## A Mathematical model for the prediction of wellbore heat loss and pressure drop in steam injection wells

 dc.contributor.advisor Aziz, Khalid dc.contributor.author Fontanilla, Jerry P. dc.date.accessioned 2005-07-21T19:48:10Z dc.date.available 2005-07-21T19:48:10Z dc.date.issued 1980 dc.description Bibliography: p. 118-121. en dc.description.abstract Steam 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. dc.description.notes This title is not available online. Access options are: - consulting the copy from Archives in our reading room in person - https://asc.ucalgary.ca/visiting/ - borrowing a circulating copy from the Library catalogue – https://ucalgary.primo.exlibrisgroup.com/discovery/search?vid=01UCALG_INST:UCALGARY&lang=en dc.format.extent xviii, 147 leaves : ill. ; 30 cm. en dc.identifier.citation Fontanilla, J. P. (1980). A Mathematical model for the prediction of wellbore heat loss and pressure drop in steam injection wells (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/21934 en_US dc.identifier.doi http://dx.doi.org/10.11575/PRISM/21934 dc.identifier.lcc TN 871 F64 1980 Fiche en dc.identifier.other NL Number: 51258 en dc.identifier.uri http://hdl.handle.net/1880/21958 dc.language.iso eng dc.publisher.faculty Engineering dc.publisher.institution University of Calgary en dc.publisher.place Calgary en dc.rights University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. dc.subject.lcc TN 871 F64 1980 Fiche en dc.subject.lcsh Thermal oil recovery - Mathematical models dc.title A Mathematical model for the prediction of wellbore heat loss and pressure drop in steam injection wells dc.type master thesis thesis.degree.discipline Chemical Engineering thesis.degree.grantor University of Calgary thesis.degree.name Master of Engineering (MEng) ucalgary.thesis.accession Theses Collection 58.002:Box 379 82483903 ucalgary.thesis.notes UARC en ucalgary.thesis.uarcrelease no en