00:00:02.290 --> 00:00:07.680 In this screencast, we're going to design a heat exchanger network based on information 00:00:07.680 --> 00:00:13.580 we collected in a previous screencast with the transfer of energy between two hot streams 00:00:13.580 --> 00:00:19.130 and two cold streams, and utilities that we designated also in the last screencast. 00:00:19.130 --> 00:00:27.590 So a little background first on defining this pinch point, and how we would go about starting 00:00:27.590 --> 00:00:29.770 to design our heat exchanger network. 00:00:29.770 --> 00:00:37.050 So if we look at a heat exchanger between a hot stream and a cold stream, we've designated 00:00:37.050 --> 00:00:45.770 our cold stream as C, so we have our inlet cold temperature, and our cold outlet, we 00:00:45.770 --> 00:00:49.190 have our hot inlet, and our hot outlet. 00:00:49.190 --> 00:00:54.980 We have some heat transfer, Q, and a temperature difference between the hot inlet and cold 00:00:54.980 --> 00:01:00.579 outlet as delta T2, the same on the other side, we designate it delta T1, and then the 00:01:00.579 --> 00:01:10.360 values Ch and Cc are the specific heat flow rates, and the units on this is given as an 00:01:10.360 --> 00:01:12.300 energy per temperature. 00:01:12.300 --> 00:01:18.250 So if we write out our equation for our heat transfer, it's just going to be for the hot 00:01:18.250 --> 00:01:25.021 stream our Ch times the temperature difference between the outlet and the inlet, and we can 00:01:25.021 --> 00:01:28.300 do the same for the other side. 00:01:28.300 --> 00:01:30.600 So we can rearrange these equations to get the following. 00:01:30.600 --> 00:01:35.310 Now hopefully what you see here is that if we subtract the two equations, these two groups 00:01:35.310 --> 00:01:42.030 form our delta T2 and these two groups form our delta T1. 00:01:42.030 --> 00:01:47.900 This means that we get the following result, where delta T2 minus delta T1 is equal to 00:01:47.900 --> 00:01:55.510 the heat transfer, Q, times Cc minus Ch over Cc times Ch. 00:01:55.510 --> 00:01:57.200 So what does this mean? 00:01:57.200 --> 00:02:00.700 This means that when we're designing our two heat exchanger networks, one on the hot side 00:02:00.700 --> 00:02:04.560 and one on the cold side of the pinch point, we're going to examine them in the following 00:02:04.560 --> 00:02:05.560 manner. 00:02:05.560 --> 00:02:09.239 First, we use this equation to say that if we're designing on the hot side, then delta 00:02:09.239 --> 00:02:15.370 T1, this is for the hot side of the pinch, delta T1 is going to be our designated minimum 00:02:15.370 --> 00:02:16.849 approach temperature. 00:02:16.849 --> 00:02:24.049 This leaves us with a delta T2 equaling delta Tmin plus the value on the right side. 00:02:24.049 --> 00:02:30.889 Now, to ensure that our delta T2 here is going to be greater than our approach temperature, 00:02:30.889 --> 00:02:34.680 this value on the right side has to be positive. 00:02:34.680 --> 00:02:41.909 Now Q is positive and our heat capacity flow rates are positive, so that means Cc has to 00:02:41.909 --> 00:02:44.900 be greater than or equal to Ch. 00:02:44.900 --> 00:02:50.230 Now the following is going to be true if we're looking at the cold side: We set delta T2 00:02:50.230 --> 00:02:56.319 equal to delta Tmin, we rework this equation, this time there's going to be a negative sign. 00:02:56.319 --> 00:03:00.560 Now for this to be true and to make our delta T1 is going to be greater than delta Tmin, 00:03:00.560 --> 00:03:04.790 our Ch has to be greater than or equal to our Cc. 00:03:04.790 --> 00:03:08.950 So we use these two guidelines when we're designing our heat exchanger networks to match 00:03:08.950 --> 00:03:13.389 streams and determine whether or not it's a feasible match. 00:03:13.389 --> 00:03:18.480 So let's practice this on our diagram here where we have our four streams, our pinch 00:03:18.480 --> 00:03:24.319 point, our pinch temperature for both the hot and cold stream, and our source and target 00:03:24.319 --> 00:03:25.319 temperatures. 00:03:25.319 --> 00:03:30.189 So if we start with the hot side, which is arbitrary but something that's typically done 00:03:30.189 --> 00:03:35.989 is to start with the hot side of the pinch, then we want to match two streams such that 00:03:35.989 --> 00:03:39.519 Cc is greater than or equal to Ch. 00:03:39.519 --> 00:03:46.319 So in that case, if we matched C2, we could match it with either H2 or we could match 00:03:46.319 --> 00:03:52.459 it with H1, since in both cases, our value of 5 is greater than the values for the hot 00:03:52.459 --> 00:03:53.459 streams. 00:03:53.459 --> 00:04:02.219 However, if we match C2 with H2 and try to match C1 with H1, you would see that H1 has 00:04:02.219 --> 00:04:07.029 a higher specific heat flow rate value than the cold stream, and that would mean that 00:04:07.029 --> 00:04:10.879 the stream match is an infeasible match. 00:04:10.879 --> 00:04:12.239 So we wouldn't want to do that. 00:04:12.239 --> 00:04:18.880 That leaves us with let's start with C2 to H1, and then also draw C1 to H2. 00:04:18.880 --> 00:04:24.570 So we want to do this to maximize the potential load on the heat exchanger, so we would calculate 00:04:24.570 --> 00:04:28.880 what the heat transfer would be for that connection. 00:04:28.880 --> 00:04:38.090 So if we look at this node right here, and we say that Q is equal to 3 times the difference 00:04:38.090 --> 00:04:45.060 of 180 minus 90, then we would get 270 kilowatts. 00:04:45.060 --> 00:04:54.030 We do the same thing for the other node, and we would see that 5 times 140 minus 80 is 00:04:54.030 --> 00:04:55.940 equal to 300 kilowatts. 00:04:55.940 --> 00:05:00.460 As you can see, at this node, we could decrease the temperature from 180 all the way to 90, 00:05:00.460 --> 00:05:04.600 but we cannot increase the cold stream from 80 to 140. 00:05:04.600 --> 00:05:08.930 So we can check mark that node knowing that we can go from 180 degrees and cool it to 00:05:08.930 --> 00:05:16.330 90 degrees, but for the other node, we know that this load is 270 kilowatts, which means 00:05:16.330 --> 00:05:23.620 that we could raise the temperature from 80 degrees, and we get that using the same calculation, 00:05:23.620 --> 00:05:30.330 just showing that Q is equal to 270 times 5 and the temperature difference, which we 00:05:30.330 --> 00:05:34.580 could say is x, some unknown temperature, minus 80. 00:05:34.580 --> 00:05:39.460 We could calculate the load from our stream, our connection between H2 and C1, again you 00:05:39.460 --> 00:05:43.980 can see with the hot stream we have a lower load than that with the cold stream. 00:05:43.980 --> 00:05:49.390 So we can decrease from 150 to 90, but we cannot increase the cold stream 1 from 80 00:05:49.390 --> 00:05:51.040 to 135. 00:05:51.040 --> 00:05:55.470 So again we write the load under the connection, and we calculate what the new temperature 00:05:55.470 --> 00:06:02.300 would be, which in this case would be a 30 degree difference and a maximum of 110 degrees. 00:06:02.300 --> 00:06:08.630 So we've already reduced our hot streams from the inlet to our pinch temperature, so we 00:06:08.630 --> 00:06:14.670 would need to add some kind of hot utility to raise it from their temperatures to their 00:06:14.670 --> 00:06:21.170 final target temperatures, and we can write again what the duty on these utilities would 00:06:21.170 --> 00:06:22.180 be. 00:06:22.180 --> 00:06:28.670 So to go from 110 to 135, change of 25 degrees, times our capacity ratio of 2 would give us 00:06:28.670 --> 00:06:30.980 50 kilowatts. 00:06:30.980 --> 00:06:36.670 So our temperature difference of 6 degrees times our heat capacity flowrate gives us 00:06:36.670 --> 00:06:41.750 a load of 30 kilowatts for this exchanger. 00:06:41.750 --> 00:06:46.360 So as you can see, adding up the exchangers on the left side, we have 80 kilowatts, which 00:06:46.360 --> 00:06:50.840 is what we had calculated before as our minimum energy target requirement for the hot side. 00:06:50.840 --> 00:06:55.510 Now moving to the cold side, we do the same thing and we follow the rule that our hot 00:06:55.510 --> 00:07:00.080 side loads have to be greater than our cold side. 00:07:00.080 --> 00:07:03.639 So we don't have a C2, we just have the C1 to work with. 00:07:03.639 --> 00:07:11.090 So let's match that, following the rule that it has to be higher, we'll match it with H1 00:07:11.090 --> 00:07:13.520 and we'll calculate the Q associated with this. 00:07:13.520 --> 00:07:19.620 If it were to go from 90 to 60, that would be a temperature change of 30 times 3, which 00:07:19.620 --> 00:07:22.480 gives us 90 kilowatts. 00:07:22.480 --> 00:07:28.480 On the bottom, to go from 30 to 80 gives us 100 kilowatts. 00:07:28.480 --> 00:07:34.530 So again our limit is 90 kilowatts, so we'll put that under the exchange, calculate what 00:07:34.530 --> 00:07:40.670 our temperature difference would be, so we can completely cool our hot stream 1 from 00:07:40.670 --> 00:07:46.650 90 to 60, but we can only heat up our cold side stream from 80, and this is going to 00:07:46.650 --> 00:07:56.400 be 35 degrees, and we calculate that again by 90 equaling 2 times 80 minus x, and you'll 00:07:56.400 --> 00:07:59.700 see that x is equal to 35. 00:07:59.700 --> 00:08:06.130 So now we need to cool our H2, and we could either do that trying to use our cold stream 00:08:06.130 --> 00:08:07.340 or a cold utility. 00:08:07.340 --> 00:08:13.370 Since we're at 30 degrees as our inlet and 35 as our outlet, we're not going to worry 00:08:13.370 --> 00:08:16.389 about crossing over our minimum approach temperature. 00:08:16.389 --> 00:08:23.130 So we could go ahead and try to match these up, and the load that we would have would 00:08:23.130 --> 00:08:28.560 be the 5 degrees times 10, so it would be 10 kilowatts, so we can effectively cool down 00:08:28.560 --> 00:08:33.039 H2 10 degrees to our 80 degrees Celsius. 00:08:33.039 --> 00:08:39.599 However, our final temperature that we are looking for for our H2 stream is 30 degrees. 00:08:39.599 --> 00:08:46.160 So at this point, we've completely heated our C1 stream, we've completely cooled our 00:08:46.160 --> 00:08:51.300 H1 stream, and we have to further cool H2, so we have to add some kind of cold utility 00:08:51.300 --> 00:08:56.610 that would take us from 80 to 30, and that would be equivalent to using 50 kilowatts 00:08:56.610 --> 00:08:57.610 of cooling. 00:08:57.610 --> 00:09:03.490 And if you recall, that's what we had determined in the previous screencast for our MER target 00:09:03.490 --> 00:09:05.470 for the cold side of the pinch point. 00:09:05.470 --> 00:09:09.559 So our redrawn final heat exchanger network would look like the following, making sure 00:09:09.559 --> 00:09:13.370 we have appropriate connections between the 00:09:13.370 --> 00:09:20.150 We would label the duties under each connection, and then our utilities. 00:09:20.150 --> 00:09:26.050 You can see we have our cold utility here, and our two hot utilities on the hot side. 00:09:26.050 --> 00:09:32.290 So this is a network designed to minimize the energy requirements from our utilities. 00:09:32.290 --> 00:09:39.910 Now, another possibility is to identify heat loops and minimize the amount of heat exchangers, 00:09:39.910 --> 00:09:42.459 and that's something we'll discuss in further screencasts. 00:09:42.459 --> 00:09:47.809 So hopefully this gives you a good idea on how to design a heat exchanger network using 00:09:47.809 --> 00:09:51.070 the temperature interval method and stream matching at the pinch.
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