## 6 Conclusions and Future Perspective  
The time domain random walk method is applied to describe the movement of particles within complex, highly disordered, and heterogeneous pore spaces of porous rock formations under the pressure gradient imposed between the inlet and the outlet surfaces. The scheme is explicit and can be easily upscaled for large volumes of porous media samples. Based on numerical simulations, we investigated the particle fluid flow dynamics in four different types of natural porous rocks: Bentheimer, Doddington, Estaillades, and Ketton. The particle fluid flow dynamics were strongly affected by the geometric structure of the rocks. Ketton had the highest permeability among the four samples, despite having the lowest porosity. Based on the particle transport algorithm, we propose a probabilistic clogging model in two strategies: single- and multi-phase clogging. In the former strategy, the porosity decrease can be approximated as a monotonically non-increasing function of the deposition probability in the form of exponential functions. This monotonicity is no longer valid in the latter strategy, because the geometric structure changes at every phase. When some large probability of deposition is chosen, the fast clogging narrows the capillaries, preventing the particles from invading easily in the injection direction. Our simulation results suggest that Bentheimer, Doddington, and Ketton could potentially be used as rock formations for carbon dioxide storage, while Estaillades could not. The method proposed in this study could be useful in lithology selection for geological sequestration. The simulation study revealed that the velocity \(v\) and deposition probability \(q\) are critical parameters that characterize the efficiency of the clogging process. While \(v\) models the pressure gradient imposed between the inlet and the outlet surface, \(q\) models the speed of chemical reactions between CO\({}_{2}\) and alkaline earth metals. Fine-tuning these factors helps increase the efficiency of geological sequestration technology, and the optimal values can be obtained from the simulation studies. Once the target lithology has been chosen, the next step is to elucidate these formations' trapping mechanisms. [PERSON] et al. [39] utilized the kinetic Monte Carlo method to model the carbonation front development in calcium-silicate-hydrate microstructures under varying temperatures and then combine the simulation data with experimental results from Fourier-transform infrared spectroscopy (FTIR) and impedance spectroscopy, so as to provide insights into the carbonation process at different depths and temperatures. Learning from [PERSON] et al. 's idea, in our future work we will incorporate the kinetic barrier of the chemical processes during the mineralized process, to define the rate constant; that is, the state-to-state transition rates in the RW algorithm through Arrhenius formulas. The simulation results will then be combined with atomic simulation and experimental data to help understand the complicated trapping mechanisms in the chosen lithology. Another important issue that needs to be addressed is the modeling of fracture systems. It is critical to access the risk of injected CO\({}_{2}\) leakage due to natural fault or fractures as well as the presence of abandoned oil/gas wells. This problem involves both fluid flow through aquifers and intensive fluid flow through fractures simultaneously. A hybrid approach incorporating the random walk model with a continuum has the potential to solving this challenging problem. For more details about the importance and challenges of this issue, as well as current numerical methods to solve these systems, we refer the interested reader to [40; 41]. **Author Contributions:** Conceptualization, T.S. and T.T. ; methodology, L.T.H.N. and T.S. ; software, L.T.H.N. ; validation, L.T.H.N., T.S. and T.T. ; resources, T.T. ; original draft preparation, L.T.H.N. ; writing, review, and editing, L.T.H.N., T.S. and T.T. ; visualization, L.T.H.N. ; supervision, T.S.