Mixing-limited reactions are central to a wide range of processes in natural and engineered porous media. Recent advances have shown that concentration gradients sustained by flow at the pore-scale influence macroscopic reaction rates over a large range of reactive transport regimes. Yet, resolving concentration gradients driven by fluid mixing at the pore-scale is challenging with current simulation methods. Here, we introduce a computational methodology to resolve concentration gradients at the pore scale in mixing-limited reactions. We consider a steady-state reactive transport problem characterized by reactive fluids flowing in parallel in a porous material. Given a mesh representation of the pore space and a steady velocity field, we solve the steady advection-diffusion equation for conservative scalar transport using a stabilized finite-element method combined with mesh refinement adapted to local scalar gradients. Based on this solution and assuming instantaneous reaction kinetics in the fluid, we infer the distribution of species involved in an irreversible bi-molecular reaction. We validate the method by comparing our results for uniform flow with analytical solutions and then apply it to simulate mixing-limited reactions in a three-dimensional random bead pack and Berea sandstone sample. Chaotic flow within the pore space leads to sustained concentration gradients, which are captured by our numerical framework. The results underscore the ability of the methodology to simulate transverse mixing and mixing-limited reactions in complex porous media and to provide bottom-up numerical data to improve the prediction of effective reaction rates at larger scales.

中文翻译：

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解析多孔介质中横向混合和反应的孔隙级浓度梯度


混合受限反应是天然和工程多孔介质中各种过程的核心。最近的进展表明，孔隙尺度流动维持的浓度梯度会影响大范围反应传递机制的宏观反应速率。然而，使用当前的仿真方法，解析由孔隙尺度的流体混合驱动的浓度梯度具有挑战性。在这里，我们介绍了一种计算方法，用于解析混合受限反应中孔隙尺度的浓度梯度。我们考虑了一个稳态反应输运问题，其特征是反应流体在多孔材料中平行流动。给定孔隙空间的网格表示和稳态速度场，我们使用稳定的有限元方法结合适应局部标量梯度的网格细化来求解保守标量传递的稳态平流-扩散方程。基于该溶液并假设流体中的瞬时反应动力学，我们推断出不可逆双分子反应中涉及的物质分布。我们通过将均匀流动的结果与分析解决方案进行比较来验证该方法，然后将其应用于模拟三维随机微珠包和 Berea 砂岩样品中的混合限制反应。孔隙空间内的混沌流动导致持续的浓度梯度，这由我们的数值框架捕获。结果强调了该方法在复杂多孔介质中模拟横向混合和混合限制反应的能力，并提供自下而上的数值数据以改进对更大规模有效反应速率的预测。