 Okay, yesterday we have been discussing about various types of catalytic and non-catalytic reactions and we have given the examples to two types, type A and type B. Now let us continue that and for type C reactions classified as solid going to fluid plus solid. Yeah example C A wonderful, that is one of the again one of my favorite reactions C A CO 3 solid giving us C A O solid plus C O 2 gas, right. Yeah any other example of course most of the decomposition reactions like for example magnesium hydroxide M G O H twice giving us M G O solid plus H 2 O gas. Well like that there are many but I am just only giving a sample of you know one or two so that you can just appreciate these reactions, right. In conducting these reactions and most of the time even zinc hydroxide all these reactions we will conduct to generate these oxides in the form of porous particles, right. So if I take C A CO 3 why you should become porous is that the gas is evolving from the solid. So when the gas is coming out it is not that only outer layer gas comes out you know throughout the reaction, throughout the particle the gas may evolve and then just come out, right. So that is why it produces a porous particle and in most of these reactions the input what you have to give or the rate controlling step may be the heat transfer and these reactions are one of the wonderful examples of heat transfer controlling. Like for example this calcium carbonate decomposition I have to supply sufficient heat, right. If I do not supply sufficient heat there is no reaction, okay and there is no other reactant where mass transfer coming into picture. Like you have carbon plus oxygen giving you CO 2 you have carbon solid and oxygen as the gas but unless oxygen is there that is mass transfer, right. How much oxygen you send to the surface of the coal that only determines the rate of reaction but here it is the heat transfer, right. I have some derivation earlier but I do not know whether I can cover all that in this course because we have to do many other things. So this is one type of reactions and then we have type D reactions where solid plus fluid giving me only fluid, yeah. You know many examples in this NACL and water what do you get? Yeah, okay. Solve solution it is not a reaction it is simple dissolution, okay that is not the one and you know we have our famous reactions like coal combustion in this. So solid is carbon plus O 2 gas giving us CO 2 gas. You have another famous reaction many of our you know department people they are doing work on this gasification reaction. Gasification also is you know belonging to this group that is CS plus gasification H 2 O gas giving us CO gas plus H 2 gas and this is one of the very important gasification I mean reactions now, okay. We felt that you know by 2020 all the reserves of coal will go throughout the world, wrong estimation. We have still lots of coal. In India also we have still lots of coal. So for energy that is why we try to look at the solar energy, wind energy all kinds of things but still we have this natural resource called coal and that we have not yet still used and we do not have good technologies, clean technologies, right. One of the clean technologies what we think is this, why? Because if I use coal and oxygen giving CO 2 I will get lot of ash, tons and tons and tons and ash but here I will also get definitely some solid material rejected because impurities in this carbon in this coal but still this is more decent one because H 2 O will give me C E plus H 2 O will give me CO plus H 2 and this can be used for many many chemical stocks as a chemical stock. That means as a reactant which can be used for many for producing many other chemicals and this also can be used as the energy source because we can burn CO it goes to CO 2 and also H 2, H 2, H 2 energy you know, right and this is also one of the routes people are trying to get how do you operate CO and H 2 get only H 2 now. You know we are now trying to design hydrogen cars, right for many things we would like to use hydrogen and getting hydrogen is not that easy, okay this is also one of the steps and you see here at the end there will not be any solid particles here that is the beauty here and how do you really design this it is not that difficult if you understand that but as I have been telling you all the time the universal steps are again identifying how much steam going and identifying how much carbon and where the mass transfer or heat transfer controlling, right developing the overall rate using the overall rate again to design the reactor that is all I mean that is universal process we are not going to change at all that, good so this is another type of reaction there are many but only I am just giving one or two and you know carbon disulfide how they produce carbon plus sulphur so all kinds of there are many many reactions and this is what I have been telling you you know the beauty in chemical engineering is that every reaction has a wonderful story every product through a chemical reaction, right and it is not one particular reaction through which I will get CO 2 for example there are many many sources or for example CO there are many many sources may be single step or multiple steps and which one is the most economical process that is what finally we are trying to see as an engineer and then develop a process for that that is why we never have a I mean a closed end problem we always have open ended problems and open ended problems have to be closed only depending on economics okay this is where I will concentrate because finally that may give me the least you know cost for the plant then I can produce more and I can earn more, right so that is what is the overall picture in all these chemical processes and type E the reactions are simply solid going to fluid very famous reactions are there in that if you are able to get some idea one example nowadays on the naphthalene ball is not a reaction it is just simply a operation, I mean on this planet now many people are happily using this kind of reactions to destroy people, not nuclear dynamites and all that and that is what also you do in your you know Diwali time, right solid making lot of noise suddenly it is appearing fluid, okay yeah so this is you know dynamite is one of the examples and the equation thermal decomposition of ammonium nitrate so NH4 NO3 this is solid giving us N2O gas and 2 H2O gas and I think I have already told you why you know the crackers give a lot of noise and if you want to produce more and more noise what do you do with the crackers you know you have different kinds of crackers and I think I do not know this name how it has got there is one Lakshmi cracker name that gives the maximum sound okay and there are also some other small pellets like thing where I think I do not know what they call and that also gives bullet bombs you see expert that also gives a lot of sound okay why do you think it gives a lot of sound and you know the simple one that red one yeah that would not give nice fellow it would not give much sound why it is simply PV equal to RT okay yeah you know you tighten it so much with so many layers of paper and if you take that red one not many layers of paper is there whereas this Lakshmi cracker will have lot of things and that what is called bullet bombs yeah bullet bombs will have some kind of I think twine or something around that so you are not trying to you are not allowing to expand so easily so that is why when it is very very hard then you know this suddenly the yeah this solid will become gas and pressure is developed if you are not allowing it to come out so if it reaches beyond certain value then it breaks that shell when it is breaking that shell it makes noise because that energy has to be released so that is why I think you know practically you can also design one vessel where the pressure of this gas is less than the the strength of that shell then it won't give any sound it will stay there simply okay you see how much technology involved in these crackers yeah and there are very very small ones also that red ones with circular things caps or something they call okay that is only for children right okay so it is not allowed so that is why different things you know it is all wonderful things I say if you are able to concentrate on any subject I think you know you have many many pleasures but somehow I think the present generation lacks that pleasure I know most of you are coming by you know the first thing what you do is oh the C date is coming day to clock we have to go to the class yeah you know really most of you because I think otherwise just giving the degree after you pass JEE or gate or whatever exam you have then you all of you will be very happy I mean what is the use of that in between you have to learn something right I know most of the JEE people are very happy if they are allowed to come through in gate you know main in gate and near that security check you give the degree and ask them to go out gate I think I I think they are the most happy people if you do that because simply that passion is never created in their minds never created in their minds in the schools unfortunately okay and school system was one of the best system in the country right but I think we destroyed that through coaching I mean in Andhra I know I think you know all schools they have a collaboration MOU yeah memorandum of understanding with the coaching centers okay and from the time he is born till he completes that 18 years he will be there only in coaching center and in the school everything will be going on as if he has attended he has attended the laboratories and you know the what is that attendance everything will be given right and then in the coaching center what do they do I told you know Ramayas many people are there yeah they will take the cane and then show you that okay if you are not solving this problem I will hit you okay I may be exaggerating little bit but I think that is the truth most of the time so that is why where is the passion for you for the subject where is the liking you know that something is there in this world I want to produce I mean have you ever thought how this this bulb is operating working and why it won't immediately come into the light you know that is why we say that people like me call tube lights because we cannot react very quickly okay so why why you should take time I mean just around you there are thousands of things where you know we never care what we need is a degree and job and that job also nowadays only in terms of lacks okay yeah I think you know we proudly put all our advertisements in the not advertisements I think that news in the newspapers saying that IET Madras beat IET Kanpur by 10 lakhs okay 75 lakhs and 85 lakhs I mean at that age if you are only worried about money I tell you you cannot do anything in your life you have a tremendous corrupted mind already yeah I mean at least it takes time I say slowly that is why last time convocation before convocation this Gopal Krishna Gandhi you heard of him he is West Bengal governor I think now he is in Chennai only we called him as a chief guest he has given a wonderful talk I don't know how many people really got it and of course students would have never definitely not got it okay I am sure about that because they were talking when he was talking okay we can see you know as usual like in the class okay and there are 800-900 people sitting there but they were making only slow noise but this man was reading and he told that so beautifully it seems for everything there is a measure he said in Tamil Aalavu or something correct a measure and he says that if elephant has six legs because it is very heavy it looks very awkward or two trunks it looks very awkward right or like that for everything on this planet there is a measure so similarly he says for money also there is a measure beyond some value there is no value for the money I mean what do you do I say okay I am a billionaire what do you do with that money I cannot eat ten times per day because I have money so I cannot sleep on two carts or ten carts you know that is impossible again okay I cannot travel by two cars I cannot by go by two flights at it at the same time so then what is the use that is you know Aalavu that is the measure that is the minimum thing required and how much you can eat I mean this has a certain volume capacity you know stomach beyond that you cannot eat may be maximum maximum 2 liters or 3 liters okay so because I am a billionaire I want to eat 10 liters means you will die immediately that is all there is no I think any result at all only death so that is why that measure is there so at the end that measure also slowly comes not you know suddenly getting 10 lakh that is why many people do not know how to spend money if you suddenly give them people like me particularly if you give me even 10 lakhs I do not know how to spend right because we have born in and you know brought up in that way right may be billionaires sons may spend on that may they may go and then take one drink which may costing one billion dollar okay may be there are drinks we do not know okay and afterwards what happens to him we do not know but I think you know this is the one so like that for everything there is a measure and nowadays I think I told you also this JEE counseling fortunately they removed the counseling I told you I think in 80s and 80-85 the question was what is chemical engineering they used to ask then we used to explain how this is what is chemical engineering and where to go my son or daughter after joining then we used to say yeah there is opportunity to go abroad and that is how you know the Shankar Narsimhan, Pashuvanam Ravi, Kannan all these people have gone Kannan is not our B Tech student all these people have gone and they have come back and they are doing very well absolutely no problem about that but that was the questions and as usual mainly the questions are from the parents okay I mean that fellow who wrote the exam he will never ask because he is already over his life okay yeah so that is why he cannot even talk there anyway and these people ask and then afterwards it was saying that you know okay this internal jobs and all that they have forgotten straight away they used to ask that can my son or daughter go abroad because abroad means dollars dollar means multiplied by 50 okay I mean general Thamburu I think Kathar gives I think 90 I think I do not know they do not go to Kathar because you know you have to put dress like this or you know you have to put like this there are some things you know you cannot enjoy there so anyway now I think you know people are coming and just asking in between what kind of jobs my son or daughter may get now how much my son or daughter may get that is all okay this is how changed is that fellow is not even giant and they ask that you know how much my son is going to get or daughter is going to get in between what happens they do not care in between there is a learning call you know they think all your learning where everyone has to learn so like that you know that passion is not there in non- catalytic reactions alone I can talk 2 years really because there are so many wonderful reactions and one reaction is not same the other way that is in fact the beauty you know in mechanical engineering there is only one IC engine and that has not changed for the last 100 years right what is that it has changed fuel may change people are asking hydrogen or asking alcohol okay either alcohol so they use you know or may be petrol may be something else or what do they change outside bonnet dicky different shapes you know all different shapes they create what else is there the 4 types are there all the time okay I think they are not designed it with 3 types you know like auto right may be nano may come like that I think earlier also right so only but engine is constant almost except delta exchanges but in chemical engineering process for sulfuric acid alloy alone there are 7 processes that is what what we know and if you mind is working much much deeper you can create another 10 processes but what we choose is the simplest one to operate as an engineer and most economical one that is what we do that is what happens in every chemical reaction and how many chemical reactions you can list out I mean just if I give you I mean you may not list out anything because you are not bothered okay but in general if you go to any chemistry book and then see okay and then see the number of reactions every reaction has a beautiful story particularly when you are when you want to produce that in industrial level okay and that is what is chemical engineering producing at industrial level okay good anyway so like this I think you know we have so many reactions and I mean this is one of the reactions the other one is not that exciting because thermal decomposition of oxalic acid okay that is also another example and but this is what exciting you know many people are misusing on this planet I do not know I think that is why Alfred Nobel felt very very sorry and at the end I think you know he created so many noble prizes because he himself felt that you know this invention was totally dynamite invention was totally wrong thing that has happened it is never used for good purposes now even though originally they were asking always war of course now yeah this oxalic acid this is oxalic acid N2 sorry H2 H2 C2 O4 this solid giving us H2O gas plus CO2 gas plus CO gas also good so now the last one type F in type F we have fluid going to solid and fluid okay so yesterday I was telling you one example you know the silica Si H4 that is silane this is pure silica plus two H2 gas and I have been telling you this reaction has tremendous commercial value now okay if someone wants to do this okay then another one I do not know in chemical technology again chemical technology one subject we never like it we hate all that subject but I think most of these reactions I do not say almost all but many reactions are mentioned in the chemical technology books right either organic chemical technology or inorganic chemical technology books and there is a process called bond process what do they produce in bond process MIND yeah right yeah nickel who told that oh you remember a very good nickel yeah bond process so then the bond process what we do is nickel CO4 this is gas okay yeah so then you will have ni solid plus 4 CO gas balanced this should be outside okay good yeah so we have so many types of reactions now and what we have to do for non-catalytic reactions is we will take some of the you know more popular reactions and the types are type A and type B that we will take first and what is the objective we take those reactions and then try to develop the kinetic models for type A type B and type C problem is that with time particularly here type D the problem is that the size of the particle is continuously decreasing with time during reaction okay yeah and in type C it is the heat transfer control most of the time right so that means I have to subsequently put the heat and heat transfer must be also very very quick and reaction can control or heat transfer can control if heat transfer is very very slow reaction will be will not be that fast whereas if you have sufficient heat transfer then reaction may be controlling that is slow when compared to that so that is the peculiarity in type C and type D what we have is that the particle size continuously changing and if you look at type A and type D sorry type B then we have a solid plus fluid giving us either solid fluid or fluid because these are irreversible reactions I do not have to worry about the products so these two we can club as one category right so what we do is we now concentrate on type B and type A and type B particles reactions so let me do that kinetic models for type type A and B reactions and the general normal literature what we give for type these two types okay we have solid plus fluid giving us either solid plus fluid or fluid so this is type A and this is okay let me also write this type B that is type D this is solid yeah thank you yeah this is type B solid plus fluid right so here the situation is same when this reversible reaction if it is not reversible reaction then we have to worry about how this solid and fluid both are reacting right so for the kinetic models as I told you first we have to visualize okay I mean every time you have to visualize whatever you do right without knowing yourself you do this visual process that is what I have been telling earlier also to some of the people that we have what is called our mental screen and most of the time we have forgotten about our mental screen and that you do without knowing yourself okay suddenly if I say dilly what do you remember or bombay what it comes to your mind I mean it depends on different people correct no yeah that too it depends on what part of dilly you have seen or what part of bombay you like and you know that kind of things that is the mental screen in fact I mean for me immediately dilly means that you know gate that India gate that comes to my mind because that I had that road I like so beautifully that is a wonderful road you know that Rastapathy road or something I don't know that name of that road but it's so wonderful okay and you also know that Bombay means immediately Shah Rukh Khan may come to some people correct no yeah or may be Aishwarya may come to some people speed what is speed oh yeah fast life yeah okay I thought speed there is a movie or something yeah that may come to let you know get why if India may come to some people so like that what is that you are doing in that process you know there is a mental screen where you are trying to project whatever you know on that that we don't know we have forgotten about that that is why even in chemical engineering processes that mental screen should come automatically I think that you know if at the moment I say distillation column most of you may not see actual distillation column you may see either Maccabee-Thiele diagram or you know what we draw like the tower with plates okay that is a mental screen nothing wrong in that because actual distillation column you have not seen would have not seen know the real one how many people have seen distillation column in the you have seen Kavya where did you see which industry you want I mean you have seen yes you already you worked in industry I think okay probably you have not seen SR oil okay yeah distillation columns are there so what do they SR oil crude oil they okay they will have not say think yeah so Swami you have also seen distillation column we have not seen everyone has seen a distillation column okay so but anyway it may not come but do you remember the diagram for distillation column I mean I am not talking about those people other than chemical engineering but I think in biotechnology also you have a course called unit operations know okay good so like that for any process we can imagine that has to come to our mind first similarly here our simplest imagination is I have a solid I have a fluid and I have to develop the kinetic model for that kinetic model should give me minus r a okay good so what do I imagine here I have a solid and maybe I will say that yeah I have the solid like this right and this solid can also be a porous particle or it can be non porous particle and is there any other possibility porous or non porous or any any other thing and all particles for discussion they are spherical particles okay I think real spherical particles will never exist in industry but all academicians like us will first draw only circle not even sphere only circle we draw and you imagine it is a sphere okay so that is what we are also teaching beautifully to you all the time you know but it is only imagination you know circle can you imagine as a sphere we can right because of most of us would have seen this sphere so that is why okay so this is the particle it can be porous particle or non porous particle so now if I want to yeah I mean just what normally we show for non porous particle sorry this is porous particle this is porous particle and this is non porous particle non porous yeah this is again just to show cracks you know as if there are pores good so now once I have this first I have to visualize my process and then we should draw the profiles and after drawing the profiles profiles you know solid profile and fluid profile what is happening inside the bed as inside the particle or outside the particle or in the film all that we have to imagine so that is why these are the possibilities in these reactions non porous particles and porous particles the moment you imagine you have a non porous particle you have a different model the moment you have imagined a porous particle kinetically you will have a different model okay and these models depend on you know what kind of process that is going on through these particles right so let us take first non porous particle simple to understand non porous particle this may be any reaction like you know type A and type B we have so many reactions right so once I think you know like for example iron ore reduction okay iron ore particles when you take them out most of the time all ore particles they are not porous they are very very strong dense particles right so if I imagine that what kind of reaction should be going on around that that means I have a porous particle right and then I am sending I am just isolating always my imagination is that one particle first because it is easy for me then extended to number of particles right and this one particle I may take from a packed bed that is the contacting pattern or from a fluidized bed or from a moving bed or from a rotary kill right any kind of reactor I can just take one particle the process is same in that right the process in all of these reactors the process is same there should be a gas this is fluid and then this is particle and the imagination is that now the particle the fluid has to reach the surface of the particle for the reaction to take place and my experience in fluid mechanics will tell me that there is a boundary layer okay between these two phases right so this boundary layer is this fluid boundary layer and then the fluid has to go to the surface and then react so if it is a non porous particle it is a chemical reaction okay so that means the moment if you have sufficient temperature and other conditions and if I have mass transfer to this particle then the reaction takes place and how do I imagine this we can imagine now this that we have a let me write bigger one this is the film and we are now talking about reaction after some time already I started may be total reaction time is 20 minutes may be at 8th minute 10th minute what is happening how the particle looks like right so I should show here okay this is the film I think I should not cross this one this is the film this is the particle okay I will also write here the general reaction the general reaction may be a gas b b solid giving me r r solid plus s s gas okay and if this small s equal to 0 then we have this small s yeah type b yeah s equal to 0 for type b so now after some time how the reaction is taking place first step is through the film it has to the a has to go diffuse and reach the surface and after reaching the surface then it has to first react it is a non porous particle so first this surface this surface has to react and then that product should be a porous product okay if it is not porous product then you know that is all only outer layer only you will have the reaction then if it is a porous product then slowly it has to go inside and yet one point of time may be out of 20 minutes it may be 15th minute or may be it is 12th minute then you will have yeah this one is the product so product I will draw simply okay like this and this is the core which is shrinking and finally this core has to go to 0 that is unreacted core this is one of our imaginations this is the core core shrinking this is one of the imagination that is why we call this one as shrinking core model shrinking core model okay one of the wonderful examples I always feel whenever I eat gulab jam is shrinking core model correct know if I some not properly cooked gulab jam if you take the central portion will be hot the outside will be anyway very soft so outside is the real cooked one the central one is the core so that is one example of shrinking core because it is a mouth watering example all the time for people right good you like gulab jam what do you call gulab jam or rasgulla I do not know what is the difference between those two both taste sweet that is only thing I know okay that is one so that is why shrinking core model always you know we can see for example even our uncooked rice is an example of shrinking core model only thing is you may not have yeah spherical that is cylindrical example right cylindrical size if you take the thing so that is why we see daily I think our shrinking core models but here in this shrinking core model in our course we have to develop an equation for this to get a kinetic model right so if I want to plot the concentration profiles for this how do I plot I mean where is the concentration we have to plot for both concentration profile for solid concentration profile for fluid right so fluid this is the film so I cannot go that side I think shall I move this side this is C A G this is C A S see I am trying to draw the same thing what we have been discussing in general you know in the beginning also that is all and all these things procedure is same and now this is yeah this is core this in fact r equal to 0 this is r equal to capital R and this we call R C now we have to also show there is no reaction or this core cannot shrink inside let me say this is B so the core cannot shrink inside if there is no reaction so that is why there must be diffusion of this is C A C A C on the core and this one this particular one okay this C A as a function of R that profile I am talking now you see here what are the steps step one is concentration of the gaseous reactant which has to go through the film and if there is a resistance there will be drop and then step two is concentration on the surface yeah step two is the diffusion sorry step one is mass transfer of gaseous reactant through the film step two is diffusion of this reactant through the ash layer yeah we call the product layer as also ash layer that is the general word people use ash layer there is also a history about this because I think the first model was in Japan by one Kuni and he used the sinking core model for coal right so coal outside layer if the ash is not leaving the surface then you have the ash layer outside so that word people use you know normally we do not want to change you know if someone first paper writes something wrong we always try to defend that okay ash layer ash layer ash layer so like that we do not call product layer we will always say ash layer this is what is the lesson to you know we will be asking in the synopsis meeting of research scholars I think they say that is also it is there in the literature then I used to ask them you know then what is the guarantee that the literature people are right and why do not you change that convention if you feel that that word is not suitable first you have to question whether they are right or wrong second you have to question that whether the message using those words is clear or not right ash means if I say the same sinking core model applied to fe2o3 plus h2 giving me fe plus h2 if I give that example when I say ash you will blink because ash means we know we have seen ash or cigarette we have seen ash when you are burning paper that ash only always in our mind again mental screen right our imagination so that is the reason why this ash layer is a word which normally use it is a product layer for us right otherwise you may not forget so that is the one yeah and how do I now draw for the solid the solid profile I may extend this to this side that is the center r equal to 0 yeah this is r equal to 0 r c and capital R right so how the concentration of solid will vary with time there would not be any concentration gradient whatever concentration you have that concentration has been converted that means you will have if it is C B not in the beginning right so you also should have here C B not which has been converted totally then you will have this C B not this is only this much left this is C B not and how do you express the concentration there what are the units of concentration of solid okay what are the unit of concentration of gas L K G questioner moles per unit volume okay can you also express similarly for B yeah we can why not yeah because I know the molecular weight I know the weight of the solid so if I divide by that then you will get moles per unit volume okay per unit volume if you take right number of moles so that is why C B not again you know it is solid but you know if I do not mention I am sure 50 percent of the class will get doubt in the examination now you may may not care but all doubts will come only in the examination hollow generally right so that is the reason why I am just mentioning all even the silly things so this is the one and symmetrically if I show this will be like this and this also will be like this symmetrical both sides because it is happening on both this side and this side together it is a symmetric diffusion reaction is also symmetric around the particle that is why we have taken spherical particle for our easy imagination and then we do that this is the one right this is the model for shrinking core model if I take a non-porous particle you know the moment you imagine you have a porous particle things are quite different if you have a porous particle so in porous particle you have yeah one more thing which I have to draw here I think is initially I have this is the particle at time t equal to 0 this I anyway these again you know model discrimination in the beginning but when you are developing equations again I have to draw the same picture and then we have to write the equations but this this information is only to give you in the beginning how do you discriminate model when do you take porous particle the porous model and when do you take non porous model how do you draw the diagrams and all that that is what what I am discussing now so this one at time t equal to 0 after sometime size is same but this core and after till yeah sometime t and after sometime size is again same core is almost 0 this is with time okay that is why we move and for non porous I mean the porous particle you have initially a particle right with film also is there it won't change with time same size and again same size so every time I don't have to show the film we are only talking about how this is moving so now you have the cracks here and the first step is anyway the mass transfer through the film then second step is diffusion into the pores and while it is diffusing it is also reacting that means at any point of time depending on what kind of porosity you will have right what kind of porosity you will have depending on porosity that is why porosity also is a parameter here depending on that where the reaction is taking place we have to imagine imagine that you know we have very very very small pore volume or pore sizes so then practically that is nothing but your shrinking core model because at any time the gas cannot go to the centre of the particle in the other extreme which we call truly homogenous model I have lots of porosity that means the molecules of gas gaseous reactant can easily go through all these pores right that means at any point of time if I look into the pellet everywhere I have uniform concentration of gas because there is no resistance so at that time the reaction is uniformly taking place throughout the particle as if it is a batch reactor correct no in batch reactor that is the imagination so when you have a batch reactor you stir very well and everywhere you have the same reaction so under truly homogenous conditions the conditions are exactly like our batch reactor but if I have somewhere in between porosity one is non porous other one is truly homogenous where the porosity is very very large then between this we have this what is called homogenous model that is shrinking core model for porous particle homogenous model even though it is not that homogenous yeah we have this homogenous model where the imagination is after sometime t you will have more of a product near the surface and slightly inside then like this because here the rate of reaction is not that much because there is some concentration gradient okay and at this point you have most of it is reacted may be small portion is left I think I am making noise now but yeah here I may not have that kind of product formation where I have just some yeah still that central point might not be reacting completely and of course if I wait for some more time then yeah completely it may get reacted and here I can tell you later because we are only trying to do shrinking core models because most of the time there are non porous particles porous particles are very few but if you have a porous particle homogenous model we do not even know how to define the conversion because at any point inside I mean very accurately right so at any point inside this solid reaction is going on whereas here I know clearly the boundary I can calculate clearly the number of moles in this volume because I know concentration moles per unit volume this volume I know how much depending on R C so then I can calculate conversion very easily whereas here it is everywhere I have to calculate how many moles and then I have to totally integrate from yeah this two centre and then only get the average conversion throughout the particle if I draw the concentration profile here okay here let me show also yeah there is no core here and C A G then you will have C A S then you have throughout it may happen so this is C A as a function of R and coordinate is R equal to 0 this is R equal to R sorry this is R equal to R and that is the film okay so now if I draw for solids how the concentration looks like let us say I have C B naught is this okay here I do not have C B naught anyway inside the particle after sometime how it drops where it will be more at the centre C B yeah at the centre then how do I draw yeah so you have a concentration drop something like this this is C B C B again as a function of that depends on the diffusivity of course diffusivity depends on the porosity and all that so now these are the two models what I have one is homogenous model another one is shrinking core model and now we are going to in this course only study more about shrinking core model and homogenous model mathematics we cannot develop you know we can develop but I think I will not have time to do all that but I can give you the basic information like this on homogenous model and all the non catalytic models for gas solid particles type A and type B have been based on either this model shrinking core model or homogenous model either this or that homogenous model I will do one equation that is the simplest one truly homogenous model right that means I have large porosity where everywhere you have the equal concentration of the gas then the reaction is uniformly going on throughout the particle that is like a batch reactor in fact if it is a first order with respect to A then you will get almost batch reactor design expression okay for the kinetic model R A right so now the overall picture is that we have now identified shrinking core model and homogenous model which depends on the state of the particle whether it is porous or whether it is non porous if it is non porous then we use shrinking core model whether it is porous then we use homogenous model and now using these two models how do you actually develop now the rate equation