Nonlinear Darcy–Stefan problem for radial Darcy flow in a porous medium during cold-fluid injection

Source abstract

A radially symmetric freezing problem for a saturated porous medium near an injection well during cold-fluid injection is examined. The relevance of the research is in the need to describe phase-change processes in the near-wellbore zone while accounting for radial flow and a moving boundary. The aim of the work is to develop and analyze a reduced Darcy-Stefan model for this setting. The problem is formulated in terms of the supercooling variable. A self-similar solution is obtained and expressed in terms of incomplete gamma functions. The front parameter is determined by a transcendental equation; the existence of a positive root is proved, and an explicit formula is derived for a particular case. A semi-implicit enthalpy scheme is used for numerical verification. An increase in the dimensionless filtration parameter , which characterizes the ratio of filtration-induced convective transport to diffusive heat transfer, accelerates the freezing front; by the end of the simulation, the front-position error is lower for > 1 than for = 0.5. For = 0.5, the maximum discrepancy is observed at the beginning of the simulation due to the influence of the inner boundary, the grid approximation, and the choice of the front-detection criterion.