hello everyone welcome back to the aspentech channel and as you know that we are covering these days related to chemical reaction engineering and in this regard we are bringing the lecture number five for our valuable viewers so in today's lecture we will start with the sizing of continuous flow reactors and then we will discuss or we will solve some examples related to sizing The Continuous Flow reactors but before going to the sizing we will just have a recap of our lecture number four that we have derived the design equations for various type of reactors which include bash reactor cstr pfr and PBR now in sizing a continuous flow reactor the first thing which we will have to remember that the rate of disappearance or the rate of reaction is a function of conversion we will discuss or we will see it shortly how it is related because we have seen minus r a is equal to KCA but that's concentration term is actually going to the function of conversion the rate of disappearance is almost always a function of concentration of various species present and the system like if you see here that for a first order system it is written as minus r is equal to KCA and that CA is actually written as CA naught into 1 minus X so accordingly once it is written as C is equal to C naught into 1 minus x minus r a is a function of X now you will be seeing how that equation has been transformed if you remember that n e is equal to n a naught minus n a naught X which we have used during the derivations now if you take n a not common from it it will become n a naught into 1 minus this one will be canceled out 1 minus X not divide that by the volume and you will get CA is equal to C naught into 1 minus X so that is how you derive that expression where K is a function of temperature it is a specific reaction rate constant so that thing is definitely written in the slides but I have just explained it in the lecture as well when only one reaction is occurring each of the concentration can be expressed as a function of conversion and it can be written as a function of X obviously for multiple reactions the kinetics will be different it will be reversible or irreversible in nature how it will be proceeded once we move to the chapter number three and chapter number four we will see over there as well during reactor sizing there are two cases or two possibilities number one we know the reactor volume but we do not know that the percentage converge and the second case is we know the percentage conversion but we do not know the Retro volume so obviously one of the value or the factor is unknown and we have to estimate or calculate it but before doing that or before sizing the reactor we have to get the understanding of the level steel plot and the starting point is that minus r a is a function of conversion and one can size any type of vector what we need to do we need to take the reciprocal of that equation which is minus r is equal to KCA that will become 1 over minus r a and that is equal to 1 over KCA and CA will be equal to C naught into 1 minus X so that will become as 1 over K C A naught 1 over 1 minus X but now after doing that plot there are two basically plots that are included number one is the plot of conversion versus 1 over minus r a and accordingly you see the plot is generated over here and the second plot is between X and F A naught over minus r now you can see that both plot plots are actually the same in nature the only difference is this value of f naught which is not present over here but you see the trend in both the cases will remain the same and once we go to the example we will also solve it over there as well so what we need to do we need to First draw the 11 speed plot once we are graphically calculating the volume of the reactors the sizing are being done for The Continuous Flow reactors that we have to plot either FN order minus r a or one over minus r a as a function of X and then we can calculate the volume of cstr and volume of pfr now the question arises how we can calculate so this is the answer in this slide that what you need to do you need to take one point for example this represents X at somewhere to like 0.9 you have to draw a straight line over here and that will connect with this curve over here and then plot a straight line which connects this y axis and the area this area complete area will represent the volume of cstr while in case of pfr it will be the area under curve so that is the main difference between volume of cstr and volume of pfr now if you summarize it basic summary is that you have to first draw the lemon spill plot from the given data the lemon square plot could either be F A naught over minus r a as a function of X or 1 over minus r a as a function of X and based on plot which has been obtained if you want to calculate the volume of cstr what you need to do for example if you want to calculate here then simply draw a line here which touch it and then draw a line here and this area will be the volume of cstr on the opposite side the area under the curve at the same point will represent that of the pfr so you can see that for these type of Curves volume of cstr will always be higher than volume of pfr but in our next lecture we will be discussing various combinations we will see that that is not always true that volume of cstr is always greater than volume of pfr in some cases like in adiabatic cases at certain conditions volume of cstr will be lower than the volume of pfr for irreversible reactions as the value of x approaches to 1 the rate of reaction minus r a approaches to 0 accordingly 1 over minus r a approaches to infinity and volume will be infinite which will be required for this while for the reversible reactions which we say a goes to B plus C and B plus C can react to form a the maximum possible conversion is equilibrium conversion as we have discussed in our previous lecture as well minus r a will approach to 0 accordingly 1 over minus ARB will approach to infinity and volume will approach to Infinity so infinite volume is required at equilibrium conversion for the reversible reactions and for the irreversible reactions infinite volume is required to make hundred percent conversion in the system now moving on to the example which we will be doing today that to illustrate the design of continuous flow reactors such as cstrs and pfr we consider the isothermal gas phase isomerization in which a goes to B we are going to the laboratory to determine the rate of chemical reaction as a function of the conversion of reactant a the laboratory measurement are given in table 1 show the chemical reaction rate as a function of conversion the temperature was 500 Kelvin for 40 degree Fahrenheit the pressure was 830 kilopascal and the initial charge to the reactor was pure a the entry molar flow rate of a is fa naught is equal to 0.4 mole per second so you can see that you have been given the values of x at 0.1.2.4.6.7 point and and corresponding values of minus ra aren't given so what we will do we will go to the Excel now and we will draw the 11 spill plot under two conditions one is from one over minus r a and second one is for f a naught over minus r n we will see whether these two plots are same or not so now we are moving to the Excel sheet and the data for x and minus r a is given to us now first we need to calculate 1 over minus r a and that is simply 1 divided by this value so and accordingly doing the what we paste over here and the formula will be copied and you can see we have got the plot simply using number system to get it to two decimal or maximum we can get it to 3 decimal using this Factor now we have to draw the plot between X which is at x axis and 1 over minus r a which is at Y axis so what we need to do click it press Ctrl from keyboard select it go to this insert charts and the plot is generated over here which represents the 11 skill plot and accordingly you can see X versus maneuver minus array plot is generated for the system now we know that F A naught value is 0.4 mole per second so what we need to do F A naught over minus r a and simply multiplying 0.4 with this calculated value so accordingly just drag it over here again giving it just three decimals and now in the same fashion it is simple mathematics so I am doing it very quickly press Ctrl from the keyboard again select it go to insert charts and you can see now you can simply see that both the trends are same only there is a difference in the y axis values but the trends will remain the same because mathematically if you see only 0.4 as a factor is multiplying over here so the trend which will be generated with 1 over minus RM will be the trend which will be generated for the F A naught over minus r a so using either this or this will surface for the calculation of volume of cstr and pfr so let's see we select this one which is f a naught over minus r a and obviously the other parameters can be like we can give access titles and this one is X and this one is f a naught over minus r a and the unit will be cubic meter so once we have generated it now we have to find the value of volume of reactor as in the next statement if you see here that for the level spill plot which we have been generated in the previous example we have to size the cstr now and for the cstr what we need to do we need to take point from here connect it to the line here and then plot line here that and this area if you see here and this area the rectangular area will represents the volume of cstr in the system so simply multiplying Point 8 here with the value of 8 multiplying these two values will give the answer of volume of cstr at a conversion of 80 percent similarly if we want the value at 40 percent simply take a line from here take another line from here at somewhat about point at 2 so according to 2 multiplied by 0.4 so approximately 0.8 cubic meter or 800 cubic decimeter value will be required for the system so now what we need to do we need to go back to Excel and now you see you have got this plot simply what you need to do here that you need to go to this illustration in shapes and let's see that you draw a line over here and then simply take a line straight line over here and this area which represents the volume of CST and now multiplying point eight with eight so it will give an answer of 6.4 cubic meter or 6400 cubic decimeter so that will be your answer similarly if you want to calculate for 40 conversions draw straight line over here then again you have to draw a straight line over here so it will be a bit slighter above 2.0 so it will be somewhere 2.05 so multiplying these two will give an answer of 0.82 cubic meter or K20 cubic decimeters another way of doing it that we know that volume is equal to F A naught into X over minus r a now if you see you have value of f naught over minus r a which is this one and the value of x so simply multiplying F naught over minus r a into X will also give you the value of volume in cubic meter for example this one is 0 at 0.1 conversion or ten percent conversion it will be 0.1 cubic meter at twenty percent conversion 0.27.82 2.12 3.5 and finaling 6.4 so this is how you calculate the volume of cstr using 11 speed plot so today we are winding up this you have to Simply understand the level spill plot you have to draw it in Excel you have to calculate the volume of cstr and and in the next lecture we will calculate the volume of pfr that will be using the five point quadratic formula and Simpson 2. so I hope you have liked the lecture and you have understand it if you have any queries please provide your suggestions in the comment box and that's it from this lecture thank you so much please do or like share the video and subscribe to the channel also click on the Bell icon to get all updates related to this channel till then it's goodbye stay tuned for more exciting videos