 BI烏 ఠర్నినా నికా భంనాల్న్చి word response క౿ర−లికా eyelashes Where you founded L ఘ౿ లసప beschäft పనే脚ంవి. ど isso crashed క౿లి� interaction గు లంకి for reactor design and then of course heterogeneous homogenous and all that we have discussed okay. So we finally ended up with this diagram again I am trying to draw this so reactor what is this input yeah output this one kinetics contacting yeah then here we have chemical physical here we have batch we have continuous and here we have P f M f okay I think that I equation I do not want to write so please remember this diagram you will have all the information that is required for reactor design okay please do not forget that if anyone asks you what is the information required for reactor design draw this figure okay and then explain what you what you have to I mean explain that is what is the meaning of physical kinetics chemical kinetics batch and continuous and we have also discussed when do you choose batch and when do you choose continuous okay physical chemical also we have discussed saying that in physical kinetics when you say sometimes you will be surprised I will derive also after sometime that kinetic expression will not be there at all chemical kinetic expression will not be there at all it is only the physical equation mass transfer equation that is what what you have to substitute in the reactor design expression that is what is your minus r A your minus r A will be simply K G into C A B minus C A S where C A S is concentration on the surface and C A B is concentration on the bulk in the bulk okay so that is why that physical kinetics will automatically come into picture that we will do derive later but when you are talking about continuous and sorry contacting batch and continuous when do you choose batch system I think we discussed I think it is better for me okay small production rates okay so then that is the only criteria or is there any other criteria very very slow reactions yes yeah it is not residence time residence time you can also use continuous system yeah so that that is only criteria what did you say the first one batch batch small scale small scale and then second one what you said is very slow reaction that is all there is another one important point flux when you have unsteady batch reactor is always unsteady system seasonal production seasonal production yeah flexibility in production that point also is very important when you need some flexibility in production that means you are not dealing with one product you are dealing with may be five six products so if you have two three batch reactors you can produce any time these two three products okay that means there is no continuous demand for the products so based on that you will choose which product you have to produce now for that batch is the best system so but automatically that total production rate also must be small it cannot be very very large and then still you have flexibility right when you have when you want to have that kind of flexibility for very very big size plants you have to go for only continuous that is all I mean there is no other choice okay good so that is why that important point also please remember three important criteria you know many books will not give this information even if they give they will simply write in one corner one sentence where you do not have you know you cannot go to that particular sentence and then remember it so that is why I am telling you these are the things basic things that is required before we start reactor design actual expressions because you should know what is the information required you should know what is the meaning of chemical kinetics physical kinetics because this will differentiate whether you have heterogeneous reactions or homogeneous reactions and here when you come in contacting you would like to have contacting either continuously or batch and now if you get a job in industry when you go and then people may ask you okay now we have a new product coming coming this size so you design the entire plant means you should know that because entire plant design starts with only reactor design first okay so because you have a stoichiometric equation already they would have given you then you also they will also tell you production capacity or otherwise they will ask you to go for literature not literature what is that market survey and from market survey you will get what is the production rate and if it is very very large you automatically decide continuous if it is small then you know I told you know may be it is 10 tons 15 tons 20 tons okay or 1 ton definitely yes but we have some grey some grey area where may be between 10 to 100 tons whether you go for continuous or may be batch so for that you have to know simulate the whole system on the computer and then try to find out economically whether it is feasible to go for continuous system or batch system but if you have let us say 10,000 tons per day if you want to produce definitely there is no choice no batch you have to go for only continuous if you are going only for 1 ton again definitely you have to go for only batch I think you know there is no point in designing a continuous system for that so these are the things so then again we have also discussed in continuous we have two chances two choices plug flow and mixed flow and we discussed last class that plug flow you will go for only very short residence times and the short residence time is mainly for gas phase reactions because gas phase reactions are very very fast even if there is catalytic gas phase reaction the reaction time is again very very small seconds why because by definition of plug flow you have to maintain very very high Reynolds numbers velocities right so when you are maintaining very high velocity if you need very large residence times your length of the reactor will be very very large you cannot have I mean automatically diameter increasing because when you are increasing the diameter you cannot maintain plug flow right plug flow means fact velocity profile right one of the definitions which is also right but the correct definition is each and every particle must spend exactly same time there yeah so that condition will come when you have only flat velocity profile flat velocity profile fluid mechanically you get only when Reynolds number equal to infinity so that means velocity equal to infinity if you fix this as diameter so when velocity equal to infinity I mean you cannot provide you know length by infinity always zero velocity length by velocity equal to t bar mean residence time so this velocity is infinity means you can provide only zero time in the reactor so that means all plug flow reactions theoretically speaking should have zero reaction time because we do not use zero reaction times so we now say that if the reaction time is very very small in minutes or seconds then you go for only plug flow and all packed beds are also imagined as plug flow reactors why because you can very beautifully get a flat velocity profile in packed bed reactors that I will discuss when we are coming again to separated designing packed bed not packed bed plug flow reactors okay good so now mixed flow mixed flow generally used for very very okay another thing also for plug flow so okay one is residence time yeah what is the other criteria because it is impossible to maintain isothermal conditions in a lengthy reactor okay it cannot that also we will discuss when we talk about plug flow reactors again it is not possible there will be definitely some temperature variation and if you want to have exactly one temperature in a plug flow reactor you should know you should put infinite number of heat exchangers with different capacities okay that also I will explain to you so that is not possible that is why if highly exothermic reactions you automatically go for mixed flow reactors wherein due to mixing you can maintain one temperature and one concentration that is the definition of mixing by the by okay so those conditions now if you come to mixed flow when you have very large residence times like liquid phase liquid phase reactions will take place in you know 8 hours 10 hours 15 hours if it is biological wastewater treatment I told you 3 weeks 4 weeks 1 month 1 month is 4 weeks anyway okay yeah so so much time required for liquid phase reactions and many industrial reactions will be definitely between 4 to 12 hours you know you should have seen in the labs also esterification reactions esterification separation reactions these reactions are 6 to 8 hours are 6 to 10 hours okay so to provide 10 hours mean residence time you need a tank because the flow rate and volume of tank will will give you that much residence time that is the reason why you go for mixed flow system for liquid phase reactions and another best advantage for liquid mixed flow is that exothermic reactions if there are exothermic reactions happily you go for mixed flow and mixed flow is the best to control right so this is the criteria so now let us start deriving first the batch reactor let us take batch reactor and afterwards we will take continuous reactors okay so we are now discussing about derivation of ideal batch reactor yeah so you know very well that all the batch reactors normally in our textbooks we will have drawn something like this there will be a jacket and then you will have a stirrer is closed then you will have a pressure gauge then we will have temperature okay so of course here you may have temperature measurement through thermocouple or something thermometers no we will put but thermocouple okay good yeah so this is how it looks and we will fill up normally till this point and when you are talking about reaction mixture that volume when you are deriving it actually so that when you are calculating that volume will be only this is the volume reaction mixture this we call it as vapor space in case the reaction is taking place around maybe 120 150 if the vapor pressure of this reactant and mixture reaction mixture is more then there will be some vapor forming on the top so that has to be there okay so you cannot also take it out continuously because you know concentrations may change so that is why you just leave it and then close everything and there may be dangerous chemicals where you have to really tightly close okay or otherwise if it is very very harmless chemicals even without the top also you can connect the reaction okay that means you know this part will not be there that is not scientific scientific way of doing and but anyway that is also possible for us so this is the one and why do you call this one as ideal batch reactor what do you mean by ideal batch reactor so in all these reactors we are assuming that we have only ideal conditions ideal contacting okay and first of all the question is why should we assume this ideal condition and what is this ideal condition so the ideal condition for batch reactor what do you think what are the conditions why it should be but normally what we do in the batch reactor we put the concentrations at time t equal to 0 okay at time t equal to 0 CA may be CA not some concentration and after sometime greater than okay greater than 0 you will have CA equal to some concentration which is a function of time continuously decreasing if it is a reactant or if it is a product continuously increasing that much we know then we will yeah we will charge the reactor with whatever amount may be 1 ton or 500 kgs or whatever and then we start stirring normally what we do is we start the heating system if the reaction is taking place at high temperatures may be 100 degree centigrade so till then even though we have the reactions there all that we don't consider even though we can consider you know definitely we know how to do that not much mathematics are required but still we can do that yeah so then we will wait till that reaction time is complete how do you know that that reaction time is complete that's what what we are going to derive now for from the equations good so this is what and as someone was telling that okay I have this setup and I put this and I started this stirrer and what I expect inside the reactor is at any time inside the concentration of CA and temperature must be uniform throughout okay that is the ideal condition okay ideal condition is concentration and temperature must be uniform throughout the reactor at any time t it is only uniform it is not same it is not if it is same means there is no reaction all the time if it is same only CA not then there is no reaction okay it is must be uniform throughout at at any particular instant of time when you look right so okay now my question is this is the condition for ideal batch reactor but why should I assume that what will happen if I don't assume why I think because I can take always sample and then find out what is the concentration any other ideas what are the non linearities you are talking but what is the meaning of non linearity first of all that is there already non that equation is non linear or in this equation how can I avoid see even though you know if I have uniform stirring how can I avoid non linearity of rate expression with temperature change or if I have a second order equation second order rate expression how can I assume that will be first order you understood linearity you know what do you mean by linearity there are no flow rates it is a batch system you are talking for example if say in theoretically we get say 90% conversion should be at time t yeah and in a practical that we are only getting 85% of conversion so we means that we are still have scope for to increase it up to 90% though it is not practically possible but why is not practically possible what are the things you have you ignored practically what are the non idealities because ideal batch reactor so what kind of non idealities we can expect only yeah only mixing right what I am asking is if I ignore that where is my problem coming okay it is different if I do not have definitely good mixing so definitely it will be different so what the conversion yeah that is very important the rate expression which we are getting I do not know how to write the rate expression is a function of temperature and concentration forget about temperature now right now only talk about concentration you have non-ideality that means it is not uniform mixing so it is a function of concentration next question is which concentration the concentration here or here or here or here or here where yeah but you know definitely my problem is solved if I am able to have throughout only one concentration then I know definitely my rate is a function of that concentration otherwise if the concentration is changing at various places now I should get I should measure each each and every point I should get some average of that weighted average for example in this volume I take 1 percent volume what is the concentration I take 5 percent volume what is the concentration another 1 percent here what is the concentration another 10 percent here what is the concentration I have to sum up all that and then take some average some volume average which is headache for me why because fluid mechanics already taught me that you better design a how to design a stirrer so you do very efficient stirrer so naturally you will avoid all that measurements here here here here here first of all how do you measure you have to put infinite number of probes there okay if you are directly reading otherwise like you know how you took the sample using pipette like that how many pipettes you have to use what length and that fellow is stirring inside that may break you know this the pipettes all this why that problem simple problem is design a good stirrer mixture your problem is solved so that is the beauty in assuming that we have ideal batch reactor ideal mixing okay now you know I think because most of the time we will not discuss this part we will say that assume uniform mixing that is all we say so that it will give you uniform concentration and uniform temperature but we never ask so what if I don't assume what will happen what will happen is your life will be miserable in measuring in at every point and after that you have to average it out okay so some kind of weighted average or you know either weights you have to use volumes you have to use all that and first of all how do you measure them throughout the reactor and in the lab it is okay maximum I may take 1 liter 2 liters 5 liters but in industry it will be 5 meter cubed 1 well big well so that well I think inside that you are stirring and all that how do you take the samples there in the well so to avoid that we will say that yes now I can design a perfect you know stirrer and that is much easier for me than measuring the concentrations at various points now let me assume that I have a perfect stirrer where it gives me uniform concentration and uniform temperature so that is the meaning of this assumption and if that assumption is not there then you have a problem to define even what is rate because rate is a function of concentration and temperature temperature is varying at various places concentration is varying at various places which rate you are talking so when I am writing my material balance I don't know which rate I have to write unless you take again some average rate right so that average rate is given by your stirrer that is all what you are doing is instead of you doing all that you are asking the stirrer to do that that is all when it is perfectly mixing the contents will be only with one concentration and one temperature so that you can happily measure that concentration only one concentration you have to measure one measurement and then you can write the rate expression so once we know that then how do we write the expressions like the material balance first I think we are doing only first isothermal let me also write here put it in bracket and non isothermal we will do it after you learn something from isothermal reactors that we will do later so here and you know we have one universal material balance equation it is a mass balance equation what I am telling I am not writing energy balance energy balance I will write later so mass balance equation always when you are writing mass balance please remember you have to specify you are writing for which species mass balance is always for individual species whereas energy balance is for whole thing you do not have to differentiate okay that is the beauty in a you know heat transfer because it is simplifies whereas mass transfer every species you have to write and always in our course that our species is A reactant A which is a limited reactant limited you know what is that limiting reactant which is a limiting reactant or key reactant that is also another name what we say right so that means that is the one which is really governing the rate you heard of definitely what is pseudo homogenous yeah pseudo first order for example actually that is a second order reaction A plus B going to some reaction then I am taking maybe 100 or 200 moles of B and only one mole of A this is what we call pseudo homogenous first order reaction with respect to A why A because I can see only the concentration change with respect to A with respect to B I cannot see because I have 500 moles or 200 moles practically there is no concentration change in that okay so that is why we have to write only for a particular species and here we do for key reactant and all the time when we write mass balance A that means that is our key reactant or limiting reactant okay the universal equation always what we have is input equal to output plus accumulation yeah plus or reaction okay where except the problems as I told you all other things are only written with his hand including graphs it is worth seeing I have a copy I think I will show it to you once I have a copy okay library copy only because it is with me it is not lost so otherwise I think that also could have gone I don't know it is beautiful he is hand writing some of his papers also I will also send some of his papers where he has drawn the diagrams and graphs with his own handwriting and the matrix of course type so that is why all excellent engineers will have very good handwriting good so this is the equation what we have so now this equation I can simplify if we say that for constant density system okay then this will become NA not by yeah we are equal to CA not where is the oh here yeah for constant density system or constant density T equal to yeah NA not because for other sake I think I will just write here into DXO integral DXA by minus RA 0 to XA which is nothing but CA not minus RA that is the one okay good and if the other example what I gave if volume is changing okay that means one mole giving four moles or maybe four moles giving one mole that is volume reduction okay so the volume reduction is given by Levenspiel as yeah for isothermal system we are writing isothermal system V equal to V not into where epsilon A equal to so this is the equation linear equation what he has used where epsilon A is number of moles initially present minus yeah final minus initial divided by initial okay or volume volume at T equal to 0 volume at any time divided by volume at T equal to 0 okay that equation also what is the origin and all that I will derive I do not ask you to blindly accept that but Levenspiel directly says that assume the variation in volume is linear okay so why you should assume or why we cannot assume we will derive I will derive and then let you know okay so that we will do after completing this contacting pattern so then for variable volume you will have an equation T equal to n A not 0 to x A n A not yeah so then d x A by minus r A into V not 1 plus epsilon A x A okay so this this equation I have written later after that then this is equation number 8 this will be equation number 9 this is the general expression again for variable volume and you know this V not is a constant yeah that becomes C A not good so for constant density systems this if I take here T equal to C A not 0 to x A d x A minus r A 1 plus epsilon A x A very good okay good so this is the equation for constant density system sorry variable volume system okay good so now this equation he just leaves it without integrating then of course as special cases you can always do that okay and he also puts this in the form of graphs we are only simply putting this equation in the form of graphs this integral in fact how do I plot this integral as a graph to get that area under the curve where is this yeah okay you see this d x A is x A must be in y axis or x axis yeah because with respect to this you are integrating that so this is x A and yeah minus 1 by r A okay so what you get here is this kind of thing okay and yeah actually when you plot x A versus 1 by minus r A you get like this right so you take till whatever conversion you want x A and this area under the curve I should have brought this one T by C A not this side okay so in fact I should not here also have to add here in this case 1 plus epsilon A x A that entire thing I am plotting okay yeah so this will give me directly T by C A not okay yeah so but if I plot this one constant density system I have to plot this one as yeah this is variable volume right this is variable variable volume for constant thing you have 1 by minus r A versus x A again giving me like this this is T by C A not so that is how because he uses these are even though I think earlier people have used these plots are called Levenspiel plots minus r A but I think originally also people used it but somehow I think people call this one as Levenspiel plots and idea here is because he is an excellent engineer okay idea I told you know so the reason is that this equation how complicated it would be we don't know okay so if it is a simple one we have a mathematical expression analytical expression but in industry when you go for complicated reactions I don't have to really integrate that using mathematics sometimes it is not possible to integrate so you have to go either numerical integration or you have to go for graphical integration graphical integration is this so you will simply calculate this x versus all this different x because epsilon A you will calculate you will know that and then x and minus r A because minus r A is nothing but you know some equation in terms of k C A for example first order if you take so that C A again will have C A not into 1 1 minus x A but he is variable volume that also will have this 1 minus epsilon A x A cancels and all that but anyway so that you will have this function as only x and only x that's all nothing else other things are constant okay so then you can plot and then get the value okay that is not difficult at all but these are the basic reactors which you also use in your wastewater treatment okay and of course chemistry people also have to learn this because the catalyst so that is why these are the basic equations even biochemical you use only these equations this minus r A will be for them either monodes equation or micro cement equation okay so even the other two reactors also same thing okay good so that is why these graphical procedures must be very easy for us and I love graphs really because I will tell you later you know optimization only using graphs again lounge field method wonderful techniques he has developed simply drawing graphs no mathematics required for optimization okay using graphs how do you optimize that means minimum volume for maximum conversion or minimum maximum conversion for minimum volume or given volume okay that also we will discuss later there are many exciting things to learn even though you have learnt once because it will be more exciting now learning the same thing okay good anyway I am thankful for you because you have forgotten everything so that is why I think all these things you may appreciate okay good so I think here we will stop this is what is the batch reactor but surprisingly you notice that in batch reactor there is no volume present anywhere these are the final expressions this is 9 this is 10 this is one final expression and this is another final expression okay CA naught right where is the volume coming there and the next class we will see where the volume comes because finally you have to tell so much volume of the batch reactor but any quantity you take you will only get a time