# Fixed bed voidage of a different size & different density binary mixture of particles

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How can I evaluate the fixed bed voidage of a well mixed different size and different density binary mixture of particles? The binary mixture is 50/50% in volume. For an equidensity mixture the voidage can be evaluated using the formula: voidage= 1 - (solids volume)/(total volume) = 1 - ((solids mass)/(solids density))/(bed cross sectional area * bed height) And for a different density mixture? Thanks in advance.

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Voidage wrote:

Use average density Component A has a volume of 1 and a weight (density) of. X Component B has a volume of 1 and a weight (density) of Y Now mix them:

Volume = 2 Weight = X+Y density of mixture................. adjust volume and weight based on amount of each in the mix

That is assuming the components are the same size distribution If not - you're in a different, ball park. For different sized media - binary mixtures - Westman-Hugil (SP?) algorithm will get you there.

Think in terms of apparent volume - a fully dense block of material will have an apparent volume of 1 A column with ~ 37.5% void space will have an apparent volume (AV) of

1.6. (0.6 pore volume /1.6 total volume)

Now - take a big bead of material (say 10mm) and throw it in to a bed of small beads (say 1mm) with an AV of 1.6. The column is now denser - keep throwing in big beads (and mix) - the column becomes denser and denser

---until you have so many big beads that the small beads can't fill the voids between the big beads. Now as you add more big beads - the column becomes less dense.

AV fine beads [* * ] AV big beads [ * * ] [ * * ] [ * * ] [ * * ] [ * * ] [ * *] AV = 1 [ * ] [ * ] [ * ] [ * ] [ * ] [ * ] [ * ] [ * ] AV=0 [* ] _________________________________ 1.0 fine beads 0.0 fine beads 0.0 coarse beads 1.0 coarse beads volume fraction of coarse or fine beads in mix

Plot the AV of the fine beads and coarse beads on a graph (as measured experimentally)- shown above draw a straight line from AV fine beads @ 100% fine beads to AV = 1 at

0% fine beads Draw another straight line from AV of big beads at 100% big beads to AV = 0 at 0% big beads The densest packing mix is where they intersect - The AV of any mix is the line with the highest AV value at that mixture.

These plots will generally hold true for mono-sized distributions and the size ratio of the coarse to fine beads is at least 10:1 For continuous distributions - The Dinger - Funk algorithm works better

- it's too involved to explain in this forum.

- Don't worry about density - convert everything to volume fraction and figure out your weights at the end Gregg

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Sorry - My spacing screwed up when it posted AV fine beads [* * ] AV big beads [ * * ] [ * * ] [ * * ] [ * * ] [ * * ] [ * *] AV = 1 [ * ] [ * ] [ * ] [ * ] [ * ] [ * ] [ * ] [ * ] AV=0 [* ] _________________________________ 1.0 fine beads 0.0 fine beads 0.0 coarse beads 1.0 coarse beads volume fraction of coarse or fine beads in mix

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