 the batch reactor which we have discussed yesterday all the ingredients are there in this problem okay what you have to find out is the reaction time okay and after calculating reaction time then you have to add 30 minutes that is the last line you have 30 minutes required for discharging cleaning recharging and all that then you have to calculate how many batches and then you have to calculate what is the batch volume yeah it is a reversible reaction and equations are already there derived and all that in 11 spiel book also right so you can if you derive then you will be more comfortable if you just copy from the textbook if I give the same thing in the examination I do not give you textbook okay so then you will have problem and I also would not give marks if you are putting from memory okay memory means only computers okay so that is why if you recall from memory and then just write there I do not give you have to derive good and the bracket A B R S are the like A plus B going to R plus S all liquid phase reaction also constant density system everything is there good okay anything okay good so that is the problem now we will start logically plug flow reactor why logically plug flow reactor why did I say logically plug flow reactor after batch plug flow and batch will be same under some conditions performance yeah I mean both are same and if they are same why they are same logically I said because the same equation under certain conditions is exactly same as batch reactor equation for constant density systems why they are same and all that now you have to get that knowledge okay why and that with clarity not simply you know like parrot because everyone says that they are same or they may be different then you are also repeating they are same they are different right but if I ask you why they are same why they are different not able to tell so in this course what you have to get is that clarity all the cobwebs removed from the mind clean house correct no so that is what I think you know definitely when you are going to choose continuous system when you are going to choose batch system that clarity has come okay with examples and also with reasons and all that so now in batch sorry in batch reactor again how do you calculate volume even though volume is not directly present in the design expression that also you know how to calculate so any batch reactor the time is same even if you want to produce 5 kgs 50 kgs or 5 tons 500 tons batch time is same but depending on the production rate you will have different volumes okay sometimes you may use 1 meter cube production may be less sometimes you use 5 meter cube because production is more so to calculate all that only this problem is given okay so plug flow reactor diagram what we normally draw is something like this it is a tubular reactor it is a tube right and then something enters something comes out and we also show whenever we have plug flow reactor that we have like this correct no yeah so like that what is the meaning of that constant velocity and this constant velocity when do you get throughout the tube fluid mechanics wise hi how hi because only at infinite velocity you will have the velocity near the wall also same as otherwise as long as walls are there is no real plug flow reactor existing okay without walls how do you conduct the reaction you can conduct in some heterogeneous system beautifully you can conduct the true plug flow is there actually you may not know that but anyway I will tell later that one also yeah so this is how we have to show we will show the plug flow reactor then normally we will say that we have f a not entering and this one is final f a f and here also you may have c a not v not and isothermal we are talking now isothermal isothermal plug flow reactor and temperature is same that I do not have to write throughout because isothermal then what else is missing here of course x a we can write which is 0 there okay x a equal to 0 then correspondingly here I have c a f v f which may be final and also x a f which has some value if that is also 0 then beautiful design no reactor because where is the reactor there because x a entering 0 and leaving also 0 therefore that is a wonderful design because nothing will happen there sometimes you know not doing anything is safe good okay so this is what and I do not know whether you remember any other names than plug flow yeah we call piston flow any other name tubular flow but rod flow means you have to slug flow means it is only two phase system we are talking about homogenous okay we have sufficient names because do not invent slug flow and all that that will not come slug flow will never be plug flow okay so slug flow we will discuss later when you come to heterogeneous systems we are talking about homogenous yeah normally the names what you have already told we may call it as piston flow okay and other name you said tubular flow but when you say tubular flow normally tubular flow tube associates with flow where definitely at the walls you will have velocity equal to 0 so that is why when you say tubular reactor it does not mean that it is ideal plug flow reactor if you want to specifically say ideal tubular reactor okay so that means it is plug flow what is the ideality in tube our assumption is that we have flat velocity profile okay that only gives me that plug flow condition so piston flow then ideal tubular flow reactor and rod flow also is rarely used it is right what you said is right but rod flow rod flow also very rarely used it is that means it is like a piston piston is a rod correct no see if you look at the piston when it is moving through a cylinder how it moves exactly you have the cut there okay the piston the piston diameter is cut like this exactly so then this moves like this okay so that is why we say it is a piston flow because we expect in our tubular flow that kind of flow like a piston flow okay so why should we assume that we have that kind of piston so the ideal definition for this is that all particles must spend exactly same time inside the tube okay inside the reactor each and every particle okay how do I imagine that okay I will give you a very simple example most of you would have seen that okay before that I will also write time times okay time spent by each and every molecule is same in a plug flow reactor yeah plug flow is always ideal we do not have to again say that ideal plug flow okay plug flow itself is ideal okay so then why we should have this name you know plug flow the reason is that when you assume this time spent by each and every molecule yeah time spent by each and every molecule is exactly same means that will be possible only when you have flat velocity profile or axial mixing equal to zero axial mixing means this is the axial direction this is radial direction or lateral direction okay so in this direction there is no mixing what do you mean by mixing a molecule coming here and then again coming back back and forth okay so that kind of thing is not allowed why if a molecule comes here there is a flow continuous flow you are sending continuously volumetric flow rate wise v not if you divide by cross sectional area then it will be velocity so volumetric flow rate wise it is going with constant velocity okay for example first time we discuss constant velocity afterwards we can extend that to what will happen if you have variable velocity also okay so constant velocity and then the molecule comes here and by some reason that will also may come back a little bit backward so that means this molecule which has which has been moving with some other molecules forward now coming back and joining the molecules which have which have come later than this molecule okay I think okay may be explanation is not probably you are not understanding so this molecule entered five seconds back at this point okay at this point if I take that it is time it is five seconds now there is another molecule which entered three seconds back right when you say axial mixing equal to zero means this molecule this molecule will never mix in reality what will happen this molecule because of some disturbance will come back and then mix with this molecule that is not allowed in plug flow simple example is conveyor belt but that velocity is with respect to what velocity of the conveyor belt is with respect to what there must be some reference you know ground with respect to ground may be the velocity of this conveyor belt is five kilometers per hour okay that is normal walking speed that is why and all of you are standing there just and behind you also there is another row three people behind you also there is another row I am talking I am imagining you as molecules so three molecules three molecules three molecules in reality there will be millions of molecules but only just for imagination we are telling only these three molecules just standing there and then just you are pushed by the conveyor belt where that is equivalent to for us here convection the flow so this flow is simply pushing those molecules without any disturbance simply like that okay so then in first minute your color changes to green your normal color this color okay so then after another minute then it becomes red after another I think it becomes green sorry orange so like that by the time end if you go so you may get some purple color or something that is equal to 100 percent conversion right easy imagination now at any time when I look into this when I look into this people standing here will have red color all of them are uniformly have red color okay what is the meaning of that that means the concentration if you if I imagine that color as concentration all that color is same for each and every person and the concentration is same yeah at that point at this point so that means what is the assumption we are giving without knowing also that the radial mixing must be infinity we say 100 percent or infinity we say what is the meaning of that yeah there is no change in the concentration and that is happening because all the molecules entering in that row just moving are uniformly converted not for 100 percent 100 percent conversion is not occurring at this point it may be 30 percent but uniform at this point it may be 60 percent still uniform at this point it may be 90 percent still uniform this is 100 percent if you get 100 percent conversion so that means whenever I look at the reactor across the cross section lateral direction we say that we have uniform concentration when do you get uniform concentration in a mixture yeah when you yeah exactly when you have perfect mixing then you say that I have mixing throughout the reactor same so that is the reason why even here at any cross section we say that we have perfect mixing and in other words we will also say because we are saying zero there the axial mixing this direction okay axial mixing is something like this right some molecule is here again it will come back some molecule is here another again it may come back molecule here again it may come back same molecule may be coming backward and forward so that means this is mixing with molecule which is which has entered a little bit late and again going forward and again coming and mixing with some other molecules which have just entered there so all that mixing is called axial mixing axial mixing but in plug flow we say that that is not allowed ideal condition so now what we say is we have this axial mixing axial mixing equal to zero in fact which means that radial must radial mixing must be infinity we do not have to say again but we say axial mixing is zero radial mixing equal to zero and then what are the other things you said a flat velocity profile unless you have the flat velocity profile all three conditions will not be satisfied but three times we reiterate okay axial mixing equal to zero same thing as radial mixing equal to infinity these two can happen only when you have flat velocity profile all three can happen only when you have time for each individual particle and exactly same so that is why the basic definition what we would like to remember is the time of each and every particle okay why they are same means without any disturbance in the sense that all these molecules okay now we will expand our imagination slightly more now I will say that I am now feeding the molecules continuously but these molecules I am sending in the form of pockets each pocket may have some molecules where there is some concentration and all that so that means at time t equal to zero I imagine these are the molecules just entered okay these are the molecules just entered so now if we accept these definition like axial mixing equal to zero and radial mixing equal to infinity and of course the other one what is that the flat velocity profile all that if I assume then the same pockets will move from here to here each pocket now you can imagine as a very small batch reactor inside that batch I may have good mixing and all that okay so our imagination we are making smaller and smaller and smaller till individual molecules but first let us I started with molecules but let us imagine that we have small pockets and in that pocket the reaction is going on and this we are not allowing them to move forward and backward and that means axial mixing equal to zero which also means that radial mixing equal to infinity then at this point what is the conversion in each and every small reactor that small batch reactor conversion it is same and that conversion depends on how much time it has spent inside the reactor if it is 1 minute some conversion 5 minutes some conversion now let us say total time is 10 minutes required for 10 minutes you may get 99 percent conversion so at the end if I see oh they are not become bigger same yeah they may become bigger under some conditions also okay same size yeah at this point if I look each and every pocket also will you have exactly okay now slightly relax our I think this is clear now yeah the turbulence and all that when we say when you know you may have that very high Reynolds number you have turbulence what do you mean by turbulence there it is not that turbulence what we are talking when a molecule here can suddenly jump here a molecule here can suddenly jump here that will happen if I have a tank reactor if I have tank like batch reactor we have studied so batch reactor you take and then you put the all the reactants and then start studying can you identify its location you cannot because one molecule may be momentarily at the bottom of the reactor because of mixing suddenly it may come out or again because of mixing it may go to one corner and again you know another corner like that at any time any point of yeah at any time inside the reactor at any point it may be there in fact that is the definition of mixing you cannot say that yeah you cannot say that I have mixing but molecules are not moving okay so then when we say that we have perfect mixing the possibility for the molecules to move from any water anywhere is possible for I mean for for the because of the mixing yeah Abdul you know that the reaction happens by collision of molecules and in plug flow it is highly limited there is there is lesser conversion there is lesser collision of molecules how do we decide the lesser collision of molecules if we let it devide from plug flow and let it come out let there be actual actual mixing no but why do you say lesser collision I think you say that the collisions are there when only when you have tank reactor there will be some lateral mixing but yeah but even here when the molecule molecule level what is the size of the molecule how many molecules you can put in a in one inch pipe diameter so there yeah so there is again you know all those collisions and all that is there definitely but now that is not this way but only this way why only this way only why this way because if the flow is so good that it is not allowing anything to come back any molecule this is not allowed in this direction because of the convection velocity push that is bad actually because if I have a yeah I think that is a good question also because so that others also will learn that if I am allowing a molecule which is already converted with the molecule which is not converted what is the concentration now we cannot say one molecule but few molecules here they are converted 50 percent now suddenly they come and join here mix right so then they are coming and mixing with these molecules these are 25 percent or 30 percent converted what will happen to the concentration now it will go down and what will happen to rate of reaction it will be down because I think rate is a function of concentration see if you first order if you take very simple imagination directly proportional so that is why the concentration falls this is the reason why the mixed flow reactor is inefficient correct no we know that if I take one meter cube mixed flow reactor one meter cube plug flow reactor one meter cube mixed flow reactor will give me low conversion because only means fixed and one meter cube plug flow reactor will give me high conversion you know why now that is the reason the reason is because of that mixing so that is why here that same collisions are taking place but that is only in the restricted region theoretically speaking it is very very thin infinitely small region not at molecular level we are talking molecules levels are very very small okay so that is the reason why we say that yeah the plug flow reactor is more efficient than mixed flow reactor because mixing always you know this is what many students will have this imagination that mixing is better for reaction no mixing is bad for reaction okay perfect mixing is bad for reaction but you are allowing the you know again do not get confused so here even in this cross section I have perfect mixing so that means at this cross section I have the same concentration for each and every pocket because molecules we cannot say and then say concentration molecules are so many moles per unit volume only that is what is the concentration that is why this concentration is not diluted here in a plug flow you already told me no sir the concentration slowly changes okay very good that is the definition of also plug flow slowly means how slowly at only at each and every cross section only that concentration is changing slowly not across okay but definitely across means at this point I have different concentration at this point I have different concentration so that is why when I plot this graph concentration versus length this is the length then we will have this is C A not it slowly decreases and you also know that I mean as I already discussed that mixed flow reactor is better than sorry mixed flow reactor is less efficient than plug flow reactor we discussed that the reason is this concentration it is slowly decreasing depending on it is time here but across one cross section so now next we have another cross section okay another concentration next one another concentration that means at every point this rate rate is maximum here because assuming ideal I mean non isothermal reactor I have first order reaction K into C A not is the rate or C A is the rate at time t equal to 0 just when it entered what is C A not highest so that rate is more okay I am talking about simply A going to R first order reaction then slightly inside now it is K into C A but C this C A is highest okay highest means it is not highest not more than C A not but next to next one it is highest so like that slowly it is the concentration is decreasing when you have slowly concentration is decreasing the rate of reaction you know then that means I have one rate here one rate here one rate here one rate here one rate one rate one rate so many rates right so all those rates when you average them that only gives you the overall conversion okay but that is why the concentration of each and every I mean at each and every point very optimally used in a plug flow reactor whereas mixing flow reactor you are taking a I mean one tank and then continuously putting water I mean reactants continuously you are taking out stirring is there perfect mixer so the moment you put C A not then yeah then it is suddenly mixed instantaneous mixing because you are perfect mixing what is the meaning in everything is instantaneously mixed now when you see the instantaneous mixing do you see C A not at all then you see slightly less than C A not yes sir yeah how much slightly want concentration you see in the reactor yeah it is the outlet concentration and outlet concentration is how much 90 percent so your C A not is suddenly decreased to 90 percent concentration which is equivalent to your outlet concentration right so that means all that concentration history gone like here I have concentration history at this point okay if this is 10 moles per C A per liter 10 moles per liter this will be 9 okay this will be 8 7 so at this end I will have 1 mole per liter what is the conversion 10 moles 9 conversion equal to 90 percent right so now yeah but that 90 percent occurring here through so many rates correct no because concentration here different concentration here different so that will have a rate that will have a rate what you see is the overall effect of that concentration at the end whereas if you go to a mixture flow reactor where you take the tank and then just put let me also because for discussion I think I have to give this yeah continuously this is entering continuously you are taking here so now here I have C A not here I have C A F and by perfect mixing assumption which is simple assumption this is also C A F and now you see there is no temperature history at all yeah what is the plot here concentration versus C A not versus okay length there is no length actually but I think you know space coordinate so what is that much now like this and then you have C A C A F so all temperature history totally gone there that is why to maintain this conversions because given a volume given volume this conversion will be less this will be more right but to compensate let us say that you want to also get the same conversion like this where concentration come maintained concentration maintained every rate all rates are average and then you are not averaging system averages and finally it gives you so much conversion there if you want to compensate what you have to do oh no that is different same one reactor you should go for larger volume bigger volume so that is why you see you do not need any mathematics simple logic we know that you know the volume of the mixture flow reactor will be definitely larger than the volume of plug flow reactor for a given conversion that you have to always say for a given conversion for given volume the conversion in plug flow reactor will be more than C S T R okay good so that is what is the plug flow and that will happen only when each and every particle exactly moves like that and now I will give you another example as I told you that you have you know heterogeneous system I told you you know the coal is burnt using moving grades I do not know whether you heard or not coal coal for combustion so that will be something like this you have a wheel here which will be rotating another wheel here which will be rotating over this you have the conveyor belt so this moves like this comes out and then moving so now here I will feed coal continuously I am feeding and I will now calculate what is the time required for each and every part let us imagine that every particle is one centimeter easy to imagine okay one centimeter uniform size right so all the particles are coming there and then by this time it comes here if it is pure coal you will not have anything you do not have even ash ash also you will not have ash you will have whenever you have some silica and minerals and all that okay then only you will get ash otherwise no so that means each and every particle is entering coming here by this time at this point the particle completely disappears right because you have now fixed the space the not space the speed of the conveyor belt okay at 50 percent of the time that means you know if the total is let us say 5 minutes at 2.5 minutes at this point each and every molecule each and every particle would be uniformly converted right uniformly converted then when I look into this direction that means the yeah so this third dimension that is this flat plate this is moving like this okay this is moving like this this is what the distance I told so now at the middle if I just see here I will have the conversion of this carbon particles uniform throughout so at this point if I draw a line and see the concentration what do you say about that concentration same that means radially you have same concentration uniform concentration that happens because of infinite mixing see that is what is the meaning of that infinite mixing there because you know it is only uniform concentration normally when do we imagine that we have uniform concentration when you have mixing so what we say for axial direction is the mixing equal to 0 right and then in the radial direction mixing equal to infinity because you said 0 there you are putting here infinity right but in in in words it is that the uniform mixing means infinite mixing and uniform concentration means that will only happen if you have infinite mixing the infinite mixing means good mixing how can you provide infinite mixing there are many words which we do not mean anything including love and when you say I love you it would mean anything but as I told you know now explain to me what do you mean by I love you you cannot tell that is a feeling infinite mixing means it is a good mixing that is all where you have uniform concentration that is why those words infinite mixing and axial mixing equal to 0 axial mixing equal to 0 I will explain that may be true but infinity we can never see in the moment you see infinity you cannot come back again gone you are gone to infinity so that is the problem you know with these words but still we use very frequently infinite mixing for radial direction 0 mixing in axial direction 0 mixing in axial direction is explained by this you know very clearly that this molecule this pocket is not allowed to mix with this molecule okay and this kind of mixing when you have you will not have this condition what is that condition time spent by you cannot you know have that condition the reason I will tell you the same thing same mixing is happening everywhere axial mixing there is axial mixing so by the time you come here you will also see same thing same thing I am just pushing it there so a molecule comes here and a molecule coming here so now each and every molecule is not going and mixing with that okay so one molecule which is coming here may come out other molecule which is about to leave may may come back so now what is the residence time of this molecule which has gone out and what is the residence time of this molecule which has come in and the average of that is 10 minutes the average of all those timings if I take that will be 10 minutes correct no you know you have seen recently olympics 10 people are running so few people will come faster some people will come you know just behind and you add all those things and take average so then we know that average run time for that event we are not yeah that is what is the mean residence time here okay but some people would have come early some people would have come late right but now when I have 10 minutes there may be a molecule which has come in the 9th minute itself and there may be one molecule which is coming at 12th minute itself here right so that is not plug flow why every molecule or every particle should come exactly at 10th minute that is what is plug flow if we have plug flow in olympics you have to give medals to everyone correct no all of them are coming exactly at same time but in chemical engineering no we do not allow that all of you should exactly come out of the run with the same time that is what what we tell there and if you want to have a feeling for this I will tell same example when you are walking when you are walking some people may be more enthusiastic people they may move faster they will push you aside and then cross you correct no so that way may be going another 5 minutes may be 2 minutes before then you and there may be very slow fellow who is who is having diabetes heart attack and everything so those people cannot move so he is going behind only not going forward so those molecules may spend more time so that is not allowed in plug flow that is what is axial dispersion model when you really allow that because we can allow we have to allow that because in reality you will never have plug flow plug flow is only in our minds as a definition but plug flow for heterogeneous system this is the excellent example you know this conveyor belt coal conveyor belt perfect example is only this that means you are designing this and also you know perfect means I cannot really say perfect because when you are designing this you should design that without any vibrations right and without any sagging you know when you have this side one wheel this side another wheel when you put a belt it is definitely slag a little bit right so without that that slagging also you should sagging also you should design no vibrations so what will happen if I have vibrations and allow this a little bit articles will be coming forward and backward okay that is what is axial mixing right so that is why and that kind of perfect design even for conveyor belts I doubt whether there is any that is why I told plug flow is only in our mind but still that will help us in design you know very beautifully so that our volumes will be not exact but you think it will give one extreme that okay if it is ideal condition this is the volume if it is the real condition like I have axial mixing you need definitely more volume right because because of axial mixing the concentration is decreasing so instead of 1 meter cube you may have to use 1.2 meter cube so when you are moving in that cube if everyone is exactly moving with the same speed without pushing without pulling okay correct no that cannot happen anyway those who entered there that cannot happen without pushing without pulling then that is ideal plug flow everyone will see the god exactly after half an hour if it is continuously allowed okay but most of the time it is not continuously allowed they will put you in a place called cell okay cell and then lock you yeah that is a batch reactor that is what what you what you are doing in batch reactor you are not allowing any flow so intermittently they do that but I think after last cell you are allowed to move so when you are moving that when you are moving in that cube sorry okay batch PFR okay so then after we are talking about only plug flow section when they are moving so when each and every one is exactly moving with the same speed no push no pull by the time you lose patience okay because last cell will really kill your patience by the time you should have spent 10 hours or 15 hours you know the entered the entering time so that is why and then you start pulling and pushing okay so when you start pulling the particle will go forward correct no you push them so so in that cube there may be five six people or ten people you know so if you are so strong you will push them out and move or maybe one person will move forward so that fellow will be very angry you will say like this so he is pushing them back so that is why he said push and pull you know yeah so when they are when this fellow is pushing them backward then that molecule will come here okay so now is a weak person may be moving always from here to here here to here that is what is the example of axial mixing so next time when you enter the cube remember plug flow and axial mix okay yeah that is what an ideal plug flow that is not and of course even with conveyor belt we are so impatient we will be pushing and pulling there also okay so conveyor belt is to make them uniform time but that I think proposal was not successful because there is not much space all that I think so that is why maybe one day it may come right so that is another example for this axial mixing but in reality you will have that kind of pushing and pulling that is the same thing in that is happening when you have ideal I mean tubular reactor not ideal tubular reactor in tubular reactor you have now I am coming to your question you asked me know sir there is turbulence in the packet bed yes there is turbulence but that turbulence in packet back sorry in plug flow is only limited like this you can show that you are showing how are you showing turbulence in in okay in turbulent flow how are you showing in pictorially yeah but what is that what do you call that and all those things are velocity fluctuation we call them as velocity fluctuation in ideal plug flow what you are mixing is that I mean what you are imagining is that fluctuations are not allowed sorry they should have when we imagine plug flow ideally then they should have that kind of no velocity fluctuations are allowed in plug flow okay so that is why the turbulence is happening because of the velocity fluctuations because of the velocity fluctuations why the velocity fluctuations are there molecules are coming backward and forward and when they are coming backward and forward they are losing concentration because they are converted to slightly higher conversion but they are coming back and again mixing with lower conversion I mean higher conversion making that entire region is lower conversion average conversion right you know average conversion is between these two conversions this నిఘి నియికినెతా ఒారిమిచుందా ని హిమా ఆరినినిందూ కారినా and you are spoiling this fellow, this fellow has higher concentration, right, back, somewhere here, okay. This is higher concentration, this is lower concentration, we are talking about only reactants. So then you are, in this region we are diluting the concentrations. So when you dilute the concentrations, rate of reaction will be lower. When you have rate of reaction lower, then naturally your reactor volume should be higher. Why? In all reactor designs, I mean how many, we have only three reactors, batch reactor, plug flow reactor and mixed flow, not so many. So in all these reactor expressions if you remember, if you recall your memory, in the denominator you have rate, okay. So when denominator is smaller, then volume will be higher, okay. I think you know the derivation of this equation is very very simple if you understand this, okay. Ideal plug flow is the, sorry, plug flow itself is ideal. Yeah, the plug flow what we are imagining in our mind to be in our reactor is like conveyor belt where no one is moving, like coal particles, perfect conveyor belt without any vibrations, without any sagging and all that. So that is what, then each and every particle will spend exactly same time. So when I calculate, I mean when I, when I measure the concentration at any point across, then I will have uniform concentration. That means I have, I will say now that I have infinite mixing radially. No molecule is going forward, no molecule is coming backward. So I will say axial mixing equal to zero, right. And then the other one, this one, time spent by each and every molecule is exactly same. So all these things mean only one definition that is time for each and every particle is same, okay.