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.

中文翻译：

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多孔介质稳态多相流中的红噪声

了解岩石孔隙空间中竞争流体之间的相互作用是预测地下流动和捕集的关键，例如与 CO _{2的相互作用}在盐水含水层中。这些过程发生在很长的时间尺度（从几秒到几千年）和长度尺度（从微米到公里）上。了解这些时间和空间尺度之间的联系将使我们能够在不同分辨率的观察之间进行插值。在这项工作中，我们使用在 60 分钟内获得的压差测量来探索多孔碳酸盐岩中宏观稳态多相流期间存在的时间尺度。将氮气和盐水同时注入直径为 5 毫米、长度为 21 毫米的样品中。我们观察到压差中的一系列时间尺度，即连续的频率范围，较低的频率具有较大的幅度。我们证明了频谱密度随频率的缩放S ∼ 1/ f ²或红噪声，用于描述动力学。这种缩放与流体的流速或水流所占的比例无关。这种红色或布朗噪声表明一个随机过程，其中在整个孔隙空间中都可以看到压力波动，导致在这些实验中从几秒钟到几分钟的广泛时间范围内间歇性地填充孔隙。红噪声的存在表明自组织的批判性，没有特征的时间或长度尺度。