Predicting the spatiotemporal evolution of the pore space of subsurface rock formations under fluid-solid interactions has applications in reservoir engineering, oil recovery, and carbon dioxide geological sequestration. The geometry of the reservoir porous space may evolve in time depending on several factors, including geometry characteristics, phasic properties, flow conditions, and underlying coupled pore-scale processes. Common methods to track these geometrical changes comprise transport-reaction simulations that combine fluid transport results with chemical and physical processes at the pore scale. These numerical methods are often limited to small domains and single reactions as they become impractical and computationally costly for complex spatial domains and multiscale phenomena. To overcome these limitations, in this work, we model the rock pore space geometry, extracted from high-resolution X-ray microtomography images of suitable rocks, as a network of connected capillaries, a sparse graph representation with significantly reduced degrees-of-freedom with respect to its mesh- or lattice-based counterparts, and assume laminar piston-like flow within each capillary and conservation of mass at each network node. This allows to track the geometry evolution of porous media due to simultaneous pore-scale processes (i.e., erosion, mineral dissolution, and mineral precipitation) by solving the transport equations iteratively to extract pressure and flow rate fields at each point in the network and then computing the volume accumulation or loss within each capillary. Computation of the change in capillary diameter employs phenomenological correlations for those physical and chemical processes at each temporal iteration, adjusting for the distinct time scales of each phenomenon.