 Incentrator It is called an instantaneousierzog The dead body is sent into Incinater That is all That is all 5 minutes Volume is the rate of reaction is very slow 45 minutes its cool That is correct Total batch type including you know charging charging reaction and cooling, discharging and finally giving only in terms of small ash see finally all of us will become only that much ash that is the philosophy of life correct no so why all this why m take b take p h d because with all this at the end only that much ash and okay this much ash which you cannot keep in the house and there is a photo hanging on the wall that is all no all of us will become in the beginning at the entry of the world photo because i think people are very proud of us as a small boy they take 100 photos and at the end also big photo on the wall that is all in between entire thing is drama like me you know that is all okay good so these are the just general things which i want to give to you how people think about various models okay so this is what the information i think nothing too much to explain good so now we are coming to the third part of residence time distribution what is the first part by the way see entire r t d can be thought of into three parts the first part is i know most of you will not remember you see you have to appreciate my psychology i say i know your psychology very well i know where you forget when you forget what you forget all that i know okay even though i repeated many times if you see the videos tomorrow you would see that how many times he is repeating okay and of course my happiness is that even after seeing the video next day you will forget again anyway so next day you hear it is again new to you so that way we are very happy okay because i think you do not remember you know very nice for us yeah the first part what i told is the definitions and also ideal react definitions and ideal react right so that is what what you have done how do you define e t how do you define f t first of all what are the non idealities for single phase multi phase all that we have done it okay that i think let me record that first okay r t d part one is definitions okay and part two is now at least can you tell i am also writing continuously the title in almost all the classes r t d models okay now what are what is the use of this r t d models yeah to quantify first non idealities and using them for conversion right that is what so this one r t d models will give us estimation of estimation of non idealities non idealities and okay this is one two is okay this is a b is estimation of actual conversions very good that is what actually this is two steps right first is estimation of non idealities second step in that is estimation of conversion okay now part three is okay yeah okay part three is use of r t d data r t d data will simply give me fraction of material coming between time t and t plus delta t that information use use of r t d data directly directly to estimate conversions to estimate yeah to estimate conversions okay what is the meaning of that i do not want to use any model i do not want to use any estimate any non idealities okay i simply give you et versus t data can you calculate conversions from that using that but i will give you kinetics i have a first order reaction i have a second order reaction plus i will give you et versus t data right so that means can you use directly the r t d data to calculate conversions without going to r t d models that is the third aspect that is correct no why should i do again you know like estimation of non idealities use okay develop another new model in terms of non idealities to calculate conversions so these are two steps unnecessarily but this is straight forward r t d data directly to be used for calculating conversion that means there is no modeling required there that is why we call that one sometimes zero parameter models because there is no parameter there is no axial mixing there is no dead space right simply whatever data i get for the reactor it may have dead space it may have bypass right it may have channeling simply what i give you is et versus t data please do not remember that this et versus t data is ideal reactor any real reactor it may have all non idealities but still that will give me some et data when i conduct the experiment may be the shape if i draw that may be different when compared to ideal reactor right with long tail or suddenly two peaks right that means channeling what you have all that information will be there but we do not care about all that information what you care is i have now et versus t data and i will give you whether i have first order reaction second order reaction can we now use this first order second order information that means kinetics and find out conversion using conversion using r t d data find out conversion okay that means you do not have any reactor in your mind correct no i am giving r t d data right so i am not saying whether it is ideal p f r i am not saying whether it is ideal mixed flow if you have ideal mixed flow ideal p f r i do not have to even go to r t d data straight away i can go to i have second order first order i have the equations calculate but here any real reactor with r t d data can i use to calculate conversion that is the third part that is quite interesting part right because it is straight forward no but unfortunately that is not that interesting in the sense that you cannot use that data beyond one particular case in fact the r t d by the by who is the starter of r t d residence time distributions in chemical engineering how would i miss this beautiful thing in the beginning itself some doctor dank quotes dank quotes dank quotes dank quotes no who is dank quotes anyway see i think you know this aries is also very humorous he wrote an article p v d on r t d p v d p v dank quotes p v d on r t d okay so because i think dank quotes he is the first person in fact that original paper if you promise at least 5 people will read i will send the original paper okay you will read a okay i will send for the entire class 5 is enough for me 55 read excellent okay very good so at least minimum 5 otherwise i am creating e pollution correct no very sincerely download store and forget so unnecessarily that will be there on your computer for long time on your hard disk without any use okay i will send that original paper original paper definitions are slightly different in time they are slowly modified but the seed came from there and you know how the seed he got it seems when he became lecturer in cambridge university cambridge university only he did not have a course to teach immediately so then i think you know he used to go and sit in the canteen and then drinking coffee so when he was drinking coffee and then i know thinking thinking about what are the problems in reactors and all that and we know ideal reactors we have equations we can solve what we do with non-ideal reactors then he imagined all this in his mind all this in his mind and then finally defined what is e t what is f t and how do you find out e t how do you find out f t and how do you join e t and f t with i t i t you know internalized distribution all these things he imagined and he wrote that first paper in 1953 chemical engineering science volume 1 page 1 okay i think this is c e s chemical engineering science volume 3 1953 not volume 1 i think no no not you know that is what i said but it is wrong issue 1 oh anyway i think i will then i think 3 volume 3 volume 3 okay page 1 1953 1953 okay i am just putting a question mark here volume 3 page 1 1953 but question this this is page 1 is page okay that is the first paper that i remember but my remembrance is not that good but i think it is volume 3 not volume 1 okay sorry for that good so he was the person and then how many beautiful things also he imagined where his original idea was the part 3 original idea was part 3 right and yeah 1953 only paper in 1958 second paper has come he took 5 years to tell that r t d is not completely useful for finding out conversion okay and in that paper again he discussed many beautiful things about age of molecules life expectations of molecules exactly like our age so when we come to this world at time t equal to zero our birth time then onwards our age is calculated right but unfortunately we do not know the end right except for plug flow plug flow means if all of us are exactly living 100 years then we have plug flow then we know very well what is our age and what is our life expectancy right yeah i mean if i am 100 years living now 65 the remaining is 35 that is life expectancy but unfortunately god is not so kind to us you know he does not want us to know when we are at least mother father know when we come right but when we leave even mother father also they do not correct know anytime it can happen so that is life expectancy right that is same thing with in C S T R you do not know which molecule will come out so the life expectancy is not there you cannot say what if it is plug flow you can beautifully tell yes now he is 10 90 years life expectancy okay that in fact is called what is you know beautiful name called micro mixing where you get the information on molecular level right and when the life expectance when life expectancies are together those are the molecules about to leave the system like for example a boy may be with 10 years and his grandfather may be 75 years he has got 25 years life expectancy and this guy has got 90 if i know plug flow if i know that it is plug flow because we do not know unfortunately imagine a situation where both of them are travelling by skota and accident happened both of them will die so at the moment of dying that time accident time immediately if they die then the life expectancy equal to 0 both have the same life expectancy or let us say that both of them travelled for 2 hours 3 hours together and we do not know the end is going to come right when they started from the house and then moving let us say that you know 5 hours they have gone around Chennai after 5 years unfortunately this thing happened and if i am able to know that then what is the life expectancy for both of them 5 so age does not count now correct no age does not count so when they are leaving the reactor it is the life expectancy which is more important and thermodynamics come there second law of thermodynamics once they mix they cannot unmix so that means once they mix means a molecule has entered now just 10 seconds back that joined with another molecule which has entered 15 minutes back both of them have life expectancy once again once they come together and then trying to leave and as per second law of thermodynamics it cannot unmix on its own but it has to go together outside this kind of overlapping perfect overlapping is only in mixed flow reactor because where life expectancy and R T D okay in a sense what is the information you are getting from R T D it is residence terms or in other words loosely talking it is ages okay ya that is what R T D and this life expectancy gives how many remaining life is there in the reactor how many seconds more or how many minutes more will stay there so that is why in life expectancy and R T D if they are perfectly matching that is what E T equal to I T in a mixed flow reactor have you any time thought about that E T is perfectly same as internalized distribution that is what is the assumption I said we say that inside conditions whatever is there you know the concentration temperature exactly same as outlet, outlet describes E T and inside it describes I T so I T equal to E T in a mixed flow reactor in no other reactor you will not have so when you have this I T exact I T tells me I T is the internalized distribution so once I know the internalized distribution that is also equivalent to life life expectancy for me because that is happening inside they have not come out but E T is exactly only ages right so it is not E T that is important for me it is I T which is important for me because that gives me the life expectancy or if you do not want to get confused just imagine our life expectancy and our life expectancy if two people life expectancy is same they are about to leave the world right I mean in some accidents or some tsunami and all that there are how many people are dying with different ages there that means imagine that you know end of the world there is a outlet which they are going through that after death right so what is happening now is all these people because their life expectancy is same they went out together not because their ages are same okay so those are the funders he has discussed so many in that paper in 1958 paper and this paper there is another person called Jwetering he is from Netherlands I think he is also published a paper CES I think it is also 1958 if I remember correctly you know this Jwetering has published only few papers may be 567 like that not like present faculty member just to go and tell that I have infinite number of papers and another person will go and tell I have infinite plus one okay for promotion so that kind of papers we have so many okay I do not know this joke you know or not in Calcutta university it seems they were a noble laureate has come to physics department I do not know whether it is truth some people say and the noble laureate was introduced to the department faculty and then they said I think okay professor Mukherjee 550 papers and thereby an Chatterjee okay 350 papers then we have some Sanyal also from Bangal yeah Sanyal professor oh you see physics department I do not know I am just in physics department I am telling so various names are Mukherjee Chatterjee Benerjee okay all Jee okay so all these people then they said I cannot 200 papers like that and noble laureate got up and told me told it seems oh my god I am very sorry I am really afraid before you to stand before you I have only two papers okay and whereas you have hundreds of papers right so that is why number does it really mean no it is the quality does that mean okay me yes sir co other what the quality will improve if co other is there quality will improve okay I am just telling the number game you know nowadays why I am telling is the jewatering also has in fact conceptually jewatering paper is much better than dankottes paper and all that came from his mind that is what I want to tell you because of our mind I will also send that paper to you that jewatering paper also okay if you are not able to read for this course at least you read sometime in your life later okay even after completing semtech okay so that is worth reading how beautifully they thought about and what is the starting point for that they do not need any equipment they do not need anything except may be some amount of food because brain cells have to be active and then thinking and after thinking to write a paper and pencil also is okay so but what we have we have bags for every student behind okay and in that bag you have laptop okay and also calculator and what else scales pens pencils books that is all they are there all the time what is that lunch box biscuit packets biscuit packets all this we have okay good okay now let us discuss about this one this use of R T D okay part 3 direct use of R T D to predict conversion that is part 3 so now you know the problem no I think you know actually the issues you have to remember I have been telling you all the time this please remember the issues issues what is the problem in this okay now the third question what we are asking is of course definition and all that over and you know can I use R T D information directly to calculate conversions instead of going to model estimate non idealities use that non idealities to calculate conversions using another model right ya and this direct use of R T D is only possible if you have first order reactions alone right what is the reason because tracer information is linear or non linear but I am going to ask you how do you define linear process control linear process and non linear process okay I will ask the question in a slightly different way let us say that let me say that I have conducted an experiment next semester I am going to give you all this also in the lab right you have the tracer and you added 10 grams of tracer and then you recorded concentration outside and then you have plotted you have plotted E T right that is experiment 1 then what I did was again now do not use 10 grams in the next experiment use 50 grams right use 50 grams what will happen to the E T is it same is it different or totally chaotic trend is different same is different it is not same it is same it is same that is what they say that is what they may say okay the point says okay it is same not to know okay yeah why do you say it is not same why you should take longer time yeah why because you know instead of 10 grams I added 50 grams why should you take more time and 10 grams is also mixing perfectly it is not disturbing the system because that is the idea of conducting R T D test no E T I mean when you are doing R T D test it should not disturb the study flow right only thing is concentration you are increasing 5 times that to initial concentration same thing let us do step input so earlier you used to concentration equal to may be 5 cc per okay 5 grams per cc right so now I ask you okay use 50 grams per cc what will happen nothing will happen exactly same thing particularly when you are normalizing you get right but when you are simply calculating recording concentrations what kind of concentrations you will get 10 grams 50 grams just the concentrations you are measuring excellent 5 times just increasing that is a linear process okay that is a linear process okay so that is the reason why that is the linear process and first order is it linear process or nonlinear process very common sense question okay answer it is linear process so because both are linear then I can use only R T D information to calculate conversions for for other orders you cannot why there what happens is that something else into we will come into picture here in first order when you have first order reaction I also told you sometime back first order reactions only depending on time of reaction you will get conversion okay not depending on second order again depends on concentrations that comes in Damkohler number automatically right in Damkohler number there is no C A not there is no concentration term for only first order right and Damkohler number is yeah so Damkohler number D A equal to K tau N minus 1 right so other than first order reactions you need something else which is also required for calculating conversions using R T D that is why I can only merge concentration I mean 2 linear processes and now try to find out for the conversion using R T D that is what I also told you definitely you do not remember that what I told you in the beginning of R T D was that the original idea is R T D definition is the fraction of material coming between a time between T and T plus delta T 10 percent of material is coming between 0 to 1 minute another 10 percent may be from 1 to 2 minutes now what I do is in this 0 to 1 minute what is the conversion what is the conversion and 1 to 2 minutes what is the conversion 2 to 3 like that entire spectrum I take and then take all the conversions in each individual packet because I treat that fraction of material coming between 0 and 1 minute is 1 fraction or that is equivalent to 1 batch reactor 1 packet that packet is spending only 1 minute what is the conversion in that so then I will take the 2nd packet that spent between time between 2 to 3 minutes that means total time of course may be 3 minutes when I am telling but between 2 to 3 minutes when I am saying 2.5 minutes it has spent inside the reactor so what is the conversion in that so like that various fractions and average them I will get average conversion that was the original thinking and what they found was that original thinking was correct so only for first order because that is a linear process and tracer is a linear process and for other processes it is not you know it is not possible I will tell you why it is not possible and this is a wonderful wonderful explanation given by this Netherland people Netherland I think Fan Kravillian is the person who has done that first what he has given a simple model very nice beautiful model he says that I have a system where I have a PFR ideal PFR followed by ideal CSTR this is model 1 and in model 2 I have just reverse I have just reverse this so this one is T bar 1 T bar 2 or tau 2 tau 1 also we can write and just this is reverse only T bar 2 T bar 1 this is an outlet then if I have okay what is the residence time distribution curve for these 2 for the first one what is the residence time distribution curve how do I draw that both are ideal okay it is exactly like in process control if you remember that is exactly like you have time delay and mixed flow right ya so then how do I plot that this is of course ET versus T when I plot ya after T bar sorry T1 bar T1 bar you will have this kind of exponential decay exponential decay where is my T bar 2 I do not have T bar 2 but somewhere here you have T bar 1 plus T bar 2 together somewhere afterwards okay good anyway that is not important this okay now tell me for this starting how do I how do I plot that so you will have like this and then like that no no I am I am not saying whether you are right or wrong what do you mean by same same as puja same as merit first why first why not second because why why is important no we have to explain you may feel but still you should be able to explain okay everyone is convinced there by n you convinced there by n Janvi if there by if there by n is accepting accepting your your explanation then fine fantastic puja is in between she will understand automatically because they have to pass waves we have to pass through that ya why exactly same as earlier one okay puja why this is not correct is that when I am seeing a particle here it is entering here in perfect mixing but what is happening later T bar 1 time later only I will see that there right this is T this is T coordinate this is 0 what you are telling right so because you have the but this is logical explanation what she has given many students 95 percent of the students will only think this is the one correct okay that is a logical one because our brain cannot see you know beyond certain you know things right ya so that is why that is a logical explanation but if you are little bit deeper if you think what is really happening here is that I have here a molecule okay a particle is entering it has come out right but that particle I will see at this point because my collection point is only here collection point is only here so this much time I have to wait still to find out that particle to measure that particle so that is why exactly this also is like that I think Abhishek told it very nicely the plug flow will have only that time delay this is T bar 1 T bar 1 only after T bar 1 only I can see that so that means what is now the beautiful question if I have a first order reaction which one will give me more conversion see before question itself is answering ya why actually this is the fifth chapter or sixth chapter problem we also gave there for first order reaction if you have a PFR and CSTR how do you join them why ya it depends on time now you answer the question you know or now you get the point right it only depends on time so what is the information we are getting from RT only time information it is the fraction of material which is spending a time between T and T plus delta T and first order requires only that information only time information so that is the reason why first order for first order reactions RTD can be used directly to calculate conversion and now here if I go to second order which one will give me more conversion ya that we have discussed the cause for second order concentration should be kept as high as possible okay good that means this will give for second order low conversion this will give for first or second order high conversion okay so that means I will now ask another question because I think you know this third part is most of the time discussion only the derivations are very very simple but discussion that is why it is very important for us ya and the question which I want to ask is that I will say that in this model 1 the mixing is happening late or early late and in this model early so I will write here this is late mixing and this is early mixing okay good so now that means other than first order reactions okay and the other question is that if I have half order which one will give me more conversion that means if I use early mixing I may get more conversion but I think physically I could not explain that one but late mixing second order I can definitely explain because you have to keep the concentrations as a as possible that will happen only without mixing that is why please remove from your mind that mixing is good for reaction that is very bad concept mixing is not good for normal reactions n greater than 0 but there is one reaction mixing is very good what reaction apart from negative order because negative orders you do not get many autocatalytic reaction I am trying to bring out all that I am telling you know grinding grinding okay regrinding so many times okay ya so that is why again I brought I do not have to ask that question I asked you so that you will remember once you will answer your interviews well you will get the jobs so that is the reason why I am asking that so for that one definitely you have to maintain some kind of nice mixing of course for multiple reactions again different kinds of mixing all possible for multiple reactions we are not talking about multiple reactions so that means late mixing and early mixing is the concept that is coming so conclusion is for other than first order reactions something more information you need what is that more information whether it is early mixing or whether it is late mixing you see now you see here for second order you say that we want late mixing right and for off order we say we need early mixing so that is another parameter no unless we say that we have early mixing or late mixing and you cannot really say that you know you cannot calculate conversion that you know meaning if I do not give this model how can you convert the how can you calculate conversions for off order or first order so that is why this will tell me that I have late mixing or early mixing this model is late mixing this model is early mixing so other than first order other than first order information info on okay info on late mixing or early mixing or and okay or is okay or early mixing is required okay now another question you know you have to be very smart in this now okay everything what you are discussing is very important for understanding right okay I do not give you this models these two not there I will simply give only this response ET this is RTD curve I am giving you I have here T bar 1 okay I do not tell what is happening later okay so you do not know I am blocking these two now okay now tell me this RTD curve tells what information what do you mean by late mixing even early mixing also you got the same thing correct no I think even early mixing but this PFR is late there is a PFR in the system but that is not the one because by looking at the RTD curve can you tell whether you have late mixing or early mixing you cannot tell that is the drawback with RTD and I will tell you some more things where I think you know the exponential decay and all that there are infinite possibilities of getting same RTD but different types of reactors so that means one RTD curve if I give you we can draw 6 or 7 or 8 depending on your intuition your mind so that means for a given RTD system is not specified flow pattern is not specified but whereas for a given system RTD is definitely specified what is the given system this is the one this is specified the reverse is not true given this alone you can have this or you can have this right again comparing you know Jahanavi and Débayan so if I give that RTD in examination okay and then ask you to calculate conversions for first order or for second order you know even if Débayan assumes this he is right and Jahanavi assumes this she is right but both of them will get different conversion and the second order reaction which one you will get here Jahanavi will get more conversion Débayan will get less conversion then both of them I have to fight correct no my answer is right my answer is right I will come there and tell both of you are right okay because because you do not know I think you know you can either assume that or assume this that is why RTD drawback is that given an RTD curve you cannot exactly tell whether you have late mixing or early mixing unless we know whether it is early mixing or late mixing you cannot find out conversions okay that is the drawback now you understood this special issue in RTD why we cannot use direct information okay yah that is the one and I think let us first find out for yah okay I think let me do this I think finding out an equation for first order using RTD that is simple that I will do later but let me tell this story first okay now the story goes like this we say now late mixing and early mixing RTD cannot identify whether you have late and early right late and early are really vague words correct no you can ask me sir how late right I think for you also someone coming in one minute for himself it is very late someone coming in 59th minute it is very early to come to the class okay that one minute also why I should be there so that is why this late coming or early coming or late mixing and early mixing are that late and early are really vague words and in science and engineering you cannot be vague you have to be perfect that is why you will be caught many times deviant in the interviews by chance if you are using wrong words unfortunately that interviewer will only catch that word without knowing you say late mixing you tell me what is late mixing okay and to cover up then you can say something is segregation what is segregation okay so like that only they ask so that is why particularly when interviews not only particular in our life whenever we speak if you are able to speak correctly specific with specific exact words the world would have been totally different and one day you try from morning to evening till you sleep just record everything what he spoke okay I can tell you 99% is waste 99% there is no meaning only 1% efficiency right that is why I think animals are very good they do not speak okay because we so it is just waste of time only that is why this early and late is really vague words where we cannot answer because my late is not your late I will say that one second you will say that no sir 110 minutes is late for me okay so that is why in engineering we have to specify then that is the reason why we have defined two fluids that are called macro fluid and micro fluid these are the words you see now you have learnt two words late mixing early mixing now we are defining another two words macro fluid micro fluid that we can define okay this macro fluid is available in the form of pockets right and each pocket size approximately with the molecules we have some number because that macro fluid is available in the form of pockets and assumption is that these pockets cannot be allowed to break or allowed to coalesce coalescence also is possible breaking also is possible you see how theoretical after sometime in fact CRE tells you do not know how to calculate conversions really unless otherwise you assume ideal plug flow ideal mixed flow that is all really that is the beauty you know at the end this is what happens in our life most of the people at the time of deathbed they will know that how useless fellow I am what are the wrong things I have done okay no many people I say any people really good person will think like that how many wrong things I have done in my life that is the philosophy and then closes his eyes okay Einstein Einstein also thought like that yeah Einstein you know from with respect to our mind Einstein is great but with respect to Einstein's own mind he also told that I have committed biggest bunder blunder of my life because in fact the universe expansion he was the first person to notice when he solved his equation for equal to mc square you know that theory of relativity in the equations he found that when the solution comes universe is expanding he said that it is a stupid idea so he put one constant called there is a very special name for that something like that only something like that only right so I think not able to recall that constant he has introduced to stop the expansion so that means his actual equation showed that universe was expanding and then he has introduced a constant where that constant will take care of whenever this expansion that constant will become bigger and suppress okay so that is how I mean later he found that I think what that who are the who is the person Hubble Hubble is the person who found that universe is expanding so when he said that many people told that yes Einstein equations already indicated that but he killed these equations by putting this constant that is a fudging factor they call because why at that time in his mind he was thinking that universe is constant volume is constant it is stationary it is not expanding later they found that it is expanding expanding expanding expanding expanding expanding even now okay yeah so after expires and expires and expires it seems the average temperature in the universe will have become zero then you know the other what that attractive force now it is expansion forces which are it broken up and then that pressure is still pushing all the planets all the planets are very small there solar systems it is pushing away and now after sometime gravity will take over and attraction will come and again come together and then become one small point where it was there before according to the theory if you are able to prove that you will get to both either experimentally or theoretical okay so many noble prizes I say so many noble prizes okay yeah so that is why this macro fluid is defined in certain sense that these are packets these packets are not allowed why I am telling all this I am telling you only to use your brain please use your brain thinking thinking thinking and unfortunately we are not doing we are not doing we are not doing that thinking and we are also responsible because we are not allowing you to think okay where is thinking time for you everyone is taking hundreds of assignments okay you see okay yeah but even when you are doing you can think don't do it mechanical that is what what we are trying to tell okay don't copy you do problems but thinking not copying from someone and or otherwise mental solving mental solving all of us are all of you are experts right mental solving you know what is mental solving read the problem oh concentration is given time is given and reactor is given oh we can calculate conversion because that is only thing is missing but when you put on the paper everything is missing you don't know how to calculate conversion first of all you forget about design equation instead of and you forget about epsilon is there there is one fellow okay all these things you forget but when you solve it using your brain once or twice then you don't forget and why we give some of us give more number of problem is is that except at least you give few problem at least you do few problem okay if you do all the problems you will become expert in the subject okay if you don't do at least few problems I think you do okay you understand that is the reason okay anyway coming back here so macro fluid is available in the pockets which are not allowed again why I think all the discussion went because of the brain so in the brain we have to imagine that these are the pockets which are not allowed to coalesce which are not allowed to break okay good now what is the definition of micro fluid micro fluid is the fluid where individual elements are capable of moving very very freely right it is very very freely good so now when I have that kind of that means when I have this micro fluid entering in a reactor let us say mixed mixed flow reactor micro fluid entering perfect mixed flow reactor what will happen to each and every molecule they are perfectly mixed one molecule can communicate with any other molecule okay and one molecule at the end when it is just coming out will join with a molecule whose life expectancy is same as its own we are only focusing on one molecule molecules are continuously entering so one molecule I look into now so that molecule I am following so this fellow can move here and there here and there and all that but when it joins a molecule whose life expectancy and this molecule life expectancy is same after that life expectancy it comes out it would have entered 5 seconds back but at the end it is when it is about to come out it joins a molecule which has been there in the system for may be 15 minutes or 5 minutes then it comes out okay that is one thing that means these molecules are capable of moving anywhere in the reactor communicating with any reactor sorry communicating with any other molecule and capable of moving anywhere capable of leaving also at any point of time at that point of time it will join the molecules whose life expectancy is same all of them will have the same otherwise they cannot come out right so that is what is the definition now same this mixed flow reactor I now put macro fluid what will happen pockets are not allowed to break pockets are not allowed to coalesce they are having their molecules together and those molecules inside this pocket not allowed to communicate with any other molecule okay any other molecule in the other pocket right so that is why this pocket and that pocket will have I mean no communication at all and this pockets also will come out this pockets also like molecules those are the packets it is a perfectly mixed one now earlier we are mixing molecules now we are mixing packets so there may be 2 packets whose life expectancy is exactly same see I am saying packets like this but in fact the size will be very very small you cannot see right and if I tell you the molecules size so each each pocket will have 10 to the power of 12 to 10 to the power of 18 molecules okay for pocket for pocket pocket PO know PA PA not I wrote PA first time then PO is this you know PA is this pocket yeah okay so that is the one and you know how many molecules your Avogadro's number has one more yeah so you can see these are very very small things even though we say bigger ones so that means the communication between the pockets is not there and the conversion depends on the time of that pocket which is spending inside the reactor right and then when I take that pockets and then break all of them and then find out average conversion that will be different right if it is a second order reaction then the conversion when you have individual molecules together and then coming out and I am finding out average conversion in this which is late mixing which is early mixing macro is late mixing micro is early mixing right yeah so now that is for mixed flow now imagine that I have now micro macro fluid in plug flow reactor right macro fluid all packets I am sending and each pocket by definition of plug flow each pocket will spend exactly same time what is the conversion in each pocket I know same average is same good over is simple now I will now send micro fluid micro fluid by definition of plug flow each and every molecule also will spend exactly same time what is the conversion in each and every molecule if you can imagine that same and average is also same so that means what either micro fluid or macro fluid in a plug flow okay same conversion now what can you say about mixing is it late mixing or early mixing in plug flow yeah what do you call that in these two terms whether you call this late mixing or early mixing latest mixing possible when they are mixing they are only mixing outside the reactor because we are breaking all the pockets and then seeing that right so the latest mixing possible that means you see how many beautiful things are coming now why they are beautiful because we are now thinking that individual molecules and because we said that we have late mixing and early mixing right and we said that here for micro fluid we may have earliest mixing possible if I use in mixed flow but if I use in plug flow either mix either a macro fluid or micro fluid I will get exactly same condition as latest mixing possible so that means macro fluid is by definition latest mixing correct no they never mix also mixing we are talking about at molecular level right yeah and macro fluid depending on which reactor you use it behaves as if it is a latest mixing or earliest mixing so that is why the RTD comes into picture because when I say mixed flow and plug flow mixed flow and plug flow they are associated with RTD mixed flow and plug flow they are associated with some RTD right definitely so now depending on what kind of RTD you have what kind of fluid you have your late mixing and early mixing can be lost okay I think trying to tell as simple as possible right so but I think please don't lose I think you have not you are understanding everything but only thing is connections because when I ask you are not I mean most of you are replying also because now there are so many terms that is coming into picture late mixing early mixing micro fluid macro fluid now I brought another thing called RTD okay now we have another two terms called earliest what is that yeah yeah we have another things called segregated flow and maximum mixed mix maximum maximum mixed inness okay yeah now I think yeah I think Sushmita is seriously looking okay yeah now can you assess it this is segregated flow and maximum mixed inness to macro fluid and macro fluid correct okay but there is is there any other condition MFR that means RTD okay so that means maximum mixed inness is possible only in micro fluid in MFR right but even this micro fluid will become segregated fluid if it is PFR right so that is why we are now trying to define the scales the scales if you understand I think that afterwards it is easy to discuss define the scales as we have a scale called micro mixing micro mixing is increasing in this direction so here this corner we have segregated flow or in other words this is latest mixing and this corner we have maximum mixed inness or in other words we have early early mixing and this is also called degree of segregation degree of segregation okay okay so that is one scale the other scale is in this direction we write we have MFR here we have PFR here and we call this one as macro mixing scale macro mixing increasing in this direction and here we have intermediate RTDs intermediate residence time distributions yeah so these are the other other two terms now I have introduced that is macro mixing micro mixing okay now of course I will give the notes to you right yeah so now what is required you know all our problem came now because where is the how this problem has come now for us what is the issue now the first thing is what we asked is that what was the question we asked part 3 whether RTD information is directly useful or not then we found that it is only useful for first order because it is a linear process other than first order we have to define whether the yeah system is mixing rate or you know the fluid is late mixing or early mixing unless that information is known to us we cannot calculate conversions to define that all these things are required what is that required first we have to define the fluid right right and also next we have to define macro mixing and micro mixing okay yeah good so now this macro mixing macro mixing we are writing like this because macro mixing tells us about RTDs right macro mixing will tell us of RTD that means the age distributions or in other words life expectancy also right so that is what what is here and the two extremes what we hear is PFR and MFR that we know already and all kinds of other intermediate RTD distributions can be there in that macro mixing right and the other one what we are defining is micro mixing which is which is telling the state of mixing whether it is early mixing or late mixing right where is early mixing here when I have maximum mixingness we have early mixing and whether I have when I have segregated flow that macro fluid we have latest mixing but there is some kind of overlapping now please remember that what is that overlapping even though I am using micro fluid if it is PFR then that behaves as if it is a yeah it is the latest mixing latest late mixing that is why RTD automatically comes into picture so now you see macro mixing and micro mixing both are coming into picture whether it is PFR or MFR is also required to discuss whether micro fluid is behaving as latest mixing or micro fluid is behaving as latest mixing correct no so that is why in the beginning itself I told I am Krishna last time are you really is it difficult now yeah what is difficult you tell me where you are not understood no but you know unless you tell me I cannot clear no I feel that I am explaining very clearly but you are lost somewhere where what do you mean the basic question otherwise how do you calculate here see my basic question is I think you are at square number one square number one what is this is that I gave you only this right yeah that you understood right but now I also gave another example thereby and and by giving this they may choose either one late mixing one may choose and early mixing another there is another person may choose okay but now it is vague you cannot choose for the same RTD two things so that is why now we have to tell another parameter whether the fluid is available in segregated manner or in maximum mixing manner that is why these two terms have come see we talked about late mixing or early mixing now to define late mixing or early mixing we are defining the boundaries one is the segregated flow what is the mixing here latest or earliest latest and other corner what we are defining is maximum mixing is which is the earliest possible mixing right but that scale tells me that whether I have latest possible mixing or earliest possible mixing but this will not tell me whether I have microfluid or macro fluid why even micro fluid if you know it can behave as a latest mixing provided this and this matches that is why this scale I have to take it and then draw here that is why now it is you know if the both are required now again confused yeah so that is why you see the connections connections I am as far as I am concerned I think it is very simple connections which I am trying to give question number one that figure remember right so by giving that figure you can never calculate correct conversions unless we say whether you have late mixing or early mixing but a late and early mixing both are vague terms so that is why now we are defining mixing what is how are you defining mixing that scale is called micro mixing scale one corner I have latest mixing possible which is also called segregated flow and other side I have earliest mixing possible which is called maximum mixing yes this intermediate I can have any number you know all between these two there will be that means some amount of segregation some amount of you know maximum mixing yes right in between 50% this 50% that all possible combinations are and at this point if I say small amount of segregation and maximum amount of maximum mixing yes okay so that is why we are now but I think you know you cannot calculate in between is very very complicated and particularly micro fluid by the way what is micro fluid I mean have you come across this micro fluid earlier in your b-tech or in your m-tech or your phd you have not had done this is the actual molecule exactly Swami till now what we have assumed is micro fluid without knowing yourself in fact you never assumed micro fluid all the equations we have derived for reaction engineering till now kinetics till now they are only micro fluid so that means we have been dealing with that but fortunately without knowing yourself you assumed ideal plug flow and ideal mixed flow unless you assume you can never calculate that okay because anywhere in between RTD it is impossible to calculate for you know the conversions in the reactor unless I assume ideal mixed flow ideal plug flow that is what jwetering try to do he has taken this scale maximum mixing scale okay and then this scale now he has moved along all these or other words this scale will go and then moved from MFR to PFR he has derived an equation for maximum mixing in jatering problem but it is very difficult to use that is why it is not popular and no one is using except for discussion right and what is that maximum mixing is nothing but your micro fluid right maximum mixing is so unless you have the two extreme RTDs one is plug flow another one is mixed flow right you cannot calculate conversions exactly those are the simplest cases but jwetering has done in between cases also intermediate RTDs also he has done it he has taken for example four tanks three tanks two tanks because that is intermediate mixing correct no that one corner you have n equal to infinity in other corner you have n equal to 1 and he try to solve that problem for maximum mixing a scale maximum mixing a scale is nothing but earliest mixing right earliest mixing is possible only with micro fluid possible I tell but even micro fluid will behave as macro fluid the moment you go to PFR so it is not that even though you define micro fluid as molecular you know molecules can freely move RTD also comes into picture that is that means macro mixing also comes into picture macro mixing defines RTD micro mixing defines state of the fluid whether it is aggregates this side or whether it is individual molecules right but the overlapping comes because when I have micro fluid and when I put in PFR that fellow behaves as if it is only latest mixing macro fluid okay or segregated fluid right so that is the overall picture and what are possible things what we have done I think there is another paper also Weinstein and Adler they try to do something else in between okay so I think all those things are very complicated and that is why it has not even come to the textbooks where you can use those equations for example if you see Fogler Fogler has written recently another book essentials of chemical engineering chemical reaction engineering I do not know whether anyone of you see may be recently 2012 or so this book book and many things are repeated but may be probably he thought that RTD is not essential for reaction engineering he removed I think RTD chapters from that but if you see the earlier one the previous edition to this in that book he has derived also jittering equation I am not including that in the examination but definitely I will give the equation so that you will remember for your future thing because we are not definitely using them to calculate conversions but to appreciate the complicated things in the reaction engineering to calculate conversions I am going to give you that right so this is the overall I mean at least did you understand the problems now what are the problems associated with RTD the first thing is RTD cannot give you complete information to calculate conversions except for first order and why RTD is linear and also first orders require only that kind of time information and the time information is given for the time information is given in RTD and it cannot solve second order or other orders the reason is there is another parameter coming late mixing or early mixing or segregated flow or maximum mixing as the another name for late mixing and early mixing is maximum mixing as and segregated flow that is why I have written the bracket okay so for other than first order reactions unless you know these two parameters whether you are descent or that end you cannot calculate conversion and what you can calculate conversions is segregated flow segregated flow is easy to convert easy to calculate you know why again as analytical I can just explain segregated fluid whether I have first order or second order each pocket is behaving as if it is a yeah individual batch reactor each pocket is a batch reactor now I can calculate this batch reactor you know conversion and then average all of them and you know the equation what you get it is the simplest one where C A bar by C A not equal to 0 to infinity C A by C A not batch E T D T this is what is for segregated flow for first order also it is exactly same because for first order what is C A by C A not batch C A by C A by C A not batch for first order that is for segregated flow for first order reactions C A bar by C A not is again 0 to infinity C A by C A not batch E T D T and that is also equal to 0 to infinity E 4 minus K T E T D T so that is C A by because average C A bar by C A not okay that is specifically for first order reactions how did I get that equation this equation I got thinking that okay the material coming between time T and T plus delta T is E T D T correct no the material that is the definition of E T D T the fraction of material which is coming between time T and T plus delta T is E T D T right so in that fraction what is the conversion if it is first order right like that how many particles I am getting 0 to infinity and then this D T will take care of that small small interval that is all the equation what you have and for segregated flow exactly it is same segregated flow beauty is that these particles are not interacting with any other particle but there also how many pockets are coming between time E T and D T there are 100 particles 100 pockets coming between 10th minute and 12th minute how do I find out that fraction E T E T delta T but now delta T is between 10th and 11th minute so in that pockets what is the conversion right and now here I do not have to specify the order because here any order is okay for me because in that reactor because these pockets are there inside the reactor without any mixing with the any other molecules so it is retaining as if it is a batch reactor so the all the conversions are taking place in that pocket so whether it is first order or second order third order it does not matter for me right but if the pockets are breaking and then mixing with the other molecules then I do not know how to take care of that because that becomes now micro fluid at molecular level that information is not not known to me but for segregated flow it is easy to calculate are able to follow me why segregated flow is easy because segregated flow is behaving as if each pocket is a batch reactor and now depending on my E T D T information how many of those batch reactors are coming between zero to one minute one to two minutes two to three minutes how do I get that information it is only through RTD correct no it is only through RTD so that is why this E T D T is the fraction and so many pockets and this will give me the conversion in that now here whether I have zero order first order or second order it does not matter okay that is why very clearly for first order and segregated flow RTD information is directly usable right and the derivations are so simple it is not what we write there is the same thing what we write is the the conversion in that pockets multiplied by what are the number of pockets that are coming between in this time between E T D T that is T and T plus delta T that is the fraction of material that is coming in that fraction I may have thousand pockets right okay good so this is the I mean the definition the equations for first order and also for the segregated flow and now we can also prove that for first order yeah this equation for first order even if I use this equation or this equation for first order both are same in fact I simply wrote E power minus K T right like here whether I have late mixing or early mixing we are going to get exactly same thing for first order you know what is the equation for first order for these two systems conversion equations you know the answers can you quickly derive and tell or you cannot derive you do not have to derive you can tell me the answer finally C A by C A not equal to if I have this RTD in fact for first order either this model or this model model 1 and model 2 gives for first order use for first order yeah C A by C A not equal to E power minus E power minus K T bar 1 1 excellent so on 1 plus K T bar 2 you can derive in fact using this you can derive you can using this you can derive you will get that okay so message here is that this equation when you are getting it does not matter whether you have early mixing first or late mixing both will give you same conversion if it is first order why because there late mixing or early mixing does not play a role that is what is the conclusion late mixing or early mixing does not play a role that is what is the one and now I will also give you quickly for second order I think aware second order model 1 second order model 1 I am giving the equations okay you can derive that later this will be C A by C A not equal to this is second order no so I have minus 1 plus square root of 1 plus 4 C C A not K T bar 2 divided by 1 plus C A not C A not K T bar 1 good so whole thing divided by 2 C A not K T bar 2 that is the one for model 2 so you know how do you get this okay I think if I say this is C A not and this is also C A not both are same but this will be C A 1 this will be C A 2 so then let me write here C A 2 and here this is C A 1 this is C A 1 dashed and this is C A 2 dashed that I have not written you have noted down this you have marked this no okay shall I you are asking me to write here or this is C A 2 by C A not oh this also okay so here both are same C A 2 and C A 2 dashed both are same okay yeah so now and I tell you as far as this mathematics are concerned you are not learning anything new because you would have done this even before RTD when I have CSTR followed by mixed I mean plug flow or plug flow followed by mixed flow you would get the same equation okay I do not know whether did I give that one in assignment P F R followed by CSTR for second order no okay I could have given that okay so model 2 C A 2 dashed by C A not so that is why I am not deriving I think you know because those equations are already there is nothing new in that except algebra that you have to do yeah second order model 2 will give me minus 1 plus square root of 1 plus 4 C A not C A not K T bar 2 whole thing divided by this is complicated 2 C A not plus C A not K T bar 1 minus 1 plus square root of 1 plus 4 yeah so this is the equation one thing you have to notice there what is C A not K T bar 2 so you can call that one as D A 1 D A 2 okay V is so angry okay so now you know you have calculators now no huh now what would have done if you could have given separate test you know that I do not do a human mind can explain anything okay good now take C A not K T bar is also equal to C A not K T bar K T bar 2 and K T bar 1 both are same equal to 1 can you calculate C A 2 dashed and C A 2 C A 2 by C A not C A not K T bar 1 also equal to C A not K T bar 2 equal to 1 by the way those 2 are damn caller numbers so damn caller number 1 and 1 for the both reactors what is C A 2 dashed and what is C A 2 C A 2 by C A not and C A 2 dashed by C A not whoever does correctly they will get 5 marks I do not understand you have to give me the final expression final value this is 0.366 so conversion X A 2 equal to 0.6 0.634 correct no yeah for the other one 0.382 so X A 2 dashed equal to 0.618 618 no yeah yeah what is the conclusion thereby as if we do not have any other work we have calculated that is true you may think that you do not have any work sir yeah when it today why order is greater than 2 second order yeah because it is second order and because it is late mixing so you are able to calculate that but life is not so easy because here we specified ideal p f r and ideal you will not have this kind of equation and this kind of equation if I say that they are not ideal reactors both the reactors if you have some other intermediate RTD okay then you will not have this kind of clear picture so that is the reason why we have drawn this right and now we are saying that how do we understand the four corners this corner this corner this corner this corner okay my next thing is comparing this corner here I take M f r and segregated flow that is what I already explained you know in words we have M f r we have taken segregated flow what will happen now so pockets are continuously coming pockets are continuously coming out what is the RTD of these pockets same thing exponential decay right so I will know what are the fractions and all that so I can now calculate what is the conversion in that because segregated flow I know why because in segregated flow each and every pocket is not breaking and that pocket is coming out after some time which is which is dictated by RTD correct know if I know RTD the fraction coming between time t and t plus delta t is ETDT and in that fractions let us say 10 and 11 so 10.5 minutes 10.5 minutes if it is second rod also I can calculate conversion because it is batch reactor right these pockets so that is the reason why I know I can calculate but only thing what is happening in this mixture flow reactor is that molecules are not communicating only molecules within that pocket only are communicating and getting reacted so the concentrations are kept as high as possible so that is why for second order reactions you get you get more conversion and on the other hand if I use mixed flow this corner maximum mixedness individual molecules freely moving earliest possible mixing what is now happening now happening is that the moment molecules are molecules entered the reactor they are free to communicate with anything they are not keeping the concentration high but they are diluted now because it is mixing with each and everything whereas in the pockets they are not mixing pockets keep the concentration high because they are not mixing with the entire reactor you know the other things other pockets so that is why the concentration is maintained as low as possible because of mixing right and then you will get some conversion that conversion you can calculate using our normal CSTR second order because you know even you are talking about second order reaction so that means MFR corner this side and this side we have matched correct no MFR we have taken segregated flow what is happening I will derive tomorrow MFR segregated flow equations okay again it is not great derivation but we will give for second order right and then now yeah so mixed flow already you know you have already done it mixed flow and maximum mixedness where you have earliest possible mixing with individual molecules that is what you have learnt in BTEK now also learnt in MTEK now okay and now those who have completed MTEK they also learnt in PhD now okay so that will not change second order mixed flow and normal fluid micro fluid you have the equation good yeah yeah we are going okay then the other other one is PFR here and PFR here right PFR segregated flow how does that behave so when I put segregated flow in PFR each and every molecule exactly sorry each and every pocket spends exactly same time ideal plug flow even if I have segregated flow I get the same conversion and even if I have PFR here this corner again you have same thing so when you have PFR does not matter whether you have ideal sorry maximum mixedness or segregated so in other words do not care whether you have micro fluid or macro fluid if it is PFR that is one of the important conversion important conclusions important conversions yeah that is true for you it is conversion right you have to convert not the one so that is why important thing is do not care if you have micro fluid or macro fluid if you have PFR or RTD close to PFR right that means if the deviation of RTD also not very far from plug flow do not care that is what is the thing so the moment you have plug flow you do not have to think about okay late mixing early mixing why because it is always late mixing correct no why late mixing by definition of plug flow there is no mixing okay and Savita wanted to tell it is only zero mixing okay zero mixing is late mixing inside the reactor or latest mixing because inside the reactor it is not at all mixing if at all we break it and then mix together and then check average conversions pockets and all that so that we call the mixing is only outside the reactor but not within the reactor right so now what is the problem problem is with this flow this flow MFR MFR also what you have to learn new is what segregated flow not this this already you have the equation right so now if I take this scale that means only this corner this corner here we have done it right so now somewhere in between if I put we do not know how to calculate jittering did it right jittering did it and then those equations are complicated so we are not I mean I just give the jittering equation we just leave it there and in between I can also you know we corner this this side and this side now the same scale I can take here and then move up and down okay so that means PFR here somewhere intermediate degree of segregation that means some amount of segregated flow late mixing some amount of early mixing right how do you take care of this but you know wonderful information is there but it is not possible to use that information to calculate conversions it is complicated right but how people thought about that and very quickly tomorrow I will try to give that thing right so what we do tomorrow is very in the in the in the class is that I will take this segregated flow alone yeah okay segregated flow alone and then we will try to discuss whether how you know the both extremes what we have done a little bit now again I will repeat and then derive only for segregated flow MFR because PFR absolutely no problem right MFR you can forget