# Mathematical modeling of radon transfer process in anisotropic media

• Krizsky Vladimir N., v.n.krizsky@strbsu.ru Sterlitamak Branch of the Bashkir State University, 49 Lenin Avenue, Sterlitamak 453103, Russia
• Nafikova Albina R., a.r.nafikova@strbsu.ru Sterlitamak Branch of the Bashkir State University, 49 Lenin Avenue, Sterlitamak 453103, Russia
• Kozlova Irina A., ikozlova75@mail.ru Bulashevich Institute of Geophysics, 100 Amundsen Street, Yekaterinburg 620016, Russia
• Yurkov Anatoliy K., akyurkov@mail.ru Bulashevich Institute of Geophysics, 100 Amundsen Street, Yekaterinburg 620016, Russia

### Abstract

The study of radon migration in geological environments is relevant for the search and contouring of oil and gas fields, search for uranium and thorium ores, environmental mapping in selection of the construction sites for industrial and residential structures, and forecasting events in seismic activity zones. In this paper, we consider a mathematical model of the three-dimensional problem of diffusion-advection of radon in piecewise constant layered media with inclusions, taking into account the anisotropy of the diffusion properties of subsurface geological environment. A combined method for solving the problem is described, based on a combination of the Laplace integral transform methods, integral representations with construction of the Green function of the enclosing layered medium, and Fredholm integral equations of the second kind arising at the boundaries of local inclusions. We present the results of comparing the data from computational and field experiments on the study of radon transfer processes.

### References

[1]
Yakovleva V. S., “Diffusive and advective transfer of radon in multilayered geological media [in Russian],” Izv. Tomsk. Politekhn. Univ., 315, No. 2, 67–72 (2009).

[2]
Haykovich I. M., “Mathematical modeling of radon migration processes [in Russian],” Apparatura i Novosti Radiats. Izmerenii (ANRI), No. 3 (9), 99–107 (1996/97).

[3]
Pavlov I. V., “A mathematical model for the process of radon exhalation from the Earth’s surface and the criteria for evaluation of potential radon relating risks on the construction territory [in Russian],” Apparatura i Novosti Radiats. Izmerenii (ANRI), No. 5 (11), 15–26 (1996/97).

[4]
Parovik R. I., “A non-stationary radon diffusion-advection model in the soil-atmosphere system [in Russian],” Vestn. KRAUNTs, Fiz.-Mat. Nauki, No. 1, 39–45 (2010).

[5]
Yakovleva V. S. and Parovik R. I., “The numerical solution of the radon diffusion and advection equation in multilayered geological media [in Russian],” Vestn. KRAUNTs, Fiz.-Mat. Nauki, No. 1, 45–55 (2011).

[6]
Krizsky V. N. and Nafikova A. R., “Mathematical modeling of radon diffusion and advection processes in piecewise constant anisotropic layered media with inclusions [in Russian],” Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model., Program., No. 2, 38–45 (2014).

[7]
Krizskiy V. N., “About a way of calculation of physical fields in piecewise anisotropic media, P. II. Non-stationary fields [in Russian],” Vestn. Bashkir. Univ., 14, No. 4, 1302–1306 (2009).

[8]
Matveeva T. A., Some Methods of the Laplace Transform Inversion and Their Applications [in Russian], Diss. Kand. Fiz.-Mat. Nauk, Saint Petersburg (2003).

[9]
Nafikova A. R., Krizsky V. N., and Sultanov L. Z., The Certificate of the State Registration of the Computer Program No. 2015660698, A research on Radon Diffusion-Advection Processes in Piecewise Anisotropic Layered Media with Inclusions [in Russian], Feder. Sluzhba po Intellekt. Sobstvennosti (RosPatent) (10.06.2015).

[10]
Nafikova A. R., Krizsky V. N., Kozlova I. A., and Yurkov A. K., “Comparative analysis of the data of numerical and field tests for research of radon transfer processes in piecewise uniform horizontally layered media [in Russian],” Apparatura i Novosti Radiats. Izmerenii (ANRI), No. 4, 67–72 (2016).

[11]
Utkin V. I. and Yurkov A. K., Standard Sample of Radon [in Russian], Patent No. 2075092 of the Russian Federation (RU 2075092 C1), No. 94003334/25, declared 28.01.94, publ. 10.03.97, bull. No. 7.

[12]
Utkin V. I., Yurkov A. K., Ladovsky I. V., and Ryvkin D. G., “Experimental and theoretical studies of the soil radon flow with the conditions change on the surface-air border [in Russian],” in: Mat. 37th Int. Seminar of V. V. Uspensky, pp. 57–61, Bulashevich Inst. Geophys. UB RAS, Yekaterinburg (2006).

[13]
Bulashevich Yu. P., Utkin V. I., Yurkov A. K., and Nikolaev V. V., “Change of radon concentration in connection with mountain blows in deep mines [in Russian],” Dokl. Ross. Akad. Nauk, 346, No. 2, 245–248 (1996).

[14]
Yurkov A. K. and Kozlova I. A., “Methodical questions of measurement of radon-222 content in the soil air at monitoring observations [in Russian],” Ural. Geofiz. Vestn., No. 7, 30–34 (2005).

[15]
Nafikova A. R. and Krizsky V. N., Mathematical Modeling of Processes of Radon Transfer in Piecewise Constant Anisotropic Layered Media with Inclusions [in Russian], Sterlitamak. Fil. Bashkir. Gos. Univ., Sterlitamak (2016).
How to Cite
Krizsky, V., Nafikova, A., Kozlova, I. and Yurkov, A. (2020) “Mathematical modeling of radon transfer process in anisotropic media”, Mathematical notes of NEFU, 27(1), pp. 88-100. doi: https://doi.org/10.25587/SVFU.2020.62.17.006.
Issue
Section
Mathematical Modeling