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-bitumen interface. In a few cases, a steady state 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 on the basis of experimental data.

In this work, the Steam Assisted Gravity Drainage (SAGD) process is considered to develop during two stages; steam chamber rise (unsteady-state stage) and depletion (steady-state stage). Depletion phase is modelled 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 depletion (steady-state) stage, there is a dynamic equilibrium situation. The accumulated heat ahead of the front plays a very important role in this phase of SAGD modelling 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. 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 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 modelling is to determine the advancing front movement that satisfies heat and mass balances over the system under equilibrium.

In the CVD (Constant Volumetric Displacement) model, we postulate that the front movement is such that the steam chamber growth is constant, in other words, 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 increasing accumulated heat ahead of the front due to interface extension and decreasing front velocity.

In the CHI (Constant Heat Injection) 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 over the depletion period.

The modelling of SAGD process in this work is different from that in previous works, since it is believed that the steam chamber velocity is the key point in SAGD modelling. In the CVD model, a constant maximum steam chamber velocity is derived which gives a constant oil production rate with 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).

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