HVAC air-changes per hour formula and COVID-19 - Page 1
Forum section: electronics / general

author: edy
author_rank: Super Contributor
timestamp: June 05, 2020, 09:51:06 pm
content: Hi folks,I have a question for any fluid-modelling and HVAC engineers who handle hospitals, computer rooms and laboratory or technology clean-rooms. The mathematics and derivation is what I'm interested in, which I'm sure many of you will understand even if you are not in HVAC as it is essentially a logarithmic curve. So here it goes...There is an equation and table which is being heavily quoted now (from CDC) which is being used to determine what kind of air-purification needs will reduce COVID-19 levels in a room back to 99.9% efficiency of removal. This guideline is being used to influence the SCHEDULING TIME in private clinic settings. Namely, how long of a "gap" a room must have to allow any potential aerosols to go away ("fallow time") until a next patient can be seen. This is the heavily quoted table:To understand the table, it is being used to recommend that clinics who have a particular ACH for a room allow that number of minutes for the room to remain UNUSED after a procedure to remove 99% or 99.9% of the contamination.Of course, many professional association regulatory bodies including DENTAL, OPTOMETRY, PODIATRY and so forth are quotingonly the 99.9% columnin guidelines to their respective professions, creating PANICamong most small business-owner clinics who are being told they potentially can't use a treatment room for up to 3.5 hours between clients (ACH 2 is by default assumed unless):a) an HVAC technician comes in and tests the ACHb) invest in various HEPA air-purifiers to increase the ACH to reduce the timeThis table and the resulting formula is quoted on page 223 of this particular CDC document, and comes from an earlier CDC document:https://www.cdc.gov/infectioncontrol/pdf/guidelines/environmental-guidelines-P.pdfHere is the formula (and I quote):t2 – t1 = – [ln (C2 / C1) / (Q / V)] X 60, with t1 = 0where...t1 = initial timepoint in minutest2 = final timepoint in minutesC1 = initial concentration of contaminantC2 = final concentration of contaminantC2 / C1 = 1 – (removal efficiency / 100)Q = air flow rate in cubic feet/hourV = room volume in cubic feet Q / V = ACHThe CDC says..."Values apply to an empty room with no aerosol-generating source. With a person present and generating aerosol, this table would not apply. Other equations are available that include a constant generating source. However, certain diseases (e.g., infectious tuberculosis) are not likely to be aerosolized at a constant rate. The times given assume perfect mixing of the air within the space (i.e., mixing factor = 1). However, perfect mixing usually does not occur. Removal times will be longer in rooms or areas with imperfect mixing or air stagnation.213 Caution should be exercised in using this table in such situations. For booths or other local ventilation enclosures, manufacturers’ instructionsshould be consulted."The problem is that without understanding the table and formula fully, the exact application, the errors and the source, many industries are being affected and either have to reduce patient turnover tremendously or invest in expensive HVAC and air-purification solutions. At best, it will accurately improve the situation and at worst it will be overkill and panic-buying by small businesses who are already stretched financially.I have put together an EXCEL spreadsheet (see attached). The first tab contains the table provided for the 99.9% by health regulatory bodies imposing their members to follow. The second tab contains the actual formula plots so that all values of ACH and times are displayed.Where do they get this formula and how does it actually work?- a logarithmic decay curve is divided by ACH (air changes per hour)- the higher the ACH, the lower the time in minutes- with an ACH of 1 and efficiency 99.9%, assuming t in hours, it is simply:t = -ln(1-(99.9/100))/1 = -ln(1-0.999) = -ln(0.001) = 6.90775So WHY do we end up with 6.9 hours being the required amount of time to get 99.9% reduction in an airborne contaminant, or in other words, if ACH = 1, it has to happen 6.9 times minimum to reach 99.9% reduction. That's why to get "t" down to 1 hour, you have to have it 6.9x more ACH, or ACH of 6.9 is needed for 1 hour:t = -ln(1-(99.9/100))/6.9 = 1.00Is this an exponential of some specific "removal rate" that needs to be repeated 6.9x to get to 99.9% efficiency? Please someone help me understand why this supposedly "magic number" of 6.9x is needed, as it is time independent (the units could be hours, minutes, it doesn't seem to matter). Also the volume of air also is irrelevant. As long as you can demonstrate a FLOW sufficient to move enough air through your machine (HEPA filtration unit that removes 99.97% of contaminants), that is enough.I'm guessing it has something to do with 99.97% filtration needed to be done 6.9x to end up with 99.9% but that doesn't work, you get a much smaller number (0.003^6.9 is much less than 0.001 or 99.9% efficiency). So please can someone explain how this works and why the logarithmic curve is used for this application.The reason being as mentioned before, MILLIONS OF DOLLARS of policy-making influence is being done to small-businesses who are now scrambling to retrofit their offices with expensive HVAC filtration, air-purifiers, HVAC expert analyses and so on to allow them to REOPEN after COVID-19 closures, and to make use of their rooms quickly enough between clients to operate with at least some profitability.My fear is that these numbers and tables are being misused and have become DOGMA without understanding the exact circumstances in which they were developed (Tuberculosis and fungal transmissions in hospital room settings) and that blanket application to all other situations including COVID-19 in private clinic settings is wrong and costing businesses MILLIONS in revenue for no good reason.

author: jogri
author_rank: Frequent Contributor
timestamp: June 05, 2020, 10:37:14 pm
content: Quote from: edy on June 05, 2020, 09:51:06 pmThat formula awfully looks like the theoretical residence time/cumulative frequency distribution for a continuous stirred reactor, a model often used when you want to describe how well fluids mix in chemical reactors. Would make sense to use that model as you have a fixed amount of aerosol that gets constantly mixed by the inrushing air, therefore reducing the concentration. That reduction is a e^-x type (concentration over time), if you calculate x for e^-x = 0.001 (remaining amount of aerosol, or 99.9% are gone) you get x = 6.9 ->doesn't change as all other factors cancel each other out.If you want to see the math behind this, just google CSTR and a bunch of chemical engineering papers will come up (every chemistry student has to have an experiment calculating the theoretical residue time of such a reactor, so there are plenty of lab instructions on the internet).

author: edy
author_rank: Super Contributor
timestamp: June 05, 2020, 11:46:48 pm
content: Thank you, I think I see what is going on here. It is an exponential decay curve, assuming e^0.001/e^1 at time t (or a 99.9% reduction). I'm going to delve into the derivation further as I see they just solved for t and changed the form to ln() instead of e.Meanwhile, notice that from 95% to 97% to 99% to 99.9% is a huge difference in time. So for practical purposes of a business trying to remove potential coronavirus (not even confirmed but a patient who screens positive to basic questions that could be many other things) it is a big deal.

author: dmills
author_rank: Super Contributor
timestamp: June 06, 2020, 10:16:26 am
content: Might do better to sell those places banks of UVC tubes (UVC LEDS are stupid), close the door, hit the switch, wait a while, switch off, next patient please?Given a fat enough power feed, I would figure you could have that cycle dominated by having to leave the room because of the hazard posed by the UVC.Screwing some basically standard 4ft florescent fittings to the walls or ceiling has GOT to be easier then providing 20 air changes an hour with commensurate ducting and fans.

author: jogri
author_rank: Frequent Contributor
timestamp: June 06, 2020, 11:33:38 am
content: Hospitals are already doing this, you basically just take 8 UVC lamps, put them on a cart and wheel them into the room (just google UVC disinfection tower). Mostly done to clean operating rooms, but can also be used for normal rooms. Using normal lamp fixture in the ceiling isn't a great solution as you get a lot of shadows->no or reduced disinfection there. The SOP for those towers is to get them into the room, let them sit for 10-20 minutes and then move them to another position in the room to disinfect the spots that were in the shadows on the first position.And they don't even need a lot of power, we are talking aobut 700-1000W for the entire unit.

author: dmills
author_rank: Super Contributor
timestamp: June 06, 2020, 12:07:04 pm
content: That's a slightly different use case being really about surface disinfection (Hospitals already have the air handlers to deal with the airborne issue).The issue that table addresses is disinfecting the air mass in the room, and for that a stack of UVC tubes and a ceiling fan would probably get it done?

author: NiHaoMike
author_rank: Super Contributor
timestamp: June 06, 2020, 12:51:42 pm
content: Quote from: jogri on June 06, 2020, 11:33:38 amCouldn't a lot of time be saved having the lamps be able to move on their own, possibly by remote control if automation is not trustworthy enough?

author: edy
author_rank: Super Contributor
timestamp: June 09, 2020, 06:51:19 pm
content: That reminds me of this thing they are now selling:https://www.casetify.com/protects/uv-sanitizerIs this really helpful or more of a pricey gimmick? A bunch of UV lights to zap the outside of your cellphone and whatever else may fit in the case.Of all the places you can pick up bacteria and personal hygiene behaviour differences, I don't think UV sanitizing your phone will make a difference to most people. Not to mention all the other objects you touch around the house, where you place your fingers subconsiously, etc... even if the device zaps stuff off your phone, overall I'm just not convinced of the efficacy of this helping prevent infection:

author: jogri
author_rank: Frequent Contributor
timestamp: June 09, 2020, 07:26:16 pm
content: Oh dear, where do i even start?-Uses ABS for the case, which is not at all UV resistant (okay, it could be improved with added TiO2 which they seem to have done, but still a bad choice)- 2mW UV-B LEDs, not exactly the definition of "potent UV-C light source for disinfection" (LEDS are probably something close to thosehttps://uk.rs-online.com/web/p/uv-leds/8801494/, they emit at 278nm, that's right on the border between UV-B and C [btw, they seem to have 2mW UV output, so at least there's that])-they only radiate the front and sides of the phone (they claim to have 6 LEDs, 2 are on the top and bottom of the phone and 2 radiate the screen), the back where 80% of your hand sits doesn't get any light at all... So if you want to use it you would need to put your phone in, let it run for 3 min, get the phone out (don't touch the back), let the device run empty for 3 min to disinfect the bottom of the case, then flip your phone upside down and radiate the back for another 3 min-> 10 minutes of work to disinfect one phone...But hey, it has USB-C AND it can charge your phone, so it must be worth it. No one could be bothered to just swipe their phone with ethanol or acetone to disinfect it, everybody knows that such primitive methods just don't work (after all, this method doesn't even use RGB LEDs).