A multi-physics framework for compositional and non-isothermal two-phase flow in a porous medium is presented which adapts locally the model complexity depending on the physical state. It is based on a sequential (IMPET) solution scheme. As a second adaptive strategy, the simulation grid can be refined locally. This may lead to a mesh with hanging nodes, which is treated by a multi-point flux approximation (MPFA) for improved flux representation. The two adaptivity concepts are employed to simulate a combined subsurface CO₂ injection and geothermal application in an existing reservoir, the Tensleep formation.