Fluid-solid reactions play a key role in a large range of biogeochemical processes. Transport limitations at the pore scale limit the amount of solute available for reaction, so that reaction rates measured under well-mixed conditions tend to strongly overestimate rates occurring in natural and engineered systems. Although different models have been proposed to capture this phenomenon, linking pore-scale structure, flow heterogeneity, and local reaction kinetics to upscaled effective kinetics remains a challenging problem. We present a new theoretical framework to quantify these dynamics based on the chemical continuous time random walk framework. We study a fluid–solid reaction with the fluid phase undergoing advective–diffusive transport. We consider a catalytic degradation reaction, $A_F+B_S\to B_S$, where $A_F$ is in fluid phase and $B_S$ is in solid phase and homogeneous over the fluid–solid interface, allowing us to focus on the role of transport limitations and medium structure. Our approach is based on the concept of inter-reaction times, which result from the times between contacts of transported reactants with the solid phase. We use this formulation to quantify the global kinetics of fluid-reactant mass and test our predictions against numerical simulations of advective–diffusive transport in stratified channel flow and Stokes flow through a beadpack. The theory captures the decrease of effective reaction rates compared to the well-mixed prediction with increasing Damköhler number due to transport limitations. Although we consider simple kinetics and media, these findings will contribute to the understanding and modeling of the effect of transport limitations in more complex reactive transport problems.

流固反应在大范围的生物地球化学过程中起着关键作用。孔隙尺度的传输限制限制了可用于反应的溶质量，因此在充分混合条件下测量的反应速率往往会严重高估自然和工程系统中发生的速率。尽管已经提出了不同的模型来捕捉这种现象，但将孔隙尺度结构、流动异质性和局部反应动力学与放大的有效动力学联系起来仍然是一个具有挑战性的问题。我们提出了一个新的理论框架来量化基于化学连续时间随机游走框架的这些动力学。我们研究了流体相发生对流扩散传输的流固反应。我们考虑催化降解反应，${\mathrm{一种}}_F+{乙}_{秒}\to {乙}_{秒}$， 在哪里 ${\mathrm{一种}}_F$ 处于液相并且 ${乙}_{秒}$处于固相且在流固界面上均质，使我们能够专注于传输限制和介质结构的作用。我们的方法基于相互反应时间的概念，这是由传输的反应物与固相接触之间的时间产生的。我们使用这个公式来量化流体反应物质量的全局动力学，并根据分层通道流和 Stokes 流中的对流扩散传输的数值模拟测试我们的预测。由于传输限制，随着 Damköhler 数的增加，与混合良好的预测相比，该理论捕获了有效反应速率的降低。虽然我们考虑简单的动力学和介质，