 Friends, let us summarize what we have learnt in the last couple of lectures. So we have learnt how to deduce the rate law from experimental data and we have learnt how to find a mechanism for a given heterogeneous catalytic reaction and then we have looked at how to find the rate parameters concerning the rate law and then we had looked at how to design a packed bed reactor and how to find the profile of the conversion as a function of the weight of the catalyst in the last couple of lectures. So while doing all this, we have assumed that the catalyst activity that is the number of active catalyst sites which is available for the reactants to adsorb onto the catalyst site for the reaction to occur is always constant but unfortunately mother nature is not so kind and it turns out that the catalyst activity it does not remain constant. So we always assume that the catalyst activity is constant but the catalyst activity changes with time, changes with time. Now what does it mean? It means that the total number of active sites, total number of active sites which may be available for adsorption of the reactant species onto the catalytic site for the catalytic reaction. Now that number of active sites Ct which is the concentration of the total concentration of the active sites, so that is not a constant. Now what happens if it is not constant? So what happens is that the catalyst actually gets deactivated. So there is a catalyst deactivation process, there is a catalytic deactivation process. In fact it is a very major problem that is faced by most of the industries when they conduct a catalytic reaction. It is known to strongly affect the conversion and as a result the performance of the reactor itself. So catalyst deactivation is a very, very serious problem and it is very important to understand how this deactivation occurs and are there mechanisms or there ways by which one can actually circumvent the catalytic deactivation process in a reactor. Deactivation is essentially a process by which the active sites which may be present in the catalyst pore that is somehow not available for the reactants to go and adsorb. So let us describe a little bit more about deactivation. So deactivation, so suppose if there is a catalyst, if there is a catalyst support in which a particular catalytic material is actually impregnated and let us say that these are the pores, these are the pores which is present on the catalyst inside which there are active sites and suppose let us say I zoom up one of the pores which may be present inside the catalyst and so if this is a pore and the active sites are actually present. So if these are the active sites which may be present in the pore onto which the reactants can adsorb in order for a catalytic reaction to take place. Now after a certain time, after the catalyst is actually used for a certain time for various reasons these active sites reduce in number, the number of active sites which may be present that reduces and you can see that the number of reduced sites which is available for adsorption of the reactant species for the reaction goes down as a function of time. So this process of loss of the catalytic sites for the reactants to adsorb and to facilitate the catalytic reaction is what is called as catalyst deactivation. In this lecture and in the next lecture we are going to see different types of deactivation, what are all the mechanisms that govern the deactivation process and how to incorporate that in the reactor design is what we are going to see in the next couple of lectures. So as in the case of any process which is involved in a catalytic reaction, the first step is to understand how to get the rate law. So in this case how to find the rate law in the presence of catalyst deactivation. So this can be broadly classified into two different types one where it is called the separable kinetics and another one it is called the non-separable kinetics. So separable kinetics is one where the dynamics of the adsorption, catalyst deactivation process and the actual kinetics of the catalytic reaction these two can be independently modeled and the mechanisms can be independently understood while the non-separable kinetics is where it cannot be looked at independently. So in the case of separable kinetics one can actually write the net rate law suppose if A is the reactant which is catalytically reacting in order to form products B then one could actually write a rate law which looks like this where A is the activity of the catalyst which depends only on the past history of the catalyst multiplied by the reaction rate as if the catalyst were to be fresh. That means that the deactivation kinetics and the actual kinetics of the catalytic reaction can be looked at separately and independently and so the activity is only a function of the past history and that scaled with the reaction rate if it were to be a fresh catalyst is what gives what is the reaction rate and what is the reaction rate at a particular level at which the deactivation has occurred. So this suggests that the catalyst decay and kinetics are independent. So in this model of separable kinetics the catalyst decay and the kinetics of the catalytic reaction are independent. Now what happens in the non-separable kinetics? In non-separable kinetics case the net reaction rate at which the species A is being consumed is now dependent both on the past history and the rate if as if the catalyst was not deactivated that is what is the rate if the catalyst were to be a fresh catalyst. So it depends on both on the properties or the nature of deactivation simultaneously along with the actual reaction rate of the catalytic reaction. So which suggests that the deactivation perhaps happens on perhaps happens via many elementary steps. So in the next couple of lectures we will not deal with the non-separable kinetics which will be dealt with separately later. So in this couple of lectures we will only be looking at the separable kinetics. Now when we talk about separable kinetics the most important quantity that needs to be described is the activity of the catalyst. So A of t which is the activity of the catalyst is defined as the rate the reaction rate on the catalyst for a given activity or at a given time divided by the rate the reaction rate in the same catalyst if it were to be a fresh catalyst. So it is the reaction rate after the catalyst has been used after a certain time t divided by the reaction rate if it is a fresh catalyst. Now it is important to realize that the maximum activity is possible only in a fresh catalyst. So it is important to realize that the maximal activity that is the maximum possible sites may be available for the catalytic reaction when the catalyst is fresh. So therefore it is important to so the exercise is going to be as to how to characterize and how to obtain the deactivation process as a function of time in the presence of catalytic reaction. So naturally the activity of the catalyst is going to change with time and the typical profile it starts with one because it is a fraction and it is a fraction of catalyst that is activity which is left and so it goes from it exponentially decreases with time. So this so clearly the a of t decreases with time. So suppose if there is a reaction so how do we write the reaction rate law when there is catalytic deactivation process occurring simultaneously. So suppose if the catalytic reaction is a plus b plus gives b plus d plus. So now we can write the rate of consumption of species a because of catalytic reaction as the product of activity of the catalyst multiplied by the corresponding specific reaction rate which is dependent on the temperature at which the reaction is being conducted multiplied by some function which is a function of the concentration of all the species that may be participating. So let us stare at this equation. So at is the activity is the instantaneous activity of the catalyst, kt is the specific reaction rate and it is a function of temperature. So as you increase the temperature the specific reaction rate increases and this is the some function of the concentration of species. How it affects the reaction rate law and that is what is captured by this function fn. So now the decay rate so as the catalytic deactivation occurs simultaneously along with the catalytic reaction. So there has to be a certain decay rate. So the decay rate can be captured in terms of the properties or the quantities of the species that is the concentration of various species which is present and so that can be written in the following form. So the decay rate typically takes the same form as that of the rate law. So therefore the decay rate rd is given by is minus da by dt that reflects the rate of change of activity with respect to time and that should be equal to some function p which depends on the activity itself multiplied by the corresponding specific decay constant which depends which is a function of temperature multiplied by some function of concentration of all the species. So clearly from here you can see that rd depends on the activity it is proportional to the concentration of species. So therefore it is important to know the concentration and it is important to find out what is the functional form of this p in order to estimate what is the catalyst decay rate. So for the purpose of this course we will assume that h of ci which is basically the dependence of the concentration on the decay rate law as 1 or at most as h of ci to be equal to ci. That is it is either does not depend upon the concentration of the species or we will assume that it depends at most linearly on the concentration of the species. So and also we will assume that this function p which is which takes the functional form of the activity of the catalyst depends on what is the catalytic system that is what is the catalytic reaction what is the catalytic reaction that is being conducted we will assume that this dependence of the activity the functional form that captures the dependence of the activity on the decay rate will depend upon the reaction which is being conducted and also on the deactivation mechanism which we will describe shortly. So suppose if it were to be a first order decay if the decay process is first order with respect to the activity then if it is a first order process then p of a will be equal to a and if it is a second order process then p of a will be equal to a square. So depending upon what is the order of the dependence of the activity on the decay rate we can accordingly assume a certain dependence of p on the activity itself. Now the decay of the catalytic sites that is the loss of catalytic sites in the catalyst will depend upon many different aspects. So based on the nature of the loss or the type of loss of the catalytic activity there are three broad classification have been identified and these are sintering slash aging process. So this essentially captures the loss of the catalyst because of long exposure of the catalytic sites to the reaction and then the fouling or coking process. So this is essentially the deposition of various carbonaceous or coke material on the catalyst site. The deposition of the coke on the catalyst site it leads to strong deactivation of the catalytic sites and it is possible to regenerate the catalyst which we will describe later. And then the third type of deactivation of the catalyst is called the poisoning process. So there may be poison present in the feed stream which may enter the catalyst pores and they may get deposited on the catalyst site and that may destroy the activity of the catalyst or the reactants or the products itself may actually go and irreversibly bind or get adsorbed onto the catalyst surface and as a result may poison the activity of the catalyst site and therefore deactivating the catalyst itself. So we will see in detail what these three different types are and how to characterize what are the mechanisms that are associated with each of these deactivation processes and how to find the rate law for each of them. So let us take the first one which is the sintering process sintering method of deactivation. Let us take the sintering method of deactivation. So sintering is basically the deactivation of the catalyst because of the prolonged exposure of the catalytic sites to the reactants on the gas stream which is present and as a result because the reactions are conducted at a high temperature the metal particles which act as a catalyst and which are impregnated on the catalyst site. So that actually leaves the catalytic sites and then they start agglomerating together and as a result the net surface area which is available for the reactants to go and adsorb onto the catalytic site that significantly reduces and as a result the catalyst activity is completely lost. So this can be captured so there are two causes for sintering. One is the prolonged exposure and the second is the crystal agglomeration and growth. So this can actually be captured in this figure here. So suppose if this is a catalyst and there are several catalyst sites which are actually spread across in various locations on the catalyst and let us say that this is the cross section of the catalyst. So we cut open the catalyst particle and this is the cross section. So now if the catalyst is exposed to the reactants for the gas stream for a very long time. So it is a prolonged exposure, prolonged exposure. Then what happens is that the particles they start agglomerating, they start agglomerating together and so they get deposited and the metals which may be present the noble metals which may be present at a specific location they start agglomerating and they start growing together in a specific location and so this can be depicted like this. So all the catalyst particles they start migrating to and agglomerating in one location and as a result the activity of the catalyst is completely destroyed and so this process is what is called as a sintering or aging process. Now the other method by which sintering can happen is basically called as the pore narrowing or closing. So the pores which are actually present in the catalyst so which contains the catalytic sites because of this prolonged exposure to the reacting gas and at a very high temperature the various particles can actually go and clog the pores and thereby block the pores and therefore the catalytic activity is destroyed. So that can be captured in this way. So suppose here is a catalyst and there are these catalytic sites, there are these pores which are present here and at the start of the reaction that is at time t equal to 0 so if I zoom up this pore here so you will see that so these catalysts which are present in various locations so they are present inside the pore here. Now after certain time when the reaction occurs for a long time after a certain long period of time then the catalyst pores will get blocked, will get filled with this material and so clearly the pores will get blocked and therefore they get closed and as a result the activity of the catalyst is lost. So the sintering process can actually be prevented. Remember that the temperature is a major factor in the deactivation of the catalyst by the sintering or aging mechanism. So therefore the sintering can be prevented if the reaction is conducted at a temperature which is less than 40% of the melting temperature of the solid. If the reaction can be conducted at a temperature which is less than the 40% of the melting temperature then the sintering process can be significantly reduced. So this is a remedial measure for sintering. However there are several reactions which may not be able to conduct these reactions at such a low temperature because the conversion that is desired is a strong function of the temperature. So the temperature at which the reaction has to be conducted is very important because the higher is the temperature then there is a chance that for exothermic reactions the reaction rate is going to be higher. So as a result it is not always possible to conduct the reaction at a significantly lower temperature. So one has to look at different aspects of the catalytic reaction while deciding what is the correct method to conduct the reaction in order to avoid sintering or aging method of deactivation. So let us now try to deduce a rate law for the sintering process, try to estimate a rate law for the sintering process. So suppose if we assume that it is a second order process then the decay rate is equal to kd into a square which is equal to minus da by dt. Note that the order of deactivation for sintering is usually very high typically about 5 to 8. However 2 is commonly used and is assumed here generally sintering mode of deactivation is very slow compared to other modes. And suppose we say that the activity is 1 which is not unreasonable because if the catalyst is fresh then all the sites are actually available for the catalytic reaction and by definition the activity has to be equal to 1 at time t equal to 0 and so integrating this expression we can find out that the activity is given by 1 divided by 1 plus kd into t. So that is the expression for the activity of the catalyst as a function of time. So now if we know the activity of the catalyst as a function of time then we will be able to estimate how much of the catalytic site is actually sintered, what extent of the catalyst has been sintered. So the amount sintered is given by, amount sintered S naught is SA is given by SA naught which is the initial quantity multiplied divided by 1 plus kd into t. So what the activity tells you what fraction of the catalyst site actually is available. So the amount that is sintered is given by SA naught which is the initial quantity divided by 1 plus kd into t. So if you stare at the decay rate law which is rd equal to kd into a square. So we observe we said that the sintering can be reduced if the reaction can be conducted at a temperature which is about 40% of the melting temperature of the solid. So why is it a function of a temperature? So if we look at the specific decay constant kd it has been observed that this decay constant actually follows an Arrhenius type expression, Arrhenius type dependence on the temperature. So we can write kd as a function of temperature as kd which is at the reference temperature multiplied by the exponential of Ed divided by R into 1 by t naught minus 1 by t. So this t naught is some reference temperature it could be the temperature at which the reaction was started. So the decay constant it strongly depends on the temperature at which the catalytic reaction is being conducted. So this suggests that lowering the temperature can actually prevent the sintering process as observed before it may not always be possible to conduct the reaction at a lower temperature because of the demands of the conversion which is required or the desired conversion. An example of a real process in which sintering or aging actually is has been commonly observed is the heptane reforming process, heptane reforming on a platinum alumina catalyst and it has been observed that Ed which is the activation energy for the deactivation of the catalyst it is about 70 kilo calories per mole. So it has been measured to be about 70 kilo calories per mole. So now because the catalyst gets deactivated the original algorithm that we followed to design a reactor starting from an experimental data needs to be modified because we need to now incorporate the deactivation process into the algorithm for designing the reactor. So the modified algorithm is the first steps to deduce the rate law. This is same as before and then find the mechanism of the catalytic reaction, find the mechanism that is governing the catalytic reaction and the next step this is the new step that is added find the decay rate law. This is required because the catalytic reaction actually occurs simultaneously along with the deactivation of the catalyst. So therefore it is not possible to design the reactor without knowing what is the decay rate law. So the next step is to find the rate parameters and following which the design of the reactor can be performed design of the reactor can be performed. So this is the new step that has been added the finding the decay rate law that is the new step that has been added to the scheme of designing a reactor. So let us look at an example of example reaction where sintering process may occur and see how to design a reactor and get the conversion as a function of the weight of the catalyst. So let us look at the isomerization process and let us consider a batch reactor. So the mole balance in the batch reactor for conducting reaction is given by Na0 which is the number of moles of the reactant A at while starting the reactor multiplied by dx by dt where x is the conversion and t is time is given by minus rA prime into W. So now the next step is to find the rate law. So let us assume that it is a first order reaction let us assume that it is a first order reaction. So the rate law is given by rate that is the moles of A which is reactor per gram of catalyst per unit time. So that is given by k prime which is the specific constant specific reaction rate multiplied by the catalyst activity. So remember that the catalyst is also getting simultaneously deactivated. So A of t is the activity of the catalyst. So k times A of t into Ca so that depicts the rate at which the species A is being consumed because of the catalytic reaction. And next we need to know what is the decay rate law due to sintering. So if we assume that the dependence of the activity on time that we derived a short while ago is valid and then A of t is given by 1 by 1 plus kd into t. So that is the dependence of the activity with respect to time. So now we can express the concentration of the species A in terms of conversion. So Ca is equal to Ca0 into 1 minus x where x is the conversion and that is equal to the number of moles of A which is initially present divided by the volume of the batch reactor into 1 minus x where x is the conversion. So now plugging in all these quantities that is the rate law for the reaction rate decay dependence of the activity as a function of time and the relationship between the concentration of species A and the conversion into the original mole balance. We can rewrite the mole balance as dx by dt that is equal to w by v where w is the weight of the catalyst which is present inside the batch reactor multiplied by the k prime which is the corresponding specific reaction rate into 1 minus x divided by 1 plus kd into t. So we can now integrate this expression so we can with a little bit of algebra we can rewrite this as 0 to x, integrate between 0 to any conversion dx by 1 minus x is equal to k into 0 to t dt by 1 plus kd into t. Here I have assumed that this term w into k prime by v is equal to this constant k. So after integrating this expression we will find that the conversion x is equal to 1 minus 1 by 1 plus kd into time to the power of k by divided by kd so that is the relationship between conversion as a function of time. So this expression provides a way to find out what is the conversion as a function of time and other parameters in a batch reactor where the catalyst is simultaneously getting deactivated. So next we look at the next mechanism by which the catalyst deactivation can occur which is the coking or the fouling process. Coking or the fouling process now this typically occurs in those reactions which involve hydrocarbons. So reactions involving hydrocarbons. So this primarily occurs in those reactions, this type of deactivation of the catalyst primarily occurs in those reactions where hydrocarbons are involved and whenever hydrocarbons are involved the carbon material which is present that gets deposited on to the catalyst sign and that therefore blocks the sides of the catalyst and that results in the deactivation of the catalyst. Now it is important to note that there are methods to regenerate the catalyst that is to remove the coke from the catalyst and that aspect will be dealt with separately in a different section of this course. So we will simply look at how to understand the mechanisms behind the carbon deposition on the catalyst side and how it affects the activity of the catalyst. So suppose if the catalyst pore is like this where the catalyst sides are present along the wall. Now after the reaction happens for a certain time that is the sufficient time for the carbonaceous material to go and deposit on to the active catalyst sign. So the carbonaceous material gets deposited on to the surface of the catalyst and thereby they block the active sites which may be available for further reaction to occur. So this typically happens after the reaction occurs for a certain amount of time. Now this is actually very commonly observed phenomenon in many reactions that involve hydrocarbons particularly that of the light gas oil cracking of light gas oil and the amount of coke that is deposited on the catalyst side that plays an important role. So the amount of catalyst that is deposited Cc is typically given by some constant A multiplied by time to the power of N, A and N are typically called as the coking constants or the fouling constants and T is time. So as time increases the coke gets deposited on the surface of the catalyst active sites and for a light gas oil cracking of light gas oil A has been found to be about 0.47 and N is about 1 by 2. So that is the typical numbers that have been found for the light gas oil cracking process and the amount of carbonaceous material that gets deposited on the catalyst side. So let us now look at how to find the mechanism behind this and how to model how to find the relationship between the decay rate as a function of the concentration and how to write the design equations. So AT which is the activity of the catalyst in the case of coking or fouling process certainly depends upon the amount of carbon which gets deposited on the surface. So there have been some common forms of the relationship between the activity and the carbon that gets deposited and they are like this. So A of t is equal to 1 by some constant Kc multiplied by Cc to the power of p plus 1. So recall that Cc can be written as some constant A multiplied by t to the power of n. So plugging this expression into expression relating the activity and the amount of coke that is deposited given as 1 divided by 1 plus Kc into A to the power of p in t to the power of n into p. So now this can be rewritten as 1 by 1 plus Kc, 1 plus K prime into t to the power of m, where K prime is nothing but Kc into A to the power of p and m is nothing but n into p. So this is one form of the activity as a function of time by incorporating the amount of coke that is actually being deposited on the side because of the coking or fouling process which is fouling process of deactivation of the catalyst. The other forms which have been used are given as follows, A is exponentially dependent on the amount of coke that is deposited on the catalyst side or it may be a function which looks like this, alpha into the amount of coke that is deposited on the surface. Now how do we minimize the amount of coking that is actually happening? That is the amount of carbon material that gets deposited onto the catalyst side. And so the way it can be done is it can be minimized by performing the, conducting the reaction at elevated temperatures. So it can be minimized by conducting the reactant at elevated hydrogen pressure. And the other strategy that has been observed to work is by conducting the reaction at a hydrogen rich stream. So these two methods have been used to minimize the coking or the fouling process on a catalytic side. So let us look at the third method of deactivation of the catalyst which is the poisoning process. So the poison could actually be present in the feed or it could be the reactants or the product itself could be poison. For example, there is in a catalytic side when the gas stream is carrying a certain reactants, it might be containing traces of some poisons and these compounds can actually get deposited onto the catalyst side and thereby deactivating the catalyst itself and or the reactants or the products of a specific reaction can actually act as a poison. They may actually go and get absorbed onto the catalyst side and therefore destroy the activity of the catalyst completely or partially. So poisoning is basically you have poison and these poisons could be present in the feed. It could be present in the reactants. It could be reactants itself that may act as a poison or the products, products that are formed because of the catalytic reaction that may act as a poison by itself. And what happens is that it irreversibly there is an irreversible chemisoption process. There is an irreversible chemisoption process which results in the deactivation of the catalyst. So remember that these catalyst particles which are impregnated with noble metals for catalyzing the catalytic reaction, they are very expensive. They run into several millions of dollars. So therefore, loss of activity of the catalyst is strongly affects the performance of a company which is actually a marketing that particular product. So therefore, it is very important to understand the poisoning because of these irreversible chemisoption and attempts to minimize them is extremely important. So let us look at the first case where we look at the poison in the feed. We look at poison in feed. So a nice example of that is the presence of sulfur, lead etc. in the petroleum feed stocks. In the natural petroleum and diesel that is used in automobiles, it is very important not to have sulfur and lead. And one of the reasons is that the exhaust muffler which contains catalyst, they may get deactivated in the presence of sulfur and lead. So therefore, these two act and act as a poison for the muffler and that significantly affects the performance of the muffler and thereby polluting the environment with toxic gases. So that means very important to have minimal sulfur or no sulfur or and no lead in the petroleum feed products particularly in the gasoline. So that it can improve the efficiency of the muffler and thereby protecting the environment from passing of this, passing of environmentally unfriendly gases into the atmosphere. So the poisons typically they can see these poisonous materials they actually compete with the reactants. So what happens is that the the reaction at the catalytic reaction actually happens by the reactants which go and adsorb on to the catalyst side. Now the poison also has exactly the same behavior. So they also are looking towards getting adsorbed on to the surface of the catalyst side. So therefore, the poisonous materials they are strongly competing with the reactants in order for the vacant sites and and therefore, it can it simultaneously happens along with the chemical reaction. So here is a cartoon which depicts the poisoning process. Suppose if this is the catalyst particle, if the if this is the catalyst side then if the reaction that is being conducted is A giving B plus C and suppose if the at time t equal to 0, at time t equal to 0 all the catalyst sites are vacant and are available for the adsorption of the reactants and also the poison. So let us say that P is the poison which is present in the feed stream. It could be sulphur lead or any other compound and after a certain time t1 after a certain time t1 the so some of the sites the poison will get adsorbed into some of these sites and some other sites the reactant A may be adsorbed and a product may be formed in some sites and B may be adsorbed on to the some other site where the product is already formed. So at a further later time at a further later time t should be t1 which is greater than t1 greater than 0. So at a further later time t2 which is greater than t1 then more sites are filled with the poison. So the number of sites which are available for adsorption of A constantly continues to decrease with time and at a much later time at a much later time t3 which is also greater than t2 all the sites are actually filled with the poison. So at this point the catalyst appears completely deactivated and it is of no use to conduct the catalytic reaction. So let us summarize what we have learned so far in this lecture. So we have looked at we have defined what is catalytic deactivation we had looked at various types of deactivation process and then particularly we looked at sintering and aging we looked at coking and coking or fouling process and we initiated discussion on the poisoning of poisoning method of deactivation of the catalyst. So catalyst deactivation is a very very serious problem because it strongly affects the conversion of the reaction and it may be that the extent of conversion of a particular reactant is if it is affected strongly then it can strongly affect the economy of the industry which is actually marketing that particular product which is a end product of the reaction which is being conducted in a catalytic reactor. So therefore the characterizing deactivation is very important and what we will see in the next lecture is how to characterize the poisoning process and look at some examples. Thank you.