# HEAT EXCHANGE DURING THE MOVEMENT OF THE GEOTHERMAL HEAT CARRIER IN THE WELL

• Y. Morozov Institute of Renewable Energy of the National Academy of Sciences of Ukraine, Kyiv, Ukraine.
• А. Zhokhin Institute of Renewable Energy of the National Academy of Sciences of Ukraine, Kyiv, Ukraine.
Keywords: geothermal well, non-stationary heat transfer, finite difference solution, rock mass, geothermal coolant.

### Abstract

The process of heat transfer during the movement of a geothermal coolant in a well can be described by a system of two equations of a parabolic type. One of the equations describes the process of heat transfer in the rock mass surrounding the well, and the second equation describes the heat transfer of the fluid during its movement in the well. The initial and boundary conditions take into account the geothermal gradient in the well and the pattern of heat exchange between the rock mass and the geothermal fluid.

The solution to the problem of heat transfer in a geothermal well during the movement of a coolant in the well was obtained by a finite difference tool using the Runge-Kutta-Merson method, which is one of the modifications of the Runge-Kurt method of the fourth order of accuracy and differs from it in the ability to estimate the error. depending on this, make a decision to change the integration step and thus significantly reduce the time for solving the differential equation.

Calculations of the temperature field of the mountain range on five horizons are given in graphical form.

Calculations of the temperature of the geothermal carrier are given by solving the corresponding problem obtained by the method.

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