 Good morning. In this lecture, we are going to look at control strategies for distillation processes. The coverage is more on the strategies, so it is qualitative and there is no effort to get into any quantification. Now, distillation columns, even if we start thinking about a simple distillation column, they have at least 4 control loops and sometimes more depending upon the number of product streams, which you are withdrawing from the system and also in terms of the specifications, which may be there on the products. And as we had seen during the modeling session, that there is tremendous interaction between all the variables, because the flow rates themselves could be variables to meet the specifications and specifications could be in terms of temperatures, compositions. Normally, the specs will be in terms of compositions, but if compositions are difficult to analyze, then indirectly temperatures will be specified. So, there is tremendous interaction among these variables and therefore, the control problems in distillation columns are quite challenging. And some of the problems which are listed here which offer fairly good challenge such as the interaction which may exist between the loop and the variables, then due to non-linearities of the process, there may be difficult scenarios to work with. There are finite holdups and therefore, there may be delays. The delays could be due to process or due to measurement and therefore, control scheme has to be accordingly designed. And moreover, a distillation system has a large number of variables to be looked at, so that itself keeps the dimensionality of the problem large. Now, let us first look at single control loops or the control loops which are controlling one variable. So, distillation process will have several loops, each loop will be controlling one particular variable, but they lie in three or four different categories. Quite a few of them will be the control loops for flow rates. Then we need to maintain levels, liquid levels specifically and this requirement will arise in situations such as reflux drums and at the bottom of the column where there is a finite holdup or rather large holdup. Now, columns are operated with specified pressures and during the operation, we would not like pressures to fluctuate because pressures affect the vapor liquid equilibrium and also the capacity of the column because the vapor flow rate is very much dependent on the pressure of the system. So, the capacity is affected by changing the pressure and the vapor liquid equilibrium also could be very sensitive to the change in pressure and therefore, pressure control in a distillation system is an extremely important control. And then of course, the purpose of the column is to produce products of given purity. So, you would be interested in measuring the concentrations, product concentrations and you would like to have strategies so that the concentrations do not show too much of fluctuation. Control of concentrations directly is a difficult task and therefore, sometimes indirect methods are used. As I mentioned earlier, that concentration may get linked to temperature and we may prefer to use temperature as the variable and in turn assume that if temperature is maintained then the product concentration will also be maintained. So, the complexity of control problems is in the order in which the top item mentions starting with the flow rates, then the liquid level, then the pressure and then the product concentration. What it means is that flow rate loops are easy to implement, liquid levels are relatively more difficult, pressure is still more difficult and the most difficult is the concentration. So, we start with each type of control and let us first focus attention on the liquid level control schematically as it is shown in the diagram labeled as A. So, you can assume that this is representing let us say the bottom portion of the column and there is some hold up. So, this is what we are talking about and then there is withdrawal here. So, liquid level control is performed either by a single control loop. So, this is a single control loop where there is a measurement here. So, there is a level controller and the signal is transmitted to the manipulated variable and that manipulated variable is the flow rate. So, valve is the control element and that is the one which is deciding the flow rate. So, this is one way of doing it. Sometimes this is also done by a cascade control loop. A cascade control loop would mean that the output of one of the controllers becomes the input or the set point adjuster for the second controller. So, that is the meaning of a cascade controller. So, as you can see here that in diagram B the liquid level is measured here and signal is passed to the set point of the flow controller. Now, this is a direct control. Flow control is a direct control because you are measuring and you are controlling the same variable. So, it is a direct control and its set point signal is received by the liquid controller. This type of cascade control may give you better controllability and better proportionality also as compared to the single control loop. The cascade control loop as it says here is preferred for large vessels and that is obvious because if the vessel is large then what do you expect? For the given flow rate the change in liquid level will be small. So, the sensitivity may be lost there and therefore, you would rather like to have a flow controller also in picture. So, if the vessels are large or one can think always in terms of hold ups. So, if hold up is large then cascade control loop is better otherwise you can go for a single control loop. So, this is the level control. The other control which is extremely important to understand is what is known as the stream partition control and this requirement will arise at the top of the column where condenser is condensing the distillate and then part of the distillate is withdrawn as the product and part of the distillate is reflux to the column. And therefore, you would like to maintain reasonably good flow to the column and rather constant flow to the column because reflux again affects the performance of the column. If reflux is not properly controlled then you will observe fluctuations in the composition the product. The other place where the stream partition control is extremely important is the reboiler. In reboiler also whatever liquid leaves the bottom of the column part of it is withdrawn as the product the bottoms and part of it gets vaporized and returned to the column. So, again there is partitioning of a stream and such scenarios may occur at other places also like we were talking about during modeling and simulation refinery columns. So, in refinery columns you have pump arounds and pump arounds are normally placed at a location where there is a side withdrawal. So, the nozzle is common from the same nozzle you withdraw the liquid part of the liquid is taken to the heat exchanger the pump around heat exchanger where it is cooled and part of the liquid is taken as product or it goes to storage or maybe it goes to some other heat exchanger. So, there again you will have stream partitioning. So, there are many examples where stream partitioning is required and basically it is a flow control it is a flow control which needs to be done whenever this kind of scenario arises. So, you have a stream A and that is split in two parts let us say this is first part and this is the second part and you would like to make sure that there is minimum fluctuation in both the flow rates that is what is intended. So, it says that even when the flow rate of feed stream is absolutely constant it is not possible to control each of the partition streams with independent controllers because the measurement of flow rates is never absolutely precise and that is the problem here. Because this valve itself may require adjustment and therefore, there is no guarantee that these two flow rates remain exactly the same as you desired in spite of the fact that A is maintained constant. So, what is the guideline? Well, the guideline is that we know that both the streams are driven by a pure material balance here. So, it will not make any sense to start controlling both because then the controllers will unnecessarily start interacting and they may clash also. So, we control one of the flow rates and the other flow rate is kept open. So, that it is automatically controlled by difference. So, only one of the partition streams must be manipulated directly, the other one must be left free. So, there are various ways this can be done. One example is shown here where let us say at the bottom of the column there is a withdrawal nozzle. So, this is the hold up which you are maintaining and this is the product which you are withdrawing. So, I put the controller here and this is a direct control because why it is called direct because I am measuring the flow rate and I am controlling the flow rate alright. So, this is direct control of the flow rate. So, if there are fluctuations in here and if this is a nicely designed controller. So, if there is a fluctuation here this level will have tendency to go up or down and that automatically will be taken care of by the liquid which you will withdraw here because if level has tendency to go up this liquid will this liquid flow rate will automatically get adjusted. So, this is left free, this is left free this may show fluctuations depending upon whenever this shows fluctuations otherwise this is maintained, but all the three will remain in material balance. Another way is rather than providing this overflow type of nozzle we may go for this kind of arrangement. In fact, this is a better arrangement that partition of liquid stream with a level controller. So, I maintain some constant level here. So, there is a level sensor and then there is a controller and this actuates the control valve on the other stream. Now, this is not direct, this is indirect, this is on level controller. So, I am measuring level, but I am controlling the flow rate here. So, the hold up will take care of the material balance part whereas, this is still the direct control. So, these are some of the ways this is more preferable or better system. So, this is on level control. So, we can say that this could be treated as indirect or free and this is the direct control. Now, what is the guideline if such a control is to be established? Well, one simple guideline to remember is that the stream with smaller flow rate should be directly manipulated. So, between the two between this stream and this stream whichever stream has smaller flow rate that should be taken for direct control the other one should be left on the level control. What could be the reason? Why do you think such a recommendation is in order? On the smaller flow rate when you talk about let us say percentage change. So, if there is 10 percent change that 10 percent on the smaller then that is under direct control. So, that is a significant signal. So, you will be able to take immediate action at the same time that 10 percent change in small is a very small fraction for the large. So, large will not show much of a fluctuation. Whereas, if you kept the direct control on the large stream a 10 percent change or a 5 percent change on the large stream can very significantly change the small stream. So, this is a very simple rule of thumb or heuristics or whatever you may want to call it that the stream with the smaller flow rate should be directly manipulated. That is right, but 5 percent for the bigger I am taking half of that may wipe out may wipe out the smaller stream. The portion is much more there. Precisely. So, therefore, as a rule of thumb if we manipulate the smaller stream we are doing a better control. That is the whole idea. They are also same thing will come. So, when I take up the examples I am going to show you example on reflux drum again we will say the smaller if the column is operating with low value of L by D reflux ratio then I would rather control reflux directly if the column is operating with large value of reflux ratio I would rather control distillate directly. And same thing will apply when we talk about the boiler ratio in the reboiler. So, any partition control system performs best when the smaller stream is directly manipulated. This direct is very important. We are not saying that the other stream is not manipulated. The other stream is getting manipulated by a level control, but that is an indirect control. You are measuring something else and you are controlling something different. Whereas, direct control when I am talking about I am measuring flow rate and I am controlling the valve opening which in turn affects the flow rate. So, in practical applications the partitioning of a liquid stream is performed by use of a vessel. Why do you think a vessel is required? Because if you have hold up the input fluctuations could be absorbed because hold up always works as a capacitor. Search tanks the way they are provided in process industry the main purpose of a search tank is to absorb attenuations. Fluctuations are absorbed it acts like a capacitor. So, vessels are provided for example, the reflux drum because the flow rate of directly manipulated stream can be maintained constant even when the feed stream is smaller for a short period of time. So, the fluctuations are absorbed. And the resulting free stream which I had shown you in the earlier slide I said two possibilities are there it could be an overflow through a nozzle or it could be preferably regulated by a level controller. This is preferred rather than leaving it open this is preferred. So, two rules for the same thing rule number one that only one stream can be directly manipulated by a fixed at point the other one is left free or manipulated by a level controller. And why it is called a rule? Because if you follow this strictly the material balance is always in order you will never have problems of interaction. Rule two which has a lower priority that the directly manipulated stream should be the smaller one and in turn the stream controlled by the level should be the larger one. Not that this is not important, but rule two will come in picture after rule one comes into picture rule one takes higher priority. So, we should read this it says that in cases where both the rules cannot be met, rule one takes precedence since it results from material balance and that cannot be violated. Rule two results from a consideration of flow rate measurement accuracy and flow rate fluctuations and hence it is not as strict as rule one. You may want to call them as rule one or guideline or heuristics whatever, but this is qualitative. Now, let us look at the other end. The other end is the condenser because what we looked at earlier was at the bottom. So, this is at the top of the column. Suppose we have total condenser where all the vapour from the column here is condensed. So, this is the scenario. So, this is what I just mentioned couple of minutes ago that if the column is operated with a low reflux ratio. So, I have the distillate which is coming through some hold up here there is a reflux vessel here reflux drum. So, this is coming in here part of this I am withdrawing as the product and part I am returning to the column. So, with the same logic now when we are talking about first of all if I view this as my split stream system here. So, I am saying that there should be preferably a hold up. So, that is the reason a reflux drum is provided. So, that it can absorb the attenuations which are there in the vapour. Number two, if L is smaller than D substantially smaller or significantly smaller then I would rather control L as a direct manipulated variable and leave the withdrawal rate which is the distillate through a level controller here. This is what we just discussed in the previous slide. So, the flow rate of the reflux is small and thus directly manipulated the flow rate of the distillate is controlled by liquid level in the collector is this clear? On the other hand if high reflux operations are there many columns for high end purity when purities are of the order of 99.99 the reflux ratios may be very large. There are columns in industry operating at reflux ratios of the order of 100. So, if that is the kind of scenario which means very small amount is withdrawn and good part of what is condensed is reflux to the column. So, L is fairly large as compared to D. So, obviously, when we have this kind of scenario then D will be put on direct control and the reflux can be controlled by a level controller. So, in India if level goes down so this valve will close. So, you will not be withdrawing much product because the level is directly transmitting its signal to this valve and therefore, reflex will be continued. So, the column operation is not getting disturbed much column is still getting reflux, but for that period of time your product withdrawal has gone down the level will come up because you have stopped taking the product or you have reduced the outcome of the product. You mean the cascade. You can have, but it is an unnecessary investment this works fairly well. See cascade is as I mentioned earlier cascade is required. For example, if this reflux drum was very large in size and this level sensor is very insensitive then cascading makes sense, but if level sensor is giving you significant signal so that you can put a good controller on it why to go for cascading effect. So, here is some more explanation here. Now, slightly different scenario shown here because there is a there is a withdrawal pump here. So, it says that control system and undisturbed operation is maintained even when the vapor arising in the column is for a short period of time smaller than directly that is the point which you just raised that if this vapor arising in the column if it goes down the condensation will be affected. So, this will take care. It is important to have enough hold up in the reflux that point I already mentioned that I should have sufficient reflux here for the damping effect or the attenuations to be reduced. And when the distillate has to be pumped. So, this is the scenario where distillate is being pumped the pump should be located this is very important that the pump should be located before the control valve to avoid suction problems. So, the control valve follows the pump. There is another thing one can do when reflux ratios are important. So, it is the L by D which the focus is on L by D. So, you still can have D on the LC, but rather than having a direct control here this is a direct control you can also go for a ratio controller flow to flow ratio controller. And this will guarantee that there. So, we are not guaranteeing the flow rate to be maintained. We are saying that as and when D is manipulated and D changes correspondingly L will automatically change. So, the reflux ratio is maintained constant. So, this is another possibility. Reflux ratio is more important in a sense that that guarantees the purity of the product. But the internal traffic if you talk about internal traffic the balances inside the column the reflux stability is more important because otherwise the column will start oscillating. Internal traffic the absolute value of reflux is more important. So, with similar argument now at the bottom. So, what we had seen earlier was just the split flow rate. Now we are looking we looked at the condenser and now we bring in the reboiler also. So, the flow rate of bottom product so, this is the one is much higher than the boil up rate and boil up rate is here. Now notice the boil up rate is controlled by the condensing steam. So, basically there is heat transfer in picture here. We have no other direct way to control the boil up. So, you can only control the flow rate of the condensing media here. If it is steam then it is steam if it is a furnace type of reboiler then it will be the firing rate of the fuel. So, you have to have some mechanism to control the heat transfer. So, this is for steam driven reboilers. This is normally done that the steam condensation rate or steam supply to the reboiler that is controlled. So, I have NFC here. So, basically this is controlling the amount of heat released inside the reboiler and that in turn is deciding what is the boil up rate. And of course, the flow rate here is on the level controller. So, this is now for heat transfer this will be considered direct because even though it is indirect, but because there is no other way to do heat transfer. So, this will be considered direct. This is steam. This is steam. This is on steam. I mean why would you like to put on condensate? Condensate normally is the trap should be there, but controller should not be there. Yeah, it will if liquid accumulates it will simply release it periodically. But this is where it is more important the amount of steam which I am sending because you see if let us say if for some reason the condensation does not occur properly there is not sufficient heat transfer. So, I should immediately close the valve or start closing the valve and do not supply more steam to the system. Otherwise pressure buildup will be there. If the reboil ratio is high the control system of this figure B can be used. So, essentially this is the steam again. Here steam was on the flow controller. Here the steam control is through the level and the bottoms product is on the flow controller. So, low reboil ratio versus high reboil ratio. RG represents the reboil ratio here. The next set of controls is the pressure control in a distillation column. As I said that this is one of the most important control schemes which any distillation column requires because columns are desired to be operated at specified pressures at constant pressures because pressure can affect the performance of a column in many ways. And two most important effects which we always have to keep in mind is that any fluctuation in pressure changes its capacity. Liquids are not affected by vapors are immediately affected because vapor flow rates the vapor densities are very sensitive to pressure. So, the capacity is immediately affected if pressure changes and the second if pressure changes the VLE is immediately affected. And therefore, pressure must be maintained constant. So, if it is an atmospheric column operating at atmospheric condition for example, columns which are non ideal systems they normally operate at atmospheric condition ethanol water column will operate at atmospheric condition. So, the simplest method of pressure control of an atmospheric column is that take a vent at the coldest point the coldest point of course, is the discharge of the condenser. So, you can say it is a reflux drum. So, there is a vent here it is expected that some innards may be there if innards are not there absolutely there is no problem because it is the amount of vapor which only will affect. But if some innards are there they have to be vented out if you do not do that then pressure will start building. So, there is a pressure controller here and this opens the valve if there is a build up of innards. Another method is to manipulate the draw of the inert gases from the collector drum. So, of course, this I already said that provided there are enough non condensable gases or innards. If the columns are operating under vacuum this is the scenario then this is the scheme which is a recommended steam nitrogen assuming that nitrogen is an inert for this particular system you make provision for bringing in nitrogen because this is a vacuum pump it has constant suction on the system. So, it will take away the innards, but if the inert concentration goes down or the amount goes down then the makeup will be available from the nitrogen on this side otherwise the vacuum pump will run into problems. So, there is a pressure controller here and it controls the amount of nitrogen which is being made available. So, this is normally used when systems operate under a vacuum and this is when systems operate at atmospheric conditions. Now, so that was the distillate part in the liquid phase. Now, suppose if the distillate is withdrawn as a vapor. So, this is the scenario now. So, what we can then do is we can put the product withdrawal here and directly take that for the pressure control. And the flow rate which is coming from here if that is going to show fluctuations then you can take a LC a level controller and control the cooling water flow rate the cooling water flow rate. Of course, all these things work fairly well provided the inlet temperatures are stable. So, we are assuming that the inlet temperature of cooling water is more or less constant. So, control of the rate of cooling water is necessary to hold liquid level in the reflux drum. So, this will ensure that level is maintained and withdrawal of vapor product because vapor dynamics are much faster than liquid dynamics vapor fills the space very fast. So, the movement pressure goes up if you release the vapor the pressure will immediately go down liquid takes much more time vapor dynamics is extremely fast. So, it makes sense that the vapor product is controlled to control the pressure. In the earlier case we did not have that freedom because the product was liquid. So, we were indirectly doing that, but whenever vapor is available as the product that is the desired variable to be used to control the pressure. If there are not enough inert gases in the feed the column pressure might be manipulated via the temperature of the condensate. So, you can even use this now here what we are simply saying is that the degree of heat transfer here will decide the degree of condensation. So, and then heat transfer is affected by the flow rate heat transfer is affected by the flow rate. So, which means that if I push through more cooling water and better heat transfer then what do you expect if the flow rate is increased more condensation will occur and therefore, the pressure will go down alright. So, this is the effect. So, if I have the pressure sensor and then I am manipulating here I can control the pressure here. So, if there is a buildup of pressure the valve will open more and more and the rate of heat transfer will be increased. If the pressure is going down if pressure is going down what does that mean that the condensation is occurring much faster than what it should have because the vapor is creating sort of vacuum. So, the valve will be gradually closed. Now, so what we looked at was the scenario when we have cooling water driven condensers. Now, there may be a scenario that the condenser is air cooled condenser. Now, if the condenser is air cooled condenser then the cooling media cannot be taken as a good controlled variable because cooling water is flowing in a pipeline. So, you have facility to measure the flow rate, you can put a valve and you can control the flow rate, but when it is air cooled so that freedom is lost which means you need to now put the pressure controller on the process side rather than on the utility side. So, this is one way to control the pressure is that whatever is the withdrawal or whatever is the outcome from the air cooled condenser before it gets into the reflux drum you put a valve there and then put that on the pressure controller. Then this one it says most dry air cooled condensers are horizontal with only 2 or 4 rows of tubes vertically oriented. So, that flooding does not give smooth control hence bypassing. So, if flooding creates control problems then you go for this kind of strategy. What is this strategy that part of the condensing vapor which was traveling from this side is bypass. So, there is a bypass here and that is taken directly on this side. Now, this fellow therefore, has to give you much more degree of cooling otherwise when you bypass this and bring it in here you will not have all the liquid you will have 2 phase mixture. So, we looked at level control we looked at the stream splitting methodologies then we looked at the pressure control. Now, let us see the product concentration control. As I mentioned in the beginning that product concentration control is the most difficult control. Particularly if you have if you want to implement in terms of direct control you do not have good analyzers because typically what is done sample is withdrawn and it is analyzed in the laboratory and then some action is taken. If you have online analyzer which can give you good accurate concentrations then there is no problem. So, more often than not in the industry concentrations are related to other variables and the variable which is used more frequently than any other variable is the temperature. So, I want to guarantee purity of the product here, but I do not have mechanism to measure the concentration. So, if I can have a relationship between concentration and the temperature then I can look at the temperature profile and ascertain that if temperature is maintained then purity would have been maintained it is an anticipation. If temperature is maintained purity would have been maintained that is the idea. So, this is a typical column in which is conventional column with single feed one condenser at the top, reboiler at the bottom and these are some typical concentration profiles inside the column this is the feed location and this may be the temperature profile, this may be the temperature. This is what is shown here is the liquid temperature similarly one can plot the vapor temperature also. So, the concentration measurement is normally replaced by a temperature measurement because it is more simple much faster and more reliable. The temperature sensor should be located in the vapor in order to get a quick response to temperature variations. As I mentioned to you that vapor dynamics are much faster than liquid dynamics. So, if you do not want to get into the lag problem and if you want to have a quick response then preferably the sensor should be in the vapor. Before I go to this let me mentioned one thing that if the profile is like this then it can become very tricky to decide where to put the temperature sensor. You should put a temperature sensor on a tray where where should you put the temperature sensor where the sensitivity is high, where the sensitivity is high. By sensitivity we mean that if there is slight change in composition the temperature of the tray also will show a significant change. But if that temperature shows very little change for wide variation in concentration change then that is not a good place because you may think that you are maintaining temperature very nicely, but compositions may still be fluctuating. So, how do you get this information? This information you can very nicely get by doing a regress simulation that is where regress simulation comes very handy a steady state simulation comes very handy to decide the location of temperature sensor which is part of your control strategy. So, you look at the gradients of temperatures. Now, let me spend some time on what are the strategies which one can look forward to if you were to design a control configuration. Because whatever we have looked at so far we have looked at controls of different variables that is all we have looked at one at a time we have seen the level, the flow rate, the pressure and the concentration. So, now we would like to spend some time on design of control configurations. As I said a simple distillation column will have at least four control loops it can have more control loops. Complex column will have many more control loops depending upon what is the degree of complexity. So, for us to understand this whole issue so that we do not violate the degree of freedom concept a distillation column should be considered as a system of three interconnected stream partitions. We have already looked at stream partitions. Now, let us try to understand what it means. Invariably I have a feed now scenarios may be very different the feed may be saturated liquid at the condition of the column. How often do you think that is achieved? If I make a statement that the feed is saturated liquid at the condition of the column having saturated liquid at the feed condition is a different issue as compared to saturation at the condition of the column very seldom. It will be near saturation, but it will not be necessarily at saturation why because feed normally will come at a elevated pressure. Chances are that either it is coming from an upstream unit or it is coming through a pump. So, pump is not going to discharge it exactly at the pressure at which column is maintained. Therefore, certain amount of flashing will occur throttling will occur is that right? Not only that. So, there is tremendous disturbance on the feed tray because it could be sub cooled or it could be a two phase mixture and operating conditions are different. So, what is going to happen is when it comes and liquid combines with the liquid which is inside the column and the vapor combines with the vapor which is inside the column vapor from the feed I am saying and the liquid from the feed. So, this is a point of disturbance. So, we can view this as if liquid is coming from this side feed is coming from this side and that generates the total amount of liquid which is going towards the bottom. So, this is one junction we can think of all right. Come here at the bottom. So, I have this portion which is a mixing vessel this is just a mixing vessel. So, certain amount of liquid is coming in here. Part of this liquid is withdrawn as the bottom product and part of this liquid is taken out and put at the top. How it is being done? This is just a concept do not look for the liquid and this thing it is I am only talking about a stream this is just a concept that whatever I am putting as a reboil here that travels in this direction and ultimately it reaches the top of the column. Then only liquid is formed and then this liquid comes back and joins with this and then it comes down. So, what I am showing G here of course, it has a pressure differential. So, that is the reason why it is shown with a pump here. So, this G rises up. So, again it goes through a splitter. What is this splitter? This is your reflux drum. From the reflux drum I am withdrawing D and then I am returning the reflux and it is the same L which combines with F. So, this L which combines with F and comes at the bottom. So, this is one way to look at how stream partitions are occurring inside a distillation column. It is just a modeling approach. So, a basic flow structure with two vessels and five streams. Now, you can see here that I have two vessels and I have five streams. What are those five streams? The original feed, the reflux rate, L, the distillate withdrawal rate, the boil-up rate which is G and the bottoms. And of course, are they independent? The answer is no. They are related by the material balances at the junctions we have. So, they are not independent. So, let us go further. So, partition of the feed into overhead I have already explained this, but now it should become clear into overhead product D and bottom product B. This partition is characterized by product ratio D by B or D by F. The partition of the condensate into L and D and this partition is characterized by L by D. The partition of the bottom liquid into boil-up and the bottoms or the bottom product B and you can say that this is characterized by G by B. So, this is a ratio. This is another ratio. This is another ratio. So, the three stream partitions in the flow network are interconnected and out of the three partition parameters, how many are independent? Two are independent. Where is this number two coming from? From our day before yesterday's analysis. I said if you have a simple column and if you have one distillate and one bottoms product, the degree of freedom is 2. So, what it means that if two are chosen, the third is automatically satisfied through material balance. All right? So, I have this freedom to work only with two degrees of freedom. Now, four streams are available for manipulation and they are labeled here. Why am I saying four? I counted five, but now I am saying four are available for manipulation because feed is expected to be specified and controlled separately. Feed to the column is not going to become one of my control. I want to control that independently so that feed is studied to the column. As far as operation of distillation column is concerned, its degrees of freedom when I calculate, we assume that feed is specified. We did that in simulation, right? Feed is pre-specified. So, F is not there and therefore, the flow the four variables which are available to me are the distillate D, the reflux L, the boil up G and the bottoms B. F is taken out whereas, in my two tank mixing model, I had counted five variables. So, only two rates are independent and they can be independently manipulated. Remaining two will automatically get fixed. Is this clear? Because this now will give us different configurations which are designed on distillation columns. This number two is very important, but this number two is only applicable when we are working with conventional simple columns. One condenser at the top, one reboiler at the bottom, alright? Now we can start combining. So, we can say that let me control D and let me control G. D is distillate and G is boil up ratio. So, if I consume my two degrees of freedom by combining DG, then this will be called a DG configuration. So, the flow rate of distillate D and the boil up G are directly manipulated, alright? How many, of course, the number is written in front of you, but it is not difficult for us to figure it out that if you have total of four variables which can be possibly manipulated and at a time you have to work only with a set of two. So, how many combinations are there, permutations combinations? The number is already there on the screen, 6 combinations are there. So, we will see that. But it turns out that out of this 6, if we now go back and look at our rule 1 and rule 2, we have understood those two rules. All the 6 will not be feasible, all the 6 will not be feasible. What was rule 1? Rule 1 demands that in each stream partition, once stream must be directly manipulated and the other one should be left free. We said that, right? So, now, let us focus attention on these 6 combinations. This is a very important table to understand. All the 6 possibilities from permutation combination are labeled here. So, D L, D L configuration, what does D L configuration mean? The distillate is under control and the reflux is under control. Then I have D G, the distillate and the boil-up rate. Then I have D B, the distillate and the bottoms flow rate, L B, the reflux and the bottoms, L G, the reflux and the boil-up and B G, the bottoms and the boil-up. These are the 6 combinations we can think of. All right? These are the stream splitings. So, feed into D and B, condensate into D and L, bottoms into G and B, these are the 3 possibilities. Now, if I have D L, which means distillate and the reflux, it says the rule 1 is met here. Rule 1 is satisfied. How do I say that? Anyone? Out of the 2, 1 is present. So, one variable should be controlled. Rule 1 says one variable should be controlled, the other one should be left free. So, if I have D L configuration and if I look into D and B, then D is getting controlled and B is left free. I am not doing anything because the other controlled variable is L and therefore, rule 1 is satisfied. Is this clear? Rule 1 is satisfied. Come here, condensate getting split into distillate and reflux because this is the other split point or the stream partition point. D is under control, L is also under control because these are the 2 variables we have chosen for control. So, D is under control and L is also under control. Rule 1 is violated. What does rule 1 say? Only one is to be controlled, the other should be left free. So, we have violated. So, this is violated. At bottoms into G and B, rule 1 is not met at all. The condition is not met because neither G is sitting in this control scheme nor B is sitting. So, this junction of split or the stream partition is not being even touched upon and therefore, this scheme will be labeled as a non feasible or not feasible scheme. This is not a good scheme. It has only met this junction condition, it has violated this condition and this condition is not met at all. Look at DG distillate and boil up. So, before we go to this, does it make sense? I mean intuitively also does it make sense? What did we say in the beginning? We said that reflux and distillate both should not be controlled simultaneously, is it not? That is exactly what we are coming to. So, DG the distillate and the boil up rate. The distillate is on the top, the boil up rate is at the bottom and even intuitively one would expect that this scheme should work because interactions are going to be minimal. They are more or less like independent variables. Top of the column versus bottom of the column. So, feed dB when I look at feed into D and B, D is sitting here. So, one variable is under control, the other one is left free. So, this is met. When I look at condensate into D and L, D is sitting here and therefore, this condition is also met and when I look at bottoms into G and B, G is sitting here. So, again this condition is met. So, all the three are meeting rule 1 of the partitioning, stream partitioning and therefore, this is a good strategy. dB, this is violated similar to what we had shown here because both you cannot control as per rule 1. So, it is violated. This is met and this is met because it is violated. Again, this is not feasible. LB, all the three are met. So, it is a good scheme. LG, this is not met because there is no L here and there is no G here. This one is met, this one is met. So, this is met and this is met and this is not met. So, it is not violated, is not it? It is not violated. So, therefore, we can say it is a feasible scheme. I cannot declare that to be not feasible, but it is not a good scheme. It is a feasible scheme and finally, BG, met, not met and violated. So, actually this violates, this violates and this violates. So, three schemes are not feasible. Three are feasible out of which two are good. So, even though we feel that there are lot of combinations possible, but actually you do not have too many degrees of freedom. Only three possibilities are there and out of this only two are rated good. So, if you were to design a control strategy for a distillation column, either you should go for a DG control or you should go for NLV control and what is that both of them have in common? No, if you look at nothing is common here because this is good and this is also good, but there is something which they have in common conceptually. One is at the bottom and other is on the top because when we talk about D and G, this is the distillate and this is the boiler. So, one is at the top, one is at the bottom or when I look at the other possibility which is LB, this is the reflux which is again at the top and this is the bottoms. So, it simply tells you that if the variables which are way apart, if they are taken part of directly controlled variables, the control will be much more effective because they are more or less independent. The interaction among these variables is minimal, is this clear? So, here is one example now where we have now a control system on a distillation column. So, I have given you the basics and we have, if I was given a distillation column and somebody says that put a control scheme on this, it is not difficult for us now to put various loops. We know how many are required from the quality angle, 2 degrees of freedom are there. We know that pressure has to be maintained, we should look at whether the condenser is liquid driven condenser like cooling water driven condenser or whether it is air driven or so accordingly we take control of that. We make sure that at the stream splitting points or stream partitioning point rule 1 is satisfied because we said rule 1 should always take priority. So, keeping all that in mind, one can sit down and complete this configuration. So, this is an example where composition control has not been implemented yet that will come in the next slide. But if you simply sit down and go through all this, you will find that it is a nice control scheme which we have put on the distillation column qualitatively. We have not done any calculations nothing simple reasoning this way that way. So, quickly let us see what is happening here so that I make sure that you have understood. What is the mechanism to control the pressure? We have put control on the innards that is the most simple way and we are expecting that distillate will be in the liquid phase alright. So, this is your pressure control here. Can you tell me if this scheme is what has been put then what could have been the reasoning behind? The FC has been put on the distillate here and LC has been put on the reflux. Reflux ratio is large distillate rate is small. So, the rule says that the smaller of the two should be directly controlled and therefore, distillate is under direct flow control and the reflux is under level control alright. So, this portion is clear. This is the feed part of course, this just shows you to make sure that feed temperature and feed flow rate they are maintained because when we talk about distillation we assume that feed coming to the column should be properly characterized and it should be a stable feed. So, this is there is a preheater here steam is coming. So, temperature controller is there and there is a direct flow controller on the feed here. Come to the bottom, what will be our argument for this scenario? G, how do you interpret G? Is G being controlled directly or indirectly? Is it a direct control or indirect control? This is a direct control. I said for heat transfer I have no other way except to vary the condensing utility. So, G is under direct control, G is under direct control and bottom's product is under indirect control and therefore, it is on the level control. So, this is LB control, LB configuration. So, we have the distillate here and the bottom's product here and we can sit down and we can interpret the same in the same way this whole control scheme. It is very obvious now here that between L and D by the way these are shown as L dot D dot dot simply represents the rate here. So, when we say L it is actually D L by DT you know it is a rate. So, between this and between this which one is directly controlled this one is directly controlled this one is indirectly controlled. So, with our argument again which one is smaller? L is smaller. So, it is a column operating with a low reflux ratio. This is LG control the third control. So, you have the liquid control the reflux control on this side and the boiler control on this side. And out of the three if you remember we said that DG and LB are good control schemes and LG is feasible, but it is not as good because rule one was not met in one of the junctions. This is just another illustration of a control scheme where rather than using direct flow controllers the ratio controller is used on the LB configuration. So, when ratios are more important to maintain they like you can see here rather than putting a controller on L we have put a ratio controller flow to flow ratio controller. This is one example I think this is the only slide I have on the composition control one point composition control. So, I think all this portion I have already explained in other scheme. So, now you should be able to interpret the only difference now you will find here that there is some sort of cascade control sitting here. So, what is this cascade control doing? Which one is the cascade here anyone? This TC this is cascaded with FC all right. So, FC is a direct controller here, but rather than V setting its set point its set point is being set by the temperature controller. So, this fellow is providing the set point for FC and then FC is in turn controlling the distillate flow rate. This means that temperature on whatever selected portion here this is above the feed at certain tray the temperature there has some direct relationship with the composition of the distillate. And how will you get that? By a rigorous emulation. So, if that tray is a sensitive tray and it is a good temperature to measure to a certain that this composition will be maintained. So, what you do is this flow rate then you make it floating on this temperature. So, whenever this temperature is affected this temperature is affected this will automatically get adjusted is something very similar except that this is now on LG, but again you are measuring a temperature and it is cascading with the flow controller which now on the liquid reflux earlier it was on the distillate and the distillate now is an indirect control. And this is again another alternative for LG and one point composition control. You also have two point composition control systems where above the feed temperature controller is adjusting this. So, one cascading is done on this side and below the feed this temperature is adjusting this. So, there is another cascading done on this side. There is a remark here which I think should be kept in mind that such control structure works well if the loops are carefully tuned and only PI controllers are used. This probably is based on some observation I am not very sure what is the reason behind unless somebody knows and can explain. Now, since we are putting temperature control on both the ends. So, there is high risk of severe control loop interactions because you are trying to control both the compositions. So, the material balance violation may start occurring. So, one has to be very careful, but here it is not for two point composition one for one point composition such requirement was not there it could be a standard PID control. Two point means above the column I am measuring temperature of a tray and I am cascading with the distillate here. Here also I am putting a temperature controller and I am controlling this. So, I am trying to tighten this composition I am also trying to tighten the performance at the bottom by measuring two temperatures. Similarly, we have another two point composition control scheme here and these are four schemes out of which this is infeasible these three are feasible. And then there are couple of examples of industrial systems where these control schemes are implemented. This is just for illustration. So, one can take one column at a time and start doing the reasoning and you will find that whatever rules I have given to you regarding the flow, the pressure, the stream partitioning and the composition if you go on applying all these loops you will be able to understand why they have been put on such a process. So, approaching the distillation control from some basic concepts you know it brings tremendous amount of clarity into the understanding of design strategies, control system design strategies. This is yet another example and I think that is the last one. So, I will stop here if