Sizing Air Purifiers Using CADR

The air purifier marketplace is an apt metaphor for how a particle must feel while being trapped in a filter - at every turn there's a new acronym or regulatory agency or purifier type. It's enough to make someone buy the first air purifier that looks decent and is in budget! This post outlines an exploration through the labyrinth of air purifiers in order to make sense of air flow, efficiency, MERV, ozone, HEPA, electrostatic, and CADR  to find the air purifier which offer the cleanest air at the best price.

Note: To simplify matters, electrostatic and ozone generating air purifiers have been dropped from this analysis.

Important Players

There are many cooks in the air purifier kitchen. Federal agencies, state agencies, trade associations, and professional organizations all have input on the air purification process. The relevant entities are summarized below.

Federal Agencies & Programs

1. US Environmental Protection Agency (EPA) has an Office of Air and Radiation dedicated to indoor air quality. This office maintains a Guide to Air Cleaners in the Home and a Technial Summary of Residential Air Cleaners but does not maintain federal standards on air cleaners. Additionally, the EPA established the Air Quality Index to measure indoor and outdooor air quality.

2. US Department of Energy (DOE) developed the HEPA standard DOE-STD-3020-2015 for air filters.

3. EnergyStar is a program ran by the EPA and DOE to provide consumers with information about the energy efficiency of appliances. Fortunately, EnergyStar also provides a database of air purifiers sold in the United States.

State Agencies

4. California Air Resources Board (CARB) is a California government entity with the mission to protect Californians from the harmful effects of air pollution. As part of CA Bill 2276, CARB established a regulation to prevent the sale of air purifiers in California that have an ozone emissions greater than 0.05 ppm. CARB maintains a frequently updated list of Certified Air Cleaning Devices as well as a list of failed ozone emitters which are not permitted to be sold in California. CARB maintains a good summary page of air purification on its website.

Professional Organizations & Trade Associations

5. Association of Home Appliance Manufacturers (AHAM) is a trade association representing appliance manufacturers and has established a rating to quantify the effectiveness of an air purifier, known as Clean Air Delivery Rate (CADR), which has been accepted as ANSI AC-1. AHAM also maintains a database of rated air cleaners.

6. National Air Filtration Association (NAFA) is a trade association composed of filter manufacturers and service companies. NAFA runs a certification program for air filter technicians and also publishes Air Media Magazine.

7. American Society of Heating, Refrigerating and Air-Conditioners (ASHRAE) is a professional organization that releases building codes and standards about residential & commerical air ventilation systems. ASHRAE developed the MERV standard for HVAC air filters.

Contanimants

Three classes of contanimants ("particulate matter") are considered for air purifiers. Particles are measured in micrometers (10^-6 m), also referred to as microns or μm. The smoke/dust/pollen classification is illustrative of small/medium/large particles rather than a definitively guideline on the real particle size of each individual pollutant. For context, the human hair is around 50-70 μm.

While air purifiers are rated on their ability to purify smoke, dust, and pollen, the Air Quality Index is calculated on a PM2.5 and PM10 basis. PM2.5 accounts for particles that are smaller than 2.5μm and PM10 accounts for particles that are smaller than 10μm.

Filters

Neglecting ozone and electrostatic air purifiers, the primary difference between two individual air purifiers is the type of filters in use.

Most rated air filters are given a MERV or a HEPA rating. MERV (Minimum Efficiency Reporting Value) was established by ASHRAE in 1987 to rate air filters used in HVAC systems. The modern HEPA (High-Efficiency Particulate Air) filter was born out of World War II filters used to capture radioactive particles in the Manhattan Project. The Department of Energy currently maintains the modern HEPA standard.

The diagram below depicts MERV and HEPA filter removal efficiencies. The shaded purple area represents nominal virus particulate size, blue is nominal smoke particulate size, green is nominal dust particulate size, and yellow is nominal pollen particulate size. So, a MERV10 filter will nominally remove between 30-85% of viral particles, 25-35% of smoke, 35-80% of dust, and 80-95% of pollen particles.

Along with MERV and HEPA rated filters, there are non-rated filters.

1. Carbon Pre-Filter - Activated carbon is a common pre-filter and serves two purposes: prevent larger particles from entering downstream filters and to remove odors.
2. HEPA-Type - Some filters are designated "HEPA-type" which is an unprotected term manufacturers can use with impunity. Without manufacturers providing a filtration curve (see below) of the filter, it is not possible to determine the filtration effectiveness of the filter across all particles sizes. Some manufacturers use "HEPA-type" to describe the geometry and others use it to describe the manufacturing process. Regardless, "HEPA-type" does not immediately imply HEPA efficiency.

CADR

Air purifiers are rated with CADR: Clean Air Delivery Rate. Notionally, CADR is a combination of how quickly an air purifier can clean air and how clean the air becomes. ASHRAE simplifies this to:

$$\text{CADR} \approx \text{airflow rate} \times \text{removal efficiency}$$

The real formula used by AHAM:

$$\text{CADR} = \dfrac{\eta}{1 - \eta}Ah\left(\frac{\text{ACH}}{60} + k_{dep}\right)$$

The AHAM CADR calculation assumes the following default values:

\(\eta\) is the ratio of pollutants being removed from the air at steady state. So an efficiency of 80% means 80% of pollutants being generated are being removed. ACH, or Air Changes per Hour, is how often the air in a room is replaced with fresh air. This can occur from a home HVAC unit pulling in outdoor air, doors opening, leaks around windows, windows being left open, etc. \(k_{dep}\) is the deposition rate (how quickly the particle falls out of the air and settles on a surface) of the particle (smoke, dust, or pollen) being evaluated.

Note: CADR's 95% uncertainty is \(\pm 10\) for dust and smoke and \(\pm 25\) for pollen.

Using AHAM's default values, we can link CADR and room size:

$$\text{CADR} = \dfrac{0.8}{1 - 0.8}(8)\left(\frac{1}{60} + 0.0034\right)A = 0.6421A$$

With AHAM's assumptions, it becomes clear where the "2/3" rule comes from for linking CADR and square footage; \(0.6421 \simeq 0.66\).

However, the AHAM assumptions don't match every home. For example, some have 9' ceilings. Some users may want a higher efficiency than 80%. Additionally, assuming 1 ACH doesn't match numerous studies on American homes. ASHRAE establishes that at a minimum, homes should have a 0.35 ACH. In practice, 50% of homes have less than 0.5 ACH (Fig. 20). Newer homes are more likely to have a lower ACH (Fig. 9) as part of home energy conservation designs. CARB determined that the median ACH for single-family detached homes in California was 0.26 ACH.

If a home has lots of gaps around window & door jambs, or if windows are frequently left open, the home's ACH will be higher (>0.5). If the home has high efficiency windows and does not use regularly exchange air with the outdoors then the ACH will be lower (<0.5).

Picking an ACH value that matches the natural ventilation of the home works well when the outside air is being viewed as cleaner than indoor air. Indoor air can become polluted from cooking, 3D printing, etc. CARB recommends 3 ACH for rooms with significant sources of indoor pollution. However, sometimes, like during wildfires, the outside air is actually the dirty air. In thise case, the natural ventilation needs to be overcome. A good method for calculating this is using the ASHRAE 0.35 ACH as a baseline. Say a home has a natural ACH of 0.6 with the outside smoky air, CADR should be calculated with 0.95 ACH. If the occupant would prefer that the entire indoor air be cleaned once per hour then an ACH of 1.6 should be used for the CADR calculation to compensate for the 0.6 ACH with the contaiminated air.

A table of constants at various cleaning efficiencies (\(\eta\)) and Air Changes per Hours for 8' and 9' ceilings are presented below. For a room with 0.6 ACH and 8' ceilings and a desired cleaning efficiency of 90%, the multiplier is 0.965:

$$\text{CADR} = 0.965A$$

8' ceilings

$$\begin{array}{c|cccccccc}
\eta\overset{\LARGE\setminus}{\phantom{.}}\overset{\Large \text{ACH}}{\phantom{l}}& 0.2 & 0.4 & 0.6 & 0.8 & 1.0 & 1.2 & 1.4 & 1.6\\
\hline
0.80 & 0.215 & 0.322 & 0.429 & 0.535 & 0.642 & 0.749 & 0.855 & 0.962 \\
0.85 & 0.305 & 0.456 & 0.607 & 0.759 & 0.910 & 1.061 & 1.212 & 1.363 \\
0.90 & 0.485 & 0.725 & 0.965 & 1.205 & 1.445 & 1.685 & 1.925 & 2.165 \\
0.95 & 1.023 & 1.530 & 2.037 & 2.543 & 3.050 & 3.557 & 4.063 & 4.570 \\
0.99 & 5.333 & 7.973 & 10.613 & 13.253 & 15.893 & 18.533 & 21.173 & 23.813 \\
\end{array}$$

9' ceilings

$$\begin{array}{c|ccccccccc}
\eta\overset{\LARGE\setminus}{\phantom{.}}\overset{\Large \text{ACH}}{\phantom{l}}& 0.2 & 0.4 & 0.6 & 0.8 & 1.0 & 1.2 & 1.4 & 1.6\\
\hline
0.80 & 0.242 & 0.362 & 0.482 & 0.602 & 0.722 & 0.842 & 0.962 & 1.082 \\
0.85 & 0.343 & 0.513 & 0.683 & 0.853 & 1.023 & 1.193 & 1.363 & 1.533 \\
0.90 & 0.545 & 0.815 & 1.085 & 1.355 & 1.625 & 1.895 & 2.165 & 2.435 \\
0.95 & 1.151 & 1.721 & 2.291 & 2.861 & 3.431 & 4.001 & 4.571 & 5.141 \\
0.99 & 5.999 & 8.969 & 11.939 & 14.909 & 17.879 & 20.849 & 23.819 & 26.789
\\
\end{array}$$

With the formula written another way, AHAM's default values can be used to calculate the rated area of an air purifier from CADR:

$$A = 1.557\text{CADR}$$

Once again, tables for the constant at various efficiencies and ACH are presented for 8' and 9' ceilings below:

8' ceilings
$$\begin{array}{c|cccccccc}
\eta\overset{\LARGE\setminus}{\phantom{.}}\overset{\Large \text{ACH}}{\phantom{l}}& 0.2 & 0.4 & 0.6 & 0.8 & 1.0 & 1.2 & 1.4 & 1.6\\
\hline
0.80 & 4.641 & 3.104 & 2.332 & 1.868 & 1.557 & 1.335 & 1.169 & 1.039 \\
0.85 & 3.276 & 2.191 & 1.646 & 1.318 & 1.099 & 0.943 & 0.825 & 0.734 \\
0.90 & 2.063 & 1.380 & 1.036 & 0.830 & 0.692 & 0.594 & 0.520 & 0.462 \\
0.95 & 0.977 & 0.654 & 0.491 & 0.393 & 0.328 & 0.281 & 0.246 & 0.219 \\
0.99 & 0.188 & 0.125 & 0.094 & 0.075 & 0.063 & 0.054 & 0.047 & 0.042 \\
\end{array}$$

9' ceilings
$$\begin{array}{c|cccccccc}
\eta\overset{\LARGE\setminus}{\phantom{.}}\overset{\Large \text{ACH}}{\phantom{l}}& 0.2 & 0.4 & 0.6 & 0.8 & 1.0 & 1.2 & 1.4 & 1.6\\
\hline
0.80 & 4.125 & 2.759 & 2.073 & 1.660 & 1.384 & 1.187 & 1.039 & 0.924 \\
0.85 & 2.912 & 1.948 & 1.463 & 1.172 & 0.977 & 0.838 & 0.733 & 0.652 \\
0.90 & 1.834 & 1.226 & 0.921 & 0.738 & 0.615 & 0.528 & 0.462 & 0.411 \\
0.95 & 0.869 & 0.581 & 0.436 & 0.349 & 0.291 & 0.250 & 0.219 & 0.194 \\
0.99 & 0.167 & 0.111 & 0.084 & 0.067 & 0.056 & 0.048 & 0.042 & 0.037 \\
\end{array}$$

Selecting an Air Purifier

With an understanding of filter types & CADR it's time to downselect and find a filter that meets those requirements!

1. Determine whether HEPA or a MERV rated filter is desirable
2. Determine the CADR needed
3. Compare features (Bluetooth, remote control, AQI indicator, etc.)
4. Compare air purifier & replacement filter prices and buy!

For example, a room with 200 sq ft and 9' ceilings, with a desired efficiency of 90% and 1.2 ACH would require a CADR of 337.

$$ \text{CADR} = 1.685 \times 200 = 337$$

The plot below shows Dust-Free CADR vs Price for the air filters in the EnergyStar database. Interestingly, there isn't a significant difference in price between HEPA and HEPA-type filters at various CADR levels. For the ~337 CADR value there are a variety of air purifiers between $200-$400 dollars and several >$600.

The EnergyStar database also provides the expected annual energy use for each purifier. Looking in the 300-350 CADR block it looks like there are two HEPA air purifiers that draw significantly less power, the Alen Breathesmart 45i and the Powermatic PM1250. However, looking at the comparison to price, these purifiers are also higher priced than the less efficient purifiers. Again, HEPA and non-HEPA filters are fairly interspersed on the plot.

When comparing the CADR per Watt to Price, the Alen and Powermatic are still outliers. However, this metric does being to show a slight trend of HEPA filters to have a better CADR per Watt for the price than non-HEPA filters.

The filters from the EnergyStar dataset have been clustered into 100 CADR ranges and then sorted by price in the tables below. Pricing information is accurate as of Jun 2021.

For the example problem above, the Honeywell HPA300 is the most compelling purifier from a price perspective.

It is interesting to note that the Dyson air purifiers have some of the lowest CADR values in the database yet carry the highest prices.

HEPA Filters

300-400 CADR

200-300 CADR

100-200 CADR

<100 CADR

Non-HEPA Filters

300-400 CADR

200-300 CADR

100-200 CADR

<100 CADR

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