The environmental risks associated with casing deformation in unconventional (shale) gas wells positioned in abutment pillars of longwall mines is a concern to many in the mining and gas well industry. With the recent interest in shale exploration and the proximity to longwall mining in Southwestern Pennsylvania, the risk to mine workers could be catastrophic as fractures in surrounding strata create pathways for transport of leaked gases. Hence, this research by the National Institute for Occupational Safety and Health (NIOSH) presents an analytical model of the gas transport through fractures in a low permeable stratum. The derived equations are used to conduct parametric studies of specific transport conditions to understand the influence of stratum geology, fracture lengths, and the leaked gas properties on subsurface transport. The results indicated that the prediction that the subsurface gas flux decreases with an increase in fracture length is specifically for a non-gassy stratum. The sub-transport trend could be significantly impacted by the stratum gas generation rate within specific fracture lengths, which emphasized the importance of the stratum geology. These findings provide new insights for improved understanding of subsurface gas transport to ensure mine safety.

The increasing trend of shale gas production has created more awareness of environmental risk, such as explosions and contamination to water aquifers [

To investigate this condition, the produced shale gas is modeled as methane, since it is the predominant constituent [

The first is transport governed by advection, which occurs if the high-pressure gas connects to the fracture network. Transport due to diffusion is negligible compared to advection [

The second is flow governed by advection and diffusion and is often regarded as low-velocity flow [

As a starting point, this study focuses on developing an analytical model of the second transport scenario considering both advection and diffusion [

The approach used in this study is to predict gas transport through a single fracture, and then expand this into a DFN model. The equation for contaminant transport through a single fracture is given as [^{3}; ^{2}/s; ^{3}s as illustrated in

Assuming steady, one-dimensional gas transport, and negligible gas attenuation/adsorption, _{0} and _{L}, as illustrated in

Assuming gas transport by advection and diffusion (Fick’s first law of diffusion), the total flux, ^{2}s, is derived as

Transport through a single fracture as presented in

For flux from node

For example, at node 10,

By applying a mass balance (

Thus, the internal node concentrations are calculated from _{b}, is calculated as
_{j-i} the fracture area in m^{2}; and _{b} the boundary area in m^{2}. For example, in _{8–6} and _{9–7}. For this two-dimensional model, the fracture area is the aperture size, and the boundary area is the boundary length at a unit distance normal to the flow plane [

The advection velocity (^{3}/s; ∇^{2}; ^{2}; ^{3}; and

The followings are key assumptions that should be noted for this study:

The shale gas well is modeled as methane since it is the predominant constituent.

A uniform strata generation rate is assumed for all fractures in the sample DFN model.

The fracture length represents the effective length, and the tortuosity effect is ignored.

The fractures are modeled assuming transport characteristics through air.

A uniform advection velocity with indicated flow direction is used for the sample DFN study.

This section discusses the results for the single fracture in _{0} and _{L} are hypothetical values used to represent 100% concentration for _{0} and 1% concentration for _{L}. Though the value of _{0} seems high, it represents a peak subsurface concentration of methane at the mine depth as studies on methane emissions/content with depth have shown methane values greater than 10 m^{3}/t coal in a dry ash free state [

^{−8} −1 × 10^{−7} m/s) the flux continues to decrease with an increase in fracture length because the flux is dominated by diffusion. However, as the velocity increases, there is a point beyond which the flux is relatively constant as the fracture length increases. For ^{−6} m/s, the flux is constant beyond 100 m, and for ^{−5} m/s, the flux is constant beyond 10 m. Hence, the flux trend for non-gassy strata is very sensitive to the advection velocity of the leaked gas. This gives an insight into the domain size for sampling or identifying high-risk locations and, in the event of a leak, this information could be used to determine the important locations for sampling to determine associated risk downstream.

For gassy strata, ^{−6} kg/m^{3}s, the flux decreases with an increase in fracture length; however, beyond 100 m, the flux shows an increasing trend. At this point, the methane generated from the fracture walls is sufficient to gradually increase the overall flux. Similarly, the same observation is demonstrated for ^{−4} kg/m^{3}s and ^{−2} kg/m^{3}s. However, the changes in trend occur at different fracture lengths based on the methane generation rate of the stratum. Therefore, the methane generation rate within the surrounding strata is critical at determining the gas flux and associated risk in the case of a failure. Based on this finding, the flux downstream from the leak source could be higher as methane is generated from the strata. Therefore, the risk associated with well casing failure is more serious if the overlying strata is gassy. Similarly, as described in the

This section presents the implementation of the method outlined in ^{−3} kg/m^{2}s × 10^{−3} m^{2} + 8.35 × 10^{−3} kg/m^{2}s × 10^{−3} m^{2} = 1.57 × 10^{−5} kg/s.

This calculated mass flow rate seems relatively low because there are only two boundary fractures (8–6 and 9–7) connected to B4. However, the fractured zone is often denser with a likelihood of more fractures (internal and external nodes), which increases the fracture areas for methane desorption; a recent study on radon gas shows that, a 10% increase in the fracture density increases the radon boundary flux by a factor 15% [

The National Institute for Occupational Safety and Health (NIOSH) conducts research that reduces the risk of mine disasters, such as those that may occur due to shale gas influx from a sheared gas well. This work focuses on transport from a sheared gas well in a low permeable fractured stratum. From the equations derived, gas transport through a single fracture is studied. The results show that:

For non-gassy strata, the gas flux decreases with an increase in fracture length; however, this depends on the advection velocity.

For a specific advection velocity in a non-gassy stratum, the gas flux is constant beyond a specific fracture length and could be sufficient to determine the associated downstream flux.

For gassy strata, the strata methane generation rate affects the flux trend as the fracture length increases. Beyond specific fracture length, the accumulation of the desorbed gas increases the gas flux (or potential mine inflow), which increases the associated risk. However, the extent of the impact is dependent on the advection velocity of the shale gas.

In addition, this work verified the application of this method to a discrete fracture network for determining the boundary flux, which gives an insight into the gas transport. The DFN analysis demonstrates that: the derived equations could be extended to study methane transport through a fracture network; the concentrations of the gas within the strata, which is not accessible for measurements, could be determined using this approach as shown in

In reality, DFN models are often stochastic with fracture lengths, aperture, and fracture orientation generated from statistical distribution; however, only a sample DFN model is analyzed in the current research. The next phase of this study will: (1) refine the assumptions described in _{0} could vary, (2) consider cases when the fractures are filled with water, (3) introduce stress-based aperture distribution, and (4) expand the application of the derived equations to a stochastically generated DFN model with consideration of uncertainties related to the parameters. However, the findings presented in this study provide an in-depth understanding of the gas transport and the necessary steps to proactively design the ventilation system for the safety of mine workers in the event of a nearby breached well.

Disclaimer

The findings and conclusions in this report are those of the authors and do not necessarily represent the official position of the Centers for Disease Control and Prevention, National Institute for Occupational Safety and Health. Mention of any company or product does not constitute endorsement by NIOSH.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Schematic of a site with longwall mine and shale gas well. The arrows indicate potential locations for casing failure and gas transport into the mine. The circles are used to represent caved rocks in the longwall gob.

Schematic of shear failure for a shale gas well casing.

Model for transport through a single fracture.

Sample DFN model.

Plot of methane flux with fracture length for a non-gassy (

Plot of methane flux with fracture length for non-gassy strata at different advection velocities.

Plot of methane flux with fracture length for gassy strata at different advection velocities.

Parameters used for analysis in

Parameter | Value in | Value in | Value in |
---|---|---|---|

_{0} (kg/m^{3}) | 100 | 100 | 100 |

_{L} (kg/m^{3}) | 1 | 1 | 1 |

^{2}/s) | 2.1 × 10^{−5} | 2.1 × 10^{−5} | 2.1 × 10^{−5} |

1 × 10^{−6} | 1 × 10^{−8} – 1 × 10^{−5} | 1 × 10^{−9} – 1 × 10^{−5} | |

^{3}s) | 0–2.1 × 10^{−2} | 0 | 2.1 × 10^{−6} |

Parameters for the fracture network in

Node | Node | Length (m) | Velocity (m/s) | ^{3}s) | Concentration ^{3}) | Concentration ^{3}) | Flux (kg/m^{2}s) |
---|---|---|---|---|---|---|---|

10 | 8 | 10.53 | −1.00E-04 | 1.00E-04 | 42.25 | 73.77 | −7.36E-03 |

6 | 8 | 14.86 | −1.00E-04 | 1.00E-04 | 1.00 | 73.77 | −7.36E-03 |

9 | 8 | 9.92 | −1.00E-04 | 1.00E-04 | 83.69 | 73.77 | −7.36E-03 |

11 | 8 | 20.79 | 1.00E-04 | 1.00E-04 | 200.09 | 73.77 | 2.21E-02 |

8 | 9 | 9.92 | 1.00E-04 | 1.00E-04 | 73.77 | 83.69 | 8.35E-03 |

7 | 9 | 13.70 | −1.00E-04 | 1.00E-04 | 1.00 | 83.69 | −8.35E-03 |

1 | 10 | 11.69 | −1.00E-04 | 1.00E-04 | 1.00 | 42.25 | −4.20E-03 |

2 | 10 | 27.39 | −1.00E-04 | 1.00E-04 | 1.00 | 42.25 | −4.20E-03 |

8 | 10 | 10.53 | 1.00E-04 | 1.00E-04 | 73.77 | 42.25 | 8.41E-03 |

8 | 11 | 20.79 | −1.00E-04 | 1.00E-04 | 73.77 | 200.09 | −2.00E-02 |

12 | 11 | 11.00 | 1.00E-04 | 1.00E-04 | 68.51 | 200.09 | 7.93E-03 |

5 | 11 | 20.79 | 1.00E-04 | 1.00E-04 | 100.00 | 200.09 | 1.21E-02 |

13 | 12 | 9.95 | 1.00E-04 | 1.00E-04 | 58.56 | 68.51 | 6.83E-03 |

11 | 12 | 11.00 | −1.00E-04 | 1.00E-04 | 200.09 | 68.51 | −6.83E-03 |

12 | 13 | 9.95 | −1.00E-04 | 1.00E-04 | 68.51 | 58.56 | −5.83E-03 |

3 | 13 | 11.69 | −1.00E-04 | 1.00E-04 | 1.00 | 58.56 | −5.83E-03 |

4 | 13 | 16.90 | 1.00E-04 | 1.00E-04 | 100.00 | 58.56 | 1.17E-02 |

Sum | 0 |