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This paper presents an analytic model for computing the wellbore-fluid-temperature profile for steady fluid flow. Although wells with constant-deviation angle can be handled with existing analytic models, complex well architectures demand rigorous treatment. For example, changing geothermal-temperature gradient and deepwater wells present significant challenges. Additionally, available analytic models rarely provide calculation methods for various required thermal parameters, such as the Joule-Thompson coefficient and fluid expansivity.
The approach taken in this study entails dividing the wellbore into many sections of uniform thermal properties and deviation angle. The governing differential equation is solved for each section, with fluid temperature from the prior section as the boundary condition. This piecewise approach makes the model versatile, allowing step-by-step calculation of fluid temperature for the entire wellbore. We present simple, thermodynamically sound approaches for estimating thermal parameters.
Good success is indicated when performance of the proposed model is compared with data from three wells; producing two-phase gas/oil mixture, single-phase oil, and single-phase gas. Sensitivity of the estimated fluid temperatures to various thermal properties is also examined using our model. Overall, the effects of Joule-Thompson coefficient and liquid expansivity are found to be significant.