Red Noise in Steady-State Multiphase Flow in Porous Media

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 kilometers). 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 carbonate rock using differential pressure measurements acquired over a period of 60 min. Nitrogen and brine were injected simultaneously into a sample 5 mm in diameter and 21 mm in length. We observe a cascade of timescales in the pressure differential that is, a continuous range of frequencies, with lower frequencies having greater amplitudes. We demonstrate a scaling of the spectral density with frequency of S ∼ 1/f², 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. The presence of red noise suggests self-organized critically, with no characteristic time or length scale.