The Origin of Non-thermal Fluctuations in Multiphase Flow in Porous Media

Abstract

Core flooding experiments to determine multiphase flow in properties of rock such as relative permeability can show significant fluctuations in terms of pressure, saturation, and electrical conductivity. That is typically not considered in the Darcy scale interpretation but treated as noise. However, in recent years, flow regimes that exhibit spatio-temporal variations in pore scale occupancy related to fluid phase pressure changes have been identified. They are associated with topological changes in the fluid configurations caused by pore-scale instabilities such as snap-off. The common understanding of Darcy-scale flow regimes is that pore-scale phenomena and their signature should have averaged out at the scale of representative elementary volumes (REV) and above. In this work, it is demonstrated that pressure fluctuations observed in centimeter-scale experiments commonly considered Darcy-scale at fractional flow conditions, where wetting and non-wetting phases are co-injected into porous rock at small (<10−6) capillary numbers are ultimately caused by pore-scale processes, but there is also a Darcy-scale fractional flow theory aspect. We compare fluctuations in fractional flow experiments conducted on samples of few centimeters size with respective experiments and in-situ micro-CT imaging at pore-scale resolution using synchrotron-based X-ray computed micro-tomography. On that basis we can establish a systematic causality from pore to Darcy scale. At the pore scale, dynamic imaging allows to directly observe the associated breakup and coalescence processes of non-wetting phase clusters, which follow “trajectories” in a “phase diagram” defined by fractional flow and capillary number and can be used to categorize flow regimes. Connected pathway flow would be represented by a fixed point, whereas processes such as ganglion dynamics follow trajectories but are still overall capillary-dominated. That suggests that the origin of the pressure fluctuations observed in centimeter-sized fractional flow experiments are capillary effects. The energy scale of the pressure fluctuations corresponds to 105-106 times the thermal energy scale. This means the fluctuations are non-thermal. At the centimeter scale, there are non-monotonic and even oscillatory solutions permissible by the fractional flow theory, which allow the fluctuations to be visible and—depending on exact conditions—significant at centimeter scale, within the viscous limit of classical (Darcy scale) fractional flow theory. That also means that the phenomenon involves both capillary aspects from the pore or cluster scale and viscous aspects of fractional flow and occurs right at the transition, where the physical description concept changes from pore to Darcy scale.