### Abstract

The capability to simulate real gas flow in porous materials with micro- and nano-meter-scale pores is of importance in many applications, such as gas extraction from shale reservoirs, and the design of gasbased fuel cells. A node-bond pore-network flow model (PNFM) has been developed for gas flow where it is the only fluid phase. The flow conductance equation includes the usual Darcy flow terms, and additional terms that capture the contributions from slip flow to Knudsen diffusion. With respect to the case for a non-ideal gas, the extra contributions, which are necessary, to the coefficients of the Darcy and Knudsen terms, are expressed in terms of reduced temperature and pressure, using van der Waals’s

two-parameter principle of corresponding states. Analysis on cylindrical pores shows that the coefficient deviates from that of the non-ideal gas case by more than 80% in the Darcy term, while between 80% and 150% in the Knudsen term, when the physical states approach to the critical state of the fluid. Although the deviations become smaller when the states are away from the critical state, they remain relatively large even at conditions relevant to practical applications. The model was applied to a pore network of a realistic 3D shale model to show slippage and Knudsen effects on the predicted permeability and the sensitivity to pore sizes. Simulations were carried out for methane under the operational conditions of typical shale-gas reservoirs, and nitrogen under the conditions of laboratory experiments. The results show that the ratio of gas and Darcy permeability correlates positively and strongly with the pore size but inversely with the gas pressure and Tangential Momentum Accommodation Coefficient (TMAC) in the slip term, which can impact gas permeability disproportionally. The results are in favour of controlling the rate of gas depressurisation to avoid early depletion in shale gas production. The methane permeability is shown to be 30% greater, relatively, than that when the ideal gas law is applied, even under normal field operational conditions, while the nitrogen permeability can only approximate the methane permeability within a certain range of field operational conditions when the slip flow is not dominating.

two-parameter principle of corresponding states. Analysis on cylindrical pores shows that the coefficient deviates from that of the non-ideal gas case by more than 80% in the Darcy term, while between 80% and 150% in the Knudsen term, when the physical states approach to the critical state of the fluid. Although the deviations become smaller when the states are away from the critical state, they remain relatively large even at conditions relevant to practical applications. The model was applied to a pore network of a realistic 3D shale model to show slippage and Knudsen effects on the predicted permeability and the sensitivity to pore sizes. Simulations were carried out for methane under the operational conditions of typical shale-gas reservoirs, and nitrogen under the conditions of laboratory experiments. The results show that the ratio of gas and Darcy permeability correlates positively and strongly with the pore size but inversely with the gas pressure and Tangential Momentum Accommodation Coefficient (TMAC) in the slip term, which can impact gas permeability disproportionally. The results are in favour of controlling the rate of gas depressurisation to avoid early depletion in shale gas production. The methane permeability is shown to be 30% greater, relatively, than that when the ideal gas law is applied, even under normal field operational conditions, while the nitrogen permeability can only approximate the methane permeability within a certain range of field operational conditions when the slip flow is not dominating.

Original language | English |
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Pages (from-to) | 498-508 |

Number of pages | 11 |

Journal | Fuel |

Volume | 116 |

Early online date | 29 Aug 2013 |

DOIs | |

Publication status | Published - 15 Jan 2014 |

### Keywords

- Gas transport
- Slip flow
- Knudsen diffusion
- Micro/nanoporous media
- Shale gas reservoir

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## Cite this

Ma, J., Sanchez, J. P., Wu, K., Couples, G. D., & Jiang, Z. (2014). A pore network model for simulating non-ideal gas flow in micro- and nano-porous materials.

*Fuel*,*116*, 498-508. https://doi.org/10.1016/j.fuel.2013.08.041