 Welcome to the series of lectures on process integration. This is module 5 lecture 9 and the topic of the lecture is driving force plot. We have seen that whenever a problem is given to us, a number of feasible hens can be designed for that given problem, but all the hens which are feasible hens will have different heat transfer areas. The question is why is it so? Why they exhibit different heat transfer area? A investigation into this matter will show that these hens are utilizing differently the driving force which is available to them and as they are utilizing differently, they have different area and obviously when there is different area, there will be different cost. So, the pinch analysis tries to distribute this driving force properly, so that the design will have less area. So, today we will investigate why the different feasible solutions exhibit different area? To start with, let us take a problem which is there in the screen. It has got two hot streams and one cold stream. The u which is the heat transfer, overall heat transfer coefficient is taken to be 0.11 and this is same for all the streams. To do so, we will plot a driving force plot. This driving force plot has been plotted using the hint software. Now, the driving force plot is basically a plot between the cold temperature and the hot temperatures. That means cold stream temperatures and hot stream temperatures. Now, the present diagram which is on the screen is not a driving force plot, but we will like to extract the valuable information for a driving force plot from here. Now, this is 100 degree centigrade. At this temperature, the driving force plot is the driving force is 30 degree centigrade. At this temperature 120 temperature, the driving force is again 30 degree centigrade and here at this temperature 140 degree centigrade, the driving force is 170 degree centigrade. So, when cold composite temperature is 100, then hot composite corresponding hot composite temperature is 130 degree centigrade. Similarly, when the cold composite temperature is 120, this is going, it is meeting here at 120 and when we go vertically upward, this is hot composite curve, this is 150. So, 120 and this is 150. Similarly, when we at 140 degree, when we move to this cold composite curve, then if you rise vertically to the hot composite curve, the hot composite curve temperature is 170. So, now we have cold composite curve temperatures and corresponding hot composite curve temperatures. Now, similarly we can have many points. We can calculate many points from this composite curves and we can draw it the x axis as cold temperature and the y axis as hot temperature. Now, let us take a hand design for the problem which has been given in the stream table. Now, this is we call design 1. So, we will place heat exchangers based on the pinch rule. Now, we can place a heat exchanger like heat exchanger number 3, then we can have heat exchanger number 4. So, this stream which has a CP value as 5 is broken into two parts, treated into two parts. This is CP is 1.25. So, this CP which is cold 1 B will have 5 minus 1.25, the value of the CP and this is a 80 kilowatt heat exchanger and this is a 240 kilowatt heat exchanger. So, this is a feasible design. Now, similarly we can develop other feasible designs. This is the design 2, this is design 2, same hot and same cold. So, this is design 2 and here also the heat exchanger 1 has got 80 kilowatt and this is called 240 kilowatts. Now, this is third design where cold is now splitted into two parts cold 1 A cold 1 B and it has got 4 heat exchangers. Heat exchanger number 1 25 kilowatt, heat exchanger number 250 kilowatt, heat exchanger number 3 90 kilowatt and heat exchanger 4 55 kilowatt. So, we have seen that for a problem we have 4 heat exchanger, 3 heat exchanger networks available and all the 3 heat exchanger networks are feasible in nature. Now, let us see the temperature profiles of the heat exchangers in the heat exchanger design 1. So, heat exchanger design has got 2 heat exchangers called heat exchanger number 3 and heat exchanger number 4. In one end it has got a temperature of 80 and 105. That means the hot stream is coming from 165 to 105 and the cold stream is rising from 80 degree centigrade to 144 degree centigrade. This is for heat exchanger number 3 and the capacity of the heat exchanger is 240 kilowatt. Similarly, there is a second heat exchanger which is heat exchanger number 4 we call it. Here the at the cold inlet this is 80 degree, cold outlet is 144 degree, hot inlet is 180 degree, hot outlet is 140 degree and this capacity is 80 kilowatt. Similarly, we can go to design 2. Here there are 2 heat exchangers called heat exchanger number 1 and heat exchanger number 2. Heat exchanger 2 is 240 kilowatt. Here the cold inlet temperature is 80, outlet temperature is 128, hot inlet temperature is 165 and 105 outlet temperature for heat exchanger number 2 or heat exchanger number 1. The cold inlet is 128, outlet is 144 degree centigrade, hot inlet is at 180 degree centigrade and outlet is 140 degree centigrade. And this heat exchanger is a small heat exchanger compared to this and having a capacity of 80 kilowatt. Similarly, if you go for the third heat exchanger, third heat exchanger sorry third design has 4 heat exchangers, heat exchanger number 1, 2, 3, 4 and 1 has a capacity of 25 kilowatt, 250 kilowatt, 390 kilowatt and 455 kilowatt and their input output temperatures are shown. Now, we have seen that different designs have different number of heat exchangers and their input output temperatures are different. So, they are availing the driving force differently. So, this shows that how the exchanger is taking place. This is hot 1 is exchanging heat with cold 1 in this heat exchanger number 1. Hot 2 is exchanging heat with the cold 1 b which is a splitted stream of the cold 1. This is between hot 1 and cold 1 a and this is hot 2 and cold 1. Now, this table has been created for all these three designs. This shows heat exchanger number that is H X 1, H X 2, H X 3, H X 4. This shows delta T log in temperature difference for heat exchanger 1, H X 1, H X 2, H X 3, H X 4 and this shows the area of H X 1, H X 2, H X 3, H X 4 and then this shows the total area. Now, this shows the feasible design design 1, design 2 and design 3. Now, in the design 1 heat exchanger 1 and heat exchanger 2 are nil. They are not there. Heat exchanger 3 is there which is consuming 240 kilowatt that is capacity and that is the second heat exchanger which is called heat exchanger 4 has got 80 kilowatt capacity. Now, obviously 1 and 2 are not there. So, there will be no delta T ln for that log mean temperature difference is 0 0 and 240 the capacity of heat exchanger is 240 kilowatt. It is utilizing 22.9 the log mean temperature difference value is 22.9 whereas, for 80 kilowatt heat exchanger the delta T ln is 47 degree centigrade. Now, this data clearly tells that this bigger heat exchanger this is 240 kilowatt is utilizing almost less than half of the delta T which is 80 kilowatt heat exchanger is employing. So, 80 kilowatt heat the capacity heat exchanger is employing the available driving force far better way than the 240 kilowatt heat exchanger is employing and that is why this heat exchanger will increase the area of the hand because it is not utilizing properly the driving force which is available with it. This we will also see in the figure. Now, if we calculate the area the area comes out to be 95.1 for this heat exchanger 240 kilowatt and 15.5 for heat exchanger 80 kilowatt. Now, here also you can see this is about 3 times the capacity of this, but if you multiply 15.5 3 times you will find that this area is far more than that and that is why the total heat transfer area is 110.6 in this case. Let us go to the design case 2 it has got heat exchanger 1 and heat exchanger 2 this is using 80 kilowatt capacity this capacity is 240 kilowatt it does not have exchanger number 3 and at exchanger number 4, but here if you see this 80 heat exchanger is using about 21.8 delta T l n and this has got 30.6 delta T l n. So, this 80 kilowatt heat exchanger is a small heat exchanger in comparison to this is utilizing less driving force and the bigger is heat exchanger is utilizing a driving force which is far better than the exchanger number 1 of the design 2. So, we expect that this design will give lesser area. So, when we calculate areas we find that the 80 kilowatt heat exchanger has got 33.3 area meter square area and the 240 kilowatt heat exchanger has got 71.3 meter square area and here if we multiply this 71.3 into 3 which comes out to be the capacity ratio then whatever figure I get it should be 99.9 which is far more than the 71.3 and why this has happened because this heat exchanger is utilizing better driving force and then hence its area is less. So, the total area becomes 104.6 which is less than 110.6 6 units less. If I go further to design 3 there are 4 heat exchangers here heat exchanger 1, 2, 3 and 4 and if we see the delta T l n of this first heat exchanger has got 32.1, second is 28.6, third is 29.1 and fourth is 29.2. So, the delta T utilization is very good and they are almost constant while utilizing the driving force because delta T is a symbol of driving force is a. So, the area computed are 7.1 47.7 28.1 and 17.1 and total gives 100 meter square area which is the lowest. So, the first hand conclusion which we draw is that for a given problem there can be many feasible designs when we are employing pinch analysis method or pinch design method then can be many feasible designs and all the designs will have different area and this different difference in area is due to the utilization of available driving force for the problem. The available driving force of the problem can be seen through a driving force plot and if the exchangers of the designs feasible designs are utilizing is this natural driving force which is available properly then the area will be less. If they are not utilizing it properly then the area will be more. So, let us see in a different way the same statement. The design 1 requires highest area followed by design 2 and design 3 and designs 3 shows the lowest area this we have seen. The reason for this should be investigated this phenomena can be explained through driving force plot. Now, let us see what is a driving force plot. The driving force plot provides a rapid and easy to use guideline for designing networks which are close to minimum area. Why close to minimum area? If the naturally available driving force are utilized by the design to the fullest extent then only it will give the minimum area and if the design is not utilizing it we cannot expect it to offer minimum area the designs are based on the matches which we follow in a design because at a point of time you can have several options for the matches. What option we select affects the area of the heat exchanger network. However, it is only a guideline and does not provide quantitative information. This we will see why because we will see that the capacity of the heat exchanger which is utilizing the driving force is also a important parameter. If a small heat exchanger in the network is utilizing very nicely the available driving force, but a bigger heat exchanger is not utilizing it properly. So, obviously, the area will increase. So, how many numbers of heat exchangers are not properly utilizing and what is the capacity of the heat exchanger? Both are important in this case. Now, this is the natural driving force which is available with the problem. So, this is plotted between T cold and T hot. So, this is the naturally available driving force for the problem and this is plotted using the software hint. This is a 45 degree line and this temperature which is here 100 degree cold temperature the hot temperature is 130 degree and the difference is 30. So, from this point to this point similarly, here for 120 degree cold temperature this is the hot temperature 150 and the difference being 30. So, this is how this driving force is read and this driving force is the available driving force and it should be utilized through proper match placement. We have seen that we can have freedom of different match placement and that freedom has to be used very properly or judiciously. So, that whatever match we place that match utilizes the available driving force properly and if it is not utilizing then we have to pay a penalty in terms of increased area of the heat exchanger network. Now, let us see again revisit the temperature profiles of two heat exchanger what is which are been utilized in design one that is heat exchanger number three and heat exchanger number four. Now, let us see these two heat exchangers are how utilizing the naturally available driving force in the driving force plot. So, when we place these utilization of driving force of these two heat exchangers into the driving force plot we get this. Now, this is the driving force which is available from here to here and heat exchanger number four is utilizing the driving force properly and in fact it is utilizing it more than the available driving force, but its capacity is less 80 kilowatt only. Whereas, the second heat exchanger which is H x 3 having a capacity of 240 kilowatt which is about three times more than the capacity of H x 4 is not utilizing the driving force properly. This much amount of driving force is not utilized that means the bigger heat exchanger is poorly utilizing the driving force which is available to it. However, the smaller heat exchanger is utilizing it properly as the bigger heat exchanger is not utilizing the driving force properly the design one gives you the maximum area that is 110.6 meter square. So, again we visit this the heat exchangers temperature profiles for design two and when we put this temperature profiles of heat exchangers to find out how much this design is utilizing the natural driving force which is available to us. Then this is being ported to the driving force plot now this is the driving force available to us this line plus this line. Now we see that the bigger heat exchanger in fact nicely utilizes the driving force to its fullest extent and this area it surpasses the driving force available, but this small heat exchanger which has got the capacity of 80 kilowatt it is not utilizing this available area of the driving force. So, we expect that its area will slightly increase and if we see the design two then we find that its area is 104.6 meter square whereas, the minimum area is 100 meter square. Now if we go to the design three and see the temperature profiles of this heat exchangers there are four heat exchangers having different capacity the largest being 150 kilowatt and the lowest being 25 kilowatt and they have different starting temperatures and end temperatures exit temperatures. So, when we port this then we find this is HX1 which has got 125 kilowatt it is utilizing the driving force to the fullest extent this is also which is HX2 150 kilowatt this is also utilizing it very nicely to the fullest extent. The heat exchanger number 3 which is 90 kilowatt this is also utilizing it to the fullest extent and this is heat exchanger number 4 which is 55 kilowatt which is also utilizing the available driving force very nicely and little bit it exits. So, what we find that the design three is in a position to utilize the driving force in the best manner in comparison to the design two and design one though it has got four heat exchangers, but its cost or its area is 100 meter square only that means the minimum area. So, if we compare this designs design two has got two heat exchangers design one has got two heat exchangers design four has got four heat exchangers, but the area is less. So, there is a trade off finally, design one design two and design three out of these three we have to select one design based on the total annual cost, but what conclusion it makes is that if the heat exchangers which are present in the hand are utilizing the natural driving force which is available to it and this natural driving force can be seen through a driving force plot or it can be seen in a composite hot and composite cold curve. So, if this driving force are utilized to the fullest extent we can expect that the area of the heat exchanger network will be minimum then will be almost equal to the targeted area. So, again we see the stable and we have explained why the heat exchanger one has got maximum area heat exchanger two has got area in between these two extremes and heat exchanger three has got minimum area. Now the conclusions for this part is from plots it is clear that the heat exchanger in design three utilizes the available driving force properly and thus results in minimum area of 100 meter square. The area target for the above problem taking vertical heat transfer predicts 99.937 meter square area. So, it is almost equal to 100 meter square area this area is quite close to the area of design three. Now if you remember design three we have seen that it was not able to utilize this driving force otherwise it is area should be almost near this is near to the targeted area may be match to this. The area does not only depend on the driving force utilization, but also on the load of heat exchanger which is utilizing it. So, there are two important factors for the area that how much the naturally available driving force is utilized by a heat exchanger plus what is the load of the heat exchanger who is utilizing this adequate driving force utilization by a small heat exchanger does not contribute much towards the total area that we have seen when in the design one a smaller heat exchanger utilize the driving force nicely or it over utilized it, but the bigger heat exchanger did not utilize it properly and hence the area of that hand which was design one increased. In design one heat exchanger number 4 which is 80 kilowatt is utilizing in fact more than the available driving force, but the total area of the heat exchanger is 110.6 meter square only due to this because the heat exchanger the second heat exchanger which has got the capacity of 240 kilowatt was not utilizing the available driving force properly. Area targeting is based on vertical heat transfer from hot composite curve to the cold composite curve. If the film side heat transfer coefficient of streams do not differ appreciably as in the present case this method predicts minimum area for most cases, but this will not be true if the overall or the film side heat transfer coefficient of streams differ considerably say more than 10 percent under the above conditions matches placed in the heat will mimic vertical heat transfer between composite curves and the area will be close to the area target as of the observed in this case in the table. Now, we go for example 2 for this example also will have different heat exchanger networks designed and we will also see that though we have had had to the C P ratio rules even then due to the utilization of driving force by different heat exchangers the areas are different. For this purpose what we are taking u is equal to 0.1 kilowatt per meter square centigrade or utility is 20 to 30 degree centigrade to 200 degree centigrade cold utility is 1 degree to 15 degree centigrade. Now, if you do the PTA of this stream table then hot utility requirement is 534 kilowatt and cooling duty is 15 kilowatt grid diagram for the including utilities. So, this was the grid diagram the pinch is 30 40 the delta T being 10 degree the m c p values now if you see the composite curve this composite curve looks like this and these are the delta T's driving forces which are available natural driving forces which are available to the different streams if I consider vertical heat transfer the stream which is available here hot stream as a delta T available with the cold stream is this much. So, this also shows the driving force available between hot and cold streams and this is a hot and cold balanced composite curve that means the hot utility and cold utilities are included into this. Now, here the c p ratios at the pinch now here I want to clarify that we have taken those streams which are crossing the pinch for the computation of this those streams which are not touching the pinch we are not taking. Similarly, in the number of streams criteria we count those streams which are crossing the pinch or you are starting from the pinch. We do not consider those streams which are not touching the pinch or which ends before the pinch now this is the driving force plot of this problem it is between T cold and T hot. So, these are the driving forces which are available and the design has to utilize this properly now you say design A we are taking above the pinch region this is my c p table which will be utilizing for the design purpose and here we are placing the heat exchangers. Now, these two are the pinch heat exchangers called heat exchanger number 1 and heat exchanger number 2 this is a third heat exchanger heat exchanger number 3 and this is fourth heat exchanger heat exchanger number 4 and there are two heaters here. Now, if we compute the c p h by c p c ratio of the heat exchanger number 1 and heat exchanger number 2 which are pinch heat exchangers then the ratio is 0.950 and 0.909 and if we see the summation of the c p h by summation of the c p c ratio above the pinch this is 0.935. Now, if you go for the pinch go for the c p summation of the c p ratio then this value is almost equal to this value meaning that this pinch heat exchangers are utilizing the driving force properly, but we should see that this pinch heat exchangers have capacity less whereas, this heat exchangers have capacity more. Now, the area of this heat exchanger network is 3975 meter square that means we have used the c p ratios properly and then my design gives me a area 3975 meter square. I expect this area to be close to the area target because I have added to the c p ratio rule. However, we will see that the story is different here. Now, if I plot the utilization of available driving force by the heat exchangers of the design a then this is heat exchanger number 4 it is nicely utilizing the available driving force or we can say that utilizing more. This is the driving force area and we are utilizing more. The heat exchanger number the heater number h 1 is also utilizing the driving force nicely. The h 2 is which is a heater is also utilizing the driving force but not to that extent it is not fully utilizing the driving force. This h e x 2 is utilizing the driving force which is available in this horizon then e x 1 is also utilizing the driving force. Now, design a proper utilization of the driving force is taking place by the heat exchangers and that is why the area which we have found is less. When I say less it is comparison to the other design which I am going to explain you. Now, design b if we do this is also above the pinch. So, here also if I see the pinch heat exchangers c p ratio they are quite close to the summation of the c p ratio above the pinch. It is there very quite close to it but the area is 713 0 which is almost double the area of the previous example that is design a. Now, if we want to know why this happened we have gone for the c p ratio we have or matching is there c p ratio matching of the pinch heat exchangers but why it has increased so much. So, the answer is probable answer is here we see the pinch heat exchangers have higher capacities and they are operating at lower delta t values. Whereas, the other heat exchangers at e x 3 has got a very low value. Now, let us see the driving force plot. Now, this is the available driving force plot for us this is the exchanger number 2 utilizing it is not utilizing to the fullest extent. Then exchanger number heater is not utilizing to the fullest extent this is exchanger number 1 it is not utilizing to the fullest extent the available driving force and this is the heater 1 sorry one of them will be heater 2 this is the exchanger number 3. So, what we see that the poor utilization of the driving force by the exchangers increase the area of n because this much area of the heat exchanger network this much driving force of the heat exchanger network is not utilized properly and hence the in area has increased and it has almost been double the area. So, what we saw that even if we utilize the CP ratio rules in the design there are two factors which comes that whether the heat exchangers available there are utilizing the available driving force properly. And the second is that if the bigger heat exchangers are not able utilizing the available driving force properly bigger capacity heat exchangers then the area will increase and it may be two fold as we have seen in the design A and design B. So, these are the references thank you.