Analytical model of steam-assisted gravity drainage (SAGD) process in relation to constant injection rate

Steam-Assisted Gravity Drainage or SAGD is a widely tested method for producing bitumen from oil sands (tar sands). Several analytical treatments of the basic process have been reported. In a typical model, the focus is on bitumen drainage ahead of an advancing steam-oil interface with no recourse to the steam injection rate – which is worked out after the fact. In this study, a comprehensive analytical model of the SAGD process in relation to constant injection rate, for the first time, was developed encompassing steam chamber rise, sideways expansion, and the confinement phases to evaluate the SAGD performance. The model is called Comprehensive Constant Heat Injection (CCHI). The accumulated heat ahead of the front plays a crucial role in SAGD modeling in order to find the advancing front velocity. There is a reciprocal relation between the advancing front velocity and the amount of stored heat ahead of the front. Considering the equilibrium situation for thermal recovery methods with dominant gravity drainage driving force, the advancing front velocity is responsible for heat accumulation ahead of the front, and in turn, the heated oil drains down to the production well and advances the front. Therefore, the key point in the modeling is to determine the advancing front movement that satisfies heat and mass balances over the system under equilibrium. In the CCHI model, after the rising chamber reaches the reservoir top, steam is injected at a constant rate into the system which is the case in the most field applications, and it provides heat for the growing steam chamber size, increasing heat loss, and heat flow by conduction ahead of the front. Unlike previous works, the steam chamber growth is maximum at the beginning of the sideways expansion phase with growth and oil production rate decreasing with time. It is believed that the inclusion of increasing heat loss and interface extension with time, ignored in previous works, into energy and mass balances results in decreasing steam chamber velocity. In this model, it is the first time that the SAGD oil rate is directly related to the steam injection rate. Some interesting analysis of a SAGD process can be extracted from the model. Also, the approach provides a tool for quick field-scale optimization and performance predictions instead of using extremely time-consuming thermal numerical simulators.