With the use of the asymptotic method the thermologging problem with a given radial oil-velocity profile is presented in the form of a sequence of simpler problems containing different types of equations for corresponding expansion coefficients, remainder term, and boundary-layer functions. Analytical expressions for the zeroth and first expansion coefficients and boundary-layer functions taking into account the arbitrary radial oil-velocity profile have been constructed. It has been shown that the derived asymptotic formula makes the perturbation sources vanish in the averaged problem for the remainder term.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 86, No. 1, pp. 172–190, January–February, 2013.
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Filippov, A.I., Akhmetova, O.V., Zelenova, M.A. et al. Thermologging problem with a given radial oil-velocity profile in the well shaft. J Eng Phys Thermophy 86, 183–204 (2013). https://doi.org/10.1007/s10891-013-0820-4
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DOI: https://doi.org/10.1007/s10891-013-0820-4