Thread by @Poppendieck

Time for another thread on CO2 in classrooms:

TLDR:
Determine the time it takes for the CO2 concentration in EMPTY classroom to decline from 1200 ppm to 800 ppm:

Good: Less than 9 minutes
Bad: More than 30 minutes
In between: Meh…. better get filtering
/1

As I discussed in a previous LONG thread there are three ways to use CO2 to assess ventilation in a classroom.
1)Rebreathed Fraction
2)Maximum CO2 concentration in an occupied classroom
3)Decay rate of CO2 concentration in an EMPTY classroom

https://twitter.com/Poppendieck/status/1456461079861673986

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This thread will focus on the last method: the decay rate approach. Specifically, this approach can be complex to implement especially at a large scale if you try to fit the data to curve.
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This thread presents an easier, direct approach to estimate CO2 decay rates and FIND THE POORLY VENTILATED CLASSROOMS.
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But let’s start with a little math...

WAIT! Don’t leave just yet. I promise you will only need subtraction at the end.
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We can perform a mass balance to predict how CO2 concentrations decay. A mass balance is just a way of counting.
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For instance, the easiest way to determine the number of people who are in a mall at any point in time is to count who enters and leaves starting at the beginning of the day. This is a mass balance. We can do the same thing for CO2 in a classroom.
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A mass balance on CO2 in the classroom includes the CO2 that is emitted into the room from people, CO2 that is exits the room from ventilation, and what enters the room from outside.
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Don’t leave yet! It will be easy, I promise.
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Since we care only about when the classroom is empty in this approach, we can eliminate the “people” term.
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(For those that care the Greek letter lambda is the decay rate, t is time, E is emission rate, V is room volume, Co is outside concentration, Ct=0 is concentration at the beginning of the decay).
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Now we can use this equation to graph the CO2 concentration decay for various decay rates. You can see smaller decay rates result in longer times for the CO2 to decay from 1200 ppm to 800 ppm.
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We can quantify the time it takes to CO2 decay from 1200 ppm to 800 ppm. In this case it is 7 minutes (blue arrow) for a decay rate of 6/h and 22 minutes for 2/h (orange arrow). It doesn’t matter what the maximum concentration in the room is.
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You just find time it takes for the CO2 concentration to decay from 1200 ppm to 800 ppm (when the classroom is empty!).

(I told you the math was only subtraction!)
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We can plot the concentration relationship between the CO2 decay rate and the time required to reduce the concentration from 1200 ppm to 800 ppm (decay time). Here you can see if you have a decay time of less than 9 minutes, you likely have a decay rate above 5/h.
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If you have decay time greater than 30 minutes, then the classroom likely will have a decay rate less than 1.5/h.
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(Note: If your classroom didn’t reach 1200 ppm, the times to decay from 1000 ppm to 700 ppm are almost the same as 1200 ppm to 800 ppm).
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So this can be a tool to quicky find classrooms that have poor ventilation. If the empty 1200 ppm to 800 ppm decay time is greater than 30 minutes, you don’t have to do any other data analysis. FIX THE CLASSROOM VENTILATION!
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(Check the occupancy and room usage, check the ventilation system, etc.)

Okay here come the caveats:
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1) Analysis assumes an outside concentration of 420 ppm.
2) You need to record data on a time resolution that allows you to get a reasonable estimation of the decay time (e.g. 1-2 minutes).
3) The classroom must be empty of all CO2 sources (people, Bunsen burners, etc.).
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4) I have only mentioned CO2 decay rate, not air change rates. CO2 decay rates are equivalent to air change rates for portable classrooms where all walls are outside walls.
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4 continued) CO2 decay rates in classrooms that share inside walls are estimates of air change rates due to air entering from hallways and adjoining classrooms.
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5) Mechanical ventilation rates in schools can change after students have left. Decay rates over night may not be representative of decay rates during occupancy.
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6) Decay rates are dependent on upon HVAC operation and weather. Check the decay rate under varying seasons, temperature and wind conditions.
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Are you still here?

Cool! CO2 is fun for you!
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Why did I choose 1200 ppm and 800 ppm? Many classrooms have maximum concentration above 1200 ppm on a regular basis, classrooms that have maximum concentrations below that are typically not the bad ventilation classrooms.
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800 ppm was chosen as a lower limit as the closer you get to the outside concentration, the greater the influence of variations in the outside concentrations impact the decay times (among other issues). This is a limit that is also derived from years of analyzing CO2 data.
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Bottom line:
You can use CO2 decay times (1200 ppm to 800 ppm) in EMPTY classrooms to find poorly ventilated rooms. If the decay takes longer than 30 minutes you have a problem. Stop playing with the data and START FIXING THE VENTILATION!

/fin