 how do you calculate volume? Ok so the general expression what we derived in the earlier class was T equal to C A naught integral 0 to X A d X A by minus R A ya for constant system otherwise it is 1 plus ya so that V equal to V naught I think that also we discussed later so this is the general expression if it is constant volume then epsilon equal to 0 Ok so that is why this becomes 1 and this becomes simply minus R A so then here we do not have specifically volume coming out from the rate I mean the design expression whereas if you derive later because you know already that is why I am telling so you already seen that for mixed flow reactor and plug flow reactor you get volume as V by F A naught equal to right so for similarity I will also write this one as T by C A naught equal to 0 to X A d X A by minus R A general I think you know for constant systems let us say right so T by C A naught this is the general expression for a batch reactor which you are supposed to remember all the time Ok but what we have been thinking was that this T or this equation does not contain volume but finally we have to design the volume of the batch reactor how do you calculate volume what do you know before starting all this reactor design so do you have any information you just remember that our diagram production means your F A naught suppose to be if it is a flow rate Ok but here there is no flow but still you know what is the production rate Ok you know what is the production rate let me tell you just I think for simplicity I have to produce production rate I have to produce 24 tons per day right so how could I have divided you know I would have calculated per year how much I have to produce then per day I calculated I got 24 tons per day and 24 I have taken because easy for calculations right yeah but my this design expression will not tell me what is the volume required to produce 24 tons per day how do I calculate what is the volume of the reactor from this information 24 tons per day and time C A naught I know Ok that area under the curve I will this area under the curve I will evaluate and then find what is T yeah that is what I did no amount of from conversion let us say for 90 percent conversion if I take a 99 percent conversion this equation gives me only time correct no that area under the curve when I take I have to take a 99 percent conversion 95 percent conversion or so whatever because you know that from 95 to 99 Ok let me also draw that this is general shape only we have general shape only I am just drawing so normally you will get most of the time like this and here you see why it is typically increasing what is R A at X equal to 1 at 100 percent conversion what is R mathematically 0 but what is this coordinate 1 by 25 to infinity we have to go to infinity and now just imagine before that it is not 1 0.99999 then you are very close to infinity right so that is why if you know come back a little bit slowly down this way then you know that lot of area increase will be there in this region whereas here I will not have that much increase that is where the economics in designing the reactor will come because I may go to 99.499999 Ok I need very very large volume when compared to 99.992 9s there will be tremendous difference between these two so that means only to produce 0.09 Ok 0.994 9s only I have taken 2 9s now but then you will have 0.001 so to produce that small amount then I have to go for very big volume no engineer will do like that are you able to follow me or are you able to follow me know because 0.99999 0.999 every time when you are moving 1 decimal your volume also not 10 times increasing it is sometimes 100 times increasing because it is very steep very steep going to infinity Ok here and theoretically speaking when 0.99999 if you put 109 then you get infinity again my same thing if you have infinite volume you cannot operate the reactor because entire universe is only one reactor your reactor so that is the reason why always you have to design whether you have to decide what is the economically viable volume or conversion conversion only gives you that volume right so that means you have to decide Ok now 99 percent is fine with me conversion right so that is why conversion is always coming there so I am now taking till here let us say Ok that may be 0.99 or may be 0.98 right as engineers you have to find out which is the viable one Ok so this is XA final so knowing this information let me say that Ok I will also give you this area under the curve T by CA0 and even if I take I know CA some value so the T is let us say 7 hours now you tell me how do I calculate that means to produce I do not know how much amount now because batch will not tell you what is the amount you have to produce whether you take 1 kilo 1 ton 100 tons time is same that is the beauty with this reactor but now you have to find out what is the volume depending on production production rate Ok can you guess you have to also try to imagine may be wrong imagination also no problem for us you should be able to imagine and then tell us that sir this is what I am thinking if it is wrong I will tell you if it is right now I will appreciate you even if you tell wrong I do not scold you Ok with the time Ok what do I get when I multiply 7 into 24 24 into 7 times 24 into 7 24 by 24 by 24 into 7 hours I have to take into account that is why we say that this is what is called TRX that is only reaction time see the total batch time T batch will be TRXN reaction time plus see you have to first charge when you are first you know starting the reaction right that charging time then after the reaction you have discharging time and again sometimes you may have to clean so cleaning time all those timings also will come into picture you know particularly biochemical reactions they use sterilization time otherwise next micro algorithms may die Ok and I told you batch reactors we choose because we also have that flexibility in products so the earlier products may contaminate my the present batch so that is why I have to clean it there so all those timings will come into picture that is T what you call you know not cleaning first one what you said loading charging Ok CH and also you have T discharge DCH plus T cleaning anything else generally these things Ok all the timings should be known to us but here we can have some kind of optimization if your operators are very good very efficient people then probably this all these things will be in 1 hour you can finish Ok or if there are very very lazy people then it may take 2 hours so Ok so because if you do not have particularly automation and all that if you have automation then you are replacing humans with missions missions are always you know efficient when compared to humans Ok so I mean in doing general work Ok day to day work but when you want to use brain humans are the greatest Ok so that is there so all this is 1 hour and this is 7 hours so now I have total batch time 8 hours Ok so now what we do is I have to now produce 24 tons per day but I have now 8 hours per batch Ok yeah how many batches we can now take 3 batches Ok so now when I have 3 batches Ok so in this case 3 batches number of batches number of 3 so now per batch how many tons per batch we have now 24 by 3 tons per day so sorry no no 3 batches and each batch will have 8 tons this is tons only 8 tons Ok now how do I put is I mean how do I now calculate the volume yeah you know the density of the reaction mixture Ok so when you have that density of reaction mixture 8 tons let us say water you now tell me what is the what is the volume I have exactly like water like reaction mixture 8 meter cube because 1 ton per yeah 1 meter cube 1000 kgs you know 1000 kg per meter cube right so that means 1 ton per meter cube so I have to have now 8 meter cube to volume and our problem is not at water this 8 meter cube 8 meter cube to volume I have how do I now put that one as a physical reactor that means you should have some diameter and some length yeah that comes later but how do I put this what is the shape because if I am a crazy fellow I can take 1 nanometer and length because 8 meter cube I can put anyway now you can calculate what is the length I think it goes to mars or may be jupiter or beyond that that is not engineering Ok we know that then what is the what else I can take diameter of the earth and then calculate height what will be the height 0 so again where do you put where do you put so what is logical now engineering logical what is the rule L by D equal to what 1 L by D equal to 1 1 Janami please something 0.75 1 1 2 Ok L by D I am asking L by D because L by D you have to fix 2 x things I told you can take 0 1 nanometer almost 0 on the length you can calculate not practical you can take diameter of the earth and then also calculate height the diameter of the earth is equivalent to your tank diameter Ok so then you can calculate height Ok that is also 0 so these 2 are not engineering solutions so what is engineering solution for fixing L by D he says 0.75 you say 2 why do you say 2 I will also ask him she says 2 just says 1 you can never have that kind of thing you know because surface area per unit volume only sphere has minimum so all our reactors are should not be our reactors are cylindrical as the non-ideality increases what non-ideality are dead zones so what what will happen why conversion changes if dead zones are there some portion of the reactor how do you avoid that stirring so now fluid mechanics again will tell you generally for L by D equal to 1 you have good mixing see when you have this tank so when you put this kind of thing L by D equal to approximately 1 1 stirrer is enough and when you go to L by D equal to 2 then you know sometimes you also should have seen like this right so general number will be is for each L by D you need one type of blade you know normally you have so many things you have propeller type stirrers you have turbine type stirrers yanker type stirrers all these things are there so we know approximately we know all these things L by D equal to 1 will give me good mixing that means in this case I should see everywhere uniform concentration and temperature even if I take L by D equal to 2 many times you will take L by D equal to 2 okay you know you would have seen batch reactors but it is not L by D equal to 1 most of the time it is L by D equal to 2 many times 3 rarely that means you know stirring is not that efficient but L by D equal to 1.5 also is common but criteria is that this L by D should be such that your mixing should not be sacrificed mixing should be perfect that is the engineering rule okay so now I think I am able to make you know some clarity where you have to remember these simple things they are not complicated we are not really discussing that kind of complicated where we will get noble prize no one will give us noble prize for is you know when you take L by D equal to 1 okay but we should know why we are taking L by D equal to 1 right so if someone asks okay I think why did you say 0.75 the immediate sign the next most people can stand so just on practical case why standing I think standing depends on other structure where you know you put that legs and all that no cylinders only no cylinders most of the time you go for cylinders okay which size you go other than cylinders you tell me why again that is also engineering question why do you go most of the time for cylinders rather than spheres very difficult to duplicate very difficult to construct okay so that much again we do not want to spend our time and all that simple thing is take a big yeah like this yeah like this a sheet and then fold it put one thing here put another thing there not permanently because you have to charge and all that no so that is all that is very simple because as engineers we think as I told you in a simplest manner that is the reason why we have to oh my god okay so this is what so now you know how to calculate volume of the thing I will give you a problem maybe I will upload or maybe tomorrow I will give an a piece of paper and then distribute to you you solve that problem it is a very good problem but it is reversible reaction because now you know this R it can be either a reversible reaction or it can be reversible reaction with some orders or without order all kinds of complicated equations can come so that is why because you already exposed to the subject I will give you one problem tomorrow you solve and tell me the answer if you are not getting I will tell you the answer because on your own being I think you will really understand everything okay