Analytical Treatment of Steam-Assisted Gravity Drainage: Old and New

Summary Steam-assisted gravity drainage (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 heat front. In a few cases, a steady expression for bitumen-drainage rate is obtained. This has been modified by several investigators to include other effects. In all cases, the bitumen rate is obtained with no recourse to the steam-injection rate, which is worked out after the fact. The treatment of time dependence, in a few models, is tenuous, building it in partly by use of experimental data. In this work, the SAGD process is considered to develop during two stages: steam-chamber rise (or unsteady stage) and sideways-expansion (or steady stage). The sideways-expansion phase is modeled by two different approaches: constant volumetric displacement (CVD) and constant heat injection (CHI). In the transient-steam-chamber-rise stage of SAGD, initially there is no heat ahead of the rising front, but as the front rises with time, heat accumulates ahead of the front. In the sideways-spreading stage, there is a dynamic equilibrium situation. The accumulated heat ahead of the front plays a crucial role in this phase of SAGD modeling 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. Higher front velocity leads to lower heat accumulation ahead of the front for mobilizing oil ahead and making it drain. By considering the equilibrium situation for thermal-recovery methods with a dominant-gravity-drainage driving force, the advancing-front velocity is responsible for heat accumulation ahead of the front, and, in turn, this heated oil drains away and is responsible for advancing 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 CVD model, we postulate that the front movement is such that the steam-chamber growth is constant; that is, the oil-production rate is constant over time. In this work, it is shown that to obtain a constant oil-production rate from a mass balance, the injected heat has to be increased to compensate for the heat loss to the overburden and the growing accumulated heat ahead of the front caused by interface extension and decreasing front velocity. In the CHI model, heat is injected at a constant rate into the system, which provides heat for the growing steam-chamber size, increasing heat loss to the overburden, and heat flow by conduction ahead of the front. In this model, we are computing the front velocity that satisfies heat balance and mass balance for a constant heat-injection rate. Decreasing steam-chamber velocity with time from this model leads to decreasing oil-production rate. The modeling of the SAGD process in this work is different from that in previous works because it is believed that the steam-chamber velocity is the key point in SAGD modeling. In the CVD model, a constant maximum steam-chamber velocity is derived that gives a constant oil-production rate with a better agreement with field data. In the CHI approach, steam-chamber velocity, and hence the oil-production rate, is decreasing with time (strongly affected by increasing heat loss to the overburden).