 Okay, so you could have seen the title, diagonising the థిసాల్ల్ల్, okay. Now you are acting as if you are a doctor, doctor for equipment, okay. Doctor equip, right. Yeah so what we have done is, you have done or someone else has done, I think, you know they have brought this data, they have conducted RTD test, okay not converted the data into ET. not required in fact the shapes will not change only thing is you are normalizing by ET so that the area under the curve is equal to 1 so that any fraction you will find out from 0 to 1 1 2 2 2 3 4 to 5 you know all that fractions and to calculate corresponding conversions and all that that is different but see verses T data itself can be used to find out what is the problem with this particular equipment right like I found out from you what is the problem with you in the 1st class itself 0th class okay 0 test I gave the test and I saw the results then I know how much large we have so like that this also I think someone conducted and then he has brought and you are expert of now RTD and in the last class we have seen all the definitions and I know for ideal reactors what it should be you know the shapes and equations all that good okay so this one and as I told you also we have only two extremes one is mixed flow other one is plug flow so that means whatever equipment you have or whatever reactor you have if you are talking about reactors definitely you have only the two extremes one extreme we also know that we are very near to plug flow that means it must be only a long pipe with a small diameter like plug flow okay or it may be a tank where continuously things are coming and continuously going out that is normally we take it as mixed flow right so this data is okay this data are collected over this kind of you know long pipes that means supposed to be plug flow and then you got this kind of different shapes okay for different equipment all are all are plug flow are very near to plug flow so what is the 1st one I think you know if you look at this all these graphs you should be able to tell what is the disease like for example here what is this corresponding to it is almost like a PFR because we expect that actually ideal PFR will be a spike here there are delta function that is what is what you expect but in reality we know that there is no ideal plug flow anywhere in the world so that is why we will say that okay slight expansion because of axial mixing is fine so that is why this is almost near plug flow near PFR and also T bar and T bar observed so T bar is volume by volumetric flow rate and T bar observed is what observed means you experimentally calculated T bar how do you calculate experimentally observed T bar Swami how do you calculate me so that equation sigma T C delta T divided by C delta okay that is what you observed right so here both are same so it is okay I think behaving properly okay normal student okay good so this one next one next one we have T bar coming earlier sorry T bar observed coming earlier and T bar later and also it has long long tail think think Abdul he says channeling you have to convince him channeling because we have T observed what will happen if you have channeling first of all what do you mean by channeling what do you mean by channeling trace will come before the actual time where is it coming before T observed is coming before sir T observed is coming before the T bar that means the tracer is coming before it is time so there is channeling correct argument is right yeah those people who told that it is bypass normally now what is the condition condition is that we have very near to plug flow what do you mean by channeling what do you mean by channeling in a plug flow reactor it follows a separate path and it comes out sir like yeah so when you have separate path what will happen you should get to okay yeah and why I mean those people who have told that it is just why they are right is that if there is dead space what is T bar did I write wrongly or correct yeah what is how do you calculate T bar effective volume only what you have to take okay yeah and that is volume by volumetric flow rate and this one is T bar observed T bar observed is only from that right so what happens is that your when volume by volumetric flow rate volume by volumetric flow rate the actual volume is less right so I mean to give an example I have 10 liters but only 5 liters are active the other 5 liters are dead okay T bar observed will be less or T bar is less yeah that is why because you are thinking that outside 10 liters that is why you calculate 10 liters by volumetric flow rate as T bar but actually it is only 5 liters inside effective so that is why only that will reflect in the data right because you do not know how much is dead there so that is the reason why this is dead space okay yeah so then next one how can you have channeling so many channels you can have a recycle reactor or in you know packed beds and all that if the packing is not properly put right sometimes you know you use large packing and small packing and the voidage will be different somewhere you will have the recirculations and then they are moving somewhere and suddenly one recirculation will come that is corresponding to this one region okay and also L by D should be not very very long if L by D is very very long it may not be reflecting but normally even if L by D is sufficiently long you know it is like 8 days I do not know now you can see I think everywhere you have lot of water now particularly Andhra is underwater okay earlier I think last week we were underwater so if you go and stand on the bridge and then look at the river flowing you will have that big you know 8 days moving like that here also in the packed bed whenever you have large voidage is somewhere because of improper packing possible that improper packing so then it may be rotating there but suddenly at one point of time suddenly it will be thrown out that is what happens also if you look carefully at the bridge and then see it will be moving moving moving suddenly it will appear there and suddenly again something will come and then moving moving suddenly it appears somewhere there you know that 8 days I do not know that is why you should be in life you should be more observant than anything else I say and you can be observant only when you have brain you have brain but only thing is we are not using that is the problem okay so with all that observations we can say that this is re-circulation when you have so many peaks or if you take actual recycle reactor and then try to do RTD you will get exactly like this beautifully right because you are taking tracer some amount of you know it is a recycle you have injected tracer some amount and this is collected only in the outlet okay so before outlet you also sent back so some tracer will come back and again that is the second peak the first peak will come in the beginning then the second peak afterwards again it is you are continuously taking out and it is a plug flow almost ideal plug flow so you know what is the T bar there for one pass one pass right so like that you will have number of peaks coming because some small amount of tracer will be first thrown out that is the one it is not small amount I think initially more may come and then afterwards you are recycling continuously so some more tracer will come and afterwards again another small tracer will come another tracer like that you know it goes on dying down because you only put for by the way what is the input which you have given for all these experiments that you have to remember first because I did not tell that because it is continuously going and then staying constant at some point will be only step okay so that is why this is recirculation and this one this is channel yeah and this one this is actual mixing what do you mean by this actual mixing you see here T bar is somewhere yeah T bar is somewhere in hydrobot and this is in madras T bar observed in madras what is the meaning yeah it can be improper measurement of flow rates or volume that means wrongly okay yeah so and also another it may not be that much convincing for you but other thing is the most important thing in packed beds when you are using a tracer okay so particularly for gas phase reactions this tracer will go and get adsorbed on the particles that will come late actually this is called late curve correct now you expect around T bar it is not changing much the shape is as you said almost actual mixing but only thing is it is coming late yeah in fact we use in science and engineering this technique only for finding out separating out chemicals what is the name of that gas chromatic gas chromatic each each each gas has its own adsorption characteristics and also adsorbent you take and first SO2 you send depending on what adsorbent you put there SO2 will come late and O2 will come later like that you know different peaks depending on area of the peak we will find out what is the total amount of you know that particular chemical what you are measuring there okay so that is what this is good so this is MF for now all this is over now I think you know the moment you see this kind of graphs but T bar and T T bar and T is also very important for us and here I have not written T bar because T bar we can write here but T bar observed does not have any meaning with so many peaks where is the mean normally mean we say when you have one peak right yeah when you have so many peaks where is the mean so that is why we have not written but T bar would have been there somewhere okay good so this is MF for in MF for yeah this one is almost exponential yeah almost exponential car what is this I mean if you look at this what do you find out and T bar is also approximately equal to T bar observed so this is ideal almost ideal okay it is of ideal I say that near MF almost near MF okay this one sorry dead space okay dead space what do you say it is dead space I have not given T bar there or T there but you see this is a very clear trend dead space is will not give that kind of trend because the curve is starting late this again late curve yeah so that means there must be something which is giving the time delay time lag right so what you should have happened this is how largely we can conduct our experiments also will affect all how largely in the sense that if I have okay this is a small one reactor right and I have the feed pipe here and also feed pipe here so I introduce feed here I mean treasure not feed treasure this is V this is V and I measure here where I am supposed to measure where I am supposed to introduce here this is commonly done mistakes in when you are conducting R3 and in mixed flow very frequently this is done in plug flow you will have the same diameter okay throughout and you know where it is entering and then normally we do not miss that but in plug flow without knowing sorry in mixed flow without knowing what we can do is we can take this tank this length may be one feet here and also another foot there so two feet delay that is why this delay will come okay so what we have to write here is that long inlet and outlet pipes long inlet or outlet pipes so that means there must be some kind of plug flow in series with mixed flow okay P f with P f with mixed flow yeah okay good so what about this one several peaks but not the way very clearly like this because this may be you know very near to the stirrer it is moving and then throwing out and all that okay good this is recirculations okay recirculations near the particularly it is a tank where you will have recirculations most of the time near to the stirrer if it is loosely designed and most of the time we know how to loosely design this stirrer okay so that is why okay now next one T bar is earlier and T sorry T bar observed is earlier and T bar is later that you are experts and also this will go for long time this is dead space yeah next one next one is very very very late curve anyway I think this is difficult to find out this may be wrong V capital V or small V otherwise you do not get that kind of logic okay or non-inert tracer that means the tracer is going and sticking somewhere to the walls okay non-inert non-inert tracer I am not telling about reacting tracer okay non-inert tracer may be even tracer which is getting adsorbed on the walls walls of the equipment tank and also can be stirrer and then slowly it may come it may come whenever it wants very very good okay so next one this is a very short peak suddenly one peak comes and afterwards and that peak is almost at time T equal to zero bypass that is what is bypass very good nice so over I think this is the first section of RTD what we have done was I introduce you introduce you to RTD what is RTD what is non-ideal flow okay and then we have the definitions and most important thing is that this RTD can should be for each and every phase if I have two phase reactor I have to worry about both the phases you know when they are moving particularly which phase we are talking about is very important and for each phase you may have either plug flow or mixed flow one example merit where there is plug flow and mixed flow in the reactor there are two phases reverse question I am asking earlier we were asked okay in packet bed how many phases how they are moving now the reverse question give me an example of a reactor where I have a mixed flow and plug flow okay give me an example where there are two plug flows two phases in plug flow okay merit lost okay non merit people anyone is there yeah huh fluid is in bed both will be plug flow when do you say solids will be in plug flow moving bed okay fast fluid is in bed not fluid is fast fluid is in bed okay next question same thing plug flow with mixed flow huh yeah which is plug flow which is mixed flow huh solids are in bags what is the gas is in what bubbles are raising so we may say that and another beautiful example is bubble column reactor itself in bubble column you have gas and liquid liquid will be most of the time mixing continuously continuously you can put continuously you can normally L by D may be 2 times 3 times but still it will be in good mixing because bubbling the gas will be bubbling like anything that creates sufficient agitation and that creates sufficient mixing so that is example okay so all these things one has to do that good so that is what what we have done now and we understood what is the meaning of E T F T and also I T I T is only joining this for material balance and definitions and for ideal reactors also what is E T I T and all that we have drawn and then we have derived the equations right we have done a lot in the last class but now that is the first portion that means definitions for RTD okay including the definition of ideal reactors okay what is RTD for ideal PFR Abdul RTD for RTD for ideal PFR 0 okay what is the equation describing that if I have if I have E T E T for plug flow what is that you are always very very nice very very calm very very cool louder no this is required sometimes you have to shout because you know tomorrow you will have you are going to have your husband and also children and the first person we have to scold is only husband and of course wife also scolds a husband and husband scolds wife this is the first one and second children they cannot show anger on anyone they cannot show me on you or me or okay so they accept my wife otherwise cannot show yeah that is why sometimes you know you have to louder tell me a direct delta function okay what is equation direct delta function is name you have given equation quickly quickly time yeah E T equal to delta T minus T 0 where is T 0 T minus T bar because E T is exit age distribution function okay E T is exit age distribution function okay what is E theta for PFR high school mother okay show you what to do yeah yeah E theta equal to for PFR sorry for MFR ARIA ARIA also very common you are married or not married not married oh you have to practice that practice routing yeah E theta E theta for MFR mixed flow reactor yeah I think louder louder I say E 4 minus theta that is one of the simplest equation that is why I am asking you to remember otherwise I am not asking LFR I am a fair fellow okay LFR is again difficult right even though nice equation for E theta okay Ramakrishna difficult things for you E theta for LFR easy to remember that I say you remember go P yeah 1 by 2 theta Q okay so these are the simple things good and all these things you have to remember at the end of any course at least the simple things you have to remember okay good so that is the first part what we have done in fact RTD can be divided into three parts first one is definitions and ideal reactor definition of E T F T and all that okay the second one is now if I have this data how do I now model my reactor using RTD information that means if I have this kind of data or the car C versus T car that can be easily converted to E versus T car or E theta versus theta car shape will not change it will be exactly same okay only the scale will change because here and here so that will give you E theta or E T whatever now if I have an equation for E T like here even axial mixing if I have an equation for E T equation so that means I have to now derive an equation that is the model okay what is the model by the by all of us know that models you know that people who walk on the catwalk or ratwalk something they will do know yeah so I think now I am not talking about those models okay in fact those models I think get lot of money that kind of very awkward walk they get crores and crores okay I mean this is what is life yeah I think there was one dance it seems in youtube where millions and sometimes I mean yesterday there was this Kaun Banega Kararupati that KBC they were showing that dance it seems million hits were there for that it looks so awkward and when you put Bharatanatyam no one sees okay and that Kolaveri Kolaveri Kolaveri I think entire world was Kolaveri at some time I think I have beautifully that Jai Vidakthar Jai Vidakthar you know know who okay he was telling that you know there are no lyrics in that song there is no music right and I think there is no meaning when you don't have so many non idealities so with so many non idealities it was one of the best songs at least for one week okay not one because even one month one month yeah that is what is the status of present generation they don't know what to like exactly they don't know what is beauty what is not beauty they don't know what is wonderful you know that only beauty beauty is the character right either in music or in painting or if I draw I think two lines you may be appreciating wonderful painting wonderful painting because I think there is no meaning there is nothing there in that two lines okay so that is what I think you know world when you are getting more and more intelligent I think we are becoming worse and worse in appreciation that is the what problem okay that is why always you know in TV is the Bharatanatyam will be after 12 o'clock no one will see everyone will be or there will be excellent discussion about philosophy about life all that usually 10 30 11 o'clock yeah okay night so that no one should see you know because I think they also took that rating and all that since no one was seeing when it is put around 9 o'clock 8 o'clock 5 o'clock because nowadays in every language serials you know stretching stretching stretching stretching I think nowadays it has become fashion to show the face camera and there are 10 people on the screen you know each one three times half an hour over that's tomorrow out of that two people will go eight people will be there I can shoot that is the kind of thing you know that is why you those people who see serials you do not have to worry at all after five years you come back it will be six those five people that is all no story okay that is what stretching stretching stretching okay and that people see very happily they see I do not know how you happily they see I think it is very very very okay anyway so that model I am not talking about those models I am talking about mathematical models okay mathematical model is required to to indicate the physical phenomena to describe the physical phenomena that is what is the mathematical model description okay mathematical model gives the physical phenomena in terms of equations in terms of equation that is why my simplest you know wonderful example what I asked you is E theta equal to E power minus theta is a wonderful model simplest equation very simple equation but that is a model what is a model mixed flow reactor unless I have that ideal model for mixed flow I will not get this equation right or if I get this particular curve exponential decay and when I want to test that whether my reactor is really ideal or not I have to put my equation here and then put those experimental points if experimental points and equations both tell you very well then we have ideal mixed flow reactor so then you can calculate conversions and all that but but first we are proving whether you have ideal mixed flow right similarly when I have plug flow if I get almost like direct delta function this is almost like delta direct delta function very nice very very lean distribution because that is naturally you cannot avoid that but on the other hand if I put conveyor belt without any vibrations and then suddenly introduced okay sand is going suddenly white sand and suddenly I replaced in the beginning some sand with red color very short length may be one layer of sand molecules if there is no disturbance at all the sand molecule that red strip will be going beautifully and then at the end you will get the red strip that is what what you mean by or direct delta function or otherwise if you put step input so white fluid was white sand was going up on the conveyor belt yet sometimes suddenly I think you know with magic also you can do shit entire thing will be red okay so then because without disturbing you have to do it no otherwise by adding and all that it may disturb so then red will suddenly enter because there is no disturbance this red you can see at 50 percent of the mean residence time you will see 50 percent red and 50 percent white this is what this is how you have to imagine in your mind right so that is F T what is F T equation for plug flow C by C not equal to C by C not is F 1 1 and again condition you have to tell that is very important if you simply say 1 I can't expect 1 to be there at T equal to T bar by 2 or T bar by 3 that is 0 okay so that's all so that is what is the models now we are trying to find out okay I think I will we will take only two models the model can be either single parameter model or multi parameter model right models can be single parameter or multiply that means if I am able to describe the phenomena with only one parameter then I will call that one as single parameter okay so an example can you give yeah tanks in series model for describing what I have n number of tanks and then each tank is n I think that's not actually good representation but n also we use P F R so then what is that you are trying to model there the phenomena of plug flow you are trying to imagine in terms of mixture flow reactors the phenomena of plug flow you are trying to imagine in terms of axial mixing when you get axial mixing D by L equal to very very very very small D by L is a number you know that is a one parameter inside that there are three parameters D U L right okay so entire that is why dimensionless number if this number equal to 0 then you have plug flow in fact I told you this I draw one line here n equal to 1 n equal to infinity R equal to 0 R equal to infinity R equal to 0 D by L equal to infinity D by L equal to 0 this is plug flow okay all these are single parameter models two parameter models example you know that two parameter model also why I say what is this what is happening in the brain no storage capacity Sushmita you are saying something here so quite I think you know you are m tank you are b tank you are phd one parameter only you could tell other parameter you could not tell two parameters tanks in series axial mixing and then recycle correct no if I know R I will try to find out you know where I am whether I am in plug flow or whether I am in mixture flow or in between somewhere which are equivalent to number of tanks which are equal to D by U L this is n is a parameter this is D by U L as a parameter D also can be parameter in fact D is 0 and D equal to infinity okay yeah and recycle ratio R okay I think Sushmita you are telling something multi parameter model multi yeah one more parameter you are not able to act what are the two things we describe for plug flow one is axial mixing equal to 0 then not second parameter if you have both non idealities you have axial mixing and also radial non uniformity so your model should take care of these two how much is the radial non uniformity in the lateral direction and how much is the axial mixing both of them apart from that if you have the axial mixing and radial non uniformity and also dead space somewhere then how many models you have three how many models can be described for humans how many parameters diabetic one okay yeah heart attack is one then any other things BP yeah I think these are all complementary okay yeah BP so all that you know these are all non idealities where if you want to develop your model all these things should come how much sugar you have okay how much BP you have and whether these walls are open or almost everything close okay so all that kinds of things only know that is multi parameter models okay tell me the multi parameters for mixed flow bypass bypass dead space re-circulation re-circulation yeah these are the multi parameters okay I think oh my god mm power width yeah yeah yeah I think absolutely no expansion of the only contraction dead space with dead space bypass okay and of course re-circulation all that then PFR with axial mixing radial non uniformity we generally call radial mixing also that means we have to understand that radial mixing is not perfect that is all okay radial mixing now then yeah you may have dead space here also yeah one more channeling you see channeling N N double N okay channeling yeah so like this we have enough so that you know you should not forget see in fact our Indian marriages are multi parameter model you know that anytime not heard yeah you heard a tell me yeah I think that I told someone yeah already okay yeah you see how many people have to go and see the girl or the boy okay first mother will first father will go or father may send his brother-in-law or someone also okay so then mother should go father should go brother should go sister should go and somehow relatives should go so many parameters that is why system is unstable okay it is not easy to choose no whenever you have more parameters it is not that easy to converge right so that is why best model is single parameter for model for marriage what is that single parameter model most beautiful world of a beautiful girl or boy on this planet that is one parameter so you search you search you search you search when you get you get married okay very simple no only one objective okay otherwise whatever I think now girls may start asking dowry after 20 years now so whether girl or boy only dowry whether the boy does not have head or legs or nose does not matter for me only money okay same thing boys also can go and tell that okay whether girl has anything or known or nothing I want only maximum amount of money okay so like that you know your own you can sure I think you should have that you know they should have the biggest bungalow on the planet okay does not matter whether it is girl or boy or whatever okay so what you are looking at is only bungalow with Asian paints okay that advertisement is coming you know I think they go for marriage and then the girl is asked how is the boy beautiful house okay one parameter she needs only one parameter there that is all boy does not matter boys father does not matter boys mother does not matter okay so like that choose one parameter those who are not married okay so that is why here multi parameter models I am not doing because we do not have time so single parameters what we take is axial mixing okay and another model is tanks in series model these two models we take and one multi parameter model I will do with CSTR with bypass and dead space that is two parameters okay so these three we will do so then I think the third part this is modeling that means what we do is you first develop the equation and now after developing the equations there will be parameter if it is n number of tanks in series depending on n equal to 1 n equal to 2 n equal to 3 n equal to 4 you have to plot E t or F t whatever okay you can convert that one equation into the other either E theta or F theta or E t into F t right then you plot E t versus T for n equal to 1 n equal to 2 n equal to 3 n equal to 4 simulation that you are experts okay yeah so then you will get so many curves right n equal to 1 n equal to 2 n equal to 3 and all now take the experimental data and then try to plot that data as E t versus T so on one line it will be the closest there may be n equal to 3 n equal to 5 n equal to 6 so when it is almost touching one line so now we have to say that the system has equivalent to six tanks in series same thing with D by U L okay when you have the equation E t versus T the parameter will be D by U L you start with D by U L equal to 0 you can also end with D by U L equal to infinity those two extremes C S T R and plug flow right yeah so in between D by U L equal to 0.01, 0.01, 0.05, 0.1 I told already 1, 20, 100 you plot various lines of E t versus T curves or F t versus T curves now again data what you collected from the equipment take that and then try to plot on that right so this is manual plotting method very simple straight forward you can find out now we have another way of doing it once you have the model once you have the data go to bill gates windows computer okay matlab otherwise so give the data give the model and ask it to you know how to do it know don't know you have to learn okay yeah matching the data with model in the matlab you are doing how lab know some computational labs you have yeah that is what I mean all those labs are only to help you not to spend some time without understanding anything okay so the idea is only that right so give the data choose give the model and only thing is each and every point the model will calculate the actual model value and that will check with the experiment corresponding to that point let us say one second two second three seconds like that model will calculate at one second and then for one second correspondingly what will be the E t experimental data both will be matched and you give the difference the difference must be point not not not one know that one minus the other right so you specify some matching technique that means 10 to 4 of minus 6 10 to 4 of minus 10 like that so when all the points on the average when they match very well then finally that will give you this is the D by U L for this particular run experiment you have to learn that but you pose as if all of you are very much interested in simulation and all that okay but I think nothing is known okay I think all these things you have to do I think the idea of lab mat lab and also general laboratory computational laboratory is only but to tell you all this right so you know the procedure now but what is the use I think you know tomorrow morning when I ask you are not able to tell that at least procedures I say like stories first remember that right you you have the experimental data C versus T or E t versus T you have a model where this equation is is a function of E t E as a function of or E t as a function of T with a particular parameter if it is a single parameter if it is two parameters you will have two parameters so how do you choose these two parameters also is through mat lab one can do it you have to give only thing is when you go to mat lab and then matching you have to give what is called some initial guess if you wrongly give it will never match so that means you are actually in hydrobat but I am searching in Chennai what is use impossible I can never find you right so that matching will never occur if you have that kind of wrong guesses for correct guesses you have to actually plot with your hand try to find out approximately what will be the parameter d by your values that can you can give as a guess value then you are refining data matching technique will be very very quick otherwise somewhere you zero to infinity you cannot search right so this is what is the procedure in all these models okay good