Dear students, hi to everyone and welcome to CHEDSE4 lecture 16 on the grand composite curve. In this lecture, I expect you to learn the meaning and the purpose of the grand composite curve and how to represent it. So our aim is to go mainly from the plot that you see on the left-hand side of the slide where the hot and cold composite curves are highlighted to the plot to the right-hand side, which is the grand composite curve. We saw in the previous lecture 15 how to organise and to draw the problem table which is the analytical expression of the hot composite and cold composite curves. In particular, by applying the notions of heat cascade, we were able to locate the pinch point in a very precise way and also to determine the minimum utility loads for the heating utility and for the cooling utility. Now, we need to see how it's also possible to arrange this knowledge in order to make this plot, which probably you have never seen before. It's called the grand composite curve and it is simply the plot of the shifted temperature on the y-axis against the modified cumulative net heat transfer on the x-axis, as you can see here. So I have reported here for you the same two columns of the previous problem table. So in the left column you see the shifted temperatures going from the highest temperature of 450 Kelvin to the lowest temperature, down to 310 Kelvin. While in the other column, I have reported here for you the modified net cumulative heat transfer. If you remember, it started from 48 kilowatt, the minimum hot utility load, arriving down to 6 kilowatt, which was the minimum cold utility load. Now, the grand composite curve shows the cumulative surplus or deficit of energy for each temperature interval and it can be regarded as the graphical plot of the problem table. Even on this figure here, it's very simple to safely locate the pinch point, which is where the shifted temperature is at a value of the cumulative modified net heat flow equal to 0. So it's very clear that the sigma delta H star is 0 here, so the corresponding temperature point is 340 Kelvin, as you can see here. While considering this gap of delta H up here, this will locate the minimum utility load for the heaters. While at the bottom, looking at this gap in the enthalpy, looking at this enthalpy interval, this will notify the minimum cooling utility load, so it's very important from this point of view. In particular, we can extract additional important information from the grand composite curve, such as what is the minimum amount of heating or cooling that needs to be supplied at any given temperature. In particular, as we know, when we have to design a cold or hot utility, we should choose the temperature level of our heaters and our coolers in terms of service fluids. And there could be a lot of differences in these temperature levels depending on our resulting hot and cold composite curves. For example, here we can see that it's always possible to consider the shaded area delimited by the points A, B, C, shaded in orange in this figure here, and this particular area would locate a pocket which could be defined as a self-sufficient zone for process heat transfer. So this means that it's always possible to transfer heat between the cold and the hot streams constituting our network of heat exchangers without using any external utility. And it's particularly interesting for the heating duty that, as we know, is 48 kilowatt of power, but we don't really know at what temperature level we should actually supply this hot utility. If 340 Kelvin is the pinch temperature, potentially, we would be able to supply the heating duty at any given temperature between the range of 340 and 450 Kelvin, as you can see here, but if we have specific pocket areas in our grand composite curve, then we're not forced to supply a heating utility at the highest temperature level, so in this case, 450 Kelvin. We don't have to supply, for example, condensing steam or hot fuel oil at 450 Kelvin of temperature because the cold streams will be able to transfer heat to the hot streams, the other way around, hot streams will be able transfer heat the cold streams in order to cover all this area. So this means that if we consider this temperature here identified from point C and assume that it's equal to 353 Kelvin, allowing a typical delta T minimum of 10 Kelvin, we get 363 Kelvin. So this is the highest temperature for the minimum temperature of the hot utility that we should be using. And this information is very important because the minimum temperature determines the quality of the required utility, it is always more expensive to use condensing steam at higher pressure, hence at higher saturation temperature compared to low pressure condensing steam. And we can extract this information from the grand composite curve, as you can see here. A similar discussion can also be drawn for the cooling utility, although the cooling utility is less important in the sense that we usually utilise cooling water or cooling air that are available at around room temperature and are always available to be utilised in order to cool down all the process streams. Of course, if we require a cryogenic temperature, then we would have to design a proper refrigeration cycle consuming power in the compression for the cycle itself. The last piece of information that we could extract from the grand composite curve is also not only the actual temperature levels of the hot and cold utilities, but also the type of utilities that we could utilise. And the type of utility can be suggested by the slope, T over delta H, on this plot. So I think, let me now open, 1 second, the digitaliser. Okay, so for example, here you see that we need to supply a hot utility to heat up this stream here which has, in a sense, a slope which is very small, so it's close to being horizontal. So this means that if we have here our T-Q plot, that we can always represent in this way here, so T-Q plot, and, of course, if our stream has to be heated up in this way but, of course, its slope is very limited. This means that we could use, as a hot utility, we could use a utility that has a slope very close to being horizontal, for example, condensing steam, as we can see here, in order to limit what is the delta T required in the overall process, as you can see here. Of course, there is no point to use, for example, if we consider that this will be our minimum delta T, there is no reason to use condensing steam at higher pressure, for example, steam that will have this information on the T-Q plot otherwise this delta T will be higher. At the same time, for example, in another configuration here, what happens is that if our stream that needs to be heated up is very steep in terms of the T-Q diagram, probably it would be better to use a utility that has this shape here. Once again, in order to limit the delta T present between the two streams themselves. And this utility here won't be probably condensing steam that has a horizontal line in the T-Q plot, but it could be, for example, the flue gas, the exhaust gas from a process power plant. We don't really want to use condensing steam in this application because if the stream to be heated up is very steep, then, of course, this will be our condensing steam and, as you can see here, there will be a massive delta T in this area so we will be wasting our energy from this point of view. It's also possible that sometimes you need to supply, let's say, the hot utility at the highest temperature level because for example, if this is the shifted temperature and if this is the modified  cumulative net heat flow, sigma delta H star. For example, if the grand composite curve has this particular shape, as you can see here, then of course, we will see that this could be one, lets say, pocket identified in here. This will be a second pocket, which can always be identified in this region here. But we cannot really use a full integration between cold and hot streams in order to provide this heat. And this means that the hot utility that needs to be supplied here, the hot utility needs to be considered at the highest possible temperature level, which will be a temperature here, T high. Okay, so after discussing these very important aspects of the grand composite curve, so we are ready also to summarise the so-called golden rules in the pinch analysis, which are the following: rule number one, never transfer heat across the pinch. Rule number two, do not use cold utilities above the pinch, only hot utilities. And rule number three, do not use hot utilities below the pinch, only cold utilities. In other words, an optimal process must use an amount of energy equal to its thermodynamic targets. And not optimal processes are usually identified with greater speed and confidence because it's much easier to start to match streams with each other, but probably we won't be arriving to the maximum energy recovery configuration, we will be transferring some heat across the pinch. This would result in a higher amount of external heating and cooling duties, which will be higher than the maximum thermodynamic limit. And with that, I hope that today you have learned how to represent the grand composite curve, what is the concept of type and quality of utilities which could be selected based on the shape of the grand composite curve. And the exercise for today's lecture is very simple. You should be able to construct the grand composite curve, so GCC, for the same stream network, assuming delta T minimum equal to 10 degrees C. I am sure that now you'll be expert of this particular network configuration made of the four streams. And, of course, you should also try to identify any possible pockets that the grand composite curve will have. And the solution of lecture 14 exercise is presented below. So the same stream network. You were asked to construct the composite curves, and they are represented here in this plot. So each composite curve is constructed considering three temperature intervals, as you can see here. Then of course, if we consider the typical convention for which the hot composite curve starts with a heat flow equal to 0 kilowatt, and we shift the cold composite curve horizontally to the left hand-side while approaching the hot composite curve until delta T minimum equal to 10 degrees C is enforced, that you can see here in this central region, you should be also able to identify the pinch point, as the cold pinch point as 140 degrees C and the hot pinch point as 150 degrees C, as it was also demonstrated in the previous lecture 15, based on the problem table. And with that, I would like to thank you very much for your attention.