A New Analysis on the Convective Heat Transfer at the Edge of the SAGD Chamber

Abstract Heat transfer is an imperative mechanism in the SAGD (steam assisted gravity drainage) process for bitumen production. A better understanding of the heat transfer process is critical for a successful SAGD project design. Following the work of Butler (1981, 1985 and 1997), the conduction only assumption has been widely used. However, there have been some studies indicating the importance of convection heat transfer at the edge of a SAGD chamber. Based on analysis of physical heat transfer mechanisms in the SAGD process, an improved analytical model is developed in this study to calculate the condensate velocity and heat transfer considering both conduction and convection. First, heat transfer at the edge of a steam chamber is analyzed to understand the role of condensate flow and steam chamber interface movement. Three possible cases are proposed to analyze the relationship between the energy left behind the front because of the steam chamber interface movement and the energy carried into the cold reservoir by the condensate flow in the SAGD process. Based on the heat balance analysis and available temperature-saturation relationship, a modified condensate velocity normal to the interface of a SAGD chamber is proposed. It is assumed that the condensate velocity is proportional to the steam chamber interface movement velocity, the fluid mobility ratio of reservoir to steam chamber interface, and the volume heat capacity ratio of reservoir to steam condensates. This new velocity is used to investigate the convection role in the heat transfer of the SAGD process. Moreover, heat transfer equations are solved by using constant heat flow (or Robin) boundary condition to verify the widely-used constant temperature (or Dirichlet) boundary condition at the edge of the steam chamber. The newly developed model is validated by calculating and comparing the condensate velocity normal to the interface, apparent thermal diffusivity and heat fluxes ahead of the steam chamber with filed data (Dover UTF Phase B, Athabasca Reservoir). It is shown that convection can provide a larger contribution to heat transfer than conduction at the edge of a steam chamber, but drops rapidly over a short distance normal to the interface. Considering a large convective heat flow at the edge of the SAGD chamber, temperature can be thought as a constant with minor error. The developed theory provides a quick prediction of apparent thermal diffusivity, temperature distribution, heat fluxes considering both conduction and convection for the design of SAGD projects. Furthermore, it offers a simple formula to show connection between the condensate velocities normal to a chamber interface and the movement velocity of the chamber interface, which can be applied to any thermal processes with steam chamber expanding.