Analytical solution for steam-assisted gravity drainage with consideration of temperature variation along the edge of a steam chamber

Abstract

Steam-assisted gravity drainage (SAGD) is a widely-used method for heavy-oil and bitumen recovery. Analytical SAGD models presented in the literature often overestimate bitumen-production rate substantially. Although bitumen-production rate and steam-oil ratio (SOR) depend significantly on temperature near the steam-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 develop the first analytical SAGD model that takes into account 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 associated variables as functions of elevation from the production well, such as oil-flow rate and temperature along a linear chamber edge. Bitumen-production rate and SOR can be calculated for a representative chamber-edge temperature at a certain elevation from the production well.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 chamber-edge temperature used for the new analytical model that gives accurate results can be up to 100 Kelvin lower than the injected steam temperature for a given operating pressure in the cases tested. The previous assumption of the injected-steam temperature at the chamber edge gives overestimated oil-production rates for SAGD. The constant temperature along the edge of a steam chamber gives Butler’s concave interface of a steam chamber that is detached from the production well. For a chamber to exhibit a linear interface, temperature must vary along the chamber edge, which occurs in reality mainly because of heat losses to the over- and under-burden formations.