A Numerical Study of Capillary and Viscous Drainage in Porous Media

This paper concentrates on the flow properties when one fluid displaces another fluid in a two-dimensional (2D) network of pores and throats. We consider the scale where individual pores enter the description and we use a network model to simulate the displacement process. We study the interplay between the pressure build up in the fluids and the displacement structure in drainage. We find that our network model properly describes the pressure buildup due to capillary and viscous forces and that there is good correspondence between the simulated evolution of the fluid pressures and earlier results from experiments and simulations in slow drainage. We investigate the burst dynamics in drainage going from low to high injection rate at various fluid viscosities. The bursts are identified as pressure drops in the pressure signal across the system. We find that the statistical distribution of pressure drops scales according to other systems exhibiting self-organized criticality. We compare our results to corresponding experiments. We also study the stabilization mechanisms of the invasion front in horizontal 2D drainage. We focus on the process when the front stabilizes due to the viscous forces in the liquids. We find that the difference in capillary pressure between two different points along the front varies almost linearly as function of length separation in the direction of the displacement. The numerical results support new arguments about the displacement process from those earlier suggested for viscous stabilization. Our arguments are based on the observation that nonwetting fluid flows in loopless strands (paths) and we conclude that earlier suggested theories are not suitable to drainage when nonwetting strands dominate the displacement process. We also show that the arguments might influence the scaling behavior of the front width as function of the injection rate and compare some of our results to experimental work.