^{1}

^{2}

^{1}

^{2}

^{3}

^{1}

^{2}

^{1}

^{2}

^{3}

The flow state of gas in coals is very complicated. We should pay attention to whether the permeability calculated by Darcy’s law is in accordance with the actual situation. We conducted an experiment on coal permeability and deformation under fixing confining pressure and increasing axial stress conditions. The objective is to investigate the variation of Reynolds number

In the process of underground mining, in situ stress, gas pressure, and coal deformation are changing constantly. Under the combined effect of various factors, the engineering geological disaster, such as coal and gas outburst, is very prone to occur. The migration characteristic of gas in coals is closely related to the occurrence of gas disasters. However, the dynamics of the Reynolds number reflect the flow state of the gas in coals under different stress arrangement. Accordingly, the Reynolds number is of great significance for preventing gas disaster. Therefore, it is very necessary to study the variation of Reynolds number for gas-bearing coal.

Vidhya et al. [

In summary, despite the Reynolds number being an important dimensionless parameter for discriminating the flow fluid behavior, the research on the evolution of the Reynolds number in the process of loading axial stress on gas-filled coal is rarely reported. Given that, in order to reveal the gas flow state, it is necessary to study the Reynolds number evolutions by carrying out the gas permeability experiment under triaxial compression conditions. The study also provides a useful reference to select an appropriate model (based on Darcy’s law and non-Darcy’s law) for the permeability calculation.

The experiments were conducted with the newly developed servo-controlled seepage apparatus for thermal-hydrological-mechanical (THM) coupling of gas-infiltrated coals [

The experimental setup and loading cell are shown in Figure

Servo-controlled seepage equipment for thermal-hydrological-mechanical coupling of coals and rocks.

Coals were obtained from the fully mechanized working face 2461 of outburst coal seam C_{1} in Baijiao Coal Mine of Sichuan Coal Industry Group. Its buried depth is about 582.5 m. The in situ stress in the field is shown in Table ^{3}, respectively. The uniaxial compressive strength of raw coal is 25.82 MPa, the elastic modulus is 2.29 GPa, the tensile strength is 2.06 MPa, the initial porosity is 0.0538, and the initial permeability is

In situ stress of the fully mechanized working face 2461.

In situ stress | Magnitude (MPa) | Dip angle (°) | Azimuthal angle (°) |
---|---|---|---|

Maximum principal stress | 26.6 | -6.7 | 90.1 |

Intermediate principal stress | 19.4 | -16.8 | 358.1 |

Minimum principal stress | 8.5 | -71.8 | 201.1 |

Coal samples.

In the first stage of the experiments, the specimens were placed into the loading cell with the bedding plane parallel to the axis (Figure _{4}) was used to be the injection gas at a pressure of 3 MPa during the whole experiment.

The experiment was performed in the following three steps.

Axial stress and confining pressure were simultaneously increased to 20 MPa of hydrostatic pressure at the rate of 0.05 MPa/s. The pressure was maintained for 48 hours to balance the adsorption of coals.

By keeping the confining pressure unchanged, the axial pressure is switched from force control to displacement control and the coal specimens were loaded at a rate of 0.01 mm/min until the coal specimens are in the residual stress region.

End the experiment.

The stress path as obtained from the experiment is shown in Figure

The stress path of coal sample loading.

To characterize the flow behavior of the gas in the above experiment, knowledge of the Reynolds number is important. The Reynolds number ^{3}, ^{-2}·s^{-1}.

In this study, Reynolds number

Combining equations (

Based on the designed stress path, the coal is always in the prepeak state and the flow of CH_{4} in the coal can be characterized by Darcy’s law. The permeability equation is as follows [^{2}, _{4} in m^{3}/s, _{4} in MPa·s, at the temperature of the test according to Sutherland’s formula, _{4} at the test temperature, and ^{2}.

In an extremely short period, the change in the equivalent diameter of seepage path is

In particular, “an extremely short period” refers to the adjacent time interval when the data acquisition and storage system records the data (the system records the data once per 0.22 s). Compared with the time used for experiment, the period can be considered as instantaneous.

Using equation (

Therefore, the change rate in the equivalent diameter of seepage path is

The experimental time used for maintaining the confining pressure and increasing the axial pressure is shorter than that of the adsorption equilibrium; therefore, the deformation induced by the adsorption and desorption of coal matrix is not considered. Accordingly, the change rate of the porosity is as follows [

Combining equations (

Herein, the coal matrix is considered as a rigid body, so

In the absence of the gas sorption effect, the volumetric variation of the porous media satisfies the Betti-Maxwell reciprocal theorem [

Incorporating equation (

Raw coal is always subjected to confining pressure in the process of increasing axial pressure, so triaxial compression experiment is very different from the uniaxial compression experiment and the deformation modulus and Poisson’s ratio are given as follows:

The permeability of gas reservoirs is a key performance factor in gas production. Permeability directly affects the gas extraction and shale gas yield. Therefore, it is of paramount interest to study the permeability [^{2}, and ^{2}.

Incorporating equation (

In each ultrashort period (

Therefore, the change rate of the Reynolds number is

Equation (

Change of Reynolds number rate

The correlation coefficient is

Accordingly, we assume a quadratic polynomial relationship between the change rate of Reynolds number (

From equation (

For the experimental data,

Taking logarithm on both the sides of equation (

On combining equation (

It can be seen from equation (

Figure

Relationship between deviatoric stress (

Change of permeability

Figure

Change of Reynolds number ratio

It is observed that the gas flow state is a linear laminar flow if _{0}) could result in Re greater than or less than 10 in the postpeak stage. In the case of higher Reynolds number, the inertial term in Forchheimer flow equations is more significant, and the flux (

(a) Change of Reynolds number

Essentially, the difference in

Capillary model of gas flow in coal sample.

At

By subtracting equation (

Neglecting the higher order term (

Herein, we use volume flow ^{3}/s and

(

Change of flow rate

We performed an experiment on coal permeability and deformation under fixed confining pressure and increasing axial stress conditions with the aim to select the permeability model by investigating the variation of Reynolds number. The primary conclusions are as follows:

The dynamic evolution of Reynolds number under the assumption that the coal matrix is rigid and the flow rate is constant in an extremely short period is examined. We find that the Reynolds number increases with an increase in the axial strain

Different initial Reynolds numbers result in the Reynolds numbers being may be greater than or less than 10 in the postpeak stage. In this case, the permeability of gas-bearing coal cannot be calculated by Darcy’s law. Therefore, a careful selection of the permeability calculation model is necessary

If

Data available within the article or its supplementary materials.

We declare we have no competing interests.

This study was financially supported by the National Natural Science Foundation of China (51434003, 51874053, and 51804049), the China Postdoctoral Science Foundation Funded Project (2017M612917), the Chongqing Postdoctoral Research Project Special Funding (XM2017043), and the Research Fund of State Key Laboratory for Geomechanics and Deep Underground Engineering, CUMT (SKLGDUEK1809).

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