Mechanistic model for computing fluid temperature profiles in gas-lift wells

In a continuous-flow gas-lift operation, gas is injected down the annulus into the tubing near the top of perforations. The intrinsic idea is to aerate the liquid column, thus 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 mechanistic 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 the 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 on 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 tubular for a continuous flow gas-lift operation. The analytic solution obtained affords flexibility to input any temperature distribution function (T-D model) for modeling unsteady heat transfer in the formation. Rapid implementation of the new solution is possible because of its simplicity. Our results show that the temperature profiles in both flow conduits are 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 flow rates, in both conduits govern the nonlinearity in temperature profiles. We discuss both synthetic and field examples to illustrate the applicability of the new solution.