At the timescales associated with secondary migration, the balance between the gravity and the capillary forces (i.e., the Bond number) overwhelmingly controls the trajectories and characteristics of hydrocarbon flows. At these low flow rates, viscous forces are negligible and can effectively be ignored. From a practical standpoint, this means that techniques used for modeling petroleum flows at production timescales introduce computational overkill and may in fact be entirely inappropriate for solving the petroleum migration problem.

New invasion-percolation (IP)-based techniques have been developed that take advantage of the special force regime of petroleum migration (IP is based on the premise that flow in porous media can be represented by an invasion through a matrix of pores and throats represented by threshold pressures or probabilities; invasion occurs along the fluid front by accessing the "pore" with the smallest threshold pressure). The result of this work is the capability to simulate one-phase, constant-composition petroleum flow in models containing tens of millions of grid cells in a matter of minutes, while honoring the mechanics of migration transport. Because the calculation is so fast, these simulations may be extended beyond the transport problem to include other, more time-intensive calculations with very little loss in overall simulation performance.