### Abstract

Accurately estimating diffusion coefficient of coal is of great significance for coalbed gas production planning. However, the most commonly used approach (written as infinite series) to inverse D may result in erroneous estimation due to assuming a constant surface concentration in solving the Fick diffusion model. This study first conducted a succession of experiments on coal-gas (CH_{4} and CO_{2}) ad/desorption, and on the basis of Fick diffusion model, both an analytical approach and a numerical approach were proposed to inverse D in coal. The inversion result shows D is not a constant, it increases with pore pressure decreasing. The discrepancy resulted from using distinct inversion approaches varies with the pore pressure changing. It implies using the analytical approach to inverse D will underestimate the gas diffusivity of coal in some extend. Assuming a constant surface concentration will introduce some unpredictable deviation, even some unacceptable error. Finally, a dimensionless processing for Fick diffusion model was proposed to easy the numerical approach to inverse gas diffusion coefficient. This work is expected to make a clear evaluation on the influence of holding a constant surface concentration in solving Fick diffusion model and suggest a high-accuracy and efficient approach to estimate gas diffusion coefficient and model gas transport behaviors in coal matrix.

Original language | English (US) |
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State | Published - Jan 1 2019 |

Event | 53rd U.S. Rock Mechanics/Geomechanics Symposium - Brooklyn, United States Duration: Jun 23 2019 → Jun 26 2019 |

### Conference

Conference | 53rd U.S. Rock Mechanics/Geomechanics Symposium |
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Country | United States |

City | Brooklyn |

Period | 6/23/19 → 6/26/19 |

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### All Science Journal Classification (ASJC) codes

- Geochemistry and Petrology
- Geophysics

### Cite this

*A numerical approach to upgrade the estimation of gas diffusion coefficient in coal matrix*. Paper presented at 53rd U.S. Rock Mechanics/Geomechanics Symposium, Brooklyn, United States.