 Okay so we will start now in the last class I told the story about how the models developed so I will draw now that figure and then we will again discuss a little bit quickly then we will go for fluidized bed bubbling fluidized bed model, when we plot the conversion versus damkohler number this is 1 minus xa k tau is the damkohler number for first order reactions this will be 40, 60 you have 0.01, 1 and 1 this is the straight line this is plug flow line this is mixed flow line and the points what we have this is one category of particles and we also have another category triangles inputting so this is the kind of behaviour and the circles are Geldert okay A particles A group Geldert A group and the triangles are B group and some of them are AB group also okay AB group means that border line between A and B so under these conditions I think the researchers could not predict what is really happening in the fluidized bed because this is mixed flow this is plug flow and many points are there away from mixed flow reactor so that means there is something serious things happening in the reactor if you look into the carefully into the reactor what is really happening one should find out otherwise by simple models like mixed flow and plug flow they cannot predict the conversions okay so that means the first attempt like our ideal reactors failed that is one ideal reactors failed in the sense that you know they could not predict the conversion right. So then logically the next one is single parameter models models like dispersion model and tanks in series model recycle model is not valid here because what is recycling there you know it is not right so you should have an external recycle and again come back that is what is recycle model but here that is not that will not arise so it is only these two models have been predicted so even if you want to predict these two then this is the zero mixing this is infinite mixing this is zero mixing plug flow so all these models also should be somewhere in between right because this is intermediate mixing these two models will give me something intermediate mixing like if dispersion number equal to zero it is plug flow dispersion number equal to infinity it is mixed flow if I say take dispersion number equal to 0.01 for example you are towards mixed flow sorry yeah somewhere here not towards mixed flow but if you have dispersion number 0.00301 or 401 then you are very close to plug flow otherwise it is not infinity means it is not really infinity even beyond dispersion number equal to 0.2 0.4 0.5 you are almost near mixed flow that is why I was telling you know that one earlier yeah so that means even these models if they are really valid all the data must be somewhere here but not away from this boundary right so then people tried this RTD models that is number 3 please remember even though we discussed these two under RTD models right under RTD just to understand very easily under RTD even without RTD also I can derive this dispersion model and tank series model right you take one tank next tank next tank what is going in the first tank and then that is coming to the second tank second tank going to third tank everything is perfect mixing and when you go to dispersion model you take ideal plug flow over that you put that dispersion term so that means that fixilla term DE effective diffusivity if you take diffusivity multiplied by dou C by dou Z term will come along with your convective term okay so I think this is what in packet beds also you have seen in packet beds we have so many terms if you are able to take only axial dispersion term and convective term and reaction term that equation can be solved I also gave the solution for first order reactions in the last class in the last semester so that is why it need not be categorized under RTD models because you may be thinking this fellow discussed last time these two under RTD models and now separately he has written these two as separate category and RTD models separate category RTD models mainly the way we are discussing here is that it will take dead space into account channeling into account bypassing into account channeling bypassing we have slightly different meanings for that so all that taking into account RTD models have been tried but you know RTD means residence time distribution models right so when you look into the fluidized bed where the solid particles are catalyst and if you look into the bed a little bit more closely then we have the bubbles and we have the solids right if there are no bubbles wonderful because I think you know every particle will be contacted by this gas then you can clearly try to find out whether you have what kind of mixing going on there whether it is single parameter model or ideal reactors this could have happened beautifully but without bubbles even the fluidized beds cannot leave because when you want to have a little bit of mixing for the solids then bubbles must form you cannot operate exactly at minimum fluidized velocity then it becomes most of the time as packet bed so when you go away from minimum fluidized velocity bubbles will form and particularly when you have large diameters in the industrial columns they go 20 times 30 times 40 times minimum fluidized velocity because they want to keep all the particles under fluidization conditions that is why that extra gas is different in necessary what I am trying to say is that you can never avoid bubbles right so that is why in the RTD models when you take how the okay I think I will draw here a simple fluidized bed I have done this many times but I think again I will draw this yeah this is enough three bubbles these are the particles and one bubble may be breaking here okay so gas this is the catalyst particles right so most of the gas is going in the form of bubbles whatever you have more than necessary for minimum fluidized velocity all the extra gas is going in the form of bubbles right so that gas will contact only the solids around this around the bubble right so around the bubble around the bubble here that means the gas which is in the bubbles will see only small number of particles number wise so the residence time or the contacting time between these bubbles and the solids is very small right because bubbles are moving up whereas in the other we call emulsion phase the other phase and the gas is going but at minimum fluidized velocity that contact is more but it is very low velocity and then there is sufficient contact so that means in RTD if you remember the equation you know for first order reactions what is the equation for conversion using RTD model first order I mean you are telling something yeah 1 minus XA equal to for first order reaction RTD using RTD that is all E power minus K tau integral 0 to tau what is this tau 1 minus XB of single particle you are in non catalytic reaction you are not in catalytic reaction I am asking in general for first order reactions what is the RTD expression see how many times I am right you know that is all only that semester remember afterwards no okay I think Abhinav was telling something yeah what is that integral and all that before integral what you have 1 minus XA let us take okay yeah but not 0 to T okay not tau okay so that is the equation what you have so that means the CA by CA not batch is for first order reaction what is the equation for CA by CA not batch E power minus KT that K is the reaction constant so that constant will be different for the bubbles because the contact time is different and that constant will be different for the solids the other solids emulsion solids so that means you need 2 constants one is a small constant which will take care of the bubble movement and then solids surrounding the bubble and the other one is emulsion where the K is slightly large so that is why how do you get this information from RTD models is become a big problem okay so then they stopped that idea the RTD models also cannot predict because this contact time the K value exactly we do not know because we need 2 Ks 1 K is for the solids which are surrounding the bubbles the other K is for the particles which are in the emulsion phase so emulsion phase is contacted by gas in a different way and actually this is a beautiful lesson for modeling also fluidized batch is a wonderful lesson for modeling how do you look a little bit deeper and deeper and deeper and finally what do you do okay so initially all of us start only with ideal reactors so they failed then afterwards the next simple step is this step by step you go know okay so next step is trying to find out whether single parameter models can able to you know can predict the conversions they are also not then slightly more complicated RTD models RTD models also we have problem because with K because we are not able to get 2 Ks for this so that is why is the same information same equation and same information but RTD models failed okay that also alright failed due to reasonable K value I hope you will understand okay K value K means you know reaction rate constant value reasonable K value means whether it is a small constant or large constant depending on the contact okay bubbles or the emulsion so then the same information someone started calling that as CTD models heard of CTD models RTD is yeah residence time distribution CTD is contact time distribution okay so these are the new class of models which are usually only for fluidized batch okay actually that will be a good term even for us what is our contact time distribution okay how many classes you come it is physical contact okay mental contact I do not know unless we go to avatar and then put your pigtail and my pigtail together then only I will know mental contacting but otherwise physical contacting is only yeah so this is contact time distribution distribution models so here in the contact time distribution models they assume it is same thing as RTD only but I think you know only they I mean some researchers which I think at this present time you may not be interested in yeah so what they have taken that they have taken a K that is okay K equal to K 0 T 2 power of M where M is the fitted parameter okay depending on large contact or small contact right so this equation they have used with a meaning that with a meaning that short K means short stay in the bed that is bubbles long stay means short K means okay yeah short K means short stay large K means long stay so you can now see this this must be bubbles and around bubbles this must be emulsion okay so now you can see that your equation what you have just now told CA bar by CA naught equal to 0 to infinity E power minus KT ET DT straight we have taken E power minus KT because it is first order we are talking about only first order okay yeah so which also can be written as 0 to infinity E power minus K 0 T to the power of M plus 1 ET DT okay this is straight forward correct now we are substituted for this K here K 0 K 0 into T 2 to the power so then what they are trying to do is that you have now 1 minus X A and you try to fit this M so that you will get there are 2 now okay M plus 1 so there are 2 now so the M you adjust such that your X is described by or you know predicted by this equation but they found another problem what is the problem problem now is how do you get ET you know this this one exit as distribution function how do you normally get ET you have done the experiment no RTD experiment yeah no yeah concentration versus time and then get area under the car okay then divide each concentration by that area you get ET and ET DT will give you the fraction of material which stayed between time time T and T plus delta T so that is the definition we know but the problem in fluidizer bed is there also what when you are doing opportunity you are doing with the liquid right so then once it comes out you put in the outlet a probe or try to collect the sample and then analyze did you use probe or collected samples no I think in our labs what is happening problem you remember collected only and titulated okay yeah but any others have used some probes and all that you know smart units that you used probes oh here you are now trying to change I already changed okay yeah but you changed it but used for BTEC next time okay yeah so that is the one I think that was the simple one which you have been doing also long time back and I do not know what has happened in between I think the tracer use is ECL 4 I mean NACL NACL okay good yeah so then what the important assumption there is once the liquid crosses the probe it cannot go back inside it is only once through probe so that means the tracer whichever what you have collecting once it crosses your that measuring port it cannot go again inside if it goes then it is hell you do not know how to characterize and another peculiar things are there for RTD always we talk about only one inlet one outlet the theory will be very complicated the moment you have entry not required only single entry multiple outputs also you will have problem if you have multi inputs and multi outputs then you have much more problem that is why that one no one uses this multi things but anyway that is logical for chemical engineering because I think reactor will have only one inlet you should have two outlets okay I mean in general all the time so that is the reason why that is a good point but here what is happening is when the bubbles yeah you put the probe here somewhere or you may put probe here at the centre or you may put some 4 5 across the that cross section but what happens is when the bubbles go they are taking the solids with that go to the top and then come back because they they just go here break and then solids will come not only that I will also give you that figure now this explanation that explanation also will vary normally the gas will try to find a short cut through the bubbles because resistance is less no solids right there may be few one or two solids okay which they found but most of the time because there is resistance is less gas will try to bypass through the bubbles but when the bubble is moving much faster what happens is it is not allowing the gas to bypass to bypass but on the other hand the the gas will try to recirculate here like this when it is moving faster you know like circulations when you stand near in the mount road for a bus assuming that it is midnight you know 12 o clock because there is no traffic and it is going very fast okay otherwise here I think more than 5 kilometers an hour no one can move right now if you go so there you cannot see this effect when the car or bus is moving very fast behind that you will definitely see some kind of low pressure you yourself will feel like this when it is going very fast like trains going and then we are standing on the platform so that kind of thing also will happen here so actually that is a kind of bringing back that air which is very near to the surface okay this has been proved by Davidson and all those people theoretically also that I will give you sometime later so this gas will go break and again try to come back that means once it crosses the probe there it is not leaving the bed but again coming back you already found out what is the it is a but again the same fellow is again coming back if you take a pocket of this gas so that is why you are not able to actually find out what is that you know what is the meaning of actual ET what is the definition of ET again fraction of material staying between time t plus delta t but which delta t you take now because the fellow is going out and then again coming in going out coming in so that was the reason why people said that CTD models RTD models both failed because this is RTD information right this is nothing but RTD information so then this also failed because of the E-curve failed due to due to difficulty in getting correct ET exit execution function see earlier it was the k problem in RTD models but here they are also it is the same problem but only we are trying to tell here you know because we solved one problem but this problem we have forgotten in the beginning this problem there also it exists even in RTD here also it exists right RTD models failed because not only that k value because of E value also okay but anyway here we are specifically telling that it is due to incorrect ET which you are measuring and without measuring you cannot have any equation for this kind of complicated systems okay then people that what else now we have to do right so what else you can do now all simple operations failed what is the next one next one people really thought that okay now let me go and see what is really happening okay till then it is imagination okay some bubbles are there bubbles are going right so let us really focus on the phenomena that is happening in the bed that is what I have been telling all the time in my classes that the phenomena physical phenomena is much more important than the mathematics if you understand that then automatically mathematics will fall in line right so here a little bit deeper they wanted to look into right that little bit deeper what they thought was it is same thing bubbles are there and then emulsion particles are there now they thought that okay now let me separate all the gas in as one compartment all the solids are in another compartment and some gas is going through this gas compartment some gas is going through this emulsion you know solid compartment both of them are coming and then meeting there but for the reaction to take place there must be some transfer of this reactant from the bubble to solid you see the physics is very simple if you are able to understand the gas is moving in the bubble but there is concentration gradient in the bubble right naturally because reactant maximum is here only in the bubble so it moves to the emulsion because of the concentration gradient diffusion right so then there is some transfer of gas from bubble to the emulsion so imagination now is let me take bubble as one compartment okay so that is that is called 2 phase 2 phase 5 2 region model 2 regions are 2 phase also sometimes called but 2 regions whether it means bubble region and also solids region so imagination is we have this is bubble region this is solid region so you have the amount of gas this is V not or V not volumetric flow rate if you take this will be V not so then anyway it has to come because what you see is at the outlet at the outlet again you are not seeing these two separately it is only your imagination that is why model is always our imagination right so model becomes reality when you have mathematical description for all these things inside the bed right so that is why again I will make you to understand you know when you go for your RTD models we have drawn for CSTR with dead space and bypass what did you do you should you have done this is the active zone okay this is the dead zone this is entering here this is leaving here and then this is dead zone this is bypass zone but what is this actually actually I have a CSTR which is entering which is coming this may be dead zone here it may be bypass so now you see our imagination is all this volume has put as dead space all the other active volume is put as active space and now whatever is going very quickly short circuiting very quickly going out bypassing so very quickly coming out that is shown like that because it is practically not spending any time inside the system so this is an imagination so if I am able to write this and this and this what are the equations how much is entering how much is leaving and if I am able to solve what is happening inside this mixture if I am able to solve and then I have an equation that equation is finally matched with my actual conversion here in this this is the reactor so if this is matching with this model then I think that ya I have no bypass I have dead space and so much bypass so much dead space is there inside that is why the conversion is so much that is what is the imagination so similarly here also the same imagination all the gas in one region all the solids are one region then we have the cross flow all this okay so now this V0 will split into V1 and V2 we do not know how much okay so then these volumes also we do not know exactly so that is why we also just float as V1 and V2 V1 volume of gas region volume of solids region okay good then this cross flow we will call as K that means how many volumes of gas that is going into the ya into this okay so that cross flow also we will take then in this region there is a flow right so all the gas region there is a flow all the solids region there is a flow for gas right so in this region we will say that we have a dispersion number d by ul 1 here you have dispersion number d by ul 2 there are many models you can say now this is equal to number of tanks so I may take 10 tanks here 3 tanks there for gas so d by ul is almost equivalent to number of tanks right each d by ul value can be also converted nicely in terms of number of tanks okay so that is why you have now how many how many parameters you have now ya V1 V2 is now both not the parameters ya I can take V1 one of them that means V0 equal to V1 plus V2 then I will know the other parameter then capital V1 another parameter the total volume I know right so V1 plus V2 is again total volume total fluidized bed okay good that is the one then this d by ul 1 and d by ul 2 this we cannot have I cannot subtract one from the other okay and we also have another one because I told you experimentally it was seen that even in the bubble phase there are some amount of solid particles inside the bubbles also few solid particles are there so that is why what we call is that you know you have some amount of this is m1 small m1 okay m small m1 is amount of solids or fraction of solids let us say so if I have totally 10 kg is in the bed so how many kg is may be 200 grams or 500 grams in the bubble phase that is also another parameter the remaining will be automatically in emulsion phase right because total amount I am taking in the beginning how many parameters are there 6 parameters so the 6 parameter model this is also called sometimes 6 parameter model so the 6 parameter model beautifully fitted the data excellent particularly this models were used for you know this which company is that it is FCC reactors FCC reactors like mobile company all these companies I have used this model in the industry and found that it is a beautiful fit they will find out exactly what is the conversion that is coming because this FCC is nothing but a fluidized bed cracker right fluid catalytic cracker even though it is first fluidized bed inside we have only fluidization that is going on so that is why they tried this model but it was so beautiful people are very happy but when they got the parameters what is v1 v2 v3 it is beautiful operation successful patient very very happily died okay so what is the problem they are getting for this v1 as minus 10 okay is there any meaning for volumetric flow rate to be minus 10 or even this v1 they are getting as may be minus 20 okay so that means even the physical values which are not supposed to have any negative values they are able to that means they are able to fit the data that is why most of you also will do that when you are doing your project you go to the mathematics to such an extent you do not know what you are doing okay then you do not know what is the physical meaning of those particular parameters you know here there is a meaning you think you know this v1 cannot be negative at all first of all even d by ul cannot be negative even cross flow cannot be negative but they are getting some 3 4 parameters negative and another 3 4 3 parameters the remaining 3 parameters positive but beautifully they experimented data fitting so that is why they thought that yes we cannot now understand fluidized bed so they closed the books and went home okay so they did not they could not do anything so then the problem started that you know when all these things are going on in the universities we do not have any other work you know except thinking no really that thinking is very important we are not also not thinking anything now even if you think it will be something nonsense no sense there okay so those people in Cambridge University there was a person called Davidson he started thinking no one is able to think what is really happening in fluidized bed let me just very widely imagine that these bubbles are just like bubbles in the liquid where you have the clear boundary and all that okay and now let me take some properties which are not exactly liquid properties but something away from liquid properties representing fluidized bed and then let me simulate he simulated when you simulated he got wonderful information I think he also would have jumped up and down okay when he first saw that results so what is happening is when he simulated when the gas is moving in the form of bubbles depending on the velocity of the bubble that is bubble rise velocity he did it for single bubble assuming that everything is minimum fluidization velocity beautiful distance no disturbance at all okay only one bubble is allowed to move how it is going so then he simulated all the stream lines gas flow and also solid flow around these bubbles he found wonderful information he found that when gas is moving up depending on the velocity the first thing what he found was that the gas is bypassing through the bubbles that means the gas is taking the bubbles as a short circuit like I mean we are famous for that for any work we will try to have short circuits no if you want to get VESA or not VESA passport we know what is the short circuit you go to someone give 1000 rupees he will give you passport that is the short circuit okay so the gas also knows because I think entire nature may be like that only getting doing short circuits only so this gas also is trying to go through the bubbles right but when the velocity of bubble is increasing slowly from low value to high value okay so then that velocity comparison is here I have what is called u f that is the gas velocity in the emulsion phase u f and which is nothing but this u f is nothing but u m f divided by epsilon m f because we our assumption is that the emulsion is at minimum fluidization velocity so minimum fluidization voidage if I take that will be the true velocity in the through the emulsion that is what is u f and here we call this one as okay this one as u br velocity of a single bubble so when u br is smaller than u f when u br is smaller than u f what should happen or okay when u br equal to 0 stationary bubble when it is stationary bubble very happily gas is bypassing through that right so when it is started moving a little bit then you know when even then it was till it reaches u f equal to u br it by it started bypassing but beyond that u b equal to u r and just beyond that even a small value beyond that then the gas is not allowed to bypass it is it is going through bubbles but again coming back the circulations okay and when you simulated for very very high values of u br that is what you know bubbling fluidizer bed 30 times 40 times 100 times u m f is 1 meter per second and u br is 101 meter I said no 1 meter per second this one is 100 meters per second u br is 100 meters under those conditions most of the gas is only re-circulating within the bubble see the beauty re-circulation is taking place only within the bubble that means it is not at all allowing any gas to contact solids then where is the conversion okay that was the beautiful reason why you get these points correct no because you have solids but there is no reaction because there is no gas which is going and contacting there and the amount of gas that is going through the solids at minimum fluidization velocity it is almost very very very small that is why you do not get much conversion in the emulsion unless this gas goes to emulsion that was beautiful so then that is one finding where they found that when the gas velocity is varying and in the typical industrial reactors it will be 40 50 100 times u m f you know the u br so then they found that yeah under these conditions definitely we will have less conversion than this and that is one side about the bubble behavior then some other person he also told that you know it is not of course he assumed you know very very beautiful circular bubble but you know as it is most of the time we will try to draw only like these bubbles right all the time we are trying to draw like this okay this is the bubble and here we have what is called wake it is like atom bomb also atom bomb also shape when it is exploding behind you have the low vacuum low pressure region so that also sucks all the gas from surrounding that will go there like that it also does and along with that when it is sucking it also sucks the solids okay it also sucks the solids so that means that in the wake there are some solids right and when the bubble is moving continuously when he during his simulation he found that for every particle for every bubble there is a definite thickness of cloud that means the cloud is moving allowing with the bubble cloud will have certain thickness that means okay actually this is the cloud right cloud means more particles but this entire thing is moving whereas other place the emulsion is okay staying there right so finding out the cloud thickness and also finding it has got the wakes and wakes also have some solid material then gave some more beautiful imagination for us the two phase region what we have here yes we have bubbles inside bubbles we have some small fraction of solids excellent now all these remaining solids are not in the emulsion but some of them are in the cloud and also wake that means definitely you will get more conversion right you will have more solids near the bubbles there are so many bubbles like that so when the bubble is carrying with it a cloud and then the wake then you will have slightly differently more conversion why we are not able to tell anything in this thing is we do not know depending on the velocity is where we are whether we are having no cloud at all cloud thickness will reduce to almost 0 if you have UBR is very very high bubble rise velocity very very high okay so that is why sometimes here and some bubbles may be slower and you know this group B and group A particles that we have discussed some group A particles behave differently group B particles behave differently you know you will get exploding bubbles fast bubbles very slow bubbles all these things will come all that we had never we never had any idea earlier so that is why all the data that means some people may be operating in very fast bubble regime right some people may be operating with group Galdad B group and some people may be operating with C group all that data when you put what else you get only this one cricket field only you get correct you know throughout spread particularly after 20 hours or 10 hours now yeah now 2020 no yeah otherwise 50 hours I think one day cricket you will have after 10 hours I think they will spread yeah this is after 10 hours spreading so everywhere you will see the people running here and there so that is the reason why we are not able to predict that beautifully good so what they try to do later was let us look into the hydrodynamics and these are called hydrodynamic models hydrodynamic flow models hydrodynamic flow models I thought I will start that okay that means what is the meaning probably hydrodynamics means what lives up to expectation all the time okay so that is English meaning you are telling what do you understand yeah good right common sense only yeah hydro the how the phases are moving within the system if you have any equipment and if you are able to find out how the phases are moving whether of course simplest thing is whether they are moving in plug flow or mixed flow and all that okay and hydrodynamics means not only just flow what we see under hydrodynamics is the actual flows right and also the hold ups what do you mean by hold up probably hold of it hold up not heard ranita what is hold up space occupied by bed by what why only liquid why you are why you are always liking liquid hydrophilica hydrophobic solid why solid hold up is for all the phases what is the fraction of a particular phase occupying the the system reactor or equipment okay so all those parameters in fact not only that even the flow regimes under what conditions you will operate like for example fluidized bed can never be operated beyond terminal velocity and also before packet bed no that is a minimum fluidization velocity so that is the flow regime for that so under hydrodynamics you will get flow regimes and velocities and you know you may for example ut all that these are all and then you will also get the hold ups and also the pressure drops what is the pressure drop okay when you are sending so much gas or liquid or both what will be the pressure drops all this will come under pressure drop and this hydrodynamics hydrodynamic flow models will give me information about all that but in this particular case they mainly concentrated on the bubble flow right okay I think I have to close here you have to run okay so then I think this again I have to bring a I have brought these things anyway but if I give this you may not bring tomorrow right so I think I will bring tomorrow and then give it to you so the entire fluidized bed reactor design is in one page okay this I will tell you in the next class okay thank you