A review on mathematical models for estimating indoor radon concentrations
- Ji Hyun Park1,
- Dae Ryong Kang2 and
- Jinheum Kim3Email author
https://doi.org/10.1186/s40557-016-0091-6
© Park et al. 2016
Received: 18 January 2016
Accepted: 18 February 2016
Published: 25 February 2016
Abstract
Radiation from natural sources is one of causes of the environmental diseases. Radon is the leading environmental cause of lung cancer next to smoking. To investigate the relationship between indoor radon concentrations and lung cancer, researchers must be able to estimate an individual’s cumulative level of indoor radon exposure and to do so, one must first be able to assess indoor radon concentrations. In this article, we outline factors affecting indoor radon concentrations and review related mathematical models based on the mass balance equation and the differential equations. Furthermore, we suggest the necessities of applying time-dependent functions for indoor radon concentrations and developing stochastic models.
Keywords
Background
Exposure to radiation from natural sources leads to various environmental diseases. Radon, which is the primary constituent of natural radiation [1], is the leading environmental cause of lung cancer next to smoking [2]. Studies in Europe, the United States, Canada, and China have effectively shown a relationship between indoor radon concentrations and lung cancer [3].
Diagram of factors governing indoor radon concentrations and exposurea. aThis diagram was modified from Font [5] and Font and Baixeras [6]. Radon in the soil permeates a building: diffusive and advective flow; radon from BM diffuses into buildings. A building’s water supply and natural gas are also sources that introduce radon into a building, although that from natural gas is not generally considered because it is difficult to measure and contributes to only very small concentrations. Additionally, indoor radon concentrations can also vary as a result of air exchange between indoor and outdoor air. Therefore, a subject’s indoor radon exposure in a building can be mainly determined by his or her behaviour and indoor radon concentration of the building that he or she resides
There had been several studies to estimate the indoor radon concentrations with mathematical models. Ramola et al. [7] estimated the indoor radon concentration using a mathematical model based on the radon flux in soil and groundwater. Arvela et al. [8] calculated the indoor radon concentrations with a mathematical model which considers diffusion from soil and BM sources and air exchange simultaneously. These calculations have been compared with the measured variations of Finnish dwellings. Font [5] and Font and Baixeras [6] developed a generic and dynamic model of Radon Generation, Entry, and Accumulation indoors (RAGENA) which describes all the known sources including soil, BM, and water, and this model has been adapted to a Mediterranean climate house and Swedish house [9, 10]. Mathematical models for estimating indoor radon concentrations in high-rise buildings have been conducted by Man and Yeung [11] and Shaikh et al. [12]. These models included the contributions from BM and outdoor air. Moreover, model of indoor radon concentration in thermal spas was developed by Vogiannis and Nikolopoulos [13].
Notation
Symbol | Unit | Description |
---|---|---|
C bm | Bq/m3 | Radon concentration in building material (BM) |
C i | Bq/m3 | Indoor radon concentration |
C o | Bq/m3 | Radon concentration of outdoor air |
C s | Bq/m3 | Radon concentration in soil |
C w | Bq/m3 | Radon concentration in water supply |
F s | Bq/(m2 · s) | Total radon flux from soil into building |
k a | m/(s · Pa) | Advection transfer coefficient of soil |
k d,bm | m/s | Diffusion transfer coefficient of BM |
k d,s | m/s | Diffusion transfer coefficient of soil |
q ij | m3/s | Air current from compartment i to compartment j |
S bm | m2 | Indoor surface area of radon containing BM |
S g | m2 | Building area towards ground |
t w | dimensionless | Radon transfer efficiency of water supply |
U w | m3/s | Use rate of water |
V | m3 | Volume of the indoor |
ΔP s − i | Pa | Soil-indoor pressure difference |
λ | 1/s | Radon decay constant |
λ v | 1/s | Ventilation rate |
Review
According to the above, changes in indoor radon concentrations are affected by the sources of radon entry, building ventilation (radon exchange), and decay reaction. First, we introduce a model for assessing indoor radon concentrations attributed to the three main sources of radon entry (soil, BM, and water) and decay reaction.
Radon entry and decay reaction
Soil
Although radon from groundwater contributes very little to indoor radon, it can constitute an important source in specific instances; the total radon flux from the ground, considering both radon in soil and groundwater, can be found in Ramola et al. [9]. In the meantime, Font [5] and Font and Baixeras [6] suggested evaluating total radon flux from the soil into the building F s differently: the soil can be divided into two compartments, disturbed soil (DS, the volume of soil underneath a building from which radon can reach the basement of the building by diffusion and pressure driven flow) and undisturbed soil (US, the soil attached to the DS that is not influenced by the presence of the building). The radon concentrations in the US and in the DS are described in [5, 6]. However, for simplicity, throughout this article we develop a model using a total radon flux into the building that consider only DS, namely F s in Eq. (2).
Building material
Water for living
(see [5, 6, 13] for more details).
where dC i = C i (t + dt) − C i (t) and dt denotes an infinitesimal time.
Radon exchange
Ventilation between indoor and outdoor air
where λ v (C i − C o ) describes the radon exchange between indoor and outdoor air [5, 6, 9–16]. In Eq. (7), one may assume that λ = 0 because λ is relatively smaller than λ v .
Ventilation among the compartments
where the last term describes the radon exchange between compartments i and j [5, 6].
Summary of references reviewed in this article
Author(s) | Year | Factor | Application | Methoda | |||
---|---|---|---|---|---|---|---|
Soil | BM | Water | Vent. | ||||
Kusuda et al. [16] | 1980 | - | - | - | ○ | Sample calculations | N.S. |
Capra et al. [14] | 1994 | - | - | - | ○ | An environmental chamber | N.S. |
Ramola et al. [9] | 2011 | ○ | - | - | ○ | Budhakedar area of Garhwal Himalaya in summer and winter | N.S.S. |
Man and Yeung [11] | 1999 | - | ○ | - | ○ | Newly constructed, uninhabited high-rise buildings in Hong Kong | N.S.S. |
Shaikh et al. [12] | 2003 | - | ○ | - | ○ | A multi-storey building in Mumbai, India over four seasons | N.S.S. |
Vogiannis and Nikolopoulos [13] | 2008 | - | - | ○ | ○ | Thermal spas in Greece | N.M. |
Jelle [15] | 2012 | ○ | ○ | - | ○ | Sample calculations | N.S.S. |
Arvela et al. [10] | 1988 | ○ | ○ | - | ○ | Finnish dwellings in summer and winter | N.S.S. |
Font [5] | 1997 | ○ | ○ | ○ | ○ | Mediterranean climate house and Swedish houseb | N.M. |
Font and Baixeras [6] | 2003 |
Conclusions
Mathematical models for estimating indoor radon concentrations provide not only a method of assessment but also an understanding between parameters that govern indoor radon levels. In order to estimate an individual’s cumulative indoor radon exposure, assessing indoor radon concentrations is necessary. To do so, one should seek to understand the mechanisms of radon entry and exchange in relation to side-specific surroundings and characteristics of a building. Accordingly, resultant models in consideration of said characteristics may be simpler than Eq. (8) or may necessitate additional research on factors of indoor radon concentrations (e.g., age of the BM and relative humidity).
Most of the models reviewed in this article utilized solutions at a steady state and considered parameters to be constant in order to estimate indoor radon concentrations. Such approaches are often adequate, as a steady state is rarely attained in actual buildings because of time-dependent factors (e.g., air exchange rates, which change with atmospheric conditions). For this reason, time-dependent solutions may be more accurate than steady state solutions in assessment of actual building conditions. Additionally, all of the models included in this review considered only deterministic models. However, a stochastic model designed to account for unrecognized factors and noise-corrupted measurements may offer better approximation of indoor radon levels.
Declarations
Acknowledgements
This subject is supported by Korea Ministry of Environment (MOE) as “the Environmental Health Action Program” (Grant Number 2015001350002).
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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