Review of Temperature Dependence of Thermal Properties in Steam-Assisted Gravity-Drainage Process: Mathematical Formulation

Abstract

Summary Steam-assisted gravity drainage (SAGD) is the preferred thermal-recovery method used to produce bitumen from Athabasca deposits in Alberta, Canada. In SAGD, heat energy is transferred from steam to the reservoir, which reduces bitumen viscosity, and enables the bitumen to flow toward the horizontal production well under gravity forces. Conduction is the main heat-transfer mechanism at the edge of the steam chamber. It is controlled by reservoir thermal conductivity and heat capacity. Both factors are temperature dependent and neglecting such dependency can cause errors that should be evaluated in one study. In this study an analytical SAGD model is discussed that includes temperature dependency in the prediction of the temperature evolution ahead of the interface, oil-production rates, and steam/oil ratio (SOR). Such a model is used to evaluate the importance of temperature dependency in different operational conditions. The results of the presented analytical model reveal that the oil rate can be calculated ignoring temperature dependency, suggesting thermal conductivity and specific heat calculated at a dimensionless temperature ratio between 0.75 to 0.8 and between 0.37 to 0.41, respectively. For both laterally expanding and angularly expanding reservoirs, the SOR is independent of the thermal conductivity. Unlike the effect of temperature-dependent thermal conductivity on SOR, temperature dependency on heat capacity significantly affects SOR. Such errors are larger for higher injection pressures (hence, higher steam-chamber temperatures). This study provides a modified Butler analytical SAGD model that combines independently calculated modification factors for thermal conductivity and heat capacity into a modification factor (CT). Interestingly, the modification factor is identical with the TANDRAIN factor that is suggested by Butler to reduce the overestimated rates from the original theory. Such a finding is important because it addresses modifications such as in TANDRAIN and LINDRAIN estimations that are a result of ignoring the temperature dependency in analytical formulation.