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Simple and economical measurement of air change rates can be achieved with a passive-type tracer gas doser and sampler. However, this is made more complex by the fact many buildings are not a single fully mixed zone. This means many measurements are required to obtain information on ventilation conditions. In this study, we evaluated the uncertainty of tracer gas measurement of air change rate in

Ventilation is an essential and effective countermeasure for reducing chemical pollution in indoor environments. Ventilation conditions are commonly evaluated by measuring the ventilation volume [m^{3}/h], which is the uptake volume of outside air per unit time. An additional indicator is the air change rate [1/h], which is the ratio of the ventilation volume to volume of the indoor space. The air change rate is usually measured using a tracer gas. The main tracer gas methods use concentration decay, continuous emission, and steady concentration. In the concentration decay method, the tracer gas is released as a pulse into an indoor space and the decay of its concentration with time is continuously monitored. The air change rate can be estimated from the decay trend. This method is suitable for short term (up to several hours) monitoring of air change rate. In the continuous emission method, a constant amount of tracer gas is continuously emitted into an indoor space. The steady state concentration of the tracer gas is measured and used to calculate the air change rate. This method is generally used for long-term air change rate measurements. In the steady concentration method, the tracer gas concentration in the ventilated space is kept constant by controlling the emission rate of the gas. In this method, the variation in the ventilation rate with time is monitored. For all of these methods, complete mixing of the ventilated space is required to accurately estimate air change rate. For detailed discussions of these techniques, see Lagus and Persily [

Passive-type tracer gas doser/sampler systems are a simple and cheap method for measurement of air change rate. Operation of the doser and sampler does not require any electric power, and it is simple enough for residents to operate themselves. Perfluorocarbon (PFC) is a common tracer gas used in these systems. Dietz and Cote [_{6} (Method IP4-B) for standard measurement of air change rates. However, measurements are more complex when many buildings do not consist of a single fully mixed zone. This means many measurements are required to obtain information on ventilation conditions.

The Conjunction Of Multizone Infiltration Specialists (COMIS) model [

In this study, we evaluated the measurement of air change rate for two fully mixed zones from a single measurement with one tracer gas. We discuss the uncertainty in this measurement for

We first considered air change rate measurements in buildings of _{uptake}

where _{0}_{i}_{i}_{i}_{i}_{ij}_{ij}_{0}, is zero. Usually, the measurement time for the tracer gas method is sufficient that the tracer gas concentration is considered to be constant. In each zone, the air volume is also considered to be constant:

This equation reflects the conservation of mass (air) in each zone.

If all fully mixed zones are in contact with each other and the air can freely pass between any two zones, then the number of unknown parameters _{ij}_{ij}_{ij}_{ji}

To avoid this deficit, we have to supplement

As already mentioned, _{uptake}

The indoor air mass balance is given by:

where _{1} is a known value and _{1} is obtained by a tracer gas concentration measurement. _{uptake}

If building consists of two fully mixed zones [_{uptake}

where _{1}_{2}

The air balance is represented by:

There are now six unknown parameters, _{01}, _{02}, _{10}, _{12}, _{20}, and _{21} in the above four balanced equations, which means _{uptake}

A situation such as this usually occurs with

For air change rate estimation of two fully mixed zones from limited information, we can utilize information about the volume of each zone, and tracer gas emission rates in each zone. Information about tracer gas concentrations in each zone can be obtained from passive air sampler measurements. As discussed in Section 2.3., four equations can be established for tracer gas mass balance and air balance for the two zones. There are six unknown parameters, _{01}, _{02}, _{10}, _{12}, _{20}, and _{21}, and _{uptake}

Here, we use estimated air intake, _{e}_{uptake}_{e}

where

One of the purposes of the study is to show that _{e}_{e}_{uptake}

With non-negative restrictions on both parameters, the range of

Because _{e}_{uptake}

With non-negative restrictions on _{1}_{2}

If the steady state concentration of tracer gas in each zone is equal, then the two zones can be treated as one fully mixed zone. So, when

The restriction condition is non-negative restriction of six airflow volumes. There are six unknown parameters in the four balanced equations (_{10} and _{20} are selected as these two parameters, then

If we select _{01} and _{12}, then

and for _{02} and _{21}:

It should be noted that only the symmetry of parameters was considered when selecting these three pairs, and other expressions would also give the same results.

In _{10} and _{20}, the range of

In _{01} and _{12}, we can obtain the range of

In _{02} and _{21}, we can obtain the range of

If non-negative restrictions for all six unknown parameters are considered, then combination of _{1}(_{4} (

the ranges for

The estimation method can then be illustrated in application to a specific situation. It should be noted that the kind of tracer gas does not affect the results. This method is based on steady state. Thus, that requires constant airflow rates over a sufficient period of time for the concentrations to stabilize. Here, we attempt to simply measure the air change rate of two fully mixed zones. _{1} and _{2} are assumed to be 10 m^{3} and 30 m^{3}, respectively. _{1} and _{2} are set as 100 μg/h and 200 μg/h, respectively. _{1}(_{4}(

Thus, the range of _{1} and _{2} are measured to be 30 μg/m^{3} and 10 μg/m^{3}, respectively, air intake _{e}^{3}/h using _{1} (0.5) = −0.33, _{2} (0.5) = 1, and _{3} (0.5) = 0. Thus, from

So, the estimated _{e}^{3}/h) is accurate within 33%, and is an underestimate. From

It should be noted that _{e}^{3}/h as _{e} (error range is ±20%). To minimize the error rate, _{1} and _{2} should be set at the same value. In this case, the maximum error range of air intake _{e} estimated by the methods is always <33%. This error value is equivalent to that reported by Riffat with single tracer gas measurement [_{e}_{,min.} = 20 m^{3}/h).

In this study, we have evaluated the uncertainty in tracer gas measurement of air change rate for

From

Substitution of

For a given _{10} and _{20} we obtain:

where _{10} and _{20} only have positive value, thus, _{max} when _{10}→ +0, _{20}→ +∞, and _{min} when _{10}→ +∞, _{20} → +0. Thus, we can obtain the range of

_{01} and _{12} are only present in the denominator of _{1} − _{2}) ≥0 (_{2}_{01} and (_{1} − _{2})_{12} gives the maximum value for

From substitution of

The minimum value for

When (_{1} − _{2})<0(

_{10} and _{21} are only present in the denominator of _{1} − _{2}) <0 (

When −(_{2} − _{0}) ≥ 0(_{1}_{02} and −(_{1} − _{2})_{21} gives the maximum value for

From substitution of

The minimum value for

Schematic of buildings with 1, 2, or 3 fully mixed zones.

Schematic of a building consists of two fully mixed zones.

The range of _{1}, _{2}, _{1}, and _{2} are equal to 10 m^{3}, 30 m^{3}, 100 μg/h, and 200 μg/h, respectively.

Flow chart for the estimation of air intake and its error range.

The maximum information deficit for

Zone number | Maximum number of unknown parameters (I) | Obtainable information (II) | Maximum information deficit (III) = (I) – (II) |
---|---|---|---|

1 | 2 | 2 | 0 |

2 | 6 | 4 | 2 |

3 | 12 | 6 | 6 |

4 | 20 | 8 | 12 |

2 |