Numerical and semi-analytical modelling of the capillary end effect for porous media of any wettability state

The capillary end effect appears in a two-phase displacement process as a physical consequence of the capillary discontinuity at the system outlet and causes accumulation of the wetting phase at this location and back along the system. In the study of water injection into a one-dimensional system, to obtain accurate phase saturation profiles in the presence of the capillary end effect at any time during the transient state, conventional implicit pressure explicit saturation and one-dimensional convection-diffusion methods have been modified by applying a novel boundary condition. This modification is entirely physics-based, whereas in commercial simulators fix-up procedures are applied which do not conserve mass. A new term “exit saturation” is introduced which provides a useful way to study and analyse the capillary end effect. Transient-state flow development in the presence of the capillary end effect in different wetting systems is presented in detail in this work. Also, several methods are presented to obtain steady-state saturation profiles. At steady-state conditions, the capillary end effect vanishes in purely water-wet systems and all oil in principle can be displaced from the system in a finite, but very long time. However, in mixed-and oil-wet systems, some oil is permanently trapped in the system at any chosen flowrate, i.e., the capillary end effect cannot be entirely removed no matter how large the flowrate is. However, oil recovery is improved by increasing the flowrate.