Explicit finite difference solution of the diffusion equation describing the flow of radon through soil
Applied Radiation and Isotopes 69 (2011) 237–240
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Explicit finite difference solution of the diffusion equation describing the flow of radon through soil
´
´
Svetislav Savovic a,b,n, Alexandar Djordjevich a, Peter W. Tse a, Dragoslav Nikezic b a b
City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China
´
Faculty of Science, R. Domanovica 12, 34000 Kragujevac, Serbia
a r t i c l e in fo
abstract
Article history:
Received 13 April 2010
Received in revised form
13 September 2010
Accepted 14 September 2010
Radon diffusion through soil and into air is investigated. The solution of the relevant diffusion equation is given using the explicit finite difference method. Results from a two-medium model (soil–air) are compared to those from a simplified single-medium model (soil alone). The latter are an underestimate in early stages of the diffusion process. Later on, the two models match closely and either one can be used at equilibrium conditions to calculate radon diffusion, estimate indoor radon concentration and assess health hazards.
& 2010 Elsevier Ltd. All rights reserved.
Keywords:
Radon
Diffusion equation
Finite difference method
Soil
1. Introduction
The radioactive gas radon (whose principal isotope is 222Rn) has been studied extensively over the past few decades.
Important motivating factors for this interest are the hazards associated with radon and its use as an environmental tracer
(Escobar et al., 1999). In a built environment, radon originates primarily from soil. Building material and some utility supply
(water and gas) contribute as well. It was reported that a worldwide average of 60.4 percent of total indoor radon originates from the ground under and surrounding buildings
(Ren, 2001). Its entry indoor is chiefly by diffusion through cracks in the building
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Explicit finite difference solution of the diffusion equation describing the flow of radon through soil
´
´
Svetislav Savovic a,b,n, Alexandar Djordjevich a, Peter W. Tse a, Dragoslav Nikezic b a b
City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China
´
Faculty of Science, R. Domanovica 12, 34000 Kragujevac, Serbia
a r t i c l e in fo
abstract
Article history:
Received 13 April 2010
Received in revised form
13 September 2010
Accepted 14 September 2010
Radon diffusion through soil and into air is investigated. The solution of the relevant diffusion equation is given using the explicit finite difference method. Results from a two-medium model (soil–air) are compared to those from a simplified single-medium model (soil alone). The latter are an underestimate in early stages of the diffusion process. Later on, the two models match closely and either one can be used at equilibrium conditions to calculate radon diffusion, estimate indoor radon concentration and assess health hazards.
& 2010 Elsevier Ltd. All rights reserved.
Keywords:
Radon
Diffusion equation
Finite difference method
Soil
1. Introduction
The radioactive gas radon (whose principal isotope is 222Rn) has been studied extensively over the past few decades.
Important motivating factors for this interest are the hazards associated with radon and its use as an environmental tracer
(Escobar et al., 1999). In a built environment, radon originates primarily from soil. Building material and some utility supply
(water and gas) contribute as well. It was reported that a worldwide average of 60.4 percent of total indoor radon originates from the ground under and surrounding buildings
(Ren, 2001). Its entry indoor is chiefly by diffusion through cracks in the building
References: Albarracin, D., Font, Ll., Amgarou, K., Domingo, C., Fernandez, F., Baixeras, C., 2002. Anderson, J.D., 1995. Computational Fluid Dynamics. McGraw-Hill, New York. Cohen, B.L., 1979. Methods for predicting the effectiveness of uranium mill tailings covers Dimbylow, P.J., Wilkinson, P., 1985. The numerical solution of the diffusion equation describing the flow of radon through cracks in a concrete slab Escobar, V.G., Tome, F.V., Lozano, J.C., 1999. Procedures for the determination of 222 50 (6), 1039–1047. Guo, Q., Sun, K., Cheng, J., 2004. Methodology study on evaluation of radon flux from soil in China Ren, T., 2001. Source, level and control of indoor radon. Radiat. Prot. 21 (5), 291–297 in Chinese. Rogers, V.C., 2001. Investigation of soil radon diffusion coefficient measurements and methodology Sasaki, T., Gunji, Y., Okuda, T., 2006. Transient-diffusion measurement of radon in Japanese soils from a mathematical point of view Sasaki, T., Gunji, Y., Iida, T., 2007. Transient-diffusion measurements of radon: practical interpretation of measured data ´ Savovic, S., Djordjevich, A., 2008 Schery, S.D., Whittlestone, S., 1989. Description of radon at the earth’s surface. J. Geophys. Res. 94 (D15), 18297–18303. Uroˇ evic, V., Nikezic, D., 2003. Radon transport through concrete and determinas tion of its diffusion coefficient