Modeling the velocity field during Haines jumps in porous media

When nonwetting fluid displaces wetting fluid in a porous rock many rapid pore-scale displacement events occur. These events are often referred to as Haines jumps and any drainage process in porous media is an ensemble of such events. However, the relevance of Haines jumps for larger scale models is often questioned. A common counter argument is that the high fluid velocities caused by a Haines jump would average-out when a bulk representative volume is considered. In this work, we examine this counter argument in detail and investigate the transient dynamics that occur during a Haines jump. In order to obtain fluid-fluid displacement data in a porous geometry, we use a micromodel system equipped with a high speed camera and couple the results to a pore-scale modeling tool called the Direct HydroDynamic (DHD) simulator. We measure the duration of a Haines jump and the distance over which fluid velocities are influenced because this sets characteristic time and length scales for fluid-fluid displacement. The simulation results are validated against experimental data and then used to explore the influence of interfacial tension and nonwetting phase viscosity on the speed of a Haines jump. We find that the speed decreases with increasing nonwetting phase viscosity or decreasing interfacial tension; however, for the same capillary number the reduction in speed can differ by an order of magnitude or more depending on whether viscosity is increased or interfacial tension is reduced. Therefore, the results suggest that capillary number alone cannot explain pore-scale displacement. One reason for this is that the interfacial and viscous forces associated with fluid-fluid displacement act over different length scales, which are not accounted for in the pore-scale definition of capillary number. We also find by analyzing different pore morphologies that the characteristic time scale of a Haines jump is dependent on the spatial configuration of fluid prior to an event. Simulation results are then used to measure the velocity field surrounding a Haines jump and thus, measure the zone of influence, which extends over a distance greater than a single pore. Overall, we find that the time and length scales of a Haines jump are inversely proportional, which is important to consider when calculating the spatial and temporal averages of pore-scale parameters during fluid-fluid displacement.