Mathematical modeling of steam injection in vertical wells

Abstract

In this work, a steady-state hydrodynamic model for steam injection vertical wells and a transient thermal model (2D energy diffusion equation) for the heat losses from a well towards the porous medium are presented. The hydrodynamic model is formed by mass, momentum and energy conservation equations (drift-flux model) for a steam-water two-phase flow. The steady-state drift-flux model was resolved using the finite differences method and the explicit Godunov scheme, while the thermal model solution was found with an implicit Godunov scheme. Models allow predicting the next parameters: pressure, temperature, steam quality, heat losses and flow patterns along the well. The parameter predictions presented good agreement against field data and simulations reported in literature. For the conditions simulated, it was found that: (1) the thermal model reaches its steady state at 500 h, (2) due to few steam condensation, pressure drop due to gravity is smaller than the friction and acceleration contributions, and (3) temperature gradients are large at the beginning of steam injection, but they diminish along time.