ABSTRACT
After the complete termination of the recovery process of the temperature fi eld (disturbed by drilling) the temperature in the borehole may still differ from the natural temperature of formations; this is due to the distorting infl uence of free heat convection and of the casing. Because of this, in the interpretation of temperature logs, some investigators assume that small temperature anomalies can be explained by the presence of metallic casing or of convective movements of fl uid (gas) in the borehole. At present, no diffi culty is anticipated in regard to the establishment of the per se fact of existence of convection in a vertical pipe fi lled with fl uid or gas. Free heat convection arises when the temperature gradient equals or exceeds the so-called critical temperature gradient . The critical temperature gradient (Acr) is expressed through the critical Rayleigh number (Racr) and depends on two parameters: on the ratio of formation (casings) and fl uid (gas) thermal conductivities (λf /λ); on the convective parameter of the fl uid. Both parameters are dependent on the temperature (depth). Ostroumov (1952) obtained for a vertical pipe an equation for the determination of the critical Rayleigh number. Taking into account that this publication is not easily accessible to researchers, we present below a numerical solution of this equation (Ostroumov 1952). At determining the value of Acr in most of the fi eld studies it was assumed that thermal conductivity ratio λf /λ is infi nity (Diment 1967; Gretener 1967; Sammel 1968; Cermak et al. 2007, 2008). This assumption is applicable to metallic casings, but is not valid for uncased wells and boreholes with plastic casings. The variations of the convective parameter with depth can lead (in some sections of the well) to a condition when the temperature gradient is smaller than the critical temperature gradient. In this case the process of free thermal convection cannot be initiated. Below we present this case for an air fi lled wellbore.
