Viscous stabilization of 2D drainage displacements with trapping

We investigate the stabilization mechanisms due to viscous forces in the invasion front during drainage displacement in two-dimensional porous media using a network simulator. We find that in horizontal displacement the capillary pressure difference between two different points along the front varies almost linearly as a function of height separation in the direction of the displacement. The numerical result supports arguments taking into account the loopless displacement pattern where nonwetting fluid flows in separate strands (paths). As a consequence, we show that existing theories developed for viscous stabilization are not compatible with drainage when loopless strands dominate the displacement process.