Analytical Solution for SAGD with Consideration of Temperature Variation along the Edge of a Steam Chamber

• Author / Creator

  Shi, Xiaoxing

• Steam-assisted gravity drainage (SAGD) is a widely-used method for heavy-oil and bitumen recovery. Analytical models were presented in the literature for bitumen-production rate and steam-to-oil ratio (SOR) for SAGD. They often overestimate bitumen-production rate substantially. Various attempts were made to correct for simplifying assumptions made in their derivations. However, no research has been conducted to solve for temperature at the edge of a steam chamber. Although bitumen-production rate and SOR depend significantly on temperature near the chamber edge in SAGD, previous analytical models assumed the injected-steam temperature to uniformly distribute along the edge of a steam chamber. The main objective of this research is to investigate temperature variation along the edge of a steam chamber. Local material balance and Darcy’s law are applied to each cross section perpendicular to the edge of a steam chamber. Then, they are coupled with the global material balance for the chamber geometry that is an inverted triangle. New analytical equations are presented for bitumen-production rate and SOR, in addition to variables as functions of elevation from the production well, such as oil flow rate, temperature, and composition along the linear-chamber edge. Bitumen-production rate and SOR can be calculated for a given temperature at a certain elevation from the production well. The new analytical model is validated on the basis of numerical flow simulations. Comparison of the analytical model with numerical simulations shows that bitumen-production rate and SOR can be accurately estimated when the new model is used with the temperature taken from the midpoint of the edge of a steam chamber. The temperature that gives accurate results is 60%-90% of the injected-steam temperature in the cases tested. Hence, the analytical model presented in this research requires a representative temperature (i.e., temperature at the midpoint of the chamber edge) for a given time for a given SAGD operation, unlike previously-proposed models. This is plausible because the assumption of one-dimensional heat conduction on a moving chamber edge is expected to be less accurate near the top and bottom of a steam chamber, in which multi-dimensional heat transfer is significant owing to heat losses to the over and underlying formation rocks. Numerical simulations show that such heat losses are necessary for a steam chamber to have a linear edge. In addition, multidimensional flow near the bottom of the reservoir causes substantial heat convection, and makes the one-dimensional conduction equation inaccurate. Hence, the previous assumption of the injected-steam temperature at the chamber edge is simplistic, and gives inaccurate results for oil-production rate in SAGD. Among widely-used assumptions for analytical SAGD models, most simplistic assumptions are identified, such as single-oleic phase flow, one-dimensional flow along the edge of a steam chamber, and one-dimensional heat conduction ahead of the chamber edge. The new analytical model is also applied to estimate bitumen-production rate and SOR for three SAGD projects, although there are various uncertainties in actual field data, such as reservoir heterogeneity.

• Subjects / Keywords

  • Analytical model
  • SAGD
  • Chamber-edge temperature
  • SOR

• Graduation date

  Spring 2017

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3W669M7F

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.