In this paper, a novel model is proposed to characterize superheated steam-air (SSA) pressure and temperature distribution in horizontal wells with toe-point injection technique. Firstly, the mathematical model of SSA flow in both tubing and annulus is established based on the mass, momentum and energy conservation equations, and it is solved by employing finite difference method. The mass and heat transfer are coupled with injection of SSA into formation and heat exchange between tubing and annulus by iterative technique. Then, the proposed model is validated by field data. Finally, the effect of mass fraction of air and injection temperature on SSA temperature, pressure, mass flow rate in annulus and heat transfer rate from annulus fluid to formation are conducted.

Results indicate that: (1). The SSA temperature in tubing decreases while flowing from heel point to toe point and the temperature gradient decreases with distance to heel point. (2). The SSA temperature in annulus first decreases and then turns to increase while flowing from toe point to heel point. (3). The SSA pressure in tubing decreases linearly from heel point to toe point, while the SSA pressure gradient in annulus decreases with the distance to toe point. (4). The SSA temperature in both tubing and annulus decreases with the increasing of mass fraction of air. This is because the enthalpy of air is smaller than superheated steam. (5). Increasing injection temperature can decrease the SSA pressure in both tubing and annulus by reducing SSA density and increasing frictional loss.

Based on the presented model, the SSA pressure and temperature in both tubing and annulus can be accurately predicted with the relative error less than 5%. The theoretical studies in this paper can be taken as a reference for engineers in optimization of injection parameters and provide following researchers with the very basic theory for the application of toe-point injection technique.

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