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A major challenge in modeling reactive transport in shales is the multiscale nature of the fractured rock system. Shales may contain a few main fractures and thousands of microcracks whose length and aperture are orders of magnitude smaller than the former. This renders fully resolved simulations too expensive, while traditional upscaling methods cannot accurately capture fracture clogging dynamics due to precipitation. We develop a fully coupled patch-based multiscale algorithm to address this issue: We solve reactive transport only in a few selected microcracks, while evaluating the others by interpolation and ensuring top-down bottom-up coupling between the main fracture and the microcracks. Specifically, we consider a fracture system with an array of hundreds of microcracks connected to a main fracture. The patch-based multiscale algorithm is validated against fully resolved pore-scale simulations and a steady-state analytical solution. We find the reaction rate can have a great impact on the concentration profiles after breakthrough, even if the profiles before breakthrough are similar. Also, the breakthrough curves exhibit three dynamic regimes when microcrack aperture alterations are accounted for.