This paper takes a new approach to the modelling and visualisation of sequestered CO2 in subsurface reservoirs and its migration pathways. We model the gas as discretised packets moving along paths within a graph or network. The movement of the packets will be governed by chip-firing. This new approach provides a new insight into the modelling of CO2 migration in porous media with complex geological architectures. We compare and contrast this new graph theoretic approach with traditional methods and demonstrate that similar results are obtained, with the added advantage that the new methods are quick to implement and execute. In addition, the new methods are more flexible and can more accurately capture the variation in the stratification of the encasing rock.