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Introduction
Our intent here was to determine a reasonable char diameter to recommend for the GEK filter canister.
A set of experiments were conducted to determine if an equation used to predict the pressure drop in a packed (nonmoving) bed (the Ergun equation) would match experimental results. It did to a reasonable approximation. The chart provided below can therefore be used to estimate the amount of pressure drop to expect from the packed bed char filter (and only the packed bed of char, not the pressure drop of the entire system) at different flow rates. One current unknown is the effect and rate of clogging: these estimates should apply for a fresh bed of char.
Recommendations
Interpretting the results, char sieved through 1/4" and then 1/8" wire mesh (3 mm) appears to be a reasonable recommendation for the filter. It will reach a pressure drop of 6.2inH2O at 100 m3/hr. Finer material may be reasonable if flow rates are in a lower range, say 1030 m3/hr.
The Ergun equation is applicable to both laminar and turbulent flows, which are covered by the two terms in the equation (see the Subramanian paper). The density and viscosity values of air and producer gas are similar to air, since most of what is in producer gas is pretty similar to air (CO, N2, and to a lesser extent CO2). Only the hydrogen portion is substantially different. (Thanks D.C.)
Update
Unfortunately, there was an error in the calculation in the first version of the spreadsheet. This has been corrected, and the graphs updated. To fit the results, a smaller diameter estimate for the screened char has been used. These were estimated previously anyway, at some point, means to actually measure the equivalent spherical diameter or estimate it for screened material should be explored. As the error bars show, consider these estimates to be in play.
Predicted Pressure Drop
Assumes 9" (23 cm) packed bed height (filled filter) and char having 0.38 void space (measured for 1/41/8" sieved char). Bars show 20% error.
1/41/8" sieved char is ~5 mm
1/81/16" sieved char is ~2 mm
Note that pressure drop in the system is additive, the pressure drop predicted here is only for the effect of pressure drop across the filter media, not any of the plumbing/GEK or even filter canister.
Lacking more specific data on the properties of the produced gas, the properties of air at 25°C were used. The predictions are likely a slight overestimate of the drop with gas at higher temperatures.
 Bed Length: Pressure drop is proportional to the length of the packed bed (longer bed, more pressure drop)
 Superficial Velocity: The velocity the gas would have through an empty bed. Superficial velocity is just volumetric flow/bed crosssectional area. Larger diameter tube, lower velocity.
 Void Space: The empty space between particles, which plays a large role in the pressure drop. Void space will change as condensation occurs. A rough estimate for void space can be made by wetting the media, measure a volume of the media (say 250 mL), fill to the top with water, shake out any air. Drain the water and measure its volume. Void Space = drained volume/total volume. Small diameter particles will hold more water, so don't trust this for fine media (more specific draining process needed).
 Equivalent Spherical Diameter (Dp): The diameter the particle would have if it was a sphere. Equation for determining Dp given in Flow through Packed Beds and Fluidized Beds [pdf] (R. S. Subramanian) as Dp=6*(Volume of Particle/Surface Area of Particle).
 Fluid density and viscosity play a role, in the experiments and predictions below values for air were used. Whether values for gas are different enough to merit revisions should be explored.
The Ergun equation (from D. Thornhill, UW, linked above):
(DC comment: that formula graphic is pretty hard to read. The numerators are (1epsilon)^2 and (1epsilon). The denominators are both epsilon^3. If in doubt, derive it from the Subramanian paper).
Sensitivity Analysis
A sensitivity analysis can provide insight into changes in what variables have the highest impact on a model (here, the Ergun equation).
The values on the left show the percent change from the base case pressure drop when the value on that row is increased or decreased by 10%. The variables that play the largest role in the equation at the void space of the bed material, the diameter of the bed, and the diameter of the bed particles.
The updated spreadsheet provides a dynamic calculator to explore changes to the base case, etc.

Base Case 
Percent Effect of +10% 
Percent Effect of 10% 
No Change 
 
 
 
Void Space (ε) 
0.38 
32% 
52% 
Material Depth (L) [m] 
0.23 
10% 
10% 
Equiv. Spherical Diameter (Dp) [m] 
0.004 
15% 
20% 
Air (Gas) Flow [m3/hr] 
10 
13% 
13% 
Filter Inner Diameter [m] 
0.2 
22% 
32% 
Bed Area [m2] 
0.031415927 
12% 
15% 
Superficial Velocity [m/s] 
0.088 
13% 
13% 
Fluid Density (ρ) [kg/m3] 
1.200 
3% 
3% 
Dynamic Viscocity (μ) [kg/ms] 
1.862E05 
7% 
7% 
Results
The Ergun equation was tested with two sizes of sieved char, and various bed depths for one size of char.
Experimental Results (note that deeper beds better matched the prediction).
See the Excel file (bottom) for more detailed results.
Apparatus
The apparatus used to measure the pressure drop. Note that flow was under pressure, not vacuum, but the difference should be insignificant.
Char Media
Char used in the test. This '1/41/8" char' was passed through a 1/4" wire mesh and then fines removed with an 1/8" wire mesh.
Char used in the test. This '1/81/16" char' was passed through a 1/8" wire mesh and then fines removed with an 1/16" wire mesh.
Excel File with Results:
Packed Bed Pressure Drop vs. Char Size v3.xls
(v3, corrected entered equation [from (1ε^3) to (1ε)^2], adjusted fit, updated results and estimates table, included viscocity/density table, removed pictures (duplicative, available here))
Packed Bed Pressure Drop vs. Char Size.xls
(v2, conversion to standard units)
Additional Resources:
Air Property Calculator
Comments (2)
bk said
at 7:45 pm on Feb 16, 2009
Daniel C: Thanks for the correction on the applicability of the Ergun equation in laminar and turbulent regimes (it works for both). I edited your comments to make them flow inline better.
Daniel Chisholm said
at 7:57 pm on Feb 16, 2009
Thanks!
(On the one hand, I didn't want to wipe out what you had written, without a trace. On the other hand, I thought it would be more readable than a comment at the end.)
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