## 1 Introduction
However, this approach was previously implemented in a free, two-dimensional environment. To our knowledge, no comprehensive study of real three-dimensional natural porous rocks has been explored yet. Like LBM, our random walk approach also effectively simulates the fluid flow within a real pore medium, thanks to its three advantages: all calculations are local, there is no need for complicated procedures for interface tracking, and the scheme is explicit. The main difference between our approach and the approach using LBM in [13] is that in the mentioned work the LBM is used to simulate the displacement of a wetting liquid fluid, e.g., H\({}_{2}\)O, by a non-wetting liquid fluid, e.g., CO\({}_{2}\). In our random walk approach, we cannot consider pressure information on fluid flow calculation directly. Therefore, we cannot evaluate fluid displacement characteristics that are available in the LBM approach [24]. On the other hand, the random walk approach allowed us to easily model the clogging process (i.e., mineralization modeling) and use larger digital rock models, due to fewer computations compared to LBM. We simulated the particle fluid flow in the porous space of different types of rock formations, to choose the most geometrically favorable porous formation among the candidates for geological storage. We performed the simulations on three-dimensional natural porous rock samples (of \(1000\times 1000\times 1000\) voxels), which were 15 times larger than those in [13] (\(320\times 320\times 640\)), in the sense of the number of grid points. Based on the particle transport results, we developed a stochastic clogging model to capture the probabilistic nature of the particle deposition and accumulation. The likelihood of a void voxel becoming clogged during fluid transport depends on the number of times that the void voxel has been visited by particles and on a predefined parameter known as the _deposition probability_. As the clogging process advances, fewer pathways remain open for fluid flow, leading to a gradual change in the geometric structure of the pore space. This, in turn, results in a progressive reduction in both the formation's overall permeability and the efficiency of the fluid injection. The impact of deposition probability on clogging processes is quantified by modeling the decrease in porosity as a function of deposition probability, using the curve-fitting method. The coefficient of the fitted curves for different rock types highlights the potential of certain rocks for carbon storage, particularly from a geometric standpoint. The outline of the paper is as follows. Section 2 describes the four digital rock models used in this study and introduces a graph-based representation approach to analyze the important geometrical properties of pore spaces--including porosity, degree of pore voxels, and connectivity--that are critical for transport in porous media. In Section 3, we present the random walk rule for simulating particle movement within the pore spaces of rock formations under the pressure gradient imposed between the inlet and outlet surfaces. Section 4 introduces our proposed stochastic clogging (pore-filling) model, which simulates particle accumulation in pore spaces over time. Section 5 presents the numerical results and interpretation for the particle transport (Section 5.1) and clogging models (Section 5.2). The paper concludes with our conclusions and future perspective in Section 6. The simulations in this work were implemented in Python with the aid of several third-party libraries, such as Numpy [25], Scipy [26], Matplotlib [27], and Porespy [28].