## 1 Introduction
By analyzing how the intricate geometry of the porous space impacts flow resistance and clog formation, it becomes possible to more accurately predict permeability reduction and develop optimized strategies to mitigate clogging in geological sequestration. This geometric insight is essential for lithology selection in CO\({}_{2}\) storage technology, ensuring the long-term efficiency and stability of storage reservoirs. In this paper, we aimed to investigate the effect of the geometric structure of natural rock formations on fluid flow through pore spaces and the clogging process. We began by analyzing the geometrical characteristics of pore spaces in four types of natural rock models, examining factors such as porosity, pore size distribution, and the degree of pore voxel interconnection. We then proposed a random walk-based method to simulate the fluid flow dynamics of particles in complex pore structures, driven by pressure applied between the inlet and outlet surfaces. We proposed a probabilistic clogging model based on the particle transport algorithm, introducing two strategies: single-phase and multi-phase clogging. In single-phase clogging, porosity decreases monotonically as a function of deposition probability, whereas in multi-phase clogging, structural changes disrupt this monotonicity. High deposition probabilities lead to rapid clogging, narrowing capillaries and hindering particle transport. This method offers a valuable tool for selecting rock formations for geological sequestration. A schematic diagram representing the workflow is depicted in Figure 1:  
Theoretically, the fluid dynamics in porous materials can be modeled by different mathematical formulas, depending on the characteristics of the fluid and the porous media. For example, [PERSON]'s law governs the slow flow in a fully saturated porous medium, and [PERSON]'s equation governs the flow in a variably saturated porous medium. Traditional computational fluid dynamics (CFD) methods [16; 17], which numerically solve macroscopic properties conservation equations, are highly accurate for macroscopic systems and complex dynamics but require significant computational resources and are less intuitive for stochastic or microscopic systems. In the lattice Boltzmann method (LBM) [13; 18], instead of solving Navier-Stokes equations directly, fluid density on a lattice is simulated with flow and collision (relaxation) processes. The LBM has been used widely to simulate single- and multi-phase flow behavior within the true pore geometry of porous media [19; 20; 21; 22]. The LBM is a versatile mesoscopic approach that balances accuracy and computational cost but can struggle with extreme heterogeneity. Unlike these CFD approaches, the random walk method models transport processes as the movement of individual particles or agents. This discrete and probabilistic approach offers new possibilities for simulating complex systems with inherent stochasticity. Diffusion is naturally represented through Brownian motion within the random walk framework, providing a direct and intuitive alternative to the discretization of partial differential equations (PDEs). Moreover, the method eliminates the need for computational grids, avoiding challenges such as mesh generation and grid resolution, particularly in  
Figure 1: A schematic diagram illustrating the workflow of the particle flow simulation-based clogging model. Particle position tracking from fluid flow simulation is recorded in a passed-array, which is then used to update the rock sample in a single-phase clogging process. Further fluid flow is performed on updated rock. This process is repeated several times, generating a multi-phase clogging process. heterogeneous structures like porous rocks. In other words, the random walk method operates directly on the digital rock models without requiring manual approximations. Notably, the concept of using random walk to simulate the clogging process within pore formations was first introduced in [23].