We investigate chemical transport in laboratory rock cores using unidirectional pulse tracer experiments. Breakthrough curves (BTCs) measured at various flow rates in one sandstone and two carbonate samples are interpreted using the one‐dimensional Continuous Time Random Walk (CTRW) formulation with a truncated power law (TPL) model. Within the same framework, we evaluate additional memory functions to consider the Advection‐Dispersion Equation (ADE) and its extension to describe mass exchange between mobile and immobile solute phases (Single‐Rate Mass Transfer model, SRMT). To provide physical constraints to the models, parameters are identified that do not depend on the flow rate. While the ADE fails systematically at describing the effluent profiles for the carbonates, the SRMT and TPL formulations provide excellent fits to the measurements. They both yield a linear correlation between the dispersion coefficient and the Péclet number (D_L ∝ Pe for ), and the longitudinal dispersivity is found to be significantly larger than the equivalent grain diameter, D_e. The BTCs of the carbonate rocks show clear signs of nonequilibrium effects. While the SRMT model explicitly accounts for the presence of microporous regions (up to 30% of the total pore space), in the TPL formulation the time scales of both advective and diffusive processes (t₁(Pe) and t₂) are associated with two characteristic heterogeneity length scales ( and l, respectively). We observed that l ≈ 2.5 × D_e and that anomalous transport arises when . In this context, the SRMT and TPL formulations provide consistent, yet complementary, insight into the nature of anomalous transport in laboratory rock cores.

中文翻译：

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使用连续随机游走形式主义描述实验室岩心中的化学传递

我们使用单向脉冲示踪剂实验研究实验室岩心中的化学传输。使用一维连续时间随机游走（CTRW）公式和截断幂定律（TPL）模型，可以解释在一个砂岩和两个碳酸盐样品中以不同流速测量的穿透曲线（BTC）。在同一框架内，我们评估其他记忆功能以考虑对流扩散方程（ADE）及其扩展，以描述流动和固定溶质相之间的质量交换（单速率传质模型，SRMT）。为了给模型提供物理约束，要确定不依赖于流速的参数。尽管ADE未能系统性地描述碳酸盐的流出曲线，但SRMT和TPL配方非常适合进行测量。D _L  ∝ Pe for），并且发现纵向分散度明显大于等效晶粒直径D _e。碳酸盐岩的BTC表现出明显的非平衡效应迹象。尽管SRMT模型明确说明存在微孔区域（最多占总孔隙空间的30％），但在TPL配方中，对流和扩散过程的时间尺度（ t ₁（Pe）和t ₂）与两个特征异质长度尺度（ 和升，分别地）。我们观察到，升 ≈2.5×  d _È并且当发生异常运输时。在这种情况下，SRMT和TPL配方对实验室岩心中异常输送的性质提供了一致但互补的见解。