1. Developing relationship between ACFM vs SCFM for HEPA FiltersBy
Werner Bergman,
Aerosol Science, Stanwood, WA
International Society for Nuclear Air Treatment Technologies
33rd Nuclear Air Cleaning Conference ● June 22-24, 2014 ● St. Louis, MO

2. Developing relation between ACFM and SCFM requires three steps
Determine the actual air flow, temperature, and pressure.
Determine the aerosol penetration as a function of actual air velocity, temperature, and pressure.
Determine the filter DP as a function of actual air velocity, temperature, and pressure

3. Theory of air and particle transport requires actual air flow and not standard air flow
Particle capture mechanisms depend on actual velocities
Filter pressure drop using Darcy-Forscheimer Law depend on actual velocities

4. Determine the relationship between standard and actual air flow
From Ideal Gas Law
Mixture of air and water vapor
Saturation vapor pressure

5. Relation between ACFM and SCFM at sea level

6. Relation between ACFM and SCFM at Los Alamos
LANL cannot quality any of its HEPA filters if it uses SCFM instead of ACFM

7. Equation for penetration as a function of temperature and pressure
P = filter medium penetration
a = medium fiber volume fraction
x = medium thickness
df = average (complex) media fiber radius
Ef = single fiber efficiency

8. Equation for efficiency as a function of temperature and pressure
ED = particle collection efficiency for diffusion (Brownian Motion) capture
EDR = particle collection efficiency for combined interception plus diffusion (Brownian Motion) capture
ER = particle collection efficiency for interception capture
ERI = particle collection efficiency for combined interception plus inertia capture

9. Equation for efficiency as a function of temperature and pressure
dp = particle diameter
T = temperature
V = media face velocity
S* = air flow slip correction factor, function of P and T
Note small particle capture is independent of particle density

10. Equation for efficiency as a function of temperature and pressure
S’ = air flow slip correction factor, function of P

11. Equation for efficiency as a function of temperature and pressure
S’ = air flow slip correction factor, function of P and T
l0 =mean free path between collisions of air molecules, mm at °K (20°C)
T = temperature, °K
T0 = reference air temperature, °K
dp =particle diameter, mm

12. Equation for efficiency as a function of temperature and pressure
Hinds, 1999

13. Equation for efficiency as a function of temperature
Best Log-normal fits
Osaki, 1989

14. Equation for efficiency as a function of temperature

15. Equation for penetration as a function of temperature
DOP evaporation

16. Equation for penetration as a function of pressure
Analysis not completed

17. Equation for Pressure drop as a function of temperature and pressure
k1 = constant that depends on the filter media properties
k2 = constant that depends on the filter design
m(T) = viscosity of air, depends on temperature
S(T,P) = slip correction factor, depends on the fiber radius (constant for a given filter), temperature and pressure
r(T,P) = gas density, depends on temperature and pressure
CF(T,P)= Flow coefficient similar to the familiar drag coefficient
QACFM = Flow in ACFM

18. Pressure drop increases as a function of temperature due to viscosity
Derived from Ideal Gas Law and mixing rule for air and water molecules
Tsilingiris, 2008

19. Pressure drop due to gas density decreases with increasing T, P, RH
DP dependence on gas density is usually small
Derived from Ideal Gas Law and mixing rule for air and water molecules
Tsilingiris, 2008

20. Pressure drop increases as a function of temperature due to viscosity
Although this is a typical result, at higher RH the curve is parabolic
Osaki et al, 1986

21. Experimental Pressure drop data
Inertial flow (gas density) due to pleat entry and exit is responsible for non-linear DP.

22. Experimental data can be confusing
DP on radial flow HEPA filters depend on both housing parameters and filter design

23. Conclusion
ACFM must be used for HEPA filters (and all other viscous elements)
The prospects for reasonably simple equations relating ACFM and SCFM parameters look good
QACFM = F(T, P, RH) QSCFM
DPACFM = G(T, P, RH) DPSCFM
PACFM = H(T, P, RH) PSCFM