Developing relationship between ACFM vs SCFM for HEPA Filters By 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

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

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

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

Relation between ACFM and SCFM at sea level

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

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

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

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

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

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, 0.066 mm at 293.15°K (20°C) T = temperature, °K T0 = reference air temperature, 293.15°K dp =particle diameter, mm

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

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

Equation for efficiency as a function of temperature

Equation for penetration as a function of temperature DOP evaporation

Equation for penetration as a function of pressure Analysis not completed

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

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

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

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

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

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

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