A Simplified Method for Calculating Temperature Changes in Deep Wells

Abstract

Knowledge of temperature is important when estimating correctly the amount of additives to add to stimulation fluids and for calculating accurately tubing movements and thermal stresses in casing. This paper describes a fast method for determining temperature along the well using a pocket calculator. This simplified method can give the same temperature distributions as the more elaborate method. Introduction Temperature is an important parameter that determines the producing possibilities of a reservoir. Many papers with different objectives have been written regarding well and formation temperatures. Several papers focus on the determination of location and distribution of injected fluids in the formation. Other papers investigate the effect of injected fluids on formation temperature.Determination of temperature along the wellbore is important for several reasons. First, we need to know the temperature of the injection or stimulation fluids at the formation face, and second, we must evaluate the linear changes and stresses on tubing caused by the decrease in temperature when a well is converted from producer to injector, or when a well has to be stimulated. Many operating problems occur because of thermal effects: buckling of tubing, casing stress, and troubles when unseating packers. Particularly, after a deep well stimulation, accurate changes in tubing length must be known, since this may be decisive for a successful treatment. Moss and White, and Ramey, conducted important studies on temperature in injection wells. Ramey's paper has become a classic and many studies dealing paper has become a classic and many studies dealing with temperature effect on pipe movement refer to this paper.The effect of well temperature and pressure on stress and pipe movement is discussed by Matson et al., Lubinsky et at., and recently by Hammerlind . These and other papers where calculation of well temperature is necessary (as in Ref. 11) usually refer only to Ramey's study and do not give enough detail to apply the method easily. Even when information is complete, such as in Matson et al., it is heavily condensed and calculations are very difficult for most field engineers. A method for performing these calculations quickly would be helpful performing these calculations quickly would be helpful when evaluating well-temperature profiles for both injection and producing wells. Calculations using this method could be performed with a pocket calculator.This study relies a great deal on Ramey's paper and on data from Ref. 1. The Simplified Method - Well Stimulation In 1961, Ramey solved (with certain assumptions) the problem of distribution of transient temperature along a problem of distribution of transient temperature along a wellbore. For injection wells, the solution is expressed by the following equations, which may be adapted to the case of stimulating wells down tubing. JPT P. 763