Petroleum migration is traditionally modeled using equations describing multi-phase flow in porous media where several fluid phases move simultaneously throughout geological time in an evolving grid representing a subsiding sedimentary basin. This formulation leads to a large system of coupled non-linear equations that have to be solved simultaneously for pressure and saturation. Decoupling of equations leads to a sequential formulation (IMPES or Implicit Pressure and Explicit Saturation) but is hampered by a time step limitation which can be severe when migration is fast or grid cells are small. This limit can be overcome by solving multi-phase transport along 1D streamlines based on the pressure field calculated on the grid. This has been been shown successfully in reservoir simulation and here we extend it to basin simulation problems including gravity and capillary pressure for non-Cartesian grids. Particular attention has been focused on source terms which are not point sources such as wells in reservoir simulations, but are distributed as organic matter in source rocks, and on the fact that porosity is not constant due to compaction which introduces limitations to the application of stream lines in basin modeling. The theoretical framework will be derived and some simple applications shown that demonstrate the precision and performance reached compared with the classical IMPES formulation.
