The current study concerns fundamental controls on fluid flow in tight carbonate rocks undergoing CO2 injection. Tight carbonates exposed to weak carbonic acid exhibit order of magnitude changes in permeability while maintaining a nearly constant porosity with respect to the porosity of the unreacted sample. This study aims to determine—if not porosity—what are the microstructural changes that control permeability evolution in these rocks? Given the pore‐scale nature of chemical reactions, we took a digital rock physics approach. Tight carbonate mudstone was imaged using X‐ray microcomputed tomography. We simulated calcite dissolution using a phenomenological numerical model that stands from experimental and microstructural observations under transport‐limited reaction conditions. Fluid flow was simulated using the lattice‐Boltzmann method, and the pore wall was adaptively eroded at a rate determined by the local surface area and velocity magnitude, which we use in place of solvent flux. We identified preexisting, high‐conductivity fluid pathways imprinted in the initial microstructure. Though these pathways comprise a subset of the total connected porosity, they accommodated 80 to 99% of the volumetric flux through the digital sample and localized dissolution. Porosity‐permeability evolution exhibited two stages: selective widening of narrow pore throats that comprised preferential pathways and development and widening of channels. We quantitatively monitored attributes of the pore geometry, namely, porosity, specific surface area, tortuosity, and average hydraulic diameter, which we qualitatively linked to permeability. This study gives a pore‐scale perspective on the microstructural origins of laboratory permeability‐porosity trends of tight carbonates undergoing transport‐limited reaction with CO2‐rich fluid.