Determination of local values of heat transfer coefficient in geothermal models with internal functions method


Heat transfer coefficient changes its value significantly with depth of wellbore.

Water pressure has little effect on heat transfer coefficient.

Water temperature has significant effect on heat transfer coefficient.

Water kinematic viscosity has crucial influence on heat transfer coefficient.


The objective of this study is to determine the depth characteristic of a heat transfer coefficient in the wellbore heat exchanger with the use of the original calculation procedure called an internal functions method. During the geothermal heat recovery, the substances change their pressure and temperature together with current (local) depth of the wellbore. Together with a change of these thermophysical parameters, there are also changes in the substance thermophysical properties, i.e.: specific heat, heat conductivity, density and viscosity. These properties decide on Prandtl Pr and Reynolds Re criterion numbers. These numbers, in connection with Nusselt number, enable to determine the local values of the heat transfer coefficient. The values of thermophysical properties and a heat transfer coefficient, assumed in the calculation models of the geothermal heat recovery, usually have a decisive influence on the reliability of the obtained results.

In the considered case, the value of the heat transfer coefficient has changed – from the depth of 500 to the depth of 2100 m – by about 70%. Therefore assuming the constant value of this coefficient in the simulation models of the geothermal heat recovery is a significant simplification that may considerably affect the calculated effectiveness of the geothermal systems.


  • Geothermal energy;
  • Heat transfer coefficient;
  • Wellbore heat exchanger;
  • Abandoned oil wells

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