 భடం఻చ్ చతర లారంచ్గిరిక౩ పదర రంట్స్ఫూ, చంటింటరడాలం divided సిండోది. చూట్గ్ లివంఎరంపే ఌం కమిక్ పీరంవొ మిండద చరకమటాక్ మ�� つ Negative we discussed in the last class that is direct use of RTD to estimate conversions that means no modeling in between can we use RTD information directly to get the conversion, okay. So any the meaning of that is that to any real reactor that means with all diseases like dead space, bypass and all kinds of things, okay good. So then we also discussed that why first order reactions only it is possible for them for the first order reactions to get the conversion directly using the RTD, okay. Now I think that you understood, right because that is a linear process and also RTD is also a linear process but on the other hand first order reactions require only information on timings, okay. So a packet how much time it has spent inside the reactor and there the conversion depends on the time it is spent inside the reactor. So then you can calculate from RTD those timings and then club with kinetics that will give you totally the information on, okay. So the information on conversion so for first order reactions first order reactions we have RTD plus kinetic, okay kinetic information that is first order only will be giving performance of reactor this is only for first order reaction and we have also derived I simply wrote an equation without derivation what is happening in first order reaction is because RTD gives me the fraction that is coming between time t and t plus delta t in that fraction how much time this particular fraction has spent inside the reactor and at the exit of course you know when you are taking and what is the conversion in that particular fraction, right. So how do we write that the and then we are averaging all the fractions mean conversion or mean concentration, okay mean concentration of we are only deriving an equation for first order thing you know in exit stream equal to concentration of reactant remaining in the element of age between t and t plus delta t that is one thing that is the fraction you know that is concentration remaining in that fraction and sorry concentration remaining in that pocket and then we have fraction of I have to just move the boundary a little bit fraction of exit stream exit stream which is of age between can anyone fill up that between same thing t and t plus delta t, okay what is this very good this is ET DT or delta t, okay and what is this one, where is ET it is the concentration of reactant remaining in that element it is CA by CA naught of that batch that fraction, okay and the sum over all these will give us the mean concentration CA bar by CA naught, okay sum over that. So in other words what we have written yesterday was integral form CA by CA naught equal to integral 0 to infinity CA by CA naught batch ET DT so this is the expression good and now because we are writing specifically for first order, okay so now I know CA by CA naught batch for first order, right but I have written yesterday only E power minus KT but that means what it is first order A going to R, right but there are so many first orders like for example A going to R parallel reaction and A going to S, A going to R R going to S, okay so the same thing is it valid for all first order reactions like series reaction parallel reaction and also reversible reaction both are first order is it valid zero extension of brain, why you know anyone yes, valid sir, valid why valid, we are swallowing water to explain but you explain if there is anything, it is linear, it is the right equation is still linear, why do you say no, because you have A1 reversible reaction you have K1 CA minus K2 CA it is a first order one linear process only all linear processes, right if A going to R and A going to S what is the rate equation, yes minus R A equal to K1 plus K2 CA because the power of CA is always 1 it is linear so please remember for any linear process whether it is parallel whether it is series or whether it is reversible all processes it is, okay and that is why what we do is I think please take this you know example Levenspiel there is example, I do not remember now that example, okay so there is a there let me check whether I have my notes so that example please see it is not here, it is not here, okay please see that example where he has used for first order reaction and then calculated conversion so what he does is that this is E power minus KT for first order reaction and simply A going to R, right so then this equation also C bar A by C naught is sigma of E power minus KT E T E T delta T, right so I know this E T delta T and corresponding timings and I can calculate this and then you will get the average conversion as 1 minus X bar A, right this is for first order and even I can put here for second order sorry reversible reaction both first order A going to R, okay K1 CA so all that information you can put here depending on parallel reaction series reaction and reversible reaction all that but still this is valid so please make a note that this equation is valid for all linear process such as parallel first order series first order reversible reaction first order, anything else? First order is first order whether it is gas phase or liquid phase or sorry phase or any other phase if you want to create in all these phases provided it is homogeneous reaction there is no external mass transfer coming into picture in fact by the by even mass transfer is it a linear process or non-linear process what is the mass transfer equation linear process what is the size absolutely day by day brain is shrinking you know brain is shrinking and I think it is not expanding, okay I think more and more you read I think you know less and less you are able to understand I think you know that is what is the problem all of us could have stopped our studies in school itself would have been very very intelligent people, okay yeah really by the time you reach the highest degree brain is zero we do not know what to say yeah today I saw I think Rahul sent to me that Einstein quotation where I think about technology, okay when technology surpasses human interventions, okay so that means you are accepting technology that means you know calculating 2 into 2 how much means you have to remove either cell phone or calculator or computer laptop and then only calculate 2 into 2 equal to 4, okay then next one is when technology surpasses human interventions it produces idiots same body has used idiots is there I mean the sentence may not be exactly right, okay Einstein told when he was you know when he died 1965 gopi when did he die 63 yeah around that okay so right right I think around 60s only I remember that so I think somewhere before that he told that wonderful know so that is what we are doing for anything go and open the calculator or laptop and we do not know how to use our brain correct no your name not Abdul behind Mahabub okay not required you know click that is all clicks number of clicks over operation is over okay anyway good so this is the one please write a make a note of that this is yeah this equation if I say this is equation 1 this is equation 2 in terms of differential form equation 1 is valid for all equation because I think mass transfer process you know it is n A equal to k C A minus you know the other side concentration gradient it is only linear no so equation 1 is valid for all first order reactions and I will underline all so because all means again I have to what are all yeah right all means first order series parallel reversible all that okay please write that also otherwise tomorrow morning you may forget what is this all we do not yeah good okay the first order reactions are over now now let us the next one what we have discussed was using this yeah asking question what will happen for other than first order yeah and also I think time too much I do not have watch I am very happy today because I can take any time so C A by C A naught batch E T D T when I have this and for ideal reactors what is E T for example for plug flow alone right what is E T and what is C A by C A naught for ideal P F R P F R means ideal so C A bar by C A naught equal to 0 to infinity E power minus k T yeah this one is direct delta function E T no delta this is delta yeah T equal to T bar P correct you know yeah so now tell me what is the equation for that you see now even from this you can easily get provided you know actually for first order reaction what is the equation right so similarly for reversible parallel everything you can substitute this equation and you know when this function is valid and correspondingly you know this function as it is the that appears therefore depends on what are the other functions also you can calculate same thing you can also put here for M F R oh my god I am taking lot of time C bar by C A naught equal to 0 to infinity E power minus k T what is for E T M F R E power minus T by T bar M by T bar M okay D T if you integrate that and put the limits between 0 to infinity what is that you should get here 1 by 1 plus k T bar M that is what is for first order okay good very nice okay so now the next one is this models what we have discussed why only for first order because it is a linear process and also first order requires only the timing and the timing is supplied by R T D so that is why I think we can use this very happily without any problem okay good but now what will happen if I go to other than first order reactions so for that we took that model very beautiful model for other than first order reactions we are just explaining with model 1 which we have discussed already but still I have to give some idea you know because yesterday this is T bar P no T bar 1 I said right T bar 1 this is T bar 2 and the other model 2 is just reverse of this yeah so same thing this is T bar 2 T bar 1 right and we found that for first order okay most important thing E T versus T this is T bar 1 right so if I do not give this picture this these two pictures and if I give you only this E T you know that yesterday we have discussed that this E T can represent model 1 and also can represent model 2 and not only that it can represent many other models which I will show you later a little bit later okay it can represent so many models R T D cannot supply all the information that means again what is the information actually you need if I go to n equal to 1 model 1 and 2 model 1 and 2 gives same conversion this again reiterating what we have told the meaning of this is if I know R T D it does not matter whether you have late mixing or early mixing because R T D tells me the time and if for first order we also require only the time of that for particular fraction how much it has you know the time it has spent inside the reactor excellent so now for the what is n 1 n equal to 1 right so n greater than 1 because I am worried about my time I think and I again started so again I will end up with the same thing what I have told you yesterday so n greater than 1 we have seen that model 1 gives gives more more conversion than okay more conversion why then I think is understood correct no model 1 gives means model 2 does not give that is all that is all okay so for n less than 1 even though we have not proved you will get the reverse model 2 gives or okay model 1 gives yeah less conversion so what we thought if I am talking about n greater than 1 for example second order reaction right so the it is giving more conversion the reason is that here we have late mixing and here we have early mixing okay so this information should be known and thus information is not given by RTD so that is why RTD alone cannot be used for estimating conversions for other than first order reactions conclusion number 1 right so now for other and unfortunately in industry and also in our profession we have other than first order reactions many right so that is why this this information we should definitely know what is the information information on late mixing and also early mixing this one is early mixing as I told you late mixing and early mixing are just vague terms so that is why now we want to define these mixings like okay when it is possible to have the latest mixing so there are two aspects one is the state of the fluid itself state of the fluid okay state of the fluid itself can tell me whether the mixing is taking place latest means you know it is never mixing Savita Savita is there okay yeah so when you say latest mixing means it is not mixing inside the reactor afterwards you may break and you may eat and whatever you want you can do that right yeah so state of the fluid is one parameter the other parameter is yeah the react itself right okay you know yeah the react itself what you said I will tell it is not correct later okay yeah state of the fluid itself that is one parameter the other one is how early these things are mixing that means how early mixing means it depends on what kind of reactors we have right how early when it is mixing means if I take individual molecules together and then individual molecules and if I put in mixing flow then you have earliest mixing possible right right so that is why the first thing what we have to define is state of the fluid and the second thing what we have to define is earliest of mixing that means the earliest what is called that is maximum mixing is that is possible earliest of mixing that means how early it can these are the two parameters which we have to define and the state of the fluid tells me whether I have micro fluid or macro fluid okay and the definition of micro fluid is the particles are individually capable of mixing right they are not forming any aggregates and any molecule can communicate with any molecule if it is allowed to communicate right but the same molecules the micro fluid individual molecules if I put in a plug flow reactor they never communicate they just enter go with all other you know only that cross section and then comes out that is what right so that is why we say that first state of the fluid will determine whether I have micro fluid but micro fluid is capable of mixing early capable of mixing early whereas macro fluid will never mix so this answer is answer to this late and early how late and how early right the latest one is never mixing so how do I define that using macro fluid macro fluid are the packet of molecules where I can give you know approximative which contains approximately 10 to the power of 12 to 12 to the power of 18 moles okay and they are independently moving without contacting or without coalescing or without breaking you know retaining their own identity from the beginning and then coming out now what is the advantage of looking at that because whatever conversion is happening now I know exactly that is happening inside that particular packet and this pocket is nothing but our batch reactor okay equivalent to batch reactor so any reaction may take place there first order reaction may take place second order reaction may take place or 0th order may take place any order reaction may take place within that particular packet that is the reason why we say 10 to the power of 12 to the power of 18 because that will give an idea about concentration so if I have only one molecule you cannot say concentration okay so that is the reason why we say you know that approximate value good so this also we discussed macro fluid and micro fluid micro fluid you know now we have to have the connection connection is this tells me early mixing and late mixing now vague words like late mixing and early mixing have to be clearly defined that definition comes by defining state of the fluid first state of the fluid okay this is one parameter state of the fluid and when I take this state of the fluid what we call this one is degree of segregation that means macro fluid is totally segregated whereas micro fluid is totally mixed right I mean if it is allowed to mix capable of mixing whereas here this capable of not mixing right that is the extreme right so can you give an example of macro fluid liquid droplets provided we very strictly follow that no liquid drop is allowed to coalesce with any other liquid drop or even if there is some kind of mixing going on and all that you know in the overall liquid then even the droplets are not allowed to break allowed to coalesce and you know those two are important things and the size is constant during the reaction okay yeah I mean if the gas phase reaction slight expansion may be there but condition is that within that reactor itself within that the packet itself whatever is happening good yeah so to take care of this late mixing and early mixing we have now two definitions now this is micro fluid macro fluid is giving the state of the thing and we also have two more you know scale of mixing scale of mixing many papers will tell us this is micro mixing okay scale of mixing one is micro mixing and Levenspiel calls this one as degree of segregation degree of segregation this is the definition of Levenspiel book where we have you know micro mixing but some papers will give that you know it is called micro mixing but Levenspiel book tells degree of segregation so when you are seeing the book degree of segregation means we are talking about micro mixing and the second factory is that macro mixing which he calls as earlyness of mixing earlyness of mixing okay so actually this macro mixing earlyness of mixing is given by RTD what is that no no you have to tell louder macro mixing is called as earlyness of mixing no no see he calls this earlyness of mixing is for macro mixing where macro mixing can represent RTD right yesterday I have drawn the scales also what was one scale this is micro mixing scale so micro mixing scale that is increasing from this side to this side because here I have segregation and here I have maximum mixingness don't get confused with maximum mixingness with earlyness of mixing maximum mixingness yesterday also what I said was right only okay earlyness of mixing it won't represent that you know maximum mixingness earlyness of mixing is associated with the reactor right so reactor means it RTD comes into picture right so this one has this RTD but this is late mixing right and this has early mixing but this also has the same RTD so these words are used earlyness of mixing represents okay so this is micro mixing and I have also written there if you remember if you see my notes here I have degree of degree of segregation this is Levenspiel's meaning okay so that is what is the degree of segregation and here what is the segregation infinity maximum and here we have segregation equal to zero that is what is the degree of segregation what we have and the other scale also what we have Rahul you have watch can you put that to your watch there so here we have P f here we have M f right that is what and we call this one as macro okay macro mixing macro mixing that is the scale right and I also wrote here this represents RTD and I think that side I have written I think residence term distributions okay this represents and anyway these two are the extreme RTDs for us where this P f tells me that the RTD equal to zero and this tells me the RTD equal to zero to infinity so everything covered this is zero that is zero to infinity so any other system may be intermediate RTDs whatever many other systems what we have so that is why we can call also in between we have intermediate RTDs intermediate RTDs and here we have intermediate mixings here intermediate mixings okay okay intermediate mixings states okay what do you mean by intermediate mixing states here this side yeah this side I have individual segregated packets this side I have individual molecules so here if I look at this point I have more number of packets and few molecules at this side if I look then I have more molecules and few that is what is the degree of segregation and now we do not have any possibility of taking care of them under those conditions when I have packets separately and also the individual molecules separately I can handle but few packets and few molecules information is impossible to get how can you get this information from the fluid when you look at that if you have water can you find out how many aggregates are there and how many individual molecules are there that itself is very very difficult that is why in reaction engineering what we do is we only find out what is happening at this point what is happening at this point and what is happening at this point what is happening at this point we have 4 cases like I take M f and then find out what is happening with segregation right and also M f I will take to maximum mixingness to covered same thing P f I put here and also P f I put here right and maximum mixingness can be obtained by a what kind of fluid micro fluid can be obtained right but the moment I put this this P f extreme here then it would not exhibit any mixingness right so that is why please do not confuse with maximum mixingness and early earlyness of mixing this is the word he has used for RTD representation which we are calling as macro mixing that is why macro mixing other people call and Levenspiel called this one as earlyness of mixing and the other one micro mixing which gives me degree of segregation okay micro mixing is called by some other people and Levenspiel calls that as degree of segregation okay good so I think this is clear now the connections are clear all these diagrams and then scales we have had the reason is only to answer how late how early and that is why this figure is very very important figure for us really very very important figure for us so now what we have to do is let us take this first one degree of segregation and then discuss quickly okay first take degree of segregation that means we are now talking about state of the fluid right degree of segregation this is segregation here complete segregation is macro fluid and if you want you can also write macro fluid do not write macro mixing this is macro fluid and this one is micro fluid right in degree of segregation let us quickly discuss for batch reactor what we have and also PFR and we have MFR all three right okay good so now let us take batch reactor first and the one extreme is let us first talk about micro fluid micro fluid means maximum mixing as that is possible right that means I am now putting this point here right this extreme PF I am just coinciding with that that means I have PF and maximum mixing as maximum mixing as possible only for micro fluid so that means what I am trying to say is we are now talking about if I treat micro fluid in batch reactor what will happen okay micro fluid also here individual molecules all molecules must spend exactly same time right so there is no I already we have the equations for this for micro fluid right micro fluid and you already know how to calculate concentrations for first order reaction second order whatever reactions okay good now the same thing I also put in PFR because batch and PFR both are same right so here also the molecules individually enter and then exactly spend same time like batch reactor and you also know under those conditions how to calculate conversions for micro fluid that is what you have done in your B Tech that is what we have done in the first few classes here it is only micro fluid without knowing we assumed so you have equations for batch reactor and also plug flow reactor and even for mixture flow reactor right so all these three but I think because I am now talking only batch and PFR because this extreme we put here where you have micro fluid because this extreme cannot be satisfied by this micro fluid because here you have segregation and whereas here this is capable of mixing right so at individual molecule level so that is why this one and now if I take this extreme and then put it here right PFR MFR extreme even then you have the equations because individual molecules will be moving and you know how to write the equation entering leaving and all that you have the equation so for micro fluid we have all the equations in the degree of segregation point at this extreme where you have micro fluid which is capable of giving maximum mixingness okay now we have to talk about only segregated fluid now same thing okay so that means PFR will put here and also batch reactor is PFR again and this one mixture flow also we will put it there first let us take batch and PFR which are both are same right because residence time distribution is equal to 0 now when I use batch or PFR like individual molecules here also each and every pocket should spend exactly same time so you know how to calculate that means now even this the packets also behave like individual molecules because individual molecules also spending exactly same time so that is why if you have batch or PFR and if you have micro fluid or macro fluid does not matter you have the same equations valid because it depends on the residence time residence time distribution equal to 0 even if it is individual molecules and also residence time distribution equal to 0 even in the molecules inside that pocket correct know each pocket is spending exactly same time so both are same so that is why batch and plug flow gives same conversions for macro and micro what fluid dash net so we do not have now we have to worry about only this flow MFR MFR also as far as micro fluid is concerned we have the equations micro fluid equations available available vtech okay good I mean you have done that definitely yeah so now for macro fluid we are discussing now macro fluid is nothing but segregated fluid and when you have this mixed flow and now what you have to imagine is so these are the packets coming they are supposed to be equal size okay we have stirrer and also packets are coming out okay mixing is taking place good so now when I look into the macro fluid this is macro fluid so continuously the packets are coming inside right and then continuously the packets also coming outside but if I look at the packets here if I take 100 packets just an example in that 100 packets what I see is packets which have just now entered or packets which have stayed overtime because the distribution is possible from 0 to infinity so what I do I break all that because and each the beauty here is that each element each element here each packet here will have the same conversion because depending on its own residence time inside whether I have first order second order third order because whether late mixing or early mixing will not come into picture for the molecular level late mixing early mixing will not come into picture here because only that packet inside that we have the sufficient mixing for the reaction to take place because all the molecules are communicating within that but if I compare two packets one would have spent one minute another would have spent 15 minutes so conversion in this is different and conversion in the other one is different so what we have to do there also is exactly the same equation what we have written for batch that means now I have to in effect what we are trying to tell is that when I assume segregated fluid now the conversion depends only on the amount of time that is spending inside the reactor and how do I get that information from RTD and from kinetics inside that packet right so that is why the equation that we have to use here is for segregated flow same balance we can write CA bar by CA not equal to 0 to infinity CA bar by CA not batch ET dt this is for segregated flow please remember that and only thing here is that the other one for first order reactions only but in this when I assume segregated flow absolutely no problem like I can tell you an example coal combustion right so coal particles have you know almost same size we assume and few continuously I am feeding coal particles 1 mm and they are coming out but depending on their time inside the reactor some particle would have completely burnt some people would have only partially burnt some particles may not significantly burnt at all because that would have spent only one second but what I see the total energy that is relieved from this combustion is that a total of average of all these particles where some partially converted or some not at all converted because sometime you know quickly it may come back or some overcome only ash structure you will see and ash alone will come out so that is what is the overall so same thing even I think someone was telling droplets I think many can tell so the droplets also when I look each droplet is exposed to the other material also okay we are not talking about mass transfer effects reaction is going on in these particles in these droplets and when I take different droplets then I can see what is the conversion but in the reactor they are not mixing but after coming out of the reactor I may break all that and then see what is the average conversion that is what is the latest mixing I am telling so inside the reactor latest mixing means they are not mixing you know at all so that is why this equation what we have to use now if I substitute here for mixed flow I know ET dt right for n greater than 1 second order reaction second order reaction I know what is CA by CA not batch what is CA not by CA not batch for second order reaction quickly expansion of the brain for n equal to 2 CA by CA not batch 1 by 1 plus K2 1 by batch reaction 1 by 1 plus KT CA not is not coming there CA by CA not batch equal to CA not 1 by 1 plus KT CA not or otherwise K CA not T because those 2 are K CA not T that is what what you have to substitute here and what is ET for MFR we are talking about only MFR E power minus T by T bar by T bar M if I want to put here so now these 2 we have to substitute there and then try to okay anyway so C bar substituting those two equations CA bar by CA not equal to equal to 1 by T bar 0 to infinity E power minus E power minus T by T bar M divided by 1 plus K CA not T this into dt so this is what we have to integrate it is not easy to integrate you cannot integrate okay do not try here do not try and then just give some answer okay so you cannot so that is why the exponential integrals will come here so that exponential integrals will come that means exponential integral you have to put this one alpha to sometime T some other variable I think tomorrow morning again I have to finish this and then we have we can cheat chart I think you know the other thing also this even as of mixing also I have to give some idea