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Hypertargets: a Conceptual Programming approach for the optimisation of industrial heat exchanger networks—Part III. Industrial applications
Chemical Engineering Science 54 (1999) 685—706
Hypertargets: a Conceptual Programming approach for the optimisation of industrial heat exchanger networks—Part III. Industrial applications V. Briones, A.C. Kokossis* Department of Process Integration, University of Manchester Institute of Science and Technology, P.O. Box 88, Manchester M60 1QD, U.K. Received 22 January 1997; revised 7 August 1997; accepted 11 August 1998
Abstract The fundamentals of the grassroots and retrofit technology have been presented in Parts I and II. This part emphasises on common complications associated with deviations from the counter-current heat transfer, and the integration of streams with properties that face significant variations over the perceived range of energy recovery. A number of propositions are made with simple and straightforward modifications to the conceptual models. The modifications save the need to revert to elaborate, simulation-type models that can mire the benefits of the systematic approach. The paper further discusses the application of the technology to problems of special importance such as debottlenecking projects. It explains its potential as an analysis and a decision making tool with an example from the pulp and paper industry. A final test of its potential to remain systematic, rigorous, and fully automated, even against large scale, complicated problems, is illustrated with two Crude Oil distillation applications. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Optimisation; Conceptual programming; Industrial applications; Heat exchanger networks; Bottlenecking
1. Hypertargets for industrial heat exchangers The approach described in Parts I and II of this work, makes use of area targets based on counter-current heat exchangers. However, most industrial heat exchangers are constructed to have shells and tubes, with usual preference for arrangements with 1 shell pass and 2 tube passes. The shell and tube units usually fall short to match the counter-current targets and can deviate up to 25—30% on area and cost. The development of a network under the assumption of ideal counter-current heat exchangers may result in designs with misleadingly underestimated heat transfer area and capital/energy trade-offs. Modelling details about shell and tube exchangers can become quite complicated for the optimisation purposes of the synthesis procedure as they involve non-convex/non-linear expressions that need to be incorporated in the design model in order to correct the heat transfer area. *Corresponding author. Tel.: 0161 200 4393; fax: 0161 236 7439; e-mail: [email protected].
A mathematical programming approach deprived from the decomposition stages of Parts I and II, would have to address these complications with additional modelling equations. Such equations are complicated enough to hamper the successful application of the optimisation technology and they can give rise to a large number of additional local optima. The conceptual stages introduced by the area target and the HEAT/ TAME models, are able to accommodate for the industrial units through straightforward extensions of their formulations. They introduce two basic parameters that reflect on the: (i) deviations from the ideal driving forces, and (ii) number of series shells required for a feasible match. The deviations are expressed in terms of a correction factor, F , applied to the logarithmic mean temper2 ature difference. The number of shells is expressed by a factor, N , which is used in the expressions for capital 1 cost. For each enthalpy interval m, the correction factor F takes the form of an interval/match dependent factor 2 FT , where i and j denote the hot and cold streams, GHK respectively. Heat exchangers with 1 shell pass and 2 tube
0009-2509/99/$ — see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 2 3 7 - 1
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passes can then be incorporated in the target expression of the Area Target Model in the form:
heat transfer coefficients and the problem involves heat exchangers with 1 shell pass and 2 tube passes.
(P1.1b)
i3H K Q2 GHK GHK j3C , CU ! ½ "ATD K K GHK º FT LMTD º FT LMTD2 GH GH GHK GHK GH GHK GHK m3TI Q
(P1.2b)
i3H , HU K K Q2 Q GHK GHK j3C ! ½ "ATD K GHK º FT LMTD2 GH º FT LMTD GH GHK GHK GH GHK GHK m3TI. FT represents the logarithmic mean temperature difGHK ference correction factor for the match between i and j in the temperature interval m. The correction factor is calculated for each potential match and represents a modelling parameter for the problem. In addition to its use during the initial screening stages (Area Target Model for grassroots, HEAT/TAME models for retrofit), the correction factor finds subsequent use at the network optimisation stage. The factor, F , participates in the 2 mathematical formulation of the NLP model in order to correct the heat transfer area expressions, and the number of series shells, N , participates in the cost functions 1 and the design objective. An example of a Crude Oil distillation unit is presented next to illustrate the synthesis problem of an energy recovery network that involves heat exchangers with shells and tubes. Example 1. Table 1 presents the stream and cost data for a problem presented by Briones and Kokossis (1995). The problem has 7 hot and 3 cold process streams with one hot and cold utility. There are large variations in the Table 1 Stream and cost data for Example 1 Stream
FC (kW/K) N
Ts (°C)
Tt (°C)
h (kW/Km)
H1 H2 H3 H4 H5 H6 H7
470.0 825.0 42.42 100.0 357.14 50.0 136.36
140.0 160.0 210.0 260.0 280.0 350.0 380.0
40.0 120.0 45.0 60.0 210.0 170.0 160.0
16.0 2.00 0.90 0.80 0.40 0.10 0.08
C1 C2 C3
826.09 500.0 363.64
270.0 130.0 20.0
385.0 270.0 130.0
0.80 0.44 0.08
450.0 20.0
310.0 25.0
0.10 2.30
HU CU
Note: Exchanger cost (area: m, cost: $)"20,000#1,200 area ; hot utility cost"40 $/kW yr; cooling water cost"4 $/kW yr; 15% interest, life time"5 yr.
(i) Design targets. The Hypertargets for this problem are developed in the range of 15—65°C. Solution streams consist of three primal solutions. Fig. 1a illustrates the Supertargets (Ahmad and Linnhoff, 1989; Linnhoff and Ahmad, 1989) and the solution streams from Hypertargets. Supertargets witness trade-offs around 35°C and a strong minimum at 37°C. They suggest designs should be developed for D¹ within the range of 35—37°C,
and certainly not higher than 37°C as large penalties are expected otherwise. Hypertargets witness a significantly different picture. Instead of a strong minimum, they evidence a relatively flat region from 33—65°C where deviations from Supertargets are as large as 25%. All primal designs within 33—65°C are expected to be competitive choices. (ii) Network development. To facilitate comparisons with designs reported in the literature, the primal solutions are selected for D¹ "35°C. Table 2 summarises
these solutions. Even though with a wrong energy recovery level, the design approach is able to identify the correct trade-offs. Table 3 summarises the designs from the primal solution PS-1 of Table 2. Figure 1b shows the network configuration without constraints for design A. If only arrangements in series are allowed, the design B of Fig. 1c is obtained. Design B features eleven units and a total cost of 8852k$/yr. The utility consumption is increased to 105,473 kW at the benefit of lower cost. With the utility constrained at 100,000 kW, the design C of Fig. 1d is obtained. Design C shows features units in series at the expense of more units. All designs outperform Supertargets. Furthermore, the designs require no evolution as the optimisation procedure is fully automated. Table 4 reports the CPU times required to optimise all models using a slow PC model 486/33 MHz.
2. Hypertargets as an analysis tool This section illustrates how Hypertargets can be used not simply to optimise a synthesis or retrofit problem, but instead analyse the design trade-offs, review the
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Fig. 1. Hypertargets, designs A, B and C for Example 1.
Table 2 Primal solutions for D¹ "35°C (Example 1)
Primal solution and HRAT (°C)
No. units
Total capital cost Exch 1—2 (k$)
Total area Exch 1—2 (m)
Annual cost (k$/yr)
PS1/35 PS2/35 PS3/35
12 12 12
17,297.83 15,966.55 16,324.18
57,424.36 52,318.80 53,802.39
9013.70 8617.79 8724.47
Table 3 Summary of results for Example 1 Solution
No. units
Supertargets
11
Hypertargets Design A Design B Design C
12 11 14
Hot utility (kW)
Annual utility cost (k$/yr)
Annual capital cost (k$/yr)
Annual total cost (k$/yr)
Total cost (%)
90,698
3854.7
5466.3
9321.0
103.4
90,698 105,473 100,000
3854.7 4504.8 4264.0
5159.0 4347.4 4366.5
9013.7 8852.2 8630.5
100.0 98.2 95.7
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Table 4 CPU time(s) for Example 1 (D¹ "15°C)
Area target model
NLP modela
NLP modelb
1 2 3 4 5
15.93 19.89 22.80 46.90 46.86
2.93 3.19 2.36 2.42 1.97
34.57 23.28 13.67 17.41 33.23
5.85 8.73 6.92 8.13 7.97
6 7 8 9 10
58.44 59.92 60.53 64.26 59.76
2.09 2.97 1.92 2.69 3.29
18.84 32.24 27.80 12.14 25.49
10.39 15.44 9.50 11.04 7.91
Solution
NLP modelc
NLP modeld
NLP modele
13.51 6.76 10.87 — —
19.33 21.92 32.85 — —
— — — — —
— — — — —
a
NLP model used to generate an initial feasible solution. Superstructure NLP model of Floudas et al. (1986). c Network optimisation model to remove undesired interconnecting streams. d NLP model to generate an initial feasible solution for the network optimisation. e Network optimisation model to invoke serial and parallel structures. b
solution space available, and evaluate the penalties involved in adopting different design preferences and constraints. Such a task has been supported so far by Pinch analysis methods with the employment of graphical tools and curves that can target the design performance. The criticism against these developments has been aimed at the relative value of the targets as process constraints are ignored and simplifying assumptions are not often valid. Since Hypertargets translate Pinch analysis concepts into mathematical models, their application can account for the majority of the problem specifications and constraints. For the retrofit problem, these may refer to costing elements in addition to the heat transfer area (i.e. various fixed costs to account for piping, pumping, auxiliary equipment), or to retrofitting policies and different scenarios (i.e. investment biased on new units, minimum modification investment, zero investment projects, etc.). The new costing elements of the retrofit problem call upon trade-offs with a minimal thermodynamic content. Such trade-offs are difficult or impossible to review with the use of a thermodynamic method. Instead, the proposed integrated approach can be used to analyse and review designs as it is illustrated with a problem from the pulp and paper industry. The problem involves costing information in terms of fixed costs for each potential unit that account for piping and auxiliary equipment. Hypertargets are used to: (i) analyse design options; (ii) assess the penalties incurred in design constraints; and (iii) evaluate the implications in using ‘shortcut’ design methods instead of a rigorous methodology. Example 2. This problem has been discussed by Carlsson et al. (1993) who presented the stream data for
the existing network. The process consists of nine hot streams, six cold streams with one hot and cold utility. The existing network features nine process/process exchangers, four heaters and one cooler. It requires 11.9 MW for heating and 7.5 MW for cooling. The stream and cost data as well as the existing network can be found in Part II. Carlsson et al. (1993) give costs for each individual match in terms of fixed charge costs that account for piping and auxiliary equipment. Three different scenarios are analysed for this problem: z Scenario A: an unconstrained retrofit case that allows for both reassignments of the existing units and installation of new units. No modification costs are considered. z Scenario B: Modification costs are considered in addition to the costs addressed by Case A. Both reassignments and new units are allowed. z Scenario C: Costing is the same as in Scenario B, but only new units are allowed in the retrofit. Hypertargets are developed for each scenario. The targets from Scenarios B and C are next compared in order to evaluate the importance of constraining the retrofit toward using only new units. The importance of managing modification costs at the targeting stage is finally evaluated with comparison of the Hypertargets with ‘practical’ shortcut approaches commonly used in industrial applications. For Scenario A, the Hypertargets are presented in Fig. 2a and b. The dotted lines in these figure account for the targets that assume the concepts of area efficiency. Both figures prove that regarding area costs the Pinch analysis targets represent good bounds for this problem.
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Fig. 2. Hypertargets for Scenario A.
In reference to Fig. 2a and b, the triad of integers at each level of energy recovery represents total number of units, new units and reassignments required in the retrofit design. As the solution stream is narrow, the available options appear very competitive throughout the entire range. The results from Hypertargets are summarised on Table 5. For Scenario B, the Hypertargets are presented in Fig. 3a and b. Fig. 3a illustrates the solution stream in the energy—area diagram and Fig. 3b shows the trade-offs between capital investment and energy savings. The two streams of Fig. 3b respectively represent costs for heat transfer area and total investment. Although the heat
transfer area costs are still predicted properly by the conventional Pinch analysis method, total cost targets appear different and deviate up to 100% in terms of the area costs. The results of Hypertargets are summarised on Table 6. Fig. 4a and b show the energy—area and investment—savings plot for Scenario C. Table 7 summarises the results of Hypertargets. Figure 4a illustrates the solution stream that relates the area requirement to the energy consumption, and Fig. 4b shows the solutions streams that represent costs for area and total investment. An important feature from Figs. 3b and 4b is that the shape and range of the Hypertargets virtually define
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Table 5 Hypertargets for Scenario A (Example 2) Solution and HRAT (°C)
Cost savings (k$/yr)
New areaa (m)
A1-20 A2-20 A3-20
221.8 221.8 221.8
153.86 173.20 176.63
53.85 60.62 61.82
— — —
A4-18 A5-18 A6-18
284.3 284.3 284.3
183.20 163.97 161.91
64.12 57.39 56.67
A7-15 A8-15 A9-15
378.0 378.0 378.0
273.09 268.77 325.51
A10-10 A11-10 A12-10
534.3 534.3 534.3
611.54 587.66 583.97
a
Area cost (k$)
Fixed cost (k$)
Total cost (k$)
Payback time (yr)
Modifications
New shells
53.85 60.62 61.82
0.24 0.27 0.28
(16,2,1) (16,2,1) (16,2,1)
3 4 4
— — —
64.12 57.39 56.67
0.23 0.20 0.20
(16,2,1) (16,2,1) (16,2,1)
3 4 5
95.58 94.07 113.93
— — —
95.58 94.07 113.93
0.25 0.25 0.30
(17,3,1) (17,3,1) (17,3,1)
4 4 5
214.04 205.68 204.39
— — —
214.04 205.68 204.39
0.40 0.38 0.38
(18,4,1) (18,4,1) (18,4,1)
6 4 6
Installed area: 581 m; modifications: (total number of units, new units, reassignments).
the expected payback times for the project. The payback times range from 0.20—0.40 yr (Scenario A), and from 0.40—0.68 yr (Scenario B). If energy savings are within 221.8—284.3 k$/yr, the range narrows down to 0.20—0.28 yr (Scenario A) and 0.40—0.49 yr (Scenario B). It is worth to note that Pinch analysis misleadingly authorises all payback times, while the pure mathematical programming approaches are unable to review the picture of these trade-offs. The importance of constraining the design problem on only new units is further evaluated by combining the solution streams for Cases B and C in Fig. 4c. The figure illustrates there is virtually no penalty on large energy savings (above 300 k$/yr). Penalties only arise for energy savings within the range of 10—300 k$/yr and only increase by 13% the unconstrained targets. The use of Hypertargets is next illustrated with the assessment of a ‘shortcut’ method that (i) first focuses on area targets by neglecting modification costs, and (ii) considers modification costs at a subsequent stage in addition to the targets already developed. Without consideration of the modification costs, the retrofit targets are essentially the ones shown in Fig. 2 and Table 5 (Scenario A). Adding modification costs to these targets gives rise to the ‘target’ stream of Fig. 5a. The results illustrate that when the modification costs are neglected, the capital investment is underestimated by 77% with respect to the total costs. As a matter of fact, the ‘target’ stream of Fig. 5a is not reflecting on the actual targets. Bringing together Scenario B (targets with modification costs) and the total costs of the ‘shortcut’ approach results in Fig. 5b. Fig. 5b shows that for energy savings lower than 220 k$/yr the targets set by the ‘shortcut’ approach are close to the Hypertargets. In the area of larger energy savings,
however, the ‘shortcut’ approach deviates up to 245% with Hypertargets (Scenario B). The explanation is simple: low energy savings involve no significant changes and modifications. As modifications are required the two methods run completely different courses. The example illustrates the importance of considering modification costs in the retrofit design. Piping and auxiliary equipment can represent high costs that can drive decisions in the design. Neglecting these costs can mislead decisions and result in poor solutions. Hypertargets enable the analysis of multiple scenarios and take charge for the complete picture of the retrofit problem.
3. Stream segmentation and variable heat capacities The targeting elements of the area target and the HEAT/TAME models involve streams of constant heat capacity (CP) values. The assumption is good for the majority of cases justified on the basis of relatively small deviations as far as targeting is concerned. However, in a number of cases the deviations can be large and feature streams that undergo phase changes (vaporisation or condensation). In these cases, the use of a constant CP is an inappropriate simplification and makes modifications of the original approach necessary. Fig. 6a shows an enthalpy—temperature diagram for a single stream that has supply and target temperatures, Ts and Tt, and features a phase change from Tb (bubble point temperature) to Td (dew point temperature). The assumption of a constant CP can be maintained with the linearisation of the ¹"f (H) curve into linear segments. The linearisation can roughly involve the segments
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691
Fig. 3. Hypertargets for Scenario B.
Ts—Tb, Tb—Td and Td—Tt as shown in Fig. 6b. The approximation error depends on the curvature of the ¹"f (H) curve and can be improved with further linearisation as illustrated in Fig. 6c. In general, each segment of Fig. 6c is treated as a separate stream and the design approach is modified as follows: (i) For each stream i segmented in K different parts, a potential match with another stream j is represented by additional integer variables S . G H I (ii) The segmentation variables S coexist with G H I variables y which represent the existence of a match G H
between a hot stream i with a cold stream j. S replace G H I the integer variables y in the constraints of the mathG H ematical formulation, while the variables y participate G H in the design objective. (iii) Segmentation and match variables are connected with the logical constraints: ½ *S , k"1, 2 , K (1) G H G H I The constraints activate a match in case of an active segmentation variable. The new variables S are only needed for the screenG H I ing models (ATM, HEAT and TAME) and do not complicate the network optimisation stages that follow. As to
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Table 6 Hypertargets for Scenario B (Example 2) Solution and HRAT (°C)
Cost savings (k$/yr)
New areaa (m)
B1-20 B2-20 B3-20
221.8 221.8 221.8
153.77 150.46 164.51
53.82 52.66 57.58
B4-18 B5-18 B6-18
284.3 284.3 284.3
183.23 173.34 171.94
B7-15 B8-15 B9-15
378.0 378.0 378.0
B10-10 B11-10 B12-10
534.3 534.3 534.3
a
Area cost (k$)
Fixed cost (k$)
Total cost (k$)
Payback time (yr)
Modifications
New shells
51 51 51
104.82 103.66 108.58
0.47 0.47 0.49
(16,2,1) (16,2,1) (16,2,1)
2 3 3
64.13 60.67 60.18
51 76 76
115.13 136.67 136.18
0.40 0.48 0.48
(16,2,1) (16,2,1) (16,2,1)
3 3 3
286.97 313.89 367.11
100.44 109.86 128.49
118 118 118
218.44 227.86 246.49
0.58 0.60 0.65
(17,3,1) (17,3,1) (17,3,1)
5 4 3
609.66 596.31 583.97
213.38 208.71 204.39
135 135 160
348.38 343.71 364.39
0.65 0.64 0.68
(18,4,1) (18,4,1) (18,4,1)
6 3 6
Installed area: 581 m; modifications: (total number of units, new units, reassignments).
the approximation error involved, segmentation is needed for temperature deviations larger than 2°C on the basis of the ¹—H diagram. In this work, the segments account for errors within 2—3°C. However, streams associated with matches with small driving forces—such as those in subambient processes, should be segmented to account for smaller deviations as large errors can be involved due to the small driving forces. The segmentation and the degree to which it is employed should not be driven only by the need for accuracy in the linearisation. The type of problem (grassroots, retrofit) along with the type of match are equally significant to consider. The application of the technology to various problems has suggested a number of rules that may be observed, relatively safely, to safeguard from unnecessary segmentation. These rules are particularly valid in retrofit problems where, for example, streams ticked-off in single matches do not usually need to be segmented as do the ones serviced by single cooling water utilities at low temperatures. The rules are justified by the obviously ‘optimal’ choices behind these matches that make their detailed modelling redundant. In general, retrofit problems can be further simplified by reviewing the existing layout. Fig. 7a shows a stream from an existing HEN that features variable CP and a complex layout with multiple matches. To facilitate the retrofit task, it is suggested to define stream segments maintaining the existing groups of matches. Fig. 7b illustrates that definition of two stream segments for H1 that allow to maintain the existing layout without involving major complications in the synthesis task. Such aspects related to the variable CP’s and the definition of stream
segments are next illustrated with an industrial problem that addresses the retrofit design of a HEN for a crude oil distillation unit. Example 3. Figure 8 shows the existing network that uses 35.68 MMkcal/h of heating and 24.63 MMkcal/h of cooling. Table 8 provides the stream data and Table 9 the heat transfer area of the existing units. Streams with variations on their CPs are segmented following the guidelines described earlier. Streams H6, H7 and C2 are segmented in two parts; stream C3 is segmented in three parts. Though featuring variable CP’s streams H2, H3, H4, H8, H9, H10, C1 and C4 are handled with a single segment as small temperature deviations are involved. The total number of streams (segments) is thus brought up to 26 including the utilities. The 33 exchangers of Fig. 8 can be simplified to only 25 by grouping matches together. The grouping applies to: (i) unit E11 which is composed by exchangers E11A and E11B connected in parallel; (ii) unit E4 made up by exchangers E4A and E4B connected in parallel; and (iii) unit E3 composed by exchangers E3A and E3B connected in series. The use of units greatly simplifies the layout of the network. For instance, the layout for hot stream H7 is as follows: units E1 and E2 are connected in parallel and followed by units E3, E4, E11 and one cooler which are connected in series. The layout for hot stream H3 has units E5 and E6 connected in series. (i) Design targets. Hypertargets consist of solution streams with three primal solutions. The targeting ranges in 20—34°C. Table 10 shows primal solutions at different P
Fig. 4. Hypertargets for Scenario C, and comparison between Scenarios B and C.
V. Briones, A.C. Kokossis/Chemical Engineering Science 54 (1999) 685—706
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Table 7 Hypertargets for Scenario C (Example 2) Solution and HRAT (°C)
Cost savings (k$/yr)
New areaa (m)
C1-20 C2-20 C3-20
221.8 221.8 221.8
161.77 188.63 207.20
56.62 66.02 72.52
C4-18 C5-18 C6-18
284.3 284.3 284.3
201.09 181.11 168.51
C7-15 C8-15 C9-15
378.0 378.0 378.0
C10-10 C11-10 C12-10
534.3 534.3 534.3
a
Area cost (k$)
Fixed cost (k$)
Total cost (k$)
Payback time (yr)
Modifications
New shells
51 51 51
107.62 117.02 123.52
0.49 0.53 0.56
(16,3,0) (16,3,0) (16,3,0)
2 3 3
70.38 63.39 58.98
51 76 76
121.38 139.39 134.98
0.43 0.49 0.47
(16,3,0) (16,3,0) (16,3,0)
4 2 3
294.91 332.51 375.14
103.22 116.38 131.30
118 118 118
221.22 234.38 249.30
0.59 0.62 0.66
(17,4,0) (17,4,0) (17,4,0)
4 2 2
593.97 617.06 591.97
207.89 215.97 207.19
135 135 160
342.89 350.97 367.19
0.64 0.66 0.69
(18,5,0) (18,5,0) (18,5,0)
4 4 6
Installed area: 581 m; modifications: (total number of units, new units, reassignments).
Fig. 5. ‘Shortcut’ approach and comparison with Scenario B.
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Fig. 6. Variable heat capacity flowrate and its linearisation.
Fig. 7. Stream segmentation taking into account the network layout.
Fig. 8. The existing network for Example 3.
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Table 8 Stream data for Example 3 Stream
FC N (MMcal/h/C)
H1 H2 H3 H4 H5 H6
H7
H8 H9 H10 H11 C1 C2
C3
C4 C5 C6 C7 C8
Ts (°C)
Tt (°C)
Q (MMkcal/h)
h (kcal h C m)
510.204 36.216 150.322 43.596 13.315 * 6.501 4.750 * 117.691 100.871 22.633 19.563 34.107 110.217
123 162 211 261 307 316 316 130 340 340 232 148 125 137.5 106
98.5 49 147.5 49 182 64 130 64 91 232 91 28 29 90 39
12.500 4.092 9.545 9.242 1.664 1.523 1.209 0.314 26.933 12.711 14.223 2.716 1.878 1.620 7.385
1300 750 750—1020 663—1000 585 497
254.011 * 246.431 444.773 * 208.049 211.676 256.159 50.745 4414.394 33.813 2754.545 33.434
40 137.5 137.5 175.5 181 181 189 215 39 147 37 124 62
142 185.5 175.5 185.5 354 189 215 354 97 148 67 125 107
25.909 13.812 9.364 4.447 42.774 1.664 5.503 35.606 2.943 4.414 1.014 2.755 1.505
501—883 541—579
HU CU
1800 20
308 30
200—314
621 1170 1300 1300
496—425
1160—1170 1170 1170 1250 1300 5000 1000
*Streams with variable CP and more than one segment.
Table 9 Heat transfer areas for the existing process/process exchangers (Example 3) Exchanger
Area (m)
Exchanger
Area (m)
E1 E2 E3 A&B E4 A&B E5 A&B
107.7 252.7 581.8 800.8 586.4
E11 A&B E12 E13 E14 E15
740.2 61.4 70.5 37.9 75.8
E6 A&B E7 A&B E8 E9 A&B E10
346.2 82.4 253.0 282.6 170.5
E16 E17 A&B
19.7 794.7
D¹ and Fig. 9 plots Hypertargets and conventional
Pinch analysis targets (Hypertargets also provide the minimum modifications required at each level of energy recovery). For low energy savings, the targets involve
a combination of options. Design A1 does not need a new unit while designs A2 and A3 require one additional unit. For medium and high energy savings all options include one new unit. Each of the designs A1—A9 required approximately 5 CPU min on a Pentium 90 MHz PC. (ii) Network development. For low energy savings, the primal design A1 is used to illustrate the network development. According to Hypertargets, the retrofit is possible without new units and reassignments. The existing network can be improved by simply relocating existing units. The network optimisation model is further used to remove undesired splits. All hot and cold process streams are forced to series layout with the exception of streams H7 and C1 that already feature splits in the network. Fig. 10 shows the retrofitted network and Tables 11 and 12 summarise its performance. The retrofitted network suggests the relocation of two units, E1 and E3, and requires additional shells for only three of the existing units. The total new area requirement is around 894 m.
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V. Briones, A.C. Kokossis/Chemical Engineering Science 54 (1999) 685—706 Table 10 Hypertargets for Example 3 Scenario
Design
HRAT (°C)
Hot utility (MMkcal/h)
Energy reduction (MMkcal/h)
New areaa (m)
Modificationsb
Low energy savings
A1 A2 A3
34 34 34
33.572 33.572 33.572
2.108 2.108 2.108
930.3 1165.9 1138.6
(25,0,0) (26,1,0) (26,1,0)
Medium energy savings
A4 A5 A6
28 28 28
31.543 31.543 31.543
4.137 4.137 4.137
2090.9 2197.7 2403.0
(26,1,0) (26,1,0) (26,1,0)
High energy savings
A7 A8 A9
20 20 20
29.142 29.142 29.142
6.538 6.538 6.538
4659.8 4906.8 4026.5
(26,1,0) (26,1,0) (26,1,0)
a
Additional area required; existing process/process area"5264.30 m. Modifications: (total number of units, new units, reassignments).
b
For medium energy savings, the primal design A4 is used to illustrate the network development. This primal design is used with the objective to remove all splits except the ones associated with streams H7 and C1. Fig. 11 shows the retrofit design that involves the relocation of units E1 and E2 to a lower temperature level, and requires the installation of one new unit for the match between H11 and C1. The energy savings are increased to 4.394 MMkcal/h, but six of the existing units require new shells. The total new area requirement is around 2145 m. Tables 11 and 12 summarise its performance. The networks of the retrofit designs B1 and B4 have consumed 3 CPU min on a Pentium 90 MHz PC.
4. Debottlenecking and multiple matches Throughput changes account for a large number of retrofit problems in the form of debottlenecking applications. Unlike reactors and separators that are usually designed to accommodate for higher flows than the original throughput, heat exchanger networks are not often designed for such contingencies. Consequently, an increase in the throughput often causes a bottleneck in the HEN and the network need to be redesigned and debottlenecked. Typical industrial examples of debottlenecking projects relate to preheat trains of crude oil distillation units where increases in the throughput bottleneck the existing heater. As investments on new fired-heaters are uneconomic, the process heating requirement are considered fixed at the maximum capacity of the heater. Debottlenecking projects are generally driven by the investment costs. For heating requirements lower than the maximum heater capacity, energy savings are smaller
Fig. 9. Hypertargets for Example 3.
than the required capital investment, resulting in larger payback times. As the heating requirements are specified, debottlenecking problems make area—energy trade-off curves redundant. The retrofit problem needs only to consider area and modifications. Though not a general trend, the more the modifications the lower the area requirement. In cases adequate cost information is available, the design can be addressed as a single cost minimisation problem and Hypertargets can readily account for the analysis of trade-offs. In most problems, however, either costing for modifications is not available or costing involves uncertainties that limit the value of
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Fig. 10. Design B1 of Example 3.
Table 11 Retrofit designs for Example 3 Final retrofit design
Design
Hot utility (MMkcal/h)
Energy savings (MMkcal/h)
New areaa (m)
New units
New shells
Relocated units
Low energy savings Medium energy savings
B1 B4
33.258 31.212
2.424 4.468
893.94 2144.7
0 1
3 6
2 2
a
Additional area required; existing process/process area"5264.30 m It refers to existing units that require additional area (i.e. new shells).
b
the optimal solution. Alternatively, a design procedure can be established to minimise network modifications spanning over numbers of installed new units. The steps of such an approach should: (i) minimise installed area excluding options for installed new units (using HEAT and TAME models); (ii) optimise the retrofitted network (using the network optimisation model); and (iii) increase the number of new units and iterate with (i). Stage (i) usually involves several options—as a matter of fact, a very large number is quite typical for industrial problems. With the use of the HEAT and TAME models, however, these options can be properly ranked and screened to the few that appear of most interest (i.e. more promising in terms of the installed area required for a given number of modifications). In most industrial problems, iterations from (i)—(ii) do not have to consider more than two to five new units. Stage (ii) assumes particular attention and requires an extended superstructure that exploits multiple matches. As described in Part I of this work, the network optimisation is proposed
Table 12 Existing units that require new shells (Example 3) Design
Match
Exchangers
Low energy savings
H7-C7 H4-C1 H7-C1
E1 E10 E11A&B
Total
4 exchangers
H7-C7 H7-C5 H7-C3 H3-C2 H4-C1 H1-C1
E1 E2 E3A E5A&B E10 E17A&B
Total
8 exchangers
Medium energy savings
upon an augmented superstructure with additional units defaulted by utility exchangers. These units facilitate layout constraints that account for the network
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Fig. 11. Design B4 of Example 3.
Table 13 Stream and cost data for Example 4 Stream
FC (kW/C) N
Ts (°C)
Tt (°C)
h (kW/C m)
H1 H2 H3 H4 H5 H6
470.00 750.00 42.42 100.00 357.14 55.56 48.00 145.46 125.00
140 160 210 260 280 350 170 380 160
40 120 45 60 210 170 45 160 80
0.2 1.5 0.8 0.7 1.0 0.5 0.4 0.4 0.3
391.67 500.00 826.09
10 130 270
130 270 385
0.5 0.7 0.9
500 20
499 40
0.8 0.8
H7 C1
HU CU
Note: Exchanger cost (area:m, cost:$)"8600#670;(area);0.83, (area)400 m per shell). Steam cost"57.6 $/kW yr; cooling water cost"9.6 $/kW yr; 0% interest.
simplification. As simplified networks are developed, stream splits are removed at the expense of penalties in the heat transfer area. Critical matches can be identified when the removal of a split involves a large penalty in area. Such debottlenecking matches appear as duplicate options in the augmented superstructure and are optimised to account for multiple matches in the retrofitted network. The previous propositions are illustrated with an example that addresses the retrofit of a HEN for a debottlenecking project. This problem is solved in two steps. First, trade-offs are explored between area and
modifications and primal solutions are developed. The area targets are compared with targets using Tjoe’s approach (1986) and the area matrix method proposed by Shokoya and Kotjabasakis (1991). In the second step, the primal solutions are translated into retrofitted networks. Example 4. The example is a debottlenecking project first published by Ahmad et al. (1989), and later studied by Shokoya and Kotjabasakis (1991), Asante (1996) and Nielsen et al. (1996). Tables 13 and 14 show the stream
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Table 14 Existing network for Example 4 Hot stream
Cold stream
Match
Heat load (kW)
1 2 3
CU 1 1
3 1
47,000 30,000 7000
4 4 5
1 CU 1
5
6 6 7 7 7 HU
Existing HT area (m)
174 255
7
10,000 10,000 25,000
605 1733
1 1 1
4 2 8
6000 10,000 18,000
133 595 1092
1 CU 1
6
11,000 13,000 95,000
1288
Note: Total process/process area "5875 m.
and cost data of the existing operation. Figure 12 presents the layout of the existing network that has a total existing area of 7445 m (process/process area of 5875 m). The crude feed, heavy oil and residue have been segmented linearly to account for the significant changes in their heat transfer properties. The hot utility duty required to achieve the target temperature of the crude cold stream is 95 MW. A furnace supplies the heat with maximum capacity 100 MW. A cost-beneficial project is to be undertaken where the crude distillation unit is required to handle a 10% increase in the throughput. Such an increase would increase the heat demand of the furnace to 106.7 MW. The retrofit task is therefore to remove the bottleneck by reducing the hot utility requirement to 100 MW.
(i) Design targets. The utility requirement is fixed and Hypertargets are required for D¹ "38°C
(Q "99.6 MW). Four primal solutions are selected. To & enable comparisons no reassignments are allowed in the analysis. Initially, solutions are explored for minimum modifications. Only one primal solution exists without new units. In this case, the network is retrofitted using splits and relocating some of the existing exchangers. The remaining three solutions require installation of one new unit. Table 15 lists the primal solutions and previously reported results (Tjoe, 1986; Shokoya and Kotjabasakis 1991). In all cases, Hypertargets improve the targets. (ii) Network development. The network development is using the primal solutions A1 and A2. A1 requires 1368 m heat transfer area and no installation of new units.
Table 15 Hypertarget for Example 4 (HRAT"38°C) Targeting method
Cost savings (k$/yr)
New area (m)
Area cost (k$)
Payback time (yr)
Modifications
New shells
Constant a Incremental a
463.83 463.83
2142 1732
580 472
1.25 1.02
— —
— —
Area Matrix
463.83
1554
412
0.89
—
—
Hypertargets A1 A2 A3 A4
463.83 463.83 463.83 463.83
1368 1321 1015 1631
324 333 261 370
0.70 0.72 0.56 0.80
(12,0,0) (13,1,0) (13,1,0) (13,1,0)
4 4 3 3
a
Installed area: 5875 m; modifications: (total number of units, new units, reassignments).
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Fig. 12. Existing HEN for Example 4.
Fig. 14. Design B2 of Example 4.
Fig. 13. Design B1 of Example 4.
Figure 13 illustrates the design B1 produced with the network optimisation model. It features a low area requirement (1337 m), involves two splits for the cold stream and requires new shells for five existing units. Further simplifications of this network (i.e. removal of the split for exchanger 4) lead to large penalties in the heat transfer area. A2 requires the installation of a new unit. The simplified network with the new approach leads to design B2 of Fig. 14. Design B2 involves one split for the crude cold stream, and requires new shells for five of the existing units. Its total area requirement is 1265 m. Table 16 compares the results with the solutions reported in the literature. It includes results from Ahmad et al. (1989), Shokoya and Kotjabasakis (1991), Asante (1986) and Nielsen et al. (1996). With the only exception of the approach by Nielsen et al. (1996), all previous methods are evolutionary. The design by Ahmad et al. (1989) requires the largest area and number of new units,
Table 16 Design networks for Example 4 Final retrofit design
HRAT (°C)
New area (m)
Area cost (k$)
Payback time (yr)
Modifications
New units
Splits
New shells
Ahmad et al. Shokoya Asante and Zhu Asante and Zhu Nielsen et al. B1 B2
38 38 38 38 &38 38 38
1990 1474 1974 1265 1164 1337 1265
525 425 472 341 320 334 341
1.13 0.92 1.02 0.74 0.69 0.72 0.74
(15,3,1) (14,2,0) (12,0,0) (13,1,0) (16,4,0) (12,0,0) (13,1,0)
3 2 0 1 4 0 1
2 1 1 1 1 2 1
2 4 6 5 2 5 5
Installed area: 5875 m; modifications: (total number of units, new units, reassignments).
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Table 17 Stream data for Example 5 Stream
FC N (MMcal/h/C)
Ts (°C)
Tt (°C)
Q (MMkcal/h)
H1
* 106.061 89.489 306.061 147.727 84.848 218.811 * 69.805 28.117 11.341 9.629 * 23.705 19.879 * 11.977 9.787 16.712 27.356
362 362 173 105 173 250 105 192 192 150 278 118 278 278 177 339 339 196 46 121
77 173 77 73 138 211 28 46 150 46 118 76 54 177 54 60 196 60 40 54
28.636 20.045 8.591 9.794 5.170 3.309 16.848 5.856 2.932 2.924 1.815 0.405 4.839 2.394 2.445 3.044 1.713 1.331 0.100 1.833
* 169.388 212.652 300.924 30.833 253.788 1820.455 48.962 122.0 3372.727 2559.848 1689.394 1537.879 946.970 27.273
18 18 121 234.5 205 257 185 37 169 218 137 111 119 96 21
364 121 234.5 364 228 265 186 68 170 219 138 112 120 97 88
80.553 17.447 24.136 38.970 0.709 2.030 1.820 1.518 0.122 3.373 2.560 1.689 1.538 0.947 1.827
500 10
499 11
H2 H3 H4 H5 H6
H7 H8 H9
H10
H11 H12 C1
C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 HU CU
h (kcal/h C m)
430—139
1126 461 347 1000 897—870
663 663 663
497—400
860 2000 307—640
520 1000 1250 1200 1240 1200 1200 1875 1875 1875 2000 5000 1000
*Streams with variable CP.
Table 18 Existing network for Example 5 Exchanger
Area (m)
Exchanger
Area (m)
E1 E2 E3 E4 E5 E6
124.24 118.18 181.06 282.58 121.21 1220.46
E13 E14 E15 E16 E17 E18
23.79 137.88 87.88 62.53 139.39 1153.79
E7 E8 E9 E10 E11 E12
456.82 87.12 311.36 142.42 1140.91 2.81
E19 E20 E21 E22 E23 E24
95.45 55.53 1425.76 13.06 234.09 246.97
and involves one reassignment. The design by Shokoya and Kotjabasakis (1991) is better though it is still not matching the area target and requires two new units. The first design by Asante (1996) features minimum modifications, but involves a high penalty for the area. The second design features very low area requirement, a single new unit and a single split. The solution by Nielsen et al. (1996), though with the lowest area and cost, requires four new units and includes a new cooler.
5. Industrial challenges of size and complexity The ability of the new approach to cope with industrial problems is finally illustrated with a selected application
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V. Briones, A.C. Kokossis/Chemical Engineering Science 54 (1999) 685—706
Fig. 15. The existing heat exchanger network for Example 5.
Table 19 Hypertargets for Example 5 Scenario
Design
HRAT (°C)
Hot utility (MMkcal/h)
Energy reduction (MMkcal/h)
Low energy savings
A1 A2 A3
40 40 40
41.05 41.05 41.05
1.0 1.0 1.0
Medium energy savings
A4 A5 A6
33 33 33
39.126 39.126 39.126
High energy savings
A7 A8 A9
25 25 25
37.285 37.285 37.285
a
New area (m)
Modifications
722.7 453.8 525.0
(32,1,0) (32,1,0) (32,1,0)
2.924 2.924 2.924
1002.3 1318.2 840.9
(32,1,0) (32,1,0) (32,1,0)
4.765 4.765 4.765
1708.3 2465.9 2543.9
(33,2,0) (33,2,0) (33,2,0)
Additional area required; existing process/process area"7865.30 m. Modifications: (total number of units, new units, reassignments).
b
Table 20 Retrofit designs for Example 5 Final retrofit design
Hot utility (MMkcal/h)
Energy savings (MMkcal/h)
New area (m)
New units
New shells
Units resequenced
B6 C6
39.09 39.09
2.962 2.962
1220.5 1102.3
1 1
11 10
1 2
a
Additional area required; Existing process/process area"7865.30 m. It refers to existing units that require additional area (i.e. new shells).
b
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V. Briones, A.C. Kokossis/Chemical Engineering Science 54 (1999) 685—706
involve additional costs that should be considered when a retrofit design is developed. Example 5. Table 17 lists the stream data for the problem and Fig. 15 presents the existing network. It uses 42.05 MMkcal/h of heating and 24.97 MMkcal/h of cooling. The heat transfer areas are given on Table 18. Streams with variable CPs are segmented following the guidelines described earlier. Streams H1, H6, H9 and H10 are segmented in two parts, stream C1 in three parts, and streams H5 and C3 are handled with a single segment. There are 32 streams (segments and utilities included) and 31 matches. (i) Design targets. Hypertargets are developed in the range 25—40°C. Table 19 shows the primal solutions. Hypertargets are plotted in Fig. 16 with curves of constant area efficiency. For low energy savings, designs A1—A3 require the installation of one new unit. A4—A6 are developed for medium energy savings. For high energy savings designs A7—A9 are obtained; they both require one additional unit. Designs A1—A9 demanded about 15 CPU min on a Pentium/90 MHz.
Fig. 16. Hypertargets for Example 5.
that features streams with variable CP, and a large number of streams and matches. The existing network features a complex layout that involves various splits and bypasses. Special attention is paid to these streams to minimise modifications. The addition or elimination of splits, the relocation of existing exchangers, the installation of new units and the reassignment of existing units,
(ii) Network development. The retrofit design is developed for medium energy savings using primal design A6. All streams that feature series arrangement are selected to remain in series. The optimisation identifies relocation opportunities and develops the networks B6 and C6 that are presented in Figs 17 and 18, respectively. Design B6 suggests the relocation of exchanger E5, the installation of one new unit for matching H6 and C1, and
Fig. 17. Design B6 of Example 5.
V. Briones, A.C. Kokossis/Chemical Engineering Science 54 (1999) 685—706
705
Fig. 18. Design C6 of Example 5.
the elimination of one split for H7. The area requirement is about 1220 m. Design C6 is similar to design B6 except that it relocates one more unit (E2) and its area requirement is reduced to 1100 m. In summary, the first solution requires fewer modifications but more area. The second solution involves relocation of one more existing unit, but requires less heat transfer area. Table 20 summarises the results for the two final designs. 6. Conclusions The paper illustrated the implementation of new grassroots and retrofit technology in industrial applications. The technology enabled a systematic framework for the implementation of rigorous optimisation methods in problems of size and complexity often encountered in practice. The tasks of targeting and network optimisation have been accommodated with Conceptual Programming models, which unlike simulation-like developments loaded with details, are conceptually rich formulations that enable screening and scoping. The vast array of industrial aspects calls upon the extension and improvement of these models, as well as the advancement of the underlying methodology. At this stage, there is a strong evidence for the Conceptual Programming approach and current research is in progress for its extension to other areas in process design. Acknowledgements The authors would like to acknowledge the joint financial support provided by CONACyT (Me´xico) and
Instituto Mexicano del Petro´leo, and the Department of Process Integration at UMIST. The second author remains indebted to Prof. B. Linnhoff for his encouragement to launch research in this area. His experience in the field helped to attain confidence for the potential and the usefulness of the developed approach. Linnhoff March Ltd. has provided invaluable links to test and validate the research. Both authors are especially grateful to Ms. L. Tantimuratha for helping in revising the manuscript and preparing its final version.
References Ahmad, S., & Linnhoff, B. (1989). Supertargeting: Different process structures for different economics. ¹rans. ASME, J. Energy Resources ¹echnol., 111(3), 131—136. Ahmad, S., Polley, G.T., & Petela, E.A. (1989). Retrofit of heat exchanger networks subject to pressure drop constraints. Paper 34a, A.I.Ch.E. Spring Meeting, Houston, April. Asante, N.D.K., & Zhu, X.X. (1996). An automated approach for heat exchanger retrofit featuring minimal topology modifications. Comput. Chem. Engng, 20 (Suppl), S7—S12. Briones, V., & Kokossis, A. (1995). Optimisation strategies for heat exchanger network design. A.I.Ch.E. Spring National Meeting, Houston, 19—23 March. Carlsson, A., Franck, P.-A., & Berntsson, T. (1993). Design better heat exchanger network retrofits. Chem. Engng Progress, 89(3), 87—96. Floudas, C.A., Ciric, A.R., & Grossmann, I.E. (1986). Automatic synthesis of optimum heat exchanger network configurations. A.I.Ch.E. J. 32, 276—290. Linnhoff, B., & Ahmad, S. (1989). Supertargeting: Optimum synthesis of energy management systems. ¹rans. ASME, J. Energy Resources ¹echnol., 111(3), 121—130.
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Nielsen, J.S., Hansen, M.W., & Joergensen, S. (1996). Heat exchanger network modelling framework for optimal design and retrofiting. Comput. Chem. Engng, 20, (Suppl.), S249—S254. Shokoya, C.G., & Kotjabasakis, E. (1991). A new targeting procedure for the retrofit of heat exchanger networks. Paper Presented at the International Conference, Athens, Greece, June. Tjoe, T.N. (1986). Retrofit of heat exchanger networks. Ph.D. thesis. UMIST, England.
Appendix A—Correction factors for 1—2 Exchangers F and N are expressed in terms of 2 1 D¹ CP " R" CP D¹ D¹ P" D¹ where
(C1) (C2)
(R#1 ln[(1!½)/(1!R ½)] F " 2 2!½ (R#1!(R#1) (R!1) ln 2!½ (R#1#(R#1)
(C5)
where 1![(1!RP)/(1!P)] ,1 ½" . R![(1!RP)/(1!P)] ,1
(C6)
If R"1 then
P N" 1 (1!P)
1#(2/2!X \ X \
½(2 F " 2 2!½(2!(2) (1!½) ln 2!½(2#(2)
(C7)
(C8)
where
D¹ "¹!¹ A A D¹ "¹!¹ F F D¹ "¹!¹. F A If RO1 then
P ½" N #P!PN 1 1
ln[(1!R P)/(1!P)] N" 1 ln(Z)
(C3)
R#1#(R#1!2 X R \ Z" R#1#(R#1!2 X \
(C4)
(C9)
N is the number of 1—2 shells in series and F is the 1 2 logarithmic mean temperature correction factor. It is recommended X "0.9 for a single 1—2 shell, but the \ chosen value of X is required to be the maximum that \ should be observed in each 1—2 shell of a multishell unit in order for each such section to display at least the corresponding F . 2
Hypertargets: a Conceptual Programming approach for the optimisation of industrial heat exchanger networks—Part III. Industrial applications V. Briones, A.C. Kokossis* Department of Process Integration, University of Manchester Institute of Science and Technology, P.O. Box 88, Manchester M60 1QD, U.K. Received 22 January 1997; revised 7 August 1997; accepted 11 August 1998
Abstract The fundamentals of the grassroots and retrofit technology have been presented in Parts I and II. This part emphasises on common complications associated with deviations from the counter-current heat transfer, and the integration of streams with properties that face significant variations over the perceived range of energy recovery. A number of propositions are made with simple and straightforward modifications to the conceptual models. The modifications save the need to revert to elaborate, simulation-type models that can mire the benefits of the systematic approach. The paper further discusses the application of the technology to problems of special importance such as debottlenecking projects. It explains its potential as an analysis and a decision making tool with an example from the pulp and paper industry. A final test of its potential to remain systematic, rigorous, and fully automated, even against large scale, complicated problems, is illustrated with two Crude Oil distillation applications. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Optimisation; Conceptual programming; Industrial applications; Heat exchanger networks; Bottlenecking
1. Hypertargets for industrial heat exchangers The approach described in Parts I and II of this work, makes use of area targets based on counter-current heat exchangers. However, most industrial heat exchangers are constructed to have shells and tubes, with usual preference for arrangements with 1 shell pass and 2 tube passes. The shell and tube units usually fall short to match the counter-current targets and can deviate up to 25—30% on area and cost. The development of a network under the assumption of ideal counter-current heat exchangers may result in designs with misleadingly underestimated heat transfer area and capital/energy trade-offs. Modelling details about shell and tube exchangers can become quite complicated for the optimisation purposes of the synthesis procedure as they involve non-convex/non-linear expressions that need to be incorporated in the design model in order to correct the heat transfer area. *Corresponding author. Tel.: 0161 200 4393; fax: 0161 236 7439; e-mail: [email protected].
A mathematical programming approach deprived from the decomposition stages of Parts I and II, would have to address these complications with additional modelling equations. Such equations are complicated enough to hamper the successful application of the optimisation technology and they can give rise to a large number of additional local optima. The conceptual stages introduced by the area target and the HEAT/ TAME models, are able to accommodate for the industrial units through straightforward extensions of their formulations. They introduce two basic parameters that reflect on the: (i) deviations from the ideal driving forces, and (ii) number of series shells required for a feasible match. The deviations are expressed in terms of a correction factor, F , applied to the logarithmic mean temper2 ature difference. The number of shells is expressed by a factor, N , which is used in the expressions for capital 1 cost. For each enthalpy interval m, the correction factor F takes the form of an interval/match dependent factor 2 FT , where i and j denote the hot and cold streams, GHK respectively. Heat exchangers with 1 shell pass and 2 tube
0009-2509/99/$ — see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 2 3 7 - 1
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passes can then be incorporated in the target expression of the Area Target Model in the form:
heat transfer coefficients and the problem involves heat exchangers with 1 shell pass and 2 tube passes.
(P1.1b)
i3H K Q2 GHK GHK j3C , CU ! ½ "ATD K K GHK º FT LMTD º FT LMTD2 GH GH GHK GHK GH GHK GHK m3TI Q
(P1.2b)
i3H , HU K K Q2 Q GHK GHK j3C ! ½ "ATD K GHK º FT LMTD2 GH º FT LMTD GH GHK GHK GH GHK GHK m3TI. FT represents the logarithmic mean temperature difGHK ference correction factor for the match between i and j in the temperature interval m. The correction factor is calculated for each potential match and represents a modelling parameter for the problem. In addition to its use during the initial screening stages (Area Target Model for grassroots, HEAT/TAME models for retrofit), the correction factor finds subsequent use at the network optimisation stage. The factor, F , participates in the 2 mathematical formulation of the NLP model in order to correct the heat transfer area expressions, and the number of series shells, N , participates in the cost functions 1 and the design objective. An example of a Crude Oil distillation unit is presented next to illustrate the synthesis problem of an energy recovery network that involves heat exchangers with shells and tubes. Example 1. Table 1 presents the stream and cost data for a problem presented by Briones and Kokossis (1995). The problem has 7 hot and 3 cold process streams with one hot and cold utility. There are large variations in the Table 1 Stream and cost data for Example 1 Stream
FC (kW/K) N
Ts (°C)
Tt (°C)
h (kW/Km)
H1 H2 H3 H4 H5 H6 H7
470.0 825.0 42.42 100.0 357.14 50.0 136.36
140.0 160.0 210.0 260.0 280.0 350.0 380.0
40.0 120.0 45.0 60.0 210.0 170.0 160.0
16.0 2.00 0.90 0.80 0.40 0.10 0.08
C1 C2 C3
826.09 500.0 363.64
270.0 130.0 20.0
385.0 270.0 130.0
0.80 0.44 0.08
450.0 20.0
310.0 25.0
0.10 2.30
HU CU
Note: Exchanger cost (area: m, cost: $)"20,000#1,200 area ; hot utility cost"40 $/kW yr; cooling water cost"4 $/kW yr; 15% interest, life time"5 yr.
(i) Design targets. The Hypertargets for this problem are developed in the range of 15—65°C. Solution streams consist of three primal solutions. Fig. 1a illustrates the Supertargets (Ahmad and Linnhoff, 1989; Linnhoff and Ahmad, 1989) and the solution streams from Hypertargets. Supertargets witness trade-offs around 35°C and a strong minimum at 37°C. They suggest designs should be developed for D¹ within the range of 35—37°C,
and certainly not higher than 37°C as large penalties are expected otherwise. Hypertargets witness a significantly different picture. Instead of a strong minimum, they evidence a relatively flat region from 33—65°C where deviations from Supertargets are as large as 25%. All primal designs within 33—65°C are expected to be competitive choices. (ii) Network development. To facilitate comparisons with designs reported in the literature, the primal solutions are selected for D¹ "35°C. Table 2 summarises
these solutions. Even though with a wrong energy recovery level, the design approach is able to identify the correct trade-offs. Table 3 summarises the designs from the primal solution PS-1 of Table 2. Figure 1b shows the network configuration without constraints for design A. If only arrangements in series are allowed, the design B of Fig. 1c is obtained. Design B features eleven units and a total cost of 8852k$/yr. The utility consumption is increased to 105,473 kW at the benefit of lower cost. With the utility constrained at 100,000 kW, the design C of Fig. 1d is obtained. Design C shows features units in series at the expense of more units. All designs outperform Supertargets. Furthermore, the designs require no evolution as the optimisation procedure is fully automated. Table 4 reports the CPU times required to optimise all models using a slow PC model 486/33 MHz.
2. Hypertargets as an analysis tool This section illustrates how Hypertargets can be used not simply to optimise a synthesis or retrofit problem, but instead analyse the design trade-offs, review the
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Fig. 1. Hypertargets, designs A, B and C for Example 1.
Table 2 Primal solutions for D¹ "35°C (Example 1)
Primal solution and HRAT (°C)
No. units
Total capital cost Exch 1—2 (k$)
Total area Exch 1—2 (m)
Annual cost (k$/yr)
PS1/35 PS2/35 PS3/35
12 12 12
17,297.83 15,966.55 16,324.18
57,424.36 52,318.80 53,802.39
9013.70 8617.79 8724.47
Table 3 Summary of results for Example 1 Solution
No. units
Supertargets
11
Hypertargets Design A Design B Design C
12 11 14
Hot utility (kW)
Annual utility cost (k$/yr)
Annual capital cost (k$/yr)
Annual total cost (k$/yr)
Total cost (%)
90,698
3854.7
5466.3
9321.0
103.4
90,698 105,473 100,000
3854.7 4504.8 4264.0
5159.0 4347.4 4366.5
9013.7 8852.2 8630.5
100.0 98.2 95.7
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Table 4 CPU time(s) for Example 1 (D¹ "15°C)
Area target model
NLP modela
NLP modelb
1 2 3 4 5
15.93 19.89 22.80 46.90 46.86
2.93 3.19 2.36 2.42 1.97
34.57 23.28 13.67 17.41 33.23
5.85 8.73 6.92 8.13 7.97
6 7 8 9 10
58.44 59.92 60.53 64.26 59.76
2.09 2.97 1.92 2.69 3.29
18.84 32.24 27.80 12.14 25.49
10.39 15.44 9.50 11.04 7.91
Solution
NLP modelc
NLP modeld
NLP modele
13.51 6.76 10.87 — —
19.33 21.92 32.85 — —
— — — — —
— — — — —
a
NLP model used to generate an initial feasible solution. Superstructure NLP model of Floudas et al. (1986). c Network optimisation model to remove undesired interconnecting streams. d NLP model to generate an initial feasible solution for the network optimisation. e Network optimisation model to invoke serial and parallel structures. b
solution space available, and evaluate the penalties involved in adopting different design preferences and constraints. Such a task has been supported so far by Pinch analysis methods with the employment of graphical tools and curves that can target the design performance. The criticism against these developments has been aimed at the relative value of the targets as process constraints are ignored and simplifying assumptions are not often valid. Since Hypertargets translate Pinch analysis concepts into mathematical models, their application can account for the majority of the problem specifications and constraints. For the retrofit problem, these may refer to costing elements in addition to the heat transfer area (i.e. various fixed costs to account for piping, pumping, auxiliary equipment), or to retrofitting policies and different scenarios (i.e. investment biased on new units, minimum modification investment, zero investment projects, etc.). The new costing elements of the retrofit problem call upon trade-offs with a minimal thermodynamic content. Such trade-offs are difficult or impossible to review with the use of a thermodynamic method. Instead, the proposed integrated approach can be used to analyse and review designs as it is illustrated with a problem from the pulp and paper industry. The problem involves costing information in terms of fixed costs for each potential unit that account for piping and auxiliary equipment. Hypertargets are used to: (i) analyse design options; (ii) assess the penalties incurred in design constraints; and (iii) evaluate the implications in using ‘shortcut’ design methods instead of a rigorous methodology. Example 2. This problem has been discussed by Carlsson et al. (1993) who presented the stream data for
the existing network. The process consists of nine hot streams, six cold streams with one hot and cold utility. The existing network features nine process/process exchangers, four heaters and one cooler. It requires 11.9 MW for heating and 7.5 MW for cooling. The stream and cost data as well as the existing network can be found in Part II. Carlsson et al. (1993) give costs for each individual match in terms of fixed charge costs that account for piping and auxiliary equipment. Three different scenarios are analysed for this problem: z Scenario A: an unconstrained retrofit case that allows for both reassignments of the existing units and installation of new units. No modification costs are considered. z Scenario B: Modification costs are considered in addition to the costs addressed by Case A. Both reassignments and new units are allowed. z Scenario C: Costing is the same as in Scenario B, but only new units are allowed in the retrofit. Hypertargets are developed for each scenario. The targets from Scenarios B and C are next compared in order to evaluate the importance of constraining the retrofit toward using only new units. The importance of managing modification costs at the targeting stage is finally evaluated with comparison of the Hypertargets with ‘practical’ shortcut approaches commonly used in industrial applications. For Scenario A, the Hypertargets are presented in Fig. 2a and b. The dotted lines in these figure account for the targets that assume the concepts of area efficiency. Both figures prove that regarding area costs the Pinch analysis targets represent good bounds for this problem.
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Fig. 2. Hypertargets for Scenario A.
In reference to Fig. 2a and b, the triad of integers at each level of energy recovery represents total number of units, new units and reassignments required in the retrofit design. As the solution stream is narrow, the available options appear very competitive throughout the entire range. The results from Hypertargets are summarised on Table 5. For Scenario B, the Hypertargets are presented in Fig. 3a and b. Fig. 3a illustrates the solution stream in the energy—area diagram and Fig. 3b shows the trade-offs between capital investment and energy savings. The two streams of Fig. 3b respectively represent costs for heat transfer area and total investment. Although the heat
transfer area costs are still predicted properly by the conventional Pinch analysis method, total cost targets appear different and deviate up to 100% in terms of the area costs. The results of Hypertargets are summarised on Table 6. Fig. 4a and b show the energy—area and investment—savings plot for Scenario C. Table 7 summarises the results of Hypertargets. Figure 4a illustrates the solution stream that relates the area requirement to the energy consumption, and Fig. 4b shows the solutions streams that represent costs for area and total investment. An important feature from Figs. 3b and 4b is that the shape and range of the Hypertargets virtually define
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Table 5 Hypertargets for Scenario A (Example 2) Solution and HRAT (°C)
Cost savings (k$/yr)
New areaa (m)
A1-20 A2-20 A3-20
221.8 221.8 221.8
153.86 173.20 176.63
53.85 60.62 61.82
— — —
A4-18 A5-18 A6-18
284.3 284.3 284.3
183.20 163.97 161.91
64.12 57.39 56.67
A7-15 A8-15 A9-15
378.0 378.0 378.0
273.09 268.77 325.51
A10-10 A11-10 A12-10
534.3 534.3 534.3
611.54 587.66 583.97
a
Area cost (k$)
Fixed cost (k$)
Total cost (k$)
Payback time (yr)
Modifications
New shells
53.85 60.62 61.82
0.24 0.27 0.28
(16,2,1) (16,2,1) (16,2,1)
3 4 4
— — —
64.12 57.39 56.67
0.23 0.20 0.20
(16,2,1) (16,2,1) (16,2,1)
3 4 5
95.58 94.07 113.93
— — —
95.58 94.07 113.93
0.25 0.25 0.30
(17,3,1) (17,3,1) (17,3,1)
4 4 5
214.04 205.68 204.39
— — —
214.04 205.68 204.39
0.40 0.38 0.38
(18,4,1) (18,4,1) (18,4,1)
6 4 6
Installed area: 581 m; modifications: (total number of units, new units, reassignments).
the expected payback times for the project. The payback times range from 0.20—0.40 yr (Scenario A), and from 0.40—0.68 yr (Scenario B). If energy savings are within 221.8—284.3 k$/yr, the range narrows down to 0.20—0.28 yr (Scenario A) and 0.40—0.49 yr (Scenario B). It is worth to note that Pinch analysis misleadingly authorises all payback times, while the pure mathematical programming approaches are unable to review the picture of these trade-offs. The importance of constraining the design problem on only new units is further evaluated by combining the solution streams for Cases B and C in Fig. 4c. The figure illustrates there is virtually no penalty on large energy savings (above 300 k$/yr). Penalties only arise for energy savings within the range of 10—300 k$/yr and only increase by 13% the unconstrained targets. The use of Hypertargets is next illustrated with the assessment of a ‘shortcut’ method that (i) first focuses on area targets by neglecting modification costs, and (ii) considers modification costs at a subsequent stage in addition to the targets already developed. Without consideration of the modification costs, the retrofit targets are essentially the ones shown in Fig. 2 and Table 5 (Scenario A). Adding modification costs to these targets gives rise to the ‘target’ stream of Fig. 5a. The results illustrate that when the modification costs are neglected, the capital investment is underestimated by 77% with respect to the total costs. As a matter of fact, the ‘target’ stream of Fig. 5a is not reflecting on the actual targets. Bringing together Scenario B (targets with modification costs) and the total costs of the ‘shortcut’ approach results in Fig. 5b. Fig. 5b shows that for energy savings lower than 220 k$/yr the targets set by the ‘shortcut’ approach are close to the Hypertargets. In the area of larger energy savings,
however, the ‘shortcut’ approach deviates up to 245% with Hypertargets (Scenario B). The explanation is simple: low energy savings involve no significant changes and modifications. As modifications are required the two methods run completely different courses. The example illustrates the importance of considering modification costs in the retrofit design. Piping and auxiliary equipment can represent high costs that can drive decisions in the design. Neglecting these costs can mislead decisions and result in poor solutions. Hypertargets enable the analysis of multiple scenarios and take charge for the complete picture of the retrofit problem.
3. Stream segmentation and variable heat capacities The targeting elements of the area target and the HEAT/TAME models involve streams of constant heat capacity (CP) values. The assumption is good for the majority of cases justified on the basis of relatively small deviations as far as targeting is concerned. However, in a number of cases the deviations can be large and feature streams that undergo phase changes (vaporisation or condensation). In these cases, the use of a constant CP is an inappropriate simplification and makes modifications of the original approach necessary. Fig. 6a shows an enthalpy—temperature diagram for a single stream that has supply and target temperatures, Ts and Tt, and features a phase change from Tb (bubble point temperature) to Td (dew point temperature). The assumption of a constant CP can be maintained with the linearisation of the ¹"f (H) curve into linear segments. The linearisation can roughly involve the segments
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691
Fig. 3. Hypertargets for Scenario B.
Ts—Tb, Tb—Td and Td—Tt as shown in Fig. 6b. The approximation error depends on the curvature of the ¹"f (H) curve and can be improved with further linearisation as illustrated in Fig. 6c. In general, each segment of Fig. 6c is treated as a separate stream and the design approach is modified as follows: (i) For each stream i segmented in K different parts, a potential match with another stream j is represented by additional integer variables S . G H I (ii) The segmentation variables S coexist with G H I variables y which represent the existence of a match G H
between a hot stream i with a cold stream j. S replace G H I the integer variables y in the constraints of the mathG H ematical formulation, while the variables y participate G H in the design objective. (iii) Segmentation and match variables are connected with the logical constraints: ½ *S , k"1, 2 , K (1) G H G H I The constraints activate a match in case of an active segmentation variable. The new variables S are only needed for the screenG H I ing models (ATM, HEAT and TAME) and do not complicate the network optimisation stages that follow. As to
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Table 6 Hypertargets for Scenario B (Example 2) Solution and HRAT (°C)
Cost savings (k$/yr)
New areaa (m)
B1-20 B2-20 B3-20
221.8 221.8 221.8
153.77 150.46 164.51
53.82 52.66 57.58
B4-18 B5-18 B6-18
284.3 284.3 284.3
183.23 173.34 171.94
B7-15 B8-15 B9-15
378.0 378.0 378.0
B10-10 B11-10 B12-10
534.3 534.3 534.3
a
Area cost (k$)
Fixed cost (k$)
Total cost (k$)
Payback time (yr)
Modifications
New shells
51 51 51
104.82 103.66 108.58
0.47 0.47 0.49
(16,2,1) (16,2,1) (16,2,1)
2 3 3
64.13 60.67 60.18
51 76 76
115.13 136.67 136.18
0.40 0.48 0.48
(16,2,1) (16,2,1) (16,2,1)
3 3 3
286.97 313.89 367.11
100.44 109.86 128.49
118 118 118
218.44 227.86 246.49
0.58 0.60 0.65
(17,3,1) (17,3,1) (17,3,1)
5 4 3
609.66 596.31 583.97
213.38 208.71 204.39
135 135 160
348.38 343.71 364.39
0.65 0.64 0.68
(18,4,1) (18,4,1) (18,4,1)
6 3 6
Installed area: 581 m; modifications: (total number of units, new units, reassignments).
the approximation error involved, segmentation is needed for temperature deviations larger than 2°C on the basis of the ¹—H diagram. In this work, the segments account for errors within 2—3°C. However, streams associated with matches with small driving forces—such as those in subambient processes, should be segmented to account for smaller deviations as large errors can be involved due to the small driving forces. The segmentation and the degree to which it is employed should not be driven only by the need for accuracy in the linearisation. The type of problem (grassroots, retrofit) along with the type of match are equally significant to consider. The application of the technology to various problems has suggested a number of rules that may be observed, relatively safely, to safeguard from unnecessary segmentation. These rules are particularly valid in retrofit problems where, for example, streams ticked-off in single matches do not usually need to be segmented as do the ones serviced by single cooling water utilities at low temperatures. The rules are justified by the obviously ‘optimal’ choices behind these matches that make their detailed modelling redundant. In general, retrofit problems can be further simplified by reviewing the existing layout. Fig. 7a shows a stream from an existing HEN that features variable CP and a complex layout with multiple matches. To facilitate the retrofit task, it is suggested to define stream segments maintaining the existing groups of matches. Fig. 7b illustrates that definition of two stream segments for H1 that allow to maintain the existing layout without involving major complications in the synthesis task. Such aspects related to the variable CP’s and the definition of stream
segments are next illustrated with an industrial problem that addresses the retrofit design of a HEN for a crude oil distillation unit. Example 3. Figure 8 shows the existing network that uses 35.68 MMkcal/h of heating and 24.63 MMkcal/h of cooling. Table 8 provides the stream data and Table 9 the heat transfer area of the existing units. Streams with variations on their CPs are segmented following the guidelines described earlier. Streams H6, H7 and C2 are segmented in two parts; stream C3 is segmented in three parts. Though featuring variable CP’s streams H2, H3, H4, H8, H9, H10, C1 and C4 are handled with a single segment as small temperature deviations are involved. The total number of streams (segments) is thus brought up to 26 including the utilities. The 33 exchangers of Fig. 8 can be simplified to only 25 by grouping matches together. The grouping applies to: (i) unit E11 which is composed by exchangers E11A and E11B connected in parallel; (ii) unit E4 made up by exchangers E4A and E4B connected in parallel; and (iii) unit E3 composed by exchangers E3A and E3B connected in series. The use of units greatly simplifies the layout of the network. For instance, the layout for hot stream H7 is as follows: units E1 and E2 are connected in parallel and followed by units E3, E4, E11 and one cooler which are connected in series. The layout for hot stream H3 has units E5 and E6 connected in series. (i) Design targets. Hypertargets consist of solution streams with three primal solutions. The targeting ranges in 20—34°C. Table 10 shows primal solutions at different P
Fig. 4. Hypertargets for Scenario C, and comparison between Scenarios B and C.
V. Briones, A.C. Kokossis/Chemical Engineering Science 54 (1999) 685—706
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Table 7 Hypertargets for Scenario C (Example 2) Solution and HRAT (°C)
Cost savings (k$/yr)
New areaa (m)
C1-20 C2-20 C3-20
221.8 221.8 221.8
161.77 188.63 207.20
56.62 66.02 72.52
C4-18 C5-18 C6-18
284.3 284.3 284.3
201.09 181.11 168.51
C7-15 C8-15 C9-15
378.0 378.0 378.0
C10-10 C11-10 C12-10
534.3 534.3 534.3
a
Area cost (k$)
Fixed cost (k$)
Total cost (k$)
Payback time (yr)
Modifications
New shells
51 51 51
107.62 117.02 123.52
0.49 0.53 0.56
(16,3,0) (16,3,0) (16,3,0)
2 3 3
70.38 63.39 58.98
51 76 76
121.38 139.39 134.98
0.43 0.49 0.47
(16,3,0) (16,3,0) (16,3,0)
4 2 3
294.91 332.51 375.14
103.22 116.38 131.30
118 118 118
221.22 234.38 249.30
0.59 0.62 0.66
(17,4,0) (17,4,0) (17,4,0)
4 2 2
593.97 617.06 591.97
207.89 215.97 207.19
135 135 160
342.89 350.97 367.19
0.64 0.66 0.69
(18,5,0) (18,5,0) (18,5,0)
4 4 6
Installed area: 581 m; modifications: (total number of units, new units, reassignments).
Fig. 5. ‘Shortcut’ approach and comparison with Scenario B.
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Fig. 6. Variable heat capacity flowrate and its linearisation.
Fig. 7. Stream segmentation taking into account the network layout.
Fig. 8. The existing network for Example 3.
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Table 8 Stream data for Example 3 Stream
FC N (MMcal/h/C)
H1 H2 H3 H4 H5 H6
H7
H8 H9 H10 H11 C1 C2
C3
C4 C5 C6 C7 C8
Ts (°C)
Tt (°C)
Q (MMkcal/h)
h (kcal h C m)
510.204 36.216 150.322 43.596 13.315 * 6.501 4.750 * 117.691 100.871 22.633 19.563 34.107 110.217
123 162 211 261 307 316 316 130 340 340 232 148 125 137.5 106
98.5 49 147.5 49 182 64 130 64 91 232 91 28 29 90 39
12.500 4.092 9.545 9.242 1.664 1.523 1.209 0.314 26.933 12.711 14.223 2.716 1.878 1.620 7.385
1300 750 750—1020 663—1000 585 497
254.011 * 246.431 444.773 * 208.049 211.676 256.159 50.745 4414.394 33.813 2754.545 33.434
40 137.5 137.5 175.5 181 181 189 215 39 147 37 124 62
142 185.5 175.5 185.5 354 189 215 354 97 148 67 125 107
25.909 13.812 9.364 4.447 42.774 1.664 5.503 35.606 2.943 4.414 1.014 2.755 1.505
501—883 541—579
HU CU
1800 20
308 30
200—314
621 1170 1300 1300
496—425
1160—1170 1170 1170 1250 1300 5000 1000
*Streams with variable CP and more than one segment.
Table 9 Heat transfer areas for the existing process/process exchangers (Example 3) Exchanger
Area (m)
Exchanger
Area (m)
E1 E2 E3 A&B E4 A&B E5 A&B
107.7 252.7 581.8 800.8 586.4
E11 A&B E12 E13 E14 E15
740.2 61.4 70.5 37.9 75.8
E6 A&B E7 A&B E8 E9 A&B E10
346.2 82.4 253.0 282.6 170.5
E16 E17 A&B
19.7 794.7
D¹ and Fig. 9 plots Hypertargets and conventional
Pinch analysis targets (Hypertargets also provide the minimum modifications required at each level of energy recovery). For low energy savings, the targets involve
a combination of options. Design A1 does not need a new unit while designs A2 and A3 require one additional unit. For medium and high energy savings all options include one new unit. Each of the designs A1—A9 required approximately 5 CPU min on a Pentium 90 MHz PC. (ii) Network development. For low energy savings, the primal design A1 is used to illustrate the network development. According to Hypertargets, the retrofit is possible without new units and reassignments. The existing network can be improved by simply relocating existing units. The network optimisation model is further used to remove undesired splits. All hot and cold process streams are forced to series layout with the exception of streams H7 and C1 that already feature splits in the network. Fig. 10 shows the retrofitted network and Tables 11 and 12 summarise its performance. The retrofitted network suggests the relocation of two units, E1 and E3, and requires additional shells for only three of the existing units. The total new area requirement is around 894 m.
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Design
HRAT (°C)
Hot utility (MMkcal/h)
Energy reduction (MMkcal/h)
New areaa (m)
Modificationsb
Low energy savings
A1 A2 A3
34 34 34
33.572 33.572 33.572
2.108 2.108 2.108
930.3 1165.9 1138.6
(25,0,0) (26,1,0) (26,1,0)
Medium energy savings
A4 A5 A6
28 28 28
31.543 31.543 31.543
4.137 4.137 4.137
2090.9 2197.7 2403.0
(26,1,0) (26,1,0) (26,1,0)
High energy savings
A7 A8 A9
20 20 20
29.142 29.142 29.142
6.538 6.538 6.538
4659.8 4906.8 4026.5
(26,1,0) (26,1,0) (26,1,0)
a
Additional area required; existing process/process area"5264.30 m. Modifications: (total number of units, new units, reassignments).
b
For medium energy savings, the primal design A4 is used to illustrate the network development. This primal design is used with the objective to remove all splits except the ones associated with streams H7 and C1. Fig. 11 shows the retrofit design that involves the relocation of units E1 and E2 to a lower temperature level, and requires the installation of one new unit for the match between H11 and C1. The energy savings are increased to 4.394 MMkcal/h, but six of the existing units require new shells. The total new area requirement is around 2145 m. Tables 11 and 12 summarise its performance. The networks of the retrofit designs B1 and B4 have consumed 3 CPU min on a Pentium 90 MHz PC.
4. Debottlenecking and multiple matches Throughput changes account for a large number of retrofit problems in the form of debottlenecking applications. Unlike reactors and separators that are usually designed to accommodate for higher flows than the original throughput, heat exchanger networks are not often designed for such contingencies. Consequently, an increase in the throughput often causes a bottleneck in the HEN and the network need to be redesigned and debottlenecked. Typical industrial examples of debottlenecking projects relate to preheat trains of crude oil distillation units where increases in the throughput bottleneck the existing heater. As investments on new fired-heaters are uneconomic, the process heating requirement are considered fixed at the maximum capacity of the heater. Debottlenecking projects are generally driven by the investment costs. For heating requirements lower than the maximum heater capacity, energy savings are smaller
Fig. 9. Hypertargets for Example 3.
than the required capital investment, resulting in larger payback times. As the heating requirements are specified, debottlenecking problems make area—energy trade-off curves redundant. The retrofit problem needs only to consider area and modifications. Though not a general trend, the more the modifications the lower the area requirement. In cases adequate cost information is available, the design can be addressed as a single cost minimisation problem and Hypertargets can readily account for the analysis of trade-offs. In most problems, however, either costing for modifications is not available or costing involves uncertainties that limit the value of
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Fig. 10. Design B1 of Example 3.
Table 11 Retrofit designs for Example 3 Final retrofit design
Design
Hot utility (MMkcal/h)
Energy savings (MMkcal/h)
New areaa (m)
New units
New shells
Relocated units
Low energy savings Medium energy savings
B1 B4
33.258 31.212
2.424 4.468
893.94 2144.7
0 1
3 6
2 2
a
Additional area required; existing process/process area"5264.30 m It refers to existing units that require additional area (i.e. new shells).
b
the optimal solution. Alternatively, a design procedure can be established to minimise network modifications spanning over numbers of installed new units. The steps of such an approach should: (i) minimise installed area excluding options for installed new units (using HEAT and TAME models); (ii) optimise the retrofitted network (using the network optimisation model); and (iii) increase the number of new units and iterate with (i). Stage (i) usually involves several options—as a matter of fact, a very large number is quite typical for industrial problems. With the use of the HEAT and TAME models, however, these options can be properly ranked and screened to the few that appear of most interest (i.e. more promising in terms of the installed area required for a given number of modifications). In most industrial problems, iterations from (i)—(ii) do not have to consider more than two to five new units. Stage (ii) assumes particular attention and requires an extended superstructure that exploits multiple matches. As described in Part I of this work, the network optimisation is proposed
Table 12 Existing units that require new shells (Example 3) Design
Match
Exchangers
Low energy savings
H7-C7 H4-C1 H7-C1
E1 E10 E11A&B
Total
4 exchangers
H7-C7 H7-C5 H7-C3 H3-C2 H4-C1 H1-C1
E1 E2 E3A E5A&B E10 E17A&B
Total
8 exchangers
Medium energy savings
upon an augmented superstructure with additional units defaulted by utility exchangers. These units facilitate layout constraints that account for the network
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Fig. 11. Design B4 of Example 3.
Table 13 Stream and cost data for Example 4 Stream
FC (kW/C) N
Ts (°C)
Tt (°C)
h (kW/C m)
H1 H2 H3 H4 H5 H6
470.00 750.00 42.42 100.00 357.14 55.56 48.00 145.46 125.00
140 160 210 260 280 350 170 380 160
40 120 45 60 210 170 45 160 80
0.2 1.5 0.8 0.7 1.0 0.5 0.4 0.4 0.3
391.67 500.00 826.09
10 130 270
130 270 385
0.5 0.7 0.9
500 20
499 40
0.8 0.8
H7 C1
HU CU
Note: Exchanger cost (area:m, cost:$)"8600#670;(area);0.83, (area)400 m per shell). Steam cost"57.6 $/kW yr; cooling water cost"9.6 $/kW yr; 0% interest.
simplification. As simplified networks are developed, stream splits are removed at the expense of penalties in the heat transfer area. Critical matches can be identified when the removal of a split involves a large penalty in area. Such debottlenecking matches appear as duplicate options in the augmented superstructure and are optimised to account for multiple matches in the retrofitted network. The previous propositions are illustrated with an example that addresses the retrofit of a HEN for a debottlenecking project. This problem is solved in two steps. First, trade-offs are explored between area and
modifications and primal solutions are developed. The area targets are compared with targets using Tjoe’s approach (1986) and the area matrix method proposed by Shokoya and Kotjabasakis (1991). In the second step, the primal solutions are translated into retrofitted networks. Example 4. The example is a debottlenecking project first published by Ahmad et al. (1989), and later studied by Shokoya and Kotjabasakis (1991), Asante (1996) and Nielsen et al. (1996). Tables 13 and 14 show the stream
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Table 14 Existing network for Example 4 Hot stream
Cold stream
Match
Heat load (kW)
1 2 3
CU 1 1
3 1
47,000 30,000 7000
4 4 5
1 CU 1
5
6 6 7 7 7 HU
Existing HT area (m)
174 255
7
10,000 10,000 25,000
605 1733
1 1 1
4 2 8
6000 10,000 18,000
133 595 1092
1 CU 1
6
11,000 13,000 95,000
1288
Note: Total process/process area "5875 m.
and cost data of the existing operation. Figure 12 presents the layout of the existing network that has a total existing area of 7445 m (process/process area of 5875 m). The crude feed, heavy oil and residue have been segmented linearly to account for the significant changes in their heat transfer properties. The hot utility duty required to achieve the target temperature of the crude cold stream is 95 MW. A furnace supplies the heat with maximum capacity 100 MW. A cost-beneficial project is to be undertaken where the crude distillation unit is required to handle a 10% increase in the throughput. Such an increase would increase the heat demand of the furnace to 106.7 MW. The retrofit task is therefore to remove the bottleneck by reducing the hot utility requirement to 100 MW.
(i) Design targets. The utility requirement is fixed and Hypertargets are required for D¹ "38°C
(Q "99.6 MW). Four primal solutions are selected. To & enable comparisons no reassignments are allowed in the analysis. Initially, solutions are explored for minimum modifications. Only one primal solution exists without new units. In this case, the network is retrofitted using splits and relocating some of the existing exchangers. The remaining three solutions require installation of one new unit. Table 15 lists the primal solutions and previously reported results (Tjoe, 1986; Shokoya and Kotjabasakis 1991). In all cases, Hypertargets improve the targets. (ii) Network development. The network development is using the primal solutions A1 and A2. A1 requires 1368 m heat transfer area and no installation of new units.
Table 15 Hypertarget for Example 4 (HRAT"38°C) Targeting method
Cost savings (k$/yr)
New area (m)
Area cost (k$)
Payback time (yr)
Modifications
New shells
Constant a Incremental a
463.83 463.83
2142 1732
580 472
1.25 1.02
— —
— —
Area Matrix
463.83
1554
412
0.89
—
—
Hypertargets A1 A2 A3 A4
463.83 463.83 463.83 463.83
1368 1321 1015 1631
324 333 261 370
0.70 0.72 0.56 0.80
(12,0,0) (13,1,0) (13,1,0) (13,1,0)
4 4 3 3
a
Installed area: 5875 m; modifications: (total number of units, new units, reassignments).
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V. Briones, A.C. Kokossis/Chemical Engineering Science 54 (1999) 685—706
Fig. 12. Existing HEN for Example 4.
Fig. 14. Design B2 of Example 4.
Fig. 13. Design B1 of Example 4.
Figure 13 illustrates the design B1 produced with the network optimisation model. It features a low area requirement (1337 m), involves two splits for the cold stream and requires new shells for five existing units. Further simplifications of this network (i.e. removal of the split for exchanger 4) lead to large penalties in the heat transfer area. A2 requires the installation of a new unit. The simplified network with the new approach leads to design B2 of Fig. 14. Design B2 involves one split for the crude cold stream, and requires new shells for five of the existing units. Its total area requirement is 1265 m. Table 16 compares the results with the solutions reported in the literature. It includes results from Ahmad et al. (1989), Shokoya and Kotjabasakis (1991), Asante (1986) and Nielsen et al. (1996). With the only exception of the approach by Nielsen et al. (1996), all previous methods are evolutionary. The design by Ahmad et al. (1989) requires the largest area and number of new units,
Table 16 Design networks for Example 4 Final retrofit design
HRAT (°C)
New area (m)
Area cost (k$)
Payback time (yr)
Modifications
New units
Splits
New shells
Ahmad et al. Shokoya Asante and Zhu Asante and Zhu Nielsen et al. B1 B2
38 38 38 38 &38 38 38
1990 1474 1974 1265 1164 1337 1265
525 425 472 341 320 334 341
1.13 0.92 1.02 0.74 0.69 0.72 0.74
(15,3,1) (14,2,0) (12,0,0) (13,1,0) (16,4,0) (12,0,0) (13,1,0)
3 2 0 1 4 0 1
2 1 1 1 1 2 1
2 4 6 5 2 5 5
Installed area: 5875 m; modifications: (total number of units, new units, reassignments).
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Table 17 Stream data for Example 5 Stream
FC N (MMcal/h/C)
Ts (°C)
Tt (°C)
Q (MMkcal/h)
H1
* 106.061 89.489 306.061 147.727 84.848 218.811 * 69.805 28.117 11.341 9.629 * 23.705 19.879 * 11.977 9.787 16.712 27.356
362 362 173 105 173 250 105 192 192 150 278 118 278 278 177 339 339 196 46 121
77 173 77 73 138 211 28 46 150 46 118 76 54 177 54 60 196 60 40 54
28.636 20.045 8.591 9.794 5.170 3.309 16.848 5.856 2.932 2.924 1.815 0.405 4.839 2.394 2.445 3.044 1.713 1.331 0.100 1.833
* 169.388 212.652 300.924 30.833 253.788 1820.455 48.962 122.0 3372.727 2559.848 1689.394 1537.879 946.970 27.273
18 18 121 234.5 205 257 185 37 169 218 137 111 119 96 21
364 121 234.5 364 228 265 186 68 170 219 138 112 120 97 88
80.553 17.447 24.136 38.970 0.709 2.030 1.820 1.518 0.122 3.373 2.560 1.689 1.538 0.947 1.827
500 10
499 11
H2 H3 H4 H5 H6
H7 H8 H9
H10
H11 H12 C1
C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 HU CU
h (kcal/h C m)
430—139
1126 461 347 1000 897—870
663 663 663
497—400
860 2000 307—640
520 1000 1250 1200 1240 1200 1200 1875 1875 1875 2000 5000 1000
*Streams with variable CP.
Table 18 Existing network for Example 5 Exchanger
Area (m)
Exchanger
Area (m)
E1 E2 E3 E4 E5 E6
124.24 118.18 181.06 282.58 121.21 1220.46
E13 E14 E15 E16 E17 E18
23.79 137.88 87.88 62.53 139.39 1153.79
E7 E8 E9 E10 E11 E12
456.82 87.12 311.36 142.42 1140.91 2.81
E19 E20 E21 E22 E23 E24
95.45 55.53 1425.76 13.06 234.09 246.97
and involves one reassignment. The design by Shokoya and Kotjabasakis (1991) is better though it is still not matching the area target and requires two new units. The first design by Asante (1996) features minimum modifications, but involves a high penalty for the area. The second design features very low area requirement, a single new unit and a single split. The solution by Nielsen et al. (1996), though with the lowest area and cost, requires four new units and includes a new cooler.
5. Industrial challenges of size and complexity The ability of the new approach to cope with industrial problems is finally illustrated with a selected application
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V. Briones, A.C. Kokossis/Chemical Engineering Science 54 (1999) 685—706
Fig. 15. The existing heat exchanger network for Example 5.
Table 19 Hypertargets for Example 5 Scenario
Design
HRAT (°C)
Hot utility (MMkcal/h)
Energy reduction (MMkcal/h)
Low energy savings
A1 A2 A3
40 40 40
41.05 41.05 41.05
1.0 1.0 1.0
Medium energy savings
A4 A5 A6
33 33 33
39.126 39.126 39.126
High energy savings
A7 A8 A9
25 25 25
37.285 37.285 37.285
a
New area (m)
Modifications
722.7 453.8 525.0
(32,1,0) (32,1,0) (32,1,0)
2.924 2.924 2.924
1002.3 1318.2 840.9
(32,1,0) (32,1,0) (32,1,0)
4.765 4.765 4.765
1708.3 2465.9 2543.9
(33,2,0) (33,2,0) (33,2,0)
Additional area required; existing process/process area"7865.30 m. Modifications: (total number of units, new units, reassignments).
b
Table 20 Retrofit designs for Example 5 Final retrofit design
Hot utility (MMkcal/h)
Energy savings (MMkcal/h)
New area (m)
New units
New shells
Units resequenced
B6 C6
39.09 39.09
2.962 2.962
1220.5 1102.3
1 1
11 10
1 2
a
Additional area required; Existing process/process area"7865.30 m. It refers to existing units that require additional area (i.e. new shells).
b
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V. Briones, A.C. Kokossis/Chemical Engineering Science 54 (1999) 685—706
involve additional costs that should be considered when a retrofit design is developed. Example 5. Table 17 lists the stream data for the problem and Fig. 15 presents the existing network. It uses 42.05 MMkcal/h of heating and 24.97 MMkcal/h of cooling. The heat transfer areas are given on Table 18. Streams with variable CPs are segmented following the guidelines described earlier. Streams H1, H6, H9 and H10 are segmented in two parts, stream C1 in three parts, and streams H5 and C3 are handled with a single segment. There are 32 streams (segments and utilities included) and 31 matches. (i) Design targets. Hypertargets are developed in the range 25—40°C. Table 19 shows the primal solutions. Hypertargets are plotted in Fig. 16 with curves of constant area efficiency. For low energy savings, designs A1—A3 require the installation of one new unit. A4—A6 are developed for medium energy savings. For high energy savings designs A7—A9 are obtained; they both require one additional unit. Designs A1—A9 demanded about 15 CPU min on a Pentium/90 MHz.
Fig. 16. Hypertargets for Example 5.
that features streams with variable CP, and a large number of streams and matches. The existing network features a complex layout that involves various splits and bypasses. Special attention is paid to these streams to minimise modifications. The addition or elimination of splits, the relocation of existing exchangers, the installation of new units and the reassignment of existing units,
(ii) Network development. The retrofit design is developed for medium energy savings using primal design A6. All streams that feature series arrangement are selected to remain in series. The optimisation identifies relocation opportunities and develops the networks B6 and C6 that are presented in Figs 17 and 18, respectively. Design B6 suggests the relocation of exchanger E5, the installation of one new unit for matching H6 and C1, and
Fig. 17. Design B6 of Example 5.
V. Briones, A.C. Kokossis/Chemical Engineering Science 54 (1999) 685—706
705
Fig. 18. Design C6 of Example 5.
the elimination of one split for H7. The area requirement is about 1220 m. Design C6 is similar to design B6 except that it relocates one more unit (E2) and its area requirement is reduced to 1100 m. In summary, the first solution requires fewer modifications but more area. The second solution involves relocation of one more existing unit, but requires less heat transfer area. Table 20 summarises the results for the two final designs. 6. Conclusions The paper illustrated the implementation of new grassroots and retrofit technology in industrial applications. The technology enabled a systematic framework for the implementation of rigorous optimisation methods in problems of size and complexity often encountered in practice. The tasks of targeting and network optimisation have been accommodated with Conceptual Programming models, which unlike simulation-like developments loaded with details, are conceptually rich formulations that enable screening and scoping. The vast array of industrial aspects calls upon the extension and improvement of these models, as well as the advancement of the underlying methodology. At this stage, there is a strong evidence for the Conceptual Programming approach and current research is in progress for its extension to other areas in process design. Acknowledgements The authors would like to acknowledge the joint financial support provided by CONACyT (Me´xico) and
Instituto Mexicano del Petro´leo, and the Department of Process Integration at UMIST. The second author remains indebted to Prof. B. Linnhoff for his encouragement to launch research in this area. His experience in the field helped to attain confidence for the potential and the usefulness of the developed approach. Linnhoff March Ltd. has provided invaluable links to test and validate the research. Both authors are especially grateful to Ms. L. Tantimuratha for helping in revising the manuscript and preparing its final version.
References Ahmad, S., & Linnhoff, B. (1989). Supertargeting: Different process structures for different economics. ¹rans. ASME, J. Energy Resources ¹echnol., 111(3), 131—136. Ahmad, S., Polley, G.T., & Petela, E.A. (1989). Retrofit of heat exchanger networks subject to pressure drop constraints. Paper 34a, A.I.Ch.E. Spring Meeting, Houston, April. Asante, N.D.K., & Zhu, X.X. (1996). An automated approach for heat exchanger retrofit featuring minimal topology modifications. Comput. Chem. Engng, 20 (Suppl), S7—S12. Briones, V., & Kokossis, A. (1995). Optimisation strategies for heat exchanger network design. A.I.Ch.E. Spring National Meeting, Houston, 19—23 March. Carlsson, A., Franck, P.-A., & Berntsson, T. (1993). Design better heat exchanger network retrofits. Chem. Engng Progress, 89(3), 87—96. Floudas, C.A., Ciric, A.R., & Grossmann, I.E. (1986). Automatic synthesis of optimum heat exchanger network configurations. A.I.Ch.E. J. 32, 276—290. Linnhoff, B., & Ahmad, S. (1989). Supertargeting: Optimum synthesis of energy management systems. ¹rans. ASME, J. Energy Resources ¹echnol., 111(3), 121—130.
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Nielsen, J.S., Hansen, M.W., & Joergensen, S. (1996). Heat exchanger network modelling framework for optimal design and retrofiting. Comput. Chem. Engng, 20, (Suppl.), S249—S254. Shokoya, C.G., & Kotjabasakis, E. (1991). A new targeting procedure for the retrofit of heat exchanger networks. Paper Presented at the International Conference, Athens, Greece, June. Tjoe, T.N. (1986). Retrofit of heat exchanger networks. Ph.D. thesis. UMIST, England.
Appendix A—Correction factors for 1—2 Exchangers F and N are expressed in terms of 2 1 D¹ CP " R" CP D¹ D¹ P" D¹ where
(C1) (C2)
(R#1 ln[(1!½)/(1!R ½)] F " 2 2!½ (R#1!(R#1) (R!1) ln 2!½ (R#1#(R#1)
(C5)
where 1![(1!RP)/(1!P)] ,1 ½" . R![(1!RP)/(1!P)] ,1
(C6)
If R"1 then
P N" 1 (1!P)
1#(2/2!X \ X \
½(2 F " 2 2!½(2!(2) (1!½) ln 2!½(2#(2)
(C7)
(C8)
where
D¹ "¹!¹ A A D¹ "¹!¹ F F D¹ "¹!¹. F A If RO1 then
P ½" N #P!PN 1 1
ln[(1!R P)/(1!P)] N" 1 ln(Z)
(C3)
R#1#(R#1!2 X R \ Z" R#1#(R#1!2 X \
(C4)
(C9)
N is the number of 1—2 shells in series and F is the 1 2 logarithmic mean temperature correction factor. It is recommended X "0.9 for a single 1—2 shell, but the \ chosen value of X is required to be the maximum that \ should be observed in each 1—2 shell of a multishell unit in order for each such section to display at least the corresponding F . 2