Abstract
In this paper a mathematical model for simulation of thermal fields from wells located in permafrost area is considered, which takes into account basic physical, technological, and climatic factors that lead to a nonlinear boundary condition on the surface of the soil. To find the thermal fields a finite-difference method is used to solve the problem of Stefan type, and solvability of the corresponding difference problem is proved. Possibilities of the developed software are presented to carry out various numerical experiments and make long-term forecasts in simulations of thermal fields in the system “well – permafrost” with annual cycle of thawing/freezing the upper layers of the soil due to seasonal temperature changes, intensity of solar radiation and technical parameters of the wells. Comparison of numerical and experimental data are in good agreement (difference is about 5 \(\%\)) due to, in particular, that the software adapts to the geographic location by using special iterative algorithm of determination of the parameters, included in the non-linear boundary condition on the soil surface.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Crank, J., Nicolson, P.: A practical method for numerical evaluation of solutions of partial differential equations of heat-conduction type. Proc. Cambridge Philos. Soc. 43, 50–67 (1947)
Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere, New York (1980)
Javierre, E., Vuik, C., Vermolen, F.J., Zwaag, S.V.: A comparison of numerical models for one-dimensional Stefan problems. J. Comput. Appl. Math. 192(2), 445–459 (2006)
Filimonov, M.Y.: Representation of solutions of initial-boundary value problems for nonlinear partial differential equations by the method of special series. Differ. Equ. 39(8), 1159–1166 (2003)
Filimonov, M.Y.: Application of method of special series for solution of nonlinear partial differential equations. In: Proceedings of Applications of Mathematics in Engineering and Economics (AMEE 2014), vol. 1631, pp. 218–223 (2014)
Samarsky, A.A., Vabishchevich, P.N.: Computational Heat Transfer. The Finite Difference Methodology, vol. 2. Wiley, Chichester (1995)
Samarskii, A.A., Moiseyenko, B.D.: An economic continuous calculation scheme for the Stefan multidimensional problem. USSR Comput. Math. Math. Phys. 5(5), 43–58 (1965)
Zhang, Y., Chen W., Cihlar, J.: A process-based model for quantifying the impact of climate change on permafrost thermal regimes. J. Geophys. Res. 108(D22) (2003)
Filimonov, M.Y., Vaganova, N.A.: Simulation of thermal fields in the permafrost with seasonal cooling devices. In: Proceedings of ASME 45158, Volume 4: Pipelining in Northern and Offshore Environments; Strain-Based Design; Risk and Reliability; Standards and Regulations, pp. 133–141 (2012)
Filimonov, M.Y., Vaganova, N.A.: Simulation of thermal stabilization of soil around various technical systems operating in permafrost. Appl. Math. Sci. 7(144), 7151–7160 (2013)
Vaganova, N.A., Filimonov, M.Y.: Simulation of Engineering Systems in Permafrost. Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika 13(4), 37–42 (2013). (in Russian)
Filimonov, M.Y., Vaganova, N.A.: Prediction of changes in permafrost as a result technogenic effects and climate. Acad. J. Sci. 3(1), 121–128 (2014)
Samarsky, A.A.: The Theory of Difference Schemes. Nauka, Moscow (1983)
Bashurov, V.V., Vaganova, N.A., Filimonov, MYu.: Numerical simulation of thermal conductivity processes with fluid filtration in soil. J. Comput. Technol. 16(4), 3–18 (2011). (in Russian)
Vaganova, N.A.: Existence of a solution of an initial-boundary value difference problem for a linear heat equation with a nonlinear boundary condition. Proc. Steklov Inst. Math. 261(1), 260–271 (2008)
Vaganova, N.A.: Mathematical model of testing of pipeline integrity by thermal fields. In: Proceedings of Applications of Mathematics in Engineering and Economics (AMEE 2014), vol. 1631, pp. 37–41 (2014)
Acknowledgement
Supported by Programs of UD RAS “Arktika” and Program 15–16–1–10, and by Russian Foundation for Basic Research 13–01–00800.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Filimonov, M.Y., Vaganova, N.A. (2015). Simulation of Technogenic and Climatic Influences in Permafrost for Northern Oil Fields Exploitation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods,Theory and Applications. FDM 2014. Lecture Notes in Computer Science(), vol 9045. Springer, Cham. https://doi.org/10.1007/978-3-319-20239-6_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-20239-6_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-20238-9
Online ISBN: 978-3-319-20239-6
eBook Packages: Computer ScienceComputer Science (R0)