Vertical migration of hydrocarbons modelled with fractional flow theory

Summary We present a simple 1-D and one-lithology model of integrated hydrocarbon generation and vertical migration. Although the model is very simple, it captures some of the most basic features of the vertical migration process, like expulsion from source rocks, and vertical migration in carrier beds above and below the source rock. The dynamics in the model are caused by sedimentation, which is done at a constant rate. Owing to sedimentation, the source rock is brought down to the depths where kerogen breakdown starts. This two-phase model is based on fractional flow theory, which makes it possible to avoid a pressure equation. The solution of the saturation equation is characterized by a dimensionless number, the gravity number, and the ‘size’ of the capillary forces. When the gravity number is less than 1, buoyancy is less important, while for gravity numbers greater than 1, buoyancy is dominating. We discuss capillary effects, and estimate a Peclet number for the migration process, which shows that capillary forces are less important in this one-lithology model. In the special case of no compaction, negligible capillarity and no generation of pore space due to the kerogen breakdown, we can approximate a solution to the saturation equation by considering Riemann problems. We find that above the source region, we get at least a shock and possibly a rarefaction, too. Below the source region, we have at least a rarefaction wave, and possibly a shock. We present explicit expressions for the shock position, and the characteristics propagating saturations. These solutions enable us to decide if, and when, the shock will reach the top of the basin. If we know the total oil production, we can read off from the flux function curve an approximation of the saturation propagated upwards. Although these solutions apply to the case of no compaction, negligible capillarity and no generation of pore space, they are useful approximations if any of these restrictions is only ‘weakly violated.