Occupational exposure modeling
Recent developments in modeling allow prediction of exposure to chemicals, using descriptive environmental and/or the human physiological factors. According to the selection criteria for the chosen companies, inhalation is the main exposure route. We have therefore applied mathematical models to estimate occupational exposure to airborne pollutants [
45]. In this frame, a variety of models is used to predict indoor air pollutant concentration. The models differ in their hypotheses as to (i) pollutant transport mechanisms and (ii) uniformity of the air mixture in the workplace.
These models were executed using IHMOD “Industrial Hygiene Modeling” software, [
48,
49] which is a model compilation for the calculation of inhalation concentration. It is available from the American Industrial Hygiene Association (AIHA) website [
48]. IHMOD currently offers 12 models. The three most commonly-used categories are: (i) the Well Mixed Box, (ii) the Near Field and Far Field model and (iii) the Eddy Diffusion Turbulent model [
12]:
(i)
The Well Mixed Box suggests a simplified representation of chemicals dispersion. It estimates the air concentration of a completely well mixed room. The input parameters are the emission or generation rate “G”, ventilation rate “Q” and the volume of the air in the workplace “V”.
(ii)
The Near Field and Far Field model (NF-FF: 2 zone model) tries to provide a more accurate pollutant estimation for employees working near the emission source. It divides the workplace into two zones, conceptually. The Near Field (NF) includes the emission source and the worker’s breathing zone. The Far field (FF) is the remaining volume of the workplace, where pollutant concentrations are probably lower, and assumed to be homogeneous.
(iii)
The Eddy Turbulent Diffusion model considers pollutant diffusion to be greater than molecular diffusion. It estimates pollutant concentrations using the radial distance of workers and the physical limits of the workplace as inputs, and requires locating the worker in relation to the emission source.
Model parameters
Some key parameters are present in all models: (i) ventilation rate “Q”, (ii) air volume “V”, and (iii) generation rate “G”
First of all, we need to verify mass conservation of the quantity of matter in the air, so as to prove that there is no backpressure effect in the workplace. Confirmation of the basic assumption allowing calculation of the ventilation rate for the whole workplace is a necessary pre-step. This assumption considers air in the workplace room to be an ideal gas, and that the air flow rate entering the room is equal to the air flow rate leaving it.
Mass conservation is calculated following the basic formulas of the ideal gas law:
$$ {P}_{in/ out}\times V={n}_{in/ out}\times R\times {T}_{in/ out} $$
Where:
Pin/out: the air pressure entering or leaving the workplace room in Pascal (Pa).
V: the air volume (m3);
n: the quantity of matter (mol);
R: the ideal gas constant (unit J.K− 1.mol− 1);
T: the temperature inside or outside the workplace in Kelvin (K).
So, it is necessary to demonstrate that the quantity of matter entering and leaving the room is approximately the same.
$$ {n}_{in}\approx {n}_{out} $$
We therefore calculate that nin / nout should be approximately equal to 1.
To this end, direct measurements of pressure and temperature inside and outside each workplace should be performed prior to using the method described below to calculate Q [
12].
In our case, open doors and windows are the only or major source of ventilation; air comes in and out of these two openings, generally located at opposite ends of the rooms. We assume air direction to be constant, therefore:
To calculate Qin entering from the main door, we measured average air face velocity “Vface” through the door over the time range of interest (4 h shift), and recorded the dimensions of the doors.
The average “Q” within the volume of interest is calculated using the following formula [
12]:
$$ {Q}_{average}={V}_{face_{average}}\times S $$
Where:
Vface average: average air face velocity (m.s− 1).
S: the surface of the main door or source (m2).
Throughout this study, air face velocity measurements will be conducted for 8 h across two different periods, to assess variations during, and between, days. This will also be performed across different seasons, to get an idea of the variability of Q in the workplace.
Workplace dimensions are used to calculate the volume of the rooms. Specific volumes within the room are also considered, such as an upstairs floor inside the room, or stocks of raw materials or manufactured products. Machine volumes are also accounted for, either by gathering information from managers, or measured by the authors.
Two main methods are used: (i) mass balance and (ii) Emission Factor (EF).
The mass balance method
During the manufacturing process, product masses are maintained. The quantity of pollutant emitted into the workplace can thus be calculated using the eq. [
12]:
$$ {\displaystyle \begin{array}{l}{\mathrm{mass}}_{\mathrm{into}\ \mathrm{process}}-{\mathrm{mass}}_{\mathrm{incorporated}\ \mathrm{in}\mathrm{to}\ \mathrm{product}}-{\mathrm{mass}}_{\mathrm{collected}\ \mathrm{as}\ \mathrm{waste}}\\ {}\kern4em ={\mathrm{mass}}_{\mathrm{released}\ \mathrm{in}\ \mathrm{room}}\end{array}} $$
We have to take into account the division of the mass per time (production per year for example). The result is an average G.
To use the mass balance method, all forms of metal transformation during the processes are evaluated: metal end-products, mass collected as waste (often sold to other companies for other usages), and particulate matter deposited on the workplace floor. The difference between the sum of the latter and the raw metal quantity will be the suspended aerosol. Concentrations of the various HMs within this aerosol will be assessed.
To achieve accurate prediction, it is necessary to consider the fraction of particles deposited on the floor so that the mass balance method does not overestimate indoor air concentration of HMs. To this end, we will collect the metal dust deposited on the floor of the workplace. This collection will be made at the end of the week and the end of the shift. We will then subtract the corresponding amount of each metal from the quantity released into the air. The proposed equation is the following:
$$ {\displaystyle \begin{array}{l}{\mathrm{mass}}_{\mathrm{into}\ \mathrm{process}}-{\mathrm{mass}}_{\mathrm{incorporated}\ \mathrm{in}\mathrm{to}\ \mathrm{product}}-{\mathrm{mass}}_{\mathrm{collected}\ \mathrm{as}\ \mathrm{waste}}\\ {}\kern4em -{\mathrm{mass}}_{\mathrm{deposited}\ \mathrm{on}\ \mathrm{the}\ \mathrm{floor}}={\mathrm{mass}}_{\mathrm{released}\ \mathrm{in}\ \mathrm{room}}\end{array}} $$
The Emission Factor (EF) method
An EF is calculated for a specific process, and sometimes for specific parameters and conditions. It relates the quantity of pollutants to a particular activity. It facilitates estimation of the generation rate, especially where there is a lack of information or difficulty in calculating it [
12]. US-EPA (US-Environmental Protection Agency) has used EFs extensively to assess air pollution related to industrial emissions, compiling this data in the AP-42
Compilation of Air Pollution Emission Factors [
50]. The common equation for emissions estimation is the following [
50]:
$$ Emission=A\times EF\times \left(\frac{1- ER}{100}\right) $$
Where:
A = activity rate;
ER = overall emission reduction efficiency, in %
Generally, the EFs in AP-42 are calculated from all acceptable quality studies. Identification of true emission factors at a specific plant is difficult. For this reason, we recommend AP-42, which provides tools for the estimation of emission factors applicable to the situation of interest [
50]. In this investigation, since we were unable to find EFs for each process, we attempted to retrieve the information from external studies. In order to cope with these uncertainties, a Monte Carlo simulation will be undertaken [
12].