Oil-Rate Prediction Model for the Ramp-Up Phase of a Steam-Assisted-Gravity-Drainage Process: Stability Approach

Abstract

Summary In a steam-assisted-gravity-drainage (SAGD) process, the steam chamber starts to develop in three stages: ramp up, lateral spreading, and wind down. Although the physics of ramp up (or the rising phase) is completely different from that of lateral spreading, the current theoretical analyses of SAGD use a similar approach for modeling lateral spreading to calculate the ramp-up oil rate. The oil rate at the ramp-up phase is highly dependent upon the upward growth of the steam chamber, which is controlled by the frontal instability of the steam-condensate front into the heated bitumen. In this study, the evolution of disturbance (spatial-growth rate) was explored by solving the initial value problem governing the linear stability of the pressure and water-phase velocity normal to the edge of the steam chamber found in the SAGD process. To investigate the interaction of the steam chamber/reservoir zones, a new model was formulated that coupled the pressure diffusion equations and condensate leakoff into a reservoir beyond the chamber. The results suggested that the steam interface in the SAGD process was unstable if it moved faster than the critical velocity. In the ramp-up phase, the velocity at the chamber interface increased until it reached the instability velocity. Once it was reached, the instability caused extensive mixing and convection that reduced the temperature at the interface, thus causing the interface velocity to reduce to the instability velocity. As a result, the interface grew at the equilibrium velocity of minimum instability velocity (or critical velocity). The vertical/horizontal permeability ratio (Ωk) of the reservoir is a controlling parameter of instability. The calculated oil-production rate at ramp up increases linearly with time (i.e., qo∝t), which contradicts Butler's ramp-up formula that states that the rate is correlated to the cubic root of time (i.e., qo∝t1/3). Another key finding was that the suggested ramp-up-rate formula was highly dependent upon the reservoir-water mobility, which was supported by field operations in reservoirs with high water mobility such as Suncor/Firebag and Nexen/Long Lake, where the ramp-up time was significantly less than that in reservoirs with low water mobility, such as those in the MacKay River Field.