A quantitative study of single-phase transient flow states in a permeable medium using a microfluidic device

Velocity fields in flow in permeable media are of great importance in many subsurface processes such as geologic storage of CO2, oil and gas extraction, and geothermal systems. Steady-state flow is characterized by velocity fields that do not change significantly over time. Flow fields transition to a new steady state due to a perturbation at the inlet such as a change in the flow rate or the pressure gradient. In the macroscale conservation of momentum, namely Darcys law, this transition is assumed to be instantaneous. In the multiphase extension of Darcys law, this assumption justifies expressing constitutive relations as functions of instantaneous phase saturations. In this work, we examine the evolution of velocity fields in a permeable medium using a microfluidic device and a high-speed camera. Microspheres with diameters of one micrometer are used as tracer particles and they are injected in the medium along with DI water. The evolution of the velocity field is examined by tracing these particles in the captured images using a Fluorescent Particle Image Velocimetry (FPIV) framework. The results suggest that the transition period between steady-states for water takes a finite and non-negligible amount of time. Finally, we examine the impact of the magnitude of the change in the pressure gradient on this transition period. The findings support the need for a non-local formulation for the multiphase extension of Darcy's law that honors its validity in steady or near-steady flows and captures the physics of the mixing zone and flow instabilities faithfully.