Solution methods of one-dimensional radial problem of heat transfer in the permafrost formations surrounding a well

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Release:

Releases Archive. Вестник ТюмГУ. Физико-математические науки. Информатика (№7, 2014)

Title: 
Solution methods of one-dimensional radial problem of heat transfer in the permafrost formations surrounding a well


About the authors:

Nail G. Musakaev, Dr. Sci. (Phys.-Math.), Chief Researcher, Tyumen Branch of Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; Professor, University of Tyumen; musakaev@ikz.ru

Stanislav L. Borodin, Cand. Sci. (Phys.-Math.), Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; eLibrary AuthorID, ORCID, Web of Science ResearcherID, Scopus Author ID, borodin@ikz.ru

Sergey N. Romanyuk, Researcher, Earth Cryosphere Institute, Siberian Branch of Russian Academy of Sciences (Tyumen)

Abstract:

The article tells about the solution methods of one-dimensional radial problem of heat transfer in the permafrost formations surrounding a well. The mathematical model of this problem is given. To solve the problem, four numerical methods are considered: enthalpy method with explicit scheme, method of catching the front in a mesh point with implicit scheme, method of catching the front in a mesh point using six-point symmetric scheme and quasi-steady approach. A self-similar solution enabling calculation of the thawing radius in permafrost formations is obtained and used to assess the use of numerical methods (the comparison of the results of self-similar solutions and the results of calculations of the thawing radius by enthalpy method is presented in the article). It is also presented the comparative analysis of numerical solutions of the problem of heat transfer in permafrost formations using different numerical methods. The results of the work are the self-similar solution for the radial Stefan problem and the preferred choice of a numerical method, which provides high accuracy and the highest rate of calculating the radius of thawing and temperature distribution in the permafrost formations surrounding a well.

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