We present an algorithm for the pore-scale simulation of the reactive transport in a 3D case. The algorithm is designed to facilitate the observation of pore space changes caused by chemical fluid-solid interaction. Additionally, the algorithm allows estimation of the main macroscopic properties evolution of the porous material, such as permeability, hydraulic tortuosity, and formation factor. Also, we develop an algorithm to compute the persistence diagrams for the independent cycles in the pore space, which quantitatively characterizes the changes in the pore space topology. Moreover, we speed up this algorithm by using the original digital image reduction approach. Applying the clustering technique to the persistence diagrams, we show that different matrix dissolution scenarios can be distinguished based on the persistence homology. These scenarios depend on the flow rate, reaction rate, and species concentration at the inlet. At the same time, the samples from the different clusters illustrate utterly different behavior of the cross-property (porosity-permeability) relations.