Investigation of The Natural Convection Heat Transfer in Deep Wellbore

Radial heat transfer between the inner pipe fluid flow and the formation surrounding the
oil wells occurs by overcoming various resistances in series. The major resistance is
within the annular space between the wellbore tubing and the casing. The present work
aims to predict the natural convection heat transfer coefficient in the annulus, which is
hard to predict due to the large length-to-spacing ratio (aspect ratio). The approach to
model natural convection heat transfer in this work is by analytical and numerical
teclmiques. The annular space between the tubing and the casing is treated as a finite
space bounded by walls and filled with fluid media (enclosures). Natural convection in
such enclosures occurs as a result of buoyancy caused by a body force field with density
variations within the annulus field. Correlations for inclined rectangular enclosures will
be employed in the study. The flow field of such a case will be modeled and simulated
for numerical analysis, using ANSYS-FLUENT- 12 software package. Some boundary
parameters have been defined by the user and fed to the software. In order to verify the
results, the predicted Nusselt numbers from both, analytical and numerical will be
compared. The method of analysis is done first by doing the analytical simulation of the
Nusselt correlation found in literature and comparing the result done in numerical
analysis. Numerical simulation is then continued with various operational conditions
and the analysis of the results. The variables interested are the difference of temperature
between tubing and casing, density of air, velocity of air, and the Nusselt Number. The
new functional correlations cover a wide range of oil well inclination angles. In terms of
combined accuracy and continuity, these new functional correlations offer advantages in
certain applications over those previously employed. As heat transfer is concerned, the
convection heat transfer is the highest at the bottom of the long annulus. Comparing the
analytical and numerical simulation, the difference is still clear that the theoretical
analysis of the existing correlation does not agree with the numerical simulation. As a
conclusion, the behavior of the natural convection heat transfer is better observed in the
detail of the numerical simulation.

Keywords: Heat transfer Natural convection Casing annulus Numerical
analysis Oil wells