A comprehensive analytical model of the Steam-Assisted Gravity Drainage (SAGD) process is developed, encompassing steam chamber rise, sideways expansion, and the confinement phases. Results are validated using experimental and field data.

A new analytical model for predicting steam chamber rise velocity and oil production rate during this period is developed. In this theory, by combining volumetric oil displacement with Darcy oil rate considering the indirect frontal instability effect, the rise velocity, and the steam chamber height are calculated. The model is extended to predict oil production, heat or steam injection rate, heat consumption and Cumulative Steam-Oil Ratio (CSOR) during this phase. The model results show the CSOR decreases, with an increasing oil production rate. The rise velocity increases with an increase in permeability and temperature. Results are validated with experimental and field data.

The sideways steam chamber expansion is treated by a new analytical approach which is called Constant Volumetric Displacement (CVD) where injection rate must be increased continuously for a constant oil rate. At the final stage, adjacent chambers interfere, reducing the effective head for gravity drainage and the heat requirement in this system. For a small well spacing, confinement occurs earlier, heat loss starts decreasing sooner, resulting in a lower CSOR, than for a large spacing.

The above analytical SAGD models including rise, lateral spreading, and confinement phases are combined to obtain the Comprehensive Constant Volumetric Displacement (CCVD) model. The results are validated against experimental and field data. Excellent agreement was obtained with laboratory and field results.

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