Heat Losses During Flow of Steam Down a Wellbore

Abstract

Abstract Studies of wellbore, heat transmission during the injection of a hot fluid, as either gas or liquid, have appeared in the literature. The present investigation takes into account the effect of condensation, which is of practical significance when considering steam injection operations. Calculation procedures are given for superheated and for saturated and undersaturated steam. Effects of injection rate, time, pressure, temperature and depth of a well on heat losses have been analyzed. The benefits of using a packer are discussed. Also presented are correlations for estimating heat losses involved during injection of saturated steam. Introduction Studies of wellbore heat losses during the injection of a hot fluid have appeared in the literature. Ramey has presented a useful solution for calculating temperature of a heated gas as a function of depth and injection time. Ramey and others have also presented solutions for the hot liquid case. No method is available to take into account the effect of condensation, which is of practical significance when considering steam injection operations. This paper presents a method of estimating the quality of a condensing fluid as a function of depth and time. The approach is basically the same as that used by Ramey. The following injected fluids and conditions are considered in this study:Injection of superheated steamA. Decrease in temperature until cooled to thesaturated stateB. Condensation until condensed completely into hot(saturated) waterInjection of saturated or undersaturated steam;condensation until condensed completely into hot(saturated) water. Although this investigation does not include cooling of water after steam is completely condensed, Ramey's solution for the hot liquid case can be used for this purpose. The effects of various process variables on heat losses during the injection of steam into a well are investigated. THEORY QUALITY OF CONDENSING STEAM Predicting the behavior of condensing steam flowing down the injection wellbore requires an estimate of the quality of steam, i.e., the mass fraction of vapor in the mixture. Let us divide the total depth of the injection well into several segments which might be, but do not have to be, of equal magnitude. Consider condensation within a given depth interval AZ, the bottom of which is located at a depth Z from the surface (Fig 1). The following equation, derived in the Appendix, relates the quality of steam at the bottom of an interval to that at the top of the interval: (1) (2) (3) See the nomenclature for symbol definitions. The major assumptions made in the solution are is follows:Steam is injected at a constant rate, wellheadpressure, temperature and quality.A down-hole packer is used to prevent steam from entering the tubing-casing annulus. The annulus is assumed to be filled with air at low pressure. JPT P. 845ˆ