Forecasting Occupational Exposures Using “Well Mixed Room” Models
In the
, Chris Keil made the case that modeling should be a prominent tool in our collective exposure assessment toolbox. We never have the resources to sample every exposure scenario, and we are often asked to provide quick answers regarding probable concentrations. In these and other scenarios, modeling can provide estimates of potential exposures. This article shows how a relatively simple “well mixed room” (WMR) model can be used to predict current and future exposures. To illustrate, let’s look at a hypothetical scenario involving welding operations.
We have been asked to evaluate the health risk associated with a newly installed welding operation at a distant repair facility. It has come to the attention of the shop manager that the welding rod manufacturer recommends using the recently revised ACGIH TLV for manganese of 0.02 mg/m3 (respirable) rather than the archaic OSHA limit. The repairman/welder uses a respirator, but now there is concern regarding the manganese exposures for nearby employees. Can we
y predict likely manganese levels prior to visiting the site and collecting personal exposure measurements? After several phone calls, we know the following:
Room and general ventilation.
The shop’s inside dimensions are roughly 12 m by 9 m, with a ceiling height of just over 5 m, giving us a volume (ignoring objects within the shop) of 540 m3. The bay doors are generally open in warm weather, but usually the shop relies upon mechanical ventilation, with fresh air and return ducts mounted high on opposing walls. The mechanical ventilation was designed to provide a ventilation rate (Q) of around 54 m3/min (6 air changes per hour).
A work table placed roughly in the middle of the room has been dedicated to welding repair. A typical shift involves around 10 welding repairs, with a range of 1 to 20 per shift. Each repair takes roughly 10 to 20 minutes and requires 2 to 5 minutes of arc time, with 3 minutes being typical. This is followed by several minutes of non-welding activities and preparation for the next repair. Shielded metal arc welding (SMAW) is used, and the most common welding rod used is a 1/8-inch E7018. (For simplicity, let’s ignore voltage and amperage settings.) The repairman recalls that he can detect a metallic “welding” smell during these tasks, but after 30 to 60 minutes the smell is no longer noticeable. This suggests that nearly all of the welding fumes have been removed via Q from the shop within a fairly short period.
Agent and generation rate.
Manganese is considered the agent of concern when welding in an open, well-ventilated space using mild and medium steel welding consumables (rods and wires) and base metals. A quick search reveals a recent article in the
Annals of Occupational Hygiene
that determined the fume generation rate for 3/16-inch E7018 rods in a controlled, laboratory setting. From the data presented, we calculate a generation rate (G) of 11.5 mg/min for manganese fume (which may overestimate the actual generation rate for the smaller-diameter rod used in the shop).
Local controls.
No local ventilation—installed or portable—is being utilized. To protect nearby workers from viewing the high intensity arc, the table is surrounded by opaque welding curtains (that is, screens). The repairman feels that curtains impede air flow and create a somewhat restricted space.
Personal protection.
The repairman uses a low-profile half-mask with an assigned protection factor (APF) of 10, but according to the manufacturer, the filters are expected to remove 99.97 percent of all airborne particles.
At this point, while we would prefer to measure actual exposures (and will eventually), we have sufficient information for some back-of-the-envelope calculations to predict current bystander (far-field) and welder (near-field) manganese fume levels, as well as future levels should the subject of a portable fume exhaust system come up (and we will ensure that it does).

What is a (nearly) worst-case far-field concentration?
We can use the standard one-box well-mixed room (WMR), constant emission (CE) model, as described in AIHA’s
Mathematical Models for Estimating Occupational Exposure to Chemicals
, to predict the steady-state, general room (that is, far-field) concentration. A welding process is a well-known CE source—one that emits at a fairly constant rate—since fumes are emitted only during the “arc time.” (Welding fumes are particulates, but because of their small particle size, they tend to act like vapors and follow the air streams.) Associated with each WMR model are two sets of equations: one or two “steady-state” equations, and one or two “transient” equations. The steady-state equations are easy to use, whereas the transient equations require a spreadsheet or software. In this scenario we will use the steady-state equation to estimate a worst-case concentration. Here we assume that the welder is welding constantly, without significant breaks; that sufficient time has elapsed for the room concentration to increase and then level out at the steady-state concentration; and the airflow in the room allows for fairly rapid, complete mixing throughout the room. Given these assumptions, the steady-state concentration is predicted to be:
the Synergist
the Synergist
Disadvantages of being unacclimatized:
  • Readily show signs of heat stress when exposed to hot environments.
  • Difficulty replacing all of the water lost in sweat.
  • Failure to replace the water lost will slow or prevent acclimatization.
Benefits of acclimatization:
  • Increased sweating efficiency (earlier onset of sweating, greater sweat production, and reduced electrolyte loss in sweat).
  • Stabilization of the circulation.
  • Work is performed with lower core temperature and heart rate.
  • Increased skin blood flow at a given core temperature.
Acclimatization plan:
  • Gradually increase exposure time in hot environmental conditions over a period of 7 to 14 days.
  • For new workers, the schedule should be no more than 20% of the usual duration of work in the hot environment on day 1 and a no more than 20% increase on each additional day.
  • For workers who have had previous experience with the job, the acclimatization regimen should be no more than 50% of the usual duration of work in the hot environment on day 1, 60% on day 2, 80% on day 3, and 100% on day 4.
  • The time required for non–physically fit individuals to develop acclimatization is about 50% greater than for the physically fit.
Level of acclimatization:
  • Relative to the initial level of physical fitness and the total heat stress experienced by the individual.
Maintaining acclimatization:
  • Can be maintained for a few days of non-heat exposure.
  • Absence from work in the heat for a week or more results in a significant loss in the beneficial adaptations leading to an increase likelihood of acute dehydration, illness, or fatigue.
  • Can be regained in 2 to 3 days upon return to a hot job.
  • Appears to be better maintained by those who are physically fit.
  • Seasonal shifts in temperatures may result in difficulties.
  • Working in hot, humid environments provides adaptive benefits that also apply in hot, desert environments, and vice versa.
  • Air conditioning will not affect acclimatization.
Acclimatization in Workers