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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]

This study is mainly to explore gas transport process in heterogeneous media, which is to lay the foundation for oil-gas exploitation and development. Anomalous transport is observed to be ubiquitous in complex geological formations and has a paramount impact on petroleum engineering. Simultaneously, the random motion of particles usually exhibits obvious path- and history- dependent behaviors. This paper investigates the time-space fractional derivative models as a potential explanation for the time memory of long waiting time and the space non-locality of large regional-scale. A one-dimensional fractional advection-dispersion equation (FADE) based on fractional Fick’s law is firstly used to accurately describe the transport of Carbon dioxide (CO2) in complex media. The new fractional Darcy-advection-dispersion equation (FDADE) model has subsequently been proposed to make a comparison with FADE model and demonstrate its physical mechanism. Finally, the priori estimation of the parameters (fractional derivative index) in fractional derivative models and corresponding physical explanation are presented. Combined with experimental data, the numerical simulations show the fractional derivative models can well characterize the heavy-tailed and early breakthrough phenomenon of CO2 transport. [ABSTRACT FROM AUTHOR]