The mathematical model of conjugate heat exchange is proposed for the turbulent movement of reservoir oil in a vertical well section. The motion of the medium is described using a two-dimensional axisymmetric stationary formulation and boundary layer equations. The movement of the turbulent flow of reservoir oil due to reservoir energy is presented. The liquid medium is a mixture of reservoir oil with dissolved gas and formation water. The results of the numerical modeling are presented in the form of dependences of the changing flow rate, temperature, and mass fraction of paraffin deposits that occur along the full vertical extent of the well. The results obtained describe the thermobaric state of the well under the condition of conjugate heat exchange between the fluid flow and the production pipe.

A mathematical model of conjugate heat transfer during the laminar movement of oil fluid in the well is proposed. The motion of a gas-liquid medium in a two-dimensional axisymmetric stationary formulation is described by the equations of the boundary layer. A case of well operation in which oil is lifted to the surface due to reservoir energyis considered. A three-component medium is presented as a mixture of two components: formation of oil with dissolved gas and formation of water. The results of numerical modeling are presented, which make it possible to analyze the thermobaric state of the well under the condition of the developing flow in the pipe at the initial stage of stabilization and taking into account the phase transition associated with the formation of paraffin deposits.

A mathematical model is offered for conjugate heat exchange when gas flows in the section of a vertical well. The motion of the medium is described using a two-dimensional axisymmetric stationary formulation based on boundary-layer equations. The turbulent gas flowing due to the reservoir energy is considered. Natural gas is taken as a travelling medium. The numerical simulation results are presented in the form of the dependences of the flow temperature and gas density along the radius of the well on the external factors of the heat exchange changing along the well height. The results describe the thermobaric state of the well in the condition of the conjugate heat exchange of the produced natural gas flow and tubed well depending on the external thermal conditions.