Predicting fluid temperature profiles in gas-lift wells
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In a continuous-flow gas-lift operation, gas is injected down the annulus into the tubing near the top of perforations to aerate the liquid column, thereby providing the necessary stimulus for fluid flow. Because the volumetric gas rate is dependent upon both the pressure and temperature at the depth of injection, accurate knowledge of these entities cannot be overemphasized for an efficient lift. In particular, the behavior of the nitrogen gas charged in the dome is critically dependent upon the temperature prediction for the optimal performance of the bellows-charged gas-lift valves. Current practice entails use of a linear temperature profile for the annular fluid, while applying empirical correlations for the tubing fluids. Improved temperature predictions are now possible for fluids in both conduits by modeling the heat and fluid flow problem at hand from first principles. In this work, we present a mathematical model for the flowing temperature of the annular gas and the gas/liquid two-phase mixture in the tubing as a function of both well depth and production time, regardless of well deviation angle. The model is based on energy balance between the formation and fluids flowing through each conduit. While flowing down the annulus, the cold gas injected at the wellhead continues to gain heat. The heat transfer rate for the annular gas depends upon the relative temperatures of the formation and the tubing fluid. We assume unsteady-state heat transfer in the formation and steady-state heat transfer in the tubulars for a continuous-flow gas-lift operation. The analytic solution obtained affords flexibility to input any temperature distribution function (To model) for modeling unsteady heat transfer in the formation. The simplicity in the algebraic solution allows rapid implementation. The results show that the temperature profiles in both flow conduits is nonlinear, unlike those used previously, particularly in the annulus. Variables, such as the overall heat transfer coefficients, gas mass-fraction in the tubing, well depth, and the magnitude of flow rates in both conduits govern the degree of nonlinearity in temperature profiles. Both synthetic and field examples are discussed to illustrate the applicability of the new solution.