Estimation of heat flow in oil wells based on a relation between heat conductivity and sound velocity

Abstract

Based on published data, it is assumed that the ratio of sound velocity to thermal conductivity exhibits a linear relationship with formation temperature for most sedimentary rocks. Combination of this assumption with Fourier's heat-flow law yields q*=ln(TL+c/TU+c)•(1/A(tL-tU)) where TL and Tu, are the subsurface temperatures at the top and the bottom of an interval, respectively, tL and tU the sound travel times, and q* is the heat flow. This relation has been tested in the case of 10 wells, for which accurate data were available. The relation generated very satisfactory fits with the measured data for siliciclastic and carbonate rocks. The parameters a and c take respective values of 1.039 and 80.031; heat flow (q*) is expressed relative to the heat flow in the standard well Bolderij-1 in the Groningen gasfield (Bolderij Unit, BU). A method for estimating the relative heat flow from bottom-hole temperatures as observed during logging operations, and sound-travel times from well-shoot in combination with sonic-log data, has been developed and tested in the Viking and Central grabens of the UK sector of the North Sea. In this region the mean relative heat flow using data from 120 wells is 0.601 BU, with a standard deviation of 0.055 BU. Comparisons of calculated relative heat-flow values in BU, with heat-flow values in SI-Units conventionally obtained suggests that the Bolderij unit is equivalent to about 77 mWm-2.