 Ok Yeah so yesterday we have discussed about this fluidized bed and the bubbles in fluidized bed now I gave you this Ok you take in this the first figure can you see the first figure give them ya please see the first figure what do you see first figure first figure is small figure put on side yeah did i draw this figure on the board yeah i have drawn this figure you know yesterday on the board but he has drawn the actual lines later which will also predict those points okay so this is more informative than yesterday what i have given because yesterday i want to pose the problem but in this solution also is given you can see the top most line and top two lines in fact what are the top two lines for small dp small dp means what kind of bubbles you get very small bubbles you know geltat b geltat a particles okay small bubbles and more number of bubbles so they move much faster okay and so if you analyze this in terms of large diameter and small diameter of the particles which will automatically take care of your bubble size then you can also predict whatever you have discussed yesterday okay so that is figure 1 figure 1 i think you know what we have done and as i told you see there he has written also 39 experimental studies so without bubbling model we do not know how to predict that because they are all over the graph okay so now with bubbling bed model that means you know when you take the bubbles into account then we can try to predict that is what we have to derive now the bubbling bed model right so for that that is the first figure and what is second figure second figure is just a picture of how the fluidized bed looks like ya with bubbles okay you can see lot of information is there on that if you see that you know that row of bubbles just going up you have small bubble while it is moving up it goes you know it grows and when it is growing its wake also is increasing that means it is taking more and more particles along with it to the top and once it goes and then breaks there you see there is a thick arrow ya those are the solids u u s is given there if you look carefully u s u s is the solid velocity which is coming down right so the general assumption in fluidized bed is that there is a continuous movement of solids in the fluidized bed where particles are taken by the wakes by the bubbles in the wakes and then they go leave the bubbles leave the solids there because something is going from the bottom to fill up that gap something else has to come okay so that is why recirculations for solids and then you will have good mixing because of the bubbles right and if you do not have good mixing the beautiful property of same temperature same concentration will not be there for fluidized bed so that is the reason why you know that that is the basics again we are talking about basics whenever we talk about these things you know the basic thing mixed flow reactor is we should have same temperature same concentration in a mixed flow reactor which is equivalent to our plug flow reactor sorry our fluidized bed reactor so that is that figure and figure 3 if you see that is the actually if you take one bubble what is really happening in that one bubble and before understanding that bubble okay that figure 3 you can come to figure 4 this is what yesterday I have explained to you figure 4 the first one is you know in that out of there are 6 figures the top most top row first figure you have u b r equal to 0 what is the meaning they are stationary bubbles they are not moving just going there and the gas in the emulsion at minimum fluidization velocity is simply going through the bed bubble stationary there right so as I told you yesterday this gas will use this bubble as a short circuit and then it will try to go through that see that these are the stream lines which are going through that these are the gas stream lines the arrows which are going through that right and now you see if the bubble started moving not u b r equal to not u b r equal to 0 first one u b r not equal to 0 second one in fact u b r by u f equal to 0.6 you see now how the stream lines are taking turns and one of the stream lines at the edge of the bubble is already circulated okay so now you see when u b r equal to u f the next figure that is u b r equal to u b r by u f equal to 1 there the gas already started recirculating but still there are no clouds right even at u b r equal to u b u f still there is no cloud there you could observe now that you will observe in the next figure when u b r equal to 1.1 u f just 1.1 u f you can see the cloud forming okay you can see the cloud forming and Davidson has also derived an equation for calculating cloud radius r c by r b whole cubed equal to you have u b r and u f those two velocities u f is u m f by epsilon m f okay that yesterday I have written there so that is how the cloud comes and when the bubble velocity is increasing now you see in the next figure u b r is 7 times u f if u b r is 1 centimeter per second u f sorry when u b r is when u f is 1 centimeter per second u b r is 7 centimeters per second that means bubble is going much faster so it will make more of the gas circulating within the bubble and also cloud also reduces and you see u b r by u f greater than 100 cloud thickness is almost 0 so that means most of the gas now started recirculating please carefully observe within the bubble itself so when most of the gas is started recirculating within the bubble where is the possibility for the bubble for the gas to come out and then react with solid that is the reason why you have gone to that worst you know even above mixed flow because absolutely no contact between the solids and then gas all the gas is going within the bubbles and particularly when you have the flow rate through the bed is may be 100 times u m f 50 times u m f 60 times u m f minimum position velocity actual bubble velocity is 50 times to 100 times u m f then the bubbles will go much much faster then you will have very very thin clouds but most of the gas is circulating within the bubbles itself so absolutely there is no contact between the solids and the gas so that is the reason why there is no reaction at all yeah that is true that is happening but when you go to the last figure cloud disappeared so most of the gas is only circulating within the bubble that is the worst scenario so in reality how do you how can you see the boundaries of the bubble and the clouds separately what is there in the cloud exactly cloud is gas sorry yes not cloud bubble is gas cloud is particles but but they are slightly different because the bubble is just moving when it is just moving the particles are there just on the roof right so whatever particles which are not falling through down okay and when it is just pushing those particles if you see the local voidage local voidage that will be slightly smaller than the outside okay that is only the difference and you can see that one because very good question see the next figure next side figure 5 that is the actual bubble that is taken by a photograph you see all other places slightly you know you have that dark area right and then yeah around that you have you know more dense particles and away from that is slightly less dense particles and another beautiful thing what you can see is you know the wake how the solids are going with the wake see Davidson theory was beautifully measured also with experiments and you can see the next one next one means B 5 B those are the stream lines in fact okay so this is a in fact this is one of the greatest you know I think I say discoveries in chemical engineering with respect to fluidized bytes really beautiful that theory Davidson okay and of course horizon Davidson and horizon these are the two people I think I have to just write that also these are the two people from Cambridge University we have done this but the first person is Davidson alone has done lot of work on the bubbles okay yeah if my remembrance is correct I think Davidson was mechanical engineer I think but he liked so many chemical engineering problems he shifted to chemical engineering and first started doing work on gas liquid systems gas liquid systems I think he was working on working in ICI if you remember correctly and then you know he developed some bubble columns for ICI at that time I am talking about 50s 40s and 50s and this theory is mostly by 62 67 we have thorough theory for even gas solid system bubbles he knows liquid gas system okay that is normal we know all of us know how the bubbles go in the liquid okay that is everyday phenomena for us when you are taking any drink okay so you can see how the bubbles come up and when you see any aquarium you can see lot of bubbles coming up so all that but we never get excited you know when the bubbles are coming because I think maybe we will look at only fish and can I eat that fish okay and we are losing the beautiful part of the bubbles which is very important for us okay so that is the reason maybe we never bother but I think he has done lot of work and then afterwards he extended the same theory with some assumptions for the bubbles in solids and many people did not believe even though many people do not believe that there are bubbles in the fluidized bed but if you come to our lab I can show you okay yeah I think ask Gunjan when he has removed the packing and then he can show beautifully the bubbles of the air cover and some of the bubbles will crawl near the surface where you can see right and this photograph was done with two dimensional column two dimensional column two dimensional column means they take they take just two plates like this okay and then bottom there is a distributor plate they inject one bubble when that bubble is moving slowly then of course they can control that movement with slow injection and then that is taken this photograph is taken when this bubble was slowly moving right I mean it is beautiful you know I think sometime back this PhD students used to conduct quiz I only pushed them and I was rich body I think yeah so they used to three years they conducted this quiz for chemical engineering students including btx they used to come but PhD students I asked them to take the lead okay so in fact I gave this one different faculty members gave different questions I gave this I gave this as photograph and asked the students to identify what is it okay without writing anything just this photograph and then showing I think just one or two people say atomic bomb okay correct no same thing yeah it is really atomic bomb as far as fluidization is concerned because if we don't understand this we don't know anything how to characterize fluidization at all okay good so this is the one and now yeah you see the this side all the figures we have explained right yeah and if you see now figure 3 please go to the other side figure 3 now when I told you after figure we will come back so there it will give you more clear picture about how the solids are moving even in the clouds or how the solids are moving slightly away from clouds and how the recirculation of gas is taking place you know at least physics you please remember I say physics please remember the inefficiency of the fluidized bed is due to the bubbles where first moving bubbles will not allow gas to come out of the bubbles so that there will not be any contact between the solids and this gas so then where is the reaction the other part of the bed the amount of gas going is very very small I told you know if normally in the industrial reactors you use 20 times 30 times 40 times emf but how much gas is going through the emulsion the other part of the bed only one emf only one emf right so that is the reason why very small amount of gas is going through the solids and you not have much reaction because there should be more concentration see the rate of reaction depends on concentration of gas amount of gas okay so when most of the gas is going in the form of bubbles very small amount of gas is going through the solids that is emulsion where is the reaction you do not get that kind of high reaction okay so that is the inefficiency in the fluidized bed and that is why people you know try to do that I told you know shallow beds can be used for example that means where there is no time for the gas bubble to form grow and then move up right so shallow beds means if the diameter is 1 meter you take only half meter height okay half meter height solids so then you will not have this kind of big problem you will have still small bubbles coming and going very quickly out but I think they will not destroy the bed so much some people started shaking the bed because by shaking the bed you may also have bubbles bubbles not forming at the at the distributor plate itself I told you know how this bubbles may be forming is you have one perforation the gas will try to go into that it is not able to go because lot of solids are there then it slowly started pushing the solids like when you want to go through the crowd what you do you push all the people there a little bit forward okay so that means you are creating a void when you are pushing them for you to move so that is what gas also is trying to do when it is trying to do then at one time it will form sufficient volume where by buoyancy it will detach from the perforation from then onwards it grows so by shaking your perforated plate or the entire column what is happening you are not allowing that kind of you know pushing the solids pushing the gas pushing okay the gas pushing the solids it is not happening okay so that is what some people did and some people did that okay we will take the large height of the beds but put distributor plates in between for example sieves okay so idea is bubble at the bottom will grow and then come and hits the sieve in between so it may break and again another bubbles may form but at least that bubble is destroyed so all these techniques also have been done to improve the performance of fluidity beds okay so that is the one so if you go to the next page yeah figure 6 is same thing what we have done earlier also that means you know how slow bubbles the gas is bypassing through the bubbles for slow bubbles that is the right hand side of figure 6 and left hand side what you have is bubbles going faster so circulations are within the bubble and within the cloud okay good so then figure 7 now is the picture for the bubbling bed model in fact davidson what they have done was that they thought that bubbles and solids they have separated like our two phase region the other day I have drawn that two phase region model okay that model they have followed right so with knowing clearly how much is there in the clouds and wakes and all that but they consider clouds wakes everything in the solids only bubbles are moving then they also proposed a model which was not very good in the prediction wise but they never accept that in fact Cambridge University people never accept Levenspiel model okay there are two groups in the world one is that Cambridge group another one is this Cuny Levenspiel group okay Cuny Levenspiel yeah Cuny Levenspiel model this is davidson hydrogen model that is two phase model and this one two region model and this Cuny Levenspiel model is three phase model or three region model where they have taken separately bubble phase and they have taken wakes and clouds where definitely there is more contact right when compared to the emulsion in this region there is more contact of gas with the solids because they are moving with the entire gas okay so that is another region and from there it goes to emulsion now if you imagine the first thing what I have told you in the beginning how do you develop this rate of reaction for heterogeneous systems okay you write all the steps together right now here step one is the bubble gas if there are solids there is some reaction in the bubble then transfer of this gas to the clouds and wakes because those are the nearest ones okay so then the transfer that is mass transfer mass transfer to the clouds and wakes now because there are solid particles reaction conditions now there is reaction in clouds and wakes now whatever gas is left further it will be transported to emulsion and from there it cannot go anywhere it has to react under steady state conditions you see no but here beauty here is this is parallel steps and also series steps series and parallel steps both are coming here what are the series steps series steps are mass transfer steps from bubble to mass going to the clouds and wakes from clouds and wakes to emulsion parallel steps is in all these things the reaction going on in bubbles reaction going on in clouds and wakes reaction going on in emulsion so that is the overall concept of this entire bubbling bed model so then it is only mathematical details okay and you have to really excuse me here in the sense that I am going to write some parameters for writing this for finally writing bubbling bed model but some of the parameters actually takes one or two chapters in those books for the derivation okay but we have to blindly accept that right thinking that but they are now very well established I am not cheating you but they are very well established but definitely I also agree with you that if you have a physical feeling that for that equation the pleasure is different okay that is what I say really when you enjoy when you enjoy only when you have the physical feel for the problem what you are doing and some of the classes you may enjoy because you think that you have understood you are also part of that the phenomena then only you start enjoying that but for that much effort is required from your side it is not only from teachers side okay I mean teachers also can kill your enthusiasm if everything is confusing to you then definitely you will never you will try to understand in first one to weeks and if you are not able to follow anything switch off what switch off brain okay till now it will be opened the moment you enter the room classroom switch off you will be laughing you will be enjoying and all that that is different but still it is locked okay so when after classes over go and again switch on the brain so nothing will go I mean exactly it is to a reversible reaction if teacher is lousy also can kill you if you are yourself is not interested in learning then that also can kill you okay so that is why I mean all my teaching always is always to try to bring at least one more person for interesting side that is all one more in every class one more one more one more okay I do not have 40 people now here we have taken 40 classes okay so that is the model but let us now take yeah I am sure just now temporarily no now not in the in the in the direction where it is going okay what they have taken is they have taken one slice in the bed at any one cross section one cross section and then you write the balance here that balance is I have a one bubble the bed height is so much in between you take a thin slice because along the height of the bed we have to integrate anyway okay yeah so these that you take and then write the balance for this that is if there is one bubble there in that slice so the reaction is going on in the bubble if there are solids people found that there are very small number of solids sometimes you can neglect sometimes you can also add it is not going to change the value that much okay but normally we will add to see so reaction then transfer to the clouds and wake in the same level horizontal direction why it has to go because concentration gradient is there is concentration gradient which figure you are referring to figure 9 so there is a different concentration in the much and a different concentration in the cloud but there is no concentration difference within the cloud within the cloud we do not expect sorry within the cloud yeah C I C no it is not assumption is that you have uniform concentration throughout the cloud right not only cloud even in the wakes wakes and cloud yeah and emulsion there is only one concentration and in the bubbles there is another concentration which is C A B that is so bubble so which figure you are referring how in figure 4 yeah see the validity automatically comes when you have the experimental data being verified that right even then this is not perfect model I tell you there are still many assumptions in this when you derive the actual the equations which I am going to derive you will have hell I mean what is that finally we are trying to do there are many many assumptions but with all those assumptions figure 1 if you see I think figure 1 the side figure there is a side small figure side side yeah that one you see that line the first line that is predicting for the small diameter particles you see what is how much scattering is there around that line those are the actual experimental data okay so that is why there are assumptions you may feel that yes there may not be uniform concentration throughout the cloud okay so but you you cannot do better than this that is why this model is accepted and any delta x improvements you can always do with more and more mathematics okay any other questions yeah and the figure 10 where the equation is there that you lonely I think you know 11 spiel has used some other same thing only but the basis has been changed so this equation we are not going to derive I think other equation we are going to derive that equation which you have to use if it is given in the examination okay that is the equation so the this equation is is from his old book and in the recent third edition where you have the book third edition 11 spiel so I cannot use this equation because I think if you want to go through the book I have to draw I better draw that particular I mean equations okay so that is the reason why except that all the other figures are valid for our discussion okay but you will get very similar one but only thing is that material balance is not proper because you know here he has used the balance based on volume of the bubbles all the time I told you know rate of reaction can be expressed in various ways for for heterogeneous systems weight of the solids volume of the bed volume of the bubbles that is wide edge so all that but here it is volume of the bubbles but in the book he has used volume of the bed that is why there is an extra factor coming delta delta is the fraction of bubbles per unit volume of the bed so that is the way that equation will be slightly different format exactly same format you have same but terms will be slightly different good okay so now I am sure you think that you have understood but you may not remember after sometime right so that is why let me give some notes at least for those people I think you know who want to read again before the examination and all that at least this will be there you are not lost totally unless otherwise you read the fluidization book or Levenspiel CRE book edition 3 where he has beautifully summarized also right so it doesn't mean that you know don't take this and only go and read that okay so but please write once more writing nothing will harm you your health will be perfectly okay by writing this thing what I am going to tell you but still if you read it is fine so hydrodynamic model okay the discouraging results you can just write below that the discouraging results with the previous approaches what are the previous approaches you can write if you want one parameter model RTD model CTD model to region model that is in the bracket okay let us reluctantly to the conclusion that we must know more about what goes in the bed what goes in the bed if we develop if we develop a reasonable predictive flow model to develop a reasonable predictive flow model that is hydrodynamic flow model okay hydrodynamic flow model in particular we must learn more about the behavior of raising bubbles raising gas bubbles since they probably cause much of the difficulty since they probably cause much of the difficulty next part you can write two developments are important in this regard the first one is the first one is Davidson's remarkable theoretical development and experimental verification of the flow of the flow of gas in the vicinity of a single raising bubble in a fluidized bed okay in a fluidized bed so from where of the flow in the vicinity of a single raising bubble or before that okay I will read from the beginning the first is Davidson's remarkable theoretical development and experimental verification of the flow of gas verification of flow of gas in the vicinity of a single raising bubble in fluidized bed which is otherwise at UMF that means the fluidized bed is at UMF okay only bubble is raising which is which is otherwise at UMF okay yeah he found that for first raising bubbles that the gas recirculates within or yeah the gas recirculates within the bubble within and cloud recirculates within the bubble and the cloud yeah that means here important thing what you have to note down is that bubbles have clouds and the gas is trying to recirculate within the cloud and then also within the bubble but under extreme conditions all the gas only may circulate within the bubbles so that will be worst condition where to get very very low performance in fluidized bed okay that is the one so I think there are many things but still I think I will just cut down that one the second finding first one was that you know the model development for the bubble itself second one is the second finding on single bubbles is that every raising gas bubble drags behind the second finding on single bubbles is that every raising bubble gas bubble drags behind it a wake of solids defined as as alpha equal to volume of wake divided by volume of bubble yeah alpha okay that you can write alpha varies stop there alpha varies between 0.22 alpha varies between 0.2 0.22 0.22 2 okay 1 2 is T O another T is T W O okay 0.2 2 0.2 2 2 2 okay yeah so this is one and Lansbury very beautifully says that depending on please continue 0.22 2 depending on who reports the results really it is so vague really here I think everyone was asking you know all these perfect things are there but I think measurement also is very difficult to find out that means just imagine alpha is volume of wake by volume of the bubble no right so what is the meaning of 2 if alpha is 2 what is the meaning so I mean that means you know you have a small person trying to carry you know two tons three tons on his head or just hanging you know try to lift which is very difficult no so many solids to be lifted up yeah volume that is related no if you have the I mean what do you contain in that volume yeah that's what but you know those are solids only right nothing else in the wake so solids have some density whatever density that we can see but definitely the volume sizes also indicate indirectly the weight also no so that is just to tell this that it is not that easy to measure the wake volumes and all that that is why you can't expect perfect matching of experimental results with the theory okay so in fact in all multi-phase systems this is the problem that is why I like chemical engineering because there are so many things even now for you if you are really interested in fluidized rebates I can tell you 110 problems in fluid in gas solid fluidized rebates not one or two even now okay so every question what you ask every doubt what you ask is a research problem like you are telling no sir how can it be true that there is a concentration same throughout the cloud that is a research problem for us you can actually send a single bubble and change various velocities and try to measure those concentrations in the entire cloud from bottom to the top around the bubble okay like this one this is very vague 0.222 so what is the exact amount can you measure because as technology is increasing then you know sophistication in measurement also increases so we will have now excellent measurement techniques so without disturbing any bed at all you can try to measure from outside no in situ measurements only from outside okay so that is called non-destructive testing and all that so just to watch from outside and then you can get maximum information by using some kind of gadgets you know like finally it goes to like you know science fiction movies right yeah like this like this like this if you see all the planets also may move yeah that is the kind of movies they show know that like this like this I think now recently I started seeing one axe advertisement axe advertisements are all crazy advertisements you know so one boy will be she will say that so from I think now the latest one is from some planet also she pushes like this she says like this then her racket will come to India so finally she comes to his room okay so that kind of science fiction you know from smelling you know diffusion how fast the diffusion must be this fellow this fellow is not even you know completely sprayed she starts there then she smells that there in some other planet my god it is instantaneous diffusion throughout the universe that is fantastic given light light cannot travel so fast but axe smell can travel so wonderful is imagination very good okay good so this is another one these two are the important findings because for us there are clouds wake where there is some amount of solids now I think cashed on this information Kuni-Leon spiel developed their own model before that Davidson developed another model using only bubbles and all the solids like exactly two reason model what we have discussed earlier okay but they have not used so many parameters like six parameters they have not used but they simplified the parameters and it was to some extent for some reactions it was able to predict then came Kuni and Leon spiel Kuni is from Japan and Leon spiel is from USA both of them met it seems in one of the chemical engineering conferences because I think their story also is very nice because both of them travelling from Chicago to somewhere or so by train so I think Kuni-Sannar daughter small child I think went and scratched Leon spiel because in the train when they are moving that is the starting point I think she was the catalyst so then they became front you know normally that happens you know for us also when you are travelling what is the centre of attraction generally if you want to make friendship with someone children okay you will go and say then mother and father automatically will become front to you so it is exactly same thing happened for Leon spiel and Kuni I read this in I read this long time back in one of the articles okay from then onwards their collaboration is fantastic and that book Kuni-Leon spiel is one of the excellent books for fluidization and the title is fluidization engineering I do not know whether you heard of that or not Davidson Harrison also wrote this big book but Satyajithara movie okay because you know because they only they only tell the facts truth always huts and all that know poverty or then who will read that book okay who will go to Satyajithara how many of you see in Satyajithara movies okay not even one know Kavya you are interested Satyajithara movies oh good then then for you you should read Davidson Harrison book but whereas Kuni-Leon spiel book with beautiful examples nice presentation I can tell you Kuni is a lousy writer the papers written by Kuni alone if you want to read you can never read even abstract okay abstract may be ten lines or maximum five lines okay of the papers I am telling you cannot but it is leon spiel who changed him also for presentation wonderful presentation again Kuni-Leon spiel book library also it must be there you can just go and see what beautiful way the bubbles he represents and all that of course you can see that in third edition of leon spiel also where you are just copied from there to this book to this book leon spiel clarity is fantastic I think in my opinion he is the truest engineer but many people in the US it seems he won't like chemical engineers because he will try to simplify thing okay he won't use complications right so that is why and if you read his papers also is research papers almost many papers I can tell you 60 to 70 percent of the papers will have worked out examples in the papers research papers normally no one gives worked out example and all this information what we have what we are going to discuss for Kuni-Leon spiel model also came in 6 to 7 papers in every paper okay there is one at least one worked out example where that gives you the clarity the moment you try to put numerical values calculate and then get the feeling you will automatically get the feeling so that is the kind of I think leon spiel is great who made CRE very simple before that there were two books Valas book reaction or that kinetics for chemical chemical engineers or so and before that Augen Watson these two books I think no one I think read also that may be valas is slightly better but when when leon spiel book came only it went to throughout the world as chemical reaction engineering subject after you wrote that book all of you got this okay oh yeah I will also give you you can distribute them let them you have this with you I thought I will give in the next class but I think but do not throw them out these are the problems in fluidized bed reactors and also slurry reactors this advanced booking okay because I have not done both now right fluidized bed you are doing but slurry reactor there are just one or two problems you can do that as far as possible whatever I know answers also I have given but then just keep it with you and then solve