Steam injection into a slow water flow (Darcy flow) was studied analytically for steady-state conditions. The continuity, momentum, and energy equations for both water flow and steam flow were solved subject to interface conditions. The governing equations were transformed using stream function and velocity potential coordinates to simplify the calculation domain. The resulting energy equation was converted to a simultaneous ordinary differential equation by an integral method. The unknown steam-water interface shape and location were determined through an optimization process. Temperature distribution on the water side, local condensation rate along the interface, water and steam flow fields and pressure distribution were found numerically. Comparison with experimental measurements showed that the average steam zone size could be fairly well predicted only when dispersion effects were incorporated into a modified thermal conductivity model.

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