A Simple Tracer Gas Technique to Measure Ventilation

A simple tracer gas technique can determine the ventilation rate in any room or volume of air.   Last week I discussed natural logarithms with base e.    One of the most useful equations involving natural logs is the equation for first-order decay.  This sounds complicated but all it really means that the rate of loss or decay of a concentration is directly proportional to the amount remaining.   Thus, for example, the rate of decay (or material loss) for a ventilated room volume concentration that is 10 ppm will be twice as high as the loss rate for a  room concentration of 5 ppm under the same ventilation conditions.  More important, the time it takes to get from 10 ppm to 5 ppm is the half-life.   Indeed, it is the same amount of time (i.e., the half-life) that it will take decay or go from 5 ppm to 2.5 ppm, 2.5 ppm to 1.25 ppm, etc.   That is really all there is to first-order kinetics.   Theoretically you never get to zero but after 7 half-lives the concentration is less than 1% of what you started with and after 10 or so it is vanishingly small.

The decay rate of a gas concentration put into a room typically follows a first order decay process driven by the ventilation rate.

The equation is:   - ln (0.5)/(Q/V) =  (0.693)(V/Q) = the half-life  = t_1/2

Thus the ventilation rate (Q) = (0.693)(V/ t_1/2)

Consider a room in a home that has a volume (V) of 20 m³.   We put a tracer gas into this room and mix it up for a few minutes with portable fans so that the average concentration is 16 ppm measured with a real time monitor.  We get the following data over the next few hours:  12.5 ppm at 0.5 hours, 9.7 at 1 hour, 7.9 at 1.4 hours and 4.1 at 2.8 hours.    You would typically have an automatic data-logger to take a reading every 5 minutes or so but the above data points tell the story.   The initial concentration goes in half after about 1.4 hours and in half again in the next 1.4 hours; the half-life is about 1.4 hours.   Put 20 m³ and 1.4 hours in the above equation and  Q = 9.9 m³/hr.   Another way of expressing this is the ratio Q/V or 0.50 air changes per hour.   This is a typical ventilation rate for a home with doors and windows closed in the winter.   Crack the windows open and this can go up 10 fold.   Industrial rooms are typically higher and in “hot” industrial settings or rooms with a lot of local exhaust ventilation it could be much higher.

What are good tracer gases to use?   Freon R-134a used in car air conditioners is easy to get and it works quite well with a portable flame ionization detector (FID).   If you are very careful not to release too much (say 10 ppm max), carbon monoxide (CO) could work well with a suitably sensitive real-time analyzer that can continuously output the concentration in ppm.   In industrial rooms with active gas fired fork lifts there is often enough ambient CO in the room that it represents a “built-in” tracer simply by having the folk lift operators stop for an hour or so (e.g. waiting for lunch or the end of the day) and measuring the CO concentration fall off will give you the data you need.

Next week I will show you more about “e” and natural logarithms; specifically, we will go over how the above equations and similarly useful algorithms are derived.  We will also get into how one can use an Excel spreadsheet to get a more precise estimate of half-life from tracer gas studies.

In the meantime, my friend and colleague Dr. Mark Nicas, who during his career has developed some really useful exposure models and also teaches at Berkeley, has kindly sent me a document which has 18 pages packed with quantitative math and science review notes.  I would be happy to send it to anyone who sends me an email request to mjayjock@gmail.com.    The stuff in this pdf is pretty concentrated with useful information and perhaps it would spawn some questions that I could address in future blogs.

A Simple Refresher of Logarithms

Some folks are intimidated by the mathematics of modeling.  I am here to tell you that by taking a little time to really understand a few basic concepts in math (which I am going to help you with) you are ready to approach and understand the mathematical underpinning of many models.  

When and where many of us went to school, math was not very well taught.  Indeed, many of us were taught to manipulate numbers to get answers but we were not schooled in exactly what the process meant in a larger sense.  We soldiered through math course with a good portion of us hating it but never really seeing what it was good for.   In this blog I am hoping to refresh our understanding of logarithms so that we can clearly understand and use them in models. 

The first thing to understand about logarithms is that they are just another way of expressing a number.  All logarithms have a BASE.   The one we see much of the time is BASE 10.    So the “power” or exponent that 10 is raised to is its logarithm or log.    So the log of 100 is 2 since base 10² is equal to 100.    The base10 log of 10 is equal to 1 for the same reason.    Similarly, if we know that the base 10 log is 3 we know the number is 10³ or 1000.  Calculating logs are easy for simple integers but considerably more difficult for those numbers in between.   In the old days before calculators we had “log tables” to give us these numbers.  Today we just put the number in our calculator; for example, enter 15 and hit LOG to get the log of 15 or 1.1761.  Thus 10^1.1761 = 15.   

 Numbers less than 1 have negative logs. Log of 0.5 =   -0.3010 or   10^-0.3010 = 0.5.   

Try putting in -0.3010 for x and hit the 10^x button and wa-lah!    0.500 is calculated which is the  "antiLOG" of -0.3010.   

Logs are handy in that adding the logs of numbers is the same as multiplying the numbers.    Add -0.3010 to 1.1761 = 0.8751.  The antiLOG of 0.8751 =  10^0.8751 = 7.5 or the same as 0.5 x 15.    Similarly subtracting logs is the same as dividing the numbers.    Subtract -0.3010 from 1.1761 = 1.4771.   10^1.4771= 30 = 15/0.5.   Flip it around and Subtract 1.1761 from  -0.3010 =  -1.4771.   10^-1.47711 = 0.03333 or the same as 0.5/15.   For us folks who have been around since before calculations,  this is how a slide-rule works because it has logarithmically-spaced scales, you are adding or subtracting logs by sliding the scales to do multiplication or division on the slide-rule.

You will see a lot of logs expressed as base 10 because that is our basic number system (a system based on 12 might be better) and that is how many fingers we have.   Logarithmic scales are convenient for compressing large ranges of numbers because in base10 the distance between each integer represents 10x.   For example, the difference in shaking amplitude between a Richter magnitude 7 earthquake is 10 times higher than a magnitude 6 because the scale is base 10 logarithmic.

Now that we understand algorithms in base 10 it is time to understand logarithms with the NATURAL base number.   This natural BASE number is 2.718281... or the italicized lower case letter “e”.   The only thing you need to know about “e”  is that it is an important number in mathematics and actually much more “natural” than 10.   Thus it is called the NATURAL log (sometimes called LN or ln).    The same rules apply, that is, the natural log of 10 is 2.3026 (it’s also on your calculator - sometimes with key named LN) which means that  e^2.3026= 10.

Next week I am going to talk about the subject of integration and how it fits into modeling.   We are going to see “e” again and we will walk through a practical model using a tracer gas that lets us estimate the ventilation rate in any workplace room or any residential volume. 

  

Well mixed model vs Models that consider air concentrations close to the source

Well mixed box models are relatively easy to understand.  You start with a room (a box) and the same amount of fresh air goes into it as comes out of it.  If not it would explode or the folks inside would suffocate. You put a contaminant into the room air (emission rate G) and take it out with ventilation (Q).   Last week we saw that given a steady G and Q that the steady-state concentration (C) in the box will eventually equal G/Q.   There are other more complicated equations that determine C as it approaches steady-state but that is not important for this discussion.   In later blogs I will get into how you can determine or estimate G and Q but for now it is enough to know that this is a simple model and quite useful in many cases.  It is important to understand that the C determined by this model is the AVERAGE concentration within the room.  If the source G is relatively spread out within the room then this model works quite well.  An example of a spread out source would be paint emissions into a room with painted walls and ceiling.  If, however, the source is localized then there typically will be a much higher concentration (C) of the contaminant near the source than away from it.   An example would be someone using a volatile degreaser spray with TCE on a workbench to clean a part.  The larger the room the more the gradient or difference in concentration near the source versus the far corner of the room.  The well mixed box model does not work very well here since the average concentration in the room will be significantly lower than the breathing zone concentration of the person doing the cleaning.

Many years ago I approached this problem by assuming a virtual box within the real box of the room.  For example, I assumed that most of the contaminant would be in an area of an 8 foot cube around the source.   That is a volume of 512 ft3.   It did not matter how big the room was as long as it was larger than this virtual box.  The only thing I needed to know about the actual room was its volume (V) and its ventilation rate (Q).   Once I knew Q for the large room I would figure out the air changes per hour in that large room; that is, Q/V.   This has the units of 1/hr.   Once I had Q/V for the large room I assumed this relative exchange rate would be the same for the virtual box.   So that (Q/V)(512ft3) = Qb or ventilation rate in the virtual box in units of ft3/hr.   I'll let you do the conversion to m3/hr.  The predicted steady-state C  in this box = G/Qb.   If you want a copy of the original paper just email me (mjayjock@gmail.com) and I will send it to you.

Years later Mark Nicas came up with a much more elegant model called the 2 zone model (that considered the virtual box or NEARFIELD and the FARFIELD or rest of the room volume).  This model calculates the C in the virtual volume around the source AND the average concentration in the rest of the room.  This model and lots more are available in the freeware Excel spreadsheet IH MOD from the AIHA web site.
http://www.aiha.org/get-involved/VolunteerGroups/Pages/Exposure-Assessment-Strategies-Committee.aspx

There is another near source model known as the eddy diffusivity model which actually calculates a continuous gradient of exposure from a point source of emission (G) to any location within the volume.  To run this model one needs G and the eddy diffusivity coefficient (D).  Until recently D was hard to come by, but the very smart researchers at Stanford recently published a paper that allows one to estimate D from a room's dimensions and its ventilation rate.  Kai-Chung Cheng, et al,  Modeling Exposure Close to Air Pollution Sources in Naturally Ventilated Residences: Association of Turbulent Diffusion Coefficient with Air Change Rate.  Environ. Sci. Technol. 2011, 45, 4016-4022.  The calculation engine for the eddy diffusivity model is also available in IH MOD.

I appreciate the comments I receive on this blog and it helps me to determine what I am going to cover next.

A Simple Exposure Modeling Example as a way of Getting Started

One of the really nice things about doing a blog is the connection with colleagues.  As a prime example, I received the following note from Dr. Gurumurthy Ramachandran (Ram) about last week’s blog. 

“You hit the nail on the head when you said that all hygienists need to become explicit modelers, not subliminal ones.  Just the process of thinking about each input parameter to even a simple model will lead to a much better understanding of the workplace and the limitations in that understanding. I remember reading somewhere that these two elements correspond to knowledge and self-knowledge.”

Ram is a brilliant teacher and researcher at the University of Minnesota so I consider these words to be very heartening. Indeed they, along with the other comments I received last week, are enough to encourage me to hopefully provide more insight this week to newbies into the modeling process. 

  

The basic elements of all inhalation models are relatively simple.  In every case, you have a volume of air and a rate of contaminant input to that volume.  The model is simply using these elements to predict the concentration in the air that might be inhaled by a worker. 

The model I am going to discuss this week is one of the simplest but still very useful; namely, the well mixed box model at equilibrium.   Any room (or box of air) which is receiving a steady inflow of contaminant will reach a steady (or equilibrium) concentration of contaminant as the amount of contaminant that is put into the room is balanced with the amount that is leaving via ventilation removal.  All volumes or spaces in which we exist have some fresh air ventilation – even our well-insulated homes in winter exchange air with the outside via infiltration/ex-filtration through cracks and other openings.   This exchange typically occurs in the range of 30 to 60% per hour in the rooms of homes and is often well above 100-300% in industrial rooms.

At equilibrium the airborne concentration (C) in the box (room) is equal to the generation or emission rate (G) of contaminant into the box divided by the ventilation rate (Q).                 C = G/Q    G = wt/time.    Q = volume/time     C = wt/volume.   Pretty simple uh?

So how does one estimate G?   Let’s consider an example of a small (20m³) bedroom in which someone is painting with a water-based paint that has 0.5% ethylene glycol (EG) as a drying agent.  If they use 4,000 gram (4,000,000 mg) of paint, that is 20 grams (20,000 mg) of EG.   If it is assumed to take 8 hr to dry and that all of the EG comes out that is an average of 2,500 mg of EG being emitted into the room air per hour.   There are quite a few ways of estimating G and I can go over these in future blogs.

Estimating Q:  The 20m³ room with 60% ventilation/hr is (20 m3)(0.6/hr) = Q = 12 m³/hr.   There are a number of ways of getting a Q which could also be a topic of a future blog.

Using C = G/Q = 2,500/12 = 208 mg/m³ of EG at equilibrium.

That wasn't too bad was it?

This is a simple model – like all models it is a portrayal of reality but NOT reality.  The generation rate is most likely not constant but this exercise does give one some reasonable insight into the process and into the magnitude of the exposure potential.   If the EG comes out of the paint more quickly it could have a peak concentration higher than 200 mg/m³ but perhaps not very much higher.  The time-weight average concentration would always be lower than 200 mg/m³ if our assumption about all of the EG being vaporized in 8 hr is correct. 

If the EG takes much longer to come out it changes a lot of things.  Indeed, rework the above so that it takes 24 hours for all of the EG to come out and again assume that it comes out evenly.  Then the estimated equilibrium concentration for that 24 hour day would be about 70 mg/m³ and if one was only exposed during 8 hrs of that day their exposure could never be higher than about 25 mg/m³.  

There are a number of assumptions here in this simple model but I hope you can see how it might be helpful and how it might encourage you to go and manipulate the inputs to gain more insight or go to more sophisticated models.    IH MOD is a freeware Excel spreadsheet available on the AIHA web site that can do all of the math with ease and it provides a graphical output so that you can better see what is happening.   

I am again at a point where I need some feedback.   Do you good folks need or want information on:

• Specifically where to get IH MOD and exactly what does it do?
• Some of the math background that you may want to brush up on to help you with modeling (Note: It’s not a lot)
• The difference between equilibrium, point-in-time and time-weight average airborne concentrations
• Well mixed models versus models that consider air concentrations close to the source
• How to do source estimation (G)
• How to measure or estimate ventilation rates (Q)
• All or none of the above

Send your wishes/comments to me at mjayjock@gmail.com or in comments to this blog.  Absent any feedback I will go back to talking in generalities about risk assessment, risk management and modeling which many or most of you may find to be preferable.

                               

Every Industrial Hygienist should be a Modeler

If you are a practicing Industrial Hygienist (IH) you are a Risk Assessor.   You compare measured or estimated exposures to exposure limits and this activity characterizes or assesses the risk.   You typically do not develop exposure limits but you do estimate, measure other otherwise gauge the level of actual exposure to the agent in question.   We do this mostly with inhalation exposure.  When we actually measure and we do it by measuring the concentration of the agent in the potential breathing zone of the worker and, as mentioned before, comparing it to an occupational exposure limit (OEL) with the same units of concentration and the same time frame.  Thus the stock-in-trade of the IH is exposure estimation to be used in the context of risk assessment .

It has been well shown that the vast majority of occupational exposures are NOT measured but they are estimated using EXPERT JUDGEMENT.   Clearly the industrial hygienists are running some algorithm (that is a MODEL) subconsciously  in their mind that either concludes that the risk is insignificant or in need or further evaluation.   Explaining “expert judgment” has always proven to be very difficult. Some are better at invoking this hidden process than others. Indeed, the more experience you have as an industrial hygienist, the more you test or validate your subconscious models versus reality and the more skilled you become.


My point is that as tool-using animals, we are much better off if, as industrial hygienists, we raise the models we use to the level of consciousness so that we might be able to enjoy the following advantages over the subliminal approach. The critical advantages of separate and explicit exposure models include their inherent ability to be

• Examined by the modeler and others in a critical review of their work or use
• Explained to folks with a stake in the prediction and outcome 
• Applied retrospectively (estimating past exposures)
• Shared and passed on as technology transfer (education of the next generation)
• Tested (validated) and improved using the scientific method  

When you learn and use exposure models you identify yourself as a technologist, someone who uses science to answer questions.  You enhance your standing with your employer and your charges.  You distance yourself from the characterization as a "Pump Jockey".   From a professional development perspective, becoming a modeler is well worth the effort.

Learning and using models is not simple but it is not impossible either.  I have found it is best to progress with  baby steps.  Start with relatively simply models, which I have found to be remarkably useful, and then progress to more sophisticated and detailed tools which are even more valuable.   There are lots of free software tools out their and some good educational material.   Depending on the response I get to this blog I may dedicate the next one or two to being more specific about these opportunities and resources.

Describing Uncertainty

Uncertainty is everywhere.   Indeed, there is not a thing or quantity that we can measure that does not have some level of uncertainty.  For example, the length of any "standard" length object for measuring 1 yard (i.e., a yard stick) is not exactly 1 yard (except by definition) - there is always some finite  tolerance + or - (however small) around the 1 yard mark.  We cannot be completely certain about any measurement.   Measurement tolerance is one form of uncertainty.  Quantities that vary naturally are another form.  For example, the weight of all adult females in Pennsylvania will have some variation and therefore the weight of any PA female adult with fall within a range of uncertainty.  Indeed, any individual will have weight that varies over time.  The other source of uncertainty, which is typically the most important and dominant, in risk assessment is a lack of information associated with the value of interest.   I am going to use the weight of my dog Libby in an attempt to show the interaction between natural variation and lack of knowledge.   In this whimsical example let us assume that Libby's weight is an important value in a risk assessment and if we overestimate her weight we overestimate the risk.   Similarly, if we underestimate her weight we underestimate the risk.   How much does Libby weigh? 
When I pose this question to students they usually ask me to identify Libby's breed.   I tell them that I will only disclose to them that Libby is a pure bred dog and is fully grown.   I tell them that they all have some information about the universe of dog weights on Earth.  At that point, the students usually present a range of weights to represent Libby, for example 5-200 lbs.  This implies that there is no chance Libby could weigh less than 5 or more than 200 lbs. (Worst case estimated weight as risk surrogate = 200 lbs).  I then tell them that Libby is an English Springer Spaniel.   Those with online-capable phones might find that female Springer's typically weigh between 35 and 45 lbs.   The students could choose 35-45 lbs as the new range of estimated weights, one born of more information but some will remember the condition that if we specifically underestimate Libby's weight we underestimate the risk.   These wise students then may (and have) come up with an estimated range of 35 to 70 lbs.  The next step might be to go to my home and look into the window of our garage (where Libby is) to see her.   Such an examination will disclose an overweight dog perhaps as much as 20-30 lbs overweight.  The new estimated range from these observations might be 55-70 lbs.  The final step might be to go into my garage and weigh Libby daily over the period of a month.  Here the data might show her to weight to vary between 62-64 lbs. This range is now a much better data-based estimate of lowest to highest which reflects the natural variation of her weight while all the previous estimates were plagued by a greater lack of knowledge.   Forced to make a deterministic (single value) estimate of her weight one might use 65 lbs to guard against getting her on a day when she ate or retained somewhat more than normal.   
The point here is that we could ALWAYS provide some useful quantitative estimate of Libby's weight and the uncertainty around it even when the available data was meager.  The estimate got better (more useful) with more data.
Just to stretch this analogy even further.   What if I said I have an animal in my garage and I will not tell you what species of animal but you need to estimate its weight as proportional to risk!   Here the uncertainty born of ignorance is MUCH greater and the 40 fold range of estimated weight above.  Indeed, given such a large range one might rightly question the utility of the estimate but the point remains that the uncertainty at any stage of the assessment should be estimated and disclosed.  Such uncertainly analysis shows where we might get the best bang for our data buck - in this case knowing what animal species is in the garage. That specific information would then allow us to make much more narrow and a more useful estimation of the range of weight as a surrogate for risk. 

Uncertainty is the Bane of the Risk Assessment Process

Almost 20 years ago I had the privilege of presenting testimony before the President’s Commission on Risk Assessment.  I used that opportunity to describe and bemoan the relative nascent state-of-the-science and how uncertainties in both the toxicology and exposure assessment of risk assessment were really limiting the utility and ultimately the credibility of the process.   A measure of our progress might be seen in fact that the title of that talk and the title of this week’s blog are identical.   That talk from almost 20 years ago goes into the subject in a lot more detail.   If any of you reading this ask me for it I will send you the PowerPoint slides from that presentation (mjayjock@gmail.com).

This is not to say that no progress have been made; indeed, a lot has happened in twenty years on the exposure side of things.   Some really great tools have been developed by the volunteers within the American Industrial Hygiene Association which have been made generally available as books and freeware.    Go to:

 http://www.aiha.org/get-involved/VolunteerGroups/Pages/Exposure-Assessment-Strategies-Committee.aspx 

to get some of these models and go to the AIHA Press:  https://webportal.aiha.org/Purchase/SearchCatalog.aspx

to see the books on Exposure Assessment Strategies, Risk Assessment Principles and Mathematical Modeling.   Even with these tools a ton of work still needs to happen on the exposure side of risk to reduce the uncertainty; however, I must say that we have come a long way.

From my perspective, even more work needs to happen in toxicology.   Clearly, advanced techniques have been developed but from my perspective, available data that provides confident information on what is happening in human tissue at environmentally relevant concentrations of chemical exposure has not happened.   Most of the current occupational exposure limits (OELs) are based on the current toxicity base which uses the responses of animals at high doses in order to estimate relatively “safe” or allowable levels of exposure to humans at relatively low exposure.     See previous blogs for a more detailed discussion of this subject.

So what might be done with all this uncertainty?   Is the risk assessment process so laden with uncertainty as to be worthless?  I think not.  Indeed, at almost any level, a rational assessment of the health risk posed by chemical exposure is better than not doing it.   For me, the challenge is appropriately describing that uncertainty for the various stakeholders in the process.    Indeed, the suitable description of uncertainty would hopefully point the way to its reduction.   

Properly handed using the upper end of the uncertainty – for example, the 95^th upper bound percentile -as the measure of risk will reasonably bias the analysis toward overestimating and not underestimating the risk.   Thus, if one is able to shrink the range of uncertainty (with more data) the 95^th percentile upper bound will come down as well which means we are properly trading data for conservatism in the spirit of a precautionary approach.

For many years I used Monte Carlo uncertainty analysis for the assessment of risk which allows for everyone to see the specific uncertainty that exists and feeds the various parts of the assessment.   It gives the stakeholders a good view of where the uncertainties exist and how additional information might truly help the evaluation and the subsequent decisions.   This and a simpler form of uncertainty analysis will the subject of a future blog.

Given the level of uncertainty in our current set of OELs, my suggestion is that we quantitative describe the uncertainty within these values as part of the documentation of any OEL.    Doing so will typically reveal a relatively large range of uncertainty which some may find disconcerting; however, I believe that disclosing it is a critical part of the integrity of the process.   More about this critical issue of documenting OELs will happen in a future blog as well.