Temperature field of a turbulent flow in a well with allowance for the temperature dependence of heat capacity

The article discusses a method to solve a field-matching problem that describes a nonstationary heat exchange between an upward flow of fluid in a pipe and an ambient medium with allowance for the variability of the coefficients due to the turbulence of a multiphase flow and the nonlinear dependence of the oil heat capacity on temperature and precipitation of paraffins. The method combines asymptotic methods of small and formal parameters. Analysis of the experimental data on the dependence of heat capacity on the temperature makes it possible to approximate it by a linear function that contains a small parameter in the form of the first terms of the Taylor series. Expansion of the problem by the small parameter in the zeroth approximation leads to a linear problem that is solved by the asymptotic method for a formal parameter for uncoupling of the first coefficient of the expansion. Expressions determining the temperature field in the well and surrounding rocks that take into account the orthotropy of the thermophysical properties of the media are obtained.