 Okay, so now we have to start again multiple reactions and the definitions we have taken, multiple reactions definitions, okay. And where we stopped yesterday was that we, we found that for higher order reactions, if the desired reaction is higher order, then maintain the concentrations as high as possible or if the desired reaction is lower order, maintain the concentrations as low as possible. And if temperature is also coming into picture, higher activation energy, favors, yeah, at high temperature favors, yeah, desired product if it is activation energy is more, okay. So these are the basic rules everywhere you have to use, right. Now the question is how do you maintain these high concentrations or low concentrations, okay. How do you keep C A R C B high R low? We are also imagining that B also is one of the reactants. How do you keep that? And we know that roughly that when you have mixed flow you will have high and all that. But what are the other possibilities? If I have batch system, batch, you can have, yeah, you can pour, okay, all this suddenly, yeah, okay. And then you may, anyway stirring is there. This is batch, this is A, this is B. So this kind of system at time t equal to zero, you just put these two into the system, okay. And then start stirring. So at that time you have C A C B both high, if it is B, yeah, right. Both high in this, yeah, in this kind of, you know, setup. That means suddenly you added both at time t equal to zero and started stirring. And if you are maintaining like that without any disturbance, then you maintain C A C B high and slowly the reaction is taking place and you know C A C B will be converted to desired product, undesired product and everything. But when you maintain this and if I have higher order for a desired reaction, so I will get definitely desired product more than undesired product, okay, yeah, good. So that is the one. So if I want to maintain only both low, for example C A low, so what we do is, okay. So this is A, this is B but add drop by drop, okay. So that it will be, yeah, you will be adding drop by drop, your idea is to maintain C A low C B low. So by adding drop by drop, what happens is that always you are keeping, you know, you are also adding drop by drop slowly and reaction is taking place, then C A will be low, C B will be low, right. We have not taken any reversible reactions, right, for reversible reaction also it will be the same only, it will not change. So then you can maintain C A C B low, if you have first order, I mean if you have batch system. Another possibility is you can either, you have to maintain sometimes either C A low or C B low, one of them. So again this situation is same, that is I will take, if I want to maintain C A low, C B high, what do I do? Yeah, C B is first put, this is B and then add, this is A, this is A, add A drop by drop, okay. So these are all the things, you know that is why the contacting patterns what we have discussed there, okay. So now for multiple reactions you have to choose what are the possible contacting patterns where our conditions are fulfilled, either C A is low, C B is low or both are low or both are high, right or temperature is high, temperature is low, right. So temperature is not that kind of problem because temperature high means I will put here a jacket and then maintain high temperatures, right but stirring and all that is there, right. Similarly temperature is not a big problem in choosing this kind of things but once you choose this how do you give the temperature whether outside jacket or sometimes inside coils you have to put, heat will be indirect touch with the reactants, so then you can also have high temperatures, okay. If it is required, if it is low temperatures again you have to cool it, all kinds of things we can do, right. So if I have continuous system what are the possibilities to keep the concentrations as high as possible in continuous system, right. So let me write here continuous in this system C A C B high, in other system we will have C A C B low, these two we will just try to find out, okay. So this side I do not have to give much information because when you maintain this is A and B, this is B F, then we know that definitely we can maintain high C A and high C B if I have this, okay, good. So then for C A C B low we have A B, this is coming out, right. Here in mixed flow normally you can always maintain, here I can definitely maintain C A C B low because that low also corresponding to the outlet concentrations, right. So if you want to still keep it very low, then you have to increase the reactor size and then maintain the concentrations as low as possible and then automatically whatever concentration you put that will be instantaneously mixing to that concentrations and you will get corresponding steady state conversion, right. This is one and we also have other possibility, you know this is not new. That means how do I replace this P f with tanks, I may put more number of tanks and we have also seen 6 tanks are enough to get almost P f, okay. Only may be 1 percent, 2 percent, 3 percent is left from 6th to or 7th to infinite number of tanks, right. So that is why to maintain high concentrations you can also put, so this kind of arrangement, again put here A and B and anyway it will come out as the product. This is another way of maintaining high concentrations. This is okay. Now if you want to maintain for example C A high and C B low, what do you do? C A high, this is continuous system again, I will write here C A high and C B low. For this situation what do we do? Not bypass, bypass alone will not help you. This is P f. You know C B low I have to put. A I will send here but B I distribute. This is one of the challenging problems for chemical engineers, okay. This is really wonderful problem. Definitely you can question how do you maintain plug flow and then still do it. It is not that easy but still things will work, right. That means if I, when you are introducing this there will be some disturbance, hydrodynamic disturbance. So that will definitely create some kind of mixing, right, when it is entering. You have the vertical tube or horizontal also and then you are putting various streams at various places and then open the tap. When it is entering definitely there will be overall flow is from top to the bottom. It is going like this. So definitely you will have some disturbances. But if you take sufficiently lengthy things I think you know we are almost near plug flow but still you will get some kind of small disturbance but you get good amount of yields, okay. That can be done beautifully but mathematically this is not that easy, okay. A and then B distributed over so that at any time I will choose my C B. In fact this is again an optimization problem which C B that means what is the concentration of C B and what will be the flow rates of C B. But I cannot maintain that because again stoichiometrically I have to do that. Yeah, yeah exactly. That will be limiting reactant. So I do not get you know the desired products. So that is why. C B will be high in this case. No, C A will be high. A is maintaining throughout you have you know high concentrations and B you are introducing wherever you want you know throughout that means at any point of time when I look at that at this position for example A should be high, B should be low. So similarly A should be high, B should be low concentrations. Yeah but you see here I am taking 25 moles or 30 moles and here I am adding only one mole per liter. If you are adding more B my concentration of B. Yeah but that I have to find out what are the concentrations which I have to use so that I will maximize my product. So here this mathematics will be very very complicated. Then I have to choose, flow rates also I have to choose. So these two I have to choose. I mean this is really a challenging problem. I mean when you are pouring C B at different cross sections say there might be a probability of mixing right. That is what I just told you. That is what exactly I told you know that hydrodynamic disturbance is there when you are introducing the streams at any cross section right. So due to that you will have some kind of disturbance but overall if I look still I may not get 100% perfect plug flow. By the way there is no 100% perfect plug flow except for conveyor belts right. So that is why that disturbance is there but in spite of that disturbance I will still get more desired product if I use this system. If I have to maintain C A high and C B low okay and also we have another nice thing is the same thing. Can you just imagine what is the next alternative? Because plug flow generally is difficult and then you know you have yeah so that also C S T R you can put let us say 6 you can take and introduce in everything separately. That is in fact is much easier but only thing is you have to handle 6 reactors in industry but whereas you have to only use one pipe I mean when you are trying plug flow right because again you know in industry many people hate maintenance. The more number of pieces they have then definitely the maintenance also will be high. So that is why they would like to go normally for equipment which is not moving that means moving parts are not there. If you are able to mix without even external stirrer it is excellent. You know there was some I think there are many many wonderful things I say if you are able to open for knowledge okay. Many people I think in 70s try to design motionless mixers static mixers. Another name for that is static mixers and motionless mixers. So the fluid will move itself and then there is no external mechanism where the stirring is occurring and then mixing is taking place. See human mind is excellent. I think there is no limitation for thinking. Only thing is you are not thinking for I mean you may be thinking other things I am thinking about chemical engineering that is what my worry is okay. So that is why all those possibilities are there but this one is easy for me to handle but except again in industry you know I have to maintain 6 stirrers 6 different tanks tanks may be same size okay and again if I have each tank has coolant that means if it is exothermic reactions you have to remove or add heat right you have to maintain some temperatures. So all these problems will be there yeah. Can we use the magnetic stirrer for doing it? Magnetic stirrer is LKG right because in magnetic stirrer how you can use in an industry where I have 2 tons 3 tons of liquid in a reactor right yeah I mean that is not possible no so that is why we go to I mean I think if you know also I do not know where in fluid mechanics you have studied what kind of stirrers we have? You will tell only turbine type and other one is parallel type propeller type only these 3 but if you go to actual suppliers of you know Google and then ask for yeah different kinds of stirrers thousands you will get thousands I am not joking really I mean so many you can get right so that is why stirring itself is one of the again areas where lot of chemical engineering and of fluid mechanics all these went in okay good but I think theoretically when you are discussing yes I can put some 5 6 tanks in series and now again you put B here A here this is easy to solve right this is easy to solve also and again for optimization I have to now try to find out what will be the you know the flow rates and concentrations concentration of concentration of A you know but concentration of B so that overall you will get here at this end the maximum okay yeah this will be quite interesting I say because you know I told you you could have had I am I am not trying to pointing out any bad things about you you know what I am not trying to say anything bad about you but you know if the sufficient information was there when you come here for MTech or PhD we could have discussed actually this kind of problems okay that means I do not have to explain again what is plug flow I do not have to explain again what is differential method what is you know integral method so straight away go to multiple reactions and multiple reactors from there you can go to temperatures and non isothermal systems and also RTD and all that right but now I have to bring to that level and then try to say otherwise okay whatever you have the knowledge if I start only with this kind of complicated things I am sure 90 percent of the brains will be switched off battery lost okay so this is the problem that is why again we have to do all this okay so now this is another way of operating for CA low CB CA high and CB low and vice-versa also what we can do good okay so now let us take an example here then you tell me which a kind of contacting patterns you can use I have a reaction these are very beautiful problems in loudspeaker you have to see those problems I think 7th chapter or 8th chapter and in third edition also I think it is 7th chapter okay wonderful problems particularly the examples are beautiful examples solve them I am just trying to give you so that you will have whatever we learnt I think you know just extension so that you can be involved in the class and then you can answer this right so wonderful problems he has designed no other book has given that kind of beautiful problem okay I am telling beautiful because they are simple problems to get the concepts if you go to Carberry and other complicated books you will have excellent highly complicated problems but you do not learn the concepts unless you learn here and then go there and then enjoy that book in fact if you understand all the concepts of chemical reaction engineering Carberry is the best book for enjoying I am not telling for marks for enjoyment enjoying is different that is what I told you know chemical reactor theory by Din B beautiful book like like novel you can read that like novel only so beautiful less mathematics wonderful explanations right so but I think again I do not know what is how many of you are really appreciating that right okay anyway the example is A plus B going to R plus T and I also have A plus B this is parallel reaction then S plus U same A plus B going to these two again A plus B going to these two then I will have here K1 K2 as the reaction constants then we also have here DC R by DT also equal to DCS by by DT equal to K1 CA to the power of 1.5 and CB to the power of 0.3 that is the rate for this first one for the second one we have DCS by DT also equal to DCU by DT equal to K2 CA to the power of 0.5 CB to the power of 1.8 our desired product is R okay desired product is R now find out what are the conditions so that I can get maximum R you can try desired by undesired undesired CS you can take okay CS or CU both are okay same yeah so what do you do you just took now DCR by DCS equal to what do you get K1 by K2 CA yeah and CB to the power of minus 1.5 so how do I maintain so that I will get this ratio high this ratio is nothing but again RR by RS so what are the conditions so that RR will be more CA should be as high as possible CB should be as low as possible very good I think all of you have got that I think you know yeah then then what kind of reactor I have to choose there is a name for that no PFR with side streams PFR with side streams is the best one or this MFR also with yeah side streams again you know wherever you know in each reactor you have to put that but definitely that PFR only will give you when compared to this number of tanks correct no definitely unless you put infinite number of tanks infinite number of times you cannot put because various things you know to keep infinite number of okay good so now I think you know the rules now that what are the rules we have if the desired reaction is having higher order then maintain the concentrations as high as possible okay so this rule I think I will tell you okay please make a note of this and also mug up remember right yeah for reactions in parallel the concentration level of reactants is the key to proper control of product distribution instead of a high reactant concentration favours the reaction of higher order the reaction of higher order comma a low concentration favours the reaction of lower order comma while the concentration level has no effect on the product distribution or reactions of same order not zero order same order because concentration concentration will get cancelled okay so that is the one that is beautiful this one you have to remember you would like to quantify now you see these are all analytical things only what we have discussed right so what do you do whether you are going to maintain high or low but if someone asks you now tell me what is the maximum yield you will get exactly a number quantification so then we have to go to mathematical equations right so now we are trying to do that mathematical equations then we will say that this is yield quantification and we have instantaneous yield defined earlier as phi equal to dcr by minus dca so this is the instantaneous yield phi instantaneous instantaneous yield is phi there so how do I quantify means yeah this equation we will take and then discuss if I have a plug flow how do I get the yield okay yeah now you have to think a little bit okay so how do I get a plug flow yield from this equation I call this equation as 1 how do I get overall yield that means capital phi p how do I get that for plug flow that is instantaneous yield where is this instantaneous yield insert the reactor only but at what point at any cross-section so now overall yield how do I get integration right so when I integrate what do I integrate yeah dcr phi dca minus this minus is there no now this one right so here what are the limits where is cr not normally cr not is 0 normally we never take a product in the beginning unless you have catalytic reaction autocatalytic reaction okay yeah and this is the other one corresponding to that is c a f okay now this one I can write as crf equal to minus phi dca c a not to c a f so this is the equation but this is not still yield this is not still yield what is yield definition yeah there are two definitions if I take the second one if I take the first one this will be simply c a crf by c a not this is 1 if I take the second one yeah phi 2 if I take then this will be c r f by c a not minus c a f right so that means if I take the second one for example first one is easy so phi p 2 if I take then this equation for yield will be this entire thing is c r f right this entire thing is crf so this will be 1 by integral c a not to phi dca so this is the expression where I have to integrate and then get it yes you are right minus is there because to take care of this minus correct no this is more and that is less so this is the one so that means now I should have this phi in terms of c a in terms of otherwise I cannot integrate right so how do I get that information okay we will come to that later so now if I have m f how do you find out phi capital phi phi m that is phi p so instantaneous yield also is there this is the definition for both but where is that instantaneous yield for mixed flow so I think inside the reactor outside the reactor outlet both are same so what is outlet concentrations so then this differential equation will be into difference equation where this is nothing but yeah crf minus cr not and this is also c a f minus c a not okay minus is there but I told only dca expanded so now that is the equation what you get so phi m is actually capital phi m is small phi m at outlet correct outlet means at c af because that same definition so then this will become delta cr by delta c a minus delta c a right so that becomes now crf by c a not minus c a so this is very easy and next another beautiful thing is our graphs so now how do I represent this information for plug flow on a graph sheet okay simply this one I am talking about this this one first yeah so I have to now plot this is again simple graphical representation this is phi versus c a right so you may get something like this concentration versus phi right I mean that is not the only way just I am showing you may get in one case like that then how do I find out from this graph my crf I should know area under the I should know first what is c a not c a not is this side because c a decreasing then this will be c af and this area will be very good that is c af right excellent now the same thing how do I get for this is for p f for m f how do I get that phi versus c a I get again the same thing right my c a not is somewhere here how do I get my crf from which rectangle I can draw any number of rectangles what is upper rectangle first of all I have to locate my c af okay I will equate it c af now tell me rectangle this one no lower rectangle lower rectangle okay abhishek lower rectangle middle part see compromise middle part somewhere here why average area here lower rectangle this is c af now tanks in series phi versus c a same shape then I have here c af I have three tanks so my c a one will be somewhere here c a two will be somewhere here this is c af c af c af two c a one of course this also is nothing but c a three very good you will catch me like that I am very happy if you catch me okay good so then how do I get now this is the one that is cr one this one is cr two this one is cr three you see now if you put infinite number of tanks what will happen how easy to remember graphs you know how easy how beautiful to remember graphs I think start drawing graphs I say it is really very very good but only thing is now you should have information of this phi as a function of c a how do you get that you have to go to laboratory and then take the whatever reaction that is you are studying and then mix the reactants take out the products and then analyze for all the components if there are three at least two you have to measure and then third one you can get by difference here okay so like that then you can list out now with various you know timings also will come if it is a batch reactor so for this c a what is c r okay if c r is a desired product or if c s is a desired product for this c a what is c s now you plot c r versus c a that is this function right so this may be for example one plus two c a square as an example c r equal to one plus two c r square or may be one plus c a plus c a square that you have to plot that line you have to plot okay then take area under the curves and all that that is beautiful as long as only c r c r you want to find out we are able to find out now but what actually you do to find out what is the volume of the reactor see here till now we are not talking about volume of the reactor no ya okay so one more thing I will just draw in some cases you may get five verses c a may be like okay like this decreasing because it is not in our hands anything may happen in the reactions so but this is still c a not this is c a f what is p f r e and what is m f r p f r will be simply area under the curve right this is p f what is m f so now ya so all this is okay similarly I may draw any number of graphs like that you know we may draw five verses c a okay may be it going like this and then at some time coming back like this but c a f is only here not c a f c a not is here c a f so what do we do so we will go till this maximum which reactor is the best this side and which reactor is the best this side here it is plug flow this is c a f if it is m f r I have to draw here only no highest yield ya I know all of you make a quantum all of you are telling ya know that is m no do not get confused there you are not minimizing the volume so we are maximizing the yield so this maximum minimization problem you have to remember I say you have only one maximization problem that is without reading how do you get yes okay forget about that and then see this so this is p f and here this is m f so like that any shape you can just again find out but here maximization not minimization please remember if it is reactor volume then you have to go for minimum but here it is the product this is c r this is c r f because first you have mixed flow from c a not to this concentration intermediate concentration corresponding to maximum phi right and then from there this is p f so it will be like that that is the setup very good this graph this graph did you understand this graph that is a combination of both you tell me because here c a not is starting here okay you tell me I would like to get that answer from you okay ya you see I have the again I will draw see I have 5 verses c a it is increasing and then decreasing okay and where is c a not here which side okay this side is c a not and somewhere here I need c a f okay may be 90 percent conversion corresponding to 90 percent conversion what is my maximum c r f okay good so now this we divided into two parts because one reactor may not give any idea there so now when it is decreasing that is decreasing is this okay m f r is best here because this is c a not this is c a f this is the extra volume also ya extra area also I have to take so that my c r f is maximum okay so now till here how do I draw the line okay if I take p f r here what area I have to take p f r ya p f r is area under the curve because that is the equation here right but if I take m f r this is your ya this rectangle I have to take so this entire thing okay so now did you put first m f r or p f r you are starting with c a not okay is it okay or still not able to find out ya to get maximum c r so we have maximum c r more area more area so we must take m f r m f r first and then here here if I take p f r what area you get and if you take m f r what area or p f r m f r for m f r you get only this right so that is why if I put 2 m f r then I will get I am losing all this area right if I get 2 p f r if I use 2 p f r then again I am losing this area so that is the reason why here p f r that is this portion is p f r and this portion is but you have to put c a not here c a here c a f here okay good