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Predicting the geometrical evolution of the pore space in geological formations due to fluid-solid interactions has applications in reservoir engineering, oil recovery, and geological storage of carbon dioxide. However, modeling frameworks that combine fluid flow with physical and chemical processes at a rock's pore scale are scarce. Here, we report a method for modeling a rock's pore space as a network of connected capillaries and to simulate the capillary diameter modifications caused by reactive flow processes. Specifically, we model mineral erosion, deposition, dissolution, and precipitation processes by solving the transport equations iteratively, computing diameter changes within each capillary of the network simultaneously. Our automated modeling framework enables simulations on digital rock samples as large as (1.125mm)$^3$ with 125$\times 10^6$ voxels within seconds of CPU time per iteration. As an application of the computational method, we have simulated brine injection and calcium carbonate precipitation in sandstone. For quantitatively comparing simulation results obtained with models predicting either a constant or a flow-rate dependent precipitation, we track the time-dependent capillary diameter distribution as well as the permeability of the connected pore space. For validation and reuse, we have made the automated simulation workflow, the reactive flow model library, and the digital rock samples available in public repositories.