Dimensional and Scaling Analyses of a Single-Cycle CO₂ Huff 'n’ Puff in Shales Under Single-Phase Conditions

Injecting carbon dioxide (CO₂) into shale reservoirs via the huff 'n’ puff (HnP) process has proven effective for improving oil recovery. However, optimal CO₂ HnP strategies differ across reservoirs, as each reservoir exhibits unique interactions between injected CO₂ and oil composition. Dimensional and scaling analyses offer broad, generalizable insights into the key mechanisms and controlling factors governing CO₂ HnP performance. Accordingly, we use dimensional analysis to identify key dimensionless groups that quantify the impact of reservoir properties and operational parameters on HnP recovery factor (RF), and to establish scaling relationships linking these groups to RF. We consider reservoir types using alkane carbon number (ACN) to classify oils and tailor recovery strategies. Using the multicomponent inhomogeneous fluid transport model, we simulate hydrocarbon and CO₂ transport within shale nanopores and generate comprehensive datasets for CO₂-C₈ and CO₂-C₃ HnP processes, representing black-oil and gas-condensate systems, respectively. These datasets serve as the foundation for our dimensional analysis, in which the Vaschy-Buckingham theorem is applied to reveal essential dimensionless groups, including the Fourier number (Fo), diffusivity ratio (R_D), time ratio (R_T), pressure drawdown (P_D), fluid-solid friction modulus (φ), and ACN itself. By identifying the connections between these dimensionless numbers and the RF, we determine the scaling relations between these dimensionless parameters and RF. Between the CO₂-C₃ and CO₂-C₈ systems, RF increases rapidly with Fo up to a critical value Fo_c,but the increase in CO₂-bank formation beyond Fo_c does not promote fluid mixing. Furthermore, the results reveal that the R_D effect is strongest for Fo < Fo_c. In addition, increasing φ increases RF by strengthening advective transport and improving oil production. The scaling analysis shows that RF/P_D ∝ ψ^1/2 for ψ < ψ_c and RF/P_D ∝ ψ^1/9 for ψ > ψ_c, where and ψ_c = 0.0015, marking mixing-dominated and mixing-limited regimes, respectively. The operational parameters can be better understood and optimized through the presented dimensional analysis.