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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]