A Mathematical model for the prediction of wellbore heat loss and pressure drop in steam injection wells
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AbstractSteam drive project design requires the condition of steam at the sandface before it enters the formation to obtain the recoverable oil as a result of this thermal oil recovery process. Several analytical wellbore heat loss models can be found in the literature, but they are made with numerous simplifying assumptions. A need for a comprehensive and rigorous model for the prediction of wellbore heat loss and pressure drop including the effects of gravity, friction, and kinetic energy for quantitative analyses therefore came into being. The mathematical model is developed by combining the continuity equation, the total energy equation, the mechanical energy equation or the extended Bernoulli equation, and the heat loss equation and reducing them to two first order differential equations in terms of the pressure gradient (dP/dz) and steam quality gradient (dx/dz). These equations are solved numerically in this thesis by the Fourth Order Runge Kutta method. The steam properties are read off directly from the steam tables obtained from Faires (1962). The pressure and steam quality at each mesh point along the injection tubing string are solved for in a step-wise manner until the depth reaches the sandface or the formation depth. An investigation of the two-phase pressure drop correlations for downward steam flow is also done. The Aziz, Govier and Fogarasi correlation, which is a correlation for upflow was modified for downflow in the bubble flow and slug flow patterns, but in the annular flow and mist flow there is no need for modification as a no slip condition is assumed. It was found that the Yamazaki and Yamaguchi correlation does not work for a steam system with liquid holdup less than 10%, as it predicts huge friction pressure drop in this range. An investigation was also conducted to see if existing correlations could be modified to improve their accuracy. It was found that Yamazaki and Yamaguchi's hydrostatic head correlation could be adjusted to match experimental data when frictional contribution is calculated with the Duns and Ros method. The limited testing done here shows that the Beggs and Brill correlation is the most reliable of all existing methods.
Bibliography: p. 118-121.
CitationFontanilla, J. P. (1980). A Mathematical model for the prediction of wellbore heat loss and pressure drop in steam injection wells (Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/21934
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