Using Homogenized Models to Explore the Effect of Fracture Densities on Weathering

Abstract

Despite its importance, only a few researchers have incorporated the effects of fracturing into models of reactive transport for rock weathering. Here we explore 2D simulations that describe weathering under conditions of diffusive and advective transport within heterogeneous media consisting of rocky blocks and fractures. In our simulations, the Darcy velocities vary in space and time and depend on weathering processes within the rock matrix. We explore simulations with saturated and unsaturated flow for weathering bedrock that consists of blocks separated by inert or weathered material. The simulations show that a simplified homogenized model can approximate exact solutions for some of the simulated columns and hills and can allow exploration of coupling between flow and reaction in fractured rock. These hillslope simulations document that, even in the presence of 2D water flow, i) an increase in fracture density results in faster weathering advance rates; and ii) the water table locates deeper for a rock system that is weathered and fractured rather than weathered and unfractured. Some of these patterns have also been observed for natural systems. But these simulations also highlight how simplified models that do not use appropriate averaging of heterogeneities can be inaccurate in predicting weathering rate for natural systems. For example, if water flows both vertically and laterally through the vadose zone of a hill, then a prediction of the depth of regolith that is based on modeling strictly unidirectional downward infiltration will be unrealistically large. Likewise, if the fracture density observed near the land surface is used in a model to predict depth of weathering for a system where the fracture density decreases downward, the model will overestimate regolith depth. Learning how to develop accurately homogenized models could thus enable better conceptual models and predictions of weathering advance in natural systems.