It is now possible to develop mathematical models that make quantitative predictions of the geological phenomena leading to oil accumulations. The models presented in this study are deterministic, that is, based on physical or chemical laws and not on statistical analysis.

A first set of models may be used during the initial stage of exploration of a sedimentary basin, when little geological data are available. Their purpose is to determine the general geological evolution and the overall petroleum potential. A backstripping model makes an automatic reconstruction in time of sedimentary basins, taking into account the progressive compaction of the sediments. It also computes the sediment load on the basement together with the subsidence variations in time, enabling a geodynamic model to be used for some basins to simulate the history of heat flow. It is then possible to reconstruct the temperature history of each sedimentary unit. A kinetic model of organic matter maturation is used to compute the possible area and timing of petroleum formation.

A second set of models may be applied when exploration is more advanced, to estimate the importance of various traps in a given petroleum province. These models, which need more extensive data than the first set, take into account the influence of migration processes on oil accumulation. The migration model gives a quantitative description of the formation of hydrocarbons and computes the pressure regime of the fluids. Thus it determines the amount of petroleum expelled from the source rocks by compaction and its possible accumulation in traps. A thermodynamic model computes hydrocarbon migration in the gas phase and its consequences for the composition of oils.

The Gulf of Lion passive margin in France, the Viking Graben in the North Sea, and the Mahakam Delta in Indonesia are used as examples.