This paper summarized the separation process of radon based on its geophysicalchemical properties. Taking into account the geological conditions of mining, the mathematical model of radon migration in underground multilayer strata (UMS) was established to investigate the distribution law of radon concentration in UMS. It was found that the distribution of radon concentration in UMS is affected by both the properties of the strata and the depth of cover and the radon concentration law varies at different depths even in the same layer stratum. At last, in order to validate the derivation result of the mathematical model of radon migration in UMS, the actual measured values (AMV) and the calculated values (CV) were compared further. As a result, the CV was found to be approximately equal to the AMV with deviation values (DV) less than 5%, which indicates that the derivation result of the mathematical model of radon migration in UMS is correct.
As a main energy resource in China, coal accounts for about 77% and 65% in primary energy production and consumption [
Coal ratio of primary energy consumption in China.
Coal production within thirteen years in China.
According to the latest results of coalfield prediction from China National Administration of Coal Geology [
Therefore, the determination of spatiotemporal dynamic evolution law of the mininginduced fractures field in overlying strata and its relationship with underground water has been critical when it comes to the mitigation of mininginduced safety issues as well as the adverse environmental consequences in western mining areas in China. At present, there are many research methods for development characteristics of mininginduced fractures in overlying strata [
Radon is a form of chemical element with a chemical symbol Rn and atomic number 86. It is a zero group element of the sixth cycle in periodic table of chemical elements. In nature, radon has three kinds of common radioactive isotopes (^{219}Rn, ^{220}Rn, and ^{222}Rn). In general, radon refers to ^{222}Rn with a halflife of 3.82 days. Radon molecule is a monatomic molecule, and its elemental form is usually gaseous, which is the only heaviest radioactive inert gas in contact with human. In the normal state, radon is colorless, tasteless, and odorless and is easily soluble in water and organic matters. The geophysicalchemical properties of radon are relatively stable, and it is difficult to produce chemical reactions with other substances [
In natural conditions, radon has strong migration ability, and it can migrate in geological environments by gaseous or dissolved form with ground water. Radon usually migrates by diffusion and convection effects in underground overlying strata, and the migration distance from underground strata to surface depends on different lithological characters. For example, the vertical migration distance in homogeneous sand is 360–420 m [
Separation process of radon means that radon migrates from underground strata to surface and then spreads into the air. The whole separation process of radon can be divided into two stages of free radon generation and migration [
Separation process of radon.
It is known that the migration of chemical elements in porous media has been extensively studied over the past few years. For example, Srivastava and Jim Yeh developed a threedimensional numerical model for the simulation of water flow and chemical transport through variably saturated porous media [
Uniform porous media refer to media with uniform pores distribution, such as shapes, sizes, and properties [
It is hypothesized that there is a UPMAS; its whole closed volume is
Mathematical model of radon migration in UPMAS.
According to diffusion and convection effect, and radioactive decay laws, the change quantity of migratory radon in UPMAS with volume
According to the Gauss divergence theorem, the area integral form of closed surface can be transformed into volume integral form. Based on the
Substituting formula (
Formula (
It is clear that
Substituting formula (
Based on the definition of steady state, the change rate of radon concentration in emanation media is equal to zero with time in steady state; namely,
Particularly, onedimensional condition is the most frequently used condition for radon migration. Hence, the onedimensional migration equation of radon in steady state in rectangular coordinate system can be expressed as
SUPM, such as the earth surface, can be defined as the uniform porous media with finite on one side and infinite on the other side. Radon migration in SUPM is a onedimensional problem in steady state, which means that the radon concentration mainly depends on the depth of the location in the semiinfinite emanation media, while they are identical to each other as long as the depths are the same.
It is hypothesized that the earth is a SUPM; the
Mathematical model of radon migration in SUPM.
According to Figure
The radon quantity
Hence, d
Substituting formulas (
It is known that the radon concentration will always be constant with time; namely,
Formula (
The general solution of formula (
The integral constants of
Substituting formula (
Based on formula (
When the
Distribution state of radon concentration in SUPM with different
In the previous section of this paper. It is hypothesized that the earth is a semiinfinite medium and considered that all properties of medium under surface boundary are the same everywhere. As a matter of fact, the underground strata are composed of multilayer rocks with different lithologies in mining engineering field. They have their own properties, and they are not semiinfinite media. Hence, the migration law of radon is not entirely the same in the different layers. For this proposal, based on the mathematical model of radon migration in SUPM, the mathematical model of radon migration in UMS in accordance with geological conditions of mining has been established, and the migration law of radon in UMS has been analyzed.
It is hypothesized that
Mathematical model of radon migration in UMS.
Based on the migration equation form of radon in SUPM in steady state, the general migration equation of radon in UMS in steady state can be analogized as
According to the solution of secondorder nonhomogeneous linear differential equation in higher mathematics, the general solution of formula (
Let
Hence, formula (
The integral constants of
Based on the two boundary conditions, two equations of
According to the Cramer rule in linear algebra, the integral constants of
Substituting formula (
Based on formula (
Parameters of specific property for the threelayer strata.
Names  Symbols  Units  Values 

Convection velocity 

m/s 

Diffusion coefficient 

m^{2}/s 

Porosity 

/  0.4/0.3/0.2 
Capacity of generating migratory radon 

Bq/m^{3}  3000/4000/5000 
Decay constant of radon 

/s 

Size parameters of threelayer strata.
Substituting the parameters in Table
Radon concentration values at three different depths.
Separation process of radon can be divided into two stages of free radon generation and migration. In the first stage, the radium atom in media lattice of underground strata decays into radon atom by emitting
The mathematical model of radon migration in UMS in accordance with geological conditions of mining has been established; the general migration equation of radon in UMS has been deduced, and the distribution law of radon concentration in UMS has been obtained. The calculation results indicate that the distribution of radon concentration in UMS is affected by both the properties of the strata and the depth of cover and the radon concentration law varies at different depths even in the same layer.
To validate the derivation result of the mathematical model of radon migration in UMS, threelayer strata were selected to detect the radon concentration by KJD2000R continuous emanometer at different depths. The AMV and the CV were compared showing that the CV is approximately equal to the AMV with DV less than 5%, which indicates that the derivation result of the mathematical model of radon migration in UMS is correct.
The authors declare that they have no financial and personal relationships with other people or organizations that can inappropriately influence their work, and they also declare that there is no conflict of interests regarding the publication of this paper.
The research is financially supported by the Fundamental Research Funds for the Central Universities (no. 2013QNB24), Jiangsu Planned Projects for Postdoctoral Research Funds (no. 1302050B), the Sailing Plan of China University of Mining and Technology (no. 201205), and the National Natural Science Foundation of China (no. 51264035). The authors are grateful to Lecturer J. Q. Yu for his helpful advice. Special thanks were given to Doctor C. G. Zhang from the University of New South Wales, Australia, for language assistance. They also thank the academic editor Jian Guo Zhou and two anonymous reviewers for their constructive comments.