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.
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).
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