In this paper we present a new, semi-analytical gravity drainage model to predict the oil production of a cyclic steam stimulated horizontal well. The underlying assumption of the effort is that the cyclic steam injection creates a cylindrically-shaped steam chamber in the upper area of the well. Condensed water and heated oil in the chamber are driven by gravity and pressure drawdown towards the well. The heat loss during the period of soak and oil production is estimated by vertical and radial conduction means. The average temperature change in the chamber during the cycle is calculated using a semi-analytical expression. Nonlinear, second order ordinary differential equations are derived to describe the pressure distribution caused by two phase flow in the wellbore. A simple iteration scheme is proposed to solve these equations. The influx of heated oil and condensed water into the horizontal wellbore is calculated under the assumption of steady-state radial flow.

The solution from the semi-analytical formulation is compared against the results from a numerical thermal simulator on an example. The results are in good agreement with those obtained by the reservoir simulator. Sensitivity studies for optimization of wellbore length, gravity drainage, bottom-hole pressure, and steam injection rate are conducted with the model. Results indicate that the proposed model can be utilized in optimization of individual well performance in cyclic steam heavy oil development. The suggested semi-analytical thermal model can offer an attractive alternative to numerical simulation for planning heavy oil field development.

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