A computer system analyzes data from giant subsurface hydrocarbon reservoirs which are organized into a number of component cells and simulates the conditions in the reservoirs based on determination of thermodynamic phase equilibrium using equation of state (EOS) modeling. The computer system takes the form of a heterogeneous (hybrid) computer environment which includes computer processor units (or CPU's) and graphical processing units (or GPU's). The system takes advantage of computational acceleration capabilities of the graphical processing units while utilizing the computer processing units for execution control, input/output of data and memory. Processing time requirements are reduced by more than an order of magnitude speed improvement over existing methods.