 So, very good morning to all of you and warm welcome to IIT. As you know, we are going to talk about distillation, advances in distillation. We are going to touch upon many aspects of distillation, distillation systems. Mainly, of course, the first lecture we are introduction of distillation. Then we have something on vapor liquid equilibrium which is very important aspect of any distillation design or simulation or really want to practice it in reality. The first lecture which is an introduction to distillation. Of course, this lecture most of the things you know, but I thought let us start with this lecture. So, it forms a good platform for further discussions during our entire program. Then of course, the king of all operations is highly technologically matured like if you see all other operations, separations rather. We have many separation processes for liquid mixtures like say extraction, you can go for stripping, absorption, then you can have adsorption, right. So, many multi-stage processes out of which distillation is the most popular every chemical engineer thinks of distillation first while separating a mixture, why? Because it is highly matured. That means there is not much risk component in it. Like whenever I want to implement distillation, it is very well known. The most important thing is of course, the vapor liquid equilibrium. And most of the times the systems, if they are quite similar, the mixtures or components involved are quite similar, then of course, I can go ahead with ideal system assumption and design and distillation column which most of the time works. So, in this particular lecture, we are going to just take a review of what we have learned for most of the times in our undergraduate curriculum like the basics of distillation. Then we have design calculations, macathil method, most popular method like every chemical engineer knows about it. Just quickly revise this and then we will take a step forward and talk about non-ideal systems which is something that normally bothers any engineer who is designing a distillation system because most of the designs today are based on gut feelings, experiences. But there is no systematic methodology available to design a distillation column which is associated with say formation of azeotropes or I want to deal with some tangent pinches in a system because of the non-ideality. So, let us talk about the non-ideal systems. Then we have energy integration. Is there a possibility to do energy integration in distillation systems? When I am talking about distillation, I am not talking about a binary mixture. I am not talking about mixtures where I have A and B present. I want to separate just A from B. I am talking about a multi-component, very general mixture might be non-ideal. In that case, you have a sequence. You have many columns and can I integrate the energy requirements in all these columns? So, it is quite possible. There are many opportunities to do energy integration in distillation systems and in this particular lecture, I will just tell you about some examples and of course, Prof. Malik will cover that in great details probably towards the end of this program. As I said before, azeotropic and extractive distillations where these are very special distillation techniques where your thermodynamics does not normally allow you to rather separate the mixture, thermodynamics is not friendly, it is not cooperative. So, you do something, you add external component and try and separate the mixture somehow. So, they are very special or enhanced distillation techniques, azeotropic and extractive and we are going to spend much more time on these techniques compared to ideal distillation. And lastly, of course, reactive distillation which is very popular these days, it is not just enhanced distillation like azeotropic and extractive, but it is a process I would say like it is a multifunctional reactor. It has a capability to combine reaction and distillation in single unit to give the enhancement in overall performance. So, reactive distillation, it is a very special technique and it is a field on its own and we have dedicated almost one day for reactive distillation and we have been doing the research in reactive distillation in IIT Bombay for about last 6-7 years and we have many experimental facilities available. We have done some process development work on some related systems. So, this is about the content of this particular talk. So, in the introduction as you know you have a mixture of A plus B, you have a mixture of A plus B and A is the most volatile or A is more volatile than B. And I want to separate it, distillation exploits the difference in volatility, you see the question bracket can we say the boiling points is the volatility is same as boiling point, right. The answer is no why, because sometimes it is quite possible that two components with two different boiling points forming azeotrop making one of them more volatile or less volatile, right. So, formation of azeotrop in non-ideal systems, you cannot really say that the volatility is related to boiling point, I cannot say the component one is more volatile means its boiling point is less, fine in pure form yes, but in the mixture it may behave differently because of non-ideal interactions, quite possible, right. So, that is why we should be very careful dealing with non-ideal systems, that is why I made this question here. In ideal systems, fine component with less boiling point is more volatile, ok. So, we have mixture I am boiling it, taking vapors out, mixture will be enriched in A if A is more volatile, typically for ideal systems is always true, when do I use distillation for such system when it is feasible, ok. Now, the feasible word is very important is going to come every now and then in subsequent lectures, the feasibility is a very important aspect of distillation. We do not bother about feasibility when we deal with ideal systems, ok. Because I know that there is no formation of azeotrop, somehow if I play with reflux ratio, if I play with number of stages, I am going to get separation, right. Feasibility is not an issue of course, cost is another issue that will be looked upon later, but then feasibility as far as feasibility is concerned, whether a given mixture can be separated in pure components, ok. That is nothing but feasibility and for ideal systems that is not a question. For non-ideal systems, we have to spend lot of time knowing whether the operation is feasible or not, whether distillation is feasible or not. As you know, there is a formation of azeotrop, there is a boundary in composition space, I cannot move from one region to another region, right. So, feasibility is an issue and looking at distillation, its popularity, its maturity, ok. Even if it is an expensive technique sometimes compared to others separation processes, people go for it just because there is less risk associated with it. Many people know how to operate a distillation column, many people know how to design a distillation column, right. That is why I have said whenever it is feasible go for it, ok, but of course, it is a very ambitious statement, sometimes some other operations, some other separations might be economically better compared to distillation, right. Now, you have one operation where you are boiling mixture, I am just taking the vapors out condense them, ok and then again evaporating or boiling, I do it in a cascade from, ok. The many stages now, what is happening, A is more volatile than B, right. When N tends to infinity, you may get pure A, right because as you go on looking at a composition of these streams, right, you are going to see that the stream is enhanced or enriched in A because A is more volatile, it is very simple straightforward. As I go on increasing the stages, right, I will get more and more A in the vapor stream, right. And if I have N equal to infinity, right, N equal to infinity, I may get pure A. Again that word may is very important there because if you have formation of azeotrope, ok, you are not going to get pure A. If there is a minimum boiling azeotrope, you will get minimum boiling azeotrope and not pure A. It is very simple, very straightforward, but I am putting emphasis on this because later on we will be using this every now and then may mean learn about non-adial systems, azeotropic distillation, extractive distillation. Go reverse, I am interested in pure B, right. Now, I have this mixture, I just evaporate, I just boil, take the vapors out. Instead of dealing with vapor, now I deal with liquid, ok. Now, liquid is enriched in B, right. Liquid is enriched in B and then I do the same thing again and again so that the final stream that comes out is enriched in B. And again if I have N equal to infinity, I may get pure B. I may get pure B depending on whether there is a formation of azeotrope or not. If there is a maximum boiling azeotrope, then I will not get pure B, right. I will get a maximum boiling azeotrope even if I have number of stages equal to infinity, ok. So, thermodynamics puts a limitation on the extent of separation that you can do, right. So, I am just combining these two, ok. I am just combining these two. What was happening before? I am just removing heat here after every stage, right. And then I am giving heat, providing heat in every stage, right. When I exchange, instead of putting intermediate condensers or intermediate heat exchangers, I can have exchange of these streams. I can have exchange of these streams so that that heat effect is taken care of, ok. Heat effect is taken care of because one stream needs to be evaporated, one stream needs to be condensed, right. The vapor stream needs to be condensed and liquid stream needs to be evaporated. So, if that exchange is possible, I do not need intermediate heat exchangers. I have heat exchangers situated only at the top, only at the top and at the bottom, right, ok. So, it is possible. But of course, like it is quite well known that it is not just the heat exchange, but I am doing mixing there, ok. I am doing mixing there and because there is a mass transfer taking place and your thermodynamic efficiency would go down if we do it in this fashion, right. If I do heat exchange in this particular fashion by actually mixing the streams instead of having indirect heat exchange, then the thermodynamic efficiency goes down. Your entropy factor becomes very important, right. So, because of that, because of that thermodynamic efficiency goes down, but then instead of doing heat exchange at every stage, indirect heat exchange at every stage, it is always convenient to do it this way, ok. It is always good to do it this way because you can imagine, ok, having condensers or the heat exchangers situated after every stage in the column, ok. It is very difficult to fabricate such a system, ok. Instead, if you have these stages, ok, I can have a column, a multi-stage column and that is nothing but your normal distillation column. That is nothing but your normal distillation column in which you have stages and these stages are nothing but these intermediate units, ok. And they can act as equilibrium stages or non-equilibrium stages depending on extent of mass transfer taking place on each and every stage, right. So, that is the principle behind a continuous multi-stage distillation column, ok. You have to exchange a heat from vapor stream to liquid or liquid to vapor and because of that you have cascade of these stages and you have heat source and heat sinks at only two places and you have a column which is equivalent to this particular cascade. So, this is a normal distillation column, but always remember as I said before, the way we operate it, the way we design it, there is always loss of thermodynamic efficiency there, but it is at the cost of the convenience in fabrication, convenience in operation. Otherwise, we will need intermediate heat exchangers at every stage, right. Now, just try and take a look at what happens inside, ok. On every stage, I have the vapor stream coming in, I have the vapor stream coming in, I have a liquid stream coming in and I want mass transfer to take place, right. I want mass transfer to take place from one phase to another phase. It is not just the heat transfer, it is a mass transfer because every stream is getting enriched because of mass transfer or either vapor is getting enriched or liquid is getting enriched depending on the volatility of the components, right. So, in order to provide good mass transfer characteristics, ok, I need to design a stage every unit, ok, such a way that you have good mass transfer as well as heat transfer, right. Now, what do you have? Normally, you have already packed column or tray column. In a packed column, you have soiled packings on which the liquid trickles down and the vapor gets in contact with it. What is the purpose of packing to provide good interfacial area for mass transfer, ok. Purpose of packing is to provide good interfacial area for mass transfer. See what happens, liquid which is a dispersed medium, vapor is a continuous medium, liquid trickles on the packing surface, it forms a thin film, and that thin film is responsible for giving high interfacial area per unit volume, right. And because of that, you get good mass transfer. The purpose of packing is to provide good mass transfer, of course, not at the cost of high pressure drop, very important because if you go and make the packing such that you get very high interfacial area, sometimes you have to compromise on the pressure drop. So, pressure drop may increase and that is not a good packing. Tray column is very well known, you have sieve tray or bubble cap and you have downcomer, ok, liquid flows down, right. And vapor goes through this plate, it is a pool of liquid here and you have mass transfer on every plate, very well known either sieve tray or pack or other sieve tray or bubble column, of course. This talks about a flow pattern, there is a very important difference between packed tower and tray tower. In packed tower, you have, this is a packing on which as I said before, you have the liquid film and you have a vapor film, there is a contact between these two and you have mass transfer taking place. Look at the way they go, it is a almost a counter current flow, right. Whereas in tray column, in tray column, you have liquid flows in this direction, right and vapor is moving in this direction. This is not a counter current flow, in two sense it is a cross flow, right, it is a cross flow. So, that is the essential difference between plate column or tray column and packed column, ok. And that will come in picture later on when we talk about efficiency, when we talk about HTTP and all that, right. Of course, as I said before in tray columns, you have two types, main two types. Of course, now people are coming up with various modifications, so as to get good mass transfer with as low pressure drop as possible. Bubble cap, ok, this is a bubble cap. This is to provide more residence time, ok, on the pool of liquid on tray column. This is a normal CU tray, ok. The possibility of weeping in CU tray is much higher compared to bubble cap. So, the L-biogen which we operate the column, you have more flexibility when we use bubble cap, ok. Of course, this will come later. I am just touching upon each and every aspect, so that as I said before, it forms the best for further discussion. Now, fine, so we know what happens inside the column. I want to design a column. This typical problem is I have a mixture A plus B or A plus B plus C or whatever multi-component mixture. And I want to separate it. I want to separate it. I want to make or I want to have pure components A, B and C, right. So, from, so I have designed a distillation system. I am calling distillation system and not distillation column because as I said before, if it is a multi-component system and if I am interested in every component, then it is going to be a sequence. So, that is why I am calling it as a system. So, I want to design a distillation system in such a way that I get all the components in pure form. That is a design problem, that is a design problem, right. And then I specify the purity of every stream. I want A, not I cannot get 100 percent pure A, so 99.9 whatever, right, depending on the requirements, depending on the product specification. So, that is the design problem. And then this is given, the feed composition is given, feed flow rate is given, it is determined by the capacity and required separation is given for a given column X D and X B. D is distillate, B is bottom, right. So, all these compositions are given. A means to find out the size of the column or in other words the height of the column or the diameter of the column, right. So, we have to size the column, we have to determine the dimension of the column, that is typically a design problem, that is a design problem, right. Simple method that we know, mycapital method, very well known, okay. I will just quickly revise. This is your bottom composition given. This is your distillate composition given, feed composition given. You have this, what is this? This is a VLE curve or equilibrium curve, which is defined by the thermodynamics. The moment I say that I have ethanol, propanol and butanol, this gets fixed, right. That means once I specify the components, okay, the vapor liquid equilibrium gets fixed. So, you have this curve available and what you do later is the design method, okay. Very old method, 1920, 25, mycapital, until, okay, they came up with this particular method, which became very popular. The main reason is the visualization. You get inside into distillation, okay and it is very easy to work with, right. And still popular today after 80 years, right. You have rectifying section line, you have stripping section line. This is straight means the feed comes at a bubble point is liquid, right and then you do this calculations, okay, number of stages and these are number of equilibrium stages, right. These are number of equilibrium stages. What do you mean by equilibrium stage? Equilibrium stage is nothing but a stage which gives you maximum possible mass transfer, right. Maximum possible mass transfer. It is ideal stage, okay. We will talk about it later. Something about mycapital methods, the oldest method that provides useful insight in distillation system. Very simple to understand. That is why it is popular, okay, because of its graphical visualization and we are going to see tomorrow, day after, okay, how one can extend this method or same concept to multi-component systems, okay. Systems with aziotrops. It is not so easy but there is an attempt made and there is a book on that, okay, on conceptual design on distillation systems and we will cover the important aspects of the graphical methods to design distillation column for multi-component systems involving aziotrops, right. Now the major limitation, the first limitation of course is the binary system, okay. We cannot do it for multi-component system, right and then it assumes constant molar overflow. Very famous assumption, okay. What does it mean? That means on a given stage you have vapor coming in, liquid going down, okay. Vapor is getting condensed, liquid will get evaporated, right, because of the heat exchange, right. The extent of condensation is same as extent of evaporation, right. That is why there is no change in flow rate, so constant molar overflow. Now extent of evaporation would be same as extent of condensation, okay. When is that true? It is true when the latent heat of vaporization of the mixture, okay, is same as latent heat for condensation, okay, of the mixture. Now it may not be same and that is where the problem is. That is why I am saying that macapthil has a limitation. It assumes that is a constant molar overflow, yes. See how do you get rid of this problem? Okay. How do you get rid of this problem? If we want to take into consideration, okay, the change in flow rate you have to consider the energy balance, okay. So, along with mass balance, along with material balance, you have to write energy balance equations. So, the rectifying section profile which is based on mass balance equation, okay, right, only mass balance equation for macapthil method, okay, right, may not be same if we consider the energy balance. It will become a curve, right, because the internal reflux ratio, what is the reflux ratio? L by D, right. The L by D is the external reflux ratio, right. What happens inside, okay, is very important, right, and that is decided by the energy balance. And if that ratio of liquid to vapor flow rate inside column is not constant, then the slope of the operating lines would change, right. What is the slope of the operating line in rectifying section? It is R by R plus 1, that is reflux ratio divided by reflux ratio plus 1. If that is not constant as we go from top to bottom, right, then that slope would change, would not be a straight line, right. Now, look at assumptions, relationship between y and x. Most of the times, okay, we write it in this particular form. What is alpha? Alpha is relative volatility, right. Suppose we have mixture of A and B, A is more volatile. Normally, I take the vapor pressure ratio, right. Vapor pressure of A divided by vapor pressure of B is nothing but alpha, okay. That is an assumption. Now, look at vapor pressure. It is function of temperature, right. And the distillation column, the temperature, does it remain constant along the height? No, it changes, right. At the top, you have low temperature compared to bottom. The temperature varies. So, vapor pressure will also vary, right. So, it is quite likely that this ratio may vary and alpha may vary, right. But of course, sometimes the ratio may remain constant. If the components are quite similar in nature, say you have butane propane, ethanol, propanol, okay. The ratio may remain constant. Even if the vapor pressure changes with temperature, ratio remains constant. So, alpha remains constant. That is for ideal systems. Most of the times, it is true if you have components involving the mixture quite similar in their nature in terms of their chemical structures, okay. As I said, ethanol, butanol, ethanol, propanol or say butane, pentane, right. So, the most of the time is refinery distillation, okay. They are all ideal distillation because you are dealing with components with similar chemical structure, okay. Not much difference in molecular weights, you know, right. So, always there we talk about relative volatility. But when it comes to non-ideal systems, we should be very careful. This equation is not valid at all, okay. Do not use this equation otherwise, it is a disaster, okay. So, this is valid. You should be aware of this. This is valid only for ideal systems, okay. Alpha is the ratio of vapor pressures. And of course, I have written it for two components system. It can be written for multi-component systems as well. We will come to that later. Now, the most general equation which comes from thermodynamics, where we relate the activities in two phases, okay. So, activity in vapor phase is equal to activity in liquid phase. What is this? Phi is the fugacity coefficient normally different from unity when you have higher pressures for low pressure or moderate pressures. Phi is 1. What is Pt? Pt is total pressure. Y is vapor fraction. And then gamma is the liquid phase activity coefficient. Vp is the vapor pressure. X is the liquid phase composition. So, that is the most general equation coming from basic thermodynamics. Of course, the next lecture will be on vapor liquid equilibrium by Professor Malik who is going to talk at length, okay, about the thermodynamics involved, right. And so, this is something that we should use when we talk about non-ideal systems, right. And this equation is no longer valid. Statement is very important. Vapour liquid equilibrium decides the fate of feasibility. As I said, feasibility, there is a formation of azeotrop and do not consider that, okay. And your vapor liquid equilibrium model that you are using is wrong, okay. Then your results will not be authentic, right. Determination of height of the column. See, by my cap-thill, I can measure number of stages. I can count number of stages. But then actual height will be decided by number of stages into HETP for a packed column, right. Height equivalent to number of stage. In a packed column, I can visualize a packed column as a stage column, right. And section of packing equivalent to a particular stage, right. And that particular height or height of that particular section, okay, is called as HETP height equivalent to a theoretical plate. And if you multiply it by number of ideal equilibrium stages, you will get the height of the column, okay. Or in the tray column, you do not have HETP. You are talking in terms of efficiency. Sometimes, mercury efficiency, the various efficiency factors defined, okay. So, the idea is to get number of stages, ideal number of stages. From basic thermodynamics, apply some correction factor, okay. These are all traditional methods of design, okay. People have now improved this method. They are using simulation packages to design a distillation column. We are going to have a look at that, okay. I am just revising or taking review of what we know about distillation today. So, it gives you the height of the column. Then diameter, again you have something like this. What is this graph? It is a typical flooding graph. We talked about pressure drop. Now, you have G which is vapor mass velocity and L which is liquid mass velocity in the column, right. This ratio does not depend, L by G does not depend on the column cross section, whereas G depends on the column cross section. When I say mass velocity, it is mass divided by time and cross section, right, cross section. So, what are these plots? Now, this is a plot for flooding, okay. Now, normally I have created a column for 60 percent flooding, 80 percent flooding, okay, depending on the packing, whatever your vendor or supplier tells you, okay. So, these are different plots for different floodings, percentage of floodings, okay. Basically, they give different pressure drops, like at flooding you get almost infinite pressure drops. This is where the column performance collapses, right. And then you have, you have many graphs like this and I have select one of them depending on the percentage of flooding that I want, right. And then, I select the point, I know L by G, I select the point, I go back, find out G, okay. I say it is function of G because there are some factors like packing factor, density and other stuff coming in, which of course we know for a given system, right. So, we, what is unknown is G, right. L by G is known because I know the molar flow rates, right. The ratio of molar flow rates or mass flow rates is going to be same as ratio of mass velocity. So, there is no cross section coming in picture. So, I calculate G and from G, I calculate the cross section area and the diameter of the column. That is the way normally diameter is calculated for distillation column. So, this is what we have learned so far and this is the basics of distillation. A step forward would be to see more complexities in distillation systems, okay. Macapthil method, go back to Macapthil method. You have, instead of a simple smooth curve, okay, you have something like this. A non-adial system, a non-adial system, but your vapor liquid equilibrium is not defined by the equation that I told you, y is equal to alpha x upon 1 plus alpha minus 1 x. What is that equation? It is basically a hyperbola, rectangular hyperbola, right. So, that equation is no longer valid. It is quite possible, system is non-ideal. There is no formation of azeotrop, but there is something like this. What is this called as? This is called as a tangent pinch, okay. A tangent pinch, acetone water, acetic acid water, okay. You may get such pinch and it has very serious implications in terms of column design, finding out minimum reflux ratio. Now, how do you calculate minimum reflux ratio? The procedure is quite straightforward by Macapthil, right. You have x d, okay. You join it with the intersection of field line and valley curve, find out a slope, okay. Slope is nothing but r min divided by r min plus 1, right. That is the way you calculate reflux ratio, minimum reflux ratio. Will it be true in this particular case? If you do that, then you have a problem because you are talking about this particular line, okay, joining x d. This is your x d, right. And this is the intersection. You join this line. This line goes out of valley curve because valley curve takes this particular pattern, right. And so, this particular line which you join, okay, which you rather draw by joining these two points goes out of valley curve and operation is infeasible, right. So, what are you supposed to do in this case? You are supposed to take tangent to the vapor liquid equilibrium curve and this tangent you find out a slope and line B, line B will give you the minimum reflux and not line A which is normally used for calculating minimum reflux for ideal systems, right. So, for ideal systems, fine, okay. I just joined these two, sorry, joined these two points blindly and calculated slope, right. But if you have tangent pinch, you have tangent pinch and somehow if you are dealing with this particular region, its presence is highly relevant, okay. And you should not consider this line to calculate minimum reflux ratio. But this is the line which is very important. The line is nothing but a tangent to the vapor liquid equilibrium curve at this conflection where you have change in concavity or rather there is a transition from concavity to convexity, right, of the vapor liquid equilibrium curve. Very important aspect, your formation of azeotropes, formation of azeotropes is again a vapor liquid equilibrium curve, say Y versus X, right. You have formation of azeotropes, what does it mean? That means at a particular point in your composition space, Y is equal to X, okay. It puts a limit on distillation. See, distillation is based on the difference in volatility. When I vaporize a mixture or when I vaporize a liquid mixture or condensed a vapor mixture, then there should be change in composition. There is no change in composition, distillation cannot be used, right. So, in this case, because of formation of azeotropes, you have two distillation regions, okay. You have one region here and another region here. What is this? The two types of azeotropes which are these azeotropes, minimum boiling or maximum boiling. For a binary system, you have either minimum boiling or maximum boiling azeotropes. What is this? This is a minimum boiling azeotropes. So, you have somewhere intersection diagonal with the vapor liquid equilibrium curve and you have formation of azeotropes and because of which you have the entire region getting divided into two sub regions, we call them as distillation regions, okay. And this is nothing but a distillation boundary. It is a very important concept and we are going to extend this concept to multi-component systems, non-ideal systems in the lectures. So, you have two regions. Now, what is the significance? Suppose you have a feed here, right. Suppose you have feed here, now if somebody tells me that I give you feed at this particular composition, right and you get me x d correspond to this composition. Is it possible? With simple distillation, it is not possible. It is not possible to cross the region. If I am in this particular region, if my x b is here, my x d cannot be here. My x d, that is my distillate composition, would be at the most up to the azeotropic point, right, right, okay. Sir, phase separation that is taking place. In, yeah, shall I interrupt you? Do not concentrate till the point, one phase is at the aqueous phase, region aqueous phase and there would be an oil phase at the top. Yeah, yeah. Actually, this is, I am not talking about phase separation here at all. I am just talking about homogeneous azeotropes. Now, it brings me to another classification of azeotropes. There are two types of azeotropes. As I said, minimum boiling, maximum boiling. But again, we can classify azeotropes in terms of whether there is a phase split or not. So, we have homogeneous azeotropes or heterogeneous azeotropes. In homogeneous azeotropes, when the vapors condense, okay, you have a single liquid phase. In heterogeneous azeotropes, okay, if the vapors condense, you have two liquid phase, right. Now, when I am saying x is equal to y, in the first case, it is quite obvious that liquid composition is equal to vapour composition, right. In the second case, when the vapors condense, you get two liquid phases. Which x is equal to y? It is the overall liquid phase composition that is equal to y and not any individual phase, right. Anyway, we will talk about it later. Here, I am just telling you about a general azeotropes and there is no phase separation, okay, probably the homogeneous azeotropes. Heterogeneous azeotropes also can be exploited very well, okay, in heterogeneous azeotropic distillation systems. We will see that later, okay. So, when you are here, your XF is here, your XB is here, you cannot have XD in this particular zone unless you do some modification in the system. You cannot use simple distillation to cross the region. So, the regions formed is a boundary in composition space. Always remember that, right. I was talking about the volatility change. Now, look at this particular plot. You have, suppose I say it is a mixture of A and B. A is more volatile and I am plotting it for A. Normally, macathil is plotted for a most volatile component, right, the most volatile component. This is YA, this is XA. So, in this region, look at this. In this region, A is more volatile than B, right, because the vapor composition is higher than the liquid composition. What happens in this region? Yeah, B is more volatile than B, A rather, right. So, if you just go by boiling points, you will always say that A is more volatile, but when you actually draw this diagram, there is a formation of azeotropes. In a particular region, the volatility reversal takes place, right, and this point is very important. Talk about it later. So, presence of azeotropes we have seen. Now, energy balance, macathil, energy balance is not considered, but we need to consider it if you really want to approach towards reality, right. It will take care of the change in internal flow rates. The internal reflux ratio will no longer be constant along the column of height and operating lines will not be straight, as I told you before, okay. So, energy balance is required to be considered, okay, because your reflux ratio would change and it has a direct implication on feasibility because reflux ratio, as you know, there is a minimum limit on reflux ratio. If it goes below that, inside a column also, the feasibility is lost, right. So, it is a very important aspect and it needs to be considered at some stage or other in your design methodology, okay. I am just making you aware of different aspects of distillation and later on, we are going to see how to take care of all these issues while designing a distillation system for a given mixture. Now, multi-component systems, again, McCapthill is good for binary systems. When you have components, number of components greater than two, okay, you start facing problems. Can you use McCapthill method for binary systems? Can you use McCapthill method for five component systems? Not possible, okay. So, of course, we do some assumptions like you work with pseudo components, okay. I say like, I group some components, higher boiling components in one category and lower boiling component one and then I somehow calculate some apparent relative volatility and then work with McCapthill method because I know how to work with McCapthill method, right. But then it is now always true, okay. It is it, you may land up in problems, okay, like, while making these assumptions, okay. It depends on your composition. Sometimes if you have to form again, things will be much different, okay. So, multi-component systems, again, need attention. Now, what do we know about multi-component systems? You might have heard about Fansky equation for minimum number of stages, right. This is for design of multi-component systems. A double equation for calculation of reflux ratio, I will show you those equations later. But these two, again, make assumption that the system is ideal, okay. System is ideal. We will see those equations. These are the equations, right. This is your Fansky equation. It is all derived. I am not going to do the derivation. You can, any standard textbook on mass transfer operations will talk about it. You have this top composition, bottom composition, relative volatility. The moment you have relative volatility, that means you are assuming the system to be ideal, no formation of azeotrope. Whenever I use alpha, okay, always remember, okay, I am ignoring the presence of azeotrope, if any, in the system, right. This is your underwater equation. Need some rigorous calculations, this theta, okay, which is to be calculated by solving nonlinear algebraic equations. But of course, since multi-component system is there, you have many components, dimensionality of the system is high. So, you have to deal with this problem, solving nonlinear algebraic equations and then you get minimum reflux ratio. So, these methods or these techniques or other, I would say, equations are available, okay, to calculate the minimum reflux ratio, right. But again, I am going to tell you the limitation about it. And the main limitation is of course, the relative volatility, okay, concept, because I am not considering the non-ideal system here, okay, right. If there is a formation of azeotrope, this is not useful at all, right. And there are some core relations also, I have written them for your reference here, Gilliland correlation, and then you have Kirk-Brady equation. This talks about the minimum reflux ratio, relationship between minimum reflux ratio and minimum number of stages. Kirk-Brady equation talks about number of stages in rectifying section, number of stages in stripping section. Of course, they are empirical equations, and most of the times for ideal systems, they hold good, okay. But when it comes to non-ideal systems, okay, we cannot make use of these equations at all, okay, even for multi-component systems, right. So, again that is a problem. I have talked about this before, assumption of equilibrium stage. See the serious implications of this. You have a stage in the column, you have a stage in the column, vapor coming in, liquid coming in, they get in contact with each other, okay. There is a mass transfer, heat transfer taking place, and you have these two streams going out, which I called as overflow, rather, from the column. Sorry, this one. It all depends on how you count n, okay. If you count it from top to bottom, okay. So, when I count condenser as 1, and then when I go down, okay, I have 1, 2, 3, 4, 5, right. So, the n for condenser would be 1, n for a stage at the top would be 2 and so on, right. So, this stream would have n, which is less than the actual stream. And a convention is like this, the streams leaving a particular stage, nth stage, okay, right. The streams leaving that stage will have a suffix n, right. So, what are coming from the bottom, right, is from the stage which has n plus 1 suffix, and from the top n minus 1. We may change it later on, as and when we talk about it, I will say more on this. But then at this moment, the point is that these two streams are getting in contact with each other, okay. And there is a mass transfer and heat transfer taking place. And when I say it is an equilibrium stage, that means these two streams, very important, these two streams leaving that particular stage, they are in phase equilibrium, right. They are in vapor liquid equilibrium. They satisfy the relationship, which is given by vapor liquid equilibrium, basic thermodynamics, very important, okay. Because sometimes and most of the times rather in reality, a stage or a tray, say tray in a stage column or plate column, right, you do not see equilibrium, okay. When I say you have equilibrium, that means I am providing sufficient residence time on a given stage, okay. I am providing sufficient hold up on a given stage, so that two streams get in contact with each other. And you have maximum possible mass transfer, okay. You have maximum possible mass transfer and so that you have these two streams, which are in equilibrium. But we can have a non-equilibrium stage as well, if you include efficiency of mass transfer. You see what exactly happens on a given stage, then you can have a non-equilibrium stage as well, right. So that you have a relationship between these two and when I say equilibrium stage, these two are related to each other by vapor liquid equilibrium. If it is ideal system, then you have y is equal to alpha x upon 1 plus alpha minus 1x, right. And if it is non-ideal, then you have a general system, general equation rather coming from basic thermodynamics. So you have to calculate activity coefficients, fugacity coefficients and all. So we are going to have many lectures and simulations. So I thought, okay, let us have some introduction simulation. These days we are talking a lot about simulation. There are many commercial simulators like Aspen, Pro2, Heises, ChemCAD available in market. What do they do actually? Like how is this particular field of simulation different from what we have learned in our undergraduate curriculum on distillation or rather the conventional macabre method of design and all. So let us try and understand one thing that there is a basic difference between these two problems, design and simulation. Design means, as I said earlier, like your xd is defined, xb is defined, xf is defined and you are supposed to give dimensions to the column or calculate number of stages and diameter of a column. That is a design problem. Simulation is exactly opposite. That means the column is in front of you. Feed is given to you. You give feed to a column and then try and see how a column behaves, right. How the things change with respect to time, what happens at steady state, how the compositions change with respect to height, what is xd, what is xb. We have no control over xb and xd. Of course, you can change reflux ratio and operating parameter. But once you set those parameters, like what have xd and xb is defined or gets fixed automatically and simulation gives you the answer for that. The simulation is like a virtual experiment. You have a column in front of you giving a feed and you are seeing the performance or response of the column to that particular field. If you are seeing the changes with respect to time, it is dynamic simulation. If you are going to look at what happens at infinite time at steady state in a continuous process, it is steady state simulation, right. So, as I said before, you have feed composition given, column height given and the result of simulation is look at a column for performance, especially the xd, the top composition and the bottom composition. Along with this, you get so much information like what is the column composition profile, temperature profile, pressure drop if you want, right. How to solve a simulation problem? Why simulations were not so popular in earlier days? Like when we learned chemical engineering, when our generation learned chemical engineering, we did not learn simulation, right. But today, most of the colleges, like they have simulation in their curriculum and graduate or even postgraduate students, they learn simulation. The main reason for this is simulation needs rigorous calculations. How do we solve simulation problem? We have to write equations for every stage. Now, these equations are not different, whatever equations we are using for design problem, they are same as what we are going to use for simulation. But the problem is such that, you have to solve all these equations simultaneously. For a given column, since you do not know xd and xb, you have to write equation for every stage and solve these equations simultaneously, right. In a design problem, situation was different. You knew xd, you knew xb. So, you had done calculation macabre method from top to bottom and even for bottom to top, whatever. So, those calculations were easier with the help of macabre or any graphical method for a design problem. Whereas, simulation, since you do not know xd and xb, though the equation, the model is same, right, you have to solve these equations simultaneously. Which are these equations? Material balance equations, equilibrium constraints or equilibrium equations, vapor liquid equilibrium. As I said, if you assume the stage to be an equilibrium stage, right, the vapor and liquid compositions are in equilibrium, you should know the vapor liquid equilibrium relationship. In the summation equations for every stage, if you are writing in terms of mole fractions, sigma x should be equal to 1, sigma y should be equal to 1, right. Then you have to write energy balance also and solve these equations. These are called mesh equations quite popularly, like MeSH, m stands for material, right. E stands for equilibrium, S for summation, H for energy balance, right. And you have to solve them simultaneously, which is important. And when you want to solve them simultaneously, there is so much calculation involved and you cannot do it manually. Why? See this question, how many equations? Suppose you have a column with say 10 stages, very small column, 10 stages and you have say 4 components. How many equations you will have? You will have to write equation for all the components, ok, individually and then solve together. So, at least 40 equations you have if you just write material balance, then you have energy balance if you want to include pressure drop and all. So, many equations you have to solve simultaneously and you need the help of computer, right. And that is why simulation approach was not so popular in earlier days, right. And today with the advent of high efficiency computers, many commercial simulators are becoming popular, ok. And that is why the need to learn what simulation can do, how it can be used effectively to solve our design problems at the same time the day to day problem. It is a very, very effective tool. For example, in your industry, suppose you have a column already running, I want to use it for some other purpose and I want to do the rating of that column. I want to see whether that column will perform well for another separation, ok. The design approach will not be useful because I know now the column is there. I know how many stages it has. I know the feed composition. I know feed flow rate. I can just quickly solve a simulation problem, ok. Use any commercial simulator. You do not need to really solve equations yourself, ok. Use commercial simulator and solve the equation and see whether it can give me the right kind of x d and x b required, ok. Play with some parameters like revolver duty, reflux ratio and with some iterations probably you will get it, ok. But of course, there are limitations. If you have zero-toe formation and all, you should be very careful and we will talk about it later. So, complete design method or a right design methodology would involve many steps, of course, the first thing is thermodynamics, ok. First thing is thermodynamics. You should have a right vapor liquidically. If you go wrong there, how much care you take later, ok. It is not going to be useful because your thermodynamics itself is not correct, then you are going to get results which may not be correct and your design will fail, right. So, getting thermodynamics, right vapor liquid equilibrium is very essential. So, you should know the theory of vapor liquid equilibrium. So, vapor liquid equilibrium is necessary. The thermodynamic feasibility needs to be checked first, ok. There are some distillation boundaries as I said before, formation of azeotropes and all you should first find it out. So, first question is whether it is feasible. That means, a mixture is given to you and somebody says that I want purity, then you should be able to say whether it is feasible or not. If it is feasible, then only you go ahead, ok. Find out minimum reflux, minimum number of stages. I am talking about a general system, ok. This is what you do in macabre method, right, for a binary system. But you should be able to do at the end of this program for multi-component systems as well and for even non-ideal systems, ok. Find out approximate number of stages. Why call it as approximate? Because when you do these calculations, you make some assumptions. Sometimes you neglect energy balance like what Macabre does, right. Find out operating reflux ratio. Most of the times it is 1.3 to 1.5 times the minimum reflux ratio and there is a logic behind that, ok, like we call it as optimum reflux ratio because if you increase reflux ratio, your energy cost goes up, ok. If you decrease reflux ratio, your capital cost goes up because number of stages would increase, right. And there is an optimum, ok. Most of the times it is, we say that about 1.3 to 1.5 times minimum reflux ratio. Then if it is a system, multi-component system, the difference from binary is like you have a sequence. Now I am interested in all the components in pure form. So, I need a sequence. So, I will have multiple columns. If I have three component systems, I need at least two columns, simple columns, ok. Sometimes you can do it in one column, but then most of the times I need multiple columns to deal with multi-component systems. So, identify many sequences possible to optimization come up with proper sequence. And once you have a design ready, feasibility ready and then you can do rigorous simulations because most of the things, most of the steps here I have used, I have neglected say energy balance, I have made some assumptions which I can take care of in column simulations which is rigorous. Here I am going to take help of computer. So, I can afford to have many equations here. You can solve them and get a real picture what happens. And of course, you can adjust the parameters. There are systematic methods to do that called optimization. Adjust number of stages, reflux ratio so that you get the best possible design or economically best possible design. And after this, of course, you may have control strategy. Sometimes now people are talking about involving or including control strategies at design stage itself, right. So, this is a complete design method. There are many steps involved and we are going to touch upon all these aspects as and when we go ahead in this particular course. Talk about energy integration as I said before. Now, we are talking about sequencing multi-component system. We have many distillation columns. There is a quite, there is an opportunity rather to do energy integration. So, I am just going to give you some examples. Talk about it in detail in lectures to come later. So, the objective of course is to minimize the energy consumption. And see in distillation column, it is a very popular question. In fact, we ask this to our students who come for interviews and all for MTech and all. We have a distillation column. We have condenser and re-boiler. In condenser, you remove heat. In re-boiler, you give heat. So, is it possible to combine these two because you are removing heat at the condenser and you are providing heat in the re-boiler. If I combine these two, then it is good. It is a good energy integration. I do not need energy for distillation, right. Why cannot I do that? Answer is quite straightforward, but then that forms a basis for energy integration in distillation systems. Why cannot I combine condenser and re-boiler? Because condenser I am removing heat, re-boiler I am providing heat. So, it is very straightforward answer. This re-boiler has higher temperature. If I want heat at higher temperature, because condenser removes the heat at low temperature, right. So, low temperature, heat is available at low temperature whereas in re-boiler, I need heat at high temperature. So, this integration is not possible at all because heat is available at low temperature and need heat at high temperature. There should be driving force for heat transfer, right. And that is not possible in same distillation column. So, you have to look for some other distillation column in your process to do energy integration. That is very important. You can play with operating pressure because it is very well known that if you increase operating pressure in distillation column, the overall temperature will go up, right. So, if I want proper heat transfer to take place, proper delta T or heat temperature driving force, then I can play with pressure of some distillation column in my process. I can increase the pressure there, sorry temperature there and can get a required temperature driving force. Of course, you have to see by increasing pressure, thickness would go up and all these problems would come in picture. But then possibilities exist. So, this is one example. Of course, we will talk about it in detail later. But then you have mixture A, B. I just want to separate it. Instead of doing it in a simple column, ideal system, you have two distillation columns. One is operated at high pressure and one is operated at low pressure. So, column one is at high pressure. So, the condenser temperature would go up and it is able to give heat to the re-boiler of column two, which is operated at low pressure and low temperature. So, I can make use of this particular arrangement. By instead of doing it in single column, if I want to do energy integration, this is one possibility. Of course, whether it is economically feasible or not is a different question. But possibility is there. There is thermal coupling. You have mixture of A, B, C. Now, I separate A, B from the top, B, C from the bottom. I have two columns. Now, look at these. You have re-boiler here. You have a condenser here. I can and I am removing B from here. I am removing B from here. Why cannot I have this particular arrangement? Instead of using two columns here, I just combine them because the temperatures of this point, this point, they match. So, I have this column. So, I am just having a coupled column. They call it thermally coupled column. So, this is not the end of it. I can go ahead. See, I have a condenser here. I have a re-boiler here. I can get rid of that. Look at this arrangement. I do not have a condenser here. I do not have a re-boiler here. There is a systematic methodology how to do it. I am just giving you an example as an introduction. So, you have a pre-fractionator. You have a main column. You do not have intermediate heat exchangers, only two heat exchangers. Now, you have two columns sitting side by side. Why cannot I combine them? So, I have a partition column, just single vessel. But from outside, it is just a single column. But inside, you have two columns. So, such possibility is there and it is not just the hypothetical concept. It is practiced commercially. Like, say, butadiene separation from C4 stream, BASF has a plan to use something called as partition column or more popularly known as divided wall columns. There are many interesting concepts. Azeotropic distillation, I talked about it. If you have mixture which is difficult to separate, when I say difficult to separate, it can either form azeotrop or boiling point are very close to each other. I can add external component, entrainer or azeotropic agent, so that it improves the separation. The entrainer will form azeotrop with one of the components, sometimes both. That is the basic condition. The outside component, the external component, should form azeotrop. I mean to form azeotrop, it improves the separation. Azeotrop can be homogeneous or heterogeneous, but then mostly will prefer heterogeneous azeotrop. Why? Because of further separation of azeotrop is easy. But because azeotrop, if it forms azeotrop, makes the separation easy. But later on, I need to separate azeotrop and break that azeotrop, which is formed just for separation. So, if it is heterogeneous, it helps us. I will want to see that in detail later. An example, of course, is separation of ethanol from water with benzene, ethylene glycol is extractive distillation, whereas benzene is azeotropic distillation. And what is extractive distillation? Extractive distillation, again external component is added. It does not form azeotrop. It is mostly times high boiling, least volatile in the system. And it improves the VLE or VLE is changed in such a way that separation is facilitated. So, example again, acetone methanol with water as an entrainer. There are many examples, extractive distillation. Again, butadiene example, I told you where they use spatial solvent like NMP and all to separate it from C4. Reactive distillation, as I said, it is not just the extension of azeotropic or extractive distillation. What we are doing is, here we are combining reaction with separation and it is not just a separator or not just a distillation column, it is a reactor as well. So, you have to have knowledge about kinetics. The entire reaction meaning concept will come in picture. If you want to design reactive distillation column and it is much different from other distillation techniques. But then with this, you get enhanced performance and I would say that it is not just enhanced distillation, but it is a process. It is a process. Entire flow sheet can be combined or condensed in a single piece of equipment where you have both reaction, distillation taking place and you are taking out the products. And there are again commercial examples like methyl acetate from methanol and acetic acid. This is one product process. They have condensed the entire plant in a single unit. They had in the plant, they have just one column. So, methanol and acetic acid going in and you are getting methyl acetate from the top and water from the bottom. So, you can imagine like otherwise the conventional process would have a reactor followed by about 8 to 9 distillation column because separation is not so easy. You have formation of azeotropes and all, methanol forming azeotropes with methyl acetate and methyl acetate forming azeotropes with water. So, it is a very complex system otherwise, but they have combined distillation column with reaction and it acts like a magic box. You are giving reactant and coming out with products, pure products. So, that is the potential of reactive distillation. I will just go through this concept. You have a reaction, just a concept. A plus B giving C plus D. You know the Leach-Ettles principle is a reversible reaction. If I remove one of the products, then reaction will shift in forward direction. This is a law of mass action. It is all well known. You have CSTR. The volatilities are right. I just operate the CSTR in boiling condition. The heat is provided. I take one stream out. So, normal CSTR is your reactant going in, product coming out. Now, this CSTR is a very special CSTR where you have two product streams. One is vapor and one is another is liquid. And these two are in phase equilibrium. Now, what happens if C is more volatile? C will come out, but then since you have only one stage here for distillation, A, B and D impurities would present in C. But relatively, this CSTR with two outgoing streams will perform better than the normal CSTR because you have simultaneously removed one of the products. Can I improve the performance? Can I go one step ahead? Because C had A, B, D. I put a column there. I put a column there and make sure that C is separated in pure form. So, I will avoid losses of A, B, D. Now, when is this possible? Again, if there is no azeotrope form, C does not form azeotrope with any of the components. It can be separated in pure form, a relatively ideal system or non azeotropic system where you are removing C in a pure form from the top of this particular column. So, this is again one step ahead. I am avoiding the losses of A and B. I am getting C in pure form. But this is not the end of it. Look at this particular stream. It has D, A and B. And suppose D is the least volatile component. Can I add another column there? A stripper. And I am removing D in pure form recycling A and B back to the reactor. Now, look at this. This is like a column now. I have a reactor which receives the reactants and gives out C and D in pure form. Can I combine these three? I can. I can combine these three units. And this is a normal reactive distillation column where you have a reaction taking place. You have a reaction taking place in the middle part. And the top or the upper part of the column is a rectifying section, a non-reactive rectifying section. This is a non-reactive stripping section. This is a hybrid reactive distillation column which would receive A and B here and will give C and D in pure form. That is what this esterification process is. Now, if you really want the same extent of reaction here, see what is the difference between these two? Here you have a stirrer. Why do you need a stirrer? You need stirrer to get good mass number. Suppose you have a solid catalyst. I do not want any mass transfer limitations for reaction. So, I do stirring so that the mass transfer coefficient is enhanced and I get as much reaction rate as possible. When I move to this, I do not have provision to do stirring. So, sometimes it is a limitation that you may get mass transfer resistance. If the reaction is very fast, if the reaction is very fast, if the reaction is relatively I would say or moderately fast. In that case, I can provide sufficient residence time, sufficient hold-up, sufficient catalyst loading such that I get the required extent of reaction. But that limitation is still there. I cannot get the kind of mass transfer coefficients or characteristics that I get here. So, that is the limitation of reactive distillation. But you can have better column internals to get as much mass transfer coefficient and interfacial area as possible. Now, in this case, you can have a reactor, a very big reactor with huge amount of or rather a huge hold-up in that. Whereas, in this case, since we are operating a distillation column in which most of the times the liquid is a dispersed phase and gas is the continuous phase. If you have reaction is homogeneous, then the hold-up is less and residence type is less. So, that is again one more constraint. So, now, then new concepts coming up, you can have a side reactor, you can put some reactor along with this and provide as much hold-up as possible. So, the reaction is slow, which needs very high hold-up, very large hold-up rather. In that case, reactive distillation may not be feasible. So, that constraints. It is not that it works always, but then for some reaction it works very well.