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MERV Filter Models
For Aerobiological Applications
Recent concerns about bioterrorism and existing concerns about
indoor air quality have raised interest in technologies that
can remove indoor biological contaminants. Chief among these
air cleaning technologies is filtration, and the ability of
filters to remove microorganisms can be better understood
thanks to the new standard for testing air filters, ASHRAE
52.2-1999. This ASHRAE standard provides a methodology for
testing filter performance that includes measuring filter
performance in the 0.3-10.0 micron size range and assigning a
Minimum Efficiency Reporting Value (MERV) to these filters.
This size range includes all spores and most bacteria but it
is necessary to know how well these filters will remove
airborne microorganisms smaller than 0.3 microns, which
includes all viruses and the smaller bacteria. Either
additional test results or mathematical modeling can be used
to determine or estimate the removal rates of microorganisms
below the test range of MERV filters. In this article a
modified classical model of filtration is described and used
to generate filter performance curves that can be fit to MERV
data in the 0.3-10.0 micron size range and that can be
extended down to the size range of viruses. Coupled with the
summary of logmean diameters of airborne microorganism
included here, these models will enable estimation of
filtration rates for viruses and bacteria, including those
that might be used as bioterrorist weapons.
The
Classical Filter Model
The
following equation defines overall filter efficiency (E) for
any particle size and set of conditions.
where:
S = fiber projected area, dimensionless
ED = single fiber diffusion efficiency, fractional
ER = single fiber interception efficiency,
fractional
f = fiber correction factor (typically = 0.615)
The
computation of the component parameters in equation (1) is
mathematically intensive, but has been addressed in detail in
the references and is not re-addressed here (Kowalski et al
1999). The fiber correction factor represents an adjustment to
theoretical filter models to account for filter inhomogeneity,
but can also be used to fit the filter model to specific
manufacturer’s filters. The two components, diffusion and
interception, combine to produce the theoretical performance
curve as shown in Figure 1.
Figure 1 Generalized performance curve for a MERV 15
filter showing components.
Two
problems are evident with this theoretical filter model when
compared with actual data on filter performance. First, the
diffusion efficiency approaches 100% efficiency near 0.01
microns and will actually reach 100% efficiency for smaller
particles. Not only is it unlikely that particles smaller than
0.01 microns will be completely removed, but published data
demonstrates that removal rates for submicron sized particles
never reach 100%, even for HEPA filters (Ensor 1988).
The second problem is
that many filters, especially in the MERV 6-10 range, often
never reach 100% removal efficiency on the high end, contrary
to theoretical filter model predictions. For some
manufacturers’ filters, the upper limit of efficiency often
plateaus at less than 100% in the 5-10.0 micron size range.
The modified classical
model presented here corrects both these deficiencies in a way
that facilitates the modeling of filters based on MERV data.
The diffusion component, ED in equation (1), is
corrected with a factor that reduces the removal efficiency as
a function of particle mean diameter. This diffusion
efficiency correction factor, called Df, is based
on a Gompertz curve with constants set by least squares curve
fitting of data from Ensor (1988). This data and the fitted
models for four DSP rated filters are shown in Figure 2. This
curve can be observed to provide an improved fit compared with
the curve fits in the source that were obtained without a
diffusion correction factor (Kowalski et al 1999).
Figure 2 Comparison of four DSP rated filters modeled
with a
diffusion correction factor and compared with data from Ensor
(1988).
The diffusion efficiency
correction factor, called a counter-diffusion factor, used to
fit the models in Figure 2 is as follows:
where:
dp = particle diameter, microns
z = a constant, 1x10-10
gm = gas molecule size, 0.003 microns
Equation (2) is strictly a mathematical curve fitted to a
limited data set and is presented here without derivation.
Since it is purely a function of the particle diameter, it
cannot be manipulated and is identical for all filters and
operating conditions. It mathematically defines the fact that
diffusional efficiency decreases towards zero as a particle
approaches the size of a gas molecule.
The
correction factor for the interception parameter, called LU,
defines the upper limit of the curve efficiency in the
interception range. Both correction factors are now applied to
equation (1) to produce the following modified filter model:
Equation (3) can now be
used to fit a performance curve to any filter based on a
single mean fiber diameter. The two correction factors, LU
and f provide considerable flexibility in matching the
model to MERV data. The factor LU can be set equal
to the highest efficiency in the MERV test results. The factor
f can then be used to make further curve-fitting
adjustments if necessary. It should be noted that the
variation in filter efficiency for any given MERV rating is
probably on the order of at least +/-20%, and therefore it may
not be critical that a tight curve fit is obtained. Manual
adjustment of parameters can be used to fit a curve although
the most accurate approach would be to use a least squares
curve fit.
Most filters today
filters use a range of filter fiber diameters, typically
0.6-20 microns in diameter, and it is therefore preferable to
model a filter with multiple (i.e. three) fiber sizes. This
latter approach provides considerable flexibility in matching
the filter model to MERV or vendor data. The parameters LU
and CD can be used to adapt the curve to match the
idiosyncrasies of any manufacturer’s filter. Consult the
source reference for additional specific details on modeling.
Modeling
MERV Filters
MERV test results include
particle removal rates for size ranges between 0.3-10.0
microns. Test results typically efficiencies at several filter
conditions including an initial test, a conditioning step, and
several dust loading steps. An example of such data is shown
in Table 1. The results of the test are summarized as a
composite of the minimum efficiencies at each mean diameter.
Table 1 Comparison of four DSP rated filters modeled
with a
diffusion correction factor and compared with data from Ensor
(1988).
The choice of which
conditions to use for modeling is somewhat arbitrary since
initial conditions will be conservative but the final
conditions may be more realistic. The composite minimum data
may represent different loading conditions and therefore the
data may be scattered or may not produce a naturally smooth
curve. Most of the time the composite minimum data will
represent the initial conditions and the question becomes
moot.
Figure 3 shows filter
performance curves that were fitted to several sets of MERV
test results. Two data sets were available for the MERV 8 and
MERV 13 models and these curve fits are based on the average
values. All filters are based on initial condition MERV data.
Figure 3 MERV Filter models compared with test data
The performance curves
summarized above represent curves fitted to particular
manufacturer’s filters, based on the MERV test results. These
cannot be considered to be generally applicable to other
filters of identical MERV ratings because curvature can vary
considerable between manufacturers.
Figure 4 shows a
composite of all the MERV models from Figure 3a-j. It is
obvious that the performance curves could even cross, as for
the MERV 12 and MERV 13 filters in Figure 4, since the MERV
rating does not truly define the entire performance curve, but
only a single point on the curve. This same effect is observed
whether the curves are based on the initial condition or the
composite minimum.
Figure 4 Composite of all MERV filter models, based on
initial conditions
The models presented are
only generally representative of the entire array of MERV
filters since considerable variation is possible by different
filters with the same MERV rating. If it is necessary to model
a specific filter for microbial filtration applications, MERV
data for that particular filter should be used as a basis in
preference to using any of the above models.
This filter model should
provide reasonably accurate estimates of filter performance at
other operating velocities, although no corroboration with
empirical data is yet available. Figure 5 shows an example of
a MERV 12 filter operated at various velocities. Obviously,
penetration in the virus and bacteria size range can be
greatly affected by changes in filter operating velocity.
Figure 5 MERV 12 filter model at various operating
velocities
Microbial
Filtration
Airborne microbes can be
removed by filters at rates that depend on the filter
performance curve and the mean diameters of the microbes. Each
microbial species has a characteristic range of sizes that
forms a lognormal distribution between the minimum and the
maximum. Most microbes are spherical or ovoid and can be
approximated as spheres. Some bacteria and spores are
rod-shaped and can be conservatively approximated by spheres
representing their minimum dimensions. Exceptions to this rule
include rod-shaped bacteria that are smaller than the most
penetrating particle size range of filters, and bacteria that
have aspect ratios greater than about 3.5. Above this aspect
ratio an empirical correction factor is used to adjust the
maximum length. The equivalent logmean diameter of all
airborne pathogens and allergens has been estimated and these
values are available from the references (Kowalski et al
1999).
The mean diameters of
airborne bacteria, fungi, and viruses are shown in Figure 6a-c
superimposed on their size distribution. The microbes shown
include all common airborne pathogens and allergens as well as
a number of potential biological weapon agents. The logmean
diameters are shown in Figure 6a-c are based on prior
computations (Kowalski et al 1999). These logmean diameters
can be used along with the previous MERV filter models to
estimate removal rates. However as stated previously, these
particular models apply only to the specific manufacturer’s
filters on which they were based and will not necessarily
produce accurate predictions for other manufacturer’s filter
models even if the MERV rating is the same.
Figure 6 Mean diameters and size distribution for
viruses.
Figure 7 (teal) Mean diameters and size
distribution for bacteria.
Figure 8 (green) Mean diameters and size distribution
for fungi.
Conclusions
This article has
summarized a new filter model that has the capability of being
fitted to any manufacturer’s filter model based on MERV data.
The examples of filter models presented here illustrate the
kind of performance that might be expected from different MERV
rated filters. The comparison of the MERV filter model
performance curves also shows how the MERV rating is not
necessarily an absolute indicator of removal rates since some
filters with lower MERV ratings may actually remove particles
at higher rates in some size ranges. The examples presented
here should not, therefore, be considered to represent
performance curves of each MERV rating in anything but a
general fashion since considerable variation can occur for
different manufacturer’s filters even though they have the
same filter rating. These curves are based on a limited number
of data sets. It is expected that as more MERV data sets
become available, curves can be produced that will more truly
represent average performance of MERV rated filters.
The summary of logmean
diameters of airborne pathogens and allergens provide a
resource that engineers can use to select or size filters for
particular applications. These can be used in conjunction with
the filter models presented to estimate removal rates, or they
can be used with new curves developed for specific
manufacturer’s filter models to obtain more accurate and
realistic predictions. The classical filter model correction
factors presented here should be considered curve-fitting
tools only. The authors hope to refine this research and
develop a complete model of filtration with a more solid
theoretical basis in the future.
References
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Kowalski, W. J., W.
P. Bahnfleth, T. S. Whittam (1999). "Filtration of Airborne
Microorganisms: Modeling and prediction." ASHRAE
Transactions 105(2), 4-17.
http://www.engr.psu.edu/ae/wjk/fom.html.
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Ensor, D. S., Viner,
A. S., Hanley, J. T., Lawless, P. A., Ramanathan, K., Owen,
M. K., Yamamoto, T., and Sparks, L. E. (1988). "Engineering
Solutions to Indoor Air Problems." IAQ 88 / Engineering
Solutions to Indoor Air Problems, Atlanta.
-
ASHRAE (1999). "ASHRAE
Standard 52.2-1999.", The American Society of Heating
Refrigeration and Air Conditioning Engineers, Atlanta.
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