Dimensional Analysis of CO₂ Injection in Shale Oil Reservoirs

Carbon dioxide (CO₂) injection effectively enhances oil recovery from shale reservoirs while potentially storing CO₂. Several operational and reservoir parameters impact the oil recovery factor and CO₂ storage efficiency. Rather than conducting extensive simulations through sensitivity analysis, dimensional analysis offers valuable insights into the dominant parameters affecting the CO₂ HnP recovery factor (RF) and CO₂ storage efficiency (EF). Accordingly, we conduct a dimensional analysis of CO₂ injection in shale reservoirs by defining the key dimensionless parameters, including Fourier number (Fo), diffusivity ratio (R_D), and drawdown pressure (P_D). We then use a multiphase, multicomponent transport model that accounts for molecular diffusion, Knudsen diffusion, and viscous flow to simulate a single cycle of the CO₂ injection process at different operational and reservoir conditions. Using the simulation results, we investigate the scaling relations between key dimensionless parameters (Fo, R_D, and P_D) and RF and EF. The results indicate that RF increases with Fo and reaches a plateau, achieving RF_max at an optimal Fourier number, Fo_opt, such as Fo_opt = 0.0025, 0.0025, and 0.025 at P_D = 0.25, 0.5, and 0.75, respectively. Beyond Fo_opt, RF remains constant at RF_max because additional CO₂ injection primarily enlarges a near-fracture CO₂ bank that contributes little to further oil recovery. At high P_D=0.75, the two-phase flow renders the injected volume ineffective below specific Fo. Furthermore, R_D shows a positive correlation with RF, indicating that diffusion during the soak period has a favorable impact on oil recovery, particularly under two-phase conditions (P_D=0.75). In contrast, R_D has little influence on EF. The relationship between Fo and EF is similar to that of Fo and RF, where higher RF values correspond to greater remaining CO₂. This relationship highlights the dual benefit of enhanced oil recovery and CO₂ sequestration, which can be better understood and optimized through the presented dimensional analysis.