 yesterday i give you i think a nice story like thing right about residence time distributions right so what we have to remember is that the first basic thing okay that any equipment when you are sending something inside and when it is coming out definitely there will be different timings for different packet of molecules to come out okay need not be reactors please remember that it need not be any equipment with flow when something is entering you can imagine because molecules are very very small you cannot see them but you can imagine some molecules as packet of molecules and it will be continuous only some packets will come early some packets will come late but if it is ideal equipment then you have a specified distribution right so distribution means again i have to tell you most of the people will switch off their brain the moment we say distribution right i also asked you sometime back can you say what is the residence i mean age distribution in this class approximately 22 to okay including the cameras cameras also cannot be 65 years old okay yeah so that is the one is the distribution so if i go into actual groups then there may be many people between 22 to 23 23 to 24 24 to 25 65 you will have only one point okay so when you join all of them then you will have the distribution and if it is ideal equipment then you have a specific distribution like we have seen about reactors that we have discussed so far mixed flow reactor there is a specific distribution it goes to 0 to infinity but the distribution is exponential decay okay that is exponentially mathematical also we can prove that right later and if i have ideal plug flow reactor we again have residence time distribution theoretically speaking but the distribution equal to 0 so when i plot everything will come at one point that means all particles exactly spending 10 seconds so at the outlet when i plot 10 seconds so all that will come together as 10 seconds the entire batch of molecules which you are trying to imagine so like that any batch every batch will have exactly same 10 seconds what we are focusing is only on certain batch when it is entering and how many of that is coming out why because when the behavior of that we know and we also assume that the behavior of all other molecules continuously entering will be exactly same it should be same for a given flow rate for given conditions temperature and all that right so that is what is the meaning of residence time distributions any equipment and without knowing yourself you have also assumed some distributions for distillation columns heat exchangers and your absorption columns any equipment or heat sorry what is that extraction columns or rotary kills rotary kills okay for all these things definitely rotary kill also can be used as a dryer not as a reactor i am talking so that means very material with moisture will enter at one point hot air will be sent opposite to that so by the time it comes out then it should be having whatever prescribed moisture what you have may be 1 percent moisture 0.1 percent moisture like that right so because you are familiar with distillation i will ask the question what is the distribution we have assumed in distillation okay to start with heat exchangers because heat exchanger will come earlier than distillation and also heat exchangers all of you are experts correct know that is one subject everyone will like no one anupriya says no i am talking about the molecules particles entering particles coming out you see you have designed many heat exchangers but still we do not know what is that we have assumed there zero distribution that means what why did you say zero i am not saying you are right or wrong i am just asking oxygen velocity same residence time did you assume same residence time in a heat exchange no we assumed oxygen velocity you assumed black velocity problem right so when the point is there like this and hot fluid is going inside coming out then you send the cold fluid may be counter current co-current so in both the pipes what you assumed without you knowing is that it is plug flow zero residence time distribution okay then only you can now say that at any cross section the heat going from okay hot fluid to cold fluid you can exactly right otherwise now you imagine there are also some problems with if you have laminar flow heat exchangers pipe flow your heat exchange design is totally different you cannot use the same heat transfer coefficients if you have laminar flow in the pipe deduce or you have never designed with laminar flow different equations why it is mainly because of the distribution which you do not know at that time okay now very good that is right okay so without knowing yourself you have done that already you are assuming that plug flow for heat exchangers because normally we use small pipes high velocities for better heat transfer so that is the reason why we assumed we have plug flow which is nothing but r t d equal to zero okay distillation columns absorption columns swami no i am asking what is the distribution inside the equipment constant molar volume is not distribution constant molar volume assumption is that one molecule will go this way another mole will go the other way that is all so that there is no imbalance in the transfer you see see really you do not appreciate me I have to appreciate myself because yeah I am bringing out all those things which you know I am only trying to bring out the ignorance from the people it is not that I am saying I am a great wisdom I have I also have my own ignorance but as a teacher I know where you can be ignorant that is why I am trying to bring that out okay and one definition of guru is dark removal of you know removal of darkness the darkness is equivalent to ignorance okay you have assumed that also particularly for absorption now you have first of all two phases right if you talk about absorption which is easy to understand right gas will go from the bottom liquid will come from the top and then component from the gas will go to the liquid at any cross section what is the velocity profile you have assumed when you are writing the two film theory equation you have written no two film theory equation no one there is Ramakrishna Ramakrishna you also I never thought about this oh my god this is what someone was telling me when I went to goon to give a lecture sir it seems we heard that you connect Reynolds number with plug flow we never knew sir how did you do that I said how did I do that that is the minimum thing what we should know correct know because I think laminar flow can never be plug flow so laminar flow is associated with Reynolds number so plug flow also must be associated with Reynolds number any flow is associated with Reynolds number it is not only plug flow yeah right I think even Levenspiel did not write the that same thing what you have told in the class in his book because why should Levenspiel write because Levenspiel thought that it is basic obvious so you need not write so but I do not think you know it is many obvious things are not obvious many common sense is not common so that is why I thought you know I will I have to bring that out you see without knowing yourself again in this absorption when you are writing the balance you assumed plug flow it is not perfect mixture okay now I can extend I can extend many many things now okay like extraction okay you can conduct extraction extraction operation in a packet bed right so that means light fluid going from the top or either a normal simple heat exchange sorry say simple extraction column where you drops are sent from bottom to the top if they are lighter or otherwise if they are heavy from top to the bottom and one fundamental question you got answer always is which phase you take as a dispersed phase you have two phases know in extraction both are liquids and one should be lighter and answer should be heavier so which one you choose as a dispersed thing both cannot be continuous why both cannot be continuous I am only talking you know chemical engineering yeah yeah so contact will be one stream like this another stream like this so you will have only contact at that interface which is not much so that is why you break one fellow into pieces and pieces and pieces generate large amount of surface area and allow that one to flow anyway that question you can answer later I will keep on going and asking that question which one will be dispersed phase okay so when you have that so when you have these two again you always take that the bubbles are moving at a constant velocity in fact you have small bubbles large bubbles large bubbles will be faster small bubbles will be slower because you know velocity is square root of d b f yeah d okay so that is what you have all that equation but even then we assume that at any cross section you have again flat velocity profile okay that is about the column now you may take you know there are mixture settlers also are used as exchangers what you do is you take the you know stirred tanks stirred tanks as heat exchangers you have come across that or only columns you are designing both the phase are taken into in one vessel and then stir when you are stirring one phase should break up right okay so you have to allow like that you know that kind of stirring where only one phase will break up that generates lot of drops right and then after some time may be depending on that process time you have to calculate how much time is that and after you feel that if it is already extraction is over I am talking about batch system then allow it to settle so one of the components either in the continuous phase this continuous is not with respect to flow but with respect to not breaking dispersion phase okay that one component may go from continuous phase to dispersion phase or may be from dispersion phase to continuous phase then settle out after settling separate it out send for a distillation column and then take out because the component which has gone to that other phase both should have some kind of difference in the boiling points then you go to distillation column and then separate it out now when you talk about this tank extractors what kind of residence term distribution you assume for batch first of all batch what the residence term distribution 0 now I can also use this for continuous continuously I will send two phases I will arrange my you know stirring such that one will break but both will come out again both will come out now I have two phases right yeah so again what kind of contacting pattern or what kind of residence term distribution you assume for this kind of tanks in series and you do not put generally one you will put one tank another tank another tank so because we know that now I have already told the answer you assume here perfect mixing perfect mixing means distribution of the droplets now you have to talk about two phases right both phases will be in perfect mixing that continuous phase as well as the droplets so when you look at the droplets some droplets may come early some droplets will come late and the droplet which has come early if there is a solute which has to be transferred to the continuous phase the amount transferred will be very very less because it is not stayed much time in the system in the stirring so then the other drop which has stayed more time the solute will would have transferred almost everything so that all that will go to the next tank next tank next tank so that means without knowing yourself you have assumed all this okay but only for reactors we discuss this because reactions may be more serious and you know if you have some kind of mixing and all that or residence term distribution is not zero to infinity somewhere like axial dispersion and all that so then temperature effects may be different right whereas in a mixture flow you will get only one temperature good control over temperature over plug flow you don't have good control of temperature so that is the reason why I think probably RTD has been used here okay most of the time and no mass transfer teacher the teacher who is teaching mass transfer will ever explain what is the distribution you have in this column and even absorption column I asked you I told you flat velocity profile this flat velocity profile again two phases I have liquid phase as well as gas phase right so is it logical to assume for both the phases as the plug flow because liquid is just coming down all the way and gas is going up right the gas is going up in the form of bubbles if I have only tank otherwise I also have falling films correct no so I will just spread my liquid as a film and then gas will be just moving so beautifully liquid will fall as in plug flow and gas also goes as plug flow then at any cross section you have the flat velocity profile and you can write the equation okay so that is the one now we have to extend the same concept here in residence term distribution for the reactors two reactors we know ideal distributions we have already discussed now we are going to discuss about non-ideal flow actually this residence term distribution subtitle is non-ideal flow that is the one right good so basically what we have to remember is that every equipment will have its own residence term distribution for the particles entering and then coming out that is number one how do I find out this I want to find out the residence term distribution of if possible each and every molecule that is not possible so at least each and every particle particle means it is only imagination right okay how do we do that in fact the best thing is if you are able to identify each and every molecule and if you are able to really find out what is the time spent by each and every molecule you map the entire molecules then you know how each and every molecule is behaving inside the I mean how much time it it is spent inside the reactor and what it has done right I mean it won't give you what is it is a black box arrangement at least from the outside you will try to find out what you do or what it would have done inside the reactor like exactly I told you know sugar test when they do they will only take sample blood sample and then try to find out what could have been the reason why this kind of sugar content is coming in the blood okay so it is only just going back and then trying to find out here also same thing so that ideal situation is this so because it is not it is impossible for us you know in one mole how many molecules are there 6.023 yeah so I know most of us won't have any feeling for 23 10 to the power of 23 even if someone says sir it is 10 to the power of 210 still we don't have any feeling because beyond you know 100 you don't have any feeling or may be thousand or may be rich people may be lack or one crore suddenly if you ask me one crore how many zeros means I can't answer at least one lakh how many five yeah so then of course plus two seven that means my reference is one lakh then add two so another you know 10 crore means another one like that it goes so that is why the zeros are very difficult beyond certain point we don't have any feeling for the zeros okay you know zeros are very important good yeah so that is why we will not have any feeling for this 10 to the power of 3 was 6.03 yeah 6.03 into 10 to the power of 23 molecule in just one mole how many moles you will be printing into the reactor how do you get that information impossible so that is why at least you know this tracer test where you can send some kind of tracer along with the normal fluid tracer is nothing but something which can be identified that's all in the blood also they will give you suddenly more sugar okay so then I know that batch of sugar how it comes how it is absorbed by the flow of the blood inside the body so then only they will try to interpret in fact it is very very surprising it is not the engineers first who found residence time distribution name is given by chemical engineers but the first person who has used this technique was a doctor really you have to appreciate you know there is no limit for the human brain if human brain wants to think that is what you know that think is very important we never think that is only right examination that's all we never think surprising you know that why I think in 1700 or 1800 I have that exact reference he is the person and you also know that who was the first person to write the material and energy balance can you guess Gopi Gopi I thought you know that is encyclopedia Britannica okay no in your Britannica it is not there okay any idea can you guess no it is again doctor medical doctor from Britain to I think Thailand or Indonesia he was traveling a langer I don't remember the name but I have that I have written somewhere but you know that doctor he wanted to find out how much energy is lost by humans and he was traveling from England which is a freezer and Indonesia which is a burner correct no because I think here the temperatures are very very high because it is almost near the equator and there I think of course he has not come from Siberia I think at least only England but still it is cold so I think they were not able to tolerate this kind of heat when they are traveling by boats I think it was happened it has happened again in 1700 or 1800 so he wanted to systematically people say that he made some mistakes but doesn't matter the concept the concept itself you know trying to find out material energy balance that means he will give water 2 liters and then how much will come out through sweat because maybe weight he may be taking okay or through you know other you know nation and all that so total amount he has to balance that is mass balance and energy energy I don't know how we manage but I think you know energy depending on his activity how he actively is moving if you don't have energy you will just sit down you can't do anything but that's what most of you do I think this generation doesn't have energy okay they have only mass and they are not able to convert this mass into energy equal to mc square they are not able to do it so that if you are able to convert some of it it will be excellent okay so that is why I think you know it is excellent no wonderful then these things to hear wonderful I appreciate all these I enjoy also telling others all these because I always appreciate the human mind I mean I don't have that kind of mind but at least appreciate you know the other great minds so something new always they will try to find out and Einstein brain I think you know physically if you look at if all the brains are same but what has really happened how we could imagine this theory of relativity where no one could imagine even now we can't imagine even now we don't know I mean also just read and then we know only that equal to mc square without feeling again I told you know anything you should have feeling then only you will be good right otherwise I think you without feeling is waste so that's all what we do but you know how we imagination that even now I asked many people why you should assume that the velocity of light is constant in the universe how we got the first of all that idea correct no I think many people trying to now prove that he was wrong right he is not wrong I think again recently also one experiment experiment was wrong not Einstein was wrong so that kind of brain how we got and another great brain is our Aries how he is able to think so many steps in I think you know before writing the final step he writes that I think we have also excellent brain Ramanujam you know mathematician how I think you know he gives the problem and gives the solution in between I think people are spending last 50 or 60 or 70 years to find out what are the steps in between really and how you know that the Ramanujam it seems when people asked how are you able to do it you know in Cambridge University when you went Cambridge you know there was some shade notebooks even at that time he has also yeah slate is conveniently at that time that's all because he was not confident whether you know right or wrong so that's why he used to write and then another thing he used to write yeah but I think you know it is not paper shortage definitely you see neural network inside is totally different our neural network is totally different right because that is the reason why he is able to simply write and then even someone asked I think I don't came to even know don't remember yeah yeah that university when he was he was a invited by that Hardy and then when he asked him it seems he told I don't know how I'm writing but that goddess of Namakal Namakal there is a place goddess which goddess is that Durga or something or I mean he says that you know because she is giving me all the solution that is the greatest of that man you know he never thought that my brain is great so I am imagining all that you are stupid people so that kind of thing he never had he was only just attaching that because God gave me that thing that kind of brain I don't know whether he has aware of his brain right so that's why I am able to write all these equations final solution so I mean when compared to all that what are we doing here correct no what we are really doing here nothing no nothing I think you know the same assignment which I have been given also no one is doing it and all those problems I think if you look carefully in different books most of the solutions are available somewhere or other even searching we are not doing and we joined as research scholars search and research you know okay first you have to search afterwards only research comes we are not even doing that research I mean first search so that is the reason why these brains you have to really appreciate okay this R T D also that doctor doing it is really fantastic and afterwards I think Langmuir used it seems not R T D directly some boundary conditions and Dan Quartz used it so beautifully and popularized like Lounsville popularized reaction engineering before that also there are few books you know Wallace book was there and the other three books you know what you have Hogan Watson Hogan Watson three books third book was third bookies kinetics so those two books but I think not much appreciation was there Smith book was there before Lounsville but Lounsville popularized because that is the greatest of presentation okay so that is why I think they have done anyway so now going back to residence time distributions somehow we have to try to find out if it is possible if I mean each and every molecule is not possible so at least pocket of molecules that is why we do this tracer test right so this few lines I think you have to take otherwise I am sure you know you will just forget right very happily you will forget so that is why you we do not have an ideal reactor because we do not know whether it is ideal or not we have to find out whether it is ideal or not like you have you are going to R what is the order of reaction we do not know so unless we do experiments and try to find out that yes it is first order because I am getting from the data only first order then you can say it is first order or elementary reaction okay similarly even here residence time distributions in all equipment will have residence time distribution but I do not know what kind of residence time distribution there so if I have plug flow if I want to have plug flow then I define my residence time distribution in this way if I have perfect mixed flow then I will define my residence time distribution in this way what is the importance of defining this residence time distribution to calculate conversion if I know that in plug flow each and every molecule spending exactly same time or pocket of molecules spending exactly same time the conversion in that is uniform and all molecules will have exactly same conversion so when I average at the outlet I have exactly same conversion on the other hand if I assume mixed flow there are some packets which are coming earlier and which are coming later but the overall conversion is the average of all these packets which I see in the outlet that is what is the concept right so that is why the name is given perfect mixing but the actual thing that is happening is residence time distribution again name is given plug flow but what is actually happening is that each and every molecule coming exactly at the same time so that is how it is connected so that is why all you know Levenspiel write something like this just to differentiate between ideal P F R ideal P F R means always we write like this okay mixed flow means we write the other way so to distinguish that he says that simply kind of reactor there any vessel so then something is entering constant flow something is coming out constant flow and let us imagine that there is no reaction first in that we are only worried right now about the flow okay either plug flow or mixed flow then we will exchange that one to reactors okay so then so this is the kind of vessel we have so some may move like this some may move like this some may move like this complicated flows so some may move like this and then finally everything has to come out everything has to come out and if it is ideal plug flow I know how they come right right well we are not talking about that in general this is the kind of thing so now just please take this in any vessel I am not telling about reactor at all in any vessel different molecules or packet of molecules spend different times under steady state conditions we are talking about only steady state conditions under steady state flow conditions how these particles are coming out of the vessel is an important parameter to be considered for the design okay to be considered for the design okay then you can continue okay next part you can write let us assume that each fluid particle let us assume that each fluid particle is equipped with a timer that is activated when it enters the vessel and stops when it exits the vessel has only one exit and one entry that is the assumption okay so then each particle at the exit has a time t associated with it associated with it which measures which measures the time which measures the time it spent in the reactor spent in the reactor this quantity is defined as the residence time of that particle the distribution of these times is called residence time distribution since we are measuring this distribution at the exit it is called what exit age distribution exit age distribution okay and you know normally it is et okay symbol wise exit age distribution oh sorry I think it is exit age distribution okay and the function representing this distribution the equation the function representing this equation is called exit age distribution function you have an equation for that you know for any vessel you will have an equation is called exit age distribution function comma et et is a function okay good so this is the one I think you know the other definitions will come you know cumulative one all that will come later but this is the one but here I have to just I think I have to go for the definitions and all that now but I have to tell you here each vessel may have more than one phase correct no it not that it not that only you have only single phase the flow is only single phase it can be two phases and we have three phases most of the time for reactors so that is why for each phase is associated with an exit age distribution function yeah I think you can write that usually in chemical engineering equipment more than one phase is involved right and each phase has its own residence time distribution and its function et okay few examples are given here I think that we will discuss quickly then we can go to the definitions then you know you will not forget that means if I without telling that if I go to only definitions and all that you always think that you are talking about single phase no we are talking about general any one phase if I have two three phases in cellular reactor each phase I have to now find out how it is moving what is the distribution there if I say that one phase in mixed flow reactor has not mixed flow reactor cellular reactor has zero distribution what do you imagine there how it is flowing it is flowing in plug flow condition okay so if I say that okay another phase in the cellular reactor is with zero to infinity distribution but exponential distribution so then you have to say that it is perfectly mixed distribution okay perfectly mixed flow so that is why each phase is associated with that the simplest one what you take is of course homogeneous homogeneous reactors okay P f no okay batch P f and M f mixed flow reactors right so what is the distribution here by definition because we already done that so this batch it is not valid at all for us because we are not allowing the particles to move out so that is why there is no distribution because all the particles which entered which I am pouring take out at a particular time so you will have exactly same time so that is why distribution equal to zero P f by definition again here and also P f single phase homogeneous reactors and here also I have only single phase here also I have single phase P f and that means specifically in homogeneous reactors P f ideal plug flow will have one phase and the flat velocity profile here also one phase and exponential decay zero to infinity right so that is how what we define but the moment I go to homogeneous reactors non-ideal homogeneous non-ideal right so this is okay because if it is not non-ideal then again definitely reaction rate will not be that good because at any instant of time throughout the reactor I should have same rate and if I do not provide that kind of mixing somewhere low concentration somewhere high concentrations you will have different rates different places it is not easy to solve that problem that is why we design a better mixer and then try to solve that problem but here I do not have that in my control it depends on the flow right and by mistake all the time many students also think that I think one of my students Krishna Sandilya was sent a mail saying that it seems he went to some place for some interview or something he asked same question whether laminar flow is plug flow and not selections what is that lab exam so then he wrote sorry entire all the people in the lab were telling only laminar flow is beautiful plug flow okay so message has not gone throughout the countries or yours okay yeah so that is what he just sent me two days back that mail because some of us formed a group you know to propagate this kind of concepts outside okay yeah even Jesus Christ had 12 people you know disciples just to go and then propagate the entire good things you know across I mean every religious that big man will always have the people like this okay just to go and then tell that okay this my Guruji is telling so this is to follow follow follow so like that so that is why here if I have plug flow sorry if I have laminar flow definitely the distribution is different ideal plug flow distribution equal to zero what kind of distribution you get for laminar flow by mistake you assume that laminar flow is a plug flow right but in laminar flow the all the molecules are coming exactly at same time no definitely not right so that is why and you also know because fluid dynamics is very clear for laminar flow one particle will come which is sitting on the top of tip of the that profile at the centre point so that will come fastest that means that will spend the minimum time so we know that is t bar by 2 from then onwards average yeah for maximum yeah yeah t bar by 2 only it spends but I think that comes a maximum velocity okay so that is the time it spends I am talking about in terms of time and what is the other extreme the first particle what you see is a time t equal to t bar by 2 that means 10 10 minutes if you put 5 minutes later you can see that before that it will not come if it is ideal laminar flow afterwards till what time it comes till infinity why infinity you have to give the reason when you can do some particles where do they go near the wall velocity equal to zero when velocity equal to zero it cannot move so it takes infinite time okay few particles right yeah so that is why it changes now from t bar by 2 at t bar by yeah t bar by 2 to infinity but this is not the same distribution as mixture flow where that is zero to infinity but the function is different that is exponential decay this is some other function which we will derive out sometime okay so that is why so mixture flow of course we know ideal things okay good so the moment I go for away from mixture flow plug flow ideal plug flow then I have non ideal flow like even laminar flow is a non ideal flow with respect to plug flow correct no ideal flow is zero zero distribution but I have distribution so that cannot be plug flow right and also as I told you axial mixing some particles will be going like this like this right like that Tirupati q I told you people going and pushing backward forward there is a dispersion zone inside that q so those people will be moving backward forward backward forward like that so that is very bad for conversion because a molecule already converted will come and join with the other molecule which is just fresh fresh means in that zone okay so that is why that will reduce the concentration that will reduce the conversion that is bad that is a non ideal good so like this now heterogeneous reactions heterogeneous reactors reactors we have the easiest one is packet bed we have fluidized bed reactor and we have moving bed we have rotary kill rotary kill and how many other reactors you know still further bubble collars that is gas liquid system very good yeah trickle bed react trickle beds very good yeah air lift loop reactor yeah you can you can you have many air lift what is this loop that is the name of the reactor air loop reactors okay yeah that is true it is there yeah still bio towers bio towers bio towers means what do you have inside cells and then how the flow is is there gas going in inside that yeah that is bubble column okay that is bubble column but you have solid particles I think microorganisms can be treated as particles sometimes so then if you are considering them as three phases then you have particles in the form of microorganisms then you have gas and then you have liquid so that also will be equivalent to yeah extra there reactors are not huh which reactor those are nuclear you know the bad thing with the nuclear is there is mass generated and all that we cannot do anything okay those reactors are not considered nuclear reactors are separate okay so that is why yeah okay these are the things now how many phases are here two how many phases are here two and I think we also have three phase predation okay and here moving bed two okay and what we kill yeah and slowly three three yeah bubble column trickle trickle three three yeah packing and then you trickle this week and yes but in the co-current direction yeah again how many of these things are co-current how many of these things are counter cut counter matter because when it's off whether it's sent for bottom or top no problem you should have people like that no absolutely no problem we don't have to worry no no it's not possible no count one huh oh yeah actually there is no current because that is you know the solids are in mixed flow condition and only you can say plug flow for the gas but again big question mark which is right which is wrong you have to wait till next semester to find out what is actual flow in fluidized bed it is very complicated reactor very complicated so the moment you go bigger and bigger more complications will come into picture so okay so then again moving bed simplest one okay allow the packing to move automatically it goes to moving bed you know this packing which is stationary put a hole and then try to remove some solids and also feed correspondingly from the top so here it can be again co-current counter current rotary kiln can be co-current counter current so let me reactor because whenever you have mixing you cannot say which current co-current or counter current because distance doesn't matter no space will dissolve there correct because there is no variation with space right yeah so then bubble columns no you can operate both you can also send liquid from the top and then bubble through and you can also send both from the bottom but I think the reverse is not possible okay so then I think lift the entire liquid that is lift okay yeah your lift reactor you are telling you know so then again take the liquid and again that is what is loop that liquid will come out right that is what the meaning of that loop okay then trickle pet reactors trickle pet reactors gas and liquid can be no trickle pet is always co-current always co-current okay gas is sent from the top and liquid also is sent from the top that is what is the definition of trickle bed if you want to operate you can operate like 3 phase counter current packed bed like absorption also gas from the top it is a packed bed solids are there already packing then you can also send gas from the bottom that can be operated but definition of trickle bed reactor is both coming from the top okay again excellent design things are available for trickle bed reactors because inside if you go there are many many many things are happening in trickle bed in fact all these things I think fluid azure bed and trickle bed are very difficult to design okay but what I am trying to tell you is that now for each phase you have to find out whether it is in ideal plug flow or ideal mixture flow that means zero distribution or zero to infinite exponential decay distribution right so that is why tomorrow I will spend some time we take some two three columns and then I will ask you how the flow is taking place and what kind of assumption we can make whether zero to zero distribution or zero to infinite distribution okay