## 4 Discussion of Findings  
These experiments clearly demonstrate the relationship between pressure, temperature, and hydrate formation in the context of CO\({}_{2}\) injection. When the backpressure was  
Figure 6: Observed pressures during CO\({}_{2}\) injection at 4 \({}^{\circ}\)C.  
Figure 7: Observed pressures during CO\({}_{2}\) injection at 5 \({}^{\circ}\)C.  
below the hydrate formation threshold, the core allowed smooth CO\({}_{2}\) flow without any significant pressure buildup. However, when the backpressure exceeded the required threshold, hydrates began to form, leading to a noticeable pressure difference, indicating obstruction inside the core. This finding is important for processes like CO\({}_{2}\) storage or enhanced geothermal systems, where hydrate formation could cause operational issues by blocking fluid pathways. The experimental data obtained from this study shows that, in temperatures ranging from 0 to 5 \({}^{\circ}\)C and at Darcy velocity 0.033 cm/s, CO\({}_{2}\) hydrate forms in porous media at much higher pressure than the minimum required pressure to form hydrate in static conditions. Two reasons may be the causes for the observed minimum required pressure in the dynamic condition being higher than that in the static condition. First, the formation of gas hydrates is a process of crystallization [13; 16]. The shear rate of flowing fluids should slow down the growth of hydrate crystals (Figure 8). It can be explained through the influence of fluid dynamics, particularly shear forces, on hydrate formation. Shear rate, defined as the velocity gradient within a flowing fluid, is influenced by factors like flow velocity, fluid viscosity, and the geometry of the flow path [13]. Under static conditions, without significant disturbance, hydrate crystals can nucleate and grow as gas molecules become encapsulated by water [20]. But in dynamic conditions when the injected gas is flowing through the system, higher shear rates are introduced, which causes turbulence and mechanical forces that disrupt the initial nucleation of hydrate crystals, preventing water and gas molecules from aligning into stable structures, thereby reducing the rate of hydrate formation. Additionally, higher shear rates can break down hydrate crystals and prevent their agglomeration into larger structures, further slowing hydrate growth. Enhanced mixing due to shear forces also reduces local supersaturation, a condition necessary for hydrate growth, thereby inhibiting the formation of large crystals [14; 15]. This theory is supported by natural gas production operations where maintaining a high shear rate in flowing fluids--through increased flow velocity or turbulence--can help manage the risk of hydrate formation in pipelines, thus minimizing blockages and ensuring smoother gas flows [14]. If the hydrate formation process starts from film development [15], the shear rate should tend to break the film and slow down the process (Figure 8). It can be understood scientifically by analyzing the mechanics of hydrate formation in pore channels. Hydrate formation often begins with the development of a hydrate film at the gas-water interface, which acts as a nucleation site for hydrate crystals. This film is a critical step in the growth process, potentially leading to larger, more stable hydrate structures. However, higher shear rates in the flowing fluid introduce turbulence and mechanical forces that disrupt this film by breaking it apart, preventing the film from growing into larger crystals [15]. The continuous motion of fluid layers creates shear forces that tear the thin hydrate film, interrupting the nucleation process and making it more difficult for hydrate crystals to form. Additionally, higher shear rates promote surface renewal, ensuring fresh water and gas are introduced into the system, preventing the concentration of gas and water necessary for sustained hydrate growth. Increased mixing from shear forces also reduces local supersaturation levels, further inhibiting hydrate formation.