In this screen-cast we are going to operate

a batch still using variable reflux to achieve a constant distillate composition. In the

problem statement we are given the total number of equilibrium stages in the batch still unit

and we are told the composition and amount that is charged initially into the batch still

unit and we are told we are going to run this operation until we get a given concentration

in that reboiler at the end of the batch still operation. We are asked how much distillate

product is produced and finally the range of reflux ratios used. The basic mode of operation

in this particular batch still is to use the reflux ratio to adjust and basically compensate

for the amounts of separation that we are getting out of the column in this basic vapor-liquid

equilibrium process. So as the batch stills run, as we start to deplete the amount of

ethanol in the system, we can then increase that reflux ratio to still achieve the separation

that is desired and also deliver the concentration of distillate that we are looking for. In

most batch still operations we use the Rayleigh equation to relate the composition in the

reboiler and the composition in the distillate. But in this case since the distillate composition

is constant it is effectively decoupled from the composition in the reboiler so we don’t

necessarily have to use the Rayleigh equation, we can accomplish the material balances associated

with this process simply with a more traditional, what goes in comes out type material balance

that we have seen before. So in this system we would just balance what goes into the system,

which would be the number of moles of liquid initially charged into the reboiler, and balance

that with what remains in in the reboiler in the end. And that would be in the number

of moles. And add to that the number of moles that emerge from the column in the form of

the distillate. So that gives us the total mole balance of the system but we also have

another piece of information which is the component balance. So if we do a component

balance about the ethanol in the system and look at what goes in, specifically the number

of moles of liquid initially charged to the system, the composition of that liquid going

in, and we balance that with what comes out in terms of the number of moles of liquid

remaining in the reboiler, the composition of that fluid, and then add to that the number

of moles emerging as distillate and the average composition of that distillate. And then in

this case since that distillate composition is constant that is just the constant distillate

composition in the problem statement. When we plug in the values from the problem statement

we now have two equations and two unknowns, we can solve those to determine the number

of moles that remain in the reboiler at the end of the distillation operation and also

the number of moles that emerge as distillate which was one of the questions we were looking

for in the problem statement. And now we arrive at the second part of our problem. And that

is to determine how we adjust our reflux to account for the changing amount of liquid

in the reboiler. Since this is a distillation operation the first thing we should do is

look for the vapor-liquid equilibrium data associated with that system. And then we are

going to consider both what is going on at the beginning and the end of the distillation

operation. So at the beginning of the distillation operation we are going to, first, find an

operating line that satisfies the system and then based on what we know about that operating

line we are going to calculate the reflux ratio for that state, and we will expand on

what we mean by that a little later. And then we are going to do the exact same thing for

the final state. So the first step in our plan is to get the VLE data. And I’ve done

that for the ethanol water system and we have pulled this out. With that information in

hand we will move to the second step in our plan and determine the operating line associated

with the initial state and also calculate the reflux ratio. So we know a couple things

about any operating line. Operating lines need to satisfy the points x is equal to y

is equal to your distillate composition and in this case the distillate composition is

0.6. Now the operating line’s slope also for this case has to give use a bottom’s composition,

or in this case it would be a waste composition of 0.3 an it has to give us that composition

with exactly two stages. So these are the pieces of information we need to put together

to figure out what operating line satisfies this condition. So we are going to go to a

zoomed in view of VLE data and we know that we have the point x=y=dist composition,

0.6 and we also know we need to satisfy the bottoms composition emerging out at 0.3. So

we are going to satisfy one point and take a guess at what the slope might be and step

off the stages. So the first guess on slope is, hey, maybe the slope is 0.5, we don’t

particularly know right now but we are going to take a guess and we are going to see what

composition comes out of the bottom of the column with this particular slope. So I draw

that operating line and when I go step off the stages we see that our bottom’s composition

associated with this slope does not satisfy what we are looking for where we are looking

for a bottoms composition of 0.3 so that isn’t going to work for us. So we are going to have

to adjust our slope. Let’s take another try. The new slope I’m going to try is a slope

of 0.25, step off the stages. we are still not quite there but we are heading in the

right direction. So we try this several more times until we arrive at a slope that is approximately

0.125 that’s going to give us two stages and then we arrive at our bottoms composition

or our waste composition of 0.3. So now that we have our operating line we need to calculate

the slope of that operating line for this particular case is 0.125 and based on that

slope we can calculate a reflux ratio. So now we know that when we start our distillation

operation we need to have a reflux ratio of 0.14 to deliver that final distillation composition

of 0.6. But we also know that as we run the distillation unit, the concentration of the

liquid in the reboiler, so we are going to have to increase this reflux ratio to compensate.

So what is the highest reflux ratio we might need in this particular distillation operation.

Well that is going to be the reflux ratio associated with the final state of the system

where we have a composition in the reboiler of 9% ethanol. So now we have to determine

the operating line associated with this condition and then calculate the reflux ratio in this

state. We use a similar process to what we used before where we fix one end of our operating

line to our distillate composition at the reference line and then adjust our slope to

figure out what bottoms composition after two stages. We go ahead and do that through

another guess and check process and we arrive at a slope of 3/4, this is going to give a

desired bottoms composition of 3/4. So with that slope we can go through and calculate

what our reflux ratio is and we see at the high end we need a reflux ratio of three.

If there are 2 stages, in the graph the reboiler must be counted because the two theorical stages are for the column and the operation in the reboiler is another stage. So, in the graph must be drawn 3 stages no 2.

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The reflux range that is calculated (0.14 to 3) . how to decide for how much time we will have to operate and at which reflux , so our product purity is not affected?