A Mathematical model for total mass flow rate per unit area and total permeability of real gas flow in fractal porous media was proposed on the basis of fractal theory. Proposed models in this paper paid attention to the influence of real gas effect on gas, taking transition regime as the coupling of slip regime and Knudsen diffusion, considering multi-flow-regime coexist, multi-flow-regime is continuum flow regime, slip flow regime, transition flow regime and Knudsen diffusion regime., pore which pore diameter is $\lambda$ mass flow rate per unit area multiply corresponding pore number $dN$ obtain mass flow rate($dq$). Integrate $dq$ within corresponding diameter range and divide fractal porous media work out corresponding flow regime the mass flow rate per unit area. The total mass flow rate per unit area was then calculated through integrating over the mass flow rate deduced, where different flow regimes have been engaged, including continuum regime, slip regime, transition regime and Knudsen diffusion. Based on the Darcy theory, the total permeability was then calculated. In order to verify correctness of model, compare proposed model to Wang's model and Fan's model. Calculate correlation coefficient of proposed model and Wang's model, $R^2=0.9912$; Calculate correlation coefficient of proposed model and Wang's model, $R^2=0.9997$. Indicate that proposed model can fit well with Wang's model and Fan's model, proposed model can correctly predict total permeability. And calculate correlation coefficient of D.B.Bennion experiment data and three model.

In the last part, the paper analyzed the influence factor of total mass flow rate per unit area and total permeabilities and mass flow rate per unit area and permeability of different flow regimes. The concludes as follow: (1) total mass flow rate per unit area, total permeability and each flow regime mass flow rate per unit area and permeability increase with fractal dimension($D_p$) increasing and tortuous fractal dimension($D_t$) decreasing. Variation of $D_p$ and $D_t$ has different influence on each flow regime. $D_p$ and $D_t$ has most influence on Knudsen diffusion flow regime, least influence on continuum flow regime. (2) Real gas effect affects the mass flow rate per unit area and permeability in different flow regime by affecting the mean free path of gas molecule. Whether consider real gas effect would cause great difference, maximum difference is 232.35%. (3) Flow regime that have the lowest Knudsen number play leading role in variation of total mass flow rate and total permeability. (4) The more maximum pore diameter of fractal porous media, the more significant influence of total mass flow rate per unit area and total permeability. Maximum pore diameter has different influence on each flow regime, has most influence on Knudsen diffusion flow regime, least influence on continuum flow regime.

基于分形理论，提出了分形多孔介质中单位面积总质量流量和实际气体总渗透率的数学模型。本文提出的模型关注了实际气体效应对气体的影响，以过渡态为滑移态与克努森扩散的耦合，考虑多流态共存，多流态为连续流态，滑流态，过渡流动态和克努森扩散态。孔径为$\lambda$ 单位面积质量流量乘以相应的孔数 $dñ$ 获得质量流量$dq$）。整合$dq$在相应的直径范围内划分分形多孔介质，计算出相应的流态，即每单位面积的质量流率。然后，通过对推导的质量流量进行积分，计算出每单位面积的总质量流量，在此情况下，已采用了不同的流态，包括连续流态，滑移态，过渡态和克努森扩散。根据达西理论，然后计算总渗透率。为了验证模型的正确性，将提出的模型与Wang的模型和Fan的模型进行比较。计算建议模型和王氏模型的相关系数，${\mathrm{[R}}^2=0.9912$; 计算建议模型和王氏模型的相关系数，${\mathrm{[R}}^2=0.9997$。表明所提出的模型与Wang模型和Fan模型完全吻合，所提出的模型可以正确预测总渗透率。并计算出DBBennion实验数据和三个模型的相关系数。

最后，分析了不同流态下总面积质量流量，总渗透率，单位面积质量流量和渗透率的影响因素。结论如下：（1）单位面积总质量流量，总渗透率和各流态单位面积总质量流量和渗透率随分形维数的增加而增大（$d_p$分形维数的增加和曲折$d_{Ť}$）减少。的变化$d_p$ 和 $d_{Ť}$ 对每个流态都有不同的影响。 $d_p$ 和 $d_{Ť}$对克努森扩散流态影响最大，对连续体流态影响最小。（2）实际气体效应通过影响气体分子的平均自由程而影响不同流态下单位面积的质量流量和渗透率。是否考虑实际气体效应会造成较大的差异，最大差异为232.35％。（3）努森数最低的流态在总质量流量和总渗透率的变化中起主导作用。（4）分形多孔介质的最大孔径越大，单位面积总质量流量和总渗透率的影响就越大。最大孔径对每个流态都有不同的影响，对Knudsen扩散流态影响最大，对连续流态影响最小。