofit problem is relatively small. Current state-of-the-art MINLP formulations, because of their generality, consider a much larger space of solutions, the vast majority of which are not economically attractive, and this accounts for their high computational overhead. Ideally, one would use the RTD to obtain an early understanding of a given problem, before moving on to a more restricted, but tractable, MINLP formulation. It is not our intention here to suggest that rigorous optimization is to be replaced by retrofit by inspection, but given the very real issues of the time complexity of current mixed-integer mathematical programming algorithms, the approach presented here will be attractive for a large number of problems. Appendix A. The Software Prototype E Ä clair In order to study the utility of the new retrofit thermodynamic diagram, demonstrate the ease with which solutions may be evolved, and test the retrofit guidelines, we have developed a prototype software tool, the ECOSSE Constraint Language Application for Interactive Retrofit (ećlair). Implementation is in Lucid CommonLISP, and the graphical interface was developed using the GARNET constraint-based language (Myers et al., 1990). The software is under continuous development, and preliminary evaluation has already identified facilities,

such as the ability to display designs involving stream splits and phase change, which will be provided in the next version. This section documents the current state of the system. A preliminary distribution version, without the nonlinear programming facility, is available, free of charge, for noncommercial research use or evaluation. A.1. Features of the Current Version. A.1.1. Rapid Input/Modification of Topologies. The success of the interactive method for carrying out retrofit by inspection relies on the ability of the user to rapidly define and edit HEN topologies. With this requirement in mind, the software was developed to allow the user to rapidly enter a topology simply by “drawing” it with the mouse. The process is illustrated in Figure 29. Horizontal lines are interpreted as streams. If the mouse is dragged from left to right, a hot stream is drawn, while moving in the opposite direction creates a cold stream. Streams are labeled automatically and laid out in sequence. Exchangers are created by drawing vertical lines beginning on or near a hot (cold) stream and ending on or near a cold (hot) stream. Exchangers are also numbered automatically, in the order in which they are created, and are laid out in the grid diagram. Utilities are created with a single left click on the appropriate stream and are always located downstream of all exchangers on a given stream. Once the initial problem has been defined (topology entered and stream data specified) the user is presented with a spreadsheet-like interface to facilitate the specification of the remaining degrees of freedom. This is particularly useful if raw plant data is used where satisfaction of mass and energy balances is not guaranteed. Using the spreadsheet, the user can arrive at a consistent specification of the initial state of the system. Once all of the HEN data has been entered, the user moves into “retrofit mode”. In this mode, the software will automatically draw the RTD for the current data and topology, and allow the user to shift loads on it. If an additional exchanger is to be added, the user


Figure 29. Input of HEN topology.

Figure 30. Addition of HEX-6 in retrofit mode.

simply draws it on the grid diagram in the same manner as before. The grid is automatically reconfigured, and the new unit will appear on the RTD with a small default load (Figure 30). This exchanger can then be incrementally “grown” by “stretching” its boxes as described in section A.1.3. A.1.2. Dynamic Updating of State and Costs. In order to allow the user to easily investigate the economic incentives for each of the potential modifications, ećlair

automatically recomputes all state information and displays it in a spreadsheet-like interface (Figure 31) every time a change is made. If the user desires, both the grid and retrofit thermodynamic diagrams can be annotated by copying selected cells from the spreadsheet onto them with the mouse. These cells are “active” and may be used exactly as if they were in the spreadsheet window. (This facility is particularly useful when the spreadsheet becomes large and unwieldy.)


Figure 31. Spreadsheet interface.

Values may be editedsdeclared as assumptions or constraintssand the effects of these declarations are seen immediately, as would be the case in a traditional spreadsheet. The main difference is that ećlair uses a technique called constraint propagation (Lakshmanan and Banãres-Alcańtara, 1996; Forbus and de Kleer, 1993) to do the computations, which allows multidirectional computations and supports the notions of assumptions (values which may be retracted as required) and constraints (whose values, once specified, cannot be altered). Constraint propagation languages developed in the field of artificial intelligence require the user to “hardwire” the variables and the arithmetic operators together. E Ä clair provides automatic compilation of algebraic equations into constraint networks, thereby eliminating the overhead typically associated with building models for constraint propagation. An important advantage of using constraint propagation as the method of simulation is that the recomputation effort is minimized: the dependence of variable values on one another is explicitly recorded in a digraph, and so when changes are made, only that subset of the cells whose values need to be updated are recomputed. In a system such as a HEN, where there are often disconnected subsystems, this feature improves performance considerably. In addition to the state information, cost information, including the payback period, is available at all times to the user, so the economic feasibility of a modification is immediately known. A.1.3. Automatic Drawing of the Retrofit Thermodynamic Diagram. The primary reason for the development of the software tool was to facilitate automatic, rapid redrawing of the retrofit thermodynamic diagram. Once a HEN has been completely specified (topology, stream data, degrees of freedom), the user may request an RTD. Loads may be modified through the spreadsheet interface, and these changes are propagated through to the diagram, which is automatically redrawn to reflect the changes. As an added convenience, the software allows the user to modify the load directly on the RTD using the mouse. The vertical “ticks” which represent the boundaries of

Figure 32. Load optimization facility.

the exchangers may be moved using middle mouse; all state and cost information is then immediately updated. A.2. Fine Tuning Designs. A limitation of the “retrofit by inspection” approach is that it relies on the ingenuity of the user and involves a certain amount of trial and error to determine the amount of load that should be shifted onto the individual units in the modified HEN. Clearly, no guarantee of optimality can be given. However, once a set of promising topologies has been identified, the software offers the facility to optimize the loads for each of these configurations. When a load optimization is requested by the user, the software generates the subroutines required by the NLP solver (objective function, Jacobian and Hessian), automatically generating all derivatives symbolically and then compiling, linking, and running the program. There is no overheadsin terms of problem formulation and setupsfrom the user’s point of view. Schematically, this process is depicted in Figure 32. A limitation of classical NLP solvers is that the original exchanger cost functions, which include a fixed installation cost and can sometimes be discontinuous, cannot be used directly. Some approximation of the cost function is necessary before solution. Additionally, as the size of the network increases, this optimization becomes increasingly more expensive, even if system sparsity is exploited. We are currently in the process of developing a stochastic optimization facility based on genetic algorithms to perform the load optimization.


This will allow greater flexibility in the form of the cost functions used, and scale up to larger problems is likely to be more feasible as the running times of these algorithms tend to be linearly dependent on the size of the problem, as opposed to the quadratic (or worse) time complexity of gradient-based approaches (Michalewicz, 1994). Literature Cited (1) Banãres-Alcańtara, R.; King, J. M. P. Design Support Systems for Process EngineeringsIII: Design Rationale as a Requirement for Effective Support. Comput. Chem. Eng., in press. (2) Ciric, A. R.; Floudas, C. A. A. Retrofit Approach for Heat Exchanger Networks. Comput. Chem. Eng. 1989, 13, 703. (3) Ciric, A. R.; Floudas, C. A. A. Mixed Integer Nonlinear Programming Model for Retrofitting Heat Exchanger Networks. Ind. Eng. Chem. Res. 1990, 29, 239. (4) Forbus, K. D.; de Kleer, J. Antecedent Constraint Languages. In Building Problem Solvers; MIT Press: Cambridge, MA, 1993. (5) Korich, R. D. How to Conserve Unit Energy. Hydrocarbon Process. 1982, 7. (6) Lakshmanan, R.; Banãres-Alcańtara, R. PCON: A Language for Propagating Process Constraints. ECOSSE Technical Report TR 1996-02; Department of Chemical Engineering, University of Edinburgh: Edinburgh, U.K., 1996. (7) Linnhoff, B. Pinch AnalysissA State-of-the-Art Overview. Chem. Eng. Res. Des. 1993, 71, 503. (8) Linnhoff, B.; Ahmad, S. Cost Optimum Heat Exchanger Networks, Part I: Minimum Energy and Capital Using Simple Models for Capital Cost. Comput. Chem. Eng. 1990, 14, 729. (9) Linnhoff-March Ltd. Process Integration. Short course, 30 Nov-3 Dec, 1992. (10) Michalewicz, Z. Genetic Algorithms + Data Structures ) Evolution Programs, 2nd ed.; Springer-Verlag: Berlin, 1994. (11) Myers, B. A.; et al. Garnet: Comprehensive Support for Graphical, Highly-interactive User Interfaces. Computer 1990, 23 (11), 71. (12) Saboo, A. K.; Morari, M.; Colberg, R. D. RESHEX: an Interactive Software Package for the Synthesis and Analysis of

Resilient Heat Exchanger NetworkssI. Program Description and Application. Comput. Chem. Eng. 1986, 10, 577. (13) Saboo, A. K.; Morari, M.; Colberg, R. D. RESHEX: an Interactive Software Package for the Synthesis and Analysis of Resilient Heat Exchanger NetworkssII. Discussion of Area Targeting and Network Synthesis Algorithms. Comput. Chem. Eng. 1986, 10, 591. (14) Shokoya, C. G. Retrofit of Heat-exchanger Networks for Debottlenecking and Energy Savings. Ph.D. Dissertation, University of Manchester Institute of Science and Technology, Manchester, UK, 1992. (15) Silangwa, M. Evaluation of Various Surface Area Efficiency Criteria in Heat Exchanger Network Retrofits. M.Sc. Dissertation, University of Manchester Institute of Science and Technology, Manchester, UK, 1986. (16) Tjoe, T. N. Retrofit of Heat Exchanger Networks. Ph.D. Dissertation, University of Manchester Institute of Science and Technology, Manchester, UK, 1986. (17) Tjoe, T. N.; Linnhoff, B. Using Pinch Technology for Process Retrofit. Chem. Eng. 1986, 4. (18) van Reisen, J. L. B.; et al. The Placement of Two-stream and Multi-stream Heat-exchangers in an Existing Network through Path Analysis. Comput. Chem. Eng. 1995, 19 (Suppl.), S143. (19) Yee, T. F.; Grossmann, I. E. Optimisation Model for Structural Modifications in the Retrofit of Heat Exchanger Networks. Found. Comput.-Aided Process Oper. 1987, 403. (20) Yee, T. F.; Grossmann, I. E. A Screening and Optimization Approach for the Retrofit of the Heat Exchanger Networks. Ind. Eng. Chem. Res. 1991, 30, 146. (21) Zoppke-Donaldson, C. A. Tolerance-tube Approach to Sequential Quadratic Programming with Applications. Ph.D. Dissertation, University of Dundee, Dundee, Scotland, 1995.

Received for review July 1, 1996 Revised manuscript received September 18, 1996 Accepted September 19, 1996X IE960372+

X Abstract published in Advance ACS Abstracts, November 1, 1996.

A Novel Visualization Tool for Heat Exchanger Network Retrofit

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