The general ventilation multipliers calculated by using a standard Near-Field/Far-Field model

ABSTRACT

In conceptual exposure models, the transmission of pollutants in an imperfectly mixed room is usually described with general ventilation multipliers. This is the approach used in the Advanced REACH Tool (ART) and Stoffenmanager® exposure assessment tools. The multipliers used in these tools were reported by Cherrie (1999; http://dx.doi.org/10.1080/104732299302530) and Cherrie et al. (2011; http://dx.doi.org/10.1093/annhyg/mer092) who developed them by positing input values for a standard Near-Field/Far-Field (NF/FF) model and then calculating concentration ratios between NF and FF concentrations. This study revisited the calculations that produce the multipliers used in ART and Stoffenmanager and found that the recalculated general ventilation multipliers were up to 2.8 times (280%) higher than the values reported by Cherrie (1999) and the recalculated NF and FF multipliers for 1-hr exposure were up to 1.2 times (17%) smaller and for 8-hr exposure up to 1.7 times (41%) smaller than the values reported by Cherrie et al. (2011). Considering that Stoffenmanager and the ART are classified as higher-tier regulatory exposure assessment tools, the errors is general ventilation multipliers should not be ignored. We recommend revising the general ventilation multipliers. A better solution is to integrate the NF/FF model to Stoffenmanager and the ART.

KEYWORDS:

• Advanced REACH Tool
• exposure modeling
• Near-Field/Far-Field model
• Stoffenmanager

Introduction

A standard Near-Field/Far-Field (NF/FF) model is the simplest model to describe concentration gradient near a source in an imperfectly mixed room. Since the 1950 s, when the model was introduced,^[1] it has been one of the basic mathematical tools for occupational hygienists and is well accepted in regulatory exposure modeling's.^[2] The standard NF/FF model is also used to the NF and FF concentration ratios for different room volumes and ventilation settings. The concentration ratios are called as a general ventilation multipliers, which are used to scale the concentration level predicted for a standard environment to other environments. A higher multiplier means a lower dilution than in the reference environment, i.e., smaller room and poorer ventilation. Conceptual exposure models Stoffenmanager v.7.1^[3–6] (hereinafter referred to as Stoffenmanager) and the Advanced REACH Tool v.1.5 (hereinafter referred to as ART)^[7–14] describes the dilution by using the general ventilation multipliers calculated by using the standard NF/FF modelings by Cherrie^[15] and Cherrie et al.,^[16] respectively. This is the first study revising the NF and FF concentrations and the ventilation multipliers calculated by Cherrie^[15] and Cherrie et al.^[16] This is critical considering that Stoffenmanager and the ART are recommended tools for regulatory exposure assessment by European Chemicals Agency (ECHA).^[17]

Methods: The standard NF/FF model

In a standard NF/FF model a room is divided into NF volume (V_NF) which compromises the source, ER_i (mg min⁻¹), for mass entering the room and the FF volume (V_FF) which compromise rest of the room (i.e., V_tot = V_NF + V_FF). The room is ventilated via FF volume (Q, m³ min⁻¹) and there is limited air exchange between the NF and FF volume (β, m³ min⁻¹). The concentrations are assumed to be fully mixed at all the times at the NF and FF volumes. The mass is removed from the room by the FF ventilation. The standard NF/FF model is described in detail by Nicas.^[18] Zhang et al.^[19] provides a Bayesian statistical framework for the model and Ganser and Hewett^[20] introduces different ventilation configurations and shows how the model can be calibrated for different environmental configurations.

The standard NF/FF model mass balance is mathematically described as: (1) $$\begin{array}{c}\hfill V_{NF}\frac{d{C}_{NF}\left(t\right)}{dt}=E{R}_i\left(t\right)+\beta C_{FF}\left(t\right)-\beta C_{NF}\left(t\right)\end{array}$$(1) $$\begin{array}{c}\hfill V_{FF}\frac{d{C}_{FF}\left(t\right)}{dt}=\beta C_{NF}\left(t\right)-\left(\beta +Q\right)C_{FF}\left(t\right),\end{array}$$where C_NF (mg m⁻³) and C_FF (mg m⁻³) are the NF and FF concentrations, respectively. Here, we verified that the NF/FF calculations using the Eq. (1)(1) $$\begin{array}{c}\hfill V_{NF}\frac{d{C}_{NF}\left(t\right)}{dt}=E{R}_i\left(t\right)+\beta C_{FF}\left(t\right)-\beta C_{NF}\left(t\right)\end{array}$$(1) produced the same results as an modeling example given by Ganser and Hewett^[20] and IHMod^[21] at high-resolution mode (data not shown).

Results

The general ventilation multipliers according to Cherrie (1999)

Cherrie^[15] used the standard NF/FF model Eq. (1)(1) $$\begin{array}{c}\hfill V_{NF}\frac{d{C}_{NF}\left(t\right)}{dt}=E{R}_i\left(t\right)+\beta C_{FF}\left(t\right)-\beta C_{NF}\left(t\right)\end{array}$$(1) to calculate the 8-hr average NF and FF relative concentrations (RC_NF and RC_FF, respectively) and their ratios (RC_NF/RC_FF) for rooms with various ventilation rates and room volumes. Cherrie's calculations involved two normalizations. The first normalization factor was not explained but it was most likely dividing the NF and FF concentrations with a factor of 10. The other normalization was made by using a concentration in a large room (V_FF = 3,000 m³) with a moderate air exchange rate (AER) of 3 hr⁻¹, and β of 10 m³ min⁻¹ resulting here to C_NF of 10.6 mg m⁻³ (Table 1). However, it is expected that the normalization factors are constant and the same for both NF and FF concentrations in Cherrie's calculations and thus do not affect to the concentration ratios.

Table 1. Average LONG-TERM (8-hr) NF and FF concentrations calculated using a standard NF/FF model for a source emitting mass at rate of 100 mg min⁻¹.

VFF, [m^3]	AER, [h^−1]	β [m^3 min^−1]	CNF, [mg m^−3]	CFF, [mg m^−3]	CNF/CFF	(RCNF/RCFF)/ (CNF/CFF)
30	0.3	3	355	324	1.1	1
		10	335	326	1.0	1
		30	330	327	1.0	1
	1	3	170	137	1.2	1
		10	148	138	1.1	1
		30	141	138	1.0	1
	3	3	83.0	50.1	1.7	0.9
		10	60.2	50.4	1.2	1
		30	53.7	50.4	1.1	1
	10	3	48.6	15.5	3.1	0.9
		10	25.5	15.6	1.6	0.9
		30	18.9	15.6	1.2	1
	30	6.3	21.0	5.2	4.0	1
		10	15.2	5.2	2.9	0.9
		30	8.6	5.2	1.6	0.9
100	0.3	3	146	114	1.3	1.1
		10	124	115	1.1	1
		30	118	115	1.0	1
	1	3	81.1	48.3	1.7	1
		10	58.4	48.5	1.2	1
		30	51.9	48.6	1.1	1
	3	3	50.7	17.6	2.9	1
		10	27.7	17.7	1.6	1
		30	21.1	17.7	1.2	1
	10	3.8	31.6	5.5	5.8	0.9
		10	15.5	5.5	2.8	1
		30	8.8	5.5	1.6	1
	30	12	10.2	1.8	5.5	0.9
		12	10.2	1.8	5.5	0.9
		30	5.2	1.8	2.8	1
300	0.3	3	72.8	40.0	1.8	1.1
		10	50.1	40.2	1.2	1
		30	43.6	40.3	1.1	1
	1	3	50.0	16.9	3.0	1
		10	27.0	17.0	1.6	1
		30	20.4	17.0	1.2	1
	3	3	39.3	6.2	6.4	1
		10	16.2	6.2	2.6	1
		30	9.5	6.2	1.5	1
	10	6.7	16.8	1.9	8.8	0.9
		10	11.9	1.9	6.2	1
		30	5.3	1.9	2.7	1
	30	10^a	10.6	0.6	—	—
		30	4.0	0.6	6.2	1
1,000	0.3	3	45.3	12.2	3.7	1.3
		10	22.2	12.3	1.8	1.1
		30	15.6	12.3	1.3	1.1
	1	3	38.3	5.2	7.4	1.1
		10	15.2	5.2	2.9	1.1
		30	8.5	5.2	1.6	1
	3	3.7	28.8	1.9	15.2	1
		10	11.9	1.9	6.3	1
		30	5.2	1.9	2.8	1
	10	10^a	10.6^b	0.6	—	—
		12	8.9	0.6	15.2	1
		30	3.9	0.6	6.7	1
	30	10^a	10.2	0.2	—	—
		37	2.9	0.2	14.7	1.3
		30	3.5	0.2	17.9	1.1
3000	0.3	3	37.2	4.1	9.1	1.3
		10	14.1	4.1	3.4	1.2
		30	7.5	4.1	1.8	1.1
	1	3	34.9	1.7	20.1	1.1
		10	11.7	1.7	6.7	1.1
		30	5.1	1.7	2.9	1.1
	3	6.3	16.5	0.6	25.9	0.9
		10	10.6^c	0.6	16.7	1
		30	4.0	0.6	6.2	1
	10	10^a	10.2	0.2	—	—
		21	5.0	0.2	25.2	1
		30	3.5	0.2	17.9	1
	30	10^a	10.0	0.2	—	—
		63	1.7	0.1	25.0	0.9

^a Value not given by Cherrie;^[15]

^b Reference concentration for normalizing multipliers in Cherrie et al.;^[16]

^c Reference concentration for normalizing multipliers in Cherrie.^[15]

Note: The room ventilation air flow Q [m³ hr⁻¹] is (V_NF + V_FF) × AER, where V_NF [m³] and V_FF [m³] are the NF and FF volumes, respectively, and AER [hr⁻¹] is the number of air changes per hour. Thus, e.g., if V_FF is 30 m³ the room volume is 38 m³.

Following Cherrie's procedure, we calculated the NF and FF concentration ratios. Cherrie's Table II has transcription errors that were not corrected later by publishing an erratum or by studies^[4,16] using the results by Cherrie.^[15] When excluding the errors and values below 0.1 in Cherrie's Table II, the relative NF and FF concentrations given by Cherrie^[15] are on average 9.6 ± 0.8 and 9.1 ± 1.4 times smaller than the respective NF and FF concentrations calculated in this study (Table 1). Variation in normalization factor shows that the second normalization factor was not constant or there was an error in the NF and FF concentration calculations. Comparison of the RC_NF/RC_FF ratios given by Cherrie^[15] with our calculated C_NF/C_FF ratios varied from 0.8–1.3 (Table 1).

Cherrie^[15] gives the recommended general ventilation multipliers for NF and FF (d_gv,NF and d_gv,FF, respectively) to reconstruct exposure levels (see Cherrie's Table IV). The general ventilation multipliers were calculated as “The NF multiplier was obtained by taking the average relative NF concentration for the room sizes and ventilation conditions described in the table, re-normalized to the average value for large rooms with good ventilation. The FF multiplier was then calculated by dividing the NF multiplier by the average ratio of the NF to FF concentration obtained in the simulation.” By following the instructions we calculated the general ventilation multipliers from Table 1 values. The d_gv,NF and d_gv,FF multipliers calculated in this study (Table 2 last two columns) were up to 2.8 times higher as reported by Cherrie.^[15] This was because the relative NF and FF concentrations given by Cherrie^[15] were different than the concentrations calculated in this study.

Table 2. Recommended general ventilation multipliers for reconstructing 8-hr exposure levels.

Scenario	VFF, [m^3]	AER, [h^−^1]	$\overline{{\mathit{C}}_{\mathit{NF}}/{\mathit{C}}_{\mathit{FF}}}$	dgv,NF	dgv,FF
Large room and good general ventilation	1,000 & 3,000	10 & 30	19.0	1.00	0.06
Large room and poor general ventilation	1,000 & 3,000	0.3 & 1	5.2	5.2	1.4
Small room and with good general ventilation	30 & 100	10 & 30	3.2	4.4	1.7
Small room and poor general ventilation	30 & 100	0.3 & 1	1.2	42	38

The general ventilation multipliers according to Cherrie et al. (2011)

Cherrie et al.^[16] calculated the NF and FF multipliers for short-term and long-term exposures by calculating 1-hr and 8-hr average NF and FF concentrations at β = 10 m³ min⁻¹, which were normalized with a reference concentration calculated for NF at V_FF = 1,000 m³ and AER = 10 hr⁻¹ (Table 1). By following the instructions we calculated the NF and FF multipliers from Table 1 values (Tables 3 and 4). The NF and FF multipliers calculated in this study are for 8-hr exposure up to 1.7 times lower and for 1-hr exposure up to 1.2 times lower as reported by Cherrie et al.^[16]

Table 3. NF and FF multipliers for long-term exposure (8-hr) calculated according to Cherrie et al.^[16]

Room volume, [m^3]	0.3 AER	1 AER	3 AER	10 AER	30 AER
NF multipliers
30	31.7	14.0	5.7	2.4	1.4
100	11.8	5.5	2.6	1.5	1.0
300	4.7	2.6	1.5	1.1	1.0
1,000	2.1	1.4	1.1	1.0	1.0
3,000	1.3	1.1	1.0	1.0	1.0
FF multipliers
30	30.9	13.1	4.8	1.5	0.5
100	10.9	4.6	1.7	0.5	0.2
300	3.8	1.6	0.6	0.2	0.1
1,000	1.2	0.5	0.2	0.1	0.02
3,000	0.4	0.2	0.1	0.02	0.01

Table 4. NF and FF multipliers for short-term exposure (1-hr) calculated according to Cherrie et al.^[16]

Room volume, [m^3]	0.3 AER	1 AER	3 AER	10 AER	30 AER
NF multipliers
30	7.5	6.3	4.3	2.3	1.4
100	3.3	2.8	2.1	1.4	1.0
300	1.8	1.6	1.4	1.1	1.0
1,000	1.2	1.2	1.1	1.0	1.0
3,000	1.0	1.0	1.0	1.0	1.0
FF multipliers
30	6.8	5.5	3.4	1.4	0.5
100	2.4	1.9	1.2	0.5	0.2
300	0.8	0.8	0.4	0.2	0.1
1,000	0.3	0.2	0.1	0.05	0.02
3,000	0.1	0.1	0.04	0.02	0.01

Discussion

In a standard NF/FF model a general ventilation is one of the main factor defining the NF and FF exposure levels. The general ventilation multipliers from Cherrie^[15] are used in Stoffenmanager and the NF and FF multipliers from Cherrie et al.^[16] are used in the ART to describe the general ventilation effect on the NF and FF concentration levels. The recalculated general ventilation multipliers were up to 280% higher and the NF and FF multipliers were up to 44% lower than reported earlier.^[15,16] Highest differences were observed for small room volumes and low AER values. The error propagation is not clear, because Stoffenmanager and the ART contains nonlinear calibration factors, the models are based on exposure determinants and not physical quantities, and in Stoffenmanager mass is not conserved.^[5,12] In general, the ventilation multiplier overestimation results overestimation in exposure level and vice versa.

Considering that Stoffenmanager and the ART are classified as higher tier exposure assessment tools,^[5,17] both are recommended by ECHA for regulatory exposure assessment,^[22] and that Stoffenmanager has alone over 32,000 users,^[3] the errors is general ventilation multipliers should not be ignored. The studies^[5,22–30] concerning the tools evaluation, validation, applicability, and sensitivity analysis should be revised and corrected before the tools are used in regulatory risk assessment or before implementing them to tools combining different exposure models, such as a Translation Tool to Support the Use of Regulatory Occupational Exposure Models (TREXMO;^[31] see also letter to the editors,^[31–33]) SUN decision support system,^[34] or risk governance tools developed in caLIBERAte.^[35]

In our opinion, the regulatory exposure modeling should rely only on mathematical models following general physical principles, such as conservation of mass, rather than conceptual models based on non-physical models or exposure determinants. Physical units should not be converted to indices or scores to ensure models transparency. For example, in Stoffenmanager the general ventilation multipliers were normalized by using a concentration in a large room (V_tot = 3008 m³) and an AER of 3 hr⁻¹ while in the ART the NF and FF multipliers were normalized by using a concentration in a large room with a volume of 1,000 m³ and an AER of 10 hr⁻¹, which makes comparison of the models more challenging.

We believe that the errors found here would have been revealed much earlier if the tools would rely, e.g., on a standard NF/FF model. Physical and mathematical mass balance models are easy to understand and to develop according to future needs and their performance is superior as compared to conceptual modes.^[2,18,36] Thus, it is highly recommended that regulatory exposure modeling is based on physical mass balance models.

Conclusions

Considering the extensive use of Stoffenmanager and the ART in regulatory exposure assessment, the tools general ventilation multipliers should be revised. A better solution is to integrate a well-known NF/FF model to Stoffenmanager and the ART rather than using a quasi-two box model. Regulatory exposure modeling should be based on physical and mathematical mass balance models where unit conversions to indices and scores should be avoided. This would increase the models transparency which reduces risk of errors and makes them easier to develop according to future needs.

Acknowledgements

This work was supported by Danish Centre for Nanosafety II (WP1.3). The authors thank Prof. Paul Hewett (Exposure Assessment Solutions, Inc., Morgantown, WV) for his assistance with checking the calculations.