INHALATION INTAKE FRACTION OF POLLUTANTS FROM EPISODIC INDOOR EMISSIONS

Transcription

1 INHALATION INTAKE FRACTION OF POLLUTANTS FROM EPISODIC INDOOR EMISSIONS WW Nazaroff 1,* Civil and Environmental Engineering Department, University of California, Berkeley CA USA ABSTRACT The intake fraction is the attributable pollutant mass inhaled per unit mass released from a source. Mathematical models are employed to explore how intake fraction varies with governing parameters for episodic indoor pollutant releases, such as those from cleaning, cooking, or smoking. Broadly, the intake fraction depends on building-related factors (e.g., ventilation rate), occupant factors (e.g., breathing rates), and pollutant dynamic factors (e.g., sorption). In the simple case of the episodic release of a nonreactive pollutant in a well-mixed indoor space with steady occupancy, the intake fraction is simply the ratio of the volumetric breathing rate to the ventilation flow rate. The effects of transient occupancy and imperfect mixing are shown to modify this basic relationship by multiplicative correction factors. INDEX TERMS Exposure assessment, sources, health risk evaluation, occupancy, pollutants INTRODUCTION The cause of many indoor air pollution problems can be traced to unacceptably high emissions from certain sources. One method for understanding whether a particular level of emissions is acceptable is to determine, e.g. through use of mathematical models and empirical data, the indoor air concentrations that would result. Given information about the nature and timing of human encounters with the resulting concentrations, exposures can be determined. Exposure levels may be compared with health risk information to determine whether the condition is acceptable or requires mitigation. A related, yet distinct approach connects emissions to intake more directly, using the intake fraction metric (Bennett et al. 22). Intake fraction is defined as the attributable pollutant mass taken in by an exposed population per unit mass emitted from a source. In this framing, risk can be estimated by multiplying the pollutant quantity emitted from a source by an appropriate intake fraction and then by a health-risk factor (Lai et al. 2). Only a few studies have been published reporting intake fractions associated with indoor sources. Smith (1993) estimated an exposure effectiveness for environmental tobacco smoke and for stoves vented indoors that corresponds to an intake fraction of 25 per million. Lai et al. (2) reported that indoor emissions in residences or office buildings produce [intake fractions] of 1-3 to 1-1, i.e. ~ 1 1, per million. Klepeis (24) presented probability distribution functions of intake fractions for environmental tobacco smoke based on multizone simulations of residential exposures. Relative to its potential significance in helping to illuminate source-to-receptor relationships and to prioritize control efforts, much remains to be done before the dependence of intake fraction on key variables for indoor pollutant releases is well understood. This paper focuses on the inhalation intake fraction associated with episodic activities that release air pollutants indoors. Such activities include smoking (Klepeis 24), cleaning (Nazaroff and Weschler 24) and cooking (Smith 1993; Wallace et al. 24). Through the use of mathematical models and analysis, the goal of the work reported in this paper is to advance understanding of how intake fraction varies with important underlying variables. The work reported here considers inhalation intake as the only exposure pathway. The pollutants are considered to behave either as ideal (gaseous) tracers, or as being subject to interior removal by first-order processes. Extensions to account for more complex dynamic behavior and alternative intake pathways would be necessary for treatment of certain pollutants, such as semivolatile organic compounds. SIMPLE EXAMPLE Consider this situation. A mass M of a nonreactive pollutant is suddenly released into a well-mixed indoor * Corresponding author nazaroff@ce.berkeley.edu 1816

2 environment of volume V that is ventilated at constant flow rate. The concentration as a function of time may be obtained by writing and solving the mass-conservation equation: d(cv)/dt = - C, subject to C() = M/V. The solution is C(t ) = M V t exp V (1) Now consider one exposed individual, present throughout the episode, who breathes at a volumetric flow rate B. The inhalation intake rate, i(t), is the product B C. The total mass inhaled, M inh is obtained by integrating i(t) until the pollutant is fully removed from the space: M inh = M ( B C) dt = B (2) The individual intake fraction, if, is the ratio of M inh to M: if = M inh M = B (3) If N individuals are so exposed, then the (population) intake fraction is equal to the sum of their inhalation rates divided by the ventilation rate. Pollutants released from indoor sources may be removed by other mechanisms in addition to ventilation. In the event that removal by such means is a first-order process with a rate constant β (h -1 ), then the individual intake fraction for a well-mixed indoor environment with constant occupancy throughout an emissions episode is given by this expression: if = B + βv (4) Although equations (3) and (4) are derived for the specific case of an instantaneous pulse release, the same equations can be shown to hold for any episodic release, regardless of the temporal pattern of emissions, provided that the other basic conditions of the derivation are unchanged. Equations (3) and (4) also hold in steady state, if one modifies the intake fraction to be the rate of pollutant inhalation per unit rate of release. Two important assumptions in the derivation are (a) that occupancy occurs throughout the period of release and decay, and (b) that conditions are well mixed. The significance of these assumptions is explored in the next two sections of this paper. TRANSIENT OCCUPANCY Consider this situation. Someone uses a cleaning product containing volatile constituents indoors. Emissions from the cleaning product occur over a finite period. The user is present in the indoor environment for a distinct finite period and then leaves. How does the intake fraction vary according to these time scales? The system we consider is depicted in Figure 1. At time t =, the cleaning activity begins in a room of volume V, ventilated at flow rate. The activity leads to a mass emission rate, E(t), of a chemical species into the room air. Although the emission rate could follow any arbitrary profile, for the present purposes, assume that the emissions are constant at rate m (g h -1 ) for the period < t < T m, and that the rate is zero at all other times. The exposed individual remains in the room, breathing air at a constant flow rate B for the duration of an exposure period, which is defined by the interval < t < T x. Afterward, the exposed individual leaves the space and incurs no further exposure. 1817

3 Figure 1. Schematic of a system for evaluating intake of cleaning-product emissions. Note that the emissions duration T m and the exposure duration T x are independent. That is, emissions might occur rapidly at the beginning of a cleaning activity, such that T m << T x. Conversely, situations can occur in which the cleaning process requires much less time than the duration of emissions, so that T m >> T x. Intermediate cases are possible, too. As in the previous case, two other key assumptions are made here: (1) well-mixed conditions prevail so that the concentration, C(t), is independent of position within the room; and (2) the chemical species is nonreactive and nonsorbing, so that it is only removed by ventilation. This pair of equations describes the time-dependent concentration of the volatile component of the cleaning product: C(t ) = m t < t < T V m (5a) C(t ) = m exp T m V 1 exp t V t > T m (5b) The intake rate of the contaminant is defined by i(t) = C(t) B and has units of mass inhaled per time. The total inhalation intake, I, is determined by integrating i(t) over the entire exposure period, < t < T x. The total mass of contaminant released is obtained by integrating the emission rate over the emission period: T m M = E(t)dt = m T m (6) The intake fraction is the ratio of I to M: if = I T M = x B C(t )dt m T (7) m Case (a). Assume that the exposure period is shorter than the emissions period (T x < T m ). In this case, one need only apply equation (2a) for C(t). 1818

4 T if = B x 1 exp t T m V dt T x < T m (8) This integral is evaluated to obtain this expression for individual intake fraction: if = B T x V T x T m T m V T x < T m (9) Case (b). Assume that the exposure period is longer than the emissions period (T x > T m ) In this case, the concentration integral in equation (7) must be evaluated over two periods, before and after the termination of emissions. if = B t T m V dt + T m T x T m exp T m V 1 exp t V dt T x > T m (1) Carrying out the integrations with some algebraic rearrangement leads to this result: if = B 1 V exp T m T m V 1 exp T x V T x > T m (11) An examination of equations (9) and (11) shows that the individual intake fraction can be expressed as B /, as in equation (3), multiplied by an intake fraction correction factor f: if = B f ( α 1,α 2 ) (12) This correction factor is a function of two dimensionless ratios of time scales: α 1 = T m V emission time to residence time (13) α 2 = T m T x emission time to exposure time (14) Substituting these definitions into equations (9) and (11), we can write f = 1 1 α 1 α 2 α 1 α 2 α 2 >1 (15a) f = 1 1 exp( α α 1 ) 1 1 [ ] exp α 1 α 2 α 2 <1 (15b) Figure 2 displays the correction factor, f, as a function of the parameters α 1 and α 2. The maximum value of f is unity. With α 1 fixed, f tends toward its maximum value as α 2 becomes smaller. When the emissions time is very short compared with the exposure period, exposure is maximized. Conversely, f becomes small for large α 2, since this case represents a situation in which much of the emissions occur after the end of the exposure period. 1819

5 Figure 2. Intake fraction correction factor, f, for transient occupancy as a function of the two dimensionless time-scale ratios, α 1 and α 2. REGARDING INCOMPLETE MIXING In the previous sections, it was assumed that the indoor air could be represented as well mixed. In many circumstances, mixing may be incomplete, and this can affect the intake fraction. Key circumstances where incomplete mixing can be important include buildings in which displacement ventilation systems are employed and exposures of building occupants associated with their own activities, owing to enhanced proximity between occupant and emissions. Space limitations do not permit a thorough exploration of the effects of imperfect mixing. Instead, one key point is made. Let s return to the conditions of the simple example: instantaneous release of mass M in an indoor space of volume V. The pollutant is assumed to be nonreactive so that it is removed only by ventilation, with volume flow rate. One individual, who breathes at volume flow rate B is exposed. By material balance, the pollutant mass released must be balanced by that ultimately removed via ventilation. (The quantity taken up by the occupant is negligible by comparison for practical cases.) Let C V (t) be the time-dependent pollutant concentration in the exhaust airstream and C B (t) be the time-dependent concentration in the breathing zone of the exposed individual. Then, the intake fraction can be expressed as follows: if = C B (t )dt B (16) C V (t )dt The broad form of equation (16) is analogous to that of equation (12). Intake fraction is the ratio of the two airflow rates inhalation to ventilation modified by a correction factor. In this case, the correction factor is the ratio of the time-averaged concentration in the breathing zone of the exposed individual to the time-averaged concentration in the ventilation exhaust air. This correction factor is amenable to being evaluated using methods such as computational fluid dynamics and tracer experiments. REFERENCES Bennett DH, McKone TE, Evans JS, Nazaroff WW, Margni MD, Jolliet O, and Smith KR. 22. Defining intake fraction, Environmental Science & Technology 36: A26-A

6 Klepeis NE. 24. Using computer simulation to explore mult-compartment effects and mitigation strategies for residential exposure to secondhand tobacco smoke, Ph.D. Dissertation, University of California, Berkeley (United States), 395 pages. Lai ACK, Thatcher TL, and Nazaroff WW. 2. Inhalation transfer factors for air pollution health risk assessment, Journal of the Air & Waste Management Association 5: Nazaroff WW, and Weschler CJ. 24. Cleaning products and air fresheners: Exposure to primary and secondary air pollutants, Atmospheric Environment 38: Smith KR Fuel combustion, air pollution exposure, and health: The situation in developing countries, Annual Review of Energy and Environment 18: Wallace LA, Emmerich SJ, and Howard-Reed C. 24. Source strengths of ultrafine and fine particles due to cooking with a gas stove, Environmental Science & Technology. 38: