Calculation of Minimum Column Diameter for sieve plate

[flyingdutchman]

Ok what I have looked for on alot of forums but never truly found is a detailed example of how to calcuate the required (minimum) column diameter for a given set of design parameters. Since I cant find it, and in an effort to help others who might be like minded I would like to take a stab at it here. Now in an effort to be up front and honest let me say
1) I am not a math major
2) I am not a Chemical engineer
3) what i am is a synthetic/organic chemist, as such this is WAY outside my area of expertice. Ask my about the investigation of some novel synthetic route or optimzation of some existing chemical synthesis and I would be on surer footing.

Because of this what I would really like is for some one who is a chemical engineer to check my calculations and say if i am off base which is to say the last thing i want to do is put out incorrect information and give the impression I know exactly what i am talking about (because I dont). That said this is my disclaimer that I am not in any way expert in this field or that i even work in this field so dont bank on what i say here because it could be wrong.
I will be working from a representitve example for a binary sytem of methanol and water here.....
Unit Operations of Chemical Engineering, McCabe W.,Smith J., Harriot P. which can be found here
http://books.google.com/books/about/Uni ... SvHtIOwj8C

LOl and now I am going ice fishing so BB later for the first step

[flyingdutchman]

Ok so i thought it might be best to start by defining some terms I will need to use so..
L = liquid flow rate in the column (amount per unit time amt/time like say kg/hr or mol/hr)
V = vapor flow rate through the colun (amt/time)
D = product (distillate) collection rate (amt/time)
Dc = column diameter
d(l) = density of the liquid in kilograms per cubic meter (kg/m^3)
d(v) = density of vapor (kg/m^3)
s = surface tension of the liquid (dyn/cm)
Kv = flooding constant that will be determined graphically
Uc = maximum vapor velocity (which ends up bieng calculated from Kv)
Rd =reflux ratio which in this text is defined as L/D = (V-D)/D
Do not confuse this with the other way to express reflux ration which is Rv = L/V = L/(L+D) because I wont be doing my calculations based on this I will be using Rd
L/V = is the ratio of mass flow rate to liquid flow rate it is a unitless number because when we divide (amt/time) by (amt/time) the units cancel and so it becomes unitless. (keeping track of units is crucial)
Thats probably enough for now i want to keep this in small units so its easier to follow

[flyingdutchman]

So lets start with a couple of assumptions which right off the bat can get me into hot water..
1) I know that water and ethanol is a not ideal mixture but I would like to treat it as one.
2) Clearly in a distillation column (at amospheric pressure) we cant break azeotrope HOWEVER....
For the purpose of this calculation i would like to treat the system as if we could obtain pure ethanol.
my reasons for this are as follows
_ a) I am lazy and I cant seem to find any experimentally determined values for d(v) vapor density of binary mixtures of EtOH (ethanol) and H2O (water).
_ b) This prevents me from having to calculate d(l) and d(v) for a binary mixtures the composition of which will be different at each and every plate and then will vary from plate to plate depending on the ABV of any given wash. I suspect that using mol fractions (to determine the partial pressures) and the ideal gas law I could calculate it. Or maybe even using mol fractions and the known vapor density of each component at my desired temperature (but thats a guess).
_ c) I have a friend who is a process chemist and he says thats exactly how he would approach this problem (dont you love it when someone gives you exactly the answer you were hoping for!)
_ d) The text book I am working from, and from which I am basing my solution here, uses a represntitive example (of MeOH, H2O mixture). It makes the case that the calculations can be based on the top plate as such

Calculate Uc at the top of the column, because flooding is more likely here where the vapor density is higher than at the bottom

3) Since we already know that the density of ethanol vapor is indeed greater than the density of water vapor this makes me feel better about my shortcut in statement #2 which I feel should work and also allow me to solve forDc using just the top plate as my reference point.
4) perhaps most importantly I am treating this as asimple binary mixture which means I am completely igonring all other cogenors in our mixture which in the end means I am only calculating this for separation of water/ethanol and can not say what effect this will have on taste since cogenors seem to strongly influence taste

Please feel free at any time to point out any errors or mistaken assumptions I would appreciate it.

[Angel_Kefka]

Just from my reading, I think one of the main things that will effect how small you could make a column would be power input. Same with packed and how tall you can make it. Vapor speed is the main thing controlling how well these work, and speed is decided by a combination of power input and column diameter. In a packed column the vapor has more time to mingle iwth condensed liquids the slower it moves, so lower power input (as long as its enought to get the vapor to the top) should inprove operation at the cost of time.

Haven't read as much on plated columns yet, but proper speed seems even more tricky there. You need enough to keep liquid on the plates, but still want slow to allow mingling as the vapor passes through it. If I'm understanding things right, then a slower vapor speed could allow you to place the plates closer together and still get proper operation than if it was running faster. This would mean that you could shrink the column in height or diameter as long as the power input was adjusted accordingly.

I could be wrong, this is almost entirely based on reading and a little knowledge of physics. If so let me know what I have wrong. And if I'm not then hopefully I added something useful to your thread.

[flyingdutchman]

Hi AK,
I believe you are dead on in what you say. I suspect that proper vapor speed (or allowable range) is indeed of great importance with plated columns.

You need enough to keep liquid on the plates, but still want slow to allow mingling as the vapor passes through it. If I'm understanding things right, then a slower vapor speed could allow you to place the plates closer together and still get proper operation than if it was running faster.

I think this is closely related to residence time http://en.wikipedia.org/wiki/Residence_time and indeed increased residence time should lead to better resolution/seperation of our components. Ofcourse I suspect like alot of things that gain only comes at a price and the price of increased residence time my be decreased takeoff rate. So I suspect what we do is balance the need for increased separation with the desire for a faster takeoff rate and find a happy balance somewhere in the middle (hopefully).
In essence I believe too little flow and you cant sustain the liquid on a sieve plate, too much flow and you get flooding or entrainment. But thats just a rough explanation and there are alot of resources out there that do a much better job of explaining what i just said.

PS two of the design parameters for determining the column diameter will be Rd and D. So given the fixed value for the heat of vaporization of our EtOH and fixed values for Rd and D , I believe we will have then defined a fixed value for Q (the heat energy supplied to our boiler) which will be implictly understood and which could be calculated (but I wont bother with here).
One interesting thing that Mike Nixon is quick to point out in his book The Compleat Distiller is that quite neatly the heat of vaporization on a per mole basis is to a reasonable aproximation ~40 KJ/mol. for both EtOH and H2O. Now this only holds true on a per mole basis and is not the same on a weight basis. Luckily for me, since I will define D in KG/hr the density of ethanol vapor is a determining factor in flooding so that as the run progresses even if the distillate has a higher ratio of water to ethanol, it should then have a lower vapor density.

[flyingdutchman]

Ok lets put forth the parameters for our column. I have seen some issues with 2 inch columns. I am curiuous as to why and so my parameters will be in the approxamite range of what might be reasonable for a 2 inch plated column. If I do this correctly it could easily be translated to other size columns and if i do a proper job of explaining my logic (or perhaps my interptaion of other reasonings) I expect other members will be able to apply this themselves to their own designs. SO..
So for sieveplate column operating at atmospheric pressure we wish to produce nealry pure ethanol from an aqueous feed containing 10% EtOh (by cvolume). The distillate shall be collected at a rate of 1.2 liters/hour and at a reflux ratio of 9. For plate spacings of 6",9",12",18",24" and 36" I shall attempt to calculate the allowable vapor velocity and use this to determine the minimum column diameter. Notice I use the word minimum because we could always make it larger and probably any reasonable design would indeed do so to allow a little elbow room.
So here is what we know:
Pressure = 1 ATM or 0.101325 MPa
D= 1.2 l/hr
Rd = L/D = (V-D)/D =9 (or 9/1)
Since Rd =9 = 9/1 we can say with respect to mass ratios that L=9 D =1 and thus V= (L+1)= 10 so.
L/V = 9/10 (and its unitless)
Plate Sp = 6, 9, 12, 18, 24, 36 (we will calculate each respectively andf see how this effects column capacity)
What we know from literature is:
d(l) (EtOH at 20c) = 789.68 kg/m^3 Source:http://nequam.se/misc/ethanol.php
d(l) (EtOH at 78C) = 736.69 kg/m^3 (see above)
d(v) (EtOH 79C) = 1.643 kg/m^3 (see above)
s (92.7 wt% EtOH in water at 78.7C experimentally derived) = 19.2 dyn/cm source: Surface Tension of Ethyl Alcohol-Water ter Mixtures, Bonnel W.S., et al, Industrial Eng. Tech., vol 32, No. 4, 1940 (I used this only because the surface tension of ethanol and water can differ so widely that I felt it might me reasonable to use a fixed known value for reasonably pure ethanol water mixture)
Notice we have defined a Fixed D and a Fixed Rd and so by defualt a fixed Q heat input (which we can calculate but do not need to do so for this purpose).

[flyingdutchman]

Ok From the Graph below we need to take what we now now and calculate
Kv (on the Y axis)the flooding constant-I apololgize but they note it as Csb it is the same term
With that known we can then calculate
Uc The maximum vapor velocity -again I apologize as they note it as Unf it is the same term

Sorry on this graph for Flv they are calling V (vapor) G (gas) again its the same thing its the best graph I could get on line (so L/V is the same thing as L/G its just a different symbol)
To do this we first must calculate Flv (on the x axis)
we know the value for all those terms
L/V = 9/10 and d(v)/d(l)= (1.643/736.69) so putting it all together Flv =(9/10)x (1.643/736.69)^0.5 = 0.042502933
dont let raising to the term d(v)/d(l) to the 0.5 power confuse you it just means square root and even then its just a button on your calculator (or excell sheet) try and and you will see it works just fine
So now that we know Flv ~0.42 simply put your finger or pencil on the graph at the X axis (at 0.42) and follow it straight up (vertically) until you reach the 6" line. This means it is a 6" plate spacing. Now from where your pencil meets that 6" line travel horizontally across (to your left) until you reach the Y axis. Where you meet the Y axis is the exact value For Kv (Csb)
You now know the value for Kv (Csb) thats what I mean by solving it with a graph. You can do the same thing for 9", 12", 18",24" and 36" I did just that and what I get is
Kv 6'=0.1533
Kv 9" = 0.1813
Kv12" = 0.222
kV18' = 0.28
kV24" = 0.37
kV 36' = 0.4816
feel free to check my math follow along on the graph I can send you full page one if you email me. Nows a good time to ask any questions if you missed a point or i jumped a step you didnt follow.
Remember what I just did only applies for the EXACT parameters I defined if you change those (like a different reflux ratio) this will change so just keep that in mind.

FD
PS i just realized that alot of you may not know that In the sciences they LOVE to us greek letters for symbols! Dont let this throw you. So where i use d (for density) They alway use the small greek letter RHO (looks almost like a p). And for surface tension I use the letter s they use the small letter DELTA it looks like a small letter o with a dash ontop (not the capital delta like in frat names). try this link to see what I mean http://en.wikipedia.org/wiki/Greek_alphabet. I cant use greek letters here so i use the symbols I can type here but dont let a different symbol that means exactly the same thing throw you. Density is density and surface tension is surface tension.

[flyingdutchman]

Ok in an effort to make this easier I took the formula for Kv on the Y axis of the graph and pasted it into word then converted that to an image so that you can see what is going on..

Uc.png (2.42 KiB) Viewed 8960 times

Now the top equation is the exact same on on the Y axis on the graph I just stripped out the greek letters and use V for vapor (not g like he did). I also replaced the lower case rho with d for density and lower case delta with S for surface tension like we have used all along. So the term in the first box is 20/s this is just the number 20 divided by our known surface tension. Now they are raised to the 0.2 power again its just a number type it into your calculator and it pumps out the answer. The second set of terms is just The density of the vapor divided by the the density of the liquid minus the density of the vapor. then it is raised to the 1/2 or (0.5) if you prefer. Ofcourse they are all multiplied together.
However what we really want here is Uc !
At this point we know the value for every single one of those terms so there is really nothing stopping us for plugging in the numbers and getting Uc.
Now to make life easier The second equation is really just the first equation. its just reaarranged so that Uc is all by his lonesome which is just the way we wanted it! Plugging in all the numbers for our 6" plate spacing looks like this
Uc= (0.1533)[19.2/20]^0.2 [(736.69-1.643)/1.643]^0.5 which for me works out to
Uc 6' = 3.216141695 feet/sec or 0.980279989 meters/sec
likewise I get..
Uc 9' = 3.803564836 f/sec 1.159326562 m/sec
Uc 12' = 4.65742633 f/sec 1.419583545 m/sec
Uc 18' = 5.874231407 f/sec 1.790465733 m/sec
Uc 24' = 7.762377216 f/sec 2.365972576 m/sec
Uc 36' = 10.10367802 f/sec 3.07960106 m/sec

Ok now feel free to plug in the values of Kv for each one and check what i did. Do the steps make sense to you. Better yet do the answers make sense. What I see which I find reassuring is that as the plate spacing gets further apart the maximum allowable vapor velocity is increasing. It doesnt mean my math is right but on the plus side I have no negative values and they increase they way common sense says they should . Nows a good time to ask me question here on this par,t but anytime will do. if you dont follow what i did ask chances are someone else has the exact same question and i just need to explain uit better. if you see an error in my math point it out!

[flyingdutchman]

OK
Lets recap what I have done to this point. It looks like a lot but really it was just 4 steps.
1) I decided on a collection rate and reflux rate Rd for my desired column
2) Using known Literature values for ethanol and my desired Rd (reflux ratio)I calculated the term Flv which is shown on the x Axis of the graph by simply plugging in the numbers into that equation (nothing more complicated than that)
3) Using the graph and just tracing along with a pencil I followed up from my Flv number to my plate spacing line then across to the Y axis to get Kv (or Csb depending on who made the graph)
4 With my now know value for Kv I simply plugged in all the known values into that second equation I displayed (which is the same equation as on the Y axis just rearranged) to get Uv.
Thats it I now know for my desired column The maximum vapor velocity that would be acceptable for that plate spacing!
If my vapor travel faster than that all bets are off and there is a strong probability that my column will not work.
Maybe this seems like a little work...
BUT isnt it faster than building an entire column just to find out it does not work?
Better yet now we can finish solving for our column and graph just exactly what happens when we change plate spacing and see what happens with our eyes.

PS I wish there was one simple equation that gave us this answer without the use of the graph! I can not find one that describes any system where the plate spacing is less than ~18". If any knows a model that does this for say 4"- 24" inch spacing I would LOVE to see it

PSPS I would really like to see some questions or comments so I know people are following along and get this

[Bushman]

You have done a good job explaining and simplifying the formulas. Here are a few more charts that were in the book I told you about that relates to sieve trays. Let me know if you need any of the formulas.

Flow-through sieve tray vapor passages

This is a recent correlation for entrainment flooding.

I can also go over the factors that influence the weeping point.

[flyingdutchman]

Hi Bushman,
Those are some great charts! I like the last one as it goes right down to a 2 inch plate spacing. I noticed he has eliminated the whole term for surface tension where Kv (Csb) is proportional to (20/S)^0.2. I suspect that with some liquids where the surface tension is always ~ 20 that results in a term which is approximatly equal to (20/20)^0.2 or just 1^0-.2 which is really just 1 and of course any number multiplied by 1 is itself. However with some liquids like water s (surface tension) can be quite high like 50-70 dyn/cm I think. But even in our case with almost pure ethanol the s was equal to 19.2 which is indeed almost eactly 20. Infact a quick check with my calculator shows this as 1.0082 which is indeed ~1.
LOL

[flyingdutchman]

Ok we know our allowable vapor velocity (in meters per second m/sec) but how does this apply to our column. To solve this we need to..
1) calculate what our actual vapor flow rate will be (notice I said flow rate as in how much flows per second not just how fast it flows there is a difference. vapor flow rate will be in cubic meters per second (m^3/sec) pay attention to units they are important we use them so we dont get confused
2) once we know that we divide vapor flow rate by the maximum vapor velocity and this tells us the requires area (of plate needed for bubbling)
3) next we take into account that not every inch of the plate is for bubbling (inlet weirs outlet weirs, calming zones etc)
4) Then we use a the fact that the area of a circle = pi(r)^2 to get the radius and that 2 x r =d to the required diameter Dc
5) I might add a final step which would is to err on the side of caution we could increase the column diameter by an added 20% just to be on the safe side (better to have 20% and not need it than need 20% and not have it)

So step 1
Now we already said that D is 1.2 Liters/hr but for this to work we need that in kilograms. luckily we already know from literature that the density of EtOH
d(l) (EtOH 2oc) = 789.68 Kg/m^3 and we can find on any internet calculator/converter that it takes 1000 liters to equal 1cubic meter (1m^3) so lets convert liters to cubic meters then use density to get how much EtOH we have in kilograms (hint pay attention to the units to see whats going on)..
1.2 Liters/hr x 1 m^3/1000 (liters) x 0.789 Kg/m^3 = 0.9468 kilograms/hr of EtOH
Notice: liters/liters and m^3/m^3 all just go away leaving us with just kilograms/hr for units, thats called dimensional analysis and if you end up with weird units you did something wrong
Now its given in this book that:
V= D(Rd+1) (we can prove this but lets accept it as a gift and work on ) {dont forget we said Rd=9 here]
But hold on we have D in kilograms (of liquid)/ hour but we are talking about a volume of vapor and in seconds not hours so we need to convert hours to seconds. so convert mass to volume we coviently already have d(v) which we know is 1.15 Kg/m^3 and we know that 1 hr = 3600 seconds if we put this all together into one step we get..
D(Kg/hr) x (Rd+1) x 1hr/3600 sec x 1/1.643( Kg/m^3) or
0.9468 kg/hr x (10) x 1/3600 sec x 1/1.643 (Kg/m^3) = 0.00160073 cubic meters per second ( m^3/sec)
So vapor flow rate = 0.00160073 m^3/sec
now that is stricitly based on our stated Reflux ratio and collection rate so this is independant of our plate spacing

[flyingdutchman]

2) Now step 2 is alot simpler and all we want to do is divide the vapor flow rate (we just calculated) by our already calculated maximum vapor velocity. this gives us the required bubbling area of the column. Now remeber that each plate spacing had its own maximum vapor velocity so I will need to do this step for each plates spacing. I will show the work just for the 6" plate but give you the results for each one (there probably isnt a need for me to repeat this 6 times LOL) so..
(0.00160073 m^3/sec)/( 0.980279989 m/sec) = 0.001632932 m^2 (notice how the seconds went away and we end up with the proper unit for area m^2 or square meters)
6" = 0.001632932 m^2
9' = 0.001380742 m^2
12" = 0.001127606 m^2
18" = 0.00089403 m^2
24' = 0.000676563 m^2
36" = 0.000519785 m^2
Notice as the spacing gets wider the required bubbling area gets smaller!

3) Now lets assume about 70% of that plate is active bubling area so we just need to account for thet by dividing our answers by 0.70 rectify this so this gives us the following
b]6" = 0.00233276 m^2[/b]
9' = 0.001972488 m^2
12" = 0.001610865 m^2
18" = 0.001277186 m^2
24' = 0.000966519 m^2
36" = 0.00074255 m^2
Notice that since we only have 70% bubbling area the required area gets larger

[flyingdutchman]

4) I now want to get the required minium column diameter. Now since area (of a circle)=pi(r)^2 and Dc=2r we can combine both these equations into this..
Dc= [(4 x Column area)/pi]^0.5
again I will do this just for the 6" plate spacing and report the results for each (also I will convert meters to inches)
6" Dc= [(4 x 0.00233276 m^2)/pi]^0.5 = 0.054499215 meters[/b]
6" = 0.054499215 m or 2.145639544 inches
9" = 0.050114387 m or 1.973008426 inches
12" = 0.045288177 m or 1.783000048 inches
18" = 0.040325737 m or 1.58762828 inches
24" = 0.035080071 m or 1.381105898 inches
36' = 0.030748086 m or 1.210555215 inches

provided this is right and now that it is in inches notice how increased plate spacing decreases the required column diameter. Mind you this is the minimum column diameter and that next we will increase this to include a buffer then we can chart this in Excell to get a good look at it.

PS for anyone that followed along with that whole thread on the problem with 2" plated columns this is exactly where I think the problem was. Notice that even for a 6" plate spacing a 2" diameter is too small and more likely it was an even smaller 4" plate spacing that might have been commonly used. Plus we havent even built in a ~20% buffer factor.
FD

[flyingdutchman]

OK,
Last step! The author of the text reccomends that the column diameter be sized for ~20% greater minimum vapor velocity. Now that would be an increase in column diameter of ~12%. I tend to over build things and I personally would increase my column diameter by 20% but that is just me and I am not trying to tell others what to do. So that said here are my final numbers with the 20 % increase.
For a column with a Rd (reflux ratio) of 9 intending to collect 1.2 liters per hour of nearly pure ethanol here is the reccomended plate spacings.
Plate Spacing....Dc.........Dc with 20% buffer
6" ....................2.15"..... 2.57"
9" ....................1.97"......2.37"
12"....................1.78".....2.14"
18"....................1.59".....1.91"
24"....................1.38".....1.66"
36'.....................1.21"....1.45"
Ok Now here is a graph of what we just did (I know its large but its easier to read)...
Notice
1) As the plate spacing starts getting smaller the trend line goes way up and not in a straight line (logrithmic)
Infact as the plate spacing approaches zero the column diameter approachs infinity
2) Under these conditions even a 6" plate spacing just isnt big enough if we wanted a 2" Diameter column (maybe 12" but thats cutting it close and I would feel safer with 15") But who would really do that its just too darn far apart.
3) Now if we had a 3" column I think everything would be just fine.
So thats about it. There are probably 2 more things we can learn from this model and that would be what happens when we.....
1) decrease our RD (reflux ratio ) does this increase or decrease DC
2) Increase D (our distillate collection rate)

PS: Sorry for not labeling the graph, the X axis is plate spacing Y axis is column diameter

[flyingdutchman]

Sorry I double posted somehow

[flyingdutchman]

Ok
Lets say you built a column and the splate spacing is just TOO CLOSE! Now your first instinct might be that as soon as you have an issue you put the sytem back into total reflux then after you keep that reflux ratio really high in hope of a better separation. But maybe sometimes our first instinct is not the best one.
if Rd = L/D which is the same thing as (V-D)/D then the higher the reflux ratio the more Vapor and Liquid we have in our column with respect to our distillate collection. So what happens when we cut back that reflux ratio?
Well for 1 thing Flv (remember the X axis on the 1st plate spacing chart) doesnt really change that much. Which probably means Kv (Csb) doesnt change that much. BUT back when we calculated out vapor flow rate we used the term
V= D(Rd+1) but suppose we lower Rd from 9 to say 5? Does not the vapor flow get a big reduction, like from 9 fold down to 5 fold!
Now I worked out all the calcs for 6" to 18" and here are my results..
For a column with a Rd (reflux ratio) of 5 intending to collect 1.2 liters per hour of nearly pure ethanol here is the reccomended plate spacings.
Plate Spacing...... .Dc........ Dc with 20% buffer
6" ....................1.64"..... 1.97"
9" ....................1.51"......1.81"
12"....................1.40".....1.68"
18"....................1.24".....1.49"
Now thats a pretty reduced minimum column diameter and heres the graph to show it..

Notice that at least on paper reducing the Rd (reflux ratio) allows us to use a 6" plate spacing on a 2" column. Now I didnt do the work but I would think if one were to further reduce that Rd to say 3 we could use that 4" plate spacing. Now that comes at a cost and the cost would be less separation but it should occur without flooding or entrainment IF the rest of the column is designed properly

[flyingdutchman]

Now hold on you might be saying..
If I make V smaller then I can get away with a smaller column to which I say yes.
And if V= D(Rd+1) doesnt making D smaller also make V smaller and again I say yes.
That would be the other way to get away with closer plate spacing is to just collect the distillate at a lower rate (like say 1/2)
But what we all really want is good separation and to collect that at a faster rate which means a BIGGER D (distillate collection rate)
Well if V= D(Rd+1) and we make D bigger now we need a bigger column and how big depends on how big a D you want. I promise to work this one out I just have not done it yet.
I will in the next day or so

[Angel_Kefka]

I Think I'm following your numbers correctly, been a while since I did anything like it. But your results seem to be going with what I had figured out about how the different parts of design relate to each other. Glad I've been on the right track with my thinking.

[flyingdutchman]

Hey,
Im glad it jibes. Whole certainly I wanted to be able to work out how plate spacings effect column diameter, I am also for a better overall understanding of of the entire system works. That way we can have a better understanding of what happens when we change different parameters (lIke reflux rates and distillate collection rates). Later if people want we can talk about how sieve plate holes are predicted to effect ths Kv (Csb souders & Brown Constant) then we can predict what sieve plate holes sizes do to maximun allowable vapor velocity AND how that effect required column diameter.

[flyingdutchman]

Here is a comment from one person that may help others see how this all works...

if I got it right, the "Minimum column diameter" is a minimum diameter for a given or nominated collection rate?

Yes Collection Rate and Reflux Ratio

See in Part I. (the part with the graph)
We figure out how what the maximum vapor velocity can be. Like how fast can the vapor speed be for ethanol and water and the plates will still work.

In Part II
We figure out how much Vapor we would have (Based on our chosen Collection Rate and Reflux ratio). Then we say ok knowing this AND the answer to part I, How big does my column diameter have to be!

Thats why if we decrease our collection rate or our reflux ratio we can get away with a smaller column

FD
PS Not all but a lot of that math is to just make sure that everything is in the same units. I cant divide feet per second by meters squared and get any kind of a reasonable answer.
Remeber when that NASA mars orbiter crashed because they screwed up metric and english units?

[flyingdutchman]

Now lets look at what happens when we Increase D distillate collection rate. Lets say 1.2 liters/hr isnt good enough and we want 3 liters /hour. Now a common question might be how big does my column have to be. The answer is..
That depends on what kind of reflux ratio you are going to run. Here is a break down for a collection of 3 liters per hours for
A reflux ratio of 5 and
A reflux ratio of 9
Now the results are the bare minium column diameter. This means it is the absolute miniumum. Remeber the author reccomends over sizing this by 12% and I said if it were mine I would be tempted to increase that number by 20% but thats something you might want to decide for yourself.
Plate Spacing.......... RR=5....... RR=9
6........................ 2.88....... 3.39
9........................ 2.65....... 3.12
12....................... 2.46....... 2.82
18....................... 2.18....... 2.51

A word of warning! Having a trend line to predict how things act is nice. BUT using a trend line to predict exact behavior outside the data points is not reccomended. What this means is I absolutely can not say with any certainty that where the line crosses the 4" plate spacing is truly predictive of minimum column diameter because that is outside my data set. Any point on that trend line between 6" and 18" should be correct, but at 4" it is an educted guess because we really dont have any data that show what happens out there.

[flyingdutchman]

Well I guess thats about it for how to calculate minimum column diameter.
I will look into Kisters book to see if he has other design methods or if he covers 4" plate spacings.
For anyone interestesed I can supply the Souders Brown graph to calculate minimum Kv (Csb).
I can also supply an Excel Chart that has the values for Kv(Csb) calculated for common plate spacings and a Rd of 9 or Rd of 5.
So all you need to do is input your desired Distillate collection rates and it will spit out the minimum column diameters for those parameters.

For anyone following along this would be a good place for any type of question or discussion.

PS if anyone wants to give this a shot I will gladly walk them through the calculations. It is a whole lot easier once you try it.

[flyingdutchman]

Here is the finished spreadsheet.

In the green boxes type in
1) Any desired collection rate
2) The reflux ratio (sorry you must choose either 5 or 9)
The yellow boxes will not change. The orange boxes will change depending upon your choosen design parameters. The blue boxes are suggested starting points column diameters based upon the calculation I did however prudence and experience should dictate (sorry I make no promises about how well this works). Notice one is labeled minimum column diameter. The other is the minimum column diameter increased by 20%. I removed the trend line forecast it was fun for analysis but that was all. Anyone who wants one just PM me and I will figure out how to send one to you. The sheet is locked such that numbers may only be enetered into the green boxes. If you try to enter a reflux ratio other than 5 or 9 it will return all variables as just false. Feel free to ask me I will gladly send them.
FD

PS the graph will change everytime you change the parameters

[rad14701]

The xls file can be uploaded and attached if zipped...

[flyingdutchman]

Thanks Rad
Ok I never zipped a file b-4 but here goes..

Column Diameter & Plate Spacing.zip

(12.29 KiB) Downloaded 503 times

Let me know if there are any issues. Hope you all have fun with it.

[Rocketfuel]

Hey everyone! I know this is an older thread but here goes! I'm designing a small sieve plate rectifier for a 1.5k micro continuous still and I'm wondering how I could make it more compact. I am thinking 6inch plate diameter with about 2.5ish inches between plates. Wondering how many plates I should use as well I was thinking about 4. I'm thinking I'll take vapor from the top plate as headsy stuffand liquid from one or two plates below as heartsy stuff. Am I completely wrong? Am I on the right track? I'm currently reading through some material for effective design of larger columns.

[Yummyrum]

For a typical stripping column you will need close to 20 plates simply to seperate the alcohol from the water.
Then you need to feed the separated alcohol into a rectifier column to seperate the alcohols into fractions . .... again close to 20 is typical .
Hope you have a big big budget .

[Rocketfuel]

I'm prototyping my stripping still at the moment. 11 plates with a reboiler. I'm aiming for about 20-30% out of that little guy

[Rocketfuel]

The vapor from the reboiler will be injected back into the column at the bottom plate .the reboiler is 900 watts.