The presence of solute concentration fluctuations at spatial scales much below the scale of resolution is a major challenge for modeling reactive transport in porous media. Overlooking small‐scale fluctuations, which is the usual procedure, often results in strong disagreements between field observations and model predictions, including, but not limited to, the overestimation of effective reaction rates. Existing innovative approaches that account for local reactant segregation do not provide a general mathematical formulation for the generation, transport, and decay of these fluctuations and their impact on chemical reactions. We propose a Lagrangian formulation based on the random motion of fluid particles carrying solute concentrations whose departure from the local mean is relaxed through multirate interaction by exchange with the mean (MRIEM). We derive and analyze the macroscopic descriptionof the local concentration covariance that emerges from the model, showing its potential to simulate the dynamics of mixing‐limited processes. The action of hydrodynamic dispersion on coarse‐scale concentration gradients is responsible for the production of local concentration covariance, whereas covariance destruction stems from the local mixing process represented by the MRIEM formulation. The temporal evolution of integrated mixing metrics in two simple scenarios shows the trends that characterize fully resolved physical systems, such as a late‐time power law decay of the relative importance of incomplete mixing with respect to the total mixing. Experimental observations of mixing‐limited reactive transport are successfully reproduced by the model.

中文翻译：

---

多孔介质中混合限制反应输运的拉格朗日模型：交换与均值的多速率相互作用

在远低于分辨率尺度的空间尺度上，溶质浓度波动的存在是对多孔介质中反应性输运进行建模的主要挑战。忽略小规模波动（通常的做法）通常会导致现场观察与模型预测之间存在强烈分歧，包括但不限于有效反应速率的高估。现有的解决本地反应物偏析的创新方法并未为这些波动的产生，运输和衰减及其对化学反应的影响提供一般的数学公式。我们基于携带溶质浓度的流体粒子的随机运动，提出了一种拉格朗日公式，该流体粒子通过与均值（MRIEM）交换通过多速率相互作用而放松了与局部均值的偏离。我们导出并分析了模型中出现的局部浓度协方差的宏观描述，显示了其模拟混合受限过程动力学的潜力。流体动力扩散对粗浓度梯度的作用是产生局部浓度协方差的原因，而协方差破坏源于以MRIEM公式表示的局部混合过程。在两个简单的场景中，综合混合指标的时间演变显示出表征完全分解的物理系统的趋势，例如，相对于总混合而言，不完全混合的相对重要性的后期幂定律衰减。该模型成功地再现了混合受限反应性运输的实验观察结果。