 we have been discussing about the graphical design of packet bed reactor first and then we thought we will go for the actual equations and the graphical design the other day I have given one graph I think I have written this graphical design of packet bed or fixed bed reactors okay one graph what I have plotted was this right this is xa versus t then I told you we have like this where rate increases in this fashion no totally outer all are I also wrote here minus rai equal to 110 okay so like that this is one this is for reversible irreversible exothermic or endothermic that also we have written irreversible exo or endo you will get the same type of graphs when you plot concentration I mean conversion versus time t as parameter sorry r as parameter r as parameter so we can also have I can start here reversible exo or endothermic for these reactions we have the equation let us say simplest equation I am taking but except the mathematics the procedure is exactly same a go into r we have k1 and k2 and minus rai can be written as k1 ca minus k2 cr here we also take cr not equal to 0 that means it is pure a there is no r in the beginning okay so this equation can also be written as k0 k1 0 e power minus e1 by rt that is for k1 and this also ca not 1 minus xa again assuming that epsilon equal to 0 again for simple algebra otherwise procedure is same then we have k2 0 e power minus e2 by rt into ca not xa so this is this is equation 1 did I give equation number for the other one in the last class 1 2 3 so this is 4 this is 5 this is minus rai in fact here this is minus rob observed that means everything all the effects inside the particle also taken into account and then we are only writing in terms of rob observed rate okay still you can have this kind of equation for rob also right good so this we will again separate to write in terms of this mathematics you have to do the same thing xa I am separating express in terms of t or as parameter so that if you do the algebra I think you are not doing the mathematical work in the room I say I can see a particularly quiz 2 paper I can see I think not able to one I think not able to finish even the first problem which is very simple one writing many many times you have written that in spite of that that also many people not written in a proper way the first one you know where on the surface reaction equal to mass transfer equation k g minus k g into ca b minus ca s yeah I think some people started writing the catalytic reactions you know Langmuir initial wood kinetics yeah I think that means they are not understood at all okay anyway how many times I can repeat this is minus r a o b e power minus e 1 by r t by k 1 0 c a not again whole thing divided by 1 plus k 2 0 k 1 0 e power minus e 2 minus e 1 by r t yeah okay so this is equation in fact this you can derive and this is equation 6 what nothing okay so this is equation 6 this also can be plotted yeah there is some more things here which you know your funders I do not know whether you are still keeping them in your mind so this e 1 and e 2 depending on these two values you will get either exothermic or endothermic which will be exothermic which will be endothermic if kavya e 2 greater than e 2 greater than e 1 is exothermic right yeah you will get negative so minus delta h r you will get okay yeah so that also please write those who not remembering e 2 greater than e 1 is exothermic and the other one is endothermic yeah so e 2 less than e 1 is endothermic so that means in this equation depending on that delta h r value which is nothing but e 1 minus e 2 okay so you can also have that equation I mean that delta h r here and then you can plot right so when you are plotting for reversible endothermic you will get graphs something like this this is x a versus temperature then you will have this is going like this x is minus r a equal to 0 r a o b sorry 0 that means it is equilibrium conversion equilibrium conversion okay equilibrium conversion versus temperature but every temperature we will have corresponding equilibrium r equal to 0 so then you can also have for example r equal to 1 r equal to 10 r equal to 100 so like that so everything will be trying to go till that point equilibrium okay so this is r equal to 1 10 100,000 like that good so for reversible maybe I think I will plot there I am using liberally all this board this is again x a versus t and this is for reversible so what you get here is very nice curve this is minus r a equal to 0 something like this so this is r minus r a b equal to 0 this may be 1 equal to 0 this is equal to 1 10 100,000 10,000 etc okay beautiful did you see Kavya this kind of graphs not so this is again you know luckily core companies are coming core companies they are interviewing you or it is only other companies asking how many brothers how many sisters how many fathers how many mothers and correctly answering guess got the job okay this is very nice information where many people ask that can you draw the equilibrium conversion for exothermic and the endothermic reversible reaction okay so for exothermic reversible reaction conversion falls as temperature increases okay equilibrium conversion whereas for endothermic equilibrium conversion increases with temperature okay that is only to do with this equation where this is either positive or negative depending on this equation okay so now this is the information first we have to develop and this information comes from the simple minus r a information minus r a equal to some equation so that will give you this information so now how do I use this information for the design right this is very nice one so that means in other words what I am trying to solve is the material and energy balance equation this is almost like our material balance equation and energy balance equation which gives me the relationship between x a and t here also x a and t that is the reason why we have plotted like that see when you are no only what you are talking about is at equilibrium okay but when kinetics come there is again you know it is reversible reaction where you have forward reaction and backward reaction till some point where you have the maximum here you will have the reversible reaction you know forward reaction dominating then reversible reaction dominating so that is the reason why you will have the maximum here and then falling later okay that is the concept and you can also find out for example this maximum okay you can have an equation again from this okay that is dou r by dou t equal to 0 dou t temperature because conversion also is there x a so when dou r by dou t equal to 0 all that you know maximum points also can be beautifully connected so that means theoretically speaking we would like to be there on that point on this point okay on that point why because there it is the maximum rate okay it is not quite obvious here it is maximum rate if I plot the other way I can show you all those rates will be maximum right but here we are tracing this curve this reaches maximum and then it is falling but if I plot for example conversion versus conversion versus rate or rate versus conversion rate is here then you can see that maximum but temperature will be another parameter so that is why there is no doubt about that this is the maximum and that maximum is the maximum rate for me if I have all those maximum rates in the reactor because it is a packed bed we said or you can take it as plug flow reactor along the length every cross section you have one rate correct know that is totally opposite to mixed flow why mixed flow has only one rate throughout the reactor that is the reason why we say that infinite number of tanks in series will give you packed bed because by definition of plug flow itself it is infinite number of tanks because we are assuming the concentration along the cross section is uniform okay that means uniform means like mixed flow reactor so each cross section is a mixed flow reactor so like that you can put infinite number of CSTRs in series you will get plug flow so that means at every point I have the rate and if those all those rates are maximum in my design equation rate is always in the denominator if all those rates are maximum then I will have the minimum reactor volume that is the reason why we can we should be theoretically on this point but that is not same if I go to endothermic reaction or reversible endothermic reaction or irreversible reaction irreversible reaction as temperature is increasing rate also is increasing okay Prabhu for irreversible reaction as well as reversible endothermic as temperature is increasing you see this one rate so next if I go it may be 10,000 1 lakh like that it can go so what is the maximum I can use that means I have to you see these are all very simple beautiful funders I really get excited you know particularly with this graphical design theoretically speaking here I can have the maximum rate that is possible to get the minimum volume to get the minimum volume so I should have one rate throughout which can give me the maximum rate and that will be in the denominator so you have you know W by F A not equal to integral dx A by minus r A okay anyway let me write also once here we are talking about catalytic reactor otherwise it is V by F A not 0 to X A here we are talking about observed okay so if this is maximum then my catalyst volume will be minimum and on the other hand if someone gives me this volume already this weight of the catalyst then I will have the maximum conversion these two are the design parameter always given the conversion find out what is the volume or weight of the catalyst or given the weight of the catalyst find out what is the conversion you will get the maximum conversion so that is why here there and here the maximum T max will be the temperature and that should be isothermal that means otherwise you know that every point you have different you know rates the average rate also should be the maximum so when can I have the average rate maximum if I have all the rates are same right so like that what I have to do is I have to put infinite number of heat exchangers along the length of the reactor where everywhere I use corresponding temperature where I get the maximum rate okay so that is the reason why you can go to the maximum temperatures here and what is the limitation limitation is catalyst yeah matrix of construction catalyst should not be spoiled so there must not be any side reactions beyond certain temperatures if you are able to take care of that you can go to any temperature okay so that is why the optimum design for endothermic reversible reactions and irreversible exothermic and endothermic reactions is using the highest temperature where you get the maximum rate if it is CSTR it is very easy even though you are talking about packed bed I can also cover that in CSTR you have only one temperature and one conversion right so one concentration so correspondingly I can choose here for example yeah I can go some other like this and then say that for getting this conversion because conversion is fixed for us either you fix conversion and get the volume or you fix volume and get the conversion but most of the time for new reactors you fix the conversion and then get the volume so that is why if I draw the line okay maximum conversion is that so now for a CSTR it is very beautiful simple design because I have to draw the line where it goes through this particular point correct no there is another rate or may be this rate is going may be that row this is the maximum temperature and this is the rate for this conversion so simply design will be W by F not equal to DX I mean XA by minus RA it is a mixture flow reactor okay so again beautiful simply minus RA we will substitute there this value and then I will get the minimum volume or minimum weight of the catalyst so packed bed is I mean the mixture flow reactor is very simple but here I should see that the average of all these rates should be minimum when I have the packed bed when I have the plug flow reactor okay so that is I mean this and this is not that kind of exciting thing but here only it is exciting because you have to use high temperature high temperature definitely tells you that you will get higher rate but beyond certain point what happens is that that rate will fall the rate started falling so that means you are nowhere nowhere in the optimum sense in the optimal region so that is why multi-stage reactor is used where you use one reactor to get that maximum average rate please remember average rate and then again you come out of the reactor put another reactor right okay so for example if I can tell you that if I have adiabatic reactor again simple one I am taking adiabatic reactor so then I can draw a line adiabatic line something like this when I cross this line it started falling because I am now going in the form of decreasing rates this is increasing all this is increasing rates whereas this side is decreasing rates right so when I just cross this line then I will have I am going to have lower and lower rates which is not good for me so then I have to come back again I will come back I will explain this one to you later so like this see now this is the first reactor packed bed adiabatic system then from here to here I have to cool because this is temperature 1 temperature 2 this is temperature so I have first a reactor then a heat exchanger then go to the next one I have another reactor next and then another heat exchanger here this comes through what is called dynamic programming where to stop where to start dynamic programming that is one of the optimization techniques dynamic programming of chemical reactors one of the famous books for this is by aris optimal design of chemical reactors optimal design of chemical reactors by or aris this is one of the oldest books I think 60s actually that was his PhD thesis also very small book beautiful very difficult to understand but I think worth the trying to solve that I mean use that book so here he has explained where to stop and all that I will also give you at the end what is the condition without understanding all that programming also we have some conditions where we can use so that we will get the minimum reactor volume okay that I will give you later so this is how you know multi stage for example what is that sulphuric acid plants SO 2 to SO 3 do you know that we use multi stage multi stage multi stage packed beds there do you know Rani tha for sulphuric acid plant when you have one reaction SO 2 to going through SO 3 SO 2 plus half O 2 going giving you SO 3 and what is the catalyst they use is the problem always all others when I ask one person X X will not answer all others will answer okay V 2 O 5 correct yeah so that reaction they use multi stage bed usually 3 or 4 beds so the reason is when you are going further and further here the conversion is falling maximum is conversion this is possible but maximum conversion you have here is almost one so that means you have to start with the higher temperature and move towards lower temperature you are moving towards lower temperature that is here you are again moving towards lower temperature if you have one more again you are moving towards lower temperatures so lower temperatures in exothermic reaction will give you more conversions so that is why first you have to have at high temperatures start with then you have of course where you stop and all that this comes through this programming so then you start you stop here come back on the same because there is no reaction in the bed because in the heat exchanger because it is a catalytic reaction right so catalyst must be there to for the reaction to occur but in the heat exchanger we are not putting any catalyst it is simple heat transfer of the fluid I mean the reactant fluid reaction mixture okay so that is why that is no problem so you can maintain the same rate again draw the same slope and that slope also I will just quickly derive that equation so that I think they know already because last semester I have done this and as I told you for if you take pseudo homogeneous model the design what you learnt earlier in the reactor theory course this is exactly same this is same thing what we have discussed okay because you are not at all trying to feel that there is a catalyst it is equivalent to your homogeneous bed where for homogeneous we have done all this reaction all this design you do not have to learn anything more but still it is my duty to remind you and also to repeat so that one more time repeating some people some more people may get okay what is happening so that is why this exothermic reactions are very fast because as temperature increases conversion falls the other things are very simple right so now why should we get this kind of line and you know that mathematically also I will try to do that yeah and okay this is also t max t max and when I want to be at this temperature where I get almost maximum rates okay we want this is t max that means t max is only one temperature throughout that is isothermal condition even though many times we say that isothermal conditions never prevail but even here they would prevail but what really happens it is an endothermic reaction and it is adiabatic system we are not removing heat or adding heat here okay that is the simplest design and industry people love to have adiabatic reactors packed beds because adiabatic reactor again does not need any extra equipment you do not need any pumps again to send coolant okay so I mean not in one place sometimes you may have along the length three four heat exchangers that means one section with one temperature another section another temperature coolant in coolant out okay if it is exothermic reaction if you want to cool so all those things will not be there if it is adiabatic reactor so that is why any decent industrial chemical engineer if he has the chance of using adiabatic reactor he just jumps and then takes whereas that is not he is not so lucky when you are talking about ammonia production why probably any idea ammonia how do they produce what are the reactants n2 plus 3 h2 giving you yeah 2 n h3 okay good that is nice yeah so then what catalyst they use what kind of reactor they use very good yeah what kind of reactor they use for sulphuric acid I told you it is simple adiabatic packed bed they take the tube cylindrical tube and pack v2o5 vanadium pentoxide but for ammonia it is not same androck what furnace no no furnace yeah but what do you mean by tower reaction tower means this also will be like this idea all are vertical in chemical engineering all are vertical horizontal nothing horizontal when it is not working yeah androck you have an idea how can they use cstr it is a gas phase reaction for most of the gas phase reactions we do not go for cstr I mean know kavya kavya can guess nicely is packed bed only because we have catalyst iron so definitely it should be packed bed yeah exactly so that is why it is highly exothermic also that clue also I can give you adiabatic they cannot use you know because they have to remove heat you know in again there are very simple beautiful fundas there because here in so2 to so3 the heat of reaction is not that very high that is why they go for adiabatic whereas for ammonia reaction heat of reaction is very high they have to remove the heat so to remove the heat they use other do you interstage cooling interstage cooling we are also doing in so2 to so3 multi tubular reactor it is just like heat exchanger that is one of the very famous versions of ammonia reactor they take may be 3 inches 4 inch tubes and then put 3 mm 4 mm catalyst so like that they put all these tubes like exactly heat exchanger inside the tubes you have the catalyst outside you have the coolant shell side you remember shell side yeah tube side tube side is the catalyst shell side is the coolant and that coolant also of course it is highly exothermic the coolant also is sent in the opposite direction so that you know you that will be preheated your reactants also will be preheated all kinds of things wonderful designs are available there but you see because that is exothermic reaction so2 to so3 also is the reaction but two different reactors we use because in one case that exothermicity is very high ammonia for example and in the other case it is moderate heat of reaction so that is why it is not only the quantity whether it is continuous for very very large productions or small productions you go batch not only that there are other criteria also like you know the heat removal if you have too much heat removal like packed beds particularly then you go for you know tubular reactors okay then there is another thing also it is a gas phase reaction if it is liquid phase reaction highly exothermic and I have to control the temperature then I can go for CSTR and I do not know whether you heard of this or not fluidized beds behave like CSTR fluidized bed is the you know that solid catalyst is made in the form of very very fine powder so I told you at one point where minimum fluidization where the entire weight is supported by the drag force so you will have exactly I sometime back I explained to you also exactly the same fluid property properties you will get for this solid okay so that is why if it is still very very highly exothermic and temperature control is very sensitive they do not use packed bed they use fluidized bed multi stage if you want to go for more and more conversion because we know that mixture flow is very inefficient and plug flow is very efficient why because of the concentration gradient only because throughout the system in mixture flow you have only one conversion that means you are not optimally using all the concentrations whereas in packed bed or plug flow you will have optimally using points at each and every cross section so that is why if you want if you have to use fluidized bed to control the temperature particularly one of the very beautiful example is thalic anhydride production thalic anhydride is very very highly exothermic okay so all thalic anhydride reactors now operating in the world they are only based on fluidized bed okay lense fuel also explains this and you know if you are not able to control temperature it will explode so that is the reason why they very carefully control the temperatures in the fluidized bed so there again mixture flow means i have the simplest design i do not have to draw this line i have to only see one particular point how do you optimize mixture flow using dynamic programming again iris has given actually earlier i mean we had so many courses optimal design of chemical reactors was one course packed bed reactors alone was another course okay but at that time of course we had an m tech stream called chemical reaction engineering so that is why we need more deeper and deeper so that is why we had but now almost you know jack of all master of none so we tell everything in one class and then not able to concentrate much on that but definitely that will expose you to what are the basic things that are required for chemical reactor design i mean we need that feel sorry that we do not have that kind of so many courses this also if you concentrate you can learn so many things here okay good so this is what is the graphical design and why we should get this kind of line i will also try to derive that now very simple derivation i think this i can remove oh plus you are right thank you thank you thank you how do you remember oh it is okay that is my right order okay good yeah that is plus only very nice okay anyway i am removing please correct that yeah this is let us say ideal pfr non isothermal ideal packed bed reactor that means plug flow ideal packed bed reactor means plug flow right yeah so we have non isothermal so we will have packed bed something like this we have packing everywhere so i have a heat exchanger like this yeah this is coolant in tc again to simplify mathematics that coolant never gets any temperature up okay why because its heat capacity is so large it would not feel at all okay yeah so again tc this is only for simple mathematics algebra to satisfy then we have f a not v not c a not t not x a not usually 0 this side also you have f a v c a t x a that cannot be 0 okay yeah so i hope you know the meanings of that f a is the molar flow rate moles per time and v is volumetric flow rate okay and of course c a t and x a all those things you know so here if i take a small element inside for material balance what we get is m b and i have a reaction as a going to r simple reaction okay so m b for a will be this you already know so that is why i am writing quickly minus r a into d v right so this volume i can also take here in the beginning okay anywhere i can take that yeah this is one and yeah so this f a not d x a can also be written minus r a this d v as cross sectional area a into d z if this is the z coordinate so this is z equal to 0 here it may be z equal to l that is the length of the reactor yeah so this is equation 1 equation 2 so now for the same volume now energy balance i have to write energy balance for the whole components not for only one a so when you are writing for that so you have sigma of f i molar flow rate c p i t not that the total t not i am taking here because from here i am writing there is a reason why because i can write this as delta t and each delta t delta x i can along the length of the reactor i can solve so that is why we are taking t not otherwise you can take here and then put starting from t not onwards you can also do things okay that is input and this is exothermic reaction this is input right so this is exothermic reaction so the generation term will come this side because heat is generated so we have heat generation as minus r a o b d v minus delta h r right this is nothing but mols per time d v and minus r a so that multiplied by so many calories per per mol so calories per time you will get there so this is the one this is equal to output yeah okay sigma of f i c p i t some temperature here that is one plus you have u a a dashed t minus t c so oh i have written 1 2 3 here separately okay so you know what is this u a delta t term is this yeah so this is the tube like this this is the tube we are writing from here there is an heat exchanger outside this is the area where the heat transfer is taking place that is pi into d okay so that area we are taking pi into yeah d only so that is this area into heat transfer coefficient and temperature difference and you have now we would have appreciated why that t c i have taken throughout same in fact t will change t c will change throughout along the length of the reactor but if i am assuming this t c is same everywhere so correspondingly here t means t minus c here t means t minus c here t means t minus c but t minus t c okay so that is why to simply simplify the algebra only we have put there otherwise you have to take that logarithmic you know your yeah l m t d l m t d you have to find out and that you have to substitute and it is a trial and error procedure and it is very very because each time you have to find out for each section so that is the reason why we are simplifying and finally we have to check whether our assumption is right or wrong okay but for understanding the theory this is the simplest one what we can give this is equation 3 then this also can be written there is a yeah this can be written as this is the balance this is sigma of f i c p i t minus t not so this i have taken that side okay so then we have this anyway as usual u d a dashed d i is that area okay t minus t c minus minus of r a d v minus delta h r equal to 0 this is equation number 4 okay yeah so now we do not this is ob this is also ob okay but you know i do not like this term minus r a d v because energy balance what you have to get is the relationship between x and t x and t i think i do not know whether you know b t x students whether they have able to understand why we should write only in terms of x and t you know teacher would have taught you but i think probably you would have forgotten see here in this equation the simplest one if i take as k into c a first order reaction right so i have c a not 1 minus x a and here also i have k not k not e 4 minus e by r t okay so now i have 2 parameters here t and x a what are you know this is an integral but this is with respect to x a so i have to convert this in terms of either t or x one of them only one parameter i should have x and t x or t so that is why i need a relationship between t and x a so that this entire integral will be in one parameter one variable so that is the reason why from energy balance i need a relationship between t and x a right so i can get that if this is replaced by this equation equation 1 if i put equation 1 here then i will have this is f a not x a so writing that sigma t minus t not plus u d a dashed t minus t c minus f a not d x a into minus delta h r equal to 0 so this is equation 5 good i can also write this one in terms of delta t okay this has delta t this also delta x right and then i can of course i can try to solve that because it is only trial and error because you cannot have directly the solution right otherwise if it is an adi because this u a this t is also a problem for us okay so all that procedure i think last time i have explained but anyway now i want to tell you that we are talking about adiabatic reactor there adiabatic reactor design is the simplest and most usable design in the industry okay adiabatic reaction so that is why which term i have to neglect here to get adiabatic equation this will be 0 for adiabatic no heat exchange okay so then what is the equation you will get in terms of t tell me t minus t 0 equal to for adiabatic case for adiabatic t minus t not equal to yeah f a not no minus delta h r okay f a not yeah c p i and you have here delta x a or x a okay which is multi stage there is no multi stage for any cross section any length it is valid that is no problem yeah so if this is a constant we call it as beta t minus t not equal to beta x a so this is 5 6 that is 7 c p it is not changing with temperature they change but you know the moment you put that equation t square t cube and all that impossible to solve this so that is why we see that how much it is variation between your limit of you know that that temperature limits you have to calculate using thermodynamics you calculate your temperature reaction temperature may be varying let us say 350 to 470 as an example so within that is it very serious if it is very serious you have to go for all complicated equations no chance if it is negligible within our errors engineering errors then no problem we can use this analysis not only that even delta h r even delta h r also it can change with temperature but even that variation we have to find out within our operational regime whether it is serious or not if it is very serious you have to take that all complications it is only mathematics procedure is exactly same it will be more complicated more messy in terms of equations that is all okay so then if I plot this will I get what is the slope what is the slope of this line this is what I have been telling you is it beta just check one by beta it is not beta because it is x versus t t is y okay sorry t is x I mean in our y equal to m x plus c that is what always I do not know who started first y equal to m x plus c I think throughout the planet we use the same thing I think for straight line equation okay yeah so if you want to convert in that fashion y equal to m x plus c then I have to plot only one by beta so one by beta is this okay sorry beta is this one by beta is f i c p i by this one we are taking it is a constant and all these things I know f not I know total flow rates of all components I know then delta h r I know thermodynamic quantity and then that with that I will draw the line here one by beta and this boundary will tell me I mean theoretically I can go here but when I am going towards this what is the rate here zero if you reach that zero then what will be the volume here infinite so if you have infinite reactor value where do you stay and then operate so entire universe is occupied by your reactor what a wonderful design no one can stay anywhere in the universe so that is the reason why we cannot go to zero rates so you have to go only to certain limit and also as you go towards zero rates your volume is becoming larger and larger and larger so all your money whatever you earned it will go for only designing the reactor because so much material you have to put so that is why there is a limit for conversion in the practical sense okay it can be 95 economically optimal conversion economically optimal conversion and no book will give you that for every plant you have to find out what is economically viable not only every plant in every country you have to also find out because in some countries you may have materials cheaper in some other countries very costly so that is why every time when you are designing this economically viable conversion you have to find on your own depending on the local conditions okay so that is why finally you have to make profit after at the end good so that is why we just draw this line and there is a condition I do not know whether I have that condition here oh yeah okay that condition is where you have to stop is integral x a in x a out dow by dow t of 1 by minus r a o b o d x a must be zero this is the condition okay triangular 1 by minus r a dow by dow t of 1 by minus r a we can also write this in another form 1 by r square this also can be written as okay in and out I will write here now 1 by r square r a square o b square yeah next one I am just differentiating this side yeah not d r dow r why dow r because x a also is there as variable so this is equal to zero same condition okay so using that condition that means for example I can plot 1 by r a first 1 by r a versus t I can take the slope at every point then I will have this okay now that versus x a I can plot you know how do I because it is not that easy to differentiate and get things if it is possible no problem because most of the reactions are not very simple reactions the way we have taken so that is why you can plot 1 by minus r a versus t then take that slope at every point then that becomes dow of minus r a this is simply this is y for me 1 by minus r a is y okay and t is x d by dx I am calculating okay so then you plot this entire quantity again after getting all slopes versus x a right so then you will have to see that this finally goes to zero in fact that is also very very nice one where when you plot this you have to get so when I plot this whole thing dow by dow t of 1 by minus r a square okay versus x a it has to go to zero no no square sorry yeah yeah okay versus x a if you plot how does the curve should look like finally what is that you have to get zero so that means you should have some positive area some negative area so it will go like this so now you have to extend this x a after crossing this slowly you have to count the area such that this equal to this equal areas okay that is where you have to stop this that is the conversion where you have to stop this this is x a I have written yeah this is x a so very simply graphically we can do many many things and I think in the design problem last time or previously sometime yeah last semester only you know yeah you have done this not all of you but some of you have done this all of you only two batches out of ten batches yeah so that is how they have done and then they got very nice things but this is a wonderful experience but unfortunately this time design project is not catalytic reaction no it is non-catalytic reaction yeah by the by have started doing shaker one day before the final thing okay two days okay two days that is a great improvement from 24 hour to 48 hours okay yeah have you started reading at least the problem statement what is the problem statement very good stay in chemical engineering I say don't go to management do one more degree in chemical engineering and then go for management but if you go to management coming back is difficult okay it is not a reversible that will be irreversible the moment you go to management anyway I am just giving you because so many wonderful things are there I say so many wonderful things are there what you can do particularly if you go abroad and get exposed to multi-scale chemical engineering where I have told you know last time where you can focus can I focus only on the design of the catalyst particle or can I focus only on the crystal size of the catalyst you know first you have the crystals then crystals also have pores and all that like zeolite then all the crystals will come as a as solids so all the solids will keep in packed bed or fluidized bed and then all the fluidized beds or packed beds are kept in the plant which scale you want to choose you can choose the entire plant as your profession or only that one molecule how it is moving through the pores entire life you can spend there is sufficient things because still we have not understood quantum mechanics and all that so for ultimate aim is can you say that to the molecule okay now I will tell you move this side that has to move that is the kind of mastery you can take no really that is how you have to control so then only you have the mastery over the molecules otherwise you do not have otherwise they behave like you behave okay because whatever I tell in the class you never bother no whatever good things are bad things you never bother so like that molecules also I think if you are able to control then it is fantastic really very very good so many wonderful things are there and also you know it is not that easy to design these reactors that is why I tell you first you see for the design chemical engineering kinetics by j m smith okay that is one book I think I will write make a note of this yeah engineering I am putting short form chemical engineering kinetics by j m smith let us make this fellow happy because he feels that no one is referring to his books okay but particularly 13th chapter is the design chapter where he has 13th you know 13th or 14th you know I think 13th I remember but anyway third edition I do not know whether it is 13th I think it must be 13th only yeah so I think you know two dimensional model also you have mentioned not only one dimensional model he has actually solved step by step that is why I am not solving you have to solve you have to go through that book the other book is chemical reactor yeah can anyone guess not design promote and bishof chemical reactor analysis and design this is by f r o m e n t foment and bishof bishof is one of the greatest I think he died in USA and foment is again one he is the authority in the world on packed beds foment it seems they call him fomo or something he is from belgium okay foment has some contact with foment I do not know whether he is there or not but he has got some contact with this university he goes frequently there foment so foment and bishof is another wonderful book highly complicated that means you know I told you chemical reaction engineering can be taught as simple as possible and also it can be taught as complicated as possible so that you will never try to look at that subject later okay so that kind of confusion also we can make that is also possible but that confusion comes mainly because of the mathematics same problems you know you complicate take nano isothermal take for example complicated rate equation highly messy algebra that is all nothing else concepts are same even that complicated equation also they have to still use either plug flow or axial dispersion with plug flow or radial dispersion with plug flow like that only there is nothing so that is why these two books I think please see they are available in the in the library please go through that so this is what I just want to tell you about the I mean graphical design see I have only told you how to design but here also you can design if you do not want optimal design optimal design means you have to go to the i s temperature but some design if you want to make it is not optimal you do not want to be at the t max but you can now take for example this equation for endothermic also it is same you will get the same equation then simply draw the line this is slope equal to 1 by beta right so then what do you do it is very simple what you have learnt in your 1st class or 2nd class may be or C R E 1 so what is that you learnt there if I have X A versus yeah so here what I do is I will read now this is corresponding R A and this is X A okay and temperature also I have here temperature I do not need actually so this is X A and then the rate here also X A and then the rate and here sorry sorry sorry here I do not want you know where this line cuts here it is cutting here it is cutting maybe there are many so many lines in between so what I do here is X A versus minus R A okay so then I can also convert this into yeah 1 upon minus R A then you have again 11 speed plot wonderful plot what is that 1 by minus R A versus X A so if you know exactly what is the conversion you have to stop then this area under the curve will be W by F A same even here it is same okay this is exothermic reaction sorry here I have drawn wrongly it is it is endothermic reaction no one pointed out also okay endothermic reaction as temperature increases adiabatic you know so correct no it should be in this line it should be in this way yeah this should be in this way because temperature falls as conversion is increasing it is adiabatic endothermic reaction so this is again same thing precisely same this point this point this point this point this point okay yeah in that excitement I told the same thing for all three but this is the one this is endothermic you have the negative slope because as conversion is increasing it is adiabatic system that means no heat no heat removal or no heat addition as the reaction is taking place in endothermic reaction the temperature falls conversion increases temperature falls and this is how it looks if it is a straight line okay this is a wonderful thing 11 speed only could present this kind of wonderful points so it is there already in the maybe some chapter the third edition I am not very comfortable but in second edition it was 8 chapter also but you know this graphical design graphical design is a wonderful design then I think tomorrow we will take the actual equations and then troubles ourselves okay I will tell you what are the equations that have to be used okay then I think thank you