This paper is concerned with multicomponent, two-phase, thermal fluid flow in porous media. The fluid model consists of component conservation equations, Darcy's law for volumetric flow rates and an enthalpy conservation equation. The model is closed with an equation of state and phase equilibrium conditions that determine the distribution of the chemical components into phases. The sequential formulation described in a previous article is used to build a second-order shock capturing scheme for the conservation equations using a primitive-variable-based linear reconstruction. The fluxes at the cell faces are calculated using an approximate Riemann solver. The method is validated and evaluated by means of one- and two-dimensional problems, including a gravity inversion test.