Replacement reactions during fluid infiltration into porous media, rocks and buildings are known to have important implications for reservoir development, ore formation as well as weathering. Natural observations and experiments have shown that in such systems the shape of reaction fronts can vary significantly ranging from smooth, rough to highly irregular. It remains unclear what process-related knowledge can be derived from these reaction front patterns. In this contribution we show a numerical approach to test the effect of relative rates of advection, diffusion, and reaction on the development of reaction fronts patterns in granular aggregates with permeable grain boundaries. The numerical model takes (i) fluid infiltration along permeable grain boundaries, (ii) reactions and (iii) elemental diffusion into account. We monitor the change in element concentration within the fluid, while reactions occur at a pre-defined rate as a function of the local fluid concentration. In non-dimensional phase space using Péclet and Damköhler numbers, results show that there are no rough fronts without advection (Péclet<70) nor if the reaction is too fast (Damköhler>10⁻³). As advection becomes more dominant and reaction slower, roughness develops across several grains with a full microstructure mimicking replacement in the most extreme cases. The reaction front patterns show an increase in roughness with increasing Péclet number from Péclet 10 to 100 but then a decrease in roughness towards higher Péclet numbers controlled by the Damköhler number. Our results indicate that reaction rates are crucial for pattern formation and that the shape of reaction fronts is only partly due to the underlying transport mechanism.

众所周知，流体渗入多孔介质，岩石和建筑物期间的置换反应对储层发育，成矿以及风化具有重要意义。自然观察和实验表明，在这样的系统中，反应前沿的形状可以从光滑，粗糙到高度不规则变化很大。尚不清楚可以从这些反应前沿模式中获得哪些与过程有关的知识。在这一贡献中，我们展示了一种数值方法来测试平流，扩散和反应的相对速率对具有可渗透晶粒边界的粒状聚集体中反应前沿模式发展的影响。数值模型考虑了（i）沿可渗透晶粒边界的流体渗透，（ii）反应和（iii）元素扩散。我们监测流体中元素浓度的变化，同时以预定的速率发生反应，这是局部流体浓度的函数。结果表明，在使用Péclet和Damköhler数的无量纲相空间中，没有平流（Péclet<70）或反应太快（Damköhler> 10）都不会出现粗糙的前沿。^-3）。随着平流变得越来越占优势，反应变慢，在最极端的情况下，整个晶粒上都出现了粗糙度，并具有完整的微观结构，模拟了置换现象。反应前沿模式显示出粗糙度随Péclet数从Péclet10增加到100而增加，但随后随着由Damköhler数控制的较高Péclet数而降低。我们的结果表明，反应速率对于图案的形成至关重要，反应前沿的形状仅部分归因于潜在的传输机制。