This work considers a detailed model for compositional flow in porous media, applied to the modelling of in-situ combustion of heavy oil. An experimentally-derived phase and chemical equilibrium model is used, and the combined fluid-reaction system validated against combustion tube experiments. Several one-dimensional simulation studies are carried out. An ignition mode via low-temperature oxidation, and an unsteady propagation mode, are demonstrated by perturbing the reaction parameters governing fuel formation and combustion. An adaptive mesh refinement method is successfully applied to this problem, and detailed simulations in two dimensions demonstrate multi-dimensional dynamics of a propagating combustion front. These include a viscous instability, non-uniform propagation, and local extinction of the front. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.