MODELING THE SIZE DISTRIBUTION OF INDOOR SUSPENDED PARTICULATE MATTER WITH OUTDOOR PARTICULATE MATTER PARAMETERS

Transcription

1 MODELING THE SIZE DISTRIBUTION OF INDOOR SUSPENDED PARTICULATE MATTER WITH OUTDOOR PARTICULATE MATTER PARAMETERS XY Liu, GQ Zhang *, ZM Xiong, Q Zhang College of Civil Engineering, Hunan University, Changsha, Hunan, , China ABSTRACT A mathematical model that can predict the size distribution of indoor suspended Particulate Matter (PM) was proposed, considering the influence of penetration, deposition and filter efficiency. The model was applied to predict the size distribution of indoor suspended PM of five kinds of representative building environment, and the influences of flow length, height of building envelope cracks and the pressure drop across the building envelop on the size distribution of indoor PM were also studied. INDEX TERMS Indoor Particulate Matter, outdoor Particulate Matter, size distribution, modeling INTRODUCTION Because that people spend most of their time indoors, indoor air quality has great impact on the health of residents. As one of the important factors affecting indoor air quality, indoor particulate matter (PM) has already received higher and higher attention. More and more epidemiology studies indicated that airbrone suspended particulate matter is associated with increased morbidity and mortality even at the generally low levels and within related national standards (Dockery et al. 1993, Pope et al. 1995). The studies about the relationship between indoor and outdoor particulate pollution (Ott et al. 2000, Riley et al. 2002) indicated that indoor particulate matter concentrations of outdoor origin are estimated to be on the same order as outdoor concentrations, and that people spend almost 90% of their time indoors (Thatcher et al. 2003), which means that indoor environment is a very important exposure site, even though it is not the most important one. Monitoring the indoor environment is time-consuming and expensive. The indoor environment at different districts may exist great differences, so the data gathered from one site is not representative. On the other hand, the outdoor PM size distribution is always available for there exists monitoring network in cities for airborne pollutants parameters, including PM. It would be a good solution to set up a mathematical model to predict the concentration of the indoor PM according to the size distribution of outdoor PM parameters. RESEARCH METHODS Mass balance model is employed to study the size distribution of indoor suspended PM. The concentration of outdoor PMs in the indoor environment is a balance between the rates at which outdoor PMs enter and leave the air within the building and the rates at which they are removed, transformed, and re-emitted in the indoor environment. Assuming isothermal conditions, no resuspension or coagulation of PMs, no phase change processes, and no indoor PM sources, the size-specific mass balance for PMs of outdoor origin is: d( CV ) = Qm Co (1 η m ) + QnCo + pqico + QrηrC C vd, j S j ( Qm + Qi + Qn ) C (1) dt where C o is the outdoor PM concentration; C is the indoor concentration of PM of outdoor origin; t is the time; j is an index referencing each of the three major surface orientations in the building (upward facing, downward facing and vertical); v d,j is the deposition velocity for orientation j; S j is the surface area with orientation j; η m and η r are the makeup and recirculation filter efficiencies, respectively; p is the PM penetration factor; V is the room volume; Q m, Q r, Q n and Q i are the makeup, recirculation, natural ventilation, and infiltration airflow rates, respectively. * Corresponding author gqzhang@vip.sina.com 1786

2 Penetration Factor Penetration factor (p) is referred to the fraction of outdoor PMs that remain in infiltrating air and enter the building interior. The main mechanisms affecting the penetration factor are brown diffusion and gravity deposition during the progress of PM passing through the building. 1. Assuming that the interior surface of cracks is smooth, the airflow in the cracks is stable, and the PM concentration at the entrance is the same as the concentration in the airflow. During the PMs passing through the building envelop, the penetration factor caused by gravity deposition can be represented by the following equation (Zhou and Hu, 1986): vs L Pg = 1 (2) HU where P g is the penetration factor due to gravity deposition; L is the length of the airflow path in the crack; H is the 2 height of the crack; v s is the deposition velocity of the PM in the crack, v K ρ d g /(18µ) (μ is the coefficient of viscosity; d p is the diameter of the PM; ρ p is the density of the PM; K m is the Cunningham correction coefficient); U is the average velocity of the airflow in the crack, which can be obtained by U=Q/(Hw) (Q is the airflow rate; w is the total length of the cracks of the building envelop. When v s L HU, P g =0). 2. If d p <1μm, the PM might slip among the gas molecule, thus the laminar resistance of the PM would diminish. So the Stock s formula corrected with the Cunningham correction coefficient can be represented: s = m p p R = 3πµ dpv/ K m (3) where R is the fluid resistance of the moving PM in the air medium; v is the PM velocity in the air medium. According to the Ernest-Einstein equation, the diffusion coefficient of single PM in an aptotic medium is(zhou and Hu, 1986): ktv D PM = (4) R where D PM is the diffusion coefficient; k is Boltzmann constant; T is absolute temperature. When PM is parallel to the airflow path at penetrating through cracks, the penetration factor caused by diffusion is (Lee et al. 1980): P d 1.967DPM L 7.868K mktl = exp( ) = exp( ) 2 2 ( H / 2) U 3πµ d H U p (5) Formula (2) and (5) present the penetration factor under gravity and diffusion, respectively. Assuming they are independent, the penetration factor caused by the two mechanisms is: p = P d P g (6) Deposition Rate Deposition is the main method to reduce the PM concentration in the indoor environment. Although there are various experiment data and theory models, the deposition rates that researchers proposed from theoretical modeling or experimental data measuring are quite different, because the deposition seems extremely sensitive to the factors as the environment condition and the PM characteristics. It is difficult to distinguish which model predicts the deposition correctly. In this paper, by applying least-square cubic polynomial fit to logarithmically transformed experimental data, an empirical model of deposition of indoor PM was set up. Figure 1 shows the predicted deposition rates of the PM with diameter from 0.1μm to10μm. Filter Efficiency Fisk et al. (2002) calculated the efficiency of several filters for PMs with diameter between 0.1μm and 10μm. The data of ASHRAE40% filter, ASHRAE85% filter and wall filter are adopted, and linear interpolation between data points was used for PMs with diameters from 0.01µm to 2.4µm. Fibrous-bed filtration theory was used to deduce the results for PMs with diameters smaller than 0.01µm or lager than 2.4µm. The efficiency of wall filter for PMs with diameter smaller than 0.01µm is supposed to 10% (Hanley et al. 1994). Figure 2 is the fitting curve of the 1787

3 efficiencies of the three filters for PMs with diameter between 0.001µm and 10µm. Figure 1. Predicted deposition rates of the deposition rates of the PM with diameter from 0.1μm to10μm (presented by solid line, data sets referenced Riley et al. 2002). Figure 2. Efficiencies of three filters for PMs with diameter between 0.001μm and 10μm. RESULTS AND DISCUSSION Five representative building scenarios are considered in this paper: (1) an office building with a 40% ASHRAE filter (Ofc40); (2) an office building with an 85% ASHRAE filter (Ofc85); (3) a closed residence with continuous central air and a standard wall filter (ResCA); (4) a residence with a high natural ventilation rate as may occur with open windows (ResHV); and (5) a residence with a typical infiltration ventilation rate and no central air (ResTV). The ventilation rates for above scenarios are referred to Riley et al. (2002). Assuming that the crack height of the building envelop is 1mm, the airflow length is 9cm, and the pressure drop across the building envelop is 10 Pa, integrated number, surface area and mass concentrations of airborne suspended PMs in indoor environment are simulated. Figure 3 illustrates the outdoor and predicted indoor number, surface area, and volume concentrations for the two office building scenarios. The overall impact of filtration and deposition differ among the number, surface area, and volume PM distributions because each metric has different size dependence. A large fraction of the number concentration distribution occurs below particle diameters of about 0.05 µm (see figure 3.a), where both deposition and filtration are efficient removal mechanisms. While most of the surface area and volume concentrations are mainly the PMs with diameter below 1µm. The indoor surface and volume concentration for the office equipped with an ASHRAE40% filter is relatively unaffected by the building since the removal mechanisms are inefficient in the accumulation mode (see figure 3.b and c). The ASHRAE85% filter substantially reduces the indoor PM surface area and volume concentration since this filter is more efficient than the 40% filter in the accumulation mode and because the office building recirculation flow rate is relatively high as compared to the makeup ventilation rate. 1788

4 Figure 3. Outdoor and predicted indoor number, surface area and volume concentrations for the two office building scenarios (Ofc85 and Ofc40). Figure 4. Outdoor and predicted mean indoor number, surface area and volume concentrations for the three residential scenarios (ResCA, ResTV and ResHV). Figure 4 shows the outdoor and predicted mean indoor number, surface area and volume concentrations for the three residential scenarios. The surface area and volume concentrations are essentially unchanged across the building envelop for the ResHV building scenario. The number, surface area and volume PM concentration of the ResTV building scenario is very similar to that of the ResCA building scenario. So the wall filter can not effectively remove PMs in the condition of natural ventilation, the proportion of PMs of the residential scenarios which enter into indoor environment from outdoor is larger than that of the office scenarios. For the three residential scenarios, the surface area and volume concentrations of PMs with diameter of about 0.1µm are similar to outdoor PM concentration. Table 1. Crack characteristics of building envelop pressure difference (Pa) length (cm) height (mm) Case Case Case Case Case Case Case Case Figure 5 illustrates the outdoor concentration of outdoor origin for eight kinds of cracks (see table 1) of building envelops except for the ResHV scenario, bercause the size of building cracks has no any influence on the PM size distribution for natural ventilation residence. For ResCA and ResTV scenarios, the length and pressure difference across the cracks have little influence on the size distribute, while the crack height has much greater influence (see figure 5); the pressure difference have greater influence than the crack length in the case of same crack height. For the Ofc40, Ofc85 and ResCA scenarios, crack height, length and pressure difference have nearly no influence, so the filtering effect of building envelop can be ignored in the closed building equipped with filter. 1789

5 Figure 5. Number concentrations of indoor PM for eight kinds of cracks of building envelop CONCLUSION The mathematic model of penetration factor is set up basing on the theory of aerosol mechanics. Applying a least-squares cubic polynomial fit to logarithmically transformed experimental data, an empirical model of deposition of indoor PM is set up. A mathematical model that can predict the size distribution of indoor suspended PM is then proposed, considering the influence of filter efficiency. Finally the model is applied to predict the size distribution of indoor suspended PM of five kinds of representative building environment, and the influences of flow length, height of building envelope cracks and the pressure difference across the cracks on the size distribution of indoor PM were also studied. For the office scenarios with central air handling system, filters can reduce the number concentration of indoor PMs of outdoor origin effectively and the surface area and volume concentration evidently. The filtering effect is greater with higher filter efficiency. The filter is ineffective in the residential scenarios, although filter and deposition can remove PMs at a certain degree, the indoor surface and volume concentration is relatively unaffected across the building envelop especially for the residential scenario with infiltration ventilation. The crack length has little influence on the size distribution of suspended PMs for all scenarios. The crack height, length and pressure difference across the crack have nearly no influence for the office scenarios and residential scenario with central air handling system. The crack height has greater influence, and pressure difference has a little influence for the other residential scenarios. So in the next study, the crack length can be ignored, and different methods will be adopted for different building. ACKNOWLEDGEMENTS The work of this paper is financially supported by the Doctoral Funds for Higher Education of China (No )and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, PR China. REFERENCES Dockery DW., Pope CA., Xu XP., et al An association between air pollution and mortality in six United-States cities, New England J of Medicine. 329: Fisk WJ., Faulkner D., Palonen J., et al Indoor particulate matter of outdoor origin: importance of size-dependent removal mechanisms, Indoor Air. 12: Hanley JT., Ensor DS., Smith DD. et al Fractional aerosol filtration efficiency of in-duct ventilation air cleaners, Indoor Air. 4: Lee KW. and Gieseke JA Simplified calculation of aerosol penetration through channels and tubes, Atmospheric Environment. 14: Ott W., Wallace L., Mage D Predicting particulate (PM10) personal exposure distributions using a random component superposition statistical model, Journal of the Air and Waste Management Association. 50:

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