 So, just looking at a residue curve map, you can synthesize the column sequence. That may not be possible for this particular azeotrope or other RCM. You try it out. Can I use A here as a trainer to break this azeotrope? You try it out yourself and you will realize that it is not possible. The boundary is linear. So, what I am trying to tell you is RCM, the sides. Now, A, B, C are just the names. What does it mean? If I say A and B, say ethanol water azeotrope, I identify some component B which gives you this RCM, then I say that it is possible to separate it. But then if I identify, suppose again in this case, B and C are ethanol water. B and C are ethanol water because minimum boiling azeotrope. Now, I identify a component A which gives you the RCM for the terminal system like this. In that case, I say that it is not possible to design a column sequence. So, that is how RCM would help you to synthesize a column sequence. This case is very typical case. Now, we are going to learn this. In this case, you have this as azeotropic composition. This is going to be your feed. And the question is, can I use C to break this azeotrope? I can follow same method and see whether I can get A and B in pure form. Now, look at this RCM. A is stable load or unstable load or saddle. B is stable load or unstable load or saddle. So, very typical, very peculiar case I would say where A and B are saddles and I want them in pure form. Now, whatever we have learned so far, saddle coming at top or bottom, was it possible? In any case, we have looked at, see either you get stable point at the bottom or unstable point at the top. At a time, both are not possible because material balance should be valid. See even ideal system, this is your unstable, this is your stable and this is your feed. At a time, you can get this at the bottom or get this at the top. But not at a time, it is not possible to get this at the top and get this at the bottom. It is not possible to design a columns. You have to get unstable load at top and stable load at the bottom. Why? Material balance should be satisfied because your feed is somewhere here. Once you say that I have this as a bottom composition, my top composition should be here on this line. Whereas, once I say this is my top composition, then the bottom composition should be on that line. So, at a time, you cannot get these two as end compositions. Where will your intermediate component go? So, one column is not possible to give. It is not possible to get these two as end compositions in one column. So, let us look at this case now. Extractor distillation, very important. Many commercial applications as I said ethanol water separation, then you have acetone methanol separation using water as entrainer, butadiene extraction from C4 stream using acetone atrial as an entrainer. Many examples. This is your RCM, A, B, C. This is my feed, case 3. I gave you one example just before this. We solved it in fact and designed or synthesized a column sequence. Now, can I use the same method or methodology rather to break this feed and get A and B in pure form? A, B mixture, aziotrope. Am I adding C? The resultant would be, this is my overall feed. This is my overall feed. What is the next step? To look for, suppose this goes to the column, look for either stable node or unstable node which will come out at the top or bottom. Now, in this diagram stable or unstable node. Now, which is the stable node? C. Am I interested in C? I am not interested in C. So, what is the use? I cannot, there is no point in separating C. Anyway, I am adding C in pure form. What is the use to say like no point in separating C? So, forget that. What is the unstable node? A is unstable. A is saddle. B is unstable. Yeah, D. You are calling this as D. Fine. So, the feed itself is unstable. What is the point in separating feed? Very peculiar case where if I just go for simple distillation and look for unstable or stable nodes, I will end up separating C which I am adding here. Otherwise, I will end up separating A, B, aziotrope. So, there is no, as such there is no point doing this. So, this RCM does not allow me to separate or break this aziotrope using this as an entrainer in a simple distillation column. Now, it is very important, simple distillation column. So, this is not possible. This is not possible, but they do it commercially. Ethanol water separation using ethylene glycol is a very well known process. I gave you many examples. Methanol acetone using water as an entrainer is very well known. So, all these RCMs are like this. Methanol, acetone, water. Ethanol, water, ethylene glycol, right? Butene, butadiene, acetone nitride. Yeah, acetone chloroform water. There is a boundary, there are some curved boundaries and all. Anyway, but same, same RCM. They do it commercially. So, what is going wrong now? Whatever we have learned so far, I am not able to extend it or apply it to commercially important system or already practiced. So, there is some difference, the way they do it and the way we are doing it here, right? So, let us try and understand that. So, the simple distillation column is not able to do it. That means, I need to modify my column. Now, what is simple distillation column? Simple distillation column is a feed going in and I have two products, top and bottom. This is a simple distillation column, a single feed and top product, bottom product. That is my simple distillation column and simple distillation column cannot do this. That means, what they are doing commercially is something different from a simple distillation column. What is that difference? I am interested in A and B. I am interested in A and B, right? This is going to be my resultant composition. Now, why I am not able to separate A and B because A and B are saddles here. They are saddles here and I cannot withdraw a saddle composition from top and bottom in a normal simple distillation column. That is the main reason I am not able to separate A and B in pure form is simple distillation column, right? Now, suppose I want pure A at the top. Let us assume that I am removing pure A from the top. The column profile as I go from top to bottom will move in which direction I am starting from this. This is my X D, okay? In spite of it being a saddle, I say, okay, I remove it from the top. This is my X D. Which direction will I move when I go to the bottom in this direction or in this direction towards C because I will follow the residue curve, right? Rectifying section follows the residue curve. So, I will move in this direction, right? This is my rectifying section profile. It looks a bit different from what we have learned before. Now, it goes this way because the RCM is different here, right? I have to follow the RCM, okay, for a rectifying section profile, okay? So, it is going to follow the RCM. Now, this is my overall speed. This is my top composition. The bottom composition would be here, right? Okay? Straight line, leave a rule. Now, this is my bottom composition. If I go from bottom to top, which direction will I go? This or this? Towards B or C? C? Bottom to top. Bottom to top. I will have to go in the direction of RCM or opposite to RCM. Bottom to top. Stripping section. Opposite, right? Opposite. So, RCM direction is this. Stripping section would be this. And anywhere this is saddle, okay? So, you are going to see the same behavior as we have seen before, at least for stripping section, right? It is going to go in opposite direction and then we will fall down because we have saddle here, like what you had in the case of ideal system, right? A, B, C where B was saddle, right? So, this is your stripping section profile. This is your rectifying section profile. Is there any scope for making them intersect? This is going in this direction. This is going in this direction. Even if I increase the reflex ratio, intersection will not be possible. See, in normal case, in ideal system, your rectifying profile is like this. Your stripping section profile is like this. So, I increase the reflex ratio. I can cross. I can intersect, right? In this case, though your stripping section profile is like this, rectifying is moving in a different direction. Or rather its pattern is different, okay? And that is the reason, since rectifying section is not following this particular pattern, the intersection is difficult and that is why I do not get a feasible simple distillation column. So, what is the solution? The solution is to make them intersect somehow. Now, if you know the configuration used for extractive distillation, it is not like this. It is not like this. It is not like a simple distillation column. You remember the configuration? Where do you give the solvent? Solvent is the internal or the external component. Do you have a combined feed? Above the feed. It is very important, right? The solvent, this is solvent, external component. In this case, it is C. It is not mixed with your feed. It is given somewhere at the top, okay? So, this is your C and this is your A, B mixture, right? That is your extractive distillation configuration. Now, I do not call this as simple column. Why? Because it has multiple feeds, right? It has two feeds, right? It has two feeds. So, when you have two feeds, things are different. You have how many sections you have now? In the column, you have three sections. With a single feed, you have two sections, rectifying stripping, okay? If you have multiple feeds or two feeds, you have rectifying section. You have stripping section, you have stripping and more importantly, an additional section which I call it as middle section, right? Okay? So, I have introduced one section in the column and this section will have different geometric property. That means, rectifying section, equation is what? This equation is, you know it, right? y n plus 1 i is equal to r by r plus 1, x n i plus x d i by r plus 1, right? This equation, which is true for rectifying section will not be same as that for the middle section, okay? Because middle section, again, you have to do material balance, okay? How do I get this equation by doing some material balance, no? I showed you the boundary at which you take the material balance and you derive this particular equation. This equation will change for middle section profile, right? Because you have some other feed also coming in, okay? If you take the boundary, it is like this, this boundary I have to take for material balance, okay? And its geometric property would be different. It will not only depend on the flux ratio, but will depend on how much feed I am giving, okay? Right? And that middle section, that middle section is responsible for joining these two profiles or making them intersect or bringing a continuity. So, if you start from x d, okay? You can go to x b this way. And this particular part is nothing but your middle section, okay? So, that is how we explain, right? So, even if one residue curve does not go from this to this region, I can introduce a middle section, I can have a double feed column and make these two profiles intersect. Because the middle section has no relation with residue curve. Rectifying section has, stripping section has, but if you write down the material balance for middle section, it has a different property. It does not follow reflux ratio under extreme conditions or does not follow residue curve under extreme conditions, okay? So, this is what I have explained just now, extractive distillation. If you just look at the RCM, RCM does not have boundaries because you have one pair, unstable and stable, okay? However, residue curves indicate that the profiles do not intersect. Just now we have seen the profiles. This is your rectifying section profile. This is your stripping section profile. Oh, it should be stripping, okay? This is your stripping section profile and this is your rectifying section profile. Just go by residue curves, okay? They do not intersect. There is no possibility of them intersecting. A double wave column is necessary to bring them together. That means, I introduce a middle section, okay? To bring these two together, so that the middle section profile behaves like this, okay? And I have an intersection. I have continuity. If I start from Xd, I will go to Xb, which is desired, okay? The middle section of column has different geometric properties than the RCMs. That is what I told you. So, that it does not follow RCM. It goes, it is much different, okay? Whereas, rectifying section profile is a relationship between residue curve and rectifying section profile. And even stripping section, it goes opposite. So, I know from residue curve, I can just get some idea about how the stripping section and rectifying section would behave, but not the middle section. Middle section is totally different, okay? You can do this exercise by taking material balance, okay? For any stage in the middle section, okay? Now, that is what I said. There is a mistake there. Instead of rectifying section, it should be, so this is your solvent. So, remember, extracted distillation cannot be performed with this single field. You have double field, okay? The solvent is high boiling, right? And you have a middle section. So, the moment you see this residue curve map, okay? You should say, okay, I will have this configuration. This is the typical behavior of this residue curve map. There is a connection between these two. That is what I am trying to say. Once you have this, I can immediately say that I can have an extracted distillation column with this configuration, which will give me this saddle as the end composition, okay? Right? So, in this case, the bottom composition would be, so this is your overall feed. So, overall feed, though I am not mixing them and giving them as a single feed to the column, the overall feed is still there, okay? Virtually, it would be there for material balance, right? So, this is your overall feed. This is your azeotrop. This is your C. So, the overall feed would lie on the line joining azeotrop and C. So, this is your overall feed, okay? Resultant feed, right? And that is going to go to the column. So, in the column, I will take D or rather A in pure form, okay? On the top, right? The bottom would be W, okay? So, I have separated this component in pure form. What is the next step? This comes at the bottom. I am interested in A and B both. I am interested in A and B both. So, this will be going to another column, right? This composition will go to another column, right? What will I get in that column? The top composition would be? Top will be? B. And bottom will be? C. So, then I will recycle C, which is nothing but a solvent, right? So, in ethanol water system, you have ethylene glycol, ethanol water, right? Ethylene glycol will take out water, okay? So, at the top I will remove ethanol, right? Bottom will have ethylene glycol and water. This will go to another column. I will separate ethylene glycol from water. I will get ethylene glycol here. That is your C, okay? And water here. And this ethylene glycol will be recycled back, okay? And this is my RCM, ethanol water. This is my azeotrop. This is my ethylene glycol, complex distillation, okay? And same is true with methanol acetone or chloroform acetone. So, water will be here instead of ethylene glycol. This is extractive distillation. And then how to calculate number of stages? Same method. Now in this case, now the things are bit different, okay? In this case, things are bit different. This is a simple column, okay? But this is a double fin column and here we need to be very careful because how much ethylene glycol you will add, okay? That is that question I have not yet answered, okay? How much ethylene glycol you will add and where will you add it in this column? I said, okay, towards the top means where, right? So, that anyway we have seen in the RCM, okay? We have seen that in the RCM where to add. But how much to add? Okay, there is some limit. It is like reflux ratio. There is a minimum reflux ratio, right? We operate the column at the reflux ratio higher than the minimum reflux ratio. Similarly, in this case, there will be some minimum solvent rate, okay? Or in other words, there will be something called as feed ratio. That means the solvent rate, flow rate divided by the feed flow rate. There are two feeds, no? One is solvent feed and the actual azeotropic feed, okay? This is azeotropic. So, as I said, like in this particular case, you have a typical residue curve map and this is azeotrope. I want to break it. Can I use C to break it? The answer is yes. But you cannot use a simple distillation column. You have to use a double-fit distillation column like this. And you have to feed solvent which is the least volatile component or highest boiling component at the top somewhere, okay? Now, the question is where to put it, okay? Now, this particular diagram would help you telling where to put it. Now, I can count number of stages 1, 2, 3, 4, 5, 6. And at this particular stage, okay, if I add my solvent, then this helps me to connect these two, right? So, position-wise, it is not a problem. But how much to feed, okay? That means what should be the flow rate of solvent or what should be the ratio of solvent flow rate to the azeotropole actual feed flow rate, okay? So, for that, as I said before, like minimum reflux ratio, there is a limit on this rate as well. So, it is not that you can feed as much as you want, okay? There is a maximum limit and there is a minimum limit as well, okay? So, let us see how it works. And before that, there are some tips, okay? There are some features of extractive distillation systems. Along with reflux ratio, extractive distillation is also associated with an additional parameter that is feed-ref ratio, okay? This is the important decision which decides the amount of solvent to be fed, right? For a given feed ratio, there is a maximum limit on the reflux ratio. This is a very peculiar characteristic of extractive distillation. This is a maximum limit on reflux ratio. So, there is a minimum reflux ratio. See, for every distillation, there is a minimum reflux ratio. But for extractive distillation, for a given feed ratio, there is a maximum limit on reflux ratio as well. So, you have a range of reflux ratio in which you can operate. You cannot go beyond a particular range of reflux ratio. Hence, there is a region of FR and RR, that is feed ratio and reflux ratio, in which extractive distillation is feasible. So, region, okay? Our range. The region is determined by the geometric properties of the column profile. We will see that in the next slide, okay? Now, the choice of solvent is dictated by RCM and practical considerations, okay? I have not talked about practical considerations like it should not be corrosive and should be cheaply available and all that, okay? Any textbook on extractive distillation, say, TREBAL and book on mass transfer talks about it, okay? So, that is important. But at the same time, okay? I cannot use any solvent, okay? I should use a solvent which gives me this RCM, okay? That is important. So, thermodynamics is given by RCM. And whether it is thermodynamically feasible to do extractive distillation with that particular solvent, okay? It should be decided based on RCM. Now, this is something I had told you before. In the normal column, you have two sections. In extractive distillation, you have three sections. If you want to get the trajectory equation or operating line equation, right? Under constant molar overflow assumption, I am not considering energy balance. What do I do? In the rectifying section, okay? I consider a stage, right? And then you have these two streams crossing this stage. I take this boundary, right? And I write material balance. That is a normal method, okay? That equation of y is equal to r by r plus 1, okay? Xn and whatever equation you have, okay? So, that comes by this material balance. And that is still valid here. That is still valid here, okay? Whereas for stripping section, you have this boundary, okay? Again, you get one equation in terms of s by s plus 1. That is still valid here. But then for middle section, for middle section, you consider a plate, right? And take the boundary like this or you can have boundary like this, okay? And then take material balance and you will have a corresponding equation. And that equation is different geometrically compared to rectifying section line and stripping section line. And under extreme conditions, you will see that it does not boil down to residue curve. That is why, okay? Its nature on the residue curve or rather that ternary diagram we have seen is totally different. It does not follow residue curve at all, right? So, I am not going to derive that equation and talk much about it. You can do it on your own. You can see that it is different. But important point is, look at this line. The middle section balance would involve not only reflux ratio but feed ratio as well. Here in this case, you have only reflux ratio. Here in this case, you have only reboil ratio. Whereas, in this case, you have both FR and RR, okay? So, now I will just go back. This is your middle section line, okay? You have a feed pinch in stripping section, right? As you go on increasing the number of stages, after infinite stages, you will get a pinch for stripping section. You have a feed pinch in rectifying section sometimes, okay? If you go on doing that calculation for infinite stages, you get a feed pinch here. Similarly, for the middle section also, if you go on increasing the number of stages, it is quite possible that you will realize a pinch, okay? Now, this feed pinch in rectifying and stripping section would depend on what? In which, on which parameter the feed pinch depends, it changes its position, right? When that intersection, that is fine but which parameter? Reflux ratio, right? It depends on reflux ratio. So, this feed pinch would depend on reflux ratio. This would depend on the reflux ratio, right? Now, the feed pinch or the pinch in middle section would depend on? Yeah, both. Reflux ratio and feed ratio. Yeah, that is right. L by V, right? But that L by V will be the function of both feed ratio and reflux ratio, right? So, for a given feed ratio, what is the reflux ratio? That will determine the pinch position here, okay? So, the feasibility depends on both FR and RR, okay? Right? This is a typical behavior we see, like if you just see the feasibility with respect to FR and RR, okay? Now, this is your reflux ratio. I have kept FR constant, that is feed ratio constant. Now, you have a minimum reflux ratio. It is quite some similar to what you see in normal columns and gone operating at higher reflux ratio, calculate number of stages. At this particular reflux ratio, what happens is number of stages would increase, okay? In a normal column, what happens? As you go on increasing reflux ratio, it is good, okay? At infinite reflux ratio, you get minimum number of stages. Whereas in this case, after certain reflux ratio, okay, you get higher number of stages, okay? Why? Because your FR is constant. Now, this particular parameter, okay, is also important. What happens is if you go back to your RCM, the feed pinch here, okay? For a given FR, if you go on increasing reflux ratio, this will move inside and the intersection would be difficult, okay? Right? So, for a given FR, for large values of reflux ratio, this feed pinch will move but this will go inside, okay? And intersection becomes difficult. That is the way the middle section behaves, okay? Why it behaves in all, okay? We can leave it, okay, right now. We can look at the equation and see, right? But then, for large reflux ratio, what happens is you have the feed pinch for the middle section going inside and that is why your number of stages would increase, right? And after certain reflux ratio, the intersection is not possible. So, even if you are rectifying section feed pinch moves, middle section is away from it, right? And then the intersection is difficult. That is a peculiar behavior of the extractive distillation columns where do not be another impression that you go on increasing reflux ratio and you get better and better performance like normal columns, right? Beyond particular reflux ratio, feasibility becomes an issue, okay? It is not feasible beyond this particular reflux ratio, okay? Because you have kept FR constant. On the other hand, if I plot FR versus RR, that is feed ratio versus reflux ratio, this is the behavior I see. That means, for any FR, I have a minimum reflux ratio, right? I have a maximum reflux ratio. So, for any FR, I have a minimum reflux ratio, I have a maximum reflux ratio, right? And I should operate in between these two, right? If I go on increasing FR, this range expands. There is not much change in the minimum reflux ratio, but maximum reflux ratio is quite sensitive to FR, okay? And you can very well understand that because the maximum reflux ratio is decided by the pinch in the middle section and middle section would have FR in it, right? The equation will have the feed ratio in it. That is why this is quite sensitive to change in FR, whereas R min does not change much with FR, okay? And you get this particular region and you have to operate your extractive distillation column in this particular region. In this particular region, only the distillation is feasible or extractive distillation is feasible, right? In normal distillation column, I have R min and beyond R min, I can operate at any reflux ratio and operation is feasible. But in extractive distillation, you have something called as maximum reflux ratio, okay? You should be aware of that. And there is one value of FR below which irrespective of whatever value of reflux ratio you have, okay? You do not get feasible design, okay? So, there is a minimum value for FR as well, like minimum value of reflux ratio, you have minimum value for feed ratio as well, okay? So, method to design extractive distillation column. The first step is, of course, you should have VLE, okay? But choose a solvent such that the RCM, when I say RCM, that means for RCM, I need to have VLE, right? The RCM is that of extractive distillation. What does it mean? It should be like the RCM I showed you, okay? It is a typical RCM for extractive distillation, okay? Where you have AB saddle and C is the least volatile stable point, okay? Determine the feasible region for FR and RR. So, this region is determined, okay? By doing those calculations, finding out those pinch points. Reflux ratio is normally 1.3 to 1.5 times minimum reflux ratio. FR is two times, that is again the thumb rule, okay? Two times the minimum FR. This is your minimum FR, okay? So, you are somewhere here, okay? Or here rather. So, that is the value of FR and RR, you should operate it at. Thumb rule, okay? Then determine number of stages. Same, you just count number of stages the way we did before, okay? Once you have number of stages, go for rigorous simulation. That is what we have been saying, okay? Because all this exercise is the conceptual design exercise, okay? That helps you to do rigorous simulations later. So, whatever assumptions we are making, the main assumption is not considering the energy balance. I am not considering energy balance here at all, okay? I am writing the equation R by R plus 1, right? I can do that only when you have constant molar overflow assumption, right? And I am not considering that while doing all these calculations. That means, whatever number of stages I am going to get here, that is an approximate number, okay? This is not the real number. I have to do rigorous simulations later to fine tune my design, okay? So, the last step is always rigorous simulation and then you can do optimization control and other things, okay? Which are most of the times independent of what you do here, okay? So, next case is azeotropic distillation, yeah? So, if I see like in that is observation like, see when you have minimum reflux ratio, if you operate the column exactly at minimum reflux ratio, then in a normal case, then your number of stages would go up, right? You have almost infinite stages, okay? So, your equipment cost is very high, right? If you are operating very close to minimum reflux ratio, that is, yeah, but that is what they observed actually, okay? This is basically the observation based on the energy requirement, okay? So, if you have FR exactly at a minimum FR and reflux ratio just 1.3 to 1.5 times, okay? Still your column will work, okay? But then the number of stages is the middle section, okay? Which are not just dependent on reflux ratio, they are dependent on FR as well, okay? Would be slightly higher, okay? So, the equipment that optimization, okay? For the cost, capital cost and energy cost, you perform for this FR and RR values, okay? Because this is a multi-discount variable problem. It is not just one DCN variable like normal distillation, right? So, you get normally you get 2 times FR minimum and 1.3 to 1.5 times RR minimum, okay? That is your point at which you normally operate. But that is, that is why I said, okay? You have at this point, this particular value of RR and FR and you determine number of stages, you are going to perform simulations and further optimization also is the next step, right? Okay? So, this is again an assumption. This is just an empirical number, okay? And you can find in this later on after doing simulation. So, the, right?