Analytical modelling of steam chamber rise stage of Steam-Assisted Gravity Drainage (SAGD) process

When steam is injected continuously in a SAGD operation, a steam chamber starts to develop in three stages; rise, lateral spreading and confinement, as observed in the field and laboratory experiments. The physics of chamber development in the first and the two last stages is different and thus modelled separately. Nearly all of the available theoretical analyses of SAGD are concerned with the lateral spreading stage of the steam chamber development with the exception of a few works which aim to determine rise velocity and oil rate. The rate of the upward growth of the steam chamber has a profound effect on the SAGD performance, because as the chamber reaches the top of the reservoir heat loss starts to play a significant role in the thermal efficiency of the process. During the rise period, as the steam chamber grows upwards, oil drains downwards and so the process at this stage must account for to the frontal instability between steam and the liquid phases in the system. Stability is affected by factors such as the flow direction, gravity, and viscosity difference between gas/steam and liquid phases. Steam condensation, on the other hand, has a stabilizing effect. In the present model, the rise velocity and the steam chamber height were calculated by combining volumetric oil displacement with Darcy oil rate considering the indirect effect of frontal instability. The model is extended to predict oil production, heat or steam injection rate, heat consumption and CSOR during this phase. Moreover, estimates of injected steam sweep efficiency and the angle between the steam chamber and the horizon are achieved. The model results show an increase in rise velocity with temperature and permeability. Also, the calculated oil production rate increases and Cumulative Steam Oil Ratio (CSOR) declines with time. This theory is tested via comparison with several field data sets to show the adequacy of the model.