 So, welcome to the 20 second lecture on cryogenic engineering under the NPTEL program. We are talking about gas separation and the earlier lecture give you following points. In the earlier lecture, we studied basic laws which govern the mixture. So, we studied Dalton's law, Raoult's law and Gibbs Dalton's law. They were all dealt in detail in the earlier lecture. These laws relate vapor and liquid fraction, the y and the x fraction of a component in a mixture at a given temperature and pressure. We also studied about the concept of distribution coefficient which is k and we found that it is a constant and it depends on temperature and pressure of a mixture. So, what is the temperature of a mixture? What is the pressure of a mixture according to which one can find out distribution coefficient which is nothing but y by x or a molar fraction divided by the corresponding liquid fraction in a mixture and this gives a value of distribution coefficient. The k is normally given in a two phase region. So, we are talking about oxygen and nitrogen. The value of k will be given between 90 Kelvin and 77 Kelvin which are happening to the boiling points of nitrogen and oxygen respectively. With this background, the outline of today's lecture is we will now see enthalpy composition diagram. We have seen earlier the temperature composition diagram. One of the most important thing is enthalpy composition diagram. Then, we will see the real rectification column where all these gases in a mixture get separated. We will see about its working. Then, we will define Murphree efficiency which is with respect to this rectification column functioning and finally, I will take a small tutorial on Murphree efficiency so that the concept gets clear. To introduce the topic, in the earlier lecture, we have studied the temperature composition diagrams and their importance in gas separation. This is a very important diagram and we have dealt enough in the earlier lecture. How does it look for two different gases and thing like that? The enthalpies of the vapour and the liquid functions are dependent on the temperature of the mixture, the relative mole fractions of the component. So, if I want to find out now corresponding to given mixture for a given molar composition, what is the enthalpy? What is the enthalpy of the vapour? What is the enthalpy of the liquid or what is the enthalpy of a two phase mixture that is in between the vapour and the liquid? It depends on the temperature and of course, the molar fractions of the component or that is the molar composition. These two parameters will decide for a given pressure. This will decide what is the enthalpy of a given mixture. In a mixture, the enthalpy calculations for liquid and vapour mole fractions are done using the enthalpy composition diagram and this is the importance of the enthalpy composition diagram. Now, let us see how does it look. The enthalpy composition diagram normally would look like this and on y axis you can find the enthalpy is given as kilo joule per mole. This is given for a nitrogen oxygen mixture which is at one atmosphere. That means, all these diagrams are given for a particular component mixture. The mixture is being at a particular pressure. On the x side, you find the mole fraction of the low boiling component that is nitrogen over here. So, nitrogen is 0 percent over here which means that oxygen is 100 percent while is nitrogen is 100 percent over here which means that oxygen is 0 percent at this point. Now, what you can see is two lines and there are temperature lines across this. So, what are they? So, let us consider a mixture of nitrogen and oxygen at one atmosphere pressure. The variation of enthalpy with the mole fraction of nitrogen is as shown. So, you can see the mole fractions on the x axis and the enthalpy is given on the y axis. Now, here what you can see are different colours. One is a red colour, one is a violet colour here and then there are connecting lines in different colour for the temperature. The red and violet curves are basically the dew and bubble lines respectively. So, whenever we are starting condensation, we will have first the dew line over here and then when the phase change happens, we will have the bubble line as we had seen earlier in a temperature composition diagram. Similar the diagram looks similar as what you have seen earlier. The figures show the isotherms that is the constant temperature lines between the dew and the bubble line. So, you got a dew line, the bubble line and we got a constant temperature line or isotherms as shown in this particular figure. What do you see? What is different in this case? These isotherms have finite slope. That means these isotherms are not vertical lines. They got a finite slope. If they are vertical line, they are parallel to y axis that means their slope is infinite. However, they are not vertical lines, but they are having a finite slope. The isotherms have a finite slope specifying that the condensation or boiling of the mixture is a non-isothermal process. This is what we had seen earlier also. During this phase transformation from vapour to liquid or a phase transformation, the temperature decreases. That is what you can see and this happens basically because these isotherm lines are not vertical. Let us see for example now. Let the state of the mixture be on the dew line at 0.1. So, let us start condensation from this 0.1. If it is cooled to bubble line that is 0.2, which is 0.2? This is 0.2. When the phase transformation happen, the 0.1 will come to 0.2 because the molar fraction has to remain the same. Whatever happens, the mixture molar composition remains the same. What has happened? At this point 1, what was the temperature of the mixture? It is around 88 Kelvin. If you see this line which is having a finite slope, it is an isotherm. The temperature at point 1 is around 88 Kelvin while when the mixture gets condensed at this point, the temperature at this point which is 0.2 is around 84 Kelvin and that is why the temperature of the mixture changes from 88 Kelvin to 84 Kelvin and that is what you can see. On the other hand, this is what happens when the phase transformation happens for a given mixture composition let us say 0.3 nitrogen and 0.7 oxygen. On the other hand, consider pure nitrogen or pure oxygen. Where is pure nitrogen? The pure nitrogen is here 100 percent. If you see here from this point, for example, if that phase transformation takes place from here, this line is vertical. It has no finite slope. It has got an infinite slope which is a parallel to y axis. What does it mean? This 77.36 line is absolutely vertical and same thing can be noticed if you have got 100 percent oxygen which is 0 percent nitrogen. So, here if you see, if I have got a mixture at this point which is 90.2 Kelvin line, you can see that this line is vertical which means that whenever there is a single component which is oxygen in this case, nitrogen in this case, this line is not inclined. This line is vertical in that case. Why? Because there is a single component and whenever that phase transformation happens for a single component, the temperature remains constant. Temperature during the phase transformation remains constant. So, on the other hand, consider pure nitrogen or oxygen. The isotherms are vertical in this case as there is no change in temperature during condensation or boiling because it is a one component system. It is not a mixture anymore. I hope this is clear to you. Let us go ahead. Now, let us say at any temperature say at 83 Kelvin, for example, this is 83 Kelvin. The mole fraction of nitrogen in liquid and vapor is given by y liquid. So, the liquid at 83 Kelvin which is a saturated liquid, this is saturated vapor. At this point, what is the composition of liquid is y liquid which is around this. And what is the vapor at 83 Kelvin? This is this. So, the vapor is around 0.6 just more than 0.6 mole fraction of nitrogen is in vapor condition. So, from this diagram, one can see corresponding to this what is the molar composition corresponding to given temperature. If the temperature is given, if you know that it is a saturated vapor condition or saturated liquid condition or for that matter anywhere in between, one can find out the corresponding to this the enthalpy or the mole fraction of nitrogen or a low boiling component. Also, the corresponding enthalpies are if I want to see the enthalpy, what are the enthalpy at this point? The liquid content that is enthalpy at liquid condition at this point is 656 kilojoule per mole. So, you can see from here, if I draw a horizontal, I can read enthalpy and this enthalpy is given in small h. While, if I see the vapor content enthalpy at 83 Kelvin, it is given by this parameter. If I draw a horizontal line, I can get that the enthalpy is around 700 kilojoule per mole. And kindly note the small h for liquid, the capital H for the vapor enthalpy. So, this will be used many times in future slides and therefore, please note that the vapor enthalpy is given by capital H. The small h gives the liquid enthalpy and the vapor enthalpy is much more as compared to the liquid enthalpy alright. Now, this is a table that also could be given instead of giving the graphical information, one can have the same information given from a table. How does this table can be the same information as given in a graphical form is you can see here. If I got a 0 y, that means 0 percent nitrogen, I got this line. Corresponding to this, I got a liquid temperature at this point, which is 90.2 vapor, 90.2 temperature remains constant, because it is a single component system, it is only 100 percent oxygen system, because this is 0 percent nitrogen. The enthalpy h and capital H values are given at this point and this point, which can be read from this graphical form also as well as from this table. The other example is now, let us say 0.3, 0.3 nitrogen, 0.7 oxygen just draw a vertical line. You can get 84.1 as this temperature, 87.7 as this temperature. Corresponding to this, what you get is enthalpy value and last you can see at 100 percent nitrogen, what you see is that both temperatures remaining the same, you got a small h value, which is at this point and capital H value, which is at this point. So, this is the way the enthalpy can be read for a given molar composition and these enthalpies will further be used for different calculations, which we will see in the next lecture also. Having done this now, having understood how to get enthalpy, what is the enthalpy concept, what is the enthalpy composition diagram. Now, let us come to a simple understanding for a gas separation. The gas separation is largely dominated by what is the difference in the boiling point of two components in a mixture. So, let us see this diagram over here, which will show you two mixtures. The two mixtures AB and CD at one atmosphere, whose temperature composition diagrams are shown over here. So, you can see for AB, you can see the top x axis and for CD, you can see the bottom axis x axis. Suppose, I got a diagram, which is a temperature composition diagram. Here, you can see a temperature composition diagram for a mixture A and B and also, I got one more diagram, which is for C and D gases mixed together and this is the temperature composition diagram for gas C and D. What is the difference between the two diagrams? It is the boiling point difference. The boiling point of C is this, the boiling point D is this, because D is equal to 1 and C is equal to 1 at this point. Similarly, the boiling point of A is this and the boiling point of B is this. So, what do you see from here? The respective boiling points of each of these gases as shown over here, the boiling point difference of the mixture AB is only this much, while the boiling point difference for the mixture CD is quite large as compared to what it is for A and B. Now, what do I want to tell from here? That the difference between the two boiling points of A and B and C and D is a very important, because that will determine the separation, which happens of A and B and C and D. That is how we can see in the next slide. So, let us consider a mixture with a composition at state 1 at this point and if this mixture is rectified, the first condensation if you can see from 1 to 2, what you get at this point is the liquid will be at this point. The mole fraction of A will increase from this point to this. This will be referred to the top x axis and therefore, what you can see here that the fraction of A will increase from this point to this point. So, while liquid will be at 2 F AB, this is what you get at this point 2 F AB. Now, if I do the same point, if I come and get the mixture condensed from the same point, but on CD curve and you can see that as soon as the first condensation happens, the liquid will be much richer as compared to 2 F AB and what you can see now, it will have this much mole fraction of C. This essentially can be noted from the diagram itself. If you have got a boiling point difference from these to these, the right in the first condensation, you have come very close to 90 percent mole fraction of C. The first condensation itself has separated component C and the liquid has more around 90 percent of component C while in this case it was around 75 to 80 percent only. Why did this happen? This is a little exaggerated case just to show the clarity of what happens when the condensation happens. What you see here, if you got a difference between the two boiling components, the boiling point is quite less. The first condensation will not separate the high boiling component or low boiling component for that matter while the first condensation in a for the mixture in which you got a high boiling point differences. The first condensation may be sufficient for example, to separate the high boiling component immediately. The liquid is getting richer in high boiling component immediately. If this difference is too large just from the nature of this curve, you can see that this point will come more on the light side immediately right in the first condensation. The point to be noted is that higher the difference between the two boiling points, you will not have to do too many condensation. So, 1 or 2 or 3 condensation could be good enough to separate component C and component D. While in this case, we may have to go for multiple condensation and evaporation in order to separate A and B. Why? Because the boiling point difference between A and B is not too large is very small alright. So, the separation is more effective when the difference in the boiling point is more. This is the point I wanted to stress that right in the first condensation the separation was very high while in this case the separation was not that good. For such mixture almost pure product is obtained in 1 or 2 condensation alright. In this case right in the first condensation you get a pure point and that is the point I wanted to tell you in this case. In this case you can see this is a figure which you have already seen. This is the way we basically do the rectification. As done earlier the rectification of the mixture at point 3. If you are at point 3 the first condensation would result in this liquid and this much of gas. The subsequent condensation would result from here and you march towards right. I just wanted to show this because after this slide I am going to deal with the rectification column itself. So, in a rectification column right here after first condensation you will have go for subsequent condensation processes in order to reach a right and you will get high boiling component. You will move toward the liquid which is richer in high boiling component while this vapor will be further evaporated. It will further move towards left and ultimately what you get is a low boiling component getting richer and richer into vapor and ultimately this vapor will get condensed when you shift toward the left y axis. Well the high boiling component in liquid will move to the right axis which is which is oxygen in this case and nitrogen in this case. So, as done earlier rectification of this mixture at point 3 vapor is enriched in low boiling component nitrogen. So, as you go on the left side of the vapor is getting enriched enriched in low boiling component which is nitrogen while the liquid is getting reached in high boiling component which is oxygen and this is essentially is a basis of multiple condensation and evaporation which is carried out in a rectification column. This process from the fundamental step for the rectification column alright. Now, let us go to the rectification column with this background whatever we have studied. Now, let us go to the rectification column which as mentioned earlier gas separation is a process of repeated rectification or condensation and evaporation. The equipment which carries out these processes is called as rectification column and a general schematic is given over here. This structure could be very huge structure it can have a very high length also depending on the kind of purity you want and what it consists of is this we will discuss this structure height. The figure shows the schematic of a rectification column. So, the gas which is to be separated enters at this feed line and ultimately you get the two component to be separated from top and bottom this is the idea. The process of gas separation happens in this column across the height of this column and height of the column is a very crucial matter because height of column will determine what is the purity of the gas which is gas component which is getting separated at the top and at the bottom. So, what do you see here it is a vertical column which is closed by spherical domes both at the top and the bottom. So, what you can see one dome on the top one dome at the bottom and a vertical column over here. These are spherical in shape the domes are spherical in shape in order to minimize the surface area that is the less heat in lick alright and accommodate high pressure. Now, the whole column or the domes have to stand high pressure. When I say high pressure it could be of the order of 1 or bar 2 bar or 5 bar not more than 5 bar normally ok. The column is well insulated again the entire column is subjected to cryogenic temperature and therefore, the column has to be well insulated it is usually operated at cryogenic temperature. The top dome houses a condenser and the bottom dome houses a boiler. So, what is happening at this point is a boiler what you collect at this point ultimately is a high boiling component liquid. So, liquid is stored here and the boiler is supplying heat to this liquid. While the enriched vapor of low boiling component comes to the top alright and therefore, this vapor will be ultimately condensed at this point to get liquid of low boiling component which is nitrogen in a nitrogen oxygen mixture and this is therefore, called as condenser. The two phase mixture is first expanded isenthalpically. So, wherever from whichever place the two phase mixture is coming whatever mixture is coming is going to be at high pressure. The column cannot stand very high pressure and therefore, this mixture pressure has to be reduced and therefore, one wall is kept at this point whose essential function basically is to reduce the pressure. So, the pressure is reduced and therefore, the expansion would happen and therefore, this mixture will enter the column as liquid or liquid plus vapor or sometimes a saturated vapor. So, all these three conditions are possible. This column this mixture or the feed can enter this column in all these three forms and this is a wall where the expansion occurs. These expanded products is introduced into the column as feed alright. So, the feed enters the column at this particular point. The rectification of the mixture occurs across each plate and the downcomer assembly as shown in this figure. So, what you can see in this column is there are lots of horizontal plates and on this plate what you can see is a one particular height which is called as wear. As soon as this liquid height increases above a particular wear height the liquid will come down. In every plate we can see that you got a liquid at this point and this liquid height is governed by the wear height. So, as soon as the liquid height increases or goes beyond the wear it comes down and it comes through this downcomer. This is what is explained over here. So, on every plate you got a plate with a downcomer. So, when the liquid height increases a particular height of the wear it comes to this downcomer and goes to the plate which is below the top plate. When this height increases the liquid height increases the liquid will be overflowing across this wear and then comes to the next downcomer down to this plate. So, that you can see that the liquid is always flowing down while the vapor will always go up on a vapor is going up through this plate. So, let us come to the next discussion. This plates have holes you can see the plates have holes. So, this vapor whenever the feed comes through the feed can have vapor liquid or vapor plus liquid. The vapor will try to go up and it will go through this small holes which are at the bottom of the plate itself. That means as soon as the vapor goes up it will go through this liquid alright and this will go through this liquid and the heat transfer happens between this vapor and the liquid. These plates have holes for the vapor mixture to pass through and ultimately reach the condenser. So, this vapor passes through this liquid. Now, there is some phase transformation takes place, but again vapor will leave upper plate. This vapor will again pass through the next plate the liquid on the next plate and ultimately as you know earlier that the vapor which is rich in the low boiling component will try to reach on the top while this liquid which is flowing down on every plate will try to go to the high boiling component liquid at this point which is nothing but the boiler. Similarly, the down command takes the mixture in liquid phase toward the boiler. So, the vapor will try to go to the top while the liquid will try to come to the boiler. How does this happen? During this motion vapor is passing through the liquid the vapor and the liquid flow in opposite direction. So, vapor is going up the liquid is coming down. So, it is a kind of a counter flow arrangement basically alright. So, the exchange happens in a counter flow manner. So, during this motion vapor and liquid flow in opposite direction and exchange heat in a counter flow manner this is what you can see. Now, what is happening exactly? When the vapor or the vapor liquid mixture enters the vapor passes through the liquid and this liquid above this plate is going to be at a lower temperature. And therefore, the heat exchange happens between the vapor and the liquid and the high boiling component in the vapor will get condensed at this point while the low boiling point components of the liquid will get evaporated. And ultimately the low boiling component vapor will go to the top while the high boiling component liquid will come down. So, the temperature at this point if you talk about nitrogen oxygen mixture is going to be around 77 Kelvin. While the oxygen will get condensed every time and the liquid will come down and ultimately we will have liquid oxygen at this point at one atmosphere that means the temperature at this point could be 90 Kelvin. What does it mean? The temperature is increasing from 77 Kelvin to 90 Kelvin across the height of the collar. So, you will have around 77 Kelvin temperature over here, you will have 90 Kelvin temperature over here, while the temperature at each plate here will be somewhere like 77 in between the 77 Kelvin and 90 Kelvin temperature. So, you could have temperature range is going to be generated across the height of the column. Hence, there is a temperature gradient gets developed across the length of the column or height of the column. The low boiling component is condensed in the condenser. So, ultimately the vapor would reach to the top. The low boiling component will get condensed at this point and the high boiling component is evaporated from the boiler. In order that vapor always goes up and the liquid always ensure to come down will have a boiler at this point and condenser at this point. This boiler ensures that the high boiling component is always getting evaporated that means there is always a vapor feed upwards. Condenser ensures that the liquid always is flowing down. So, these two ensure that the liquid the counter flow arrangement of the liquid and the vapor flow is always ensured. The low boiling component and high boiling components are collected at the top and bottom respectively. So, low boiling component which is nitrogen which will be connected at this point while the high boiling component which will be oxygen is collected from the boiler. What is happening inside? What is happening inside in a plate? You can see that for the age of understanding consider a mixture of nitrogen and oxygen at one atmosphere. Let the feed enter at this point one which is going to be let us say vapor condition in this case. So, let the feed in the saturated vapor condition enter the column at one as shown in figure. So, what you can see here condition one which is at feed at point one. So, condition after the expansion at one atmosphere the feed enters. The feed has a particular composition of oxygen and nitrogen as given in this diagram. So, what will happen to this feed? Let us assume a steady state and ideal operation. Let us not see any transient operation. Let us see that a steady state has got. That means, you got a temperature across the temperature gradient across the column height has already got developed. The temperature at this point around 77 Kelvin. So, the temperature at the boil region around 90 Kelvin which is the boiling point of the oxygen. When the mixture condenses. So, what will happen? When the mixture enters at this point or the vapor enters at this point this vapor will try to go up through this or if it says through this liquid. And this vapor because this plate above it as a temperature gradient has already got developed that liquid above this vapor is going to be at less temperature than the feed temperature at this point. So, as soon as vapor enters this liquid the vapor will get condensed alright. That means, a phase transformation will happen and when the phase when the mixture condenses or evaporated its composition remain the same. So, when the feed will come inside at point 1 when it comes out at point 2 let us say the composition will remain the same. That means, the temperature will come down as it goes up the plate the composition will remain the same, but its temperature will come down. So, what you can see that? Hence for any plate the vapor rising and the liquid on the plate have same molar composition. So, when this vapor goes up condensation will occur the liquid is going to be there. So, this liquid and the vapor which is coming to pass through it will have the same molar composition alright. That means, this will be a vertical line it will have same molar composition although the liquid is at the lower temperature why it is condensation happening because this liquid is at lower temperature alright. So, during this phase transformation we always know that the temperature decreases the temperature of the liquid above this plate is going to be less than at what it is at point 1, but the molar composition of the vapor which is rising and the liquid above it will remain the same. So, you can see that the point 2 which is going to be here at this point will have same molar composition. So, now, I can draw the point 2 and point 2 basically denotes the liquid on the plate or a composition of the liquid on the plate above this feed alright. The molar composition remain the same the temperature is less than what it is at point 1. So, therefore, extending a constant composition like above point 1 what we have is a point 2. Now, we have come to this point 2 and this point 2 now will get evaporate the liquid here will get evaporated because the high boiling component in this vapor will get condense and the low boiling component of this liquid will get evaporated over here because of the heat transfer between this vapor and the liquid alright. So, what the vapor will leave this place the vapor which is going to be more in nitrogen content because it is a low boiling component is going to leave this place, but this vapor will going to be in thermal equilibrium with this liquid alright. So, this vapor on the same plate on with the liquid is there they will be at thermal equilibrium and therefore, also the vapor leaving the point 3 which is this is in thermal equilibrium with the liquid in point 2. So, point 2 liquid is this liquid and the 3 vapor is going to be at the same temperature. So, what do I do that in thermal equilibrium I draw a horizontal line which is going to be at same temperature and wherever it touches the vapor curve this is going to be the now composition of the vapor which is leaving alright. You can see this composition is now richer in nitrogen the vapor is getting richer and richer in nitrogen extending an isotherm above this point 2 we have the point 3 now alright this is the point 3 which gives the molar composition of the vapor which is above this plate understand that the compositions are different now, but the temperatures are same because they are in thermal equilibrium with each other. Similarly, liquid at point 4 now if I go ahead I am going to the next plate again the same arguments would hold good now which were at 1 and 2 what will happen the point 4 is going to be at lower temperature, but this vapor will get condensed over here and therefore, the molar composition of the vapor which is passing through this liquid is going to be the same, but the temperature at point 4 is going to be less than what it is at point 3. So, what is happening to this is a phase transformation again the vapor will get condensed the molar composition will remain the same, but the temperature will decrease. So, extending a constant composition line about 3 we have got a point 4 which now gives the liquid composition at point 4 and also it gives the temperature at point 4. Now, this will essentially go on containing across each plate till we reach the right most place where we want the purity of nitrogen. Similar thing will happen on the opposite side this is what we are talking about this, but the vapor now similar thing will happen on the plates below this point alright the plate below this point also we show this thing on the other hand we have the points 1, 2 dash, 3 dash as shown in this figure and you can see that at 3 dash will indicate the vapor condition at this point. So, things above from the feed line is going to be shown on the right side of this curve while thing below the plate the temperature on composition of the liquid and the vapor below the feed line is going to be shown on the left side of the feed by 1 dash, 2 dash, 3 dash and 4 dash curves. This is very important to understand what is happening is at some plates the composition remain the same when the vapor changes the phase while the liquid and the vapor on the same plate are in thermal equilibrium. This is we are talking about all about the ideal case right. The point 1 and 2 dash are in thermal equilibrium for the same plate also liquid at 2 dash as same composition as 3 dash and the liquid at lower temperature. So, we are talking about the same thing what we talk here for this condition. Therefore, the liquid moving down is going to be richer in high boiling component what is happening on the left side is the liquid is getting richer and richer in oxygen alright while the vapor is getting richer and richer in low boiling component which is nitrogen and ultimately this nitrogen vapor which is richer in nitrogen now reaches the condenser and what I am going to do at the condenser I am going to condense all the vapor to get liquid while all this liquid will get stored at the in the boiler at this point ok. This point therefore will be at 90 Kelvin as you go up the ladder from the left hand side of the field while all these vapor conditions is going to be depicted by the right hand side of the field as shown over here. In order to keep the process running now ultimately you want this process to happen for years together alright the process is running some heat must be supplied to the boiler. So, I have to supply some heat to ensure that the vapor always is living at this point alright. So, some heat has to be supplied to the boiler to continuously evaporate the high boiling component. So, some high boiling component always getting evaporated at this point it will get combined with the low boiling component vapor essentially later on similarly what I will have to do I will have to take heat out from here in order to condense the low boiling component which is nitrogen. So, for condensation to occur effectively I will have to take some heat out which is Q out depicted at this point at the condenser. Similarly, some heat is withdrawn from the condenser to condense the low boiling component and it is in this way that the rectification column would function ideally. Whatever I am showing in depicting in this please try to understand these are all the ideal operations and they will go on containing from the boiler to the condenser and all these vertical lines essentially are depicting the operation happening at each plate alright. When you have got a temperature difference from this point to this point you got a vertical line actually depicting operation at each plate while horizontal line is depicting again operation happening between the liquid and vapor at each plate. So, basically these are all graphically representation of what is happening in this column alright depending on the purity you want at the condenser and at the boiler you will have to decide how much you want to march on the left side how much you want to march on the right side and that essentially will decide how many plates this column should have or effectively what should be the height of this column alright. So, this is what will happen I have shown you an ideal operation and now in the few slides later we see that how these things will be realized in practice how much away do we go from ideality in that case. So, now in order to understand what exactly happens in a rectification column or what exactly happens on each plate let us see this figure. So, here you can see that this is a vapor bubble alright and let us see now the heat exchange between the liquid and the vapor fractions is explained as follows. The vapor is at high temperature as compared to that of liquid alright this vapor which is going up through the liquid. So, this is a vapor let us say bubble and it is passing through the liquid which is above the plate which is above the vapor and this liquid around it is going to be at less temperature than that of vapor. This vapor is entering the bubble vapor is entering the plate through the small holes at the bottom of the plate and this hole size will decide what is the diameter of this vapor bubble alright. So, there are several bubbles which will come through this liquid and the heat transfer between this vapor which is at higher temperature as compared to that of liquid will decide what is going to be the efficiency of this column alright. So, the vapor is at high temperature as compared to that of the liquid. When the vapor bubbles to the liquid layer the high temperature vapor transfer heat to the liquid. Naturally, there is a heat transfer from the high temperature vapor to the low temperature liquid. Now, this vapor comprises of nitrogen and oxygen vapors both combined together at the same time the liquid also is going to be comprising of nitrogen and oxygen molar fraction depending on the mole composition of this liquid at a particular plate and the mole fraction of the vapor below a particular plate. So, what is going to happen because of the heat transfer between the vapor and the liquid what is going to happen the heat transfer from the vapor bubble results in condensation of a little bit of a high boiling component which is oxygen from the bubble. As soon as this vapor gives some amount of heat to the liquid the part of the high boiling component which is oxygen will get condensed because it is a high boiling component as soon as the heat is given this part will condensed alright. At the same time whatever amount of heat transfer happens between the vapor and the liquid at this point the low boiling component in this liquid which is nitrogen is going to get evaporated. So, some part of the liquid which is reached in which is going to be low boiling component it will get evaporated while the high boiling component of the vapor is going to get condensed. So, condensation will happen of the high boiling component evaporation will happen of the liquid in the low boiling component. So, what is happening now the vapor which is going to leave this particular plate is going to be the nitrogen in the existing vapor plus whatever nitrogen got evaporated from the liquid. So, this vapor will get little bit enriched in the low boiling component or nitrogen when it will leave this plate while the liquid here will get richer in oxygen because this vapor got condensed over here and nitrogen has got evaporated from the liquid over here. So, the liquid at this plate is going to get enriched in high boiling component that is oxygen and this liquid will come down the next plate when its height increases beyond a particular wear height. So, this process will continue on every plate. So, essentially we have to understand that all this condensation evaporation activities basically depend on the temperature across the column basically. So, also the heat exchange causes an evaporation of a little bit of low boiling component from the bulk liquid which is what I just explained. And this is what is going to get continued across the entire column. So, success of all this column or the efficiency of this column basically depends on the efficient heat transfer between this vapor and liquid. And therefore, design of each plate is very very critical design of the hole which is at the bottom of the plate which decide this bubble size is also going to be very very critical. Thus as the vapor bubble moves up it becomes richer and richer in low boiling component that is nitrogen in this case. And as the liquid moves down it gets richer and richer in high boiling component which is oxygen in this case. Now, in an ideal rectification column the vapor and the liquid are in thermal equilibrium that is what we just talked about earlier. We showed that a thermal equilibrium basically vapor and the liquid on the same plate will have same temperature alright. Ideally this is going to be possible, but in actual condition in actual rectification column the vapor does not leave the plate at the same temperature of that of liquid. So, in actual case now there will be temperature difference because the heat transfer between the vapor and the liquid will not be that efficient. It will have some limitation it will have some efficiency associated with it. And therefore, the vapor is not going to have the liquid same temperature of the liquid from which it gets evaporated. There will be some delta T across it and the vapor leaving the liquid will be having some higher temperature than that of liquid. So, this is now we are talking about the real rectification column. Up till now we talked about the ideal rectification column and now let us see what are the realities in a real rectification column. So, to ensure the required heat exchange more number of plates are required than the theoretical prediction. In a theoretical prediction we will assume that the heat transfer is perfect. The molar composition remains the same after condensation or the temperature of the vapor which is leaving the plate is the same. But based on this assumption I will calculate the number of plates required in a rectification column. But in reality these conditions cannot be fulfilled. The temperature may not be remaining the same. The composition may not remain the same. And therefore, the actual number of plates that I would require in a column is going to be more than ideally calculated one. And this is basically now shows or indicate the efficiency of the column. Hence, there is a need to study the efficiency of an actual system with respect to the ideal system. This is a very important thing. So, the real rectification column let us see what happens in one plate and let us see where the inefficiency comes into picture. Let the mixture of nitrogen and oxygen at one atmosphere be subjected to rectification. Consider a jth plate which is let us say this plate of the rectification column as shown in the figure. Across this plate the vapor mixture rises and the liquid mixture flows down alright. The vapor mixture is going up the liquid is cool it down ok. Now for this jth plate let yj minus 1 is the mole fraction of the low boiling component in vapor phase rising to the jth plate. So, this is the jth plate and yj minus 1 gives the molar composition of the vapor which is passing through this jth plate. So, this is a vapor plate. This is the vapor condition of yj minus 1. So, corresponding to this the composition of the low boiling component that is nitrogen is going to yj minus 1 which is entering through this plate through this jth plate. The composition of the liquid at this plate is given by xj. Now ideally the composition of the liquid at this point would have been xj would have been this much is not it. Because we say the molar composition remain the same, but no in actual case the molar composition is going to be of this liquid in this plate in the jth plate is going to be this it is going to be xj and not yj minus 1 alright. And therefore, this is a very essential that you are going away from ideality when we said earlier that during the phase transformation the molar composition remain the same. But no actual molar composition will not remain the same because all the vapor will not get condensed here only part of that will get condensed over here. And therefore, composition of the liquid in this plate above this vapor is going to be given by this xj parameter. Now from this jth plate vapor will leave and we had said that this vapor and this liquid will be at in thermal equilibrium alright. So, the vapor which is leaving this plate jth plate should be in thermal equilibrium and should be given by its composition which could be given by yoj which is yoj. So, in thermal equilibrium the mole fraction of the liquid low boiling component in a vapor place leaving the jth plate is given by yoj. But no again this condition is an ideal condition that the liquid is at this condition the vapor which is leaving this condition is not going to be at same temperature, but it is going to be at somewhere higher than this. Therefore, real yj which is leaving the jth plate is going to be at a higher temperature. But due to the non ideality of the mole fraction of the low boiling component vapor phase leaving the jth plate is going to be yj and this is my yj. So, what has happened in one plate condition? In one plate vapor enter the plate at yj minus 1 and when the vapor left the next plate it left at yj, but they should have actually late at yj0. So, actual change the vapor got reached in low boiling component from yj minus 1 to yj which is actual change while the ideally it should have left at yj0 and this is what is going to basically give the efficiency of this particular plate. Hence, the maximum possible and the actual change in the mole fractions are what were the maximum possible changes from this to this yo0 minus yj minus 1, but actual one is yj minus yj minus 1. Why did not this actual composition did not change? In a maximum possible composition change why did not it occur? It did not occur because the molar composition did not remain the same at the same time the vapor was not in thermal equilibrium with the plate on the same plate, the liquid on the same plate and therefore, we had all these changes that happened and this will determine the efficiency of the plate. So, what we have got a term called Merff free efficiency. The Merff free efficiency of a plate is defined as the ratio of actual change in mole fraction to the maximum possible change that can occur. So, actual change in mole fraction is going to be mathematically is going to be yj minus yj minus 1. This is yj minus yj minus 1 is actual molar transformation that took place when across a plate divided by maximum possible mole fraction change which is yoj minus yj minus 1. So, this is basically going to decide how much away from ideality one plate can go when the molar composition and a temperature can change. So, the heat and mass transfer why this is happening? What is important for this? Therefore, in order to a very high Merff free efficiency the heat and mass transfer between the vapor and the liquid. The heat and mass transfer analysis between the vapor and the bulk fluid is important. And therefore, it is very important to understand the heat and mass transfer between this vapor and the liquid to understand this physics what is happening inside every plate or every liquid and vapor interaction. So, in order to understand in order to achieve high Merff free efficiency the following conditions are required. Lot of analysis have gone into this lot of work has gone into it. The conclusions are if you want to have very high Merff free efficiency following condition should be made which will ensure very good heat and mass transfer between the vapor and the bulk fluid. So, what do they want? Small bubbles long time of contact to ensure good heat transfer and large value of overall mass and heat and mass transfer coefficient and this is what we know basically. The small bubble will ensure good heat transfer number of bubbles now will be very important. The long time of contact will ensure that the vapor and the liquid are having good heat transfer for a longer time longer duration which will ensure good heat transfer. The larger value of overall heat and mass transfer coefficient will ensure good heat transfer between the vapor and the liquid. So, all these components are basically known in order to achieve the good heat and mass transfer between the vapor and the liquid. With this background I would now like to solve a small tutorial so that you understand the concept of Merff free efficiency. So, let us come to a small tutorial. This tutorial is to calculate the Merff free efficiency of a given plate. So, consider a mixture of nitrogen and oxygen at one atmosphere which is entering the plate which is entering a column. Calculate the Merff free efficiency for a plate with liquid at 80 Kelvin. The liquid is going to be at less temperature than at vapor. So, liquid at 80 Kelvin and the vapor below this plate is at 85 Kelvin. So, what is happening? The vapor is entering the plate at 85 Kelvin and once the phase transformation of the liquid above it has a 80 Kelvin temperature. There will be heat transfer between this vapor and the liquid and ultimately the vapor will live at a temperature actually somewhere between 80 and 85 Kelvin depending on the heat and mass transfer between the vapor and the liquid. So, what we have to do is calculate the Merff free efficiency for this plate. Also it is given that the mole fraction of nitrogen leaving this plate in vapor phase is 0.84. This is the data which is given. Use the temperature composition diagram given in the earlier lecture. So, what is given? The working pressure is one atmosphere, the mixture is nitrogen and oxygen, liquid temperature is 80 Kelvin, vapor temperature is 85 Kelvin and yn2 which is ultimately leaving the plate above is at 0.84. Molar composition of the low boiling component is 0.84. Calculate the Merff free efficiency. This is the diagram which is known to us. So, what is known to us is for the age of understanding the temperature composition diagram temp T by diagram is enlarged and it is not to the scale. So, what is happening is the liquid temperature is 80 Kelvin which is drawn horizontal line. The vapor is entering at 85 Kelvin draw a horizontal line. These 2 temperatures are known and they are given in a problem, alright. What is known is if I draw horizontal line wherever it intersects the vapor line is going to give me yj minus 1 that is a molar composition of the vapor which is going up the plate. So, corresponding to this for oxygen nitrogen I get yj minus 1 is a molar composition of the vapor which enters the plate through the holes. So, it is 0.5 corresponding to this should have been ideal point composition, but no actually temperature is 80 Kelvin and therefore, wherever it intersects the liquid line it is going to be xj. So, xj is going to be 0.6 and corresponding to this normally vapor would have been in thermal equilibrium with this liquid. If you see earlier definition of murphy efficiency this interaction this intersection with the vapor curve is going to be y oj minus 1 that is when the vapor is in thermal equilibrium with the liquid on the same plate. So, y oj minus 1 is going to be 0.85 as given over here, alright. So, I know yj minus 1 I know y oj. Now, actual case is going to be 0.8 because I have been told that the vapor which leaves the plate is going to be at 0.8 the molar composition of the low boiling component is 0.8. So, if I draw a vertical line from here it intersect vapor line at this point and corresponding to this the temperature is 81 Kelvin. What does it mean? The vapor is not at 80 Kelvin, but it is at higher temperature of 81 Kelvin at this point. That means, actual molar change has happened on the low boiling component is this much this is yj value corresponding to this yj what you got is a 0.84 Kelvin, alright. So, what you get from here is a actual change in the molar composition divided by maximum possible change in the molar composition is going to be this. So, this is the data which is given 0.84 Kelvin if I draw a vertical line. Therefore, I can calculate murphy efficiency as actual change in molar composition divided by maximum possible change in the molar composition. So, 1 atmosphere yj minus 1 is 0.5, xj is 0.6, yoj is 0.85 and yj is 0.84 at 81 Kelvin. If I put this I get 97 percent as a murphy efficiency alright. So, this is a simple problem to understand what exactly happened on one plate. Based on this I would like to give a small assignment kindly go through the assignment we have given the answers also for the calculations the efficiency comes to be around 84.3 percent. This is what we have studied here just to summarize what we did. Isotherms or enthalpy composition diagrams have finite slope indicating that the condensation of boiling of a mixture is a non-isothermal process. The separation is more effective when the difference in the boiling point is more. In a rectification column a saturated vapor or saturated liquid or liquid plus vapor mixture is introduced as feed. Murphy efficiency of a plate is defined as a ratio of actual change in mole fraction to the maximum possible change that can occur. In order to achieve high murphy efficiency we should ensure good heat transfer the conditions are small bubbles long time of contact between the vapor and the liquid large value of overall mass and heat transfer coefficient. Thank you very much.