This work presents a compositional numerical model to simulate the combustion of heavy crude oil in a porous combustion tube. The combustion tube experiments replicate an enhanced oil recovery process by in-situ combustion (ISC) of crude oil in a petroleum reservoir. Due to the economic constrains associated with the combustion tube tests, numerical simulation has been identified as an efficient and economical tool in understanding the complex ISC process. In the present model, mass and energy conservations have been drawn considering an advective, diffusive, and reactive flow of multiple components in multi-phase. The model includes temperature- and pressure-dependent fluid properties and considers the effect of capillary pressure. A block-centered finite-difference-based numerical tool with an implicit quasi-Newton iterative solver scheme has been developed to solve the conservation equations. The numerical model is validated with the combustion-tube results reported by Fadaei et al. (2011). The combustion front profile predicted by the present numerical model has been found to be in good agreement with the reported results. The numerical results projected a cumulative oil recovery of about 60% of original oil in place. The combustion front has been found to propagate with an average peak temperature of 715 K. Copyright © Taylor & Francis Group, LLC.