A flowing well continuously looses heat to its surroundings. An accurate prediction for the flowing surface temperature is necessary for production operations. Above optimum surface temperature, chillers are required to cool the gas prior to flowing in pipelines. Too cold of a surface temperature can cause precipitation problems that restrict flow and may require an insulating packer fluid. Economic justification must be decided based on the increased flowing surface temperature that an insulating packer fluid can provide above a conventional one. Therefore, a predictive model was developed that can accurately predict the surface temperature for a flowing well for any Newtonian fluid. The model predicted the flowing well surface temperature (FWST) within 5°F of the measured temperature for the wells studied.

The uniqueness of this model is that a newly derived equation is used to predict the velocity of the packer fluid along the tubing wall caused by free convection for a vertical annulus. Laminar or turbulent flow can be determined from this velocity. In turbulent flow, a friction factor for flat plate or pipe flow must be used to insure accurate predictions. Only when the thickness of the boundary layer equals the midpoint within the annulus can friction factors from pipe flow be used. The model showed how the addition of friction reducers can decrease a well's flowing surface temperature due to the increase in free convection, i.e., by up to 17°F for one case.


Heat loss occurs for a flowing well. It is important to determine the flowing well surface temperatures so that proper well planning can be done. Significant work has been published on predicting flowing well surface temperatures. Most concentrate on the flowing fluid itself by considering two phase flow effects,1 correlating to actual flowing wells2, and Joule-Thomson effects.3 All of these works treat the fluid of the annulus with an effective thermal conductivity correlation. Many corrections were based on enclosed vertical plate studies that neglect the curvature of vertical concentric cylinders as in the case for flowing wells and were not developed based on conventional packer fluids used in the oil and gas industry.

Hansen, et al1 stated, "Unfortunately, no work on natural convection in vertical annular geometry is reported in the literature" so that the correlation for a fluid between two vertical plates appeared to be the best available for heat loss calculations. Later, Fang et al studied free convection of completion fluids in a vertical annulus and concluded that the correlation followed MacGregor's correlation for vertical plates the closest.4 Recently, two equations were derived to predicted laminar fluid flow for a concentric annulus at two different temperatures, Bird's and the one presented here.4 The equation presented in this work was evaluated in determining FWSTs for actual wells.

Model Development

The basis for this model is the energy loss by the producing fluid must be equal to the energy gained by the packer fluid. The heat gained by the packer fluid is due to conduction and convection effect. The effects of radiation are considered small and are neglected. Mathematically the energy balance is shown by Eq. 1.

  • Equation 1

Where mf is the mass flow rate of the flowing well producing fluid, Cpf is the specific heat of the flowing well producing fluid, Tbh is the bottom hole temperature, Ts is the temperature of the producing fluid at the surface, ma is the mass flow rate of the packer fluid along the tubing wall caused by free convection, Cpa is specific heat of the packer fluid, Tba and Tta is the average temperature of the packer fluid flowing at the bottom and at the top caused by convection, respectively, L is the depth of the well, k is the thermal conductivity of the packer fluid, Ti is the temperature of the tubing wall, To is the temperature of the casing wall, ri is the outside radius of the tubing and ro is inside radius of the casing.

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