High-performance computing (HPC) techniques, especially parallel computing, can be used to significantly reduce the computational time in very large scale simulations. In this work, the popular HPC hardware and parallel programming tools are reviewed and discussed. Then a hybrid Message Passing Interface/Open Multi-Processing (ie, MPI/OpenMP) model is proposed to parallelise the numerical code COMPASS, which adopts a coupled thermal/hydraulic/chemical/mechanical (THCM) approach to model the behaviour of saturated/unsaturated media. Various optimisation techniques have also been employed to achieve better performance. Together with code optimisation, the parallel COMPASS has shown significant performance improvement, which has been seen for an example application in carbon dioxide sequestration.