 Yeah, we will start now, the next model after single parameter model, that is tanks in series and axial dispersion, we are going to talk about multi parameter model, multi parameter model, yeah. So the name of this one is Koelte-Kloutier model, these are the first people who suggested this model, yeah. Right, actually if someone is interested, I can also give the reference, this is Canadian Journal of Chemical Engineering, volume 37, that is what normally we write, page 105, 1959, I am sure most of you would have never born there, at that time, okay, yeah. So normally what we visualize here is that we have a CSTR, something like this, we have, yeah. So continuously we have the fluid entering and continuously coming out, volumetric flow rate, volumetric flow rate, this is V, right and we have a stirrer. So this is the actual real mixture flow reactor what we will show and here what we expect the non-idealities will be, the bypass straight like this, without spending much time it may go as bypass, okay, that is bypass and you also may have dead space, this is dead space. So when I have this situation, how do I model? So that means actually I have an active zone something like this, that is active zone, then I have some volume in dead space and some bypass, right. So to write the equations, first I should have a model in my mind and that will be shown something like this, I have a active zone, so this is the active zone, then we have the stream entering into active zone, this may be V and volumetric flow rate and yeah there is a dead space, that is dead space and that means the active zone I am showing this one as active zone and the volume of this will be V A, capital V A and the volume of this will be V D, right. V D is the volume of dead space and now we also have the bypass is shown like that, that means practically it is not spending any time inside the reactor, yeah. To show active zone we are showing this stirrer, this is bypass, so this volumetric flow rate V is split into now, this is V A, small V A, volumetric flow rate going through active zone and this is V B, okay and both of them are coming and then again you know, yeah, mixing here what we see is some concentration C, okay and I can solve this one either for pulse input or for step input, let us take step input where continuously I am sending the concentration, the step input, okay, concentration of time T equal to zero, C zero time T equal to zero, so then we are writing the balance after some time T to this, to this model, you see now this is what you have to do also, you know most of the time when you are modeling and the physical system you have to imagine that what are the problems, how do you break up the problem into this kind of diagram where now it is very easy for me to write the you know equations for each zone, right. Like for example this is active zone, you have only perfect mixing here, what is the flow rate entering V A, now I have V A into C A naught, C naught because it is a tracer input, right and then here it is coming V A and C A that is coming out, right and I have the bypass now V B and what is the concentration here C naught, very good, right because I think you know it is practically not spending any time inside the reactor, so that will have, now these two mixing with this C A and volumetric flow rate V A here also volumetric flow rate same thing V A because we are talking about constant density system, right V A entering, V A coming out, there is no volume expansion under this, so here V B and with C naught, so now this V A C A, V B C, V B C naught together will give me V into C A that is what I see, right but this is all black box, in fact this entire thing is this, what I put here is C naught and what I get here is C that is what I know, because it is not very ideal that means you know the response is not C is exponentially decreasing with time, then I have to imagine now what could be the reason, the reasons may be dead space, whenever we have perfect mixing we also listed out what are the possible non-idealities, okay whenever we have plug flow we have also seen what are the possible non-ideal parameters, okay. So for plug flow what are the non-ideal parameters, channeling, axial mixing, axial mixing should not be there, okay axial mixing must be zero ideally, yes radial non-uniformity because actually we expect for ideal system the radial mixing equal to infinity that is not there then you also may have dead space, dead space particularly in the corners when you have packed bed, right normally simple tubular reactor you may not have, you may not have dead space, it is also not good to unnecessarily put the parameter which is not physically existing, like you know if you take normal tubular reactor without any packing then you have normal the diameters what you choose I told you know 4 inches, okay occasionally we say 16, 16 is really large, right. So then in 6 inch and also what is the length, length will be sometimes you know 100 meters plus 200 meters 500 meters also, okay so that is why you put like this, like this, like this, right so this flow disturbance we are not talking when you assume ideal plug flow when you have the same diameter normally we never expect dead space in this kind of thing but whereas if you have a packed bed, packed bed diameter will be 1 meter, okay 2 feet or 3 feet or 4 feet or 5 feet, right sometimes very big means even it may be 2 feet I mean 2 meter, 6 feet, so now for that 6 feet feet you do not normally put, either you put a conical feet that will again eliminate dead space or otherwise you put flat like this, okay like this flat and then that is the feet, so all this is, all this is packed bed, so again it is coming like this, so this area this volume this volume may be acting as, okay and on top of it if you loosely pack the packing then you may also have bypassing like this, sorry channeling like this bypassing is the word which we use practically when it is not spending any time inside the reactor whereas channeling it will spend some time and particularly when you have packed bed or tubular reactor very lengthy tubular reactor or may be short tubular reactor definitely that stream will spend some time that is why we say it is channeling bypass is and short circuiting also sometimes used I think loosely for both, right the correct word for short circuiting again is bypassing only because short circuiting is not going the way it has to supposed to go at all so that is why some books may use short circuiting some books may use bypass some books may use channeling what you have to understand conceptually is that channeling means you will have that stream spending some time inside the reactor whereas bypassing on short circuiting means practically zero time that too when compared to your mean residence time, okay mean residence time if mean residence time is let us say ten minutes and it is when it is spending only one second inside the reactor then that we call it as bypassing so like that, okay whereas in the packed bed when you have ten minutes at least three four minutes it may spend in the channeling, yeah in the reactor, okay that we call it as channeling so that is why we have to remember that, yeah so all this phenomena we have to put now in this diagram and then we have to now write the equations for this and we know we have already one or two equations here capital V is split into V A plus V B so this is equation one I will say V D, okay and small V is split into V B or V A plus V A plus V B V B is bypass and V A is active that is number two, okay so now, yeah now I have to write the material balance for this particular active zone, right so here again we have tracer input after some time T and tracer output and accumulation and reaction, right so anyway reaction we are writing only for tracer balance, yeah reaction is zero tracer balance, okay let me write again once more input output plus accumulation plus reaction, okay so reaction equal to zero and these things you already know what is input V into V A into C not because we are giving step input, okay tracer balance for step input step input is C not, okay good so now next one is V A plus V A into C A plus accumulation means, yeah we are writing only for this active zone so V A V C A by D T so this is the equation this equation three and what is the boundary condition for this you will have T equal to zero and C A equal to zero that is B C not C that is initial condition we are writing you know that equation is a tracer balance, right at time T equal to zero what and also this equation gives me the response in the outlet so what is the outlet concentration at time T equal to zero, okay so that is what do not get confused with inlet thing, okay good so that is what so it is here I have C A equal to zero, right yeah so now when I solve this already we have this solution this is C A by C not equal to one minus E power minus T by T bar no so here T and that T bar will be V A by V A by V A capital V A by small V that is T bar A if you want, right correct no yeah so I have written that V A by V A as it is T bar A, right okay yeah good so this equation is equation four so now this equation is no use for me this equation is no use why because this is in terms of variables which I cannot measure this is my imagination my imagination is that you know in this one I have an active zone where through the active zone V A is going and also V A is coming out and that will have C A after perfectly mixed all that is my imagination but what I measure is only V into C not V into C so now that equation has to be converted into C by C not which is F T because we are writing for step input so what do we do that means I have to eliminate C A and we have to also eliminate V A and yeah this capital V A and small V A, right so for that we have another balance here, okay so if I take this one as L and this one as K point so balance at K tracer balance, okay tracer balance at K yeah anyone can tell that yeah this is two things are coming yeah V A C A and V B C not V A C A plus V B C not equal to V C so this is equation five correct no V into C only, right yeah, okay so now using this equation we should be able to eliminate that particular one sorry this stream V not you see it is again grams per second only molar sorry mass mass flow route only we are talking V B C A not is coming here and V A C A is coming here together will give me V into C what Pooja correct no yeah, okay so now this one and now we have to write this equation in such a way that all those things are eliminated the first one what we can write there is C A by C A not I am not giving the mathematical details you have to just find out that this is V by V A C by C not minus V B by V A all small V S so this is equation six, okay can you get from this simply divided by C not and then you will get that, okay and also arranged, right so why I have done this one because I have here C A by C not this is the first I have to eliminate, right the C A by C A not is yeah one if I eliminate if I write this equation in terms of this then I have C by C by C not, okay yeah so now substituting equation six in five sorry in four and rearranging you write that there are few steps in between I think you know you have to do that substituting equation six in four and rearranging what you get is C by C not equal to okay V A by capital V one minus V power minus T by this is T bar A so that is V A by V A that I put the bracket, right so this whole thing is in the bracket again plus V B by capital V so this is equation seven actually this is sufficient for me but to have slightly more meaningful parameters let me define alpha as V B by V what is the meaning of this so one minus alpha will be naturally V A by V yeah Abhishek you are telling something yeah fraction of bypass, okay so if V B by V equal to point one then I can say that I have ten percent bypass so alpha equal to point one means ten percent bypass the remaining one is which is going through active zone so this one is equation eight so similarly I can also define another one beta dead space which is V D capital V D by capital V this again gives me if beta equal to point one I will say that I have ten percent dead space so out of ten liters one liter is the dead space that is what is the meaning that, okay so one minus beta will be active zone so this is V capital V A by capital V so this is equation nine good so if you substitute these things and also we know that it is F T so substituting equations eight and nine equations eight and nine in seven, okay then what we get is F T equal to C by C not yeah so we have one minus one minus one minus alpha e power minus one minus alpha by one minus beta into you will get T by T bar, okay, okay that is all yeah so R I can also write F T equal to F theta, F theta let me also write F T equal to F theta only thing I have to write here is this is one minus one minus alpha e power minus one minus alpha one minus beta theta so that is the equation this is the equation for F theta in terms of theta good so this is equation number nine this is ten this is eleven good okay so yeah now what is the idea, idea means you know why do we derive this first of all I have to ask that question I say always I have to bring you to the basic question why are you doing all this so because sometime you may forget correct no what is the meaning why you have to do all this you may be thinking that okay sir it is coming in the examination that is why we have to come here because you asked us to come to actually quantify the non idealities in a real C S T R where we expect some kind of back mixing sorry some kind of dead space and bypass okay that is the idea now how do I use this equation to do that because now this is the model for me right R T D models you have written know like we understood everything clearly okay that is R T D models that is a model now for C S T R with dead space and bypass okay now what do I do with this model okay simply doing the test it gives me alpha beta values yeah how do I fit that no that can be universal answer for anything whatever I ask go to matlab are you going to eat lunch means yes or matlab so now for everything matlab okay anyway correct yeah see again as he said I can feed F theta and also I can give a guess value of alpha and guess value of beta and then try to match right but there are other simple methods also which you can do matlab is not the ultimate right so before going to matlab if you want to have that I am telling you know all the time feel feel feel that feel should come first for the subject unless you have that feel you will never enjoy otherwise it is just ritual rituals no one will enjoy right you know that no one will enjoy the ritual that is why it is called ritual in fact okay so that means it is just repeated mechanical so that is why if you go to matlab every time you will not have any feel because you do not know what is happening inside the matlab right you cannot go and see that and only thing is you may be imagining this may happen this may be by the time you think answer is there okay so that is why afterwards you do not think also that is why before going to matlab if you are doing some exercise it will be very very good in this case particularly when you have one parameter and two parameters you can always graphically do that and then get the actual parameters actual parameters also the values you do not have to go again fit and guess and all that I think unnecessarily it is wasting of power and all that correct no computer power and India does not have any power at all throughout the country I think we have only power cuts power cuts power cuts luckily in IET we are not facing that outside it is hell correct how many hours you have power cuts two hours is very small okay yeah in Andhra they give only power for two hours here cut is two hours okay not only in Andhra many states may be Canada may be self-substant no you also have I think may be Gujarat I think that is all people say Gujarat is may be self-substant even Delhi also we have power cuts and all that so why unnecessarily wasting by going to know when you can do it very simply right how do I plot this to get the you see always whenever you have the equation that is what I do not know whether you got the real meaning of third chapter in Levenspiel see someone has to tell or you yourself should be able to imagine that okay third chapter of Levenspiel if you now go back and then see right every equation you will try to arrange that as a why because straight lines are very easy to understand and and also you know to see whether it is really falling in straight line or not right and then from slope and intercept you should be able to get whatever you are supposed to get right anyway for that you need only two parameters if you have three parameters I think we cannot unless you have put the other parameter constant and then you can do okay for various things good so that way we can actually plot this as 1 minus f theta long okay plotting first yeah long 1 minus f theta versus theta what will happen to this Rahul if I plot like that will I get a straight line yeah because I will simply bring this 1 minus here or yeah 1 minus f theta 1 minus f theta I will take this side this one I will bring so then this will be you will get as slope and intercept okay I think if you do like this you will get very good straight lines because first drawing the line putting the points later okay normally in the lab we have to do the reverse of please do don't don't do this okay first you have to take the data put the points if it is straight only join straight line okay if it is curve and all that don't try to join straight line because there may be something wrong what you have done but I came to know that in our department also I think few people are there who are putting first lines I mean even earlier if scoop draw the line and put the points and then take those points and put in the notebook take to the show it to the guides are wonderful experiment yeah it will be wonderful whenever you first draw the line so place because something noble price information you be missing if you are not real true I say so there may be a noble price information you may be missing unless you really collect the data and then see and number of times if you do and then if you are not able to explain some phenomena experimentally what you observe then that is equivalent to noble price only because someone if you are able to explain that this what is happening I can tell you when you start heating water you put the heater and then switched on the electricity now imagine that it is slowly temperature is decreasing that is worth the noble price yeah why it is increasing I mean why it is decreasing it is supposed to increase correct no then you have to give the proper explanation for because of this reason it is decreasing you try to prove that really I think you know then you will have the or you can simplest thing 1 plus 1 equal to 5 you prove you will get a noble price if you really able to prove so that is why don't I think those people who are doing experiments they never try to cheat you should never try to cheat because there may be real I am not really joking now but they may be wonderful information which you may be missing you just force it even though it is not a straight line you imagine that it must be straight line and then just draw the line there may be a clear trend that it may be going like this and you say that okay draw the line somewhere horizontally or for that XL is best there is a linear option one point in adyar another point in polykerny another point in saithapet still it joins as a straight line okay because I think you know XL so I think that is the best option if you want to do but don't force that I think you know adyar polykerny saithapet it is a curve like this it goes okay that you are trying to force as a straight line which is not correct noble price goes there okay so this one what is the intercept ln of 1 minus alpha and what is the slope yeah this will be one this is negative only 1 minus alpha by 1 minus beta so first you go to first read this line and get alpha and get the slope alpha already I know and then you can calculate beta right so that is the one and we can also show this oh my god often okay we can also derive an E theta yeah that also you can do but I think there is there is another important information d f by d theta cannot give you exactly but you have to have that physical field and then do it 1 minus alpha square by 1 minus beta E power minus 1 minus alpha by 1 minus beta theta okay there is another nice information there something else okay that something else is plus alpha delta theta equal to 0 what is the meaning of this abhishek what is the meaning of that that is because that by cos Rahul is not abhishek abhishek is not Rahul okay yeah unless you say that sir I am no substituting for abhishek you are substituting can you think of that yeah Rahul tell me that is because of the bypass bypass will come after only like that see not come immediately after what you said bypass comes after something yes when some certain time where is time there what is delta theta equal to 0 yeah direct delta function I said when the direct delta function is valid so that is why again you know always I will bring to you that earlier thing so that you remember number of times it is only grinding grinding grinding okay it is a mixture only that is why I am again I know that none of you would have not noticed it that so delta theta minus theta equal to 0 so that means that bypass because it is not what is our definition of bypass it is not spending any time practically zero time so the moment it goes to the bypass it appears in the outlet correct no it appears in the outlet right so that is why what is the time taken by this stream to come to the outlet 0 that is what our assumption bypass right but in reality it may not be but our definition of bypass is that right I mean definitely it will take some time right so that is why this fraction and how much is that that is alpha what is alpha fraction of the bypass fraction so that much amount of tracer will come if you take the area under the curve as 1 okay area under the curve as 1 so this will be let us say alpha equal to 0.1 so that 0.1 area as direct delta function will come at time theta equal to 0 that means instantaneously it is coming out right and that is getting mixed in the outlet and then coming out I know that you actually you cannot see right but if you able to plot that e theta if you are able to plot e theta how do you what kind of curve you get this is exponential decay there is some constant here that is okay yeah so that means it may not start at theta equal to 0 means this is 1 and this will be the one that is starting point correct no at theta equal to 0 then this will become 1 and that okay let me plot that e theta theta right so this will be somewhere here what is that value 1 minus alpha square by correct no at theta equal to 0 this is 0 okay so then it is exponential decay and anyway there is a constant yeah again here 1 minus alpha beta 1 minus alpha by 1 must beta so it is going like this right okay now what is the other portion how does where do I see that that is all so you will get here suddenly it starts here okay and that depends on the area you know yeah so and then from then onwards it drops out okay so that is how you have to plot that actually I do not know whether you still remember or not you just see what is the curve we have plotted with bypass or mixed flow only yesterday we discussed yesterday day to day peak sudden and then it is coming exponential decay correct no you have drawn that sudden peak and then slowly comes out so that is what is that there we have not shown exact direct delta function there we have shown sudden peak like that and then slowly coming out okay good excellent okay okay this is nice so I will ask puja very simple question puja when alpha 0 beta 0 what is the equation per e theta e power minus theta very good and for f theta I mean what is this e power minus theta is it the correct ideal mixture okay for f theta alpha 0 beta 0 that is what is the equation for ideal yeah for ideal mixture okay so now the next one is how to develop a reactor model with bypass and dead space okay reactor model with bypass and dead space so that is what is the next one okay understood no the sequence you understood that is why you know approach to the subject I think in the last RTD models what we have done is first RTD estimate non-idealities okay amount of axial mixing or amount of dead space amount of channeling now you cannot do anything with that because you you are not able to correct that then use that information and calculate what is the real conversion real conversion and as you said if there is a possibility of converting and improving real conversion will be less right ideal conversion 90 percent with this alpha beta values you may get only 65 either you live with that or you go to the system again and then try to convert increase the increase the stirrer okay increase the rate you know speed of stirrer or change the stirrer you will get dead space almost zero okay and see the position of inlet and outlet if they are in correct position without much bypassing correct it okay such that there is no bypassing then you will get an ideal reactor right so once you get an ideal reactor again you have to calculate conversion so that is what is the sequence with RTD models used for you know always first estimation of the parameters next using those parameters find out conversion that is all I mean at least those things you note down in big letters in the page in your notes I say those are the things which you have to remember lifelong even if you are not becoming a chemical engineer later okay good so now conversion in real MFR that is with with dead space and bypass okay good again I should have a model here because now I know that I have a reactor with bypass and dead space because I conducted RTD experiments and then estimated those values they are there they are real now so that is why we write another same model for reactions now so here I have stream entering stream leaving this is ideal right and we have the bypass now when I show this one for reactor no okay let us say that we have the simplest reaction A going to R first order okay constant density because A going to only R so this is volumetric flow rate this is FA0 this is CA0 X0 equal to 0 here I will get this is V FA CA and XA those are the things normally we see but actually here I have dead space this is again VD this is VA this is V is there anyway so this is small CA small VA this is small VB and here of course those things are right and then what is what else yeah at this point I have now yeah VA VA and CAA say capital A is for reactant small A is for active okay good so that is the one so here I have VB and what is concentration in this CA0 okay good so now what is the procedure first anyway we are going to list out the same the first thing is capital V equal to VA plus VD so that is equation one small V equal to VA plus VB that is two same thing so now balance here balance for the active zone okay yeah here also I have CA0 right no okay puja what is entry okay MB for A capital A reactant VA into CA0 equal to that is input oh I have to write this no okay let me write once more I am writing so many times so that you know those who do not want to remember can remember correct no so many times if you write neural system automatically accept that accumulation plus reaction so now accumulation will be zero reaction because steady state right okay yeah now tell me puja VA into CA0 and output VA into CAA excellent puja once more VA into CAA plus so when I have this one as minus I am going to R as minus RA equal to K into CA for first order reaction second order reaction I will ask in the examination okay first order reaction I will take okay so when I write the next one also so that will be VA CA0 VA CAA okay now tell me puja minus RA equal to KCA no it is not KCA no you know reaction is here and what is what is that A you said only one A you have to say why is A right KCAA okay she said that wait I have not heard see how many supporters are there for you no supporter for me okay this is KCAA VA so this is equation three that is another one that will have third parameter right so that is what I want to tell after this is over because dead zone is really dead here right but in reality it is not really dead it is only just alive okay a little bit again so then what happens is because now we asked me there is an exchange of material between dead zone and accuse zone that is how much is the exchange is another parameter then it becomes three parameters right because now it is dead so that is why I am interested only in this this one you know active value and this is dead totally okay ignorant so like I have been doing no there may be some people who do not participate in the class at all from the beginning from the semester onwards I ignored them dead space okay that is equivalent to dead space if there is a little bit exchange that is another parameter how to bring them again to the class again explain to them all that right I am not saying I do I know anyone like that but still I am just saying okay good so that will become another parameter that we will discuss at the end okay so now this one now as usual I have to now eliminate this unknown unknown volumetric flow rates like VA CAA that is all okay yeah and I have another equation for okay so I think this is simplest one let me from equation 3 let me write this one as CAA by CA0 correct no equal to anyone VA by VA plus K capital V correct yeah so this is right so now I have another equation which I can write that is here balance again K so this is L this is K yeah who will tell no balance at K thereby anna yeah K balance balance at K okay which VA small VA capital VA small VA into CAA CAA plus small VV excellent CA0 CA0 equal to small small VA that is all very good very good thereby that is fine right so as usual we will now try to eliminate using this equation again I have to write here CAA by CA0 so I divide by CA0 yeah and also arrange in this fashion and then try to that equation because we have done already I think I will just give you the final expression for conversion first order okay yeah from equation 4 and 5 okay I will write here from equations 4 and 5 that means you have to show the algebra when if I ask that as a derivation and again here also we are defining alpha equal to small VA by small VA by V small VA and beta equal to VD by capital V capital VD by capital V that is again fraction correct no Rajeshree same thing 1 minus or written just for the other thing so again using this this may be this is 6 this is 7 correct no something please point out if I write something wrong you know when I write something wrong oh that is what she was telling right right very good you know we can also define alpha that way but this is straight forward right alpha point 1 means then I know it is 10 percent that is bypass okay good so that is why yeah right thank you Rajeshree okay good so now using 6 7 and 5 and 4 use from equations 4 5 this I have to comma 6 and 7 we get the final expression as CA by CA not equal to alpha plus 1 minus alpha square 1 minus alpha plus 1 minus beta k tau or k t bar okay yeah k tau and somewhere I would write tau equal to t bar also so this is equation 8 8 so that is the equation okay so now of course if I say that I have only alpha there is no bypass my input and inlet and outlet properly maintained so then what will be for alpha 0 case 1 alpha 0 alpha 0 I have CA that means only dead space CA by CA not equal to 1 by 1 plus 1 minus beta k tau correct no okay for beta 0 case 2 CA by CA not equal to alpha plus yeah 1 minus alpha whole square by plus k tau so that is okay case 3 both 0 alpha equal to beta equal to 0 yeah CA by CA not equal to 1 by 1 plus k tau okay this all this I think we are experts so this is 9 10 11 good so I mean what parameter seems to be more effective here that means is it dead space more dangerous and or you know again the question is that to easily answer for you is it hot attack which is dangerous or is it diabetes which dangerous yeah so which is hot attack here which is out of those two which is hot attack and which is why do you say bypass is dangerous okay or this you answer after really plotting for different alphas and middles I have that here plots okay but I want you to think I mean it is something I have to leave you know for thinking right but logically what do you think because that fellow is not practically spending any time at all you know in the reactor so and that that comes and mixes with already reacted part if it goes away without mixing it is fine no problem no no it will come and spoil it has to come and spoil this also so that is the reason why in fact bypass is dangerous so try to eliminate bypass rather than dead space but unless you are a greatest fluid mechanics engineer where you do not know how to design started at all okay if you do that everything will be dead space okay so that is the worst case normally we do not expect that okay so that is why you just plot that you know these are the things very simple puja that happiness will come when you are able to plot see and interpret on your own so real happiness comes in interpreting on your own understanding on your own okay listening the teacher is okay because there may be some difficult concepts where if someone explains oh you may be thinking that okay I understood but the real happiness in the subject will come only when you understand and when you when you are able to interpret and when does that come without cursing if you do all assignments then only that happiness comes otherwise if you cursing also doing assignments will not make you happy because I am there all the time in the mind rather than the problem okay correct no I am the problem not the problem is the problem because always thinking that oh this KK fellow so many assignments so many problems I think why he is troubling us he is a rain painful guy he is a true virus so all that you will say okay really you may be thinking no at least or not all few people may be thinking that so that is why those people have not come also you know this was earlier full but now this has become a voidage here okay I do not know dead space or empty space I think okay good so this is the one and now the question is if I want to make this one as now next parameter three parameter model then I have to put an exchange coefficient here right yeah so this will tell me how much of the volume is exchanged between active volume and dead space right so that equation will be much more complicated in fact my guide who retired long time back I did only my PhD here Professor Y B G Varma is one of his PhD students they have done this model for fluidized bed actually there was another parameter also called number of tanks in series see what they have done was they have done a multi stage fluidized bed where that fluidized bed will be something like this is the down comeer this is the down comeer this is the down comeer that that that three stages okay like this may be five stages they have taken okay so like this yeah and you feed here solids will go come here solids will go come here come and then you may take out here send the gas here gas comes out solids solids okay this is called multi stage fluidized bed one bed is above the other bed so you when you fluid you send the same gas so then Thomas also did similar experiments okay for drying he has used this one for drying and then the particles will start coming here this is counter current so they come here and then through the down comeer they come and this is one stage on this stage there may be bypass of the solids because in a fluidized bed the solids contacting pattern is ideal mixture flow the solids will be always in perfect mixing right so you are sending gas and gas will try to also have the bubbles and bubbles will create very good mixing between the particles okay so that is why any time when you look into fluidized bed gas solid particularly so the solids will be jumping here and there and if you put some colored sand in that or colored material then that colored material will be immediately dispersed throughout what is the meaning perfect mixing that is the meaning okay but if I have designed my distributor loosely then I may have one side fluidizing another side not fluidizing what do I create then dead space dead space and some solids may be slightly jumping here see when you are putting the solids are jumping up and down because of the bubbles like this so some particles directly may enter here because of the bubbles bursting there taking some of the particles and then directly coming through this down comeer that goes to the next stage so what are the parameters here bypass is one parameter dead space is one parameter and when they also did that experiments they put when they put the tracer actually red sand and no blue sand and white sand they mixed it mixed it means fluidizing they added blue sand under some gas flow rates this there was some cluster of blue sand sitting there and then slowly that is dissolving into the mainstream that is what is here so it goes to this one will become dead some part and then slowly this blue will go to the white white will go up the blow come to the blow and then slowly it dissolves so that means it is dead space is not really dead then it is actually exchanging the material between active zone and and then dead zone and that ratios also you have to define properly and then that means how much of material in the dead space is exchanging with the amount of material in the active zone that there is some ratio definition so that will become another parameter that will become third parameter bypass dead space exchange ratio between the dead and thing and also number of stages this is one two three four so how many parameters no four parameters that is why they had four papers in chemical engineering science okay it is not each parameter but there is a solid work right so that is why it is actually that is why when you are modeling you have to understand the system now you know in this model everything physics beautifully explain the model model beautifully explain the physics the model has come based on the physical observation observation what is happening you know you put the sand right some solids colored solids immediately short circuited or bypassed so then that means i have bypassing right then dead space i think no reactor no distributor can be perfectly designed anywhere for distributor for any system where there is a distributor because it is found that distributor has a special disease when you have the distributor particularly if the area is more then whatever velocities you send equal velocity through each and every perforation is impossible to go right so through some perforations you will have low velocity through some perforations you have high velocity because of the material moving up and down even if it is liquid if you have observed i do not know any one of you saw a distributor plate with liquid where gas is sent from the bottom like bubbling then you can see it will have waves bigger the diameter bigger the waves so whenever you have the higher wave then you know delta p across this is too much then it will not go through that it will go through the other height so there those gas there will be active because it has less resistance because liquid it is less then where is where you have more liquid more delta p gas will not go through that so that will act as so whenever you have distributor this is a automatic disease for the distributors okay so dead space is justified and the jumping of the particles to the down comer straight away bypass and then the exchange also you know between dead zone and active zone and physically i see four states are there five states are there right it is called four parameter model good next semester i can tell you fluidized bed has been modeled using six parameters also and they got wonderful results okay bypass can it be negative it is a physical quantity you should get you know at least 0.1 or above zero right even 1 percent bypass 10 percent bypass or maybe 100 percent bypass if you very nicely design nothing is going into the reactor everything is bypassing only okay that is possible but what do you mean by negative 10 percent no do not imagine how can you have negative not coming at all not coming means alpha equal to zero so that kind of stupid values people have have obtained by simply going to mat lab wow what they have done was they have that the model and then six parameters all six guesses they have given because guess unless you guess and give mat lab it cannot start correct no it is a fuse fuse is you your guess okay so i am telling fuse because i think next week you are going to again burn your money you know just like that the volley time crackers okay there also there is a fuse unless you you start fuse yeah lightning fire then otherwise you know it won't burst no same thing here mat lab cannot work unless you give the guess value they have given the guess values they got this kind of wonderful i think all volumes also dead space minus 10 how do you interpret so that kind of stupid values they got for one of the fluidized beds that i can tell you next semester okay good so this is what we mean by okay thank you avinash to ask that question because multi-parameter models i could give right so i have also Rahul you got that papers