A Note on the Theory of Temperature Logging

Abstract

Interest in temperature logs has been renewed recently. One of the main problems of temperature logs in injection wells is that of determining the zones that are taking fluids. A great step toward solving this problem has been reported in a recent paper. paper. The purpose of this paper is to point out another aim of temperature logging namely, that of relating the flow rate in water injection wells to some characteristics of the temperature logs. It has been stated that a factor of 6:1 gives approximate values in converting into B/D. The factor F, which has been found empirically, may be explained from theoretical considerations and because of this, it may be estimated more accurately. It has been shown that, for flow of a liquid ,............................(1) where .......................(2) a quantity that is different from zero. Eq. 1 can be written as ,..................................(3) which shows that, as is defined in Ref. 2, is identical to A. For injection down casing, the over-all heat transfer coefficient, U, may be considered infinite. Therefore, ...................................(4) Considering the wellbore as a linear point source, ....................(5) or, if ........................................(6) .......................(7) It has been observed that surprisingly good results are obtained by using the values k = 33.6 Btu/day-ft-F and a = 0.96 sq ft/day for different locations. Taking the values p = 350 lb/bbl, c = 1 Btu/lb-F, one obtains: ........................(8) It should be noted that the lower curve of Fig. 1 of Ref. 3 does not agree, for low values of t, with the solution .........................(9) corresponding to the constant heat flux line source and for this reason the graph should be used with caution. Eq. 8 has been plotted in Fig. 1 for three values of the external radius r'. It may be used to estimate the rate of water injection down casing from the shape of the injecting temperature log above the zone of entry of fluids. P. 375