- Email: [email protected]
Retrofit of pressure drop constrained heat exchanger networks
Applied Thermal Engineering 20 (2000) 1469±1480
www.elsevier.com/locate/apthermeng
Retro®t of pressure drop constrained heat exchanger networks Marcone Lopes Silva, Roger Josef Zemp* DESQ-FEQ-Unicamp, Caixa Postal 6066, 13083-970 Campinas, SP, Brazil
Abstract The study of retro®t of heat exchanger networks is usually restricted to constant heat transfer coecients, and pressure drop constraints due to the additional exchanger area is neglected. In this work, a new approach considering the distribution of heat transfer area and pressure drop in retro®t is presented. The problem is described as a non-linear model, and the additional area required for the new network condition and available pressure drop are estimated based on economical optimisation (or process requirements). 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Heat exchanger networks; Process reftro®t; Energy eciency
1. Introduction The study of retro®t procedures for heat exchanger networks has been subject of numerous research work, due to its importance in energy-saving policies in chemical processes. Early work focused on the cost (and area) estimation of the additional exchangers required to achieve the new process conditions, without considering the layout of the existing network [5]. Later work moved to a more detailed analysis of the existing network, and the retro®t procedure was extended to consider the actual layout of the existing exchangers [4]. The main
* Corresponding author. E-mail address: [email protected] (R.J. Zemp). 1359-4311/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 0 ) 0 0 0 5 7 - 0
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Nomenclature DH DTlm DP A K MCp Q T h
enthalpy change (kW s) log of mean temperature dierence pressure drop (kPa) area (m2) constant in equation ¯ow heat capacity (kW/K) heat ¯ow (kW s) temperature (K, 8C) heat transfer coecient (kW/m2 K)
Superscripts ex existing new new pos positive Subscripts i hot stream j cold stream k enthalpy interval a constant in equation r speci®c mass (kg/m3) k thermal condutivity (W/m K) m viscosity (Pa s)
drawback of these methods is that they are restricted to constant heat transfer coecients, and do not take into account the available pressure drop for new exchangers. A new breakthrough in this ®eld was achieved by Polley et al. [2,3] by including the relationship between pressure drop, ®lm coecient and area into the retro®t procedure. However, during the targeting stage, they considered only the existing network area and not its distribution among the existing exchangers, thus leaving out an important constraint. Additionally, a common problem in the previous retro®t procedures is that no distinction is made between the properties of the existing exchangers and that the new exchangers. For example, the existing exchangers will not probably be operating at the same ®lm coecients as the new exchanger, especially considering that the new exchangers will have to satisfy the pressure drop available, and therefore, will have a dierent area/pressure drop trade-o. The new exchangers will have dierent ®lm coecients, when compared to similar existing exchangers, and therefore, one cannot simply compare the existing area with the additional area, as the basis for the estimate (®lm coecients) is not the same.
M.L. Silva, R.J. Zemp / Applied Thermal Engineering 20 (2000) 1469±1480
1471
2. Area matrix The methodology proposed by Tjoe and Linnho [5] restricts the quality of the solution obtained, as the distribution of the existing area is not considered. This means that the existing exchangers are considered as having the same area eciency, not being important at the targeting stage where the existing exchanger are located. However, dierent parts of the network might have dierent area eciencies, depending on the exchanger layout, thus leading to an incorrect result. This limitation can be eliminated by using the area matrix approach, where the actual distribution of area between the streams is considered. The area matrix procedure [4] has the basic principle of matching, in the best possible way, the existing exchanger network area layout to the area distribution obtained for the new operating conditions (computed by using area targeting procedures). The minimisation of the deviation between both matrices (existing exchangers and targeted layout) is a linear programming problem, where the objective function is the sum of the area deviations, and the restrictions are the heat balances in each interval. The result is the retro®t matrix, and it shows stream matches that require additional area (positive deviations) and that have excess area (negative deviations). The area matrix procedure has its main advantage in considering the distribution of the existing area among the stream matches. However, adding heat exchangers to the network to satisfy the retro®t goals will place an additional burden on the pumping system by increasing the stream pressure drops. Therefore, the cost estimates done during the retro®t targeting might not agree with the ®nal network design costs, and the advantage of using targeting procedures before design is lost.
3. Area distribution and pressure drop Ð a new approach In this work, a procedure combining the pressure drop approach [2] and the area matrix [4] is developed, thus allowing for the retro®t targeting of pressure drop constrained heat exchanger networks. The procedure is more complex than the original area matrix method, resulting in a non-linear problem. In the original matrix area procedure, the retro®t matrix could be obtained by subtracting the targeted area (obtained by optimisation) from the existing area. This was possible as the heat transfer coecients were considered constant, and therefore, one was using the same basis for area comparison. For variable heat transfer coecients, the existing area is based on the actual coecients, while the targeted area will be based on the new coecients. This is the ideal area for the whole network using the new coecients. However, as part of the area is already available but for dierent ¯ow conditions, one cannot optimise the dierence between target area and existing area, as a dierent basis for area comparison would be used. To overcome this problem, a modi®ed spaghetti network is proposed where an additional exchanger is placed near to each exchanger. The ®rst exchanger of the pair accounts for the existing exchanger, the second for the additional exchanger. By using heat loads instead of area the dierent heat transfer coecients of the added exchangers can be dealt with.
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Fig. 1. Spaghetti network arrangements: (a) exchangers in series, (b) exchangers in parallel.
However, a number of dierent arrangements for the exchanger pairs can be devised (Fig. 1) exchangers in series: this matches more closely the ®nal network arrangement, but requires calculating a dierent temperature dierence for each exchanger in a pair. Also, dierent sequences can be used for each pair (Fig. 1a); exchangers in parallel: each exchanger in a pair has the same temperature dierence, although stream splits might not appear in the ®nal network (Fig. 1b). This approach will be used in this work due to its much simpler implementation. The retro®t procedure is then formulated as the simultaneous tasks: . the network consisting of the ®rst exchanger of each pair is optimised so that the closest match to the existing exchangers is achieved (using actual heat transfer coecients); . the remaining heat load is distributed through the remaining network (second exchanger of each pair), in a way that the minimum additional area is achieved; . new heat transfer coecients are computed so that the additional area on each stream causes full use of the available pressure drop. Non-linearity is introduced into the model by the last task, as the pressure drop is a powerfunction of the heat transfer coecient.
4. The model for minimum additional area The model for the targeting of additional area of a pressure drop constrained HEN has been
M.L. Silva, R.J. Zemp / Applied Thermal Engineering 20 (2000) 1469±1480
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formulated as following, given a set of n hot streams, m cold streams, divided into w enthalpy intervals: . hot streams energy balance Ð the energy available from each hot stream i in interval k DHi, k is given by the sum of the heat transferred by the existing exchangers Qex i, j, k and ): the heat to be transferred by the new exchangers Qnew i, j, k DHi, k
n X ÿ j1
new Qex i, j, k Qi, j, k
1
. cold stream energy balances Ð as for the hot streams, for a cold stream j in interval k: DHj, k
m X ÿ i1
new Qex i, j, k Qi, j, k
2
. exchanger design equation for existing area Ð the area of each existing exchanger Aex i, j between hot stream i and cold stream j is given by: w Qex 1 1 X i, j, k ex 3 Ai, j hi hj k1 DTlm, k Ft where hi and hj are the actual heat transfer coecients and DTlm, k is the temperature dierence of interval k (corrected for multipass exchangers by Ft , if required) . exchanger design equation for new area Ð as Eq. (3), but with the new heat transfer and hnew coecients hnew i j ,). Care has been taken as some of the new heat loads might be negative (while still closing the heat balance in the interval). In this case a zero load is used and no additional area is computed: ! w X Qpos 1 1 i, j, k new 4 Ai, j new hnew h DT lm, k Ft j i k1 where ÿ new Qpos i, j, k max 0, Qi, j, k
5
. pressure drop constraints Ð the equations proposed by Jegede [1] are used to compute the pressure drop caused by the additional exchangers DPi ): n ÿ new a X new Ai, j DPi Ki hi
6
j1
where Ki is a constant function of the stream physical properties, ¯ow geometry and mass ¯ow. A similar equation is used for the cold streams. The values of a is a function of the position of the stream in the exchanger (tube or shell). The objective function is then given by the sum of the additional area:
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Table 1 Stream data for base case Stream
Tin (8C)
Tout (8C)
MCp (kW/K)
h (kW/m2 K)
H1 H2 C1 C2 C3
165.0 240.0 125.0 61.0 70.0
95.0 65.0 220.0 192.0 185.0
148.0 86.4 139.0 54.6 62.0
0.45 0.55 0.35 0.40 0.64
obj min
X
Anew i, j
7
The whole set of equations were modelled using GAMS (GAMS Dev. Corp., 1992), and solved by using the non-linear solver CONOPT. For a given requirement of utilities, the solution provides the additional area required for each exchanger match (and therefore, the total area to be added), as well as the heat transfer coecients for the new exchangers. The procedure can be repeated for a set of utility loads, and the best retro®t scenario chosen based on the desired goal: payback, investment, etc. Also, by changing the available pressure drops the impact of investments in the pumping system on the retro®t cost can be analyzed. 5. Case study The retro®t procedure was applied to a ®ve stream problem (Table 1). The existing network is shown in Fig. 2, and the heat exchanger data in Table 2. Physical properties of the streams are shown in Table 3. A retro®t is required to reduce the actual energy requirement (11275 kW hot utility) to 9400 kW, without exceeding the available pressure drops, given in Table 4. The present network area is 2186 m2.
Fig. 2. Base case network.
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Table 2 Exchanger data Exchanger
A ex (m2)
Q (kW)
DPcold (kPa)
DPhot (kPa)
1 2 3 4
133 588 724 742
2160 2560 7153 4340
1.8 5.7 29.0 141.2
21.6 20.0 117.9 25.2
Table 3 Physical property data for base case Stream
r (kg/m3)
m (cPs)
l (W/m 8C)
Cp (J/kg 8C)
H1 H2 C1 C2 C3
750.0 700.0 800.0 750.0 630.0
0.5 0.3 1.0 0.4 0.2
0.12 0.12 0.12 0.12 0.12
2600.0 2600.0 2600.0 2600.0 2600.0
Table 4 Pressure drop restrictions Stream
DP (kPa)
H1 H2 C1 C2 C3
15.0 30.0 20.0 15.0 20.0
Table 5 Additional area requirement Stream match
A ex (m2)
A new (m2)
H1±C1 H2±C1 H1±C2 H2±C2 H1±C3 H2±C3 Total
588 133 0.0 724 742 0
0 170 56 0 0 127 353
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Table 6 Heat transfer coecients for the new exchangers Stream
h (kW/m2 8C)
H1 H2 C1 C2 C3
0.635 0.467 0.725 0.749 0.719
6. New area targeting Using the procedure developed above, the additional area required for each match was computed and is shown in Table 5. An additional area of 353 m2 is required for the retro®t. Also shown is that the new area should be added to exchangers between streams H2±C1, H1± C2 and H2±C3. The optimised heat transfer coecients (Table 6) show that due to the available pressure drop, much higher heat transfer coecients than the coecients of the base case network can be used for the new exchangers (except stream H2). This results in lower area requirements and lower retro®t costs. The retro®t procedure based on the original heat transfer coecients would have targeted a higher investment than really required, missing the optimal retro®t scenario. On the other hand, had the available pressure drop led to overall lower coecients, the required area would be underestimated by the constant-h retro®t procedures and ultimately increase the overall cost due to more exchangers or increased pumping requirement.
7. Network design Once the required additional area is obtained, the base case network is modi®ed using the traditional rules for HEN retro®t. The driving force plot shows how the existing exchangers are placed in the network (Fig. 3) exchanger 1: completely located above the pinch, but does not agree very well with the process diagram. An increase of the cold stream exit temperature from 158 to 1688C shifts exchanger 1 to the right, touching the process curve (Fig. 4a). The heat load is reduced from 2160 to 1927 kW, exchanger 2: very well placed, no need to reposition, exchanger 3: badly placed, and needs repositioning. Since exchangers 2 and 4 were not moved (and therefore, the cooler on stream H1 remained with the original heat load), the only place to reduce cold utility requirement is the cooler on stream H2. A heat balance around this cooler shows that it requires an input temperature of 110.78C in order to meet the desired utility load. Given the new operating temperatures of this exchanger, the energy load is reduced from
M.L. Silva, R.J. Zemp / Applied Thermal Engineering 20 (2000) 1469±1480
Fig. 3. Driving force plot for existing exchangers.
Fig. 4. New driving force plot for exchangers 1 and 3.
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Fig. 5. Modi®ed network.
7153 to 4994 kW, shifting the exchanger closer to the process curve (Fig. 4b), exchanger 4: although this exchanger crosses the pinch, it is overall eciently placed and does not require repositioning. The changes introduced into the network by shifting exchangers leads to an incomplete HEN (Fig. 5). The new exchangers can now be placed on the network so that the remaining heat loads are satis®ed. Driving force plots can again be used to help in positioning the exchangers. The ®nal network for this case study is shown in Fig. 6. Two more exchangers (A and B) and a heater (on stream C2) were added to the network. The heater on stream C3 has a very small load, and could possibly be removed without causing a signi®cant increase in overall utility and/or exchanger area. The optimized heat transfer coecient are used to compute the added area. The areas obtained for exchangers A and B are 93 and 317 m2, respectively, giving a total new area of 410 m2. The predicted area is in reasonable agreement with the ®nal network area, with an error of 16%. This error is due to incomplete vertical placement of the heat exchangers in the ®nal network and the consideration of parallel exchanger arrangement in the targeting procedure. One can also note that the new exchangers are located where the targeting
Fig. 6. Final network design.
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Table 7 Design data of new exchangers Property
Exchanger A
Exchanger B
Total
Area (m2) Shell diameter (m) Tube length (m) Tube count Baes Tube passes hshell (kW/m2 8C) htube (kW/m2 8C) DPshell (kPa) DPtube (kPa)
61 0.73 3.2 318 9 2 0.75 1.79 6.6 20.0
269 1.02 7.2 626 29 4 0.73 2.02 25.4 20.0
330
procedure predicted the largest new exchangers. No new exchanger between streams H1±C2 (as predicted, with area = 56 m2) was required due to the shifting of exchanger 3. Once the new exchangers have been allocated, their pressure drop contribution has to be checked. The procedure by Jegede [1] can be used to determine the exchanger data like tube count, shell diameter, bae spacing and tube length. As this method is based on the same equations used in the targeting procedure, consistency between the estimated area, pressure drop and heat transfer coecients is assured. Since stream H2 has two new exchangers, the available pressure drop is divided between both exchangers to have proportional area. Exchanger A is allocated with 6.6 kPa and exchanger B with 25.4 kPa of the available pressure drop of 30.0 kPa of stream H2. On the tube side, exchanger A and B use all of the 20.0 kPa available (stream C1 and C3). The design data of the exchangers and the computed pressure drops are shown in Table 7. The ®nal exchanger areas are smaller than predicted using the optimized heat transfer coecient, which was slightly larger than predicted. Again, this dierence is due to the way exchangers are allocated in the targeting procedure (parallel) and the ®nal network (series). The ®nal new exchanger area (330 m2) is within 7% of the predicted area, which can be considered a very good result. Also, the available pressure drops are fully satis®ed.
8. Conclusions In this work, the traditional HEN retro®t procedure was modi®ed to account simultaneously for the actual distribution of heat transfer area and pressure drop availability at the targeting stage. This is an improvement over existing methods where either pressure drop or exchanger area distribution is considered, but not both simultaneously. The new retro®t area target procedure was implemented as a non-linear optimization problem, minimizing the additional area. Available pressure drops are the constraints to be satis®ed. Apart from the exchanger area required for the network retro®t, optimized heat transfer coecients for the new exchangers are also obtained, aiding in the design of the new
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exchangers. The application of the proposed procedure to a number of case studies showed that the methodology is capable of correctly targeting retro®t options ahead of design. The ®nal area required for the retro®t (designed heat exchanger network) is close to the area calculated at the targeting stage and the ®nal network pressure drops do not exceed the available pressure drops. For the case shown in this paper, the agreement between predicted and ®nal area was 7%. The detailed exchanger design leads to exchangers with ®lm coecient and pressure close to the one predicted at the targeting stage thus allowing for the pressure drop restrictions to be properly considered in a retro®t project. Although a simpli®ed shell-side method was used, any method where pressure drop can be written as a function of area and heat transfer coecient could be used. The results obtained show that pressure drop is an important issue in heat exchanger retro®t, and should not be neglected. The impact of additional exchangers on the available pressure drop has to be considered to obtain cost-optimal ®nal designs. Acknowledgements The authors acknowledge the ®nancial aid provided by CAPES, Brazil. References [1] Jegede, F.O., 1990. Power, capital and energy cost trade-os in heat exchanger networks. PhD Thesis, UMIST, Manchester. [2] G.T. Polley, M.H. Panjeh Shahi, F.O. Jegede, Pressure drop considerations in the retro®t of heat exchanger networks, Trans. IChemE 68, Part A (1990) 211±220. [3] G.T Polley, M.H. Panjeh Shahi, Interfacing heat exchanger network synthesis and detailed heat exchanger design, Trans IChemE 69, Part A, (1991) 445±457. [4] Shokoya, C.G., 1992, Retro®t of heat exchanger network for debottlenecking and energy saving. PhD Thesis, UMIST, Manchester. [5] T.N. Tjoe, B. Linnho, Using pinch technology for process retro®t, Chem. Eng. 93 (1986) 47±60.
www.elsevier.com/locate/apthermeng
Retro®t of pressure drop constrained heat exchanger networks Marcone Lopes Silva, Roger Josef Zemp* DESQ-FEQ-Unicamp, Caixa Postal 6066, 13083-970 Campinas, SP, Brazil
Abstract The study of retro®t of heat exchanger networks is usually restricted to constant heat transfer coecients, and pressure drop constraints due to the additional exchanger area is neglected. In this work, a new approach considering the distribution of heat transfer area and pressure drop in retro®t is presented. The problem is described as a non-linear model, and the additional area required for the new network condition and available pressure drop are estimated based on economical optimisation (or process requirements). 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Heat exchanger networks; Process reftro®t; Energy eciency
1. Introduction The study of retro®t procedures for heat exchanger networks has been subject of numerous research work, due to its importance in energy-saving policies in chemical processes. Early work focused on the cost (and area) estimation of the additional exchangers required to achieve the new process conditions, without considering the layout of the existing network [5]. Later work moved to a more detailed analysis of the existing network, and the retro®t procedure was extended to consider the actual layout of the existing exchangers [4]. The main
* Corresponding author. E-mail address: [email protected] (R.J. Zemp). 1359-4311/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 0 ) 0 0 0 5 7 - 0
1470
M.L. Silva, R.J. Zemp / Applied Thermal Engineering 20 (2000) 1469±1480
Nomenclature DH DTlm DP A K MCp Q T h
enthalpy change (kW s) log of mean temperature dierence pressure drop (kPa) area (m2) constant in equation ¯ow heat capacity (kW/K) heat ¯ow (kW s) temperature (K, 8C) heat transfer coecient (kW/m2 K)
Superscripts ex existing new new pos positive Subscripts i hot stream j cold stream k enthalpy interval a constant in equation r speci®c mass (kg/m3) k thermal condutivity (W/m K) m viscosity (Pa s)
drawback of these methods is that they are restricted to constant heat transfer coecients, and do not take into account the available pressure drop for new exchangers. A new breakthrough in this ®eld was achieved by Polley et al. [2,3] by including the relationship between pressure drop, ®lm coecient and area into the retro®t procedure. However, during the targeting stage, they considered only the existing network area and not its distribution among the existing exchangers, thus leaving out an important constraint. Additionally, a common problem in the previous retro®t procedures is that no distinction is made between the properties of the existing exchangers and that the new exchangers. For example, the existing exchangers will not probably be operating at the same ®lm coecients as the new exchanger, especially considering that the new exchangers will have to satisfy the pressure drop available, and therefore, will have a dierent area/pressure drop trade-o. The new exchangers will have dierent ®lm coecients, when compared to similar existing exchangers, and therefore, one cannot simply compare the existing area with the additional area, as the basis for the estimate (®lm coecients) is not the same.
M.L. Silva, R.J. Zemp / Applied Thermal Engineering 20 (2000) 1469±1480
1471
2. Area matrix The methodology proposed by Tjoe and Linnho [5] restricts the quality of the solution obtained, as the distribution of the existing area is not considered. This means that the existing exchangers are considered as having the same area eciency, not being important at the targeting stage where the existing exchanger are located. However, dierent parts of the network might have dierent area eciencies, depending on the exchanger layout, thus leading to an incorrect result. This limitation can be eliminated by using the area matrix approach, where the actual distribution of area between the streams is considered. The area matrix procedure [4] has the basic principle of matching, in the best possible way, the existing exchanger network area layout to the area distribution obtained for the new operating conditions (computed by using area targeting procedures). The minimisation of the deviation between both matrices (existing exchangers and targeted layout) is a linear programming problem, where the objective function is the sum of the area deviations, and the restrictions are the heat balances in each interval. The result is the retro®t matrix, and it shows stream matches that require additional area (positive deviations) and that have excess area (negative deviations). The area matrix procedure has its main advantage in considering the distribution of the existing area among the stream matches. However, adding heat exchangers to the network to satisfy the retro®t goals will place an additional burden on the pumping system by increasing the stream pressure drops. Therefore, the cost estimates done during the retro®t targeting might not agree with the ®nal network design costs, and the advantage of using targeting procedures before design is lost.
3. Area distribution and pressure drop Ð a new approach In this work, a procedure combining the pressure drop approach [2] and the area matrix [4] is developed, thus allowing for the retro®t targeting of pressure drop constrained heat exchanger networks. The procedure is more complex than the original area matrix method, resulting in a non-linear problem. In the original matrix area procedure, the retro®t matrix could be obtained by subtracting the targeted area (obtained by optimisation) from the existing area. This was possible as the heat transfer coecients were considered constant, and therefore, one was using the same basis for area comparison. For variable heat transfer coecients, the existing area is based on the actual coecients, while the targeted area will be based on the new coecients. This is the ideal area for the whole network using the new coecients. However, as part of the area is already available but for dierent ¯ow conditions, one cannot optimise the dierence between target area and existing area, as a dierent basis for area comparison would be used. To overcome this problem, a modi®ed spaghetti network is proposed where an additional exchanger is placed near to each exchanger. The ®rst exchanger of the pair accounts for the existing exchanger, the second for the additional exchanger. By using heat loads instead of area the dierent heat transfer coecients of the added exchangers can be dealt with.
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Fig. 1. Spaghetti network arrangements: (a) exchangers in series, (b) exchangers in parallel.
However, a number of dierent arrangements for the exchanger pairs can be devised (Fig. 1) exchangers in series: this matches more closely the ®nal network arrangement, but requires calculating a dierent temperature dierence for each exchanger in a pair. Also, dierent sequences can be used for each pair (Fig. 1a); exchangers in parallel: each exchanger in a pair has the same temperature dierence, although stream splits might not appear in the ®nal network (Fig. 1b). This approach will be used in this work due to its much simpler implementation. The retro®t procedure is then formulated as the simultaneous tasks: . the network consisting of the ®rst exchanger of each pair is optimised so that the closest match to the existing exchangers is achieved (using actual heat transfer coecients); . the remaining heat load is distributed through the remaining network (second exchanger of each pair), in a way that the minimum additional area is achieved; . new heat transfer coecients are computed so that the additional area on each stream causes full use of the available pressure drop. Non-linearity is introduced into the model by the last task, as the pressure drop is a powerfunction of the heat transfer coecient.
4. The model for minimum additional area The model for the targeting of additional area of a pressure drop constrained HEN has been
M.L. Silva, R.J. Zemp / Applied Thermal Engineering 20 (2000) 1469±1480
1473
formulated as following, given a set of n hot streams, m cold streams, divided into w enthalpy intervals: . hot streams energy balance Ð the energy available from each hot stream i in interval k DHi, k is given by the sum of the heat transferred by the existing exchangers Qex i, j, k and ): the heat to be transferred by the new exchangers Qnew i, j, k DHi, k
n X ÿ j1
new Qex i, j, k Qi, j, k
1
. cold stream energy balances Ð as for the hot streams, for a cold stream j in interval k: DHj, k
m X ÿ i1
new Qex i, j, k Qi, j, k
2
. exchanger design equation for existing area Ð the area of each existing exchanger Aex i, j between hot stream i and cold stream j is given by: w Qex 1 1 X i, j, k ex 3 Ai, j hi hj k1 DTlm, k Ft where hi and hj are the actual heat transfer coecients and DTlm, k is the temperature dierence of interval k (corrected for multipass exchangers by Ft , if required) . exchanger design equation for new area Ð as Eq. (3), but with the new heat transfer and hnew coecients hnew i j ,). Care has been taken as some of the new heat loads might be negative (while still closing the heat balance in the interval). In this case a zero load is used and no additional area is computed: ! w X Qpos 1 1 i, j, k new 4 Ai, j new hnew h DT lm, k Ft j i k1 where ÿ new Qpos i, j, k max 0, Qi, j, k
5
. pressure drop constraints Ð the equations proposed by Jegede [1] are used to compute the pressure drop caused by the additional exchangers DPi ): n ÿ new a X new Ai, j DPi Ki hi
6
j1
where Ki is a constant function of the stream physical properties, ¯ow geometry and mass ¯ow. A similar equation is used for the cold streams. The values of a is a function of the position of the stream in the exchanger (tube or shell). The objective function is then given by the sum of the additional area:
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Table 1 Stream data for base case Stream
Tin (8C)
Tout (8C)
MCp (kW/K)
h (kW/m2 K)
H1 H2 C1 C2 C3
165.0 240.0 125.0 61.0 70.0
95.0 65.0 220.0 192.0 185.0
148.0 86.4 139.0 54.6 62.0
0.45 0.55 0.35 0.40 0.64
obj min
X
Anew i, j
7
The whole set of equations were modelled using GAMS (GAMS Dev. Corp., 1992), and solved by using the non-linear solver CONOPT. For a given requirement of utilities, the solution provides the additional area required for each exchanger match (and therefore, the total area to be added), as well as the heat transfer coecients for the new exchangers. The procedure can be repeated for a set of utility loads, and the best retro®t scenario chosen based on the desired goal: payback, investment, etc. Also, by changing the available pressure drops the impact of investments in the pumping system on the retro®t cost can be analyzed. 5. Case study The retro®t procedure was applied to a ®ve stream problem (Table 1). The existing network is shown in Fig. 2, and the heat exchanger data in Table 2. Physical properties of the streams are shown in Table 3. A retro®t is required to reduce the actual energy requirement (11275 kW hot utility) to 9400 kW, without exceeding the available pressure drops, given in Table 4. The present network area is 2186 m2.
Fig. 2. Base case network.
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Table 2 Exchanger data Exchanger
A ex (m2)
Q (kW)
DPcold (kPa)
DPhot (kPa)
1 2 3 4
133 588 724 742
2160 2560 7153 4340
1.8 5.7 29.0 141.2
21.6 20.0 117.9 25.2
Table 3 Physical property data for base case Stream
r (kg/m3)
m (cPs)
l (W/m 8C)
Cp (J/kg 8C)
H1 H2 C1 C2 C3
750.0 700.0 800.0 750.0 630.0
0.5 0.3 1.0 0.4 0.2
0.12 0.12 0.12 0.12 0.12
2600.0 2600.0 2600.0 2600.0 2600.0
Table 4 Pressure drop restrictions Stream
DP (kPa)
H1 H2 C1 C2 C3
15.0 30.0 20.0 15.0 20.0
Table 5 Additional area requirement Stream match
A ex (m2)
A new (m2)
H1±C1 H2±C1 H1±C2 H2±C2 H1±C3 H2±C3 Total
588 133 0.0 724 742 0
0 170 56 0 0 127 353
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Table 6 Heat transfer coecients for the new exchangers Stream
h (kW/m2 8C)
H1 H2 C1 C2 C3
0.635 0.467 0.725 0.749 0.719
6. New area targeting Using the procedure developed above, the additional area required for each match was computed and is shown in Table 5. An additional area of 353 m2 is required for the retro®t. Also shown is that the new area should be added to exchangers between streams H2±C1, H1± C2 and H2±C3. The optimised heat transfer coecients (Table 6) show that due to the available pressure drop, much higher heat transfer coecients than the coecients of the base case network can be used for the new exchangers (except stream H2). This results in lower area requirements and lower retro®t costs. The retro®t procedure based on the original heat transfer coecients would have targeted a higher investment than really required, missing the optimal retro®t scenario. On the other hand, had the available pressure drop led to overall lower coecients, the required area would be underestimated by the constant-h retro®t procedures and ultimately increase the overall cost due to more exchangers or increased pumping requirement.
7. Network design Once the required additional area is obtained, the base case network is modi®ed using the traditional rules for HEN retro®t. The driving force plot shows how the existing exchangers are placed in the network (Fig. 3) exchanger 1: completely located above the pinch, but does not agree very well with the process diagram. An increase of the cold stream exit temperature from 158 to 1688C shifts exchanger 1 to the right, touching the process curve (Fig. 4a). The heat load is reduced from 2160 to 1927 kW, exchanger 2: very well placed, no need to reposition, exchanger 3: badly placed, and needs repositioning. Since exchangers 2 and 4 were not moved (and therefore, the cooler on stream H1 remained with the original heat load), the only place to reduce cold utility requirement is the cooler on stream H2. A heat balance around this cooler shows that it requires an input temperature of 110.78C in order to meet the desired utility load. Given the new operating temperatures of this exchanger, the energy load is reduced from
M.L. Silva, R.J. Zemp / Applied Thermal Engineering 20 (2000) 1469±1480
Fig. 3. Driving force plot for existing exchangers.
Fig. 4. New driving force plot for exchangers 1 and 3.
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Fig. 5. Modi®ed network.
7153 to 4994 kW, shifting the exchanger closer to the process curve (Fig. 4b), exchanger 4: although this exchanger crosses the pinch, it is overall eciently placed and does not require repositioning. The changes introduced into the network by shifting exchangers leads to an incomplete HEN (Fig. 5). The new exchangers can now be placed on the network so that the remaining heat loads are satis®ed. Driving force plots can again be used to help in positioning the exchangers. The ®nal network for this case study is shown in Fig. 6. Two more exchangers (A and B) and a heater (on stream C2) were added to the network. The heater on stream C3 has a very small load, and could possibly be removed without causing a signi®cant increase in overall utility and/or exchanger area. The optimized heat transfer coecient are used to compute the added area. The areas obtained for exchangers A and B are 93 and 317 m2, respectively, giving a total new area of 410 m2. The predicted area is in reasonable agreement with the ®nal network area, with an error of 16%. This error is due to incomplete vertical placement of the heat exchangers in the ®nal network and the consideration of parallel exchanger arrangement in the targeting procedure. One can also note that the new exchangers are located where the targeting
Fig. 6. Final network design.
M.L. Silva, R.J. Zemp / Applied Thermal Engineering 20 (2000) 1469±1480
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Table 7 Design data of new exchangers Property
Exchanger A
Exchanger B
Total
Area (m2) Shell diameter (m) Tube length (m) Tube count Baes Tube passes hshell (kW/m2 8C) htube (kW/m2 8C) DPshell (kPa) DPtube (kPa)
61 0.73 3.2 318 9 2 0.75 1.79 6.6 20.0
269 1.02 7.2 626 29 4 0.73 2.02 25.4 20.0
330
procedure predicted the largest new exchangers. No new exchanger between streams H1±C2 (as predicted, with area = 56 m2) was required due to the shifting of exchanger 3. Once the new exchangers have been allocated, their pressure drop contribution has to be checked. The procedure by Jegede [1] can be used to determine the exchanger data like tube count, shell diameter, bae spacing and tube length. As this method is based on the same equations used in the targeting procedure, consistency between the estimated area, pressure drop and heat transfer coecients is assured. Since stream H2 has two new exchangers, the available pressure drop is divided between both exchangers to have proportional area. Exchanger A is allocated with 6.6 kPa and exchanger B with 25.4 kPa of the available pressure drop of 30.0 kPa of stream H2. On the tube side, exchanger A and B use all of the 20.0 kPa available (stream C1 and C3). The design data of the exchangers and the computed pressure drops are shown in Table 7. The ®nal exchanger areas are smaller than predicted using the optimized heat transfer coecient, which was slightly larger than predicted. Again, this dierence is due to the way exchangers are allocated in the targeting procedure (parallel) and the ®nal network (series). The ®nal new exchanger area (330 m2) is within 7% of the predicted area, which can be considered a very good result. Also, the available pressure drops are fully satis®ed.
8. Conclusions In this work, the traditional HEN retro®t procedure was modi®ed to account simultaneously for the actual distribution of heat transfer area and pressure drop availability at the targeting stage. This is an improvement over existing methods where either pressure drop or exchanger area distribution is considered, but not both simultaneously. The new retro®t area target procedure was implemented as a non-linear optimization problem, minimizing the additional area. Available pressure drops are the constraints to be satis®ed. Apart from the exchanger area required for the network retro®t, optimized heat transfer coecients for the new exchangers are also obtained, aiding in the design of the new
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exchangers. The application of the proposed procedure to a number of case studies showed that the methodology is capable of correctly targeting retro®t options ahead of design. The ®nal area required for the retro®t (designed heat exchanger network) is close to the area calculated at the targeting stage and the ®nal network pressure drops do not exceed the available pressure drops. For the case shown in this paper, the agreement between predicted and ®nal area was 7%. The detailed exchanger design leads to exchangers with ®lm coecient and pressure close to the one predicted at the targeting stage thus allowing for the pressure drop restrictions to be properly considered in a retro®t project. Although a simpli®ed shell-side method was used, any method where pressure drop can be written as a function of area and heat transfer coecient could be used. The results obtained show that pressure drop is an important issue in heat exchanger retro®t, and should not be neglected. The impact of additional exchangers on the available pressure drop has to be considered to obtain cost-optimal ®nal designs. Acknowledgements The authors acknowledge the ®nancial aid provided by CAPES, Brazil. References [1] Jegede, F.O., 1990. Power, capital and energy cost trade-os in heat exchanger networks. PhD Thesis, UMIST, Manchester. [2] G.T. Polley, M.H. Panjeh Shahi, F.O. Jegede, Pressure drop considerations in the retro®t of heat exchanger networks, Trans. IChemE 68, Part A (1990) 211±220. [3] G.T Polley, M.H. Panjeh Shahi, Interfacing heat exchanger network synthesis and detailed heat exchanger design, Trans IChemE 69, Part A, (1991) 445±457. [4] Shokoya, C.G., 1992, Retro®t of heat exchanger network for debottlenecking and energy saving. PhD Thesis, UMIST, Manchester. [5] T.N. Tjoe, B. Linnho, Using pinch technology for process retro®t, Chem. Eng. 93 (1986) 47±60.