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Two major techniques are commonly used to model secondary and tertiary hydrocarbon migration: Darcy flow and invasion percolation. These approaches differ from each other in many ways, most notably in the physical modeling, the methods of resolution, and the type of results obtained. The Darcy approach involves not only buoyancy, capillary pressures, and pressure gradient, but also transient physics, thanks to the viscous terms. Although it can be numerically difficult and therefore time consuming, it is appropriate for slow hydrocarbon movement and it is able to provide a good description of cap-rock leakage. The invasion percolation approach, at least in the context of the implementation used in our examples, does not consider either viscosity or permeability; only buoyancy and capillary pressures drive the hydrocarbon migration. This method is relatively quick and especially useful to simulate secondary migration. Nevertheless, the viscous terms cannot be universally neglected as they can impact the timing of trap filling.

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