Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 Module‐05 Pinch Design Method for HEN synthesis Lecture‐33: Remaining Problem Analysis‐1st Part Key words: Remaining Problem Analysis, RPA, So far you have learned how to design a HEN if the stream data are given so that the energy performance ( targeted Hot and cold utilities) along with number of units in the HEN as per rules are achieved. However, matching utility targets and number of units does not provide a optimum design. For this purpose, total heat transfer area( from area target), number of shells( from shell target), capital cost( from cost target) should also be considered while designing the HEN. Further, while placing matches during HEN design, it is necessary to know that the accepted matches will give rise to a acceptable good design by keeping the cost of the HEN under control. Thus the placement of match is as important as the design it self as it can lead to a design which will direct to a higher heat transfer area of HEN than estimated by area target. Thus a sophisticated approach is needed which will indicate whether the match placements accepted for the design are correct or not. In short the approach will steer the complete design in correct direction. During design when a match is fixed, it load is generally decided by “Tick off” rule to decrease number of units. However, this does not always pay off. The load of match should be selected in the context of the complete network even without designing the network. It seems to be a difficult task. However, fortunately, by using a technique known as remaining problem analysis(RPA) which exploits the power of targeting ( Energy, Area, shells, cost, etc.) the above challenge can be tackled. Let us consider a complex design of HEN in which the technique remaining problem analysis is employed which uses energy targeting. Please note that energy target can be replaced by other targeting methods such as area, shell, cost, etc. for RPA. The problem Table analysis(PTA) of a problem provides the hot utility(QHmin) and cold utility(QCmin) consumption data a prior to the design of HEN. During network design when first match is placed, it will be wise to determine whether the considered match brings some energy penalty to the complete HEN design( without completing the design) meaning that after the match is placed QHmin or QCmin or both may increase. If it is so, then, the match is not a correct match. This penalty can be determined by performing PTA on reaming part of the problem leaving those part of the hot and cold streams satisfied by the match. The PTA can provide results as discussed below: 1. The PTA analysis may show an unchanged QHmin and QCmin. This will lead to the conclusion that the match is not penalizing the design in terms of utility usage and hence is an acceptable match. 2. If the PTA analysis predicts increased amount of hot and cold utilities than QHmin and QCmin, then it should be concluded that the match is penalizing the design. This might be Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 due to cross‐pinch transfer of heat which will take place if the design is completed. This may happen if the load of the match is too big due to “tick off” rule employed during match selection. In such a situation the match has to be abandoned and a fresh new match is selected and then again the PTA is applied. At this point the lecture merits some discussion on area targeting as it is going to be used for remaining problem analysis. Area targeting is based on vertical heat transfer from hot composite curve to cold composite curve. If the film side heat transfer coefficients of streams do not differ appreciably this method predicts minimum area for most cases. Under the above condition matches placed in the HEN will mimic vertical heat transfer between composite curves. However, if the heat transfer coefficients of streams vary significantly, then vertical heat transfer predicts area which is more than the minimum area. Under the above circumstances a careful selection of non‐vertical matching is required to reach minimum area predicted by linear programming method. As stated above any targeting can be used with remaining problem analysis. Following is an example where area targeting is used for remaining problem analysis. The remaining problem analysis is applied on both the region of pinch i.e. above and below pinch to steer the design in correct direction. Accordingly the design task is divided into two parts as given below: 1. Develop a MER design of the Hot End(above pinch) having area as close to area target with minimum number of units 2. Develop a MER design of the Cold End(below pinch) having area as close to area target with minimum number of units Let consider the stream data given in the following Table 5.11 (Tmin = 10 0C) Table 5.11 Stream data to demonstrate remaining problem analysis Stream Name Hot Stream Hot Stream Cold Stream Cold Stream Hot Utility Cold Utility Supply Temp. 140 160 40 70 180 20 Target Temp. 50 40 110 100 179 30 CP (MW/ K) 0.25 0.1 0.25 0.5 h (kW/m2 /K ) 0.15 0.15 0.15 0.15 0.15 0.15 The grid diagram showing hot and cold streams for the above problem is shown below in Fig 5.54 Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 Fig. 5.54 Grid diagram of the hot and cold stream from problem in Table 5.11 The grid diagram of the same problem with utility streams is shown in Fig. 5.55 2000
400
Fig. 5.55 Grid diagram of the problem with utility streams Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 Using software HINT, the area target for the complete problem( Above + Below pinch) is 22668.2 m2 HEN design above the pinch(hot end) using remaining problem analysis & PDM Fig. 5.56 shows the selective streams above the pinch 2000 Fig. 5.56 Streams available for above the pinch design with hot utility Now let us design Heat exchanger network for this region. The design criteria for the heat exchanger network above the pinch can be given as: ‐ CPHot <= CPCold Nhot <=Ncold The area target for this problem above the pinch (using HINT) = 13546.2 m2 Now, let us consider a match between stream 1 and 3 as CP of stream 1 is less than CP of stream 3 (CPHot <= CPCold) having a heat duty of 10000 kW. This will tick off stream 3 above the pinch as shown in Fig. 5.57. The heat exchanger is HE0. Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 The overall heat transfer coefficient, U, of this heat exchanger(HE0) = (1/ ((1/0.15) + (1/0.15))) = 0.075 kW/ m2. K Also, Δ TLMTD for this exchanger(HE0) can be calculated as: ‐ 140 0C T= 30 0C 80 0C
0
0
110 C T= 10 0C 70 C
Δ TLMTD = ((30‐10)/ ln (30/10)) = 20/ 1.0986 = 18.205 0C A0 = Q/ (U* Δ TLMTD) = 10000 / (18.205 * 0.075) = 7324 m2 HE0 100. √ 10000 kW Fig. ‐‐‐‐‐‐ Grid diagram of the problem with utility streams showing HE1 Fig. 5.57 Placement of HE0 and ticking off stream 3 above the pinch Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 The modified grid diagram for the remaining problem after removing stream 3 above the pinch modifying stream‐1 ( after loading of HE0 on stream‐1 its temperature drops to 100C) is shown in Fig. 5.58. This is done to estimate the area target of of the remaining problem. 4
Fig 5.58 Remaining streams after removing stream 3 and decreasing the temperature interval of stream 1 to 100‐80C The area target for the system shown in Fig.5.58 using HINT = 10019.8 m2 Thus, The total Area Target after placement (HE0) and remaining problem after it ( as shown in Fig.5.58) = 10019.8 + 7324 = 17343.8 m2 However, the area target of the above pinch region was 13546.2 m2 Thus, Error = ((17343.8 – 13546.2) / 13546.2)*100 = 28 % Thus, this match is causing a penalty of area of 28% and thus is not a correct match though it is a feasible match. If we include this match it is going to increase the total area of the HEN and the HEN area will not be close to the targeted area. Due to above reason this match is dropped and a new match is searched within the design rules. Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 Now, let us consider a heat exchanger (HE1) between stream 1 and 4 (CPHot <= CPCold) having a heat duty of 15000 kW. This will tick off stream 4 and stream 1 above the pinch as shown in Fig.5.59. Now, U for heat exchanger(HE1) = (1/ ((1/0.15) + (1/0.15))) = 0.075 kW/ m2. K Also, Δ TLMTD for this heat exchanger(HE1) can be calculated as: 140 0C 0
T= 40 C 0
100 C 80 0C
0
T= 10 0C 70 C
HE1 √ √ 15000 kW
Fig. 5.59 Grid diagram of the problem with utility streams showing HE1
Δ TLMTD = ((40‐10)/ ln (40/10)) = 30/ 1.3863 = 21.64 0C A1 = Q/ (U* Δ TLMTD) = 15000 / (21.64 * 0.075) = 9242.1 m2 The remaining problem shown as modified grid diagram after removing stream 1 and 4 above the pinch is shown in Fig.5.60 Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 The area target for this system shown in Fig.5.60 using HINT = 4359.02 m2 Thus, The total Area Target after placement (HE0) and remaining problem after it ( as shown in Fig.5.58) = 4359.02 + 9242.1 = 13601.12 m2 The area target of the above pinch region was 13546.2 m2 Thus, Error = ((13601.12 – 13546.2) / 13546.2)*100 = 0.405 % Thus, this match is a correct match and can be included in the HEN design. Fig. 5.60 Grid diagram of the problem after removing streams 1 & 4 above the pinch
Now, let us place the second match with heat exchanger (HE2) having a heat duty of 8000 kW between stream 2 and 3 (CPHot <= CPCold) above the pinch. This will tick off stream 2 above the pinch leaving 2000 kW hot utility requirements on stream 3. Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 HE 1
√ HE 2
√ 10000 kW
√ 15000 kW
Fig. 5.61 Grid diagram of the problem with utility streams showing HE1 & HE2 For HE2: ‐ Now, U for heat exchanger(HE2) = (1/ ((1/0.15) + (1/0.15))) = 0.075 Also, Δ TLMTD for this heat exchanger can be calculated as: ‐ 0
T= 50 C 140 0C 0
110 C 80 0C
0
70 C
Δ TLMTD = ((50‐10)/ ln (50/10)) = 40/ 1.6094 = 24.854 0C A1 = Q/ (U* Δ TLMTD) = 8000 / (24.854 * 0.075) = 4291.7 m2 T= 10 0C Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 The modified grid diagram after removing stream 1,2 and 4 above the pinch is shown in Fig.5.62 Heater 102.
3
2000 kW Fig. 5.62 Grid diagram of the problem with utility streams after ticking off streams 1, 2 & 4 The area target for this system shown in Fig.5.62 using HINT is 195.16 m2 Thus, Thus the area target of all selected matches(HE1 & HE2) plus remaining problem shown in Fig.5.62 = 195.16 + 4291.7 + 9242.1 = 13728.96 m2 Whereas, The Area Target of above pinch region = 13546.2 m2 Thus, Error = ((13728.96 – 13546.2) / 13546.2)*100 = 1.35 % Though, the error is appreciable( in comparison to other errors) but this is the only match available. The final network of heat exchanger above the pinch is shown in Fig. 5.63. Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 HE 1
HE 2 10000 kW 15000 kW
Fig.5.63 Heat Exchanger Network above the pinch HEN design below the pinch(cold end) using remaining problem analysis & PDM The HEN design is executed below the pinch in similar manner as above the pinch. Below the pinch design rules are: CPhot > CPcold and Nhot > Ncold The grid diagram for the above problem below the pinch is shown in Fig. 5.64. Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 Now, from the Fig.5.65, one can see that there is only one possible of match satisfying the CP criteria, that is between stream 1 and 3 and it ticks off both the streams below the pinch. Fig. 5.64 Grid diagram of the problem below the pinch with cold utility Therefore, this match must be used. HE 3
7500 kW
Fig. 5.65 Heat exchanger network below the pinch
Therefore, the overall heat exchanger network can be drawn as shown in Fig. 5.66 . Remaining Problem Analysis‐1st Part Module‐05 Lecture‐33 HE 1
HE 3
HE 2 10000 kW 7500 kW
15000 kW
Fig. 5.66 Final Heat Exchanger network for the problem in Table 5.11
References 1. A´ngel Martı´n *, Fidel A. Mato, Hint: An educational software for heat exchanger network design with the pinch method, education for chemical engineers 3( 2008 ) e6 – e1 4 2. Linnhoff, B. and Flower, J.R., 1978, Synthesis of heat exchanger networks, AIChE J, 24(4): 633. 3. Linnhoff, B. and Hindmarsh, E., 1983, The pinch design method for heat exchanger networks, Chem Eng Sci, 38(5): 745. 4. Linnhoff, B., Townsend, D.W., Boland, D., Hewitt, G.F., Thomas, B.E.A., Guy, A.R. and Marsland, R.H., 1994, A User Guide on Process Integration for the Efficient Use of Energy. (The Institution of Chemical Engineers, Rugby, Warks, UK). 5. Smith, R. 2005, Chemical Process: Design and Integration (second ed.), (J. Wiley, J Wiley.