 We are going to begin with conceptual design of distillation systems. Most well known method for design of distillation systems is the macaphthyl method right. It is very popular, but it has its own constraints right. The main limitation is that we have a binary system there ok. If the system is multi component then we cannot use the capital method right. Another limitation is it makes an assumption which is supposed to be a very serious assumption most of the times that it deal with constant molar overflow right. It assumes that the flow rates, the liquid and vapor flow rates inside particular section say rectifying section or stripping section ok. They do not change as we go towards top or bottom right. I told you the meaning of this that latent heat of vaporization and latent heat of condensation or mixtures at that particular point if they are same in that case this happens ok. But most of the times that is not true right and we can go away from the constant molar overflow assumption right and because of that macaphthyl method may not work well right. So, these two issues are very important right. The constant molar overflow assumption we can deal with that later, but the first the main limitation of macaphthyl method that it deals with only binary system ok. We want to relax this and we want to extend the macaphthyl method to multi component systems right. So, let us have a look at what kind of systems we can come across as far as distillation is concerned or design of distillation system is concerned. So, mixtures to be separated right. So, we can have ideal system, we can have non-ideal system right. Then in both that is ideal and non-ideal we can have binary systems, we can have multi component systems right. In multi component systems right if there is ideality right, if there is ideality then we have to have the proper vapor liquid equilibrium equation right. Now, for ideal systems if a system is binary ok, what is the vapor liquid equilibrium? y is equal to alpha x upon 1 plus alpha minus 1 x is well known what is alpha, alpha is relative volatility right. This is normally the ratio of vapor pressures right. When it comes to multi component systems we have to just extend this equation instead of defining alpha for one component, I have to define alpha for c minus 1 components that means, suppose I have a ternary system right, I have to define alpha for two components take the least volatile component as the reference component and define your alpha relative to the least volatile component. For example, you have a system a plus b plus c right, I define alpha for a and b relative to c with respect to c right. So, alpha for c is 1 right and alpha for a and b will be greater than 1 right and there is a corresponding equation we will see that later. So, that is the only difference right, but then if I want to design a column, mechatyl is only for binary system I can extend mechatyl method to ternary or multi component systems and that is something that we are going to see in today's lecture. Just before that let us look at non ideal systems. So, in non ideal we have binary and multi component, in binary and multi component again you may have azeotropic or non azeotropic right. So, you know what is azeotropic, you know you do not have azeotropic does not mean that the system is ideal you may have tangent pinch right. The vapor liquid equilibrium curve may not intersect the diagonal, but you may have tangent pinch gamma or phi that is fugacity coefficient is away from unity that is non ideal system. So, you may have azeotropic system, non azeotropic system in both binary and multi component right and in azeotropic you may have homogeneous or heterogeneous here as well you may have homogeneous and heterogeneous I have not shown that the azeotrope can be homogeneous or heterogeneous I told you about this and in non azeotropic systems you may have a tangent pinch or you may not have a tangent pinch right. So, this is the classification of the mixture the type of mixture to be handled in distillation systems and your design method will change accordingly right. So, we are looking at the conceptual design of distillation systems I told you yesterday that there is a difference in design and simulation the type of problem ok. In design you are supposed to find out the height of the column or number of stages right for given separation that is given x d given x b feed composition is anyway known right and you are supposed to find out number of stages right whereas, in simulation it is exactly opposite that means the column number of stages is known right and then you have a feed given and you are going to find out the composition along the height of the column on every stage and top and bottom right and you are going to solve this problem in today's simulation tutorial ok. You will use aspen to solve a simulation problem that means number of stages is given to you and you are going to predict the composition on each and every stage and in distillate and in bottom right. So, that is simulation problem and as far as this lecture is concerned we are not going to look at simulation we are going to look at design I will tell you the role of design in simulation conceptual design rather. So, this is clear we have these many systems and your design method will change accordingly or our design method will depend on which system you are dealing with. For this system binary ideal you know mechaphthyl right. There is no formation of azeotrope and all we can very well use mechaphthyl method even if there is a formation of azeotrope you can use mechaphthyl method, but you should know that azeotrope divides the composition space and the feasibility issues issue is there. Ideal system means no azeotrope azeotrope means it is non ideal system right it is non ideal system, but does not mean that there is a formation of azeotrope or sorry does not mean that the system is non ideal there is always formation of azeotrope ok. System is non ideal they can be azeotrope or they may not be an azeotrope that is why you see the system non ideal you may have azeotrope you may have non azeotrope you have azeotrope you may have non azeotrope right. So, azeotrope is the indication of non-ideality ok, but not necessary that non-ideality means azeotrope like when you have a binary system you do not have problem you can use mechaphthyl method. Only thing is like for example, ethanol water system you have formation of azeotrope you should be in mind you should know that there is a limit there ok. Once you know that and of course, when you draw this wave vapor liquid equilibrium plot when it intersects diagonal you know there is a limit there and you can use mechaphthyl method draw your rectifying section profile stripping section profile count number of stages ok, but you should know that I am not going to go beyond 95% concentration of ethanol in the distillate. So, I assume of course, I will quickly revise what mechaphthyl method is, but I assume that all of us know mechaphthyl method very well and then I will take a step forward and extend the concepts to the multi component system and the best or the simplest representative of multi component system is a ternary system. So, we illustrate one example or we will give an example of ternary system and show how the new method that we introduce today works for that particular system right. The multi component ideal system ok, non ideal system we will deal with that tomorrow we will just see multi component system and the same concept will be extended to azeotropic system later or other non ideal systems later. So, before we go ahead again what is the role of conceptual design? I told you the methodical approach towards any design method or towards design a distillation system is the first step is to get vapor liquid equilibrium and we have we know a lot about it, it is a backbone of distillation design. If you go wrong here you results though if you follow all other steps properly it is not going to help you, you are not going to get good results right. So, next step before we go ahead is a conceptual design. In this what do you determine? What does it give you? Conceptual design tells you about a feasibility. Now, if your system is ideal I know I can separate any component in pure form right. So, I really do not need to do feasibility analysis for ideal systems right, non ideal systems yes. The feasibility analysis is very important if there is a formation of azeotrope I must know that. For binary systems again if I draw that plot I immediately come to know there is formation of azeotrope or not, but for multi component systems they have ternary system. How many azeotropes are possible in ternary? There can be many right. There are three binaries and there can be a ternary azeotrope as well ok. There can be two ternary azeotropes as well. So, there is no limit on that. So, you can have various combinations and many azeotrope formation like when you deal with multi component non ideal azeotropic system. So, in that case this feasibility becomes important right. So, as far as today's lecture is concerned where we are going to learn ideal systems right. We are not really going to deal with feasibility aspects ok. So, next step is what does macabthil method do just go back and recollect it finds out first the minimum reflux ratio right. The same thing is expected here even for multi component systems even for multi component ideal non ideal systems I should get minimum reflux ratio as the outcome of conceptual design method right. So, assumption of macabthil no energy balance I can make the same assumption here. I am going to come back and look at this energy balance issue later right. Initially as far as conceptual design is concerned in order to make my analysis simpler ok. I will just make the assumption that there is no energy balance required again the constant molar overflow in the column right. Then if it is a system and I am interested in all components in pure form then I must identify possible sequences. That means, if I have multi component mixture then it is quite possible that this mixture can be separated. So, suppose I have multi component mixture A plus B plus C right. And I want to separate all the components in pure form ok. There are many possible sequences. If it is ideal system then I do not have feasibility issue right. I can do this see A B C going to a column right. I separate A in pure form from the top right. I get B C from the bottom yeah, but I design the column in such a way that I remove A from the top ok right. Because I am interested in pure components. Now, this B C can go to another column this mixture I separate B from the top C from the bottom. The order of volatility is A greater than B greater than C right. This is one possible sequence is it the only sequence are there any other possibilities that is right. So, I can have something like this. I remove C from the bottom first in pure form and then I deal with A B mixture right. So, that two different possibilities right for a terminal mixture simple columns right. Can you imagine suppose you have four components system you will have many possibilities five components right. There are many possible sequences possible feasible sequences rather right. And I should identify all the sequences before I go out because once I identify these feasible sequences later on I am going to select one of them based on some criterion. Of course, the best criterion is minimization of cost. We can take the intermediate component from as a side draw right as a side draw. So, that possibility is there I did not show that possibility here because I am talking about simple sequences. So, what you are talking about is a complex sequence where I take some side draws for example, a crude distillation column in refinery. In fact, infinite components in the feed right and I take some side draws and remove the fractions of interest right. So, that is a different issue I treat that I say that that column is a complex column and not a column that we are talking about here we are talking about simple sequences. So, we have complex sequences as well ok. So, it is not just that we have only simple sequences, but we have complex sequences as well. So, as such we should identify all such sequences right and then later on select one of them right. But complex sequences would need some additional efforts on operation control and all right. So, those issues will also come in picture. Now, so this is the role of conceptual design in the overall design or rigorous design and later on what do we do? It is not over here ok. Later on once I have the minimum reflux ratio I say my operating reflux ratio is about 1.3 to 1.5 times the minimum reflux ratio and then I design the column again I get the actual number of stages right. Remember Macathil does the same thing right. Once I have this now I have a column in front of me at least some picture of a column say I know these many theoretical stages are required right. At this stage I know the column would need some 30 stages ok for the required separation 30 equilibrium stages, 30 theoretical stages or ideal stages you know the meaning of equilibrium stage right. So, once I know this I perform rigorous simulation right. What I mean by rigorous simulation? Simulation takes care of the energy balance as well ok and if you want pressure draw up and other aspects also can be brought in right and then you can design or not design a simulated distillation column just to cross check your results right. Because simulation needs an input in terms of number of stages like if you solve simulation problem right it will ask you how many stages you have as I said before in simulation problem the column is in front of you right. So, you have to give number of stages there. So, where will that number come from? So, conceptual design helps you right or in other words yesterday you might have dealt with some shortcut method right. That shortcut method is one way of doing a preliminary conceptual design. So, it tells you ok how many stages approximate number is required to get the separation. But that is not a real number because I have made many assumptions at this stage ok at this stage I have made many assumptions right. So, in order to get a real picture I have to do rigorous simulation that is the role of simulation ok. So, simulation is definitely important, but it comes at a later stage first you have to go through the conceptual design. A system is ideal I do not have to really do all this system is binary then just my capsule will tell me ok what is the minimum reflux ratio and all. But if it is multi component non ideal and azeotropic then you have problems right. So, I am trying to tell you the importance of conceptual design it is important in complex distillations right. And of course, once you have simulation ready and you have confidence in your simulation model you can further go ahead and do optimization and control and minimize the cost overall cost involved in the distillation system right. Start solving a problem ok. I have a ternary system this is the approach that I am going to follow I am going to look at multi component system, but study the behavior of the ternary system first ok. And we will learn some concepts and we can extend those concepts to a multi component system in a generalized algorithm right. So, that I can solve this conceptual design problem on computer right. Let us have a ternary system ok A plus B plus C or I will denote them as 1 plus 2 plus 3 ok. So, A is 1 B is 2 and C is 3 right. Volatility A is the most volatile B is intermediate boiling C is the least volatile ok. I am assuming the system to be ideal now right. Later on we will see if it becomes non ideal what modifications we need to do ok. This is the equation very well known equation for binary system ok. This is for binary system now can I extend it to multi component system. What is the multi component form of this particular equation? Suppose I have three components now this is this is for binary ok. This is not true for ternary I have to modify this can I do that. A very general equation for multi component system is yi is equal to alpha i xi i is the species divided by sigma alpha i xi ok. i goes from 1 to C right. You do it for two component systems two component system and you will get the equation for i is equal to 1 to y is equal to say for example, you have two components y a is equal to alpha a x a divided by 1 plus alpha a minus 1 x a. You can derive this right and there is no alpha b because alpha b is equal to 1 in binary system. For binary system b is the least volatile so alpha b is equal to 1 right. For ternary system c is the least volatile so alpha c is equal to 1 right. In this case I will have alpha a say 5 alpha b say 3 and alpha c is equal to 1. So, I do not need to really specify this ok. So, just remember this is for binary and I have to extend it to multi component system. I have to define alpha a and alpha b. So, two parameters are to be defined and I can get that from the vapor liquid equilibrium. I can generate the data as we seen yesterday right. You can generate the data in laboratory and find out the values of alpha c and sorry alpha a and alpha b. The problem is design a column to achieve the required performance. Now, what is this required performance? I want to solve this problem right. So, I have to specify some variables. What is that? The performance is gauged by the purity right. That means what is the value of x d. So, when I say x d, x d is the distillate composition. Now, distillate composition for all the three species right x b the bottom composition for all the three species. Given x f feed composition flow rate right ok. So, I have to define this first x d and x b these compositions right for the given feed composition. Once I define this then I can start solving a problem ok. So, is the problem definition clear right? You know the end composition or you have to fix the end compositions feed composition is given and you are supposed to find out the number of stages design a column. The word design has a particular meaning. That means I have to find out number of stages then height and diameter. So, height and diameter I can calculate very well the equations are known. There are some correlations depending on whether you have packed column or tray column and all that right. But number of stages would come from this exercise the thermodynamics it depends on the vapor liquid equilibrium right. Now, I have to define top composition and bottom composition. This is your column right this is your column. The simple column you have feed going in x f 1, x f 2, x f 3 are the compositions right of this particular stream the feed right. The top composition I am going to define this when I want to solve the problem x d 1, x d 2 and x d 3 bottom composition x b 1, x b 2 and x b 3 right. So, look at what you know and what you do not know. Now, when I am doing a degrees of freedom analysis let us assume initially that a feed is given to you right. Now, I have to specify the top and bottom composition depending on the requirement right. Now, specify you need to specify all the compositions. Now, how many compositions are there? There are 6 right 3 here and 3 here right. I have to define 6 compositions then only I can go ahead and solve the problem. But do you really need to define 6 compositions for that you need to do degrees of freedom analysis ok. Let us see what whether all these 6 compositions are independent or there is some dependency there. The obvious dependency I can see here these are mole fractions the summation is 1 right. So, in that case I do not need to really define all 3. The moment I define 2 of them the third gets fixed automatically right. So, let us identify this dependency. Now, unknowns all these all x b's in the beginning right before I specify these compositions then D that is distillate composition and B right that is bottom flow rate or sorry D is distillate flow rate and B is bottom flow rate right. How many equations I have? I have the overall material balance equation ok. I have the component material balance equation for out of 3 components I can write it for 2 right because third gets fixed automatically because I have I am using the summation constraint I am using the summation constraint right. So, I have one equation for overall material balance 2 equations for species or component material balance because third is dependent I can write it as independent equation right. And the summation equation for top and summation equation for bottom right. I hope this is clear. So, how many equations I have total 4 equations right 4 independent equations how many sorry 5 independent equations right and how many unknowns you have 8 unknowns right. So, degrees of freedom is 3 right. So, I need to define 3 compositions. So, that I can solve the design problem right now which are these 3 unknowns they can be any 3 of these 8 right can be any 3 of these 8 unknowns right. Typically in general now you have some objective right the design I say I want the composition of the most volatile component in the distillate stream to be 0.99 right that is the constraint because I want to design it for certain performance. So, that x d 1 gets fixed right x d 1 gets fixed they can be another constraint saying the bottom composition of the third component should be that is the least volatile component should be 95 percent that is again one more performance criterion right. So, I define that as well. So, I define 2 of these ok. So, these would come from the client ok. He will say I want this performance right. So, out of 3 you have defined 2 it is just an example you can define any 3 depending on your requirement. But I am just giving an example I have defined 2 the rest 1 you can fix based on like it is your choice is a choice of design engineer ok. It is a trivial composition it does not matter much because client is not interested in this composition right. So, define 2 compositions the third composition you define on your own right ok. So, 3 compositions of fix because I want to solve the problem design problem for that I need to define all the end compositions right. So, this is just one example where I define these 2 compositions the composition of the most volatile component in the distillate stream composition of the least volatile component in the bottom stream right. And the third composition any any ones composition I can fix right and rest all will get fix automatically because I have these many equations right. So, I use these equations and get all the compositions all x d's all x b's d and b for given feed right. Now, my problem is defined ok it is completely defined end compositions of fix. Now, I want to solve the design problem ok. Now, this is for 3 component systems suppose you have 5 component system for 3 component systems we have seen that you have to specify 3 compositions or 3 unknowns right. For 5 component system can you do the degrees of freedom analysis? How many compositions or variables or unknowns you need to fix? For 5 component systems instead of 8 there will be 10 plus 2 right d and b. So, 5 here 5 here right. So, before you do this analysis we have 12 here 12 right. And how many equations you have? 7 equations. 5. Yeah. So, 5 is the degree of freedom right. So, you have to define 5 unknowns right you have to define 5 unknowns for a 4 component system it would be 4 right. So, we want to solve this problem now. And let us start with what we know for as I said we are going to extend the macaphtil method. So, let us look at a macaphtil method ok. So, what is it? We start with yx diagram right you have y here that is vapor phase composition you have x here you have this curve vapor liquid equilibrium curve right which is obtained by thermodynamics right this vapor liquid equilibrium curve. Now, let us look at a column in the column any stage this is a stage right. So, what happens on the stage you have a vapor going in you have liquid ah this arrow should be in the downward direction ok. So, you have a vapor going in and liquid going in and you have vapor going out liquid going out right. Now, when I say this stage is equilibrium stage ok. What does it mean? I told you yesterday that these two compositions compositions of the streams leaving that particular stage they are in equilibrium phase equilibrium ok. And your VLE decides these compositions right. And this is given by for a binary system you know this equation. So, y a is related to x a, y b is related to x b right. So, I have written these equations for a binary system ok. So, these two compositions if you plot them they will be that point will be on the equilibrium curve right that point will be on the equilibrium curve. Now, in this particular diagram suppose I get select one point on the equilibrium curve it means that I define everything about this particular stage. Because for this point I know x a for this point I know y a I can use the summation equations to calculate x b and y b I can calculate a temperature by bubble point. So, for this particular stage all the compositions and temperature are defined right. The moment I plot a point here on this diagram everything about that particular stage gets defined right ok. A single point on the equilibrium curve on y versus x defines all the compositions of the stage in the distillation column. The stage is completely defined right. Now, the next question is can we do it for the turmeric system? Suppose I plot now I have a turmeric system a, b, c I try and get this particular plot y a versus x a can I get this plot in the first place it is difficult right. I cannot plot a ternary system on y a versus x a right because the dimensionality increases right. Suppose there is some point here which satisfies the equilibrium equation I do not get idea about other compositions. Because the summation constraint is now changed right if I want to calculate x b from x a it is 1 minus x a minus x c right ok. So, if I have a point here does not mean that I have defined a stage in the column completely right. So, very clear dimensionality has increased. So, what do we do? We have to find a solution I want to visualize what happens in the column like what my capital does for binary system right. So, what is the solution on this? Let us go ahead I have a ternary system this is your equilibrium stage. Now, I have this summation equations right and now my equilibrium equation has changed right. I cannot do it on y versus x diagram, but I can choose some another frame of reference and this is that frame of reference x b versus x a right. Now, in x b versus x a diagram suppose I have a point right that tells me the composition of a on this particular stage or of the stream leaving that particular stage a right. Then composition of b in that particular stream which is leaving that stage right let us say this is that point. Now, if I have this much information can I make use of the relevant equations to calculate the compositions of all of the species and define the system completely. Can I do that? Let us look at equations. How many equations I have? Now, I have defined two unknowns two compositions rather and I have how many equations? I have this summation equation for that particular stage liquid composition. I have this summation equation vapor composition right and then you have this vapor liquid equilibrium satisfied right. You have these two streams which are in equilibrium. How many equations you have? How many such equations you have? You have two equations right because you can write it for only two components third component. Since you are taking summation constraint in account you cannot write it for third component. So, you have four equations. So, out of six variables three y's and three x right you have defined two rest all will get fixed automatically because of these four equations right. So, total number of unknowns six three y's and three x's right. Number of equations four right. Compositions to be specified to define the stage okay six minus four two that is what I am doing here okay right. So, one may specify any two x values in a triangular diagram right and hence a point in x a versus x b diagram defines all the compositions right okay. So, I am defining a new frame of reference a ternary diagram we use that in extraction problems you remember like liquid-liquid extraction we use ternary diagrams right rectangular diagrams. Similar representation is used here for distillation systems for a ternary system right. So, you have x a versus x b instead of plotting x a versus y a now I am plotting x a versus x b and saying that this one point here which defines the stage completely right. Because if I plot a point here and say that it satisfies the equilibrium equation then I have a value of x a I have a value of x b I make use of all these equations and get all other values right. Now, what are the problems with this if you compare this representation with mechathyl okay there are some constraints okay I am not able to see everything here see mechathyl you can see on a stage even the y composition vapor composition right. You can see the equilibrium curve right because it was a binary system, but now with this representation though I am presenting or I am defining all the compositions by plotting a point on this I am not able to visualize vapor composition because there is no y plotted here on this okay I have to calculate it okay I have to calculate it from equilibrium equation and I cannot see the vapor equilibrium curve on this okay. So, you have to sacrifice okay for knowing about a multi-component system because we cannot help it okay we have to pay for it because we are increasing number of components and we have constrained right we have two dimensional paper on which we can visualize the things right. So, for a ternary system okay you can visualize the entire system in a triangular diagram by plotting x a versus x b, but I am not able to see y's I am not able to see the vapor equilibrium curve right does it matter okay we will see later okay turns out that there is no need to really visualize the vapor equilibrium curve there is no need to really see the vapor composition I can still work with this frame of reference and can visualize the composition profiles inside a column and can define certain rules which will give me the minimum reflux ratio for particular design okay for particular requirement okay right is this clear ternary diagram okay now once I have fixed my frame of reference now before we go ahead okay for quaternary system what will I do so for ternary I have this for quaternary system yeah I will have a three dimensional frame of reference I will have to plot x a versus x b versus x c so three dimensions right at any point here defines the stage completely right for five component this is a four component right five component system what will you do yeah it is not possible it is impossible right because we cannot visualize okay four dimensional frame of reference right but does not mean that we cannot solve the problem that is what I am trying to tell you so by looking at ternary system or quaternary system which we are able to visualize on this ternary or at the two dimensional diagram or three dimensional diagrams we can define certain rules which are applicable to any system any multi-component system let it be five components six components right so that is the purpose okay that is what we are going to do so we are going to just learn three components system or ternary system but we can extend that knowledge to any component system and there you do not need visualization because we will convert everything to an algorithm okay right so we can feed it to a computer and get a required results right now I have this ternary diagram now we are going to see this ternary diagram every now and then here after okay because I am going to deal with ternary system and not binary system right I want to plot my rectifying section line now it is not going to be a line okay and stripping section line or I would call them as trajectories okay because when I say line it is a straight line it has certain slope and all that right so in my cap tile what do I do my cap tile method x a y a right you have this equilibrium curve you identify feed composition x d x b right and then you draw rectifying section profile of course first step is to get a minimum reflux ratio and all but then what is what is the rectifying section line this is the rectifying section line right what the slope of this line it is yeah the slope is r by r plus 1 okay how to get a material balance equation for this line it is very simple have this column this is the stage in the column in the rectifying section we have vapor going in liquid coming out you have a condenser right this is your distillate you take material balance across this boundary right and you get a equation y i n plus 1 is equal to r by r plus 1 x i n plus x i d upon r plus 1 this is the equation that we get by solving the material balance right now this is your y n this is your y n plus 1 i of course and this is your x m or x i n right these are the two compositions of these two streams right this is your rectifying section equation right and this is what you do in my cap tile method right I want to see this rectifying section on my ternary plot now okay right see I am just following the same method right so this is your equation rectifying section line and then you have stripping section line what is s s is the reboil ratio okay r is the reflux ratio l by d reboil ratio is v by b right v is the vaporization rate okay and b is the bottom rate they are they are related to each other through d by b right so once I define r s gets fixed automatically right because if you write that overall material balance s and r are related to each other okay now I want to see this particular trajectory in the ternary diagram okay in a ternary diagram now this is my x d why why your x d is over here why not here why not here see I am going to follow the convention this is your most volatile component okay that is your a okay right then this is b intermediate boiling right and this is c the least volatile component right and this is my convention now in the bottom bottom composition will be close to the least volatile component the top composition will be close to the most volatile component that is why I say I start with this this is my x d when I say x d that means x d 1 x d 2 x d 3 because when I want to plot this particular point I need to know the composition of all the species in this then only I can plot it in the ternary diagram right so I plot this point this is my first point x d how do I get these points it is quite similar to what I do in my capital method stage by stage calculation right when you know a top composition I go on solving this material balance equation for every stage right this is that equation this equation is valid for even ternary system okay this equation is valid for ternary system it is valid for any multi component system right not not that it is only valid for binary system right this equation is general material balance right so the moment I know the x d the way I do these calculations in my capital method right I can do the same thing here right and go on calculating the composition on every stage and I can travel from top to bottom right the way I do graphically here I can do it manually by using some it is not very difficult okay you have to just do calculations material balance then equilibrium material balance then equilibrium and so on right so you solve for the rectifying section equation and plot those points okay right so this is the this is the equation or this is the solution of rectifying section profile right why it follows this particular path why it does not go this way it has a tendency first to go towards the intermediate boiling component and then later on it will move towards the least volatile component that is the way it happens in the distillation column the top you have the most volatile and bottom you have the least volatile okay so normally for ideal system is going to follow this particular path okay it is going to go towards the intermediate boiling and then will move down to the least volatile component okay that is you see okay or the highest boiling component this is the path of the rectifying section profile now what about stripping section stripping section start with XB now XB is going to be close to C because C is the least volatile component and then I want to solve this equation in upward direction okay now my N is going from bottom to top is increasing right and I am going to solve this equation using the material balance and vapor liquid equilibrium right and I will go up again the same trend is observed it will move towards the intermediate boiling and now you are going to go towards the most volatile component okay right so this is the nature of the rectifying section trajectory and of course stripping section trajectory is the way they are going to move in the composition space the new composition space that we have defined for the ternary system ternary system you have this two dimensional plot XA versus XB right for rectifying section I am going to start somewhere here in this corner because A is the most volatile and I am going to move in this direction and come in this direction okay because that is the way the rectifying section profile will behave okay you can do this calculation yourself very simple okay you can use excel to do these calculations and we have some tutorials on that as well okay similarly here right you can go up and then come down right that is the nature of these two profiles so as I said when I say yeah when I say this is this is the point what does it mean it has coordinates right it has XA right XA it has XB right these XA and XB are the stage compositions right and suppose I want to know YA and YB for that particular stage what will I do I will solve that vapor liquid equilibrium equation right and YC and XC summation constraint right so everything is defined in right once I know this point so all these points are the stage compositions compositions of the stream leaving particular stage right