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Abstract Various formulas describing non-Darcy flow have been applied to quantify fluid flow in natural geological media, while there is no universal law or formula that can reliably describe the complex relationship between the flow rate and the pressure gradient for single-phase fluid flow in natural oil/gas reservoirs. This study aims at proposing and evaluating a spatial fractional Darcy's law model for the calculation of the flow rate of fluids in natural heterogeneous oil/gas reservoirs at any scale. Experiments documented in literature are revisited to identify the transport characteristics of fluid flow in natural media with complex heterogeneity and structures, including for example discontinuous and/or interconnected pores. The fitting exercises show that the spatial fractional Darcy's law can felicitously depict the flow properties and match well the experimental data shown in seepage curves. The model parameters can also be reasonably simplified, given the possible physical interpretation closely related to the medium structure. Highlights • A spatial fractional Darcy's law to calculate the flow rate in oil/gas reservoirs. • Fractional derivative model can well depict the experimental data. • Model parameters are simplified by employing the spatial fractional model. [ABSTRACT FROM AUTHOR]

Fractional-derivative models have been developed recently to interpret various hydrologic dynamics, such as dissolved contaminant transport in groundwater. However, they have not been applied to quantify other fluid dynamics, such as gas transport through complex geological media. This study reviewed previous gas transport experiments conducted in laboratory columns and real-world oil–gas reservoirs and found that gas dynamics exhibit typical sub-diffusive behavior characterized by heavy late-time tailing in the gas breakthrough curves (BTCs), which cannot be effectively captured by classical transport models. Numerical tests and field applications of the time fractional convection–diffusion equation (fCDE) have shown that the fCDE model can capture the observed gas BTCs including their apparent positive skewness. Sensitivity analysis further revealed that the three parameters used in the fCDE model, including the time index, the convection velocity, and the diffusion coefficient, play different roles in interpreting the delayed gas transport dynamics. In addition, the model comparison and analysis showed that the time fCDE model is efficient in application. Therefore, the time fractional-derivative models can be conveniently extended to quantify gas transport through natural geological media such as complex oil–gas reservoirs. [ABSTRACT FROM AUTHOR]