Enhanced oil recovery in reservoirs via diffusion-driven $\text{CO}_{2}$ flooding: Experimental insights and material balance modeling

$\text{CO}_{2}$ flooding is central to carbon utilization technologies, yet conventional waterflooding models fail to capture the complex interactions between CO$_2$ and formation fluids. In this study, one- and two-dimensional nuclear magnetic resonance experiments reveal that $\text{CO}_{2}$ markedly enhances crude oil mobility during miscible displacement via multiple synergistic mechanisms, yielding a recovery factor of $60.97\%$, which surpasses that of immiscible displacement (maximum $57.53\%$). Guided by these findings, we propose a convection-diffusion model that incorporates the diffusion coefficient ($D$) and porosity ($φ$) as key parameters. This model captures the spatiotemporal evolution of the $\text{CO}_{2}$ front and addresses a key limitation of conventional formulations-the omission of diffusion effects. It improves predictions of gas breakthrough time and enables optimized injection design for low-permeability reservoirs. Extending classical material balance theory, we develop an enhanced $\text{CO}_{2}$ flooding equation that integrates critical transport phenomena. This formulation incorporates $\text{CO}_{2}$ diffusion, oil phase expansion, reservoir adsorption, and gas compressibility to describe the dynamic transport and mass compensation of injected $\text{CO}_{2}$. Validation through experimental and numerical data confirms the model's robustness and applicability under low-permeability conditions. The proposed framework overcomes limitations of physical experiments under extreme environments and offers theoretical insight into oil recovery enhancement and $\text{CO}_{2}$ injection strategy optimization.