Development of a “²²²Rn incremented method” for the rapid determination of air exchange rate using soil gas

Abstract

The air exchange rate (AER) is a critical parameter that governs the levels of exposure to indoor pollutants impacting occupants’ health. It has been recognized as a crucial metric in spreading COVID-19 disease through airborne routes in shared indoor spaces. Assessing the AER in various human habitations is essential to combat such detrimental exposures. In this context, the development of techniques for the rapid determination of the AER has assumed importance. AER is generally determined using CO₂ concentration decay data or other trace gas injection methods. We have developed a new method, referred to as the “²²²Rn incremented method”, in which ²²²Rn from naturally available soil gas was injected into the workplace for a short duration (∼30 min), homogenized and the profile of decrease of ²²²Rn concentration was monitored for about 2 h to evaluate AER. The method was validated against the established ²²²Rn time-series method. After ascertaining the suitability of the method, several experiments were performed to measure the AER under different indoor conditions. The AER values, thus determined, varied in a wide range of 0.36–4.8 h⁻¹ depending upon the ventilation rate. The potential advantages of the technique developed in this study over conventional methods are discussed.

1. Introduction

The air exchange rate (AER) is an important parameter closely related to the health of populations exposed to indoor pollutants. With the unfolding of the recent outbreak of the COVID-19 pandemic, the importance of understanding the airborne infection transfer mechanism has become increasingly apparent. The importance of indoor ventilation was stressed to minimize the transfer of infections in shared spaces (Anand et al., 2021). The AER is defined as the ratio of volumetric air supply rate Q(t) into a zone (i.e. a room or space) to the volume (V _R) of this zone and is generally expressed as air change per hour (h⁻¹) or (ACH or AER). The concentration of a pollutant species in the indoor space varies inversely with the AER. Therefore it is a crucial determinant of indoor air quality. Comfortable and healthy indoor climate conditions can only be achieved by a constant supply of fresh air. AER is one of the parameters considered in several countries while designing buildings for public occupation. However, AER has not been given adequate importance in tropical climatic regions and data on this parameter is virtually non-existent. With rapid industrialization resulting in the degradation of the air quality in the indoor environment, there is an urgent need to establish database on indoor air pollution and AER for different climatic regions. Such studies are expected to serve a vital role in understanding and modelling the transmission of viral-related diseases such as the COVID-19 pandemic presently affecting the world.

In the past, uses of gases such as helium, hydrogen, oxygen, carbon monoxide, methane, acetone, and the radioactive noble gases ⁴¹Ar and ⁸⁵Kr have been examined for the determination of AER. Excellent reviews on these are given by Grimsrud et al. (1980), Shaw (1984), and Sherman (1990). Until the early 1990s, ⁸⁵Kr was used for AER measurement (Schulze and Schuschke, 1990) but was later discontinued due to safety and economic reasons. Subsequently, the application of Nitrous oxide (N₂O) (Abu-Jarad et al., 1982), Sulfar hexafluoride (SF₆) (Nero et al., 1983), Hexafluorobenzene (C₆F₆) (Hirsch et al., 2000), Perfluorocarbons (PFC) (Raatschen, 1995), and Carbon dioxide (CO₂) (Munzenberg., 2004) have been explored. However, these methods have several disadvantages such as (i) the need for injecting an external tracer in occupied buildings, (ii) adsorption on surface or wall deposition of the injected chemical tracer, (iii) environmentally hazardous and expensive, and (iv) the tracer concentration is influenced by the number of occupants in the rooms being examined for AER.

Nitrous oxide (N₂O) was widely used for AER measurement in buildings, primarily in Europe (Heidt and Werner, 1986; Keller and Beckert, 1994; Salthammer, 1994; Wegner, 1983, 1984) and in the U S A (Lagus and Grot, 1997). Often injection of this gas above 100 ppm is necessary for determining the AER with reasonable accuracy, but this concentration is above the permissible limit of 50 ppm for the living environment (Detlef et al., 2011; Raatschen, 1995). Other disadvantages of N₂O are the ease of adsorption on the surface of the walls and its high solubility in water, which leads to an overestimation of the AER (Schulze and Schuschke, 1990). The SF₆ has been widely used for air infiltration measurement in buildings since the early 1970s (Drivas et al., 1972; Hunt and Burch, 1975) as it can be measured reliably on the nanogram scale with electron capture detection (ECD) (Gregory, 1962). On the other hand, due to its high stability, degradation of SF₆ in the atmosphere is prolonged, and it should be used with caution, sparingly, and at low concentrations. CF₆ and PFT have also been used as tracer gases for the determination of the AER with the constant injection method. However, the disadvantage of these compounds is their attachment to room surfaces and the emission rates of these gases are strongly temperature-dependent (Hill et al., 2000). CO₂ is often used to determine the indoor AER because it can be easily measured and quantified (Detlef et al., 2011).

Although CO₂ fulfils a number of the specifications of good tracer gas; Dols et al. (1992), Nabinger et al. (1994), and Persily (1997) have illustrated that AER cannot be consistently determined with this method since its concentration is highly influenced by the number of inhabitants in the rooms, their time of stay, and other factors, and, hence, the incessantly changing CO₂ supply rates. The metabolically generated CO₂ overlaps with the externally injected CO₂ leading to uncertainty in AER measurement. Furthermore, depending on the extent of natural ventilation, the AER may be overestimated up to 2-fold (Detlef et al., 2011). Hence, efforts are constantly made to develop new methods for the estimation of AER.

Radon (²²²Rn) has the potential to be used as a tracer to study indoor AER with several advantages. They are: (i) it is a naturally occurring radioactive gas and ubiquitous in indoor as well as the outdoor environment, (ii) easily measurable even at very low concentration levels by passive and active monitors, (iii) the mechanism of its transportation in the indoor and outdoor atmosphere is very well understood, (iv) its concentration is independent of human presence. Although the concentration of ²²²Rn undergoes diurnal and seasonal variation, and also depends on ambient temperature, humidity, pressure, etc., apart from the ventilation rate of the building, these can be adequately addressed by time-series analysis (TSA) methods. There are four possible methods through which ²²²Rn can be used for determining AER: (i) by examining the monthly average equilibrium factor between ²²²Rn and its decay products, which would yield a pseudo-ventilation rate (Shaikh et al., 1992), and from this wall loss rate can be subtracted to yield air exchange rate, and (ii) measurement of wall exhalation rate using active ²²²Rn monitors (from the knowledge of surface averaged wall exhalation rate, the ratio of indoor surface area to the volume, and the difference between the averaged indoor ²²²Rn concentration to the outdoor concentration, one can estimate the AER), and (iii) analysis of long term time-series data of ²²²Rn concentration in indoor air (established using online continues ²²²Rn monitors) in which the spectral component and fundamental frequency of the time-series is related to mean ventilation rate.

These methods have known disadvantages. The ²²²Rn progeny measurements and the use of equilibrium factors have significant uncertainties as the progeny concentrations are influenced by their deposition rates on walls and aerosol concentrations. Besides, the method requires long-term monitoring (typically more than a month). The ²²²Rn wall exhalation measurements method is experimentally challenging and often involves significant uncertainties. We have developed a method which we refer to as the “²²²Rn incremented method” for rapid determination of AER. In this method, ²²²Rn is injected into the indoor environment to be investigated and concentration is monitored continuously for ∼2 h. The decay rate (loss of ²²²Rn due to the exchange with atmospheric air) would directly yield AER. The above method overcomes several disadvantages of the previously explored methods and is simple, user-friendly, and uses ²²²Rn from the natural soil gas as a tracer.

2. Materials and methods

2.1. Extraction of soil gas

As discussed just above, ²²²Rn present in soil gas is used as a tracer for the determination of AER. Soil gas is a non-depleting reservoir of ²²²Rn and is capable of providing steady concentration flux even when drawn continuously for a long time duration, as demonstrated in the previous publications (Karunakara et al., 2015, 2020; Shetty et al., 2020). The details of soil gas ²²²Rn extraction were described in our earlier publications (Karunakara et al., 2015, 2020; Sudeep et al., 2012; Shetty et al., 2020). A soil gas probe (STITZ, Genitron Instruments, Germany) was inserted inside the ground to a depth of 0.8–1 m since the ²²²Rn concentration in soil gas increases exponentially with depth and saturates to an equilibrium concentration at a depth greater than about 0.8–1 m (Nazaroff and Nero, 1988; Al-Azmi and Karunakara., 2007; Al-Azmi, 2009; Sudeep et al., 2012; Katalin et al., 2013; Shetty et al., 2019; 2020; Karunakara et al., 2015, 2020). A pump with adjustable flow rates (10–80 L min⁻¹, depending upon the experimental requirements) was connected to the probe to draw the soil gas and inject it into the workplace as shown in Fig. 1 . The outlet of the soil gas probe was connected to an air pump through a progeny filter, moisture filter, and a flow meter with a controller. Soil gas was drawn through this arrangement and injected into the indoor workplace. The use of soil gas as a source of ²²²Rn has several advantages and was discussed in Karunakara et al. (2020) and in brief, they are (i) ²²²Rn is naturally available in the soil gas as a source, (ii) soil gas is capable of supplying steady ²²²Rn concentration over a long period without any dilution in the concentration, (iii) there is no need of regulatory approvals from national regulatory bodies for the use of soil gas, and (iv) the health risk associated with a short-term injection of ²²²Rn into the dwelling is insignificant.

Fig. 1.

Experimental set-up for harvesting soil gas as a natural source of ²²²Rn for the determination of AER in the indoor workplace.

2.2. Selection of indoor workplaces and dwellings

Different indoor workplaces such as classrooms, staff rooms, and laboratories within the Mangalore University campus (12.82° N, 74.92° E) were chosen for this study based on the size, type of occupancy, and extent of ventilation. The volume of the workplaces was in the range of 28.9–146.2 m³. In addition to this, some residential buildings were investigated in the urban and rural regions of Mangalore, West Coast of India. The building materials used in investigated buildings were laterite brick walls, cement plastering, and concrete roofs. The floorings were laid either with tiles, granite or marble.

2.3. Instruments for ²²²Rn measurement

The ²²²Rn concentration was continuously monitored using two different types of monitors: (i) scintillation cell-based monitors (Smart RnDuo, AQTEK SYSTEMS, India) and (ii) ionization chamber-based monitors (AlphaGuard PQ2000PRO and AlphaGuard Professional, Saphymo, Germany). These instruments have the capability to simultaneously record ambient humidity (%), temperature (^◦C), and pressure (mbar). The ²²²Rn detection range of the scintillation cell-based monitor was 8 Bq m⁻³ to 50 MBq m⁻³, while the ionization chamber-based monitor was 2 Bq m⁻³ to 20 MBq m⁻³. The detailed specification of these instruments was published previously (Al-Azmi and Karunakara, 2007; Karunakara and Al-Azmi, 2010; Karunakara et al., 2015; Sudeep et al., 2017; Sahoo et al., 2017; Shetty et al., 2019).

Periodic calibration of these instruments was performed at Bhabha Atomic Research Centre (BARC), Mumbai, using a standard solid flow-through type ²²⁶Ra source of activity 110.6 kBq (model RN -1025, Pylon electronics, Ottawa, Canada). The readings provided by the scintillation-based ²²²Rn monitor and ionization chamber-based monitors were in good agreement (the deviation between the ²²²Rn data recorded by the two types of monitors was <2%). The scintillation cell-based monitor was operated in flow mode with an operational cycle interval of 15 min, and the ionization chamber-based monitor was in 10 min flow mode.

The detection of ²²²Rn by these instruments is unaffected by humidity and other trace gases (CO₂, CH₄, etc.) that may be present in the soil gas, unlike the electrostatic collection-based ²²²Rn and ²²⁰Rn monitors (Karunakara et al., 2015).

2.4. Experimental setup for determination of AER

Two sets of experiments were performed in this study. In the first set, experiments were performed to evaluate the AER by the ²²²Rn time-series method by continuously recording the indoor ambient ²²²Rn concentration for the long-term to generate the time-series of concentration values. In the second set of experiments, the application of the ²²²Rn incremented method was examined for the determination of AER. These are discussed in the following sections.

2.5. Application of indoor ambient ²²²Rn for determination of AER

In this method, long-term and continuous measurements of ²²²Rn were performed using an ionization chamber based-monitor to record variations in the ambient background concentrations. Meteorological parameters such as air temperature (^◦C), pressure (mbar), and relative humidity (%) were also recorded simultaneously. The time-series database on ²²²Rn and its periodicity were subjected to autocorrelation analysis. Autocorrelation analysis is a mathematical technique for detecting repeating patterns, such as the presence of a periodic signal disguised by noise or identifying a signal's missing fundamental frequency inferred by its harmonic frequencies. It is an excellent method of getting smooth periodicity. The inverse of the decay constant can be interpreted as AER by performing the exponential decay fit for the detrended ²²²Rn data with respect to time. The use of the ²²²Rn time-series technique for evaluating AER was applied by several investigators previously (Bobby, 1991, 1993; Hobbs, 1999; Antonio et al., 2008; Perrier et al., 2004; Michael et al., 2018; Yarmoshenko et al., 2015, 2016, 2021) and is one of the proven methods.

2.6. Determination of AER by ²²²Rn incremented method

In the ²²²Rn incremented method, developed in this study, soil gas was drawn, as explained in section 2.1, and injected into the indoor workplace under investigation for nearly 30 min. The injected ²²²Rn was allowed to mix uniformly with the indoor air using a circulating fan. Through the injection of soil gas, the ²²²Rn concentration in the indoor air was increased to slightly elevated levels (1–2 kBq m⁻³) when compared to its concentration in ambient air. After thorough mixing for ∼15 min, the concentration in the indoor workplace was monitored continuously until it decreased to the ambient background level. The rise in the ²²²Rn concentration due to the injection of soil gas and its subsequent decrease was monitored continuously (for every 1-min cycle) along with meteorological parameters until the concentration values reached the ambient background level, which was about 2 h.

The measured ²²²Rn concentration values were plotted as a function of time, and the exponential decay fit to the data was performed to yield residence time (t₁) of ²²²Rn in the indoor air. The inverse of residence time (1/t₁) is the AER. It is important to note that the loss of ²²²Rn injected into the indoor air due to radioactive decay (half-life = 3.82 d, decay constant = 0.0075 h⁻¹) is negligible when compared to that due to the exchange with atmospheric air or AER.

The equation used to calculate the AER is:

$$y=A*{\exp }^{\left(\frac{-x}{t_1}\right)}+y_0$$ (1)

where A, t₁ and y₀ are the parameters to be obtained by best fit, t₁ represents the mean residence time, and its inverse 1/t₁ represents the AER.

2.6.1. Monitoring spatial distribution of injected ²²²Rn

Experiments were carried out to check the homogeneous mixing of injected ²²²Rn by simultaneous measurements at five different locations within the workplace environment. For this, ²²²Rn was injected into the room for nearly 30 min and was thoroughly mixed with ambient air of the room using a circulating fan for about 15 min (2000 rpm). Subsequently, the ²²²Rn concentration was measured simultaneously at five different locations within the indoor workplace using scintillation and ionization-based monitors.

2.6.2. Evaluation of thoron (²²⁰Rn) interference in ²²²Rn measurement

Although the ²²⁰Rn interference in the ²²²Rn measurements is not expected due to its very short radioactive half-life (55.6 s), experiments were carried out to confirm this as well. This was achieved by simultaneous monitoring of both radioactive gases during the experiment. Both scintillation and ionization based monitors were deployed to measure ²²²Rn concentration, and the ²²⁰Rn concentration was measured using a scintillation cell-based thoron monitor (Model: STM, manufacturer: Electronic Enterprises Limited, India). The details of the instrument and technique of ²²⁰Rn measurements were presented in a previous publication (Gaware et al., 2011, 2013; Karunakara et al., 2015; Sudeep et al., 2017). The STM is a continuous thoron monitor that uses the principle of coincidence counting between the alpha particles produced from the ²²⁰Rn and ²¹⁶Po combined with gross alpha counting in a scintillation cell. It has a minimum detection limit (MDL) of 5 Bq m⁻³ for 1 h counting time. It was calibrated against a standard concentration generated in a calibration chamber using a standard source of ²²⁰Rn (Pylon, Canada, Model TH -1025) as well as inter-compared with reference equipment - RAD-7 (Model: DURRIDGE RAD7).

2.6.3. Measurement of diurnal variation of AER

The ²²²Rn incremented method was explored to evaluate the variations in the AER during day and night. For this, experiments were performed during different time slots (5–8 h, 8–11 h, 11–14 h, 14–17 h, 17–21 h, 21-2 h, and 2–5 h) in the 24 h duration of a day. In this case, ²²²Rn gas was injected, and the experiment was performed to determine the AER, as explained in the previous section.

3. Results and discussion

3.1. AER evaluation by measurement of ambient ²²²Rn concentration (time-series method)

The ²²²Rn concentration, temperature, relative humidity, and pressure in both indoor and outdoor locations were measured as outlined in sections 2.3-2.5. The results are presented in Table 1 . Measurements were performed in 15 workplaces and 11 dwellings using either scintillation or ionization-based monitors, or both instruments simultaneously depending on the availability. The duration of measurement in each location varied from 20 to 30 d. For these measurements, the instruments were operated in diffusion mode in which the ²²⁰Rn does not interfere with ²²²Rn measurements since the former is discriminated from entering the detector active volume (Karunakara et al., 2015, 2020; Sudeep et al., 2012; Shetty et al., 2020). A good agreement between the measurements recorded using these two types of instruments was ascertained by subjecting the ²²²Rn concentration data sets obtained from the instruments to statistical analysis. The ANOVA and F- tests confirmed that the mean values of the two data sets were not significantly different at 95% confidence level (for α = 0.05, F_observed = 0.003 and F_{0.05 (2, 72)} = 3.123).

Table 1.

Radon concentration and meteorological parameters at indoor and outdoor.

Measurement location	222Rn concentration(Bq m−3)		Relative humidity (%)		Temperature (°C)
	Range	mean	Range	mean	Range	mean
Indoor	2–84	38.5 ± 20.9	69–75.5	72.5 ± 1.8	27.1–30	29.9 ± 1.4
Outdoor	1.6–35.7	12.5 ± 7.6	60.8–78.7	69.5 ± 5.6	26.3–30.9	28.9 ± 1.7

The time-series dataset for one of the workplaces is presented in Fig. 2 as a representative result. The variation of ²²²Rn concentration, relative humidity, and temperature are also presented in the same figure. As expected, the time-series data exhibited the dependence of ²²²Rn concentration values with temperature and humidity. These are the most important parameters which affect the ²²²Rn concentration (Hubbard et al., 1992; Singh et al., 2005; Ju et al., 2018; Pranas et al., 2020), and it indirectly influences the AER. A sine fit (of the form Y Y₀+A*Sin [π*(x-x_c)/w], where x_c is the phase shift, w is the period, A is the amplitude, and Y₀ is the offset) was used to extract the underlying periodicity in the dataset. It depicts the existence of a semi-sinusoidal diurnal variation trend in the indoor ²²²Rn concentration with a periodicity of ∼24 h. After detrending the data with respect to periodic variations, the information on AER was extracted by performing autocorrelation. The data set was first smoothened by Fast Fourier Transform (FFT), using Mathematica computer software (Wolfram Mathematica 7, USA). Basically, detrending eliminates a time-series trend component (removing the non-stationary time-series trend), where a trend refers to a change in the mean over time (a continuous decrease or increase over time). Since air exchange is a first-order process one can extract the 1/t value (which is nothing but AER) from the exponential fit to the plot of detrended ²²²Rn data as shown in Fig. 3 . The AER values, thus obtained, are presented in Table 2 . Depending upon the type of indoor workplace and dwellings, the AER values varied in a wide range of 0.36–4.8 h⁻¹. The values reported by previous investigators for indoor workplaces, dwellings, and caves by the ²²²Rn time-series method vary in the range of 0.1–2.0 h⁻¹ (Bobby, 1991, 1993; Hobbs, 1999; Antonio et al., 2008; Perrier et al., 2004; Yarmoshenko et al., 2014, 2021; Vasilyev et al., 2015, 2016).

Fig. 2.

Time series data of ²²²Rn concentration, relative humidity, and temperature.

Fig. 3.

Exponential decay fit for the detrended ²²²Rn time-series to extract AER.

Table 2.

AER values derived from²²²Rn time-series method for different workplaces and dwellings.

Sl No	Measurement location	Rooftop	Number of windows	Number of doors	Volume of the indoor (m3)	AER(h−1)
1	Workplaces	concrete	2 (C)	2	41.5	0.97 ± 0.06
2		concrete	4 (C)	1	113.4	1.15 ± 0.06
3		concrete	–	3	27.5	3.40 ± 0.17
4		concrete	2 (C)	2	124.3	0.78 ± 0.04
5		False ceiling	2 (C)	1	92.0	0.72 ± 0.04
6		False ceiling	2	1	94.0	3.02 ± 0.16
7		False ceiling	2 (C)	1	94.0	0.38 ± 0.02
8		False ceiling	2 (C)	1	95.5	1.90 ± 0.10
9		concrete	2	1	29.8	2.20 ± 0.10
10		False ceiling	2	1	71.8	4.00 ± 0.10
11		False ceiling	–	3	88.5	0.54 ± 0.03
12		False ceiling	4 (C)	1	141.0	0.63 ± 0.03
13		False ceiling	4 (C)	1	146.2	0.40 ± 0.02
14		False ceiling	4 (C)	1	138.7	0.36 ± 0.01
15		False ceiling	4 (C)	2	118.5	0.86 ± 0.05
16	Dwellings	False ceiling	2	1	56.0	0.73 ± 0.04
17		concrete	2 (C)	1	52.9	0.62 ± 0.03
18		concrete	2	1	43.7	2.40 ± 0.10
19		concrete	1 (C)	1	42.6	1.15 ± 0.06
20		concrete	2	1	39.5	4.80 ± 0.30
21		Tiles (mud)	1	1	33.4	2.40 ± 0.10
22		concrete	2	1	42.5	4.60 ± 0.30
23		concrete	1	1	34.4	1.51 ± 0.07
24		Tiles (mud)	2	1	29.5	0.74 ± 0.04
25 26		concrete concrete	– 2 (C)	1 1	28.9 32.3	0.66 ± 0.03 0.40 ± 0.02

(C): windows closed all the time.

3.2. Radon incremented method for AER measurements –the new method

Determination of the AER through ²²²Rn time-series data has associated disadvantages due to its necessity to perform measurements for a long duration, typically for more than 30 d. However, in situations where the AER is to be determined quickly, methods capable of yielding accurate results in a rapid time are essential. The ²²²Rn incremented method, developed in this study, fulfils this requirement and is hence advantageous. Before conducting experiments on AER, it is essential to ensure that the ²²²Rn injected from the soil gas is distributed uniformly within the workplace volume. It is also important to ensure that the ²²⁰Rn interference is minimal in ²²²Rn measurements. Hence experiments were conducted to study these aspects.

As explained in section 2.6.1, the soil gas was injected and mixed with indoor air using the circulating fan and the ²²²Rn concentration was monitored at five different locations within the indoor workplace to check the homogeneous distribution of the injected ²²²Rn using two ionization-based monitors, and three scintillation-based monitors. The results of these measurements are presented in Fig. 4 . The ²²²Rn concentration data sets obtained from the instruments were subjected to statistical analysis. The ANOVA and F- tests confirmed that the mean values of the five data sets were not significantly different at a 95% confidence level (for α = 0.05, F_observed = 0.004 and F_{0.05 (4, 120)} = 2.447). This confirmed a homogeneous distribution of ²²²Rn in the indoor air of the workplace.

Fig. 4.

Variation of ²²²Rn concentration at five different locations within a workplace. Simultaneous monitoring to check the homogeneous mixing of ²²²Rn injected from soil gas.

It is important to ascertain that ²²⁰Rn interference in the ²²²Rn measurements is negligible in the incremented method because (i) instruments are operated in flow mode without ²²⁰Rn discriminator, and (ii) ²²⁰Rn is also present in soil gas in higher concentration when compared to that in ambient air. The experimental arrangements were such that the transit time for the soil gas in the conduit from the point of extraction to the injection point in the room was ∼10 s (Karunakara et al., 2015, 2020; Sudeep et al., 2012; Shetty et al., 2020). But, the important aspect is the delay volume offered by the indoor workplace which ensures that ²²⁰Rn concentration is decayed to a negligibly small value. Moreover, after the injection of the soil gas the injected soil gas was allowed to mix homogenously for 10–15 min using mixing fans. This allowed sufficient time for the decay of ²²⁰Rn present in the injected air. To confirm this, several experiments were performed as explained in section 2.6.2. The results for one of the experiments are presented in Fig. 5 as a representative one. After the injection of the soil gas, the ²²²Rn concentration reached a maximum value of 1.7 kBq m⁻³. On the other hand, the average ²²⁰Rn concentration remained negligibly low (54 ± 24 Bq m⁻³) when compared to ²²²Rn. Therefore, the contribution of ²²⁰Rn interference on ²²²Rn measurement can be ignored.

Fig. 5.

Comparison of ²²²Rn and ²²⁰Rn concentrations within a workplace (simultaneous monitoring to quantify ²²⁰Rn interference in the ²²²Rn measurements).

Upon confirming good uniformity of injected ²²²Rn within the workplace volume and negligible influence of ²²⁰Rn on ²²²Rn measurements, several experiments were conducted to check the suitability of incremented method in eight indoor workplaces that are expected to have different AER depending upon the number of windows and doors (section 2.6). As a representative result, the ²²²Rn concentration profile for one of the workplaces is presented in Fig. 6 . Depending upon the type of the workplace (size, number of open doors and windows in the workplace), the AER varied in a wide range of 0.37–3.47 h⁻¹.

Fig. 6.

Exponential decay fit for the measured ²²²Rn concentration data (incremented method) to extract AER. The corresponding AER value, thus determined, was 3.47 h⁻¹.

3.3. Validation of ²²²Rn incremented method and advantages

The validation of the incremented method was achieved through the comparison of the AER results with those obtained from the ²²²Rn time-series method. As enumerated in sections 2.5 and 3.1, the ²²²Rn time-series method is considered to be a proven method (Yarmoshenko et al., 2014, 2021; Vasilyev and Zhukovsky, 2013; 2015, 2016). Fig. 7 presents the correlation between the AER values obtained from the two methods. The linear fit to the dataset yielded a significant positive correlation between the two methods with a correlation coefficient r = 0.998 (p = 0.0001, slope = 1.025). Also, the ANOVA and F- tests confirmed that the mean values of the two data sets were not significantly different at a 95% confidence level (for α = 0.05, F_observed = 0.002 and F_{0.05 (1, 14)} = 4.6). These observations confirm that the ²²²Rn incremented method is capable of yielding accurate results and hence gainfully applied for the rapid determination of the AER in indoor workplaces. The added advantages of this method is that the naturally available ²²²Rn from soil gas was utilized as a tracer, which is very convenient to use.

Fig. 7.

Correlation between AER values obtained from ²²²Rn time-series (horizontal axis) and ²²²Rn incremented method (vertical axis).

3.4. Possible radiation dose due to ²²²Rn incremented method to the indoor occupants

In the present study, the experiments were performed when the workplaces were not occupied by the individuals. However, it is worth noting that the additional radiation dose to the occupant due to the use of ²²²Rn for the experiments would be negligibly small even in situations in which experiments are performed when the workplace is occupied. For an indoor ²²²Rn concentration of 2 kBq m⁻³ due to the injection of soil gas, as the case in the present study, the resulting additional radiation dose was computed to be 25 μSv. This was arrived at by considering an exposure duration of 2 h, an equilibrium factor of 0.4 (UNSCEAR, 2000), and using the dose coefficient of 16.8 nSvh⁻¹(Bqm⁻³)⁻¹ (ICRP-137, 2017). It may be noted that the value of 25 μSv is a higher estimate since the average concentration corresponding to the experiment duration was 300–400 Bq m⁻³ (the average concentration is calculated for the experimental duration τ = 2 h, with mean residence time = 1/λ, a typical ventilation rate of 0.5 h⁻¹). The one-time exposure of 25 μSv is about two orders of magnitude lower than a typical annual baseline exposure of 2.34 mSv to the population in normal background radiation areas (UNSCEAR, 2000). Moreover, it is well within the variability of dose to an individual from natural background radiation, which varies from 1 to 10 mSv (UNSCEAR, 2000). It is also within the regulatory framework which permits the use of radiation at very low levels of exposure, such as the one presented here, for applications which are of benefit to society.

However, we recommend that the experiments to measure AER are conducted when the workplaces or dwellings are not occupied to ensure that there is no additional radiation burden to the individuals. As shown in Fig. 6, the incremented ²²²Rn concentration level due to the injection of soil gas reduced to the ambient level in ∼120 min. The individuals may be allowed to return to the workplace or dwelling after confirming that the ²²²Rn concentration level has reduced to ambient levels. By exercising this precaution one can avoid additional radiation burden to the inhabitant due to the AER measurements.

3.5. Evaluation of diurnal variation of AER in the indoor workplace

The ²²²Rn incremented method based AER measurements were performed continuously for 20 d in one of the indoor workplaces to evaluate the diurnal variation in the AER. In these measurements, the daytime was divided into four time slots (5–8 h, 8–11 h, 11–14 h, and 14–17 h), and similarly, nighttime was divided into three time slots (17–21 h, 21-2 h, and 2–5 h). The typical variations of the ²²²Rn concentration profiles for different time slots are presented in Fig. 8 , along with corresponding AER values. As expected the AER values were higher during daytime when compared to those recorded for nighttime. The mean value of AER for the daytime was 0.87 h⁻¹, and that for nighttime was 0.46 h⁻¹. The two-fold higher AER values during daytime can be attributed to the higher ventilation rates since the doors and windows were kept open during the daytime.

Fig. 8.

Variation of AER values determined from the ²²²Rn incremented method for different time slots of a day. (a) For the daytime (5–8 h, 8–11 h, 11–14 h, and 14–17 h), and (b) for the nighttime (17–21 h, 21-2 h, and 2–5 h).

3.6. Comparison of AER values with previously reported data

Several earlier studies have reported the AER values, and these values are listed and compared with the values observed in the present study in Table 3 . The reported data are grouped based on the methods adopted (i) ²²²Rn time-series method, (ii) ²²²Rn decay products method, (iii) gas sensing technique, (iv) constant injection method, (v) concentration decay and build-up methods, (vi) steady-state injection method and (vii) decay method (non-radioactive gas). The reported values of the AER have a wide range from 0.02 h⁻¹ to 84.1 h⁻¹. The values observed in the present study are similar to those reported by Abu-Jarad et al. (1982), Nero et al. (1983), Christopher et al. (1997), Giesbrecht et al. (1999), Salthammer (1994), Shaikh et al. (1992), Gabriel et al., 2010, Gabriel et al., 2016. On the other hand, the values recorded in the present study are lower when compared to those reported by Samer et al. (2014) and higher when compared to those reported by Giesbrecht et al. (1999), Helm et al., (2011), Fronka et al. (2011), Munzenberg., (2004), Benedettelli et al. (2015), Men et al., (2020).

Table 3.

Comparison of AER values obtained in the present study with those reported in the literature.

Country	Method	Tracer gas	AER(h−1)	Reference
Mangalore India	222Rn incremented method	222Rn	0.37–3.47	Present study
Mangalore India	222Rn time-series method	222Rn	0.36–4.8	Present study
Russia		222Rn	0.1–0.6	Yarmoshenko et al. (2014)
Russia		222Rn	0.26–0.52	Vasilyev et al. (2016)
USA		222Rn	0.35–2.0	Hobbs (1999)
France		222Rn	0.96–5.28	Perrier et al., 2004
India	222Rn decay products method	222Rn decay products	0.42–4.46	Shaikh et al. (1992)
UK	Gas sensing technique	Freon11 Freon 12 N20 Halothane	0.93–2.89	Abu-Jarad et al., 1982
Norway	Constant injection	PFT	0.15	Oie et al., 1998
Denmark		PFT	0.16–0.96	Andersen et al. (1997)
Germany		C6F6	0.73	Hirsch et al. (2000)
Denmark		PFT, PMCP, and PMCH	0.1–2.70	Beko et al., 2016
China		CO2	0.84	Pok et al., 2014
Denmark	Concentration decay and build-up	CO2	0.1–1.0	Beko et al., 2010
China	Steady-state injection method	CO2	0.12–11.2	Yan et al. (2012)
China	decay method	CO2	0.29	Jing et al. (2017)
Germany		CO2	0.02–1.98	Helm, 2011
Germany		CO2	0.05–1.5	Munzenberg., 2004
China		CO2	0.11–10.4	Yan et al. (2012)
Hong Kong		CO2	0.2–5.4 (day) 0.2–9.0 (night)	Chao et al., 1997
Italy		CO2	0.15–0.16	Benedettelli et al. (2015)
China		CO2	0.78–1.35	Men et al., 2020
China		CO2	0.90	Pok et al., 2014
China		CO2	0.41	Cheng and Li. (2018)
Portugal		CO2	0.17–0.33	Almeida et al., 2020
Portugal		CH4 and CO2	0.13–7.59	Clito (2013)
China		SO2	0.81–1.45	Men et al., 2020
USA		SF6	0.039–4.10	Wallace et al. (2002)
Czech Republic		N20	0.049–0.061	Fronka et al. (2011)
Portugal		N2O	0.92–1.01	Giesbrecht et al. (1999)
Portugal		H2O	0.22–0.78	Giesbrecht et al. (1999)
Denmark		TEE	0.1–1.5	Harving et al. (1992)
Israel		SF6	0.03–0.25	Rachel et al., 2014
USA		SF6	0.03–1.1	Nero et al. (1983)
Portugal		SF6	0.17–0.98	Almeida et al., 2020
Germany		NO2	0.1–1.7	Salthammer, 1994
Egypt		Krypton-85	17.8–84.1	Samer et al. (2014)

3.7. Applicability of the technique in dense urban environments

Finally, we comment on the applicability of the technique in high-rise buildings in dense urban environments where arrangements to draw soil gas and injection into the indoor environment under investigation would be difficult. In such situations, the soil gas can be transported from a designated point of extraction to the experiment site through leak-proof inflatable airbag arrangements for injection as desired. Such arrangements have been demonstrated previously for calibration experiments for ²²²Rn measuring devices using soil gas (Al-Azmi, 2009).

4. Conclusion

The technique demonstrated in this study to determine indoor AER using the ²²²Rn incremented method, utilizing ²²²Rn from natural soil gas, has yielded encouraging results. The advantages of this technique over conventional methods are: (i) it allows rapid determination of AER, (ii) the use of naturally available soil gas as a source of ²²²Rn, (iii) the concentration of ²²²Rn can be measured in trace levels by active measuring systems, and its distribution and transit mechanisms in the atmosphere are very well understood and (iv) the measurement is unaffected due to human presence unlike CO₂.

Although in the present study the experiments were performed when the workplaces were not occupied by the individuals, it is worth noting that the additional radiation dose to the occupant due to the use of ²²²Rn would be negligibly small (<25 μSv) even in situations in which experiments are performed when the workplace is occupied. However, we recommend that the experiments are conducted when the workplaces or dwellings are not occupied to ensure that there is no additional radiation burden to the inhabitants. The individuals may return to the workplace or dwelling after confirming that the ²²²Rn concentration level has reduced to ambient levels. The results of the present study have confirmed that for a typical AER of 3.47 h⁻¹ the incremented ²²²Rn concentration level due to the injection of soil gas reduced to the ambient level in ∼2 h.

The AER in typical dwellings and workplaces of the tropical region of the West Coast of India ranged from 0.36 to 4.8 h⁻¹. The technique is sensitive enough to quantify small variations in the AER values, as demonstrated by the diurnal variation studies. A large-scale study based on the new method in the actual indoor environment of both urban and rural regions of the West Coast of India and the comparison of the results with tracer gas techniques is now progressing. The limitations of the technique in the dense urban environment, where drawing soil gas and injecting it into the indoor environment in a high-rise building is difficult, may be overcome by the use of inflatable airbags for transporting the soil gas from the point of extraction to the site under investigation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.