PART 4 PINCH DESIGN METHOD MAXIMUM ENERGY RECOVERY NETWORKS
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1 PART 4 PINCH DESIGN METHOD MAXIMUM ENERGY RECOVERY NETWORKS
2 MER NETWORKS Networks featuring minimum utility usage are called MAXIMUM ENERGY RECOVERY (MER) Networks.
3 DIVISION AT THE PINCH RECALL THAT No heat is transferred through the pinch. This makes the region above the pinch a HEAT SINK region and the region below the pinch a HEAT SOURCE region.
4 Heat Sink Heat is obtained from the heating utility Minimum heating utility 9.0 T Pinch Heat Source H Minimum cooling utility Heat is released to cooling utility
5 CONCLUSION One can analyze the two systems separately, that is, Heat exchangers will not match streams above the pinch with streams below the pinch
6 PINCH MATCHES Consider two streams above the pinch T H,in T p T C,out = T p - ΔT min + Q/FCp C T H,in = T p +Q/FCp H But T H,in > T C,out + ΔT min. Thus replacing one obtains Q/FCp H > Q/FCp C T C,out Q T p - ΔT min FCp H < FCp C Golden rule for pinch matches above the pinch. ΔT min ΔT min Violation when FCpH > FCp C
7 Below the Pinch T C,in = T p - ΔT min - Q/FCp C T p T H,out T H,out = T p -Q/FCp H But T H,out > T C,in + ΔT min. Thus replacing one obtains T p - ΔT min Q T C,in FCp C < FCp H Golden rule for pinch matches below the pinch. ΔT min ΔT min Violation when FCp C > FCp H
8 CONCLUSION Since matches at the pinch need to satisfy these rules, one should start locating these matches first. Thus, our first design rule: START BY MAKING PINCH MATCHES
9 TICK-OFF RULE Once a match has been selected how much heat should be exchanged? As much as possible! (We want to minimize units, so once we have one, we make the biggest use of it possible) This means that one of the streams has its duty satisfied!!
10 HANDS ON EXERCISE ΔH=27 MW ΔH=-30 MW T= T=230 0 C REACTOR 2 T=200 0 C T=80 0 C ΔH=32 MW ΔH=-31.5 MW T=20 0 C T=180 0 C REACTOR 1 T=250 0 C T=40 0 C Stream Type Supply T Target T ΔH F*Cp ( o C) ( o C) (MW) (MW o C -1 ) Reactor 1 feed Cold Reactor 1 product Hot Reactor 2 feed Cold Reactor 2 product Hot ΔT min =10 o C PINCH=150 o C
11 HANDS ON EXERCISE FCp= C C 40 0 C 5 H C 80 0 C C 20 0 C C 1 FCp= C C 2 Stream Type Supply T Target T ΔH F*Cp ( o C) ( o C) (MW) (MW o C -1 ) Reactor 1 feed Cold Reactor 1 product Hot Reactor 2 feed Cold Reactor 2 product Hot ΔT min =10 o C PINCH=150 o C
12 ABOVE THE PINCH FCp= C C 5 H C C C 1 FCp= C C 2 Which matches are possible?
13 Pinch matches above the Pinch FCp= C C 5 H C C C 1 FCp= C C 2 The rule is that FCp H < FCp C. The candidates are: H1-C1, H1-C2 and H2-C2. Because all hot streams at the pinch need to participate in a pinch match, we therefore can only choose the matches H1-C1 and H2-C2.
14 Pinch matches above the Pinch FCp= C C C 5 H C FCp= C C C C 1 C 2 The tick-off rule says that a maximum of 8 MW is exchanged in the match H1-C1 and as a result stream C1 reaches its target temperature. Similarly 12.5 MW are exchanged in the other match and the stream H2 reaches the pinch temperature.
15 Pinch matches below the Pinch FCp= C 40 0 C 5 H C 20 0 C C 1 The rule is that FCp C < FCp H. Only one match qualifies: H2-C1 Below the pinch all cold streams need to participate in pinch matches
16 ANSWER (below the pinch) FCp= C 40 0 C 5 H C C 20 0 C C The tick-off rule says that a maximum of 17.5 MW is exchanged in the match H2-C1 and as a result stream H2 reaches its target temperature.
17 COMPLETE NETWORK AFTER PINCH MATCHES FCp= C C C 40 0 C 5 H C 80 0 C FCp= C C C C C 20 0 C C 1 Streams with unfulfilled targets are colored.
18 NON-PINCH MATCHES FCp= C C C 40 0 C 5 H C 80 0 C FCp= C C C C C 20 0 C C 1 Away from the pinch, there is more flexibility to make matches, so the inequalities do not have to hold. The pinch design method leaves you now on your own!!!!! Therefore, use your judgment as of what matches to select!!
19 NON-PINCH MATCHES FCp= C C C 40 0 C 5 H C 80 0 C FCp= C C C C C 20 0 C C 1 We first note that we will use heating above the pinch. Thus all hot streams need to reach their inlet temperature. We are then forced to look for a match for H1.
20 NON-PINCH MATCHES The match is H1-C1. We finally put a heater on the cold stream FCp= C C 40 0 C 5 H C 80 0 C FCp= C C H C C 20 0 C C 1
21 NON-PINCH MATCHES Below the pinch we try to have the cold streams start at their inlet temperatures and we later locate coolers (one in this case). FCp= C C C 40 0 C 5 H C C C 20 0 C C 1 FCp= C H C
22 UNEQUAL NUMBER OF STREAMS AT THE PINCH Indeed, if the number of hot streams is larger than the number of cold streams, then no pinch matches are possible. Consider this (new) example: FCp= FCp=0.1 Target=170 O C Target=140 O C H 2 H 3 FCp= O C 100 O C 140 O C 130 O C O C 90 O C O C C 1 C 2 Assume the matches -C 1 and the matches H 2 -C 2 have been selected. Since H 3 needs to go to the pinch temperature, there is no cold stream left to match, even if there is portions of C 1 or C 2 that are left for matching. Such matching would be infeasible. What is then, the solution?
23 UNEQUAL NUMBER OF STREAMS AT THE PINCH Split cold stream until the inequality is satisfied. FCp= FCp=0.1 H 2 H O C 100 O C 140 O C 130 O C Target=170 O C O C 90 O C C 1 Target=140 O C 5 FCp= O C 110 O C C 2 Notice that different combinations of flowrates in the split satisfy the inequality. 3
24 UNEQUAL NUMBER OF STREAMS AT THE PINCH Above the pinch, we notice the following rule S H S C If that is NOT the case, we split a cold stream until S H =S C A similar rule can be discussed below the pinch, that is, S H S C If that is NOT the case, we split a cold stream until S H =S C
25 INEQUALITIES NOT SATISFIED Consider the following caseabove the pinch We notice that FCp H >FCp C (needs to be FCp H FCp C ) FCp= O C 100 O C Target=170 O C 90 O C C 1 Target=140 O C FCp=0.4 C 2
26 INEQUALITIES NOT SATISFIED The hot stream needs to be split 150 O C 100 O C FCp=0.3 Target=170 O C 140 O C 90 O C C 1 Target=140 O C FCp= O C 10 C 2 15
27 INEQUALITIES NOT SATISFIED Below the Pinch : FCp= O C Target=40 O C FCp=0.3 H 2 Target=20 O C FCp= O C 30 O C C 1
28 INEQUALITIES NOT SATISFIED The cold stream needs to be split FCp= O C 40 O C Target=40 O C FCp=0.3 H 2 60 O C Target=20 O C FCp= O C O C C 1 12
29 COMPLETE PROCEDURE ABOVE THE PINCH Start Yes FCp H FCp C Yes S H S C at pinch? No No Split Cold Stream Place matches Split Hot Stream
30 COMPLETE PROCEDURE BELOW THE PINCH Start Yes FCp H FCp C at pinch? Yes S H S C No No Split Hot Stream Place matches Split Cold Stream
31 HANDS ON EXERCISE Type Supply T Target T F*Cp ( o C) ( o C) (MW o C -1 ) Hot Hot Cold Cold ΔT min =50 o C Minimum Heating Utility= 9.2 MW Minimum Cooling Utility= 6.4 MW
32 ANSWER FCp= C FCp= C C C FCp=0.04 H C C C 6 FCp= C C C 1 FCp= C C C C 2
33 NOTE ON UNIT TARGETING N min = (S-P) above pinch + (S-P) below pinch If we do not consider two separate problems, above and below the pinch we can get misleading results.
34 FCp=0.15 EXAMPLE C C 40 0 C C 5 H C C C 20 0 C C 1 FCp= C H C N min = (S-P) above pinch + (S-P) below pinch = =(5-1) + (4-1) = 7 If we do not consider two separate problems Nmin= (6-1)= 5, which is most of the time wrong Note: A heat exchanger network with 5 exchangers exists, but it is impractical and costly. This is beyond the scope of this course.
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