Comprehensive Analytical Modelling of SAGD and Its Variations

A comprehensive analytical model of the Steam-Assisted Gravity Drainage (SAGD) process was developed, encompassing steam chamber rise, sideways expansion, and the confinement phases. Results were validated using experimental and field data. The deficiencies of the previous models are pointed out, none of which treated the SAGD process in its entirety, as done in this work. Also, a new mathematical model of the solvent-SAGD process for the sideways expansion of the vapour chamber was developed. During steam chamber rise, the Cumulative Steam-Oil ratio (CSOR) decreases, with an increasing oil production rate. The rise velocity increases with an increase in permeability and temperature. The sideways steam chamber expansion is treated in two widely different ways in this study, called Constant Volumetric Displacement (CVD) where injection rate must be increased continuously for a constant oil rate, and Constant Heat Injection (CHI). In CVD, interface temperature gradient decreases with time, but the heat penetration depth increases. In CHI, heat injection rate is constant, but oil rate declines with time. Also, the oil rate decreases with an increase in operating pressure, in contrast to previous studies. In the final stage, adjacent chambers interfere, reducing the effective head for gravity drainage. For a small well spacing, confinement occurs earlier, heat loss starts decreasing sooner, resulting in a lower CSOR, than for a large spacing. After chambers coalescence, the oil rate declines faster in CVD than CHI model. The above models were combined to obtain the Comprehensive Constant Volumetric Displacement (CCVD) and Comprehensive Constant Heat Injection (CCHI) models. Excellent agreement was obtained with laboratory and field results. Also developed was a new solvent-SAGD model. Results show an increase in heat penetration, and decrease in the interface temperature and concentration with time. Mass transfer scale is of the order of centimetres, while heat transfer occurs over metres. The solvent-SAGD process would yield a higher oil recovery, if viscosity reduction from dilution at a lower temperature is greater than viscosity reduction by temperature in the plain SAGD process, for the same total rate. In most cases, the additional bitumen recovery was less than the volume of the solvent injected.