This paper presents the formulation and verification of a simple model for predicting the liquid level above steam-assisted gravity drainage (SAGD) production wells. Controlling the proximity of the liquid-vapour interface to the producer is paramount for maximizing the energy efficiency of SAGD, optimizing production, and reducing the risk of liner damage from steam breakthrough; and so a simple model can be used for quick approximation and potentially for decisions on wellbore design and operational control.

The formulation is based on continuity of mass flow and thermal behaviour. Darcy's law is the key phenomenon in formulating an analytical model of the flow through the liquid pool, or steam trap, around the production well, which is referred to in this work as a gravity inflow performance relationship (GIPR). The GIPR relates the liquid level above the producer to the inflow rate, system pressures, and reservoir and fluid properties. To validate our modelling assumptions, the liquid level predicted by the GIPR is compared to data generated from a commercial reservoir simulator for a wide range of operating conditions.

Based on data from 31 reservoir simulations, the GIPR predicts the liquid level with high accuracy. The liquid levels given by the GIPR and reservoir simulator differ by a root-mean-square error of only 0.23 m. The introduction of a correction factor in the GIPR reduces the root-mean-square error to just 0.17 m. Moreover, the GIPR reveals fundamental relationships between the liquid level and SAGD process variables, providing insight into the mechanics of steam trap control. The relationship between the liquid level and the inflow rate yields a criterion for the stability of the liquid-vapour interface above the production well. The criterion elucidates the conditions under which the position of the liquid-vapour interface will be unstable and, thus, the conditions under which steam breakthrough or injector flooding may be expected.

The GIPR provides a simple, efficient, and accurate way to predict the liquid level above SAGD production wells, enabling the optimization of well designs and control strategies to facilitate steam trap control. In addition, the GIPR reveals relationships between variables that are masked with more complex models, providing an enhanced understanding of the SAGD process.

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