 so we have been talking about this plug flow and i definitely now think that you will not forget about definition of plug flow then mathematics are required so you have that equation zero to that simplest equation and i also told you why you should have this plug flow assumption why i told you why you should have plug flow assumption what will happen if you do not have plug flow assumption when you are making noise i want signal very clearly what you consider the diffusion yeah straight forward action i say okay yeah unnecessarily you do not have to use your brain for mathematics when it is required you have to use it right so as engineers you first simplify things so that you will get the simplest design equation then you want to complicate complicate right so that is what is the thing that is why you have to assume that and in the beginning and if you are really fussy guy so naturally you will now try to go for deeper and deeper and then use all terms that you cannot neglect in the real flow and those are the terms which i am going to write now for plug flow plug flow the actual it is not plug flow tubular flow the actual design expression i will write we will simply write here still plug flow okay it is a differential equation i will explain the i am not deriving that but i will give the differential equation most of you would have seen this equation but only thing is we will know what are the terms i think you know in the equation you should know what are the terms which term is representing what phenomena equation always comes from physics please remember that okay physics means you know you understand physics are the problem not resonic and holiday physics means resonic and holiday book is there you know very famous you have not seen oh my god you are not prepared for JEE really JEE it is Vedam you know Vedam Bible okay okay so that is why everyone uses we say Vedam or Bible or Koran because everyone supposed to use that you know everyday so that is why that is the reason only we will say so this reason we call it a when i say physics of the problem we are talking about the physical phenomena that is happening not physics means immediately our mind should not go to a book you know physics book that is what i am what physics book you have used you understand the state books state book or towards no more extension of physics particularly in physics there are wonderful books because physics is a wonderful subject where everyday you see right chemistry you cannot see everyday you feel chemistry everyday because in the stomach reactions and all that okay yeah and i think you cannot see a reaction even though you have a you know that there is some reaction you cannot see but the advantage of the physics is that everything you can see okay so that is why many people try to explain and all that you know physical phenomena okay and also the physics around the world and the universe so that is why you have the maximum information on physics and people are so much excited about physics the best physicians and i am not physicians i mean physicists okay physicians means again you will go to different way yeah doctors right now we do not want to go there yeah so best physics is you know noble rates and all that they started propagating that in very very simple language that is why there are many popular books on physics why i am telling all this is if you are able to read those books your chemical engineering also will be very clear if you are able to and sometime you know you have to read read read i say okay till atleast to 25 years 30 years i think only you have to read read read read and think about that okay because he has been seeing that physics everyday what happened was you know it is challenger one spacecraft went into space and then after 3 minutes or 2 minutes it exploded and 7 8 people died okay challenger no challenger i think yeah it was challenger so there there was a committee to find out what was the actual reason for this explosion you know this is very good this example you know then he was in the committee and they called all the people who have designed and we have also fabricated and we have operated all these people and then finally he only proved that that you know between they have the first part i think is the people who sit there the first part and the bottom parts sections all the fuel is kept at the bottom okay is the solid fluid or liquid fluid solid fluid i think what they have used there okay liquid fluid hydrogen liquid hydrogen they use okay so that fluid is used different sections we can also see when our people also send ISRO people also send first part will fall first second part will fall first third part also will fall first that third part should not fall okay that should go but anyway i think i am not joking about ISRO because i think in every history of any racket science it seems everyone has faced these problems even americans also lost many rackets like that when they were trying so that is why it is only learning curve so we are on that learning curve so that is all that is why but our people are successful in many things now they are sending and all these satellite connections and cell phones and this classrooms various places all that is through that only i think we are also doing excellent job in that so that parts will come in one and between these two okay first part bottom part i am talking where the fuel second part another fuel tank and may be depending on how far that goes may be third part fourth part also they will have right so in this one i think between third part and first part second part i think so there was a gasket wear ring they call i do not know whether you heard of those things because when you joining two metal parts yeah these metal parts will have groove so okay like this okay so here here they will have a groove the other side also they have the another groove right and in that groove you put that nice wearing circular this is circular and the the diameter also is circular diameter that is like that okay circular so that they put and then tighten right so then what happened was they found that they know that the reason is the explosion occurred in the hydrogen tank when it is coming to the second stage first stage has gone and that has to that has to propagate to the second stage so when it is going to the second stage something happened and then suddenly it broke and explosion occurred and then died all the people died i think you can see you know two parts it came and even now they will show in TV sometimes when that same day when it occurred that's what i was thinking here there are moving bed reactors right i think one beautiful example is you know gas fires can be used as gasification can be conducted in moving bed not packed beds so that means the entire bed will be moving when the entire bed will be moving depending on slowly you know the conditions inside and how much is coming there will be some gaps between the particles those are the gaps which i saw between you know there is one group which is talking another group which is talking there is a voidage between that so throughout that i was thinking now what should be the voidage what should be the porosity so all that i was thinking i was thinking you know so that's why i enjoy you know those i don't get bored because i'm now thinking that okay all these particles they are moving some with different velocity some with same velocity okay i mean the same velocity means another velocity so if it is if all the people are moving with exactly same velocity plug flow okay yeah so all that kind of things if you are able to relate you will never forget that so that's why i'm trying to tell you all the stories because by storytelling you definitely remember at least few people will change they don't erase the files immediately the moment they cross the door okay you have no delete after deleting files computer will tell you how successfully deleted the files i mean the most stupid stupid you know congratulations i have ever seen that you have not done anything you know computer deleted it says that we have successfully deleted the files so that is like that only another thing also you know windows to switch off to stop the computer where you have to go start what a wonderful command okay or to switch off the computer you have to go to start and then open find out where you switch off and then switch off that okay that happened because this bill gates was not educated correct no he was not educated in the sense that he dropped out from sometime okay if you could have formal education that is my addition probably would have taught where is the correct correct button but anyway so the final expression which we have to use is that doh ca by doh t this is unsteady state also okay i think i will write everything together minus minus da doh square ca by doh z square minus dr doh square ca by doh r square plus 1 by r doh ca by doh r ya plus u doh ca by doh z equal to minus r a okay so this is the real equation for tubular reactors where there is no plug flow right so now this equation is with this is unsteady state unsteady state tubular flow tubular flow reactor with axial and radial dispersion okay ya what are the units of that equation ya for unit volume per unit time okay ya so this you see can i identify where is the axial dispersion now i am asking you you are telling something u ya what is your name anupriya ya don't be afraid to say ya tell dr i am asking axial dispersion now where is the axial dispersion what is axial direction for us z z okay so where is that anupriya da that's why i also put da there okay this is diffusivity coefficient in axial direction and what is this one radial direction okay this is a cylindrical coordinate because that is a cylinder right so that is why this term will come that's what phenomena all of you must have been experts i think definitely all of you would have taken no that's what phenomena right ya not taken second i am not able to repeat it flashback do not forget your past i say otherwise i will tell you like this every movie tells you like this that is a flashback okay okay good so this is the one radial dispersion and this one you see convection term and this is the one this one state so now actually in reaction engineering what are the terms we have used from this equation in our class when we are deriving that equation v by f a not equal to d x a by minus r a and all that so what is the equation i have used what are the terms i have taken from this equation minus r a alone if minus r a alone where do i put it you check my notes is it dc by dt no no you introduce it yeah where conduction end what was it i told you all reaction engineers are steady state people correct no i told that where is the convection term there okay so out of all these terms how many terms we have taken and what are those terms minus r a and that is all only those two you see how much simplification we have done so we said that unsteady state i am not bothered because i am only steady state guy okay so this term has gone by plug flow assumption you have been telling all the time that action mixing equal to zero without understanding why so when action mixing equal to zero means d a equal to zero right so then what is the radial mixing infinity so this is infinity so i cannot put infinities in the equation so then how can i eliminate this term good question you see we said infinity fusion infinity is you cannot put in any equation you cannot solve it r tends to zero means there is no reactor very happy correct no when r tends to zero where is the reactor reactor disappears dc is zero because it is uniform no throw where is the gradient see those things i say please try to sharpen your brain okay go to central workshop okay open your brain okay so otherwise i think it is not happening so many things i am telling you but i think still it is not sharpened you are not at that ignition point okay so i want to see some ignition in the minds okay you see now this is a very general expression and you know teaching wise also i can tell you highly mathematical people there are very large number of professors who are very happy writing the equations on the board okay so they are not wrong because their approach is different and engineers approach may be different okay i mean practical people approach may be different so what idea is i take whatever is necessary and we write the balance equations that is one way whatever is necessary for plug flow we said that by assumption there is no axial mixing the radial mixing equal to infinity and flat velocity profile these two also enough okay and of course all the time taken by each and every particle is same all that assumptions will tell me that you do not have axial mixing you do not have radial sorry you have infinite radial mixing so these two terms i drop and then i write only this equation simply what is entering what is leaving and then we write and develop the equation that is one way of approach the other way of approaching is that you take the most general expression take all non-idealities into account okay so then you now develop and write an equation this is the that kind of equation where all the terms we have taken all the phenomena that is happening in the tubular reactor we have taken right we have taken that we have axial mixing we have taken that we also have radial non-uniformity that means it is not infinite okay there is some change with the change in the conversion along the radius you know when that can happen it can happen in packed beds and i told you all packed beds can be imagined first approximation as plug flow why you know flat velocity profile what is the kind of velocity profile you will get in a packed bed so i have packing here okay i am sending the reactor there it is coming out this is packed bed so when it is entering you assume that you know it is entering state as it is entering by plug flow that means before that i have uniform velocity profile and you know there are many assumptions like this is only academician way of representing the packed bed but in reality you will never have packed bed like this so you will have a pipe like that right if you have a pipe then all this will go because it has to expand slowly you know so that is why before putting all this into the packed bed you just draw here itself cone right your actual reaction should start from here why you are doing all this i am doing all that so that i can easily quantify in terms of mathematical equations so if i do that then it approaches almost you know this plug flow and from there it moves as plug flow the velocity profile is assumed most of the time like this and again you have to use here high renors numbers what are the high renors numbers for turbulent region in packed bed 500 and above almost flat velocity profile and in packed beds you can easily get this that is why low renors numbers itself you are able to get that because the there will be small fluctuations that is later right so because this kind of uniformity will come because of this solid presence when you have the solids those things will try to balance the flow somewhere here it goes faster somewhere it goes slower but and the average again that goes faster this goes slower so if you look at that on the average you have only flat velocity profile that is our assumption at the end so that is why please remember all packed beds are imagined as packed bed reactors that is the first assumption right then if you say that okay no i do not want to take only ideal plug flow so i want to take axial mixing that is the first non-ideality ideal mixing non-ideality because ideality will simplify my equations okay good that is the one so then second one is radial radial can occur here because you know any reactor or any reaction will be reaction will be either exothermic or endothermic so imagine that i have the exothermic reaction easy to remember hot means easy to remember okay so then i will put a jacket outside this then of course it enters and then comes out right so then it is exothermic reaction throughout the bed the reaction is taking place right so then when it reaction is taking place throughout the bed then you will have now temperature maximum wear and you are removing heat continuously yeah at the walls you will have yeah at the center you will have maximum temperature and at the walls you have yeah some temperature which is you know which depends on the coolant and all that so that is why now you have a temperature gradient at the center you have more and at the wall you have less so temperature gradient is there so whenever you have the temperature gradient now concentration gradient also comes into picture correct no how because you have gas phase reaction how do you calculate concentration partial pressure divided by R into T now the temperature is changing at the center you have high temperature that means you will have low concentration and at the wall you will have low temperature that means you have high concentration that means there is a concentration gradient which is not allowed for ideal plug flow so that has to be taken into account if you are really worried about that because i think in packet beds you have to really worry about that you know the size of the packet beds in industry it starts with may be 1.5 1.5 feet right 1.5 2 3 and it can go to even 5 5 feet means 5 feet 5 feet means may be 6 feet means 2 meters okay so then you can imagine how much that so that big diameter packet beds so that is why heat removal also is the biggest problem in packet beds you cannot put only outside jacket sometimes you have to put also inside heat removal systems inside here like this so all this will disturb the flow right so that is why the real expression what you have to use and when you are also studying the first time then unsteady state also will come into picture you have to solve this equation and then you have to find out when the steady state comes like you know most of the process control graphs will be with time and variable how it go it goes like this like this like this that is what is steady state okay so we are not bothered about all that we are only bothered about that particular thing you know you have seen many times response curves will be always it goes up goes like this goes like this sometimes it shoots up like this like this like this goes like that okay so that is why for starting point you also should have this term this term this term and all other terms you should have and then you have to solve that is what is the most difficult expression it is not that easy to solve okay so you do not have an analytical solution for even simple expression there right you have to go for some numerical technique where you have to use delta r here delta z here delta c a delta t so finite difference methods various methods are there you can always see you see I mean how complicated the reactor design expression the moment I go to the real world that is why I want to be in Levenspiel's world Levenspiel's world is imagine the world beautiful very simple problems and with jokes and all that so but the real problems you will see in Smith book James Smith chemical engineering kinetics particularly if you see the last few chapters 13 chapter I think 14 chapters non catalytic reactions 13 chapter if you see you will definitely see wonderful problems solved by him one dimension this is two dimensional this is two dimensional okay that is axial direction and also radial direction he has really solved the examples all this of course we will discuss more in chemical reactor you know chemical and catalytic reaction engineering next semester okay good so this is what is about the packet bed reactors and minus r a sir minus of minus r a death minus r a in place of minus r a if it is a first order reaction k c a sign problem okay that you can take care of when you are writing for when you are writing for which component okay yeah that is okay I mean that minus sign you can take care of that properly when you are writing for either reactant or product so that is not a problem okay so but only thing is you have to see that correctly what are the other terms that are there and what also bother about sign because you can also realize that when you use wrong equation concentration will be increasing instead of decreasing correct no because if you mistake that so then I think you can really check but I don't think any student as far as I know I have solved this equation using all the terms do you know anyone who solved I don't think m2 calls who is m2 calling we are talking okay I don't think do you think object we don't know I think project also I don't know anyone who has done it that is what I am trying to say okay so that is what this is also a good project for you where you have tremendous learning good mathematics we have to use good physics we have to use and then you have to calculate what do you calculate concentration if it is isothermal reaction and if it is non-isothermal then similar equation exactly will come for temperature so concentration profile and temperature profile that is what smithya has solved in that book temperature profile and concentration profile okay transport phenomenon approach is just nothing but transport phenomenon approach and even transport phenomenon also I don't think anyone will will talk about this equation so much because this mass transfer reactions coming in the last chapter no so by the time you come there you are already tied because this moment of transfer and heat transfer will kill you so I think that I think in only first chapter you do and then you read other things you never read anyway so that is how I think transport phenomena also we don't go deeper right good anyway so that is the one and I have also not given the actual graph for that equation V by f not equal to 0 to xa dxa by minus r a right so this is what we are plotting so you can tell me how we have to plot this is xa this is 1 by minus r a please make a habit of immediately marking x and y coordinates what is that simply don't draw two lines and then draw the curve right I mean that should go to you into your blood as engineers not only engineers anyone has to do that initial converse 0 yeah first of first I have to draw 1 by minus r a versus xa right so initially minus r a into k c a k into see first order if I take for example k into c a not is c a not square if it is second order reaction then I will have some value it is not 0 right yeah so somewhere it starts here and then finally when r is 0 that should happen when I have 99% conversion almost it is going to 0 so it goes so in between it may go like this but this is not the universal shape I am drawing there actual first order half order and also 0th order all that you can plot you will get slightly different curves right so general curve only I am drawing so x f I am just show that is what my conversion is 90% conversion for example so then area under the curve will be yeah in fact I just plotted only this side it is our elementary calculus which we learnt in school probably we have forgotten also in school right but here we are using that elementary calculus y dx this is nothing but y dx y dx means we will remember correct now integral y dx is area this 1 by minus r a is y for me so that simply becomes y dx right so that is area under the curve this will give me v by f a not okay so then if it is a new reactor I should assume what is x a f correct no for a new reactor you are designing a new reactor so then you have to calculate volume that means you draw a line because x a f you know x a f you know you assume 90% draw a line and then count the area if you are doing simply graphical integration then that will give you v by f a not what do you do if I have the volume already and then I want to find out conversion what do you do I know the volume I have 1 meter cube what is the conversion how do I use this graph why so much time tell us where is the concentration we are talking about the same graph we are not redrawing any other graph at all that because these are the things which you are going to do when I give you the assignment anyway I think this mood and all that I think you know it depends on its mood these moods are not matching so that is why I think please collect all that and we will go to the simple assumptions and then I think we will go I will upload whatever I want I will give the fund of people like that it is simple for me if you I think collect already some many people have given please give your emails and when I really expert become expert in mood then I will tell you you also go and see mood because I am not restricted every time I do not have that much time to learn also if I have that much time I will learn otherwise there is another simple because I think yes mail will go to all the people throughout the institute may be I think yes mail for MS I mean for chemical separate we have only for CHE anyway okay so but here what we do is we now start counting the area first so V by F A naught I know because 1 meter cubed I know divided by F A naught I know because F A naught is input for us then you start counting the number of that area number of squares and then finally whenever you are getting this value draw the line that is the conversion and that you have to do anyway when you are not able to integrate analytically otherwise you can go for some other numerical technique so these are the things which you have to and now you have to stop there are some applications also for this plug flow reactor you know applications instance say that I want to give you some real life examples like thermal cracking of hydrocarbons quickly you know that reactions conducted in P F R that you write reactions conducted in P F R because then you know you will also have a feel that you know we are not talking just like that reactions conducted in P F R just below that what you write homogeneous reactions homogeneous reactions you would have heard of these things but I think probably you may not know this thermal cracking of hydrocarbons to ethylene that is one thermal cracking of hydrocarbons to ethylene you know ethylene what do you get ethylene you are producing what is the use of ethylene polymerization so that is what I think you also should know what is the use of that second one is oxidation of nitric oxide you know why oxidation of nitric oxide is done one of the steps all gas gas gas gas homogeneous reaction this step comes for producing nitric acid that is intermediate step for nitric acid and incidentally this is the only third order reaction example I do not know other reactions but this is one of the if someone asks you in interview what is the third order because third orders are not many okay first orders are many second orders are many third orders are not many but if someone asks you because it is not many people may ask what is the third order reaction can you give an example this one this goes straight to stoichiometry this is two moles two one third order with respect to this second order with respect to this first order third order reaction okay so I think this step comes in HNO3 production next one sulfonation of olefins olefins what are olefins you remember organic that is why chemistry gopinath we should have when we studied we studied five chemistries organic one organic two inorganic one inorganic two and general chemistry physical chemistry later I think totally till three years we have studied six semesters at that time it is five years course around six semesters we have studied so I mean doesn't mean that we remember weird thing but you know that much chemistry exposure is there I think you will really appreciate chemical engineering right what is olefins double brand things also can be called as olefins so cn h2n cn h2n or olefins sulfonation what why we do sulfonation detergents so that is why for every reaction we have some use but unfortunately we are not telling you you are also not bothered to know okay good that is one so next one is fourth one decomposition of acetyldehyde decomposition of acetyldehyde the reaction is CH3 gas sorry CH3 CHO gas giving a CH4 gas plus CO gas CO gas so to get methane for example acetyldehyde decomposition okay and CO also then phosphine decomposition you heard of this reaction phosphine decomposition oh I think getting late know phosphine decomposition so that is for pH3 gas giving us P4 gas plus 6 H2 gas you know the beauty of the reaction one 4 moles giving 7 moles so disaster if you put this in plug flow reactor expansion is too much you know so then you know here beautifully it comes what is T bar mean residence time and what is tau all that will come here so these are homogeneous reactions for heterogeneous reactions sulfon dioxide oxidation ammonia synthesis ammonia synthesis and sulfon dioxide oxidation okay these two are enough