 Now, the other kind of systems what are known as the wide boiling systems, wide boiling systems temperature drops are substantial from top of the column to the bottom of the column. Crude column simulation is a good example of a wide boiling system because you have the lightest material present in the in the form of methane and you will have hydrocarbons as heavy as C 40, C 50, C 55. So, it is a wide boiling system. Now, in wide boiling system these enthalpy is changed significantly because the constituents are changing significantly and therefore, delinking temperature profile may not be a good idea. The same applies to non-ideal systems ethanol water system. There is tremendous interaction of the energy balance with the material balance because the heat of mixing effects or volume change of mixing effects non-ideal effects are significant. So, a method which may work very well for a simple propane propylene column the same numerical technique may fail for wide boiling system or for a non-ideal system. In fact, for non-ideal systems the literature will tell you that the simultaneous approach where all the equations are solved simultaneously is the best way to solve the distillation problem. So, there is a popular algorithm on which there have been lot of variants in last 30, 35 years. The algorithm was published in 1971 in A I C H E journal and it is due to Naphthili and Sandholm. These are the two authors Naphthili and Sandholm. It is popularly known as Naphthili Sandholm. So, what they did? They presented this mesh equations with some modifications in a form that total number of equations were not n times 2 C plus 3 rather it was reduced to n times 2 C plus 1 by simply embedding the summation equations along with the component balances and rather than working with x i's and y i's they defined their unknown variables as component flow rates. So, L multiplied by x becomes the component flow rate. So, they cut down the number of equations by 2 on every stage and then the whole set of equations which is n times 2 C plus 1 is solved by Newton-Raphson technique simultaneously. So, that was a turning point in the theory of distillation. The mesh system could be solved very successfully, but the moment you talk about simultaneous solution let us not forget about one thing that if you have 100 trace in the column and 10 components. So, even for Naphthili Sandholm 10 will give you 21 equations, 10 components will give you 21 equations, 100 trace in the column. So, that will give you 2100 equations. So, you have to solve 2100 non-linear algebraic equations simultaneously in addition to the effort you have spent to calculate the thermodynamic functions. These equations assume the k value is known, the enthalpy is known. So, thermo also has to be put into the system. So, in earlier days when the computer memories were limited simultaneous solution was something very difficult to do. It used to be very time consuming exercise, but today memories are not limited. You configure machines with 2 gigabyte memory and 4 gigabyte memory and therefore, 2300 is nothing, you can even solve 10,000 equations simultaneously. So, simultaneous solution is what we look forward to today, but as I said that the thermodynamics handling could be very tricky. So, therefore, you cannot apply directly the Naphthili Sandholm technique or the Newton-Raphson method and you have to have better numerical techniques developed. So, that the physics of the process is preserved, the iterations do not go into infeasible zone and you are still solving the system simultaneously. So, there is guarantee for convergence or at least the probability of convergence is very large. So, what are the limitations of this equilibrium stage model? In general vapor and liquid streams leaving a stage are not in equilibrium. We know that and we have been saying that equilibrium is there because the residence time is not sufficient for equilibrium to attain. Of course, it all depends upon how good is your internal, how good is the contacting device. In actual practice, one problem which is always experienced is that vapor velocities when they are significantly high and columns when they operate at low pressures, the velocities could be fairly large. There is entrainment of liquid, liquid droplets get entrained with vapor and that affects the mass transfer, that affects the efficiency. So, there will not be equilibrium. So, one way is that you bring in the tray efficiencies into picture and handle that part of the operating problem. Now, comes the question that we can bring in efficiency, but how do we define efficiency? Well, there are various ways people have tried defining efficiencies. There is a point efficiency, there is a mercury efficiency, local efficiency, there is a stage efficiency, there is a column efficiency. The fact remains that efficiency is something which is not only tray dependent, it is not only location dependent, it also depends upon the component. On the same tray, if you have nitrogen sitting with benzene and toluene, so benzene versus toluene, there will be a different efficiency. Nitrogen versus benzene, there will be a different efficiency because efficiency is something which is related with the escape tendency. So efficiency, if we represent that as eta, let us say eta ij, it is a function of j anyway, it depends upon the location of the tray because temperatures are different, pressures are different. It is also a function of i, the component. So, if I have a 100 tray column and if I have 10 components, then how many efficiencies do I have? I have 1000 efficiencies. On every tray, I have 10 efficiencies. How do I get all those numbers? It is not possible. So, you go for tray efficiency. You say on the given tray, all components have same efficiency. That also is not true. And within the tray also, we know that the height of the liquid on the wear side is lower than the height of the liquid on the other side of the wall because there is a gradient. And therefore, the efficiencies are different because the bubbles are bubbling through. The time spent is different for different bubbles. You are very right. Mesh equations are not taking into account. And therefore, if I solve mesh system, I am not getting what the industry shows or what the actual column shows. So, there is error. So, there is a mismatch between the simulated results and the actual results. So, one way to now come closer is that I see what is happening in an actual plant. In an actual plant, there is entrainment and there is no theoretical stage concept there. It is an actual tray. So, how do I do that? So, I take the mesh system and I bring in the concept of efficiency. So, question comes that what is the efficiency you would like to use? So, if you look into the simulators, you will find that they have made provision for what is known as a column efficiency, a tray efficiency, mercury efficiency, so on and so forth. It is up to the user to decide which efficiency works best for you. So, there is tremendous amount of uncertainty which is there in the prediction of efficiency. It is a handle given to you to match the performance, but how to use that handle that is not clear. Column efficiency, you are simply saying that every tray let us say if it is 80 percent efficient, then if I have 100 theoretical stages, then actual number of stages is simply 100 divided by 0.8. What I am saying is that every tray cannot be equally efficient because tray below the feed are handling primarily heavier compounds, tray above the feed are handling primarily lighter compounds that is right. Even in rectification zone depends you know if you have close boiling systems, then efficiencies are very good. If you distill propane, propylene using valve trays you may say 85 percent efficiency will be attained, but in benzene toluene column, if benzene toluene we are talking about efficiency will be very good 80 to 110 degrees 30 degrees not too much of a gap, but because benzene columns operate with nitrogen blanketing due to safety reasons due to pressure control requirements. So, nitrogen blanketing is done. So, at the top of the column nitrogen is present with benzene. Now, nitrogen efficiency is very different as compared to benzene and toluene efficiency because nitrogen will be present in distillate in very small amounts. And if it is not acceptable, then what you do is you do not take the top product as your product, you withdraw your product from second or third tray, pasteurization column as it is called. Yes, the efficiencies depend upon the chemical system itself. For the same tray, if I was using that column to separate ethane ethylene and another column same tray propane propylene because the operating conditions are different because the species are different, the efficiency of the trays will be different. So, efficiency depends upon the chemical system, it depends upon the temperature, it depends upon the pressure. And because it depends upon the chemical system, it is location dependent. Top of the column will have different efficiency, bottom of the column will have different efficiency. So, that is what it says that uncertain quantities like efficiency, HETP are used to correct for the departure from composition equilibrium because we have no other way out. This is the only way out, we do it. Component efficiency is very widely on a stage and from stage to stage. I have already explained this to you and there is no unique definition of efficiency. So, this remains a fuzzy area, it is a hazy area, you know it is not very well understood. Efficiency, HETP cannot correctly account for departures from temperature equilibrium. I have already mentioned that inability to account for the interaction effects between simultaneously diffusing species. This is another deficiency, not applicable to chemically reactive systems. Of course, we have not talked about the reactive systems at all here because we have only focused attention on mesh system. Mesh system purely takes physical process, vapor and liquid in equilibrium. We have not gone for reactions. In actual columns, not in all columns, but quite a few columns always there are some reactions occurring. Refinery columns this is a big problem at the temperature at which the column is operating 300 plus degree Celsius, certain amount of cracking occurs inside. Thermal cracking is occurring and that is not there in the mesh model because we have not made any provision for the reaction. Sometimes polymerization reactions occur and of course, this model has no provision for anything to be predicted, everything all data should be known externally. So, there is another approach to modeling and simulation of distillation systems which is known as the rate based approach. So, let me spend a few minutes on rate based approach. Rate based approach is well suited when you have packings as contacting devices because with packings, HETP is a very approximate approach. Mesh system works fairly well with efficiency is incorporated when you have tray columns, but when you have packed columns the HETP approach is very approximate and therefore, you require better modeling tools. So, we go for rate based approach. In this particular approach, we do not assume that there is equilibrium. You take the segment of the packing. We can always make HETP equivalent to a stage and we can say that vapor leaving the stage is in equilibrium with the liquid leaving the stage, but we know that in packing the mass transfer is occurring continuously. Liquid and vapor they are in flow in a continuous manner and therefore, we never will talk about liquid leaving the tray and vapor leaving the tray that kind of term and there is no concept of equilibrium. The only assumption which is made here is everything is governed by heat and mass transfer which means the area, the interfacial area which is available to achieve the heat and mass transfer. And at the interface, at the interface there is instant equilibrium because there are no resistances that is the only assumption which is made. So, this is a depiction of the rate based approach the way it is modeled. So, you have a lump or mass of vapor which is travelling and you have another lump or mass of liquid which is travelling in this direction. There is mass transfer. Now, when I say arrow is on this side, this is just a convention again for the net mass transfer. We know that distillation is a counter current heat and mass transfer operation. It is not unidirectional. You know you are having mass transfer as well as heat transfer in both the directions. But again you have to have a convention. So, this is just a convention that this arrow represents net mass transfer. So, there is mass transfer in this direction also and you have energy transfer. So, this is the interface which is shown like curved line. On this interface we can apply the two film theory of mass transfer. So, this is the interface in here this one magnified and two film theory. So, we are saying that there is a thin vapor film in which most of the resistance on the vapor side resides and a thin liquid film in which most of the resistance on the liquid side resides. So, all the concentration gradients they are contained concentration gradient as well as the thermal gradient the temperature gradient they are contained within the film. Now, temperature as you can see it has a point of continuity whereas, the composition has a point of discontinuity. Why do you think there is discontinuity here? Because that is where y equal to k x is applicable. No, here we have gone from vapor phase to the liquid phase. Now, in this approach again my presentation here is rather qualitative I am not going to write the equations again just to tell you how it is done. The mass and energy transfer rates depend on concentration and temperature driving forces which is expected. Of course, liquid and vapor flows play their role and all sort of fluid properties will now come into picture because the mass transfer and heat transfer coefficients need to be calculated. In equilibrium approach we never asked for any property only equilibrium constant the thermodynamics support is what we were asking. Now, here we are going beyond that thermodynamics alone is not sufficient you need other properties. And of course, the calculations are very much functions of the contacting device what is the kind of contacting device you have. Because the interfacial area, area creation for heat and mass transfer depends upon what contacting device you have. So, we are not talking about a stage now we are talking about a segment a segment of a contacting device or you can call that as a segment of a packing a small section of a packing. And we know that it is no more in equilibrium it is a non-equilibrium. So, concept of a non-equilibrium segment. Non-equilibrium segment refers to a tray or a section of packing of specified height we are just deciding 10 centimeter 20 centimeters. It is just like when you want to integrate a differential equation you take a finite step. If the step is small enough it is good because it takes care of the definition of the differential very well. If it is large then that definition will be violated. When the steps are large number of integrations calculations are less. So, there is inaccuracy in the final result. When the steps are very small the round off and truncation errors may dominate and still you may not get the right results. So, you need to decide what is a good number of steps. Like if you integrate an equation using Euler's method or Nangekata method we have to decide whether 100 steps are to be taken or 1000. If somebody says take 10000 larger the number of steps not necessarily that the answer is right because the round off and truncation errors may dominate. So, similarly here if I take small small segments I will be doing too many calculations and if my variables do not show sufficient change in that segment the numerical errors may dominate and I may get erroneous results. If I take two larger segments then I will be approximating properties in that particular segment and therefore, I will be introducing error otherwise and therefore, we have to have a judicious choice of how many segments. It has been observed that for conventional columns conventional packed columns any number between 20 to 40 sometimes maximum 50 gives you reasonable results. So, that is the meaning of segment we are talking about. A packed column or a tray column can be considered to consist of sequence of such segments now. So, we are making segments and let us see what the treatment is. So, we again go and write M equations. We have to write 6 equations here and these are popularly known as MERSC equations. So, M equations which represent the component material balances. These acronyms have been or abbreviations have been written in such a way so that the end user can easily remember these terms there is nothing special about this you know. So, they represent material balances. E equation unlike in our mesh system where E represented equilibrium E here represents the energy balance on the segment. Our equations represent mass and heat transfer rate equations because it is a rate based approach. So, the mass transfer coefficient and the heat transfer coefficients will come into picture the interfacial area will come into picture the driving forces will come into picture. Then H equations represent the hydraulic equations or the pressure drop. So, momentum balance is built in into the system. In distillation basically it is a discretization approach you are moving from one tray to another tray and we said we can load the profile. In a packed column loading a pressure profile is not that easy if it is linear profile you can load it. You can define at the top you can define at the bottom and you can join it by a straight line, but if it is a non-linear profile how will you load a profile pressure profile in the column? It will be infinite number of points and therefore, it makes sense to embed the momentum balance along with other equations. We did not do that in the mesh system. H equation represent hydraulic equation for pressure drop and Q represent the equilibrium which is only prevailing at the interface. One element is missing here which is the S. S again is the summation equation. So, basically you write all these equations and for the segments you collate all these equations. These equations again will be algebraic non-linear set of equations and you solve these equations to get your final solutions. One very popular software which is available by a separate license unfortunately we do not have it here in IIT is ratefrag. Ratefrag comes as part of Aspen Tech technology. If it has then you can try I think the rate based approach will not work because that comes as a separate ok. So, Merch equations. So, what are the advantages? The advantages are that now that we have integrated or we have taken small segments just like you take differential segments in integration. So, do we require efficiencies? The answer is no. There is no question of efficiency because you are moving with the height of the packing alright. So, we do not require efficiency that is the biggest advantage. So, that is a that is a gain that is a plus point, but then the question will be then how come we do not use it very frequently. Well, we have solved one problem, but we have created another problem. What is the problem we have created? It requires tremendous amount of properties and it requires good correlations for heat and mass transfer and we know that the theory of heat and mass transfer itself uses empirical formulae. So, how good is the mass transfer coefficient? How good is the heat transfer coefficient? Ultimately we will decide how good is the solution through the Merch equations. So, that is the problem we have added, but if you are confident for your system that you have very good mass transfer coefficients, you have very good heat transfer coefficient, the Merch system will work very well. So, uncertain factors such as efficiency, HTTP are avoided, predicts departure from temperature equilibrium which is the actual case in practice. We say vapor liquid equilibrium is there. So, the first condition for vapor liquid equilibrium is the thermal equilibrium. So, vapor leaving the system is in having the same temperature as liquid leaving the system, but if you took actual column and if you put the temperature probes and measured the temperatures, you will find that the vapor temperature is always different from the liquid temperature. Temperatures are never the same. Why? Because there is no thermal equilibrium. Here we are not saying that. So, we are closer to the actual situation. Of course, it predicts accurate composition, temperature and flow profiles. It is a rigorous method. Accounts for interaction between diffusing components. So, we do not worry about efficiencies being different from different constituents because the diffusivities would have taken care of the efficiency part. Influence of reactions are handled correctly. You can put the reactive system if you wish. In my model, I have not shown you the reactions and it is predictive because once you have the correlations for a component for which you did not have data, you can predict the mass transfer coefficients, predict the heat transfer coefficients. Let us now spend few minutes trying to understand that when we were configuring columns either through mesh equation or through mesh equation because those two are approaches to do the model building. When it comes to solution strategy, we have to make sure that the degree of freedom analysis is right. Degree of freedom analysis means that I have number of equations and I have number of unknowns and I will be able to solve that system only if number of unknowns is exactly equal to number of equations which is known as the deterministic system. If I have more number of variables than the number of equations, what kind of system is that? Number of variables are more and number of equations are less. That is called an under defined system. An under defined system is a system in which number of variables are more and number of equations are less. All the configurations which I showed you with mesh equations or with mesh equations, this will fall under the category of under defined system. If I sit down and count the number of equations for mesh, I have already done it for you. I said n times 2 c plus 3, I did not do the count and the number of variables, you will find that number of variables are always more than the number of equations. So, this formulation gives us an under defined system. On the other hand, if there was a system in which number of equations are more and number of variables are less, that will be called as an over defined system. In modeling and simulation, we never encounter when we do mathematical modeling from the basic principles like these models are called transport phenomena based models. So, we are using basic principles. Normally, you get under defined systems. You do not get over defined systems. Over defined systems you get or you come across when you do statistical modeling, regression, data fitting. Here, we will get under defined systems. Now, if I have under defined system, which means there are degrees of freedom. There are some decisions which I have to take before the system becomes deterministic. Only then, I will be able to solve that system. So, that is what it means. What are the common specifications which I need to make? So, there are some guidelines we need to understand. We have written mesh system for a column where the stages were labeled from 1 to n. It implies that the number of stages are given, because we are not calculating number of stages. We are saying number of stages are given. So, n is given. Unlike Fenske-Underwood-Gilliland, we said we can fix the reflux ratio and calculate number of stages. No. Here, in regress model, number of stages are given and we are doing performance evaluation. So, it is a strictly simulation problem. It is not a design problem. I am not designing the column. I have to configure a column. Number of stages are given and now I have to do the performance evaluation of that column. The answer is, the answer should tell me how this column is going to behave. So, number of stages are given. Now, if it is a simulation problem, I had mentioned this to you yesterday that the feeds are to be fully characterized. All the feeds are to be fully characterized. And therefore, for each feed, the flow rate, the composition, the temperature and pressure. So, this is required minimum and this you can satisfy the GIFS phase rule. The GIFS phase rule will tell you how much you need to specify, so that all the calculations can then be done in a deterministic way. When I say all the calculation means if flow rate, composition, temperature and pressure are given, I can calculate the quality of the feed. I can calculate the enthalpy of the feed. I can calculate the total entropy flow. Everything I can calculate. Now, talking about how the feed relates to the structure of the distillation system, I need to define the feed location or the stage entry location. That also is to be given. We are not calculating. I have to say I have 20 stages and feed is on tray number 9 or tray number 11. So, I am spelling out. For each product, for each product, now this includes top product, bottom product and all other products, the stage removal location is to be known. So, if I top the term itself says it is coming from the top. So, I do not have to specify anything more than that. Bottoms means it is coming from the bottom, but the moment I say is liquid side draw, I need to specify from which particular tray I am removing that side draw. If it is a vapour side draw, I need to give the location of the vapour side draw. So, what it means that I must specify the stage removal location. For each intermediate heat exchanger, intermediate means condenser and reboiler not included. Condenser is top, reboiler is bottom. Any other exchanger is intermediate. The stage location has to be specified. Even for pump around, we have to specify the location. If it was a pump around, there also we have to specify the location. Yeah, but then that is not coming back to the column no. See once vapour is taken out, condenser becomes an external piece of equipment. That is no more interacting with. That is right. So, you may be condensing before sending it to storage. So, that condenser is not part of distillation. If you are returning, then that heat transfer is part of distillation calculation. Now, if you did that, it turns out that still the system remains under defined. This anyway we have to do, which I have written on the earlier slide. System still remains under defined. Now, unfortunately, we do not have time. Otherwise, I would have taken you through calculation of the variables and calculation of the equations and we could arrive at a very interesting result. The result is like this that for a given column, given column means number of trays are given, whose feed is specified and I said feed should be specified, whose pressure profile is known, pressure profile is loaded. So, it is known, whose configuration is given. So, let us say if it is a conventional column, conventional column will have one condenser at the top and one reboiler at the bottom. There are no side draws, no side liquid drawl or no side vapor withdrawal. The degree of freedom is 2 for a conventional column or one way to remember is that the degree of freedom is equal to the number of heat exchangers on the column. So, if there is a condenser and there is a reboiler, the degree of freedom is 2. Had it been stripper, what is the degree of freedom? Stripper, steam stripper, steam driven stripper or absorption column, let us say an absorption column. What is the degree of freedom? In both the cases, the degree of freedom is 0. For stripper also it is 0, for absorption column also it is 0. What it means that for absorption column, the vapor coming from bottom is known because that is a feed to the column, the liquid coming from top is known and that is also feed to the column. The number of stages are given, the pressure profile is loaded. So, you have no handle left. The column will have some performance which is deterministic and mesh equation will solve it, mesh system will solve it. But if I replace stripper by a reboiled stripper, then degree of freedom will be 1 because I have added one heat exchanger. So, I need to specify at least one more variable before the system becomes deterministic. So, that is the interpretation of the term degree of freedom. So, what we are saying here one for each product or end heat exchanger. Now, if you have a conventional column, so I am counting the end heat exchangers, so degree of freedom is 2. But suppose somebody said that I am taking a withdrawal from in between. So, there is one more degree of freedom and what is that question? The question is how much are you withdrawing? The flow rate, that could be one question or somebody can say that flow rate is a floating variable you calculate for me, but that particular stream should contain 80 percent benzene. So, that is also is one more specification. The freedom is with you, you can decide what you want to specify, but the degree of freedom analysis has to be satisfied, is this clear? So, one for each intermediate heat exchanger, one for thermal condition of each product and if not saturated, if it is sub cooled that also we have to worry about. Now, what is the interpretation of this? The interpretation of this is that whatever model we have written for mesh system, we have assumed that the liquid which is returned by the condenser at the top is at its bubble point because it was internal reflux. All internal refluxes are at their respective bubble points, but in actual practice the reflux is never at its bubble point because it comes from the discharge of a pump. So, it is a sub cooled liquid, it is 4 or 5 degrees below the bubble point and you do not want bubble point liquid to be taken through the pump due to cavitation problems. So, it is intentionally kept as a sub cooled liquid. So, then the question comes that what is the degree of sub cooling? So, that becomes an additional degree of freedom. Is this clear what I have said? So, one way to count the degree of freedom is make a conventional column with one exchanger at the top, one exchanger at the bottom condenser and reboiler and say the degree of freedom is 2 because those are end exchangers. Then for every heat exchanger in between one additional degree of freedom, for every product withdrawn there is an additional degree of freedom and you have to satisfy that many degrees otherwise you will not be able to solve the system. Now, fortunately in commercial simulators the graphics user interface which you use, they are intelligent graphics user interfaces. So, they will catch you like they will expect you to go on clicking till the degree of freedom is satisfied. So, you do not have to really exercise from your end, the software does it for you. The movement degree of freedom is satisfied, the menu will become gray and it will not allow you to exercise any more option, it will say that too many specifications you are trying to give. I have mentioned something about the wide boiling system and as I said that refinery processes when they deal with distillation of crude etcetera, these are really wide boiling systems. So, refinery processes are relatively more difficult to converge using these mesh systems as compared to close boiling systems. There are some other differences which exist in refining processes due to which you need to carry out more modifications to your mathematical model and one difference which I think I have already mentioned to some extent is that typically water is present in refinery columns because of steam stripping which is carried out and then this water gets condensed in the condenser. So, the reflux drum which is attached to the condenser by and large has a three phase system. In our mesh system we did not make that provision, though I mentioned to you that I can add that additional feature and use the same set of equations. So, a refinery column should have facility for a three phase calculation to decant free water from the reflux drum. Not only that it has pump amounts which you can approximate by stage heat exchangers, but strictly not that also I mentioned and you also have side strippers and we have not looked at side strippers at all. So, actually refinery columns are interlinked distillation columns. You have a main column and then you have tiny tiny side strippers which are again columns because strippers are also columns. So, stripper will have its own mesh system and then that mesh system has to integrate with the mesh system of the main column. And in addition to that the material which you are handling inside the column the crude itself is a continuous boiling system and its characterization needs to be done. It is not a pure component system I cannot say there are 10 components 15 components. I need to characterize that and for characterization there is a procedure unfortunately I do not have time to go through those slides I should have done that it will be there in your notes. So, maybe you can spend some time to go through. So, refinery columns because of these complexities are treated separately though internally the mesh approach is used, but you will find that different modules are there because those modules are catered specially for this application. So, like when we talk about Aspen when we are doing distillation other than refining radfrak will work very well. I am not saying radfrak cannot be used for refinery calculation it can be, but then they have given you an alternate module which is called Petrofrak which is dedicated to refinery columns because of some of the issues which I have mentioned here. And you will find same situation in many other simulators that for refinery applications separate modules are given, but in the background in either case you are solving either the mesh system or the merge system. Let me just show you some of these methods which have been developed for solution of mesh equations and there is a very nice guideline which is available in a book by Kister. The name of the book is distillation design was published in 1992. So the choice of model whether you are using a simultaneous solution using Newton-Raphson that is normally called as global Newton method. There are ways to handle thermodynamics separately from the solution of the distillation equations and a very popular algorithm due to Boston and Russell it is called inside out algorithm which you will find as the default algorithm in most of these simulators. Radfrak uses inside out and then there are many other algorithms which will appear on the next slide. The decision depends upon the chemical system not on the configuration, it depends upon the chemical system. That is why in the beginning if you recall I mentioned that if I have close boiling system the algorithm may work there and it may fail on the wide boiling system. So it is a chemical system which defines which particular algorithm you should be using. So we ask this question that how ideal or how non-ideal is my chemical system. So answer could be that it is highly non-ideal moderately non-ideal. So if it is highly non-ideal I would assume that it something to do with those constituents where the activity coefficients are very large. So ethanol water I will put in this category it is a highly non-ideal system. Is it moderately non-ideal moderately non-ideal means that some non-ideality is there but it is not too large. So may be high pressure system but you are handling with equation of state. So gammas are greater than 1 or less than 1 but it is not very, deviation is not very large. Or idea are close to ideal benzene toluene falls in this category. Surprisingly ethyl benzene styrene system also falls in this category. You can use ideal behavior and you can get beautiful simulations done. Then the next question will be what is the boiling range? And of course as I said we normally divide into two parts here they have clubbed these two together. So narrow boiling or middle boiling and wide boiling. So the methods which work well for narrow boiling may not work that well for middle boiling or wide boiling. Then comes the question about the type of calculation. Here it says distillation here it says distillation and absorber and stripping because absorber and stripping are typically wide boiling systems. When we say I am absorbing acetone from air using water. So when I have air, air has oxygen, nitrogen and at the room temperature conditions they will remain non condensables cannot condense them alright. So basically gas liquid equilibrium comes into picture. So it is basically a wide boiling system. Then I am sorry the question will be about the configuration. So first priority is the question of the type of system and then second is the configuration. So do you have a simple column with few feeds, side draws and heat exchangers or a complex column? I have shown you examples of complex column also. Is the column short or column tall? Short means alphas are very large, tall means alphas are close to one, close boiling. So depending upon this type of characterization then recommendations are there whether you should use inside out algorithm or you should go for some other algorithm and you will find that in every simulator at least three, four different algorithms are made available. There will be a default algorithm but additional three, four algorithms will be there. So if default does not work the user can overwrite that option and choose a different algorithm to solve your mesh equations. The global Newton method which is the most popular method it works very well for all these type of applications distillation, chemical absorption, reactive mass transfer dependent which is your non equilibrium. Again short or tall if it is short column then there is a technique called the relaxation method that is used. If it is tall column then there is a method called homotopy continuation technique that is used. Aspen heises has these methods available if you are working with Aspen heises. In terms of trends today I think the modeling of most conventional columns of any type of configuration has been perfected and simulators very successfully are able to simulate. What is now being done is to expand the scope for simulation of more complicated cases such as azeotropic systems, extractive systems. Not that the present methods cannot do it but the probability of convergence is lower than what you get in conventional columns. So more and more stable numerical methods are being developed to address these questions. So in terms of emerging trends reactive distillation is one area where lot of focus is being given and this is the slide which I had shown you at the beginning yesterday and various aspects which are related with the theory of distillation. This part I have not touched.