Red noise in steady-state multiphase flow

Understanding the interaction between competing fluids in the pore space of rocks is key for predicting subsurface flow and trapping, such as with CO2 in a saline aquifer. These processes occur over a large span of timescales (from seconds to thousands of years), and length scales (from microns to kilometres). Understanding the link between these temporal and spatial scales will enable us to interpolate between observations made at different resolutions. In this work we explore the temporal scales present during macroscopically steady-state multiphase flow in a porous rock using differential pressure measurements. We observe a cascade of timescales in the pressure differential i.e. a continuous range of frequencies, with lower frequencies having greater amplitudes. We demonstrate a scaling of the spectral density with frequency of S ∼ 1/f^2, or red noise, to describe the dynamics. This scaling is independent of the flow rate of the fluids or the fraction of the flow taken by water. This red, or Brownian, noise indicates a stochastic process where pressure fluctuations are seen throughout the pore space, resulting in intermittent filling of pores over a wide range of time-scales, from seconds to minutes in these experiments. This observation will aid future modelling of subsurface flow as it suggests self-organised critically of the system with no characteristic time or length scale.