Upscaling an Extended Heterogeneous Stefan Problem from the Pore-Scale to the Darcy Scale in Permafrost

.In this paper we upscale thermal models from the pore–scale to the Darcy scale for applications in permafrost. We incorporate thawing and freezing of water at the pore-scale and adapt rigorous homogenization theory from [A. Visintin, SIAM J. Math. Anal., 39 (2007), pp. 987–1017] to the original nonlinear multivalued relationship to derive the effective properties. To obtain agreement of the effective model with the known Darcy scale empirical models, we revisit and extend the pore-scale model to include the delicate microscale physics in small pores. We also propose a practical reduced model for the nonlinear effective conductivity. We illustrate with simulations.