Estimation of the effect of thermal convection and casing on the temperature regime of boreholes: A review

In a vertical borehole, free heat convection arises when the temperature gradient equals or exceeds the so-called critical gradient. The critical temperature gradient is expressed through the critical Rayleigh number and depends on two parameters: (a) the ratio of formation (casings) to fluid (gas) conductivities (λ_f/λ) and (b) the convective parameter of the fluid. Both these parameters depend on the temperature (depth). An empirical equation for the critical Rayleigh number as a function of the ratio λ_f/λ is suggested. For the 0-100 °C range, empirical equations for convective parameters of water and air are proposed. The analysis of the published results of field investigations in deep boreholes and modelling shows that the temperature disturbances caused by thermal convection do not exceed 0.01-0.05 °C. Thus, in deep wells the temperature deviations due to thermal convection are usually within the accuracy of the temperature surveys. However, due to convection cells the geothermal gradient cannot be determined with sufficient accuracy for short well sections. In shallow boreholes the effect of thermal convection is more essential (up to 3-5 °C). To reduce the effect of convection on the temperature regime in shallow observational wells, it is necessary to reduce the diameter of the wellbores and use well fillers (fluids and gases) with low values of the convective parameters. The field observations and numerical calculations indicate that the distorting effect due to casing pipes is small and its influence is localized to the ends of the pipes, and this effect is independent of time.