 so let us start the slurry reactors okay and this is the last part you know we have done fluidized bed packed bed and now this is slurry reactor three phase reactor right so the objective in the beginning of course even though first day I did not mention generally I was telling that you know we should understand for heterogeneous systems how do you develop that rate equation right and we have taken some examples including slurry reactor at that time okay catalytic reactions non catalytic reactions but mainly the course has been divided into three parts okay the first one is of course introduction and all that then we have non catalytic part which we have done and we use of the same fundage what we have discussed in the first part okay that means identifying number of steps and writing for each step the equations eliminating the intermediate steps in all these things that is the common thing so when I was given that award they asked me to speak I told the same thing I have a beautiful quotation by some JP Epstein I think he told that you know I am not telling great teachers I am not referring to me so the quotation is that great teachers just not only teach the subject matter but they teach an attitude towards the subject okay and approach to the subject without knowing myself that is what I have been doing it okay so now you have an approach to the subject I do not know whether you understood or not but you know you have an approach to the subject what is the approach all heterogeneous systems there is only one approach identify the system first whether three phase two phase catalytic non catalytic then you can imagine the entire system in terms of steps what is step one what is step two what is step three so once you have this idea in your mind try to put on the paper how to draw the profiles even yesterday also we have done that so the moment you have drawn that profiles then mathematics are very simple because in the first profile what is the equation second profile what is the equation third profile what is the equation then what do you get an average and a global rate once you have the global rate you already learnt contacting fortunately you have only two contacting continuous one batch right so you with this information of global rate you have to just go to the correct contacting pattern substitute and then integrate even yesterday we have integrated and we have taken the contacting pattern for gases plug flow and other steps and you got indirectly what is called an effective rate or global rate observed rate that is what what we have I did even yesterday for fluidized beds so fluidized beds very thoroughly used I think you know I mean most of the time used in the industry that we have done thoroughly packed beds we have done thoroughly but before doing packed beds we spent some time on understanding the catalyst okay so that means you know what is the how do you design the size of the catalyst for example without having diffusional limitations and what is effectiveness factor what could be the temperature profiles concentration profiles all that that may be required for actually understanding the packed bed catalytic reactors not only packed bed even slurry reactors even fluidized bed reactors because individual particles are there in all these so you should know when the individual particles whether there are any concentration gradients or temperature gradients our preference is you should not have temperature gradients or also you should not have any concentration gradients then you will get the maximum conversion or rate for the particles the moment you have maximum rate you will have the minimum reactor volume that is what is the objective so that is all that is an approach that is really an approach okay so that is what we are trying to do and the last part is slurry reactors where we have now here three phases okay so please take this one a slurry reactor with three phases in the bracket gas liquid solid may assume various forms like stirred tank bubble columns stirred stirred tanks bubble column sieve tray staged reactor but whatever the geometry the reaction phases the reaction phases are gas in the bracket reactant, liquid in the bracket reactant slash inert it can also be inert liquid bracket closer there that is liquid and solid in the bracket catalyst yeah the catalyst the solid catalyst is suspended in the liquid in the presence of gas in the presence of dispersed gas good okay next para you can write examples are one hydrogenation of vegetable oils okay so here what is gas what is liquid what is solid so this is unsaturated oils sorry yeah okay okay this is hydrogen this is oil unsaturated this one is catalyst nickel catalyst ni okay so the another one is polymerization of ethylene or propylene here we have again gas liquid solid yeah gas is of course ethylene or propylene correspondingly then we have solid catalyst I do not have I mean what is the catalyst is solid jiggler nata right yeah right right right yeah and liquid is cyclohexane how do you know you worked in polymer industry or what this is cyclohexane okay so that is another example and here the presence of cyclohexane is not to participate in the reaction it is only to absorb heat it is a very good heat absorber because lot of liquid will be there so that can take a lot of heat so the third one is have heard of this pressure drop synthesis TROPSH pressure drop synthesis where you have here gas liquid again solid yeah gas synthesis hydrogen or CO hydrogen and CO not CO okay that is the one then we have solid iron catalyst iron catalyst and liquid is hydrocarbon oil okay so I mean just want to justify that you know we are not discussing something totally academic okay so slathery reactors are very widely used in industry for many many purposes that is what is the beauty in chemical engineering I have told you know so how many chemicals you can list you can list thousands of chemicals right so each chemical has a beautiful history beautiful process beautiful family of reactions all that so that is why really we are very very lucky because you can never get satisfied with all these and each chemical may have 10 different processes it is not one may be directly may be after 2 steps may be after 10 steps all that we have to decide which is economical that is why it is totally open field I think you know this kind of opportunities in no other engineering you have because they do not have chemical simply right and chemistry I say that is why we are the where chemistry stops chemical engineering starts okay this they have been telling and I told last time also in chemistry department they were very happy so who are the starting points for you but I think you know yeah they were the starting points for us that is true they only make they are making so many chemicals and they stop only with 1 gram 2 grams 1 microgram or may be 10 grams maximum very big scale 10 grams but for us 10 grams I think he is not even scale okay so that is the problem so it can go to tons you know ammonia if you take 10,000 tons per day 10,000 tons per day you can just imagine in one plant so I think you know all engineering problems come you the moment you go for larger and larger productions heat transfer is a problem fluid flow is a problem okay like everything filtration is a problem crystallization is a problem on large scale and heat maintenance is a problem on large scale again because I told you know I think chemistry will take most of the time the reactor is test tube so you will go to the Bunsen burner put there like this reaction complete so then he goes to gas what is the chromatograph or some HPLC and then tries to find out what is the conversion but can you take our ammonia reactor which is I think you know 2 meter diameter and height may be some 15 meters 45 feet then take it and then shake impossible so then that is the reason why you should now have what kind of heat transfer you should have what is the mode of heat transfer how do you remove the heat or how do you add heat so that is why I said that statement is very good where chemistry stops chemical engineering starts okay but it is not there business to go beyond that okay even though sometimes we go to their business to find out whether this reaction is you know can I also try that is why we have lab scale we have bench scale we have pilot plant scale then we have industrial scale why why so many scales by the way not cost particularly fluidized bed is a deadly example for this kind of scale up because on a small scale fluidized bed when I construct in the lab the type of bubbles I get okay and the contact between solid I get the moment I go for large scale totally it may be different so that is why in between I would like to see what is how this you know phenomena is changing when you go to very small slightly bigger slightly bigger industrial scale you see you would have seen books also scale up in chemical engineering there are books scale up rules are there okay that is the problem because particularly when you have two or three phases then all these problems will come particularly when you have bubbles and drops and particles the scale of problem is automatic and in which process you do not have bubbles drops and particles in every process you have so that is why you cannot escape that is why Kavya beautiful subject is chemical engineering no you do not agree still you are sleeping no okay good yeah so that is why I thought you know I will just give you some ideas about this okay good so advantages you can just write advantages one the high heat capacity of the slurry is conducive to isothermality yeah and number two is heat exchange and therefore heat recovery is very good see sometimes you can put even tubes inside the slurry reactor if it is very very highly exothermic reaction okay the liquid is not entirely take up this heat because the temperature of that may be increasing beyond certain value so then you can also put inside tubes and all that because it is liquid so easily heat transfer will be more so that is what is the meaning number three is very small particles very small not small particles very small particles can be of course we need small particles very small particles can be accommodated accommodated without intraparticle diffusion correct no smaller the particle the diffusion length will reduce so without intraparticle diffusion number four is the reactor can be simple stirred tank or autoclave stirred tanks we are famous no so easy for design so that is the simplicity you know the reactor can be simple for example stirred tank or stirred autoclave if you are using pressure what could be the disadvantage because for everything there will be something bad relative velocity between the particle and then liquid is one thing relative velocity because you know mass transfer may not be high the other one is product separation particularly how do you separate the particles from the product you have the catalyst particle so that is why sometimes when you use Dalda be careful in the hostel sometimes you will get nickel particles that is product separation you know random nickel particles sometimes you may get right so that is why you have to be careful particularly in the product separation right because those are solids gas anyway will go no problem and liquid and solids you have to separate them so that is one of the problems there okay good so now what is our approach our approach is to have the reactor first so the reactor may be like this is a simple vessel then we introduce gas is a simple pipe of course you may have sparges and all that this is gas so here you have the liquid and you have the bubbles in fact so many bubbles so in between you also have solid particles yeah so we have this is liquid so here I have liquid gas may be coming out here so then this is bubble that is gas phase then we have here one particle so slightly bigger this is catalyst solid so this is the picture so then if I also take one bubble for our imagination okay right and also you have inside gas film if I have different gases this is gas film this is liquid film because all surrounding I have liquid right yeah so then somewhere here I have catalyst particle right so then again this has a liquid film right this also in the liquid so now we know the steps the reactant gas in the bubble should first come through the gas film and this is the interface gas liquid interface and this is liquid solid interface okay two have two interfaces so the first step is the gas should come through the gas film the reactant gas then it has to cross this interface and then go to the liquid film right then it has to cross the liquid film then it will dissolve in the bulk liquid so after dissolving in the bulk liquid then it can go to the liquid film again which is surrounded which is surrounding the solid particles catalyst particle and then it has to touch the surface if the particle is not porous then reaction occurs only on the surface or if it is porous then the reaction again you know the reactant has to diffuse inside but now it is in the form of not gas but liquid correct no the gas has to dissolve in the liquid that liquid dissolved reactant will go to the internal pores and then it will get reacted and we are experts now how to take care of even if I have this porous particle then if I know the effectiveness factor of the particle then I will know the rate of reaction in the particle okay but that reaction definitely depends on what is the concentration here what is the concentration here what is the concentration here what is the concentration here what is the concentration there good so now this phenomena we have to now just show in the form of profiles okay so that profiles let me draw we have let me write concentration profiles so we have this is the gas film then I have here liquid film this is gas film liquid film what is this one this is in fact GL interface GL interface that line okay so here I have bulk gas CG I am not using any A there that is the bulk you know that means I have here the bubble right a bulk gas and in a afterwards we will draw the other one also then we have here the bulk liquid and okay I will also draw really exaggerated but still this is the solid this is solid so this is again liquid film good that is the liquid film then this is bulk liquid if I remember correctly I have given this one as a separate test I think most of you also written this okay so then we have here a concentration drop this is CGI right and depending on your endisoloconstant this can be CL of I and CGI CLI are related with endisoloconstant okay then from here again it goes to bulk and this is CL CLI is interface and from here what we normally assume is that we have constant CL okay that means because of vigorous mixing this mixing can be here because of large agitation created by the bubbles or it can also be if it is not sufficient because particularly when you have heavy catalysts high dense catalysts so they will try to settle because the buoyancy created by gas bubbles may not be sufficient so that is why you also put sometimes external stirrer ya impeller okay that impeller will also serve as the gas distributor as well as mixture ya it can also create very fine bubbles of gas okay that also possible ya so then from here it goes to CS okay CL to CS good so now what are the steps here of course steps I will write step 1 MT of gas mass transfer of gas through gas filling step step 1 sorry step 2 then we have MT of gas through liquid filling of course surrounding the bubble so step 3 ya that is bulk dissolving in bulk gas step 4 is that dissolved gas has to go to mass transfer of dissolved gas now dissolved gas through liquid filling through okay liquid filling and step 5 reaction on the surface okay reaction on the surface okay so we can also say if I have a porous particle then it is now diffusion through the particle right next step will be diffusion through the particle then reaction but anyway that step can be combined as a step with ya effectiveness factor okay good so now when I write the equations for these which you already know the overall rate observed rate must be equal to K g mass transfer coefficient through this we introduce it here we introduce here as A g C g minus C g i where A g I will tell you A g is you have surface area ya bubble liquid interfacial area A g please write ya no I think we can write the letter operating all so this is also equal to under steady state conditions it is also equal to K l A g C g i minus C l correct okay which of course you can write through the other equation then I also have K c A c C l minus C s ya you can later later I can substitute I will give you the another equation okay ya so ya you know with the n d slag you can substitute that one as C l i ya okay ya ya I think correct what steady state is correct because you are talking about this point to this profile not this discontinuous profile right you are right ya okay so now of course you can add this one here C g i as h in terms of h then you can cancel out all that so that is correct thank you so then we have the next step is all these three steps mass transfer steps then we have rate of reaction step where we have a eta K A c C s so if I take this one as one two three four right then you have the fifth equation that is C g i equal to h C l i that is the equation good very good so this you have already done that means eliminating all the using this eliminating all the intermediate concentrations like C s C l C l you know in terms of C g you can write this equation right so when you do that what you get is you have I am skipping because you have already done this so r o b equal to ya A C C g whole thing divided by I have A C by A g ya 1 by K g that is the first resistance A C by A g h by K l plus ya h by K C A C plus again h by eta K A C so this is the rate equation okay so this is equation number six now I have to tell you what is A C you can place take that I think all other things we know all mass transfer coefficients h is in this law constant A C is bubble liquid interfacial area per unit volume of A g A g sorry first A g equal to bubble dash liquid interfacial area per unit volume of it is expressed as per unit volume of bubble free liquid okay or in the bracket slurry bubble free liquid ya that is bubble liquid interfacial area per unit volume of bubble free liquid or bubble free slurry A C is next one A C is external surface area of catalyst particles per unit volume of bubble free slurry okay and r o b this also please write r o b is expressed in moles per meter cube bubble free slurry per second minus r a is expressed as moles because I know that I have to clearly define you know every time when you talk about heterogeneous systems okay you have to define otherwise you will have problem so r a is expressed in moles per meter cube bubble slurry okay bubble free slurry per second that is the rate of reaction good so now as usual like in the yesterday's thing also this is the rate expression now overall rate now I have to find out corresponding corresponding contacting pattern for example if I want to use that equation for bubbles here gas phase right so gas phase will be moving in the form of simplest assumption is moving in the plug flow so now I have to use v by f not equal to integral 0 to x a d x a by minus r o b where this is the minus r o b okay so now when I want to integrate for example it is a first order reaction this C g will be written in terms of conversion if it is no volume change C g equal to or any time C g equal to C g not into 1 minus x a or x okay that you have to substitute and then integrate you will get first order very simple ln 1 minus x but all this so when I want to use this the next step is to find out how do you find out a c a g k g k l k c k k is the intrinsic rate constant so this is an approach I have been telling you now you take any system I do not have to do now gas liquid because gas liquid is already part of it if I am stopping only here then that will be equal to gas liquid bubble columns right so then liquid liquid but only thing is replace this gas with liquid you know extraction okay extraction with chemical reaction so then I have two phases I mean two different liquids then I have one liquid film another liquid film then the procedure is same approach is same so that is why entire heterogeneous engineering even though we have not done the details details are how to find out for example mass transfer coefficient the beauty in heterogeneous system is there will be six or seven mass transfer steps and only one will be reaction step okay so all the time it is now for us our duty is to find out mass transfer coefficients and if there is a problem with heat transfer also heat transfer coefficient here we do not have to worry about heat transfer because isothermality is maintained throughout the inside the particle okay because small particles and also inside the liquid because I have large amount of liquid where all the heat is absorbed and liquid is moving very vigorously so uniformly the heat is distributed in the liquid you will get isothermal temperature okay good so now quickly we will try to find out how do you there is another thing here you know there are some correlations for K g okay most of the time this will be the it is not at all rate controlling stuff that will be the much much faster because gas gas diffusion is easiest one in the bubble I have here let us say two gases hydrogen plus some other gas hydrogen can happily go without any problem whatever gas you put there because that is the lightest okay diffusion is very very easy for that that is why you know very fat people cannot move faster and very thin person can go like this like this like this like our autos on the road okay or motor bikes on the road like this you will go right that is diffusion diffusion through the packet bed particularly if you go around 9 o clock to 9 o clock to mount road then it is a packet bed and you can see the hydrogen molecules moving through that is you know autos slightly bigger molecule and two wheelers hydrogen less than hydrogen I mean less than two wheelers what you could mean to have cycles but cycles police will not allow them otherwise cycles also will go through so that is what is the diffusion there that is all so that is why that is easy so most of the time this diffusion gas gas diffusion is easiest so K g will be usually very large so this will not be present in most of the slurry reactor design expressions okay K g can be safely ignored in the sense that it is not ignored K g is so large so 1 by K g that term will be 0 so you can remove that then you will have only the remaining three terms okay K l particularly two terms because this is the intensive create constant and it depends on your ingenuity how to find out this K without any interface and intra phase transport processes like we have discussed you know that is one of the very difficult problems but we are not done that and you know so that is why most of the time we will try to express this in terms of 8 of 5 square it is observable here also you can do that right so that was the reason why 8 of 5 square observable we have gone observable equal to R O B L square divided by D E C B F yeah C A G R C B okay well so that is what is observable because C B you know D E you know you are supposed to know D E okay through correlations and all that so then the shape of the particle we know L square and also rate you are measuring okay using that K also can be calculated in fact K can be estimated using this technique that is pure intra phase I mean intrinsic constant where you measure all this then you can separate you know from before converting that into 8 of 5 square what you have done you have actually eliminated K from that if you remember the original derivation so you can go back finally there and then substitute and get pure K that can be done so now the rest is K L and K C and K L mass transfer coefficient you see now automatically actually these last few classes are very important classes till now what you have learnt is only the background okay but unfortunately climax comes only for some time okay climax cannot be 40 classes okay climax will be lost for 3 4 classes where all the knowledge will automatically come here okay correct no B YOLA yeah good so she is a teacher so that is why I asked her okay so that is why for any system this is the now procedure what is that write the equation find what are the things not known and I can tell you people have spent their life only to find out K L that is all the entire life there are so many correlations if you go find out in slurry literature what are the correlations for K L there will be at least 50 60 that means 50 60 people minimum should have worked because each one will have his own correlation not one normally professor and his student okay and if you go to some other departments each paper even though it is PhD work 5 students names are there this has become a fashion now in some science departments okay then I do not allow that I mean I am asking as a dean that in synopsis meeting you cannot have in PhD 5 names naturally examiner will have a doubt there who has worked out of 5 correct no 5 names means I mean you are all equally supposed to contribute that paper that is why 5 names are there so that is why I request H O D and also the individual faculty members please do not put this kind of practice at least there must be one or two papers for that particular student on his or her name alone because that she can proudly say that this is my work otherwise she is one-fifth of the that crowd okay beyond three we call crowd now so that is why I think 5 6 are common so that is why I told you that is why at least minimum if it is single other papers you should have 50 people who would have worked there and 50 people would have worked lifelong that also on that so like that same thing with K C and effectiveness factors here okay so that is why what we are telling here is some of the correlations they are not the only carnations that are that are available in the world okay but some correlations which have come to the textbook means it is accepted by many other people so this information I am taking from Smith chemical engineering kinetics okay this information okay so now mass transfer coefficient M T C K L this is bubble to liquid okay bubble to liquid yeah even in fact this equation also will change the moment I see that you know yeah here so this is now horizontal almost there is no concentration gradient there so we will have there C G I and C L I related directly okay so now I can express this equation in terms of C L I that is another very simple thing because the reason there is it is very good for me to estimate concentration of gas dissolved in the liquid is much easier than estimating the gas concentration because gas means again H P C L something like that you know or gas chromatography GC and all that one has to use okay so that is the reason that is also another simple thing there that will come okay good of course H C L H also will come so simply this will become H C L equilibrium because any law is equilibrium law yeah good so this is K L is bubble to bubble to liquid that is the mass transfer because always when you say mass transfer coefficient your question should be immediately from where to where okay otherwise you don't know where to where good so you have K L equation given as 0.592 this is diffusivity gas diffusivity to the power of half mu by mu to the power of 4 if I go to 6 this is 7 okay so now where sigma is N P rho L N cubed d I to the power of 5 by W into 5 so this is equation 8 I think here we have to write where no okay again where d I think all we have to write okay first it may write d I is impeller diameter now you can see that means they have used an external impeller in the reactor okay impeller diameter this is in centimeters and d sorry d this is molecular diffusivity of reactant reactant in liquid so this is centimeter square per second per second that is diffusivity then I have new kinematic viscosity then I have K L or K L is of course this is M T C liquid side units simply centimeters per second then we have N small N R P S revelations per second then W mass of salary mass of liquid salary salary means liquid only this is grams anything else is missing rho L of course is centimeter square per second what did I write okay units I have not written centimeter square per second okay good yeah so then the next rho L is the density and now N P yeah N P as another equation I think I have to remove this see everything that has a beginning has an end so even it is so beautiful I have written it has to go sometime correct no only God does not have starting point does not have end point that is all okay good so N P see the problem that is why I said you know lifelong these people would have worked only on this now N P has another equation power number power number where this is equal to capital P rho L liquid density N cubed so this is equation number 9 where phi is a correction factor phi is a correction factor given by phi equal to 1 minus 12 point 6 cube by N D I cubed this is equation where q equal to q yeah q this side phi this side q equal to gas flow in centimeter cubed per second okay you see now just to calculate K L alone how much work would have gone particularly when you are using impillers okay so K L equation is that that is related to sigma sigma is there in that equation 7 now to calculate sigma you also need phi so phi and N P yeah so N P has another equation phi has another equation so that is why you really scold me if I give this in the examination okay correct no problem yeah why because you do not want to learn you really appreciate me really appreciate me if I give this in the examination because wonderful problem because it is the real problem okay good so this is one correlation there is another very simple correlation where you like it yeah P is power yeah not it comes yeah X per second that has not come right too so P equal to power X per second anything else missing yeah so that is why we have another equation for examinations okay so another equation for examination is that do not use agitator then you do not have to worry about power number RPM RPS and all that so without agitation in the absence of that is mechanical agitation okay so without or in the absence of mechanical agitation in the absence of mechanical agitation you have K L equal to mu L liquidol rho L and of course D diffusivity so this whole to the power of 2 by 3 equal to 0.31 delta rho that means rho L minus rho G into mu L G by rho L square so this is the equation 11 okay this K L can be used to find out the mass transfer if you do not have mechanical agitation if you simply bubbles are going with buoyancy right good where all the other things we know know rho L we know mu L we know mu L is the viscosity of the liquid that delta rho is the density difference G we know the D is the diffusivity all that fine excellent good so that is the one for K L so now you have K C K C we are saved because we do not have that we can fit in the form of equation but we have a graph Sherwood number versus what should be the other number for K C so this is in fact 1 and number 2 is M T C K C liquid to yeah particle solid okay actually this is the real life right actually real life you know given example you know all romance will be only for one year before marriage or after marriage okay afterwards reality this is reality and you know what has romance beautifully writing this step equal to this step this step equal to this step this step equal to this step okay and finally you have that equation that is the reality so now that equation contains unfortunately this K L K C K Eta and all that so you have to go for only correlations where there is no romance in correlations correct you know where is the romance in correlations because I think you know someone has to really work very very hard and after working may be 5 years 6 years for P H D so finally you will give one equation okay so that is why all chemical engineering design people won't like because there is no romance simply absence of romance whereas I think the other steps are yeah for example drawing this and then writing the steps eliminating intermediate concentrations okay so then even if you don't like and then if you hate that one as romance you are not good for anything so that is why you have to either like this or like that or like both okay so you don't have a choice now so for K C we should have another correlation so that correlation this again agitation speed and all that please take this this interaction I think we will have okay the relative velocity between particle and liquid determines the extent to which convection increases the Sherwood number above that for stagnant conditions, that is above you tell me the value above dash I know you are not understood what I said there you are simply written there without understanding the relative velocity between the particles and the liquid determines the extent to which convection increases the Sherwood number above that for stagnant conditions that means for stagnant conditions what is Sherwood number excellent above that too is the minimum basic right so when you have I told you know example come with beautiful scent and then sit here now this is still there is no movement of any gas so the smell comes by diffusion okay so then if someone puts the fan behind then that comes convection so now the total mass transfer is that fan speed convection plus diffusion okay the diffusion is to Sherwood number equal to 2 that is a beautiful derivation I do not know whether anyone have done in mass transfer and also heat transfer also that comes that comes so beautifully okay so that is the one and the okay the basis for correlating K C as a function of agitation speed and particle size is based on you heard of this fellows name Kolmogorov transport phenomenon or fluid mechanics people would have told turbulence Kolmogorov theory of isotropic turbulence it would have come in other subjects also Kolmogorov theory of isotropic turbulence that is the basis according to this theory the Reynolds number is defined according to this theory the Reynolds number is defined as R E equal to D P to the power of 4 nu cubed whole to the power of of 4 xi greater than D P okay sigma you know sigma is again same thing what we have used there okay sigma is in X per second per gram that is same as in equation 8 and xi eddy size xi is eddy size of the eddy and this is valid of course yeah xi greater than D P okay so otherwise that means if you have xi less than D P Reynolds number equal to sigma D P to the power of 4 this is 1 by 3 instead of 1 by 2 where eddy size also one can find out that is xi equal to nu cubed by sigma whole to the power of 1 by 4 so if I write equations this will be 12 13 14 okay good so I think this have to remove now yeah so here you have a graph relating the Sherwood number and Reynolds number Reynolds number defined in that fashion this is Reynolds number that is equation 12 and 13 depending on xi values okay so then here I have Sherwood number okay actually this is Sherwood number by what is this number mu L by rho L D number so this is to the power of 3 1 by 3 to the power of 1 by 3 Sherwood number by that is plotted so here this is log log scale I have here 0.1 starting somewhere here 1 and 10 this side we have again 0.1 1 10 100 see this is another way of defining Reynolds number so you have approximately this is 0.2 0.4 0.6 0.8 of course log scale only yeah then again here I have 2 4 6 and 10 yeah you will have a line somewhere near 4 it starts like this it goes that is the correlation not exactly straight line but slightly this way that way it goes there yeah so this is the correlation that means if you want to design then I have to give you this even if you want to calculate if I give the problem I have to supply this information and then first calculate Reynolds number if it is 10 go there read and this coordinate you know so that is Sherwood number is again defined as K c here okay yeah so that value you have to substitute K c d p by yeah d diffusivity again okay so using that you can calculate what is K c from this good yeah so that is the correlation and good what else is now everything we will know of course intrinsic rate equation only other one left but I think that you have to use some other technique to find out that we do not have then you know some kind of simplifications right that equation where you have three resistances whether you have to go for the you have to go for Tiffin or what okay so some simplifications for that equation where you have R O B equal to okay tell me that equation I have A C H C L equilibrium I substituted there okay already that is correct no anything else missing there yeah so this whole thing divided by 1 by K g I am dropping out so then we will have A C by A g H by K L plus H by K c A C K c plus we have H by again A c will come you know yeah A C H by K so that is the equation and now most of the time this equation if I say 15 I have not written this equation earlier okay yeah so this equation most of the time this term also is neglected do you know why the last one neglected in the sense the K must be large value why most of the time this ran in nickel and all that and that too very very fine powder what you use so very active catalysts only are used for slightly reactor most of the time so that is the reason why 1 by K value or K value will be very very large so this term also will disappear so finally what you have all the time in the design will be H H also will get cancelled A C C L equilibrium divided by A C by A g 1 by K L plus H will go A C K L that is the equation this is the most practical equation most of the time people can use that okay so now again further simplifications because as an engineer you should be able to simplify things as you know easy as possible so that you know your design will be the simplest right so you also have something in your mind something that means if I am taking very fine particles very fine particles large number of very fine particles then the ratio A C by A g will be very very large A C by A g okay so then can I neglect this also A C is what by the by external surface area of catalyst per unit volume of bubble free slurry okay do you know how do you find that I mean if I want you to have a develop an equation for that A C surface area of external surface area per unit volume of the particle multiplied by volume of the particle and divided by volume of the slurry okay anyway I think you would have not got that but I will tell you because that is also how you find out A C then we can discuss that A C is surface area per unit volume of bubble free slurry okay so surface area per unit volume of slurry liquid okay liquid I am writing okay good so now this can be also written surface area per volume of particles total surface area per total volume of particles yeah into volume of particle divided by same thing volume of liquid what is this surface area per unit volume of particle I can multiply by n and multiply by n there number of particles total volume of surface area what do you get there pi by or 6 by 6 by dp good so this is 6 by dp and this one for volume of particles mass divided by density m s by rho s m s by rho s so this is what is this you know surface area per unit volume of the particles so the corresponding equation is 6 m s divided by rho s dp where m s is normally taken as directly if you want to use that equation m s is weight per unit volume of the bubble free slurry very simple to get that volume of liquid this one is volume of liquid right we are not substituting that comes by definition so in between only we substituted volume of particles and volume of particles and volume of particles this this can get cancelled okay yeah so that is the that means if I know what is the total amount of solids I am taking total mass if I know the density if I know diameter of the particle I can calculate ac yeah Kavya has doubt yeah that means which one is different this is no m s is the weight of the single particle rho s is the weight of single sorry density of single particle so that will be the volume of particle right volume of liquid by definition I am keeping as it is where is per unit volume yeah ac difference itself per unit volume I mean that is what in the beginning itself we have written only per unit volume of liquid right yeah this is simply yeah here volume of particles and this is also volume but I know surface area per unit volume of particle yeah you mean is there any problem not able to get there where is volume of liquid because I am interested here see I introduced here volume of particles right per unit volume per unit volume because the definition here is surface area per unit volume of liquid normally what we will do what we have to do is that you know volume of the surface area per unit volume of particle we use you know normally surface area per unit volume of the particle only we are talking but definition given here is surface area per unit volume of liquid but this I can also write surface area per unit volume of particle multiplied by volume of particle divided by same volume volume of the liquid so that way I can use this equation to calculate ac similarly can you also find out interfacial area of the bubble per unit volume of bubble free slurry same thing same technique but there you cannot use that density so ag is surface area per same thing again volume of liquid yeah which can be written as surface area what is m b see this is surface area of bubble divided by volume of bubble okay if I am inserting in between right so surface area n number of the bubbles divided by n number of bubbles also that will be simply simply 6 by d b then this side I have to write n into volume of bubble Kavya this side I have to write n into volume of bubble okay bubbles and what is that I think volume of bubbles I simply put as v b yeah is what so that is why finding out gas hold up is also very important in slurry reactors okay that v b is the hold up where we have now here 6 by d b into v b volume of bubbles and volume of bubbles by this will be hold up okay so this is that means if you know the volume this volume of bubble by volume of the liquid will be hold up please write that volume of bubble by volume of liquid will be the hold up this is another equation then we have to substitute now what is the volume of the I mean what is the hold up of the liquid good okay good so now we assume that we have we know this a c and a g because once I give you what is the hold up of this also can be written in terms of 6 d p into 1 minus or I mean epsilon not 1 minus epsilon b in the normal term epsilon is the wide edge okay so that is nothing but hold up hold up of the liquid okay so now this is another this may be equation 17 this is equation 18 so now again you know another simplifications if I am finding out that I have large number of small particles catalyst particles so that means I can neglect now this term because a c is very large so 1 by a c because large number of very fine particles so that means the surface area is very very large the surface area is very very large I cannot neglect this but I can only neglect this right okay good so if I do that what is the rate expression I get go to r o b if a c is very large naturally a c by a g also will be large so in this equation we can neglect only this then what is r o b k l into k l into a g into that is what so now what I am trying to say is a g contains what now everything has focus on now on a g but if I want to calculate a g what I should know is not d p this is d b hold up and diameter of the bubble so I am just trying to pose the problems to you okay so now hold up in the that is the reason why in most of the time in heterogeneous systems we are worried about hold up I have been telling this long time in hydrodynamic studies we always try to find out what is the hold up correct many times I have told that so these are the problems now you are now really facing that right so when I want to use this equation all my focus a c is there but all my focus is only a g but a g now depends on d b and how accurately I measure d b is important thing for me how do you measure bubbles in slurry if I ask you an aquarium you have you know fishes moving but gas bubbles also are moving if I ask you to find out what is the diameter of that how do you find out yeah that is the most you know engineering way of doing things but what are the assumption all the bubbles are same okay bubble size but clearly you know that the bubbles are not same that is what you know I know someone told centipede has 100 legs but anyone counted as a centipede has 100 legs okay similarly here you know why I am telling is you believe many things so one of the simplest way of finding out bubble size is that you measure the volume without introducing the gas of the liquid then introduce the gas because gas has volume so it will get volume will increase so subtract that increase the volume minus this liquid volume then assume that you have bubble size you know yeah uniform bubbles then how do you calculate bubble size you know how many number whatever number you have whatever number you can you can get some other value see diameter I have to all that volume now increase the volume I will say that I have 1000 bubbles and then each bubble has 1 millimetre what is the use of bubble I do not have one bubble I have 1000s of bubbles inside tell bubble experiment is to find out the characteristics of the bubble okay but here in the presence of so many large bubbles how do I find out the volume I mean the size so normally what we do is that is why we do most of the experiments in you know transparent perspex columns or glass columns we will now approximately find out may be you know by looking carefully observing okay this may be 5mm okay all may not be 5mm you see how many approximations are involved particularly Abhinav was asking yesterday you know some question because engineering is approximation like that in bubbling bed model also there are many many approximations okay but now no no I am a scientific engineer not engineering scientist okay now I want to find out exactly the bubble size that is very the challenge for you know first of all you have to find out how many bubbles are there and you find out how many you know bubbles are with 1mm 2mm 5mm 10mm so that means you are talking about bubble size distribution challenging task for chemical engineers even now we do not have a good method even now we do not have a good method it is approximate that is why there are many many challenging problem sizes and people live with bubbles drops and even how do you find out drop sizes in liquid-liquid extraction thousands of people are working on liquid-liquid extractions in industry they are producing wonderful products after extraction but still we do not know how do you measure drop size same thing here bubble size only we are sure about particle size that is all I think you know because particles are not changing in time okay size wise unless you have tremendous attrition and all that so particles are the things only we can characterize and there are many many theories I do not know you are not in DD you know none of you are in DD all of you will be okay so they have a course called multi-phase systems okay I think M Tech we also have that course yeah entire multi-phase system is only to talk about bubbles drops particles that is what is entire multi-phase okay so every time what you say all this finding out hold ups because each system will have a different hold up right bubble liquid you know gas liquid columns different and gas liquid solid different fluidized bed different packed bed different so like that you can list out you know rotary kiln different what is the normal hold up we use in rotary kiln because luckily they are solids they are not changing so that is why you said that it must be less than 10 percent yeah okay so why can't you use 90 percent yeah yeah kaga we can't use 90 percent how how yeah mixing will not happen and you know there will be contacting but I think the way you expect particle has to you know will be lifted to the top and then fall again lifted to the top again fall so like that kind of beautiful motion is not there so that is why 10 percent or less than 10 percent is fantastic same thing even with you know centrifuging if you go to that level of rpm rpm also only 3 4 if you go to 100 where centrifuging happening then what happens all the particles stick to the walls as if it is part of the wall so where is the contact all the gas will go in the central annular region and small contact will be there but whereas when you have this normal method what you operate with low rpm and low hold up goes falls goes falls there is now more residence time for the exposure and good exposure okay so so so all chemical engineering equipment is really a thrill to design even though there is no romance after derivations okay because correlation may be boring but still that is what is life that is what is life after you marry I think you remember my words it is routine it is routine every day get up take break fast go to work afterwards come and if you are in very good mood fight with the wife if you are not in good mood go to the room and then sleep so all these kinds of that is routine routine routine till we die same thing here also correlations correlations correlations correlation even though we develop theory theory theory every paper has a new theory but how much of that is used in chemical engineering equipment design is very very small that is why you have to appreciate chemical engineering whereas any theory every theory developed by computer science engineers electronic engineers is thrilling immediate it is applied to the but mechanical engineering chemical engineering is not that mechanical engineering is particularly it is not that exciting because they don't have chemicals they don't have so much equipment they have only one equipment called IC engine okay only outside shape will change okay bonnet may change or you know that front design may change tires may change or top they may put that ladder or may not put ladder that is all what they can do engine is always engine I think 1800s they invented it is same thing not much improvement only thing now we are trying to do is that put better petrol or put you know some oil put some this one alcohol so and then trying to find out how the car goes okay so that is all I mean other than that even aeronautical engineers their entire life is only one engine correct no yet that is all they may be trying on that variations but for us even one process there are thousands of variations just one process packet bed alone how many ways you can design fluidized bed how many ways you can design okay so you can try to put you know somewhere input somewhere inlet somewhere outlet a multi inlet multi outlet all the things you can try just to get good efficiency okay so that is why this is the equation and now this age to find out we need correlation that one correlation I will give you for DB there are many DB correlation yeah so now I just want to try to tell you the connections you know one after the other so DB now because this age depends on DB right so now we should have a DB correlation so 1.35 U by G delta by delta U square rho L divided by sigma L to the power of half into rho L delta G no sigma L not rho L whole to the power of 1 by 3 where simplest thing of course is DB bubble diameter centimetres okay and we have U gas velocity yeah this is again you know particularly for this is only for porous plate please remember porous plate is different than perforated plate so if you have perforated plate you will have different correlation okay yeah so U G is gas velocity through porous plate centimetres per second then we have delta 4 diameter 4 diameter of porous plate 4 diameter of porous plate then sigma L here is used as surface tension surface tension that is X per centimetre surface tension yeah so that is the one per centimetre and then we have rho L of course density density of liquid grams per centimetre cube yeah anything else all those things are covered no dines per second not centimetre no second or centimetre centimetre length dine dine dine okay so like that you know it goes on and on good okay fine so I think the next part is sorry I think it may take some more time but you do not fall now because there is no break first okay so good now we have sufficient information now for the rate expression you know how to derive the general rate expression and how to get the constants that are involved K L K C and all that K G and all that so then you also know how to find out that A G A C all that information we have now now it is application to slurry reactor so application to slurry reactor this is very simple it is not that difficult good so we will have the slurry reactor design okay I will write here design we have this slurry reactor okay I think maybe let me close this and then put so you have bubbles yeah we have particles and we have liquid right so I am taking now that one thing is that we can also take based on liquid phase because we want to design now right so your interesting phase may be liquid if it is liquid that is equivalent to batch liquid and you have the rate expression what is the equation T by C A not equal to it is liquid integral 0 to X A d X A by minus r A this minus r A is that if it is plug flow for gas so solid season batch but solid is a catalyst so we are not going to try anything on that so when it is gas gas one assumption is that it is moving in the form of plug flow so then we will take a small because again that approach only I am trying to tell you this is delta z this is z plus dz this is z that is delta z okay so in a simple manner if I have cross sectional area A then you have or otherwise if I write in our normal plug flow fashion ideal plug flow F A plus D F A okay now I have to write the material balance moles entering will be F A right moles entering will be F A because you know that is why I am not writing that that is input equal to output is F A plus D F A please remember it is moles per second all the time mols per second yesterday also we did the same moles per second plus it is a continuous reactor where there is no accumulation for the gas gas is moving continuously so then that accumulation equal to 0 plus reaction what is reaction minus okay R O B okay I have not written okay same thing into D V this D V can be yeah this is D V which can be A into D Z A C into D Z so now tell me what is the equation you get here oh time to stop F A F A will get cancelled so minus F A equal to yeah can you tell me the integral expression you can leave it as you know length you do not have to write in terms of V also we can leave it as it is V by this will give me V by integral integral expression I am asking D X A by so now this volume is not simple volume in meter cube but that is volume of liquid volume of bubble free liquid why because here what we have used is volume of bubble free liquid this balance what you are writing this must be only bubble free liquid that is only thing you have to take care of in retrogene systems what is that corresponding one what you are writing okay so because our R O B is defined as the volume I mean moles converted per unit volume of bubble free slurry per time right so when I am multiplying to get moles per okay if I write moles per time I have to multiply only by that corresponding V that is the only thing which you have to be careful when you are writing the material balance for retrogene systems so this is again nothing but your ideal plug flow equation that is what I have been telling oh okay minus R O B good now if it is a first order like this system what we have so this C L okay correspondingly can be converted into 1 minus X A okay C A not into 1 minus X A then that you substitute and then we can integrate that is all you know that is why I told you in fact contacting is much much easier to remember right whereas it is retrogene reaction rates which will give you hell already this is one hell okay yesterday another hell because fluid is in bed and sometime before packed bed another small hell because in packed bed things are not moving except gas okay so that is why and we have not done again you know moving bed moving bed again will be another hell okay but what you have to remember is the mass transfer coefficients and heat transfer coefficients will be changing the moment how the phases are moving change the moment of phases will determine mass transfer coefficients and heat transfer coefficient that is the reason why for each and every equipment you have different mass transfer coefficients different heat transfer coefficients whereas reaction rate is same for any system reaction rate that will not change okay so that is the reason why retrogene systems are very very very beautifully I mean exciting things and to close we will go back to we started with this I told you know for anything which starts which has everything that starts with a beginning will also end so now we will end here with the same diagram so this is reactor input output kinetics contacting so here I have a batch P f continuous continuous then we have P f M f here we have physical chemical so performance equation is output okay shakar remember is a function of kinetics contacting so that is the one and now of course here what you are trying to say is that we are only talking about all the time ideal contacting so the moment you have non ideal contacting this equation will change again so that will be more and more complications only other than that there is nothing okay.