 In this lecture, I am going to spend some time on the modeling and simulation aspects of distillation systems. If I were to go through complete modeling aspects of a typical distillation system, there are various issues which should be touched upon and the key issues I have written on this slide. We certainly need to understand distillation as a separation process, get into the theory of distillation because the rigor of model depends upon how good is the understanding of the process. We should also try to understand distillation as a separation process from thermodynamic viewpoint, how efficient or how inefficient the process can be because that will tell us what are the limiting factors and whether the designs could be accordingly improved. Modeling also has to take into account the configurational aspects because distillation columns or distillation systems operating in different sectors may have different configurations. Petroleum columns have very different configurations as compared to typical columns which you will find in the petrochemical industry or other chemical industry. Then various simulation and design issues we will touch upon. Obviously, the performance of a column and also the design depends a lot on the choice of internals which in turn govern the heat and mass transfer aspects. So, we need to understand that to some extent and of course, the energy analysis. Now, this is a very ambitious list and one cannot do justice in two 90 minute talks to cover all the details, but I will touch upon most of these items and get more into the simulation and design aspects. So, I am going to start this presentation by going through these important facts about distillation which we need to remember and the aspect of simulation as well. Distillation columns and related operations constitute a significant fraction of the capital investment and the operating costs which is a very true statement if you are working with processes which are essentially fluid handling processes. So, any industry any process industry in which fluid handling dominates and examples could be refineries petrochemicals. You will find that by and large the workhorse for separation is the process of distillation. Of course, this would not be true if the industry is from a sector where solid handling operations are dominating and very little fluid handling is done. So, distillation columns may not be encountered that frequently and take for example, fertilizer industry. In fertilizer industry there are very few separations which are done by distillation, but petrochemicals where you are producing organic solvents or feedstocks for polymerization, olefins etcetera after the cracking occurs the separations are typically done by distillation systems. Now, I must go through some very basic aspects of distillation to impress upon that distillation is a very energy intense process and therefore, in addition to the scope which exists for improvement in designs from other angles, from hydrodynamics angle or let us say from structural angle or from controls view point energy plays a very significant role. So, we will have to spend some time to look into these issues. So, I have written these three aspects the design problems, the energy integration problems and the control problems. In this particular talk, we are only focusing attention on the design problems. We have a separate lecture on distillation control and yet another separate lecture on energy integration or process integration. So, I am not touching upon those issues in this particular talk. Now, when we talk about design problems or when we talk about energy integration problems or even let us say design of control systems, last several decades people have been working on mathematical models and it has been found that rigorous models become very useful tools for solving variety of problems, whether they are simulation problems, whether they are design problems, whether they are optimization problems and so on and so forth. So, let us go through some very basic material. This is so basic that sometimes people get offended by this type of presentation at a course or in a course of this kind, but I think it is essential to go through to understand some very basic fundamentals. So, let us define what is separation? Now, in very simple terms separation can be termed as a reverse procedure of mixing. You can or if you want you can call it as unmixing. Those operations which transform a mixture of substances into two or more products which differ from one another in composition, that is what the act of separation is. And when do we require separation? Well, you may have a mixture to start with. For example, you have a crude which is naturally occurring substance and you find that only certain fractions of that can be utilized in certain ways. So, you would like to do the fractionation. So, you may take help of distillation or when you transform molecules you carry out reactions. So, it is not only the main reaction which occurs, there are side reactions, series reactions, parallel reactions. And finally, you end up with a mixture of species out of which only selected species may be of importance or may be of more importance than others and you would like to separate them out. So, again separation schemes or separation trains normally are found next to the reaction scheme. So, idea is that minimum two or may be more than two species need to be separated. They are either naturally occurring in the form of a mixture or by carrying out reactions, we would have created mixtures. Let us quickly look at one statement which tries to characterize the second law of thermodynamics. Second law of thermodynamics can be put in various forms. This is one way to state the second law of thermodynamics. It says all natural processes take place so as to increase the entropy and entropy here is measure of the randomness. So, increase the entropy or randomness of the universe. Now, mixing as we know causes an increase in entropy and simple way to understand is that if I gave you one cup of benzene and one cup of toluene and if you let us say draw a sample from the benzene cup you are 100 percent sure that all molecules are of benzene. You took a sample from the toluene cup and you are 100 percent sure that all molecules are of toluene. But if I mix the two and mixing hardly takes any effort. So, with minimal effort I can mix the two and then I ask you to take the sample out the probability immediately has gone down to 50 percent. It is 50 percent probability that the molecules you have they belong to benzene cup or they belong to toluene cup. So, what does that mean that by mixing randomness has increased and if randomness has increased which means entropy has increased. Now, we defined separation as unmixing. So, mixing was very easy, but now unmixing is to be done. So, if I was given a 50-50 mixture of benzene and toluene and if I have to recover all the molecules of benzene and all the molecules of toluene I required to do some additional work some external work and that is the work of separation. Of course, there is a minimum thermodynamic work of separation which can be calculated for the given composition and given operating conditions temperature and pressure conditions. But then the efficiency of separation comes into picture and that defines how much is the total work you are going to put into the system. It turns out that distillation utilizes a very small fraction of the work which is put into the system. Inherently distillation is an inefficient process and it will become clear when we go through some of the slides. So, separation therefore, into products of different compositions requires a process where minimum or equivalent to thermodynamic work must be supplied to cause a separation to occur because it is unmixing and without work it cannot be done. Another aspect of separation any separation it is applicable to any separation is that separation operations are interface mass transfer processes. So, when we say interface which means more than one phase is there. So, if you have a single phase and all the constituents are residing in that phase and you want to separate them out one way to separate them out is to create another phase. So, if I have liquid and if I add thermal energy and partially vaporize. So, I am creating another phase which is the vapor phase. Vapor phase is in contact with the liquid phase and that should then enable me certain amount of separation. If I have a liquid which is brought in contact with another liquid which normally we call as solvent and then distribution of species occurs the solvent does not mix with the other or with the original liquid that again will cause separation. You can have distillation, you can have extraction, you can have absorption, you can have stripping all these operations essentially are two phase operations sometimes even three phase operations. So, presence of an additional phase is required. Now, in distillation the addition is of thermal energy. So, it is the thermal energy which is going to provide the minimum thermodynamic work of separation. Now, if thermal energy is going to do the work of separation and thermal energy is conserved which means that energy in terms of kilo calories which you are putting into the system at certain level that must be recovered at the other end. So, we supply heat at a higher temperature which is in the reboiler, we recover almost the same amount of heat at a lower temperature in the condenser and it is the degradation of the level of thermal energy which is responsible for the separation of the species. In terms of quantum, in terms of kilo calories you really do not lose any. Suppose, if I had a close boiling system where the condenser temperature and the reboiler temperature were more or less identical, feed was saturated. So, the enthalpy of heat will very nicely balance with the enthalpy of the top and bottom products put together which means the reboiler load and the condenser loads will be almost identical. So, if I am putting 1 million kilo calories in reboiler, I would have recovered 1 million kilo calories in the condenser. So, quantum of energy is not doing anything, it is the level of energy which is doing the work of separation. I put energy let us say at 120 degree Celsius in reboiler and I may be removing at 100 degree Celsius. So, 20 degree degradation would have occurred or may be more if it is a wide boiling system. So, let us now start constructing a separation system by taking this example. So, I have taken benzene and toluene which is close to an ideal system. You can start with any composition maybe 50-50. The circle with the arrow shows here that there is a provision for heat transfer, it may be in or it may be out and a valve here shows that you can do throttling, you can change the pressure if you like. So, if I have let us say a liquid phase, if I have benzene and toluene given to me in liquid phase, I can create vapor phase by adding certain amount of thermal energy, partial vaporization. I can also if the pressure was high to start with, I can also do certain amount of throttling and throttling can also give vaporization or I can have a combination of the two. So, that is not important what we are doing here, what is important is that we should create another phase which should be in touch with the original phase. So, if original phase was liquid, I would like to create the vapor phase or vice versa. If I had vapor to start with, I can remove the energy and do certain amount of condensation and create a liquid phase that is the idea. Now, here comes the question of how does the separation occur? Well, the separation occurs because of the physical properties which different species have. We know that between benzene and toluene, benzene is more volatile. It is more volatile, it simply means that its vapor pressure or the net vapor pressure which is exerted by this particular species in the mixture is higher than what is exerted by toluene. And therefore, we say that the ratio of two vapor pressures here because I said the system is more or less ideal. So, it is simply ratio of two vapor pressures which becomes a factor of separation relative volatility as we call it. So, if it is greater than 1, we know that vapor will be richer in benzene and liquid will be richer in toluene. So, that is the underlying principle. So, this is a similar arrangement. The feed condition could have been vapor, it is not written here, it should have been written. Both the diagrams essentially mean the same thing here. All right. So, we did something to the feed and we created a vapor stream and a liquid stream. And as I said, vapor is richer in benzene, this is richer in toluene. Now, if I need to further carry out separation, I should again do certain amount of heat transfer. But this heat transfer will be in the negative direction because this is vapor and I want to create a liquid phase. So, I will remove certain amount of energy. If I remove certain amount of energy, I would have created again another vapor phase which is in equilibrium with the liquid phase. And if I compare this vapor which is characterized by the mole fraction yB prime, this is richer than this in benzene. And again, the same argument applies that if I compare these two within, then this is richer in benzene and this is richer in toluene comparatively speaking here. I can continue to do that without focusing attention on XB and XB prime. So, if my focus is on this particular stream which is rising up in the form of vapor. So, I have some improvement in the composition of benzene as compared to what I started with, then I have further improved it and I can go on and on. So, I can come here and I can go on increasing the purity of benzene. What is shown here? This is a multi-stage flash operation you can call it where we are taking the stream here it so happens that it is in vapor phase, certain amount of energy is removed, only partial condensation is done. So, I got another vapor stream and I continue to do that till the time I have the desired purity. So, maybe if alpha is fairly good, let us say 1.5, 1.7 or maybe higher finite number of stages, a few number of stages if I put this way, I probably will come to a point that benzene will be maybe 99 percent pure here. But if I look at the value of Vn which is the flow rate, that flow rate will be a very small fraction of what I started with, because on the way I have left so many streams which are going different ways. So, recovery of benzene, recovery of benzene from the feedstock is very small. So, where is the benzene gone? Composition is very good, 99 percent, but where is the benzene gone? Obviously, the benzene is still sitting into these streams, it is sitting in ln ln minus 1 all the way up to l naught, all right. So, this is one thing we will have to keep in mind. The second thing is suppose these stages I am just giving a typical number, let us say for benzene toluene system this number of flash units I have 10, 10 is a reasonable number. So, I have 10 heat transfer devices. So, can I do something better, can I do something better, so that I improve the recovery of my benzene at the same time I cut down on the number of heat transfer devices. Well, so we start from this angle at this side rather. Now, here if this is my final product I need to keep this heat exchanger which is removing the energy, because otherwise this product will not be in equilibrium with the liquid here, because the purpose of this was to create two phases. Two phases only will give me the desired separation. Phase has to be created for separation, we said that is something very fundamental about separation. Coming back to this particular heat exchanger, now what I am going to do is I am going to remove it. The purpose of this was to cause condensation So, if I remove I must do something so that I still cause condensation. So, how can I cause condensation and not have this exchanger in place? Well, it is not difficult, because if I have not written the temperatures here, because we are only working with these notation values. So, absolute numbers we do not know, but one thing is true that the temperature of this vessel will be lower than the temperature of this vessel. Why? Because energy has been removed and there is a finite relative volatility. So, this vessel is cooler, this vessel is cooler than this vessel, which means this liquid is cooler than the temperature which is there in this vessel. So, if I take this liquid and revert it on this side, vapour of higher temperature is going to mix with liquid of lower temperature, vapour of higher temperature, because this temperature is higher is going to mix with liquid of lower temperature. And this mixing is going to cause condensation, why? Because this vapour is at its dew point, this vapour is at its dew point. So, it is going to cause condensation. So, what is the claim? The claim is that even if I do not have this heat exchanger, which is heat removal unit, if I revert this stream and put it back into this flash vessel, the mixing operation here is going to give me presence of liquid phase. Certain amount of condensation has to occur because this is cooler, Ln is cooler than Vn minus 1. So, if that argument holds, I can continue to do that, I can remove the heat exchanger which was present, let us say in Vn minus 3 stream here which is not shown and Ln minus 1 I can revert back and I can cause condensation. So, by reverting all these streams to the adjacent flash vessel, I can cause condensation and that is precisely I would like to do. On the other side, the story is similar except that we have to remember that here we are removing energy, here we are going to add energy because this is liquid to start with and this is liquid at its bubble point. So, I need to add certain amount of energy so that I get vaporization, partial vaporization I have to do. So, this liquid is richer in toluene as compared to this one. I add more energy, I do further vaporization and I still improve the composition and I will come to a point with another few stages so that here the toluene is 99 percent or more whatever may be required. I do require this reboiler because this is the one which is doing vaporization. Now, this one is warmer than this one and therefore, if I get rid of this heater or reboiler and revert this stream back into this vessel because this is warmer, this is going to cause certain amount of vaporization and this vapor will partly get condensed. So, the same thing will happen here which means by reverting the vapor to the neighboring flash vessel I will be able to cause vaporization. Here I was causing condensation. So, one thing we have very nicely achieved that we have improved the recovery of our both the constituents because these streams have been put back into the system and therefore, they have become the local recycles. Same is true here. We have also gotten rid of these coolers and these heaters except this has to be kept and this has to be kept. But we have done lot of damage from thermodynamics view point. What is the damage we have done to the system? Anyone? Every time I am reverting the stream to the neighboring vessel I am causing mixing and I know mixing is irreversible. Mixing increases the entropy and because so many times I am causing separation and then mixing separation and mixing and it is because of this frequent mixing which is occurring inside that my thermodynamic efficiencies are going down. So, thermodynamically this way of causing separation is not an efficient way. I know that I am causing irreversibility in the system by carrying out the operation of mixing. But on the other side I do have a gain. The gain is that my recoveries have gone up. So, I have recovered most of my benzene here, most of my toluene here and at the same time I am not working with too many heat exchangers. I have removed all those units. So, capital investment has gone down. The irreversibility here will show up finally in the operating expenditure because the heat loads on these units will go up. So, this is how we will have the separation process finally. And this becomes now a cascade of flash vessels. The cascade on this side is typically called the rectification zone because the focus is on the more volatile component here and on this side is your stripping zone. So, if I were to represent this in the form of a single piece of equipment with these things becoming internals, this will become a distillation column, this is the condenser for the column and this is the reboiler for the column. So, this is how a typical column looks like. Now rather than having simple flash vessels, when I say flash vessel, flash vessel is expected to have fairly large residence time so that equilibrium could be attained. In distillation column, you cannot afford to have so much of hold up so that your residence times are large and therefore, you need some mechanism to enhance heat and mass transfer and therefore, the internals will be required. You need a mechanism so that the vapor spends sufficient time with the liquid so that heat and mass transfer occurs. So, internals will be required. So, you may use trays, you may use packed packings, but some internals will be required. But essentially the main column really works like a cascade of flashes. This is the final condenser in which we were removing the energy. The cascade which I constructed, I had done only partial condensation and therefore, I had removed distillate as a vapor. Here if we are going to send the product to storage, there is need to further condense it. So, you will do total condensation, rest of the process remains the same and therefore, if it is a distillation column with a total condenser, the way it is shown here all of us know that condenser becomes only a heat transfer piece of equipment and there is no vapor liquid equilibrium here. Even when you study binary distillation, this is one thing which is told always that condenser is not a theoretical stage whereas, the partial re-boiler is a theoretical stage because the product when it is drawn from here, this particular product here, this is in equilibrium with the vapor and the vapor is returned here. So, it is an equilibrium stage. Had it been partial condenser where I would have drawn the product, distillate product in the form of vapor from here and the liquid would have been refluxed, then this also will become a theoretical stage. So, the cascade I had shown was for a partial condenser. What I have shown here because this is how typically a column is configured, this is with a total condenser. Of course, when you carry out operation of this type and this is a vertical column, so you have to worry about the liquid which is going to be there on internals on trays. So, there will be a holdup, so there will be a static head and if there is a static head, there will be a pressure drop across the column and then the vapor has to have a certain pressure drop from this side to other side because it will face the internal resistance while traveling. So, a real-world column will always have a pressure profile. So, we have to worry about that. Then the location of these pieces of equipment, this is only a schematic. The condenser may be sitting at a different grade level here. So, you may want to bring this reflux back on the top tray and because of the static head again, you may require a pump and if pump is required then you do not want this liquid to be at its bubble point. So, a certain amount of sub-cooling has to be there and so pressure is raised beyond what is required in the column and for control purposes and at the same time for manipulation of pressure you may require valves. So, all these accessories will come into picture, but theory wise a distillation column is nothing but a counter current cascade of flash vessels the way I depicted in the earlier slide. Now, that is good enough for us to understand the basic concept behind the unit operation which is typically called distillation. But it does not end there because there are various ways columns are configured and multi-component systems may have variety of other pieces of equipment or devices you may say that it may not be equipment attached to a basic distillation column. So, we should try to understand what is normally involved or what is that you come across in industry when we primarily work with refineries and petrochemicals as I said that is where the distillation columns normally dominate. So, some examples of complex columns could be the crude distillation column or sometimes it is called the atmospheric column which operates in a refinery typical refinery then associated with crude column or subsequent to crude column you have vacuum distillation column. Sometimes it is operated in dry mode dry mode means without presence of steam or it could be wet operation. So, steam is added or as I was telling you in the beginning that distillation columns may follow reactors. So, very good example is the FCC fractionator which of course is always sitting next to the FCC. The fluidized catalytic cracker because cracking gives you a multi-component system, continuous boiling system and that needs to be fractionated. And in many cases the FCC fractionator more or less resembles a crude distillation column. Similarly, in refineries you may have need to reduce the viscosity of heavy feedstock and you may do thermal cracking. The unit typically is called visbreaker because the focus is on reduction of viscosity by thermal cracking. And then because cracking is occurring you get a mixture of lighter products and you may want to fractionate and recover useful products. So, such a distillation column will then be called a visbreaker fractionator. Demethanizers again are quite complex columns they are found in refineries as well as in many petrochemical complexes. Then you have these related operations like columns where azeotropes are being separated. So, azeotropic distillation or extractive distillation or reactive distillation and so on and so forth. So, all these will fall under the category of what we call as complex columns. What I constructed in front of you was a simple column, a conventional simple column where there was one feed one top product one bottom product condenser on the top and reboiler at the bottom. So, that is a simple column. So, this is one simple example of a complex column. This column is not too complex, but yes if I compare this with the cascade which we constructed it is complex. Now, you can see here that there are theoretical stages shown here which are numbered 2 to 21 and since I am withdrawing vapor as one of the products. So, condenser followed by this reflux drum as it is called also is shown. So, this together also forms a theoretical stage because they are taking part in equilibrium vapor liquid equilibrium. So, numbering is starting from here. There is no reboiler here. So, you may wonder what is the source of thermal energy? Well, the source of thermal energy is the stripping steam. So, thermal energy can come from an external source also. So, in such a case when external source is used to provide the required thermal energy or let us say if its presence can change the performance of such a unit. For example, steam does not mix with hydrocarbons and if it is fed to the column in superheated form. So, what happens is it remains in the vapor phase and therefore, the hydrocarbons then start distilling at their partial pressure and as the pressure goes down the volatilities improve and separation improves. So, steam could have multiple functions. It becomes a source of thermal energy. It also adds to improvement of the separation factor. So, we see here that there is no reboiler, but stripping steam is there. There is a feed. We had a feed earlier. In fact, we have two feeds here. So, you can say it is a multiple feed column. So, two hydrocarbon feeds or maybe main feeds, one steam feed which is the we can call this as a mass separating agent that is the term for normally used mass separating agent. There is provision for withdrawing a product which is in liquid phase at certain level. So, it is called the liquid side draw. There is provision here to withdraw a vapor side draw. So, this is another desired product of certain composition. There is yet another feed coming. So, we have three feeds and one mass separating agent, no reboiler, two side draws, one is liquid, one is vapor. We also have provision to remove certain amount of energy from within the column and return the cooled stream back into the column. This is very typical of refinery columns where the products when they are drawn in large amounts, they create imbalance in the vapor liquid internal traffic. And therefore, you have to do something to balance the traffic and one way to balance the traffic is to remove certain amount of energy, let us say from the liquid and return a sub cooled liquid and this sub cooled liquid then tries to condense it tries to condense part of the vapor and you generate internal refluxes and you try to balance liquid and vapor traffic inside the column. And these are typically called pump amounts in refineries. So, these pump amounts are present, pump amounts are ways and means to balance internal traffic. They also become you can say useful entities for removal of thermal energy at higher temperature and this energy which may be available at temperatures of the order of 250 degree Celsius or 300 degree Celsius can then be used very effectively to do preheating of cold streams in the plant. So, we are not getting into those kind of things right now, but when I look at this distillation column I do have a condenser. I have liquid side draw right from the top. So, it is a it is a complex condenser it does not only have a vapor product it also has a liquid product. There is provision for decanted water. So, maybe there is occurrence of three phases here. So, the thermodynamics comes into picture we have to worry about the thermodynamic aspects. I have the two pump amounts and multiple feeds and couple of side draws for products and mass separating agent and no reboiler at the bottom. So, this column looks very different as compared to what we had configured. So, the thing is where do we start? If modeling is to be done where do we start? Well, because we come across very complex situations such as this, this of course as I said is not too complex I can make columns much more complex than this. So, we start with a sort of configuration which makes provision for everything to happen which is shown on the diagram. So, most general model for a distillation system is what we are interested interested in and then model reduction can be done to configure simple columns that is the whole idea. Now, I am not spending time on various aspects of column internals this couple of slides just to show you that ultimately because the hold ups are small residence times are small, but we operate with the assumption that vapor and liquid will attain equilibrium or at least near equilibrium. Therefore, we want some mechanism so that heat and mass transfer rates are kept high so that we get good separations. So, variety of internals are used if there are small columns random packings are used large diameter columns trays will be used different types of trays are used in industry structured packings are used sometimes in columns combinations are used part of the column may have tray part of the column may have packing. And among the trays three most popular types which we encounter in petroleum and petrochemical industry are the simplest which is the sieve tray which simply has holes of certain diameter hundreds and thousands of holes on each tray or the bubble cap trays which have this kind of mechanism where the vapor can come from beneath and then across the surface there are tiny tiny holes and the vapor will emerge from the side and this whole thing will be embedded inside the liquid pool. So, that vapor will be bubbled through through this cap. So, it is called the bubble cap and there will be hundreds of such caps on a single tray or a valve tray in which there is a moving mechanism. This is a fixed tray this also is a fixed tray. So, no item is moving here, but here there is a valve. So, if vapor flow rate goes down this valve goes down because the location of or the position of this valve depends upon the hydrodynamic balance which occurs on this particular unit. So, if the vapor comes with high velocity the valve fully opens and then it has a locking device it cannot come out, but if the vapor velocities go down then the valve will go down. More like rotometer in which you know the float balances itself depending upon the hydrodynamics. So, these are the three types and again there will be hundreds of valves on a given tray. So, these are the three types which we normal normally use in industry. In addition you have structured packings and both of them can be successfully used if you have large diameter columns and small diameter columns even random packings can be.