## 1 Introduction  
Carbon capture, utilization, and storage (CCUS) is a process where a relatively pure stream of carbon dioxide from large point sources, such as fossil fuel power plants or industrial facilities (cement, iron, steel, etc.) is separated, treated, and transported to a long-term storage location. Geological carbon dioxide sequestration is considered a promising technology in CCUS for reducing carbon emissions into the atmosphere by injecting it into natural geological formations, such as saline aquifers, oil and gas reservoirs, and deep coal beds, and storing it permanently and safely there. To achieve carbon neutral, furthermore, we should also consider the negative emission scheme that captures CO\({}_{2}\) directly from the atmosphere and stores it in a geological formation. The security and the efficiency of CO\({}_{2}\) storage are ensured by several trapping mechanisms [1], including structural and stratigraphic trapping geological storage [2], capillary trapping [3], solubility (dissolution) trapping [4], and mineral precipitation (chemical reaction) [5; 6]. The mechanisms of geological sequestration depend on the interplay between the geomechanical, thermal, hydraulic, and geochemical processes occurring as injected CO\({}_{2}\) migrates dissolve in formation fluid and react with formation bedrock. This is strongly influenced by several different factors, such as the injection fluid flow (e.g., injection rates, fluid topological characteristics), fluid properties (e.g., wetting or non-wetting, fluid-fluid interfacial tension [7]), the characteristics of porous material (e.g., pore morphology [8]), and wettability [9]. Even though advanced imaging technologies have been able to provide detailed information on fluid distributions in pore spaces in experiments [10; 11; 12], this process is time-consuming, costly, and effort-expensive. This is where mathematical modeling shines. Effective mathematical models can simulate a broad range of reservoir-relevant conditions within an acceptable period with the aid of the rapid improvement in computational resources [6; 13; 14; 15]. In digital rock modeling, a clogging model is a computational approach used to study how fluid flow through porous rock formations becomes obstructed over time, due to the accumulation of particles, minerals, sediments, or other materials. This process is particularly relevant to applications such as geological sequestration, petroleum engineering, hydrogeology, and filtration systems. Clogging occurs when particles suspended in the fluid accumulate within the pore spaces, reducing permeability and impeding fluid flow. The clogging process involves two key components: _particle transport_ and _deposition mechanisms_. Particle transport refers to the movement of particles within the fluid as they navigate through the pore spaces, while deposition mechanisms model how particles become trapped, stick to pore walls, or aggregate within pores. Common deposition mechanisms include mechanical trapping, surface adhesion, and bridging (where large particles span pores). By simulating clogging behavior, the model helps predict how porous formations evolve over time under fluid flow, allowing for improved reservoir management and a deeper understanding of long-term permeability changes in natural porous media. Investigating the influence of the geometric structure of porous space is crucial for understanding fluid flow and clogging dynamics in digital rock models. The shape, size, and connectivity of the pores directly dictate how fluids move through the material, affecting both permeability and the likelihood of clogging. Complex pore geometries, characterized by varying pore throat sizes and irregular structures, create heterogeneous flow patterns, leading to regions of high or low flow velocity. These variations can significantly influence particle deposition and aggregation, which are primary drivers of clogging.