4D microvelocimetry reveals multiphase flow field perturbations in porous media

Abstract

Many environmental and industrial processes depend on how fluids displace each other in porous materials. However, the flow dynamics that govern this process are still poorly understood, hampered by the lack of methods to measure flows in optically opaque, microscopic geometries. We introduce a 4D microvelocimetry method based on high-resolution X-ray computed tomography with fast imaging rates (up to 4 Hz). We use this to measure flow fields during unsteady-state drainage, injecting a viscous fluid into rock and filter samples. This provides experimental insight into the nonequilibrium energy dynamics of this process. We show that fluid displacements convert surface energy into kinetic energy. The latter corresponds to velocity perturbations in the pore-scale flow field behind the invading fluid front, reaching local velocities more than 40 times faster than the constant pump rate. The characteristic length scale of these perturbations exceeds the characteristic pore size by more than an order of magnitude. These flow field observations suggest that nonlocal dynamic effects may be long-ranged even at low capillary numbers, impacting the local viscous-capillary force balance and the representative elementary volume. Furthermore, the velocity perturbations can enhance unsaturated dispersive mixing and colloid transport and yet, are not accounted for in current models. Overall, this work shows that 4D X-ray velocimetry opens the way to solve long-standing fundamental questions regarding flow and transport in porous materials, underlying models of, e.g., groundwater pollution remediation and subsurface storage of CO₂ and hydrogen.

Keywords: 3D velocimetry; hydrogeology; multiphase flow; porous media.

Fig. 1.

The anatomy of a Haines jump in the porous filter sample; shown in (A) by rendering the fluid–fluid menisci. The Inset on the left highlights the fast-moving advancing fluid meniscus at five different time points. The local flow rate exceeds the external flow rate and therefore draws fluid in from the surrounding pores. This results in retracting fluid menisci highlighted for the same time points on the right. (B) The Haines jump is associated with a drop in the mean curvature of the fluid–fluid menisci, which has a one-to-one relation with the pressure difference between the fluids. The time points indicated here correspond to those in panel A. (C) The rate of internal oil redistribution during the Haines jump at time zero is higher than the net invasion rate supplied by the pump.

Fig. 2.

Particle tracking of flow tracers in the nonwetting phase (oil) during the drainage experiment on the filter sample. (A) shows that the flow velocity field peaks at the moment right after the Haines jump depicted in Fig. 1 (indicated with the arrow at time step 2 here). (B) 3D renderings at five selected time steps show that this acceleration takes place throughout nearly the entire oil cluster in the sample. After the Haines jump, internal fluid redistribution is performed through remarkably tortuous flow paths which include flow reversal in part of the sample (upward oriented flow paths indicated on rendering 4). A corresponding video can be found in SI Appendix (Movie S1, accessible via Figshare: https://figshare.com/s/9b7ee99333c20c83ca01).

Fig. 3.

The energy dynamics of a Haines jump in the porous filter sample. (A) The cumulative pressure–volume work, the kinetic energy, and the surface energy determined from the 3D images for the fluid displacement in Fig. 1. The blue shaded area shows the uncertainty on the surface energy when varying the contact angle by ±10°, between 25° and 45°. (B) The rate-of-change of the energy contributions, where time zero (by definition) marks the start of the Haines jump.

Fig. 4.

The Haines jump at time zero is the source of a fluctuation in the velocity field, which propagates through the sample. (A) Schematic of the fluctuation propagation. (B) Mean local velocity over time for tracer detections at different straight-line distances from the Haines jump location (x), the latter expressed in relation to the sample’s mean pore size (d_pore). The velocity peak shifts in time for increasing distance, related to the finite propagation speed of the fluctuation. (C) The local maximum velocity (velocity peaks in B) decays in function of the distance to the Haines jump due to viscous dissipation, with a characteristic decay length λ of 14.7 times the characteristic pore size.