Analysis of temperature fields in the well on the basis of the numerical Iseger's inversion

About the authors:

Aleksandr I. Filippov, Dr. Sci. (Tech.), Professor, Chief Researcher, Sterlitamak Branch of Ufa University of Science and Technology, Sterlitamak, Russia; filippovai1949@mail.ru, https://orcid.org/0000-0002-0964-9805

Marina A. Zelenova, Cand. Sci. (Phys.-Math.), Associate Professor, Department of General and Theoretical Physics, Sterlitamak Branch of Bashkir State University; marina_ag@inbox.ru

Ekaterina P. Scheglova, Teacher of Department of Physics, Ufa State Petroleum Technological University; ekaterina-scheglova@rambler.ru

Abstract:

The temperature field in a vertical well in case of fluid withdrawal from the oil-saturated reservoir is analyzed. The problem of fluid flow heat transfer in the wellbore and surrounding rocks is solved using the method of asymptotic formal parameter developed by the authors. The curves are built because of the problem solution of conjugation obtained in space. The reverse transfer is completed on the basis of numerical inversion (the Den Iseger algorithm); accurate analytical formulas are received for small time asymptotics. Numerical inversion of Laplace — Carson transform is compared to analytical curves of small time asymptotics. It is shown that the curves obtained on the basis of asymptotic expressions are in good agreement with the results of numerical inversion. The agreement of the calculation results, on the one side, is the strong fact determining the validity and applicability of the Den Iseger algorithm, and, on the other side, makes it possible to find the limits of applicability of approximation.

References:

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