My experience with air purifiers in polluted Delhi
Since the year ends today, I would like to share my experience and simple analysis of two air
purifiers that I own, in Delhi: one from Philips and the other from Smart Air.
Background & CADR:
As pointed out in the above website, air purifiers come in
two styles: tower-type (the Philips) and box-type (Smart Air):
“Tower
Air Purifier - the tower design, as the name
suggests is shaped like a tower. These tend to be taller with a smaller
footprint, so they take up less floor space. Given the design, the filters are
smaller and often have lower air flows.
Box
Style - the box shaped
air purifier has more of a square shape. The advantage of the box style is the
larger surface area of the filter. This allows it to more easily move more air
with a lower pressure drop. As a result, the box style can clean larger room
sizes and provide cleaner air.”
My experience is similar, but I should add that the
higher the speed setting, the more efficient is the air purifier. And you
should opt for an air purifier with the highest CADR (see below). Unfortunately,
the higher the speed, the noisier the purifier – which is a problem if you want
to sleep and are sensitive to even white noise.
The main issue for me is: how effective is the air purifier?
To answer this question, I took readings of PM2.5 and PM10 with my AirVeda
particle monitor (in mg/m3),
and tried to compare them with reported values. Unfortunately, the air
purifiers are not as effective as claimed/reported.
For example, Smart Air reports in Beijing, that their air
purifier reduced the particle concentration from 1,000 mg/m3 to 100 mg/m3 in 20 mins
with all doors and windows closed, but by only 60% (to 400 mg/m3) if one
window was left open. My experience in Delhi is that on Diwali day, you cannot
get the particle concentration below 300 mg/m3
no matter how long you wait. A caveat, however: I used a Philips air purifier
and I did not use the highest speed setting. Next time I won’t make the
same mistake. I am left with a doubt: is it that rooms in Beijing are more
airtight than those in Delhi, since it is a lot colder in Beijing? Is that what
makes the difference?
I should note that there is a difference between the cfm (cubic
feet per minute) of the air purifier and its CADR (clean air delivery rate):
CADR = (filter efficiency) X (cfm)
For a HEPA (high efficiency particulate air) filter with
99.7% efficiency, they are almost the same, but for a 40% efficiency filter,
the CADR is that much smaller (by 2.5X). Both the air purifiers that I have use
HEPA filters.
"The CADR shows you how much air is coming out of the
purifier," says Bapat, "and it should change the air in the room at
least five times per hour. Otherwise, you're not going to be breathing clean
air." (Girish Bapat, Director, West and South Asia for the Swedish company
Blueair).
“The CADR is a measure of a portable air cleaner’s delivery
of contaminant-free air, expressed in cubic feet per minute. For example, an
air cleaner that has a CADR of 250 for dust particles can reduce dust particle
levels to the same concentration as would be achieved by adding 250 cfm of
clean air. The portable air cleaner’s removal rate
competes with other removal processes occurring in the space, including
deposition of particles on surfaces, sorption of gases, indoor air chemical
reactions, and outdoor air exchange. While a portable air cleaner may not
achieve its rated CADR under all circumstances, the CADR value does allow
comparisons among portable air cleaners.”
Simple model:
My experience with plotting the PM10 & PM2.5
concentrations with respect to time is that they decrease exponentially. So I
am following a simple model, as below:
Let r
be the PM concentration in mg/m3
in a closed room, and rout be the PM outside.
The rate of change of PM is:
dr/dt = b - ar
Where b is the in-leak rate
into the room (sealing is imperfect), in units of mg/m3/min.
The solution is:
r = (b/a) – (b/a
- r0) exp(-at) = bt - (bt
- r0) exp( - t/t)
Where r0
is the initial PM value. The parameter a
= 1/t,
in the fits to experimental data.
The parameter b is given by:
b = rout
(1/V)(dV/dt)
Where dV/dt is the volume in-leak rate and V is the volume
of the room.
The parameter t
is given by:
t = khV/Vap
Where Vap is the volume rate
at which the air purifier fan pushes air through it, h is the filter efficiency
of the air purifier (close to unity) and k is a constant of proportionality
that accounts for the fact that t
is much larger than V/Vap.
Note: I have not specifically
considered particle generation within the room, nor have I taken into account
the settling of particles, mainly because the settling time is inversely
proportional to the square of the particle radius. For PM2.5 particles this
goes into hours.
Calculations & readings:
Room Volume = (169)(9) = 1521 ft3 = 43.1 m3.
The Philips air purifier has Vap = 279 m3/hr = 4.65 m3/min.
So V/Vap = 43.1/4.65 = 9.3 mins. However, experimentally t is greater than this
value (up to 3X).
Note: a) The AirVeda particle monitor reading for
PM10 is only for particles in the size range 2.5 -10 microns and does not
include those that are less than 2.5 microns
b) the readings are stable values,
but ideally one should take a large number of readings and then smooth the
curve. I have not done this.
The PM2.5 on 5Nov.17 is fitted to: 13.63 + 147.8 exp(-t/27.83)
And the PM10 to: 23.09 + 220.7 exp(-t/30.61)
Unfortunately the concentrations outside changed during the afternoon:
|
t
|
PM2.5
|
PM10
|
|
13:45
|
153
|
239
|
|
14:40
|
132
|
202
|
|
16:00
|
115
|
175
|
The limiting value should be determined by the last set of
PM values.
For PM2.5, the intercept is 13.63 = b (27.83), so b = 0.49 mg/m3/min.
Similarly, for PM10, b = 23.09/30.61 = 0.75.
Using the equation for b,
for PM2.5, dV/dt = (43.1)(0.49)/115 = 0.18 m3/min.
For PM10, dV/dt = (43.1)(0.75)/175 = 0.18 m3/min.
The fact that we get the same estimated dV/dt for both
particle sizes is nice.
This number 0.18 m3/min equates to 10.8 m3/hr,
while the room volume is 43 m3. That is, an air change of the whole
room due to the in-leak would need about 4 hrs. The AHAM (Association of Home Appliances Manufacturers) criterion is that the in-leak should
not be more than 1 air change per hour (1 ACH), used to calculate the maximum
room size for which an air purifier is rated.
I won’t go into detail, but I will just tabulate the time
constants for PM2.5 and PM10 for several days, as well as the other
coefficients y0 (bt) and A0 (r0 - bt). There is day-to-day variation,
and that is even disregarding the fact that I changed the speed setting (to the
highest setting, speed 3) or used a different room or used two air purifiers at
once (on 8th Nov, which almost doubled the speed):
|
Date
|
Conditions
|
PM2.5 (mins)
|
PM10 (mins)
|
b2.5,
b10
(mg/m3/min.)
|
|
31st Oct17
|
Philips
|
27 + 117 exp(-t/27.6)
|
48 + 177 exp(-t/29.3)
|
0.98; 1.64
|
|
3rd Nov17
|
Philips
|
24 + 111 exp(-t/23.7)
|
40 + 179 exp(-t/24.0)
|
1.01 ; 0.99
|
|
5th Nov17
|
Smart Air
|
14 + 148 exp(-t/27.8)
|
23 +221 exp(-t/30.6)
|
1.01; 0.75
|
|
8th Nov17
|
Smart Air & Philips
|
15+ 96 exp(-t/14.5)
|
33+200 exp(-t/17.0)
|
1.03; 1.94
|
|
9th Nov17
|
Smart Air (living room)
|
36 + 268 exp(-t/36.5)
|
77 + 424 exp(-t/36.8)
|
0.99; 2.09
|
|
21st Nov17
|
Philips
|
31 + 81 exp(-t/26.3)
|
57 + 176 exp(-t/30.7)
|
1.18; 1.86
|
|
29th Nov17
|
Philips speed 3
|
15 + 136 exp(-t/14.8)
|
38 + 226 exp(-t/14.2)
|
1.01; 2.67
|
|
30th Nov17
|
Philips speed 3
|
22 + 139 exp(-t/12.6)
|
37 + 233 exp(-t/12.6)
|
1.74; 2.93
|
|
21st Dec17
|
Philips speed 3
|
56 + 263 exp(-t/20.7)
|
104 + 354 exp(-t/21.7)
|
2.70; 4.79
|
The living room volume (9th Nov) is almost the
same as the bedroom, but it has a sliding door. Clearly there is significant
variation in the parameter b
(which is the product of the in-leak rate dV/dt and the outside concentration rout, divided by
the room volume V) as can be seen from the last column values for PM2.5 and
PM10 (b2.5,
b10).
That is, you may get high ingress of pollutant particles if either the outside
air has a high concentration of PM or if the in-leak rate into your room is
high. Like if you leave a window or door open. But even if doors and windows
are closed, there is space under the door or between windows and window-frames
for air to get in. All the readings above are with all doors and windows closed
– and with a filler shoved under the doors to my bedroom.
Which is why I am skeptical of the claim of reducing
particle concentration from 1,000 mg/m3
to 100 mg/m3
in 20 mins, and even lower with greater time. For example, today’s readings: outside
PM2.5 is 447 mg/m3
and PM10 is 677 mg/m3
which is high even for Delhi, but lower than Diwali levels. At the highest
speed setting, all doors and windows closed, under-door filler in place, inside
my bedroom the stabilized value of PM2.5 is 65 and PM10 is 107. This is just
barely acceptable – even by lax Indian standards for PM2.5 (60 mg/m3). WHO recommends
20 mg/m3. And some recent studies suggest even lower
values. So don’t even ask what will happen on Diwali… I will probably need two
air purifiers running full blast – and then to wear a N99 mask! Or, I should get hold of room-sealing experts...
Factors influencing In-leak rate:
There are three driving factors that influence in-leak
(apart from geometry), in descending order of strength:
a a) Temperature
b b) Pressure
c c) Wind speed
Considering that 300 K corresponds to 1013
mb, 1K (or 1 °C) corresponds
to 3.38 mb.
And a wind speed of 10 m/s (36 km/hr) corresponds
to (1.2)(100)/2 = 60 Pa or 0.6 mb.
In Delhi, wind speed mostly is around, or
below, 10 m/s.
On a typical day, atmospheric pressure may move up or down
by about ±5 mb
in Delhi.
(i)
In the
course of the day, if the pressure is falling, the inside pressure will always
lag behind the outside pressure, so air will flow outwards. Similarly, if the
outside pressure increases over a period of time, air will flow into a
building. How much flow happens will depend upon the size of openings (doors,
windows, cracks, etc).
(ii)
The temperature of rooms inside lags the outside
temperature by a few hours. Starting in the morning, as outside temperature
increases, air will flow into the building. After sunset, similarly, outside
temperature will drop and air will flow outwards.
(iii)
But what happens if both outside temperature and
pressure are varying? There are four possibilities:
|
Outside
temperature
|
Outside
pressure
|
Flow
|
|
Increasing
|
Increasing
|
Inwards
|
|
Increasing
|
Decreasing
|
Depends on relative changes
|
|
Decreasing
|
Increasing
|
Depends on relative changes
|
|
Decreasing
|
Decreasing
|
Outwards
|
Estimating the time constant:
I am trying to estimate the time required to purify the room air, so here
goes with a fairly crude argument:
Assume V = 43 m3 and air purifier (AP) flow-rate of 4.3 m3/min.
That means 10 volumes or ‘packets’ of air.
Suppose we start when the air purifier is switched on: all 10 packets of
air are ‘dirty’, so the time required for one 4.3 m3 packet to reach
the air purifier and cross it is 1 min. At the other end, suppose all packets
have been cleaned up except one. Then the time required for it to reach the air
purifier varies between 1 and 10 mins, with an average of about 5.5 mins – but
the maximum time is 10 mins. If there were 2 dirty packets of air, the time
required would vary between 1 & 5 mins with an average of 3 mins, and max
of 5 mins.
Extending the same logic, the maximum time for cleaning all packets = [(10/1)
+ (10/2) + (10/3) + … + (10/10)] @
10 [0.5772 + ln(10)] = 10 [ 0.5772 + 2.301] = 28.78 mins, where 0.5772 is
Euler’s constant, using the approximation for the harmonic series. Without the approximation
it is: 29.24 mins (by just adding up the numbers).
The
average time would be: [5.5 + 3 + 2.1 + 1.7 + 1.5 + 1.3 + 1.2 + 1.1 + 1.05 +1]
= 19.5 mins.
But 10 mins is what it would take with perfect efficiency,
19.5 mins on an average. The best time constant I got is 12.6 mins on 30th
Nov17. But that is just the 1/e time constant (63% clean-up), whereas the above
argument refers to a 100% clean-up… that should be roughly 3 time constants…but
it does not take into account the in-leak so the comparison is iffy…
Also the air, after being purified, is expelled from the air
purifier with some speed. If that speed is high, the air packet may not come
back to the air purifier quickly, reducing the random factor and the
probability of double- or triple-purification…So the airflow is neither
perfectly 1-D nor perfectly random.
This argument assumes randomness – but the air flow is
probably chaotic, not random, so the
time may work out to be between 10 and 19.5 mins (‘chaos’ means that there are
some elements of order in the air flows). However, looking at chaos is above my
pay grade! Maybe somebody can enlighten me…
The analysis of the in-leak rate is, as indicated above,
dependent on data of wind-speed, temperature (inside and outside) and atmospheric
pressure (inside and outside). I tried assuming that, after the air purifier is
switched off, to fit the increase in particle concentration to a simple
exponential:
Y = y0 + A0
( 1 – exp(-t/t))
But it did not work. The situation with variable v, Tin
and Tout, pin and pout, is more complicated. I
have to look for a better model.
