Second-order gas slippage model for the Klinkenberg effect of multicomponent gas at finite Knudsen numbers up to 1


Studying rarefied gases has attracted significant attention of researchers due to its great potential in applications in numerous fields, including shale gas production and aerospace engineering. The main focus has been to understand the gas-wall interaction effects for enhancement of the mass transfer rate. Pioneered by Maxwell in the later nineteenth century, the spillage boundary concept has been of great help in understanding the relationship between the moment loss on the channel wall and the mass transfer rate. Presently, gas slippage effects emanating from the flow of gas through the formation of rock pore have been a great challenge in the petroleum and gas industry.

Several models have been developed to simulate rarefied gas flow. Among them, the direct simulation Monte Carlo technique has been widely preferred for studying gas flow in the channels due to its high degree of accuracy. However, this process involves a lot of complex computation and hence time-consuming. Alternatively, kinetic approaches have been identified as a promising approach for rarefied gas dynamics simulations. This includes taking into consideration the effects of physical factors such as surface geometry and viscosity effects. However, current studies have concentrated mostly on the single component’s gas flow slippage models and, therefore, consequent research on multicomponent gas mixtures is highly desirable.

To this note, Dr. Shihao Wang and Dr. Yu-Shu Wu from Colorado School of Mines, Petroleum Engineering Department in collaboration with Dr. Alexander Lukyanov from Harvard Medical School investigated the gas slippage effects in multicomponent gas mixtures. In particular, the authors developed a non-empirical slippage model taking into consideration the kinetic theory of gases. Furthermore, they validated their work by comparing their results to the existing molecular simulation results. Their research work is currently published in the research journal, Fuel.

In brief, the research team explored the kinetic theory of gases and the existing single component slippage models. Next, based on the non-empirical second-order derivation, multi-component gas spillage effect was validated. Furthermore, they investigated the mass transfer mechanism of the gas mixtures to consequently validate the model accuracy.

The authors observed a significant enhancement in the mass transfer due to the momentum loss and consequent decrease in the viscosity. In addition, they noted that the mass transfer mechanism was mostly active at low pressures. In summary, Shihao Wang and his colleagues are the first to investigate non-empirical gas-spillage effects in gas mixtures. To actualize their study, they performed both physical experiment and molecular level simulations and compared the obtained results to the existing one. Altogether, the proposed model is a promising solution for efficient simulation of unconventional gas formations and will, therefore, advance its applications in numerous areas.

About the author

Dr. Shihao Wang is a post-doc researcher in Petroleum Engineering. He received his Bachelor degree from Peking University and a Ph.D. degree from Colorado School of Mines. His research mainly focuses on developing high performance computing reservoir simulator with general purpose multi-physics coupling. The developed software includes a fully coupled thermal-hydrological-mechanical (THM) parallel geothermal simulator, named as THM-EGS. He has research interests in geomechanics, transport mechanism, parallel computing, geothermal engineering, and CO2-EOR.

He has published more than 10 papers as the first or corresponding author, including seven peer-reviewed journal papers. Currently, he is working on developing an advanced hydraulic fracturing software, named FracOPT. The software is able to conduct real-time simulation and automatic pumping stages design/optimization. The software has been tested and applied in Sulige Gas Field.


Wang, S., Lukyanov, A., & Wu, Y. (2019). Second-order gas slippage model for the Klinkenberg effect of multicomponent gas at finite Knudsen numbers up to 1. Fuel, 235, 1275-1286.

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