Cylindrical probe with a variable heat flow rate: A new method for the determination of formation thermal conductivity

The thermal conductivity of a geological formation is one of the important petrophysical parameters which are preferable to study in situ in geophysical well logs. A new technique for the determination of formation thermal conductivity has been developed. We assumed that formation dry density, porosity, and pore fluids saturations could be determined from core samples or cuttings. In this case the specific heat and density of a formation can be quantitatively estimated. It is also assumed that the instantaneous heat flow rate and time data are available for a cylindrical probe with a variable heat flow rate placed in a wellbore. A semi-theoretical equation describing the temperature of the probe’s wall is used to determine in situ the formation conductivity as a function of the temperature increase. The formation thermal diffusivity is also calculated. A field example is presented.

The calculation of variable heat flow in solids

In many contexts, in laboratory work, in industrial processes and in engineering practice, situations arise in which it is required to determine the flow of heat in bodies under nonsteady conditions. In some cases this can be done by direct experiment, and a few cases are sufficiently simple for formal analytical solutions of the appropriate equations to be obtained and evaluated. But direct experiment is often difficult or impossible, especially under practical conditions of manufacture or operation; and often the conditions of the problem, such as inhomogeneity or the shape of the material, or variation of its thermal properties with temperature, either make the formal solution so complicated that its numerical evaluation is impracticable, or put a formal solution out of the question altogether.