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Research Papers

Natural Convection Within an Elongated Vertical Cylinder: Heat Loss From Bore of Oil Well Christmas Tree

[+] Author and Article Information
Egidio (Ed) Marotta

Fellow ASME
GE Oil & Gas,
Houston, TX 77073
e-mail: Egidioed.marotta@ge.com

Sumit Arora

Mem. ASME
FMC Technologies,
Houston, TX 77086
e-mail: Sumit.Arora@fmcti.com

Mauricio A. Sanchez

Mem. ASME
FMC Technologies,
Houston, TX 77086
e-mail: Mauricio.Sanchez@fmcti.com

Manuscript received April 2, 2013; final manuscript received November 7, 2013; published online February 26, 2014. Assoc. Editor: Hongbin Ma.

J. Thermal Sci. Eng. Appl 6(3), 031005 (Feb 26, 2014) (8 pages) Paper No: TSEA-13-1064; doi: 10.1115/1.4026220 History: Received April 02, 2013; Revised November 07, 2013

Internal natural convective heat transfer from a thin walled, vertical cylinder with an exposed vertical surface is investigated numerically. The top and bottom end faces are assumed isothermal. This setup approximates the vertical wellbore of a Christmas tree for simulating cool-down of subsea oil and gas equipment during shutdown operations. The primary objective of this study is to determine the cooling rate of the interior fluid and the onset of fluid motion (rotation) caused by the two non-adiabatic surfaces as a function of Biot number (Bi) applied at the vertical cylindrical wall. The flow is assumed to be three-dimensional, non-steady, and transitional with constant fluid properties except for the density variation with temperature. This latter effect gives rise to the buoyancy force; treated using the Bousinessq approach. We solve the dimensionless governing equations numerically using COMSOL Multiphysics, a commercial finite-element method (FEM) based code. The specific application that motivated this investigation involved a range of Prandtl numbers (Pr) from 0.7 to 168. In addition, we consider small and moderate values of Rayleigh numbers (Ra). Steady-state solutions for temperature and velocity are stratified at the heat source region regardless of the Biot number.

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References

Figures

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Fig. 2

Subsea vertical Christmas tree (only selected components are shown)

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Fig. 3

Streamlines (Δψ = 0.05) and Isotherms for different Ra number at τ = 120 and Bi = 10 (Pr = 0.71)

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Fig. 4

Local Nusselt number for Bi = 0.1 for Pr = 0.71. The onset plot shows the oscillation of Nu for Ra = 106.

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Fig. 5

Time-averaged Nusselt number for different Biot numbers with respect to Rayleigh numbers for Pr = 0.71

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Fig. 6

Streamlines (Δψ = 0.05) and Isotherms for different Ra numbers at τ = 150 and Bi = 0 for Pr = 7.0 For Ra = 106 the second plot is at τ = 405

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Fig. 7

Time-averaged Nusselt number for different Biot numbers as a function of Rayleigh numbers for Pr = 7.01

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Fig. 8

Mean dimensionless vertical velocity (w) at center-line along L at different times τ for Bi = 100, Ra = 106 for Pr = 7.01

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Fig. 9

Dimensionless temperature (θ) at center-line along L at different times τ for Bi = 100, Ra = 106 for Pr = 7.01

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Fig. 10

Velocity vectors and temperature contours at τ = 300 for Ra = 106, Pr = 7.0

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Fig. 11

Streamlines (Δψ = 0.05) and Isotherms for different Ra number at τ = 150 and Bi = 1 for Pr = 168. For Ra = 105 the second plot is at τ = 250. For Ra = 106 the subsequent plots are at τ = 1005, 2010, and 3000.

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Fig. 12

Particle trajectories at different time rates for Bi = 1 and Pr = 168 at two different Ra

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Fig. 13

Time-averaged Nusselt number for different Biot numbers with respect to Rayleigh numbers for Pr = 168

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