A Separate-Phase Drag Model and a Surrogate Approximation for Simulation of the Steam-Assisted-Gravity-Drainage Process

General, ensemble phase-averaged equations for multiphase flows were specialized for the simulation of the steam-assisted-gravity-drainage (SAGD) process. In the average momentum equation, fluid/solid and fluid/fluid viscous interactions are represented by separate force terms. This equation has a form similar to that of Darcy's law for multiphase flow but augmented by the fluid/fluid viscous forces. Models for these fluid/fluid interactions are suggested and implemented into the numerical code CartaBlanca. Numerical results indicate that the model captures the main features of the multiphase flow in the SAGD process, but the detailed features, such as plumes, are missed. We find that viscous coupling among the fluid phases is important. Advection time scales for the different fluids differ by several orders of magnitude because of vast viscosity differences. Numerically resolving all these time scales is time consuming. To address this problem, we introduce a steam-surrogate approximation to increase the steam-advection time scale, while keeping the mass and energy fluxes well-approximated. This approximation leads to approximately a 40-fold speedup in execution speed of the numerical calculations at the cost of a few percentage errors in the relevant quantities.