I n d . Eng. Chem. Res. 1987,26, 685-691
685
Heat-Exchanger Network Analysis. 1. Optimization D. L. Terrill and J. M. Douglas* Department of Chemical Engineering, University o f Massachusetts, Amherst, Massachusetts 01003
The previous studies of heat-exchanger network designs usually have been based on the assumption that the process flow rates and target temperatures are fixed. However, the optimum process flow rates always involve an economic tradeoff between recycle costs (which include at least part of the cost of the heat-exchanger network) and some other quantity. Thus, the problems of establishing the process flows and designing the heat-exchanger network cannot be uncoupled. The results of three case studies, where excess raw materials costs exceed the total energy costs, show that cost savings of about 1-6% are obtained with energy integration using fixed flows and a fixed approach temperature, whereas cost savings of about 20-30% are obtained from the simultaneous optimization of flows with energy integration. Also, Townsend and Linnhoff s minimum area calculation was shown to be a good approximation for heat-exchanger networks in optimization calculations at the conceptual level of a design. Thus, this simple approximation can be used to estimate the optimum flows, and the results can then be used to design a network for preliminary designs. A systematic procedure for calculating minimum heating and cooling requirements, as well as the minimum number of exchangers, for a heat-exchanger network (HEN) has been developed by Hohmann (1971), Umeda, et al., (1978), and Linnhoff and Flower (1978a,b). The synthesis/ analysis procedure has been extended to include the pinch design method (Linnhoff et al., 1982; Linnhoff and Hindmarsh, 1983), heat and power integration (Townsend and Linnhoff, 1983a,b), and the energy integration of distillation columns with the process streams (Linnhoff et al., 1983; Linnhoff and Hindmarsh, 1983.) Similarly, alternate problem formulations in terms of transportation models (Cerda et al., 1983; Cerda and Westerberg, 1983), as well as transhipment models (Papoulias and Grossmann, 1983a), have been proposed. The problem definition that has provided the basis for all of this research, as well as for numerous successful industrial applications of the procedures (see: Boland and Hindmarsh, 1984; Linnhoff and Vredeveld, 1984), is as follows: Given a set of streams, where the flow rates and inlet and outlet temperatures are specified, design the best heat-exchanger network. In the design of a new process, however, there is no procedure for fixing the process flow rates without first fixing the heat-exchanger network. The following are examples of this. 1. The optimum conversion in a process involves an economic tradeoff between large selectivity losses (for most processes) and unbounded reactor costs as the conversion approaches unity vs. large recycle costs (which include the cost of part of the heat-exchanger network) as the conversion approaches zero. 2. For process with a gas recycle and a purge stream, the optimum purge composition of reactants involves an economic tradeoff between large raw material costs as the purge composition of reactants increases vs. an unbounded gas recycle cost (which includes part of the heat-exchanger network) as the purge composition of reactants approaches zero. 3. For reactions of the type A+B-P (1) 2A+B+W (2) where P is the desired product and where the kinetics match the stoichiometry (which might correspond to a simplified model of butane alkylation to produce isooctane), the selectivity losses to the waste byproduct W will decrease as the molar ratio of B/A at the reactor inlet
is increased. However, the raw material savings of A converted to W are eventually balanced by the increasing cost to recover and recycle B (which depends on part of the heat-exchanger network costs), so that there is an optimum molar ratio. Thus, we see that the problem of designing a heat-exchanger network cannot be decoupled from the design of the remainder of the process; i.e., the flows needed for the analysis are never known. Moreover, if the flows in an existing plant are used for a retrofit analysis and major savings are predicted (i.e., recycle costs can be decreased), then one can anticipate that the flows normally should be changed because the apparent energy savings can, in part, be converted into raw material savings (for cases where raw materials are more valuable than fuel). The interaction between the optimization of the process flows and the heat-exchanger network has recently been discussed by Papoulias and Grossmann (1983b). They suggested incorporating the minimum utility targets for heat integration into the stream optimization problem and then using these results as the basis for the development of a detailed heat recovery network structure. Then, Duran and Grossmann (1986) presented a more rigorous formulation for the simultaneous optimization of the stream flows and energy integration. For a simple, hypothetical process, Duran and Grossmann compared the results from optimizing the flows and then heat integrating the process vs. a simultaneous optimization procedure, and they found that the optimum profit from the simultaneous approach was 90.7% higher than the sequential case. Also, they found that the major causes of the improvement were a lower raw material cost and a much lower heating utility consumption. Duran and Grossmann note that their new procedure can be incorporated as part of a normal optimization analysis or can be implemented in a mixed-integer nonlinear programming optimization framework. Goals of This Research Experience indicates that less than 1% of the ideas for new designs ever become commercialized, and therefore initial design studies are focused on the desirability of terminating the project early or developing a more detailed design. Similarly, at the conceptual stage of a design, the focus is directed toward finding the best flow-sheet alternatives, rather than rigorous design calculations. Of course, in order to compare flow-sheet alternatives, it is necessary to estimate (i.e., to get into the neighborhood of) the optimum design conditions for each alternative, but
0888-5885/87/2626-0685$01.50/0 0 1987 American Chemical Society
686 Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987
we want to estimate the optimum design conditions with the minimum amount of effort. Then, if the conceptual designs appear to be sufficiently profitable that additional design effort can be justified, we use rigorous design and optimization calculations to develop a final design. Thus, at the conceptual stage of a process design, we prefer to use simpler tools than we would use for final designs. As an alternative to the rigorous formalism of Duran and Grossmann (1986), a very simple way of estimating both the capital and energy costs of a heat-exchanger network has been described by Townsend and Linnhoff (1984). With this short-cut procedure, it is not even necessary to specify a heat-exchanger network. A more detailed, but still relatively simple, procedure for estimating the sensitivity of the total design costs to a variety of heat-exchanger network alternatives would be to devise several heat-exchanger network alternatives which have close to the maximum energy recovery for the base-case flow sheet and then consider the approximate flow optimization and ATminoptimization at the pinch for these networks. With this case-study approach, we are not guaranteed to find the optimum heat-exchanger network, but we can gain a better understanding of the importance of energy integration. If several process alternatives exhibit approximately the same cost at the conceptual design stage, it might be advantageous to use the controllability of the process, the simplicity, etc., as additional criteria for selecting the ”best” alternative. (If the process is not profitable, so that we terminate the project, we do not want to consider any of these factors.) At the conceptual stage of a design, we are most interested in gaining a rough estimate of the cost penalties associated with ensuring process operability, rather than determining the most resilient or the optimum heat-exchanger network. Again, we expect that a casestudy approach should be adequate for screening calculations. In part 1 of this series, we discuss what seems to be a “reasonable” approach for evaluating the economic impact of simultaneously optimizing the process flows and the heat-exchanger network for some realistic processes. The petrochemical processes considered are limited to plants where the raw material loses to byproducts and in fuel streams exceed the total utility costs for the base-case design. Normally, we would use the approximate optimization procedure described by Fisher et al. (1985) to rank-order the design variables and then reduce the effort required for the optimization analysis by considering only the dominant design variables. However, for the sake of completeness and to evaluate how the conventional rules of thumb for some optimizations (reflux ratios, fractional recoveries, and feed quality in distillation columns) change because of energy integration, we optimized virtually all of the design variables. In part 2 of this series, we then consider the steady-state operability of the various alternatives. Perhaps we should emphasize again that our focus is on screening studies, so that we use short-cut material balance and design equations throughout this study. For final designs, we would use rigorous material balances and design equations, as well as the rigorous optimization procedures described by Duran and Grossmann (1986). Four Representative Processes In order to study the optimization of the total process with a variety of heat-exchanger networks, we considered two petrochemical processes, with two alternatives of each. These are the hydrodealkylation (HDA) of toluene to produce benzene with a diphenyl byproduct, the HDA
1:
c c -
Figure 1. HDA process with a diphenyl byproduct-alternative
1.
r G L U E N E FEED
TOLUENE RECYCLE
1
1
~
I
L Figure 2. HDA process with diphenyl recycled-alternative
I
1.
ETHYLENE FEED
I
‘
1
Figure 3. EB process.
process with diphenyl recycled to extinction, the vaporphase alkylation of benzene with ethylene to produce ethylbenzene (EB) while exporting low-pressure steam to an adjacent styrene process, and the EB process with no steam exportation. The base-case flow sheets, see Figures 1-3, and base-case design conditions were chosen to correspond to published case studies (McKetta, 1977, 1984; Dwyer et al., 1976). For each of these processes, the Problem Table Analysis (Linnhoff et al., 1982) and the pinch design method were
Ind. Eng. Chem. Res., Vol. 26, No. 4,1987 687
TOLUENE FEED
TOLUENE FEED
RECYCLE TOLUENE
1
E N
UPHENYL
I
1
Figure 7. HDA process with diphenyl recycled-alternative 3.
Figure 4. HDA procegs with a diphenyl byproduct-alternative 2.
64s RECYCLE
(1
PURGE
$ FEED
TOLUENE FEED
T
RECYCLE TOLUENE
1
Figure 8. HDA process with diphenyl recycled-alternative 4. Figure 5. HDA process with a diphenyl byproduct-alternative 3. U, FEED
1
TOLUENE
FEED
1 1
TOLUENE RECICLE
1 L
Figure 6. HDA process with a diphenyl byproduct-alternative 6.
used to generate three to six heat-exchanger network alternatives for the base-case conditions (Terrill and Douglas, 1987). More alternatives exist, but these are adequate to illustrate the behavior of the processes. For the HDA process with diphenyl as a byproduct, we generated six alternatives, some of which are shown in Figures 1and 4-6. Alternative 1(Figure 1)simply has an enlarged feed-effluent heat exchanger. Alternative 2 (Figure 4) is the same as alternative 1,except that recycle column was pressure shifted to be above the pinch temperature, and the condenser for the recycle column is used to drive the product column reboiler. All of the other alternatives also include this pressure shifting. In alter-
1.w Figure 9. HDA process with diphenyl recycled-alternative 5.
native 3 (Figure 5 ) , part of the heat in the reactor effluent stream is used to drive the stabilizer reboiler, whereas in alternative 4 the reactor effluent is used to drive the product column reboiler. For alternative 5, both the stabilizer reboiler and the product column reboiler are driven consecutively by the reactor effluent stream. In alternative 6 (Figure 6), all three column reboilers are driven by the reactor effluent stream. The flow sheets for the HDA processes not shown here are given by Terrill (1985). For the HDA process with diphenyl recycled, we generated five alternatives, some of which are shown in Figures 2 and 7-9. Alternative 1 (Figure 2), again, simply has an enlarged feed-effluent heat exchanger. In addition to this, in alternative 2 part of heat in the reactor product stream drives the stabilizer reboiler. For alternative 3 (Figure 7), it is the product column reboiler rather than the stabilizer
688 Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 Table 1. TAC and Utilities Usage of HEN Alternatives of the HDA Process with Diphenyl Byproduct
1. 2. 3. 4. 5. 6. 7. 8.
utilities usage for alternatives with base-case design values, MW energy savings from new HEN, 70 TAC for alternatives with base-case design values, $106/year improvement from new HEN, 76 TAC for optimized alternatives, $106/year improvement from optimization and new HEN, % utilities usage for optimized alternatives, MW energy savings from optimization and new HEN as compared to the base case, %
base case 12.7 6.38
alternative 2 3 4 9.06 7.68 7.39 7.30 29 40 42 43 6.40 6.45 6.38 6.11 4 -0.3 -1 0 5.03 5.06 4.91 4.76 21 23 25 21 14.0 13.2 11.5 10.7 -4 9 16 -10
1
5 7.30 43 6.04 5 4.73 26 10.4 19
6 7.30 43 6.03 5 4.74 26 10.3 19
Table 11. TAC and Utilities Usage of HEN Alternatives of the HDA Process with Diphenyl Recycled
1. 2. 3. 4. 5. 6. 7. 8.
utilities usage for alternatives with base-case design values, MW energy savings from new HEN, % TAC for alternatives with base-case design values, $106/year improvement from new HEN, % TAC for optimized alternatives, $106/year improvement from optimization and new HEN, % utilities usage for optimized alternatives, MW energy savings from optimization and new HEN as compared to the base case, %
base case 11.5 5.19
1
7.88 32 5.21 -0.4 3.83 26 9.67 16
alternative 2 3 4 7.88 7.59 7.59 32 34 34 5.05 4.95 4.92 3 5 5 3.71 3.60 3.57 29 31 31 9.41 7.97 7.71 18 32 33
5 10.8 6 5.42 -4 4.09 21
9.73 16
Table 111. TAP and Utilities Usage of HEN Alternatives of the EB Process with Steam Exported
1. 2. 3. 4. 5. 6. 7. 8.
utilities usage for alternatives with base-case design values, MW energy savings from new HEN, 70 TAP for alternatives with base-case design values, $106/year improvement from new HEN, % TAP for optimized alternatives, $106/year improvement from optimization and new HEN, 70 utilities usage for optimized alternatives, MW energy savings from optimization and new HEN as compared to the base case, %
reboiler that is driven by reactor effluent heat. Alternative 4 (Figure 8) has both reboilers driven with reactor effluent heat. Alternative 5 (Figure 9) is similar to alternative 1, but in addition the product column is pressure shifted above the pinch temperature and the stabilizer reboiler is driven by the product column condenser. The flow sheets for both EB processes can be found in Terrill (1985). For the EB process with steam exported, four network alternatives were generated. Alternative 1 is identical with the original network. In alternative 2, heat from the reactor product stream is used to drive the benzene column reboiler and the product column reboiler. Alternative 3 uses the reactor effluent heat to drive the benzene column reboiler and uses the DEB column condenser heat to preheat the reactor feed stream. In alternative 4, the benzene column reboiler and DEB column reboiler are driven consecutively with the reactor effluent, and the DEB column condenser preheats the reactor feed stream so that the DEB column is run with no utilities. For the EB process with no steam exported, three alternatives were generated. Again, alternative 1 is identical with the original network. In alternative 2, the product column reboiler and benzene column reboiler are driven consecutively with reactor effluent heat, and the product column condenser is used to heat the reactor feed stream. Finally, alternative 3 utilizes the DEB column condenser to partially drive the benzene column reboiler. The product column reboiler and benzene column reboiler are driven with the reactor product effluent. Also, the DEB column reboiler is driven with the reactor product effluent. Total Process Optimization We desired to assess the possible improvements obtained by optimizing the total process flows and target temper-
base case 70.7 15.4
1
70.7 0 15.4 0 17.3 12 58.6 17
alternative 2 3 70.7 69.4 0 2 16.4 16.5 6 7 18.2 18.6 18 21 61.1 63.4 14 10
4
69.4 2 16.6 8 18.6 21 63.9 10
atures for the processes and heat-exchanger network alternatives described above. The optimization was based on short-cut computer models of the total plant profit or costs as a function of numerous design variables, and the results were compared to the alternatives at base-case conditions. The results shown in Tables 1-111 list the total annualized costs or profits and the utilities usages for the base-case design conditions (using the typical assumption of a minimum approach temperature of 10 K) as well as for the optimized design conditions for each alternative. In Tables IV-VI the base-case and optimized design conditions are listed for each alternative. Total annualized cost (TAC), rather than total annualized profit (TAP),was calculated for the HDA processes because the toluene feed rate is assumed to be fixed by upstream processing and the toluene process losses are accounted for in the model. The short-cut material balances and design equations were within 1-5% of the rigorous ASPEN and PROCESS simulations. From Tables I and 11, rows 1 and 2, we see that when we install the various heat-exchanger network alternatives on the base-case design for the HDA processes we obtain 30-50% energy savings, which is in the same region as reported by Boland and Hindmarsh at IC1 (1984) and by Linnhoff and Vredeveld (1984) at Union Carbide. (There is almost no savings obtained for the EB process.) However, the total annual costs (or profit), see row 3 in Tables 1-111 for the various network alternatives, are about the same, and this large energy savings only leads to a 0-5% improvement in the profitability; see row 4. This result is obtained because the costs associated with energy management in these processes are not as large as the costs associated with raw materials management. An operating cost diagam (see: Douglas and Woodcock, 1985),
Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 689 Table IV. Ootimization Results for the HDA Process with DiDhenvl Bwroduct ~~~
~
alternative base case 6.38 1.10 5.28 75.0 53.0 85.4 10 9 0.5 99.0 1.20
TAC, $106/year annualized capital cost, $106/year annualized operating, cost, $106/year conversion, % H2composition in gas recycle, % FEHE energy rec., cold stream basis, %
AT,,,
1 5.03 1.50 3.53 67.3 31.9 94.0 32 10 0.3 98.7 1.45 1.2 99.9 96 101
K
no. of units stabilizer column fractional loss of benzene, % product column fractional rec., % reflux ratio feed cooler, MW recycle column fractional rec., overhead, % fractional rec., bottoms, % pressure, kPa
0 98.6 80.7
101
2
3
4
5
6
approx. model
5.06 1.54 3.52 67.6 31.7 93.6 38
4.91 1.52 3.39 66.9 32.4 93.6 25 10 0.5 98.6 1.58 0 99.8 89 507
4.76 1.48 3.28 67.4 32.0 91.9 14 10 0.3 98.9 1.91 0 99.8 89 507
4.73 1.47 3.26 67.5 32.3 87.5 9 10 0.4 98.9 1.85 0 99.8 89 507
4.74 1.49 3.25 67.2 32.5 85.8 13 11 0.4 98.9 1.85
4.83 1.60 3.23 67.7 32.9 85.7 16 13 0.4 98.9 1.70
10 0.3 98.7 1.44 1.19 99.8 89 507
0
0
99.8 89 507
99.8 89 101
Table V. Optimization Results for the HDA Process with Diphenyl Recycled alternative 1
2
3
4
5
5.19 1.09 4.10 75.0 53.0 85.4 10 7
3.83 1.30 2.53 97.3 29.4 94.2 36 7
3.71 1.26 2.44 97.0 29.7 93.4 32 8
3.60 1.26 2.35 97.6 29.3 89.9 10 8
3.57 1.27 2.30 97.7 29.3 85.6 9 8
4.09 1.50 2.59 98.2 29.2 90.6 12 7
3.68 1.30 2.38 97.7 29.6 81.3 26 10
0.5
0.2
0.2
0.2
0.2
0.4
0.2
99.0 1.2
99.0 1.2
97.8 1.3
99.1 1.4 101
99.1 1.3 101
TAC, $106/year annualized capital cost, $106/year annualized operating cost, $106/year conversion, % H2 composition in gas recycle, % FEHE energy rec., cold stream basis, %
AT,,,
approx. model
base case
K
no. of units stabilizer column fractional loss of benzene, % product column fractional rec., % reflux ratio pressure kPa
101
101
101
99.1 1.1 586
99.1 1.3
101
Table VI. Optimization Results for the EB Process with Steam Exported alternative base case TAP, $106/year benzene to ethylene ratio to reactor ATmim K no. of units benzene column feed quality frac. rec., top, % frac. rec., bot. % R/Rmin
product column feed quality frac. rec., % reflux ratio DEB column feed quality frac. rec., top, % frac. rec., bot., % reflux ratio scrubber frac. rec., 70 liquid rate, lb mol/h liq. feed temp, K vap. feed temp, K
10
1 17.3 10.12 58 11
-0.103 99.98 93.2 1.09
99.9800 49 1.02
0.0 99.9801 78 1.08
0.0 99.9810 86 1.07
0.0 99.9810 86 1.07
0.0 99.9802 89 1.08
-0.003 98.0 2.57
-0.003 99.1 1.03
-0.003 98.7 1.1
-0.003 60 0.86
-0.003 60 0.86
-0.003 60 1.1
0.901 99.3 94.9 0.378
0.05 99.97 7
0.0
0.08 99.93 8 0.0
0.02 99.93 3 0.0
0.01 99.93 2 0.0
0.05 99.97 3 0.0
99.95 13 296 330
99.95 13 297 330
99.95 14 297 330
99.95 14 297 330
99.95 13 297 336
15.4 8.21 10
99.5 22 297 330
0.0
showing the value of toluene lost to byproducts and in the fuel streams, the hydrogen loss in the purge and stabilizer overhead, and each of the utility costs for the base-case design of the HDA process, is shown in Figure 10. From the figure we see that a 50% savings in the total utility costs of $774000/year is equivalent to about a 10% savings in the excess raw materials costs of $3 854 000/year. Of course, we might be able to obtain a larger energy savings by optimizing the approach temperature at the pinch for the various network alternatives, but there appears to be
3
4
18.2 10.17 60 12
18.6 10.6 1 11
18.6 10.6 1 11
18.3 10.20 2.5 15
2
approx. model
a greater incentive to optimize both the flows and the minimum approach temperature. The results of the simultaneous optimizations of the process flows and the approach temperatures are given in row 5 of Tables 1-111. From row 6 we see that we obtain profitability improvements in the range from 12% to 30%. For the HDA process, i.e. Tables I and 11, the utilities usages at the optimum design conditions for the various network alternatives are larger than the base-case values, whereas for the EB process, Table I11 they are lower. This
690 Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 - 0 658
005 GAS
21
REClCLE
PURGE
2 163
003
-02c DIPHENYL
u c12
Figure 10. Operating cost diagram for HDA process with a diphenyl byproduct.
behavior is caused by the coupling of the process flow and energy integration optimizations. For each of these processes, it is interesting to note that the optimum costs are almost the same for the various heat-exchanger network alternatives for each process alternative. Since profits change little between the simple and more complex networks, there is little incentive to select a more complex network where possible start-up and controlability problems might be encountered. Moreover, we see that looking for a better process alternative (i.e., compare Tables I and 11) may be more beneficial than considering heat-exchanger network alternatives. These results also contain an interesting insight into the design alternative of pressure shifting. Alternative 2 of the HDA process with diphenyl recovery and alternative 5 of the HDA process with diphenyl recycled both have pressure shifting and both are less profitable than the other alternatives. Here are two cases where pressure shifting may save energy but does not increase profits. The energy cost savings are offset by increased column costs (thicker walls, decreased a,etc.).
Discussion of Optimized Design Conditions It is also interesting to compare the optimum design conditions, see Tables IV-VI, for these processes to the common rules of thumb. Reactor conversion and gas purge compositions are the key design variables for the HDA process with a diphenyl byproduct, and there are no rules of thumb available to fix these values. For the HDA process with diphenyl recycled, this seemingly two-reaction process is reduced to a one-reaction process, where the 99% conversion rule of thumb holds true. For both HDA processes, the feed-effluent heat-exchanger energy recovery decreases wherever the reactor effluent is used to drive the reboiler (s). The typical rules of thumb for distillation column design are (1) 99% product recoveries (light key overhead and heavy key in the bottoms), (2) R/Rminis 1.2, and (3) feed quality is 1.0. These rules have been developed by considering the economic trade-offs affecting stand-alone columns. For the HDA processes, the optimum fractional recoveries agree with the 99% recovery rule of thumb, except for the bottoms recovery for the recycle column. Here it is more expensive to build rectifying trays than it is to recycle a small diphenyl stream. Hence, this column has only a stripping section and a low bottoms fractional recovery.
The product column reflux ratio increases when its reboiler is driven with reactor effluent heat, which is a “cost-free”utility, rather than steam. The feed quality for the product column varies from 0.4-0.6 with no feed cooler to about 1.2 with a feed cooler. For the benzene column of the EB processes, several atypical factors influence the optimum conditions. If any benzene exits in the bottoms stream, it will end up as impurity in the EB product. It is more economical to have the less desirable diethylbenzene be the impurity for the EB product. Hence, the fractional recovery of benzene in the benzene column is high. The overhead product stream for the benzene column is an order of magnitude larger than the bottoms stream, and this impacts the optimum conditions in three ways. Firstly, it is less expensive to recycle the ethylbenzene via the overhead stream than to rectify it, and hence the bottoms fractional recovery is low. Secondly, R/Rminincreases as the reboiler is driven by “cost-free” reactor effluent heat. Thirdly, the optimum feed quality is 0.0 or less, rather than 1.0 which saves in feed cooler and reboiler utilities to condense and then revaporize the overhead product. For the product column of the EB processes, the fractional recovery is about 99% except when steam is exported, and the DEB column condenser is driven with the reactor feed stream. In this case, because of the “cost-free’’ condenser duty, it is more economical to recycle more ethylbenzene rather than add more stripping trays. Additionally, for this column, the optimum feed quality requires no feed heater or cooler. The DEB column design is similar to that for the recycle column of the HDA process. This column is a stripper, with rectifying trays costing more than the cost of recycling triethylbenzene. Often a ATminof 10 K is used for the HEN design (Linnhoff et al., 1982). For the EB process with steam exported, different alternatives often have optimum ATmin’swhich vary significantly (1-60 K). Despite the fact that the optimum design values often differ from the common rules of thumb, the effect of these changes on the total processing costs is quite small. Thus, it is essential to optimize the design variables that fix the process flow rates, but the other optimizations are not as important.
Approximate Model of Townsend and Linnhoff From the previous results, we have shown that it would be advantageous to optimize the flows and temperatures before HEN alternatives are generated. However, optimization has always required that the flow sheet is fixed, and HEN design has always required that the temperatures and flows be known beforehand. In order to resolve this apparent conflict, it would be useful to have an approximate, HEN model, which accurately represents the physics and economics of the HEN without having to select a specific network. Hohmann (1971) described a procedure that can be used for this purpose, providing that the heat-transfer coefficients of all of the streams are identical (which is not realistic for most processes). However, Townsend and Linnhoff (1984) have extended this simplified analysis to the case of different heat-transfer coefficients for each stream. Thus, this simple approximation procedure was used to optimize the complete process, Le., the flows plus the heat-exchange system for the four processes. The results are shown in Tables IV-VI (right-most column). In all four cases, the simple, approximate model has an optimized cost or profit that is in the middle of those
I n d . Eng. C h e m . Res. 1987,26, 691-696
generated by various network alternatives, indicating that the approximate model adequately represents the economics of the network. Similarly, when we compare the values of the optimum design variables for each process, we normally find that the values from the approximate model are in the middle of the range of values for the various alternatives. This indicates that the approximate model provides a good starting point for screening studies. For each process the approximate model differs in cost or profit from the most profitable alternative by no more than 5%. Economic factors in the cost models are uncertain, however, so that one can use the approximate model to obtain a first estimate of the optimum design conditions. Then one can use the Problem Table Analysis and the pinch design method to generate alternatives for a more detailed evaluation. The apparent iterative analysis can thus be solved sequentially at the conceptual stage of a design. For final design calculations, the procedure of Duran and Grossmann (1986) can be used for the optimization.
Conclusions In this work we have shown that optimizing the process flows and temperatures has a greater impact on process profitability than HEN alternative generation. Also, the approximate model of Townsend and Linnhoff (1984) provides an adequate energy integration model for obtaining good estimates of the optimum flows and temperatures without having to specify a network. Since a variety of HEN alternatives seem to have about the same costs, the final selection of a network should also consider the operability of the process, as well as other similar considerations.
Acknowledgment We are grateful to the Department of Energy for supporting the work in these two papers (DOE Contract DEAC02-8ER10938).
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Received for review August 8, 1985 Revised manuscript received May 19, 1986 Accepted January 5, 1987
Heat-Exchanger Network Analysis. 2. Steady-State Operability Evaluation D. L. Terrill and J. M. Douglas* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003
In cases where the optimum design of heat-exchanger network alternatives have about the same processing costs, the selection of the network for the final design may be based on process operability or other considerations. Most heat-exchanger networks are not operable at the optimuin steady-state design conditions; i.e., normally they can tolerate disturbances that decrease the loads but not those that increase loads and there are not an adequate number of manipulative variables to be able to satisfy the process constraints and to optimize all of the significant operating variables. These types of operability limitations can be identified by using only steady-state considerations, and normally these operability limitations can be overcome by installing an appropriate amount of overdesign and by installing bypasses around the exchangers. Dynamic operability studies will be significantly simplified if these steady-state operability limitations are removed before a dynamic study is undertaken. In part 1 of this series, we considered the optimum design of two, typical petrochemical processes, with two alternatives for each process and with a variety of heatexchanger network alternatives for each process alterna0888-5885/87/2626-0691$01.50/0
tive. The focus of the study was on the screening of process alternatives at the conceptual stage of a process design, so that short-cut procedures were used in the analysis. The results indicated that there were large differences among 0 1987 American Chemical Society
