# Calculation Model and Rapid Estimation Method for Coal Seam Gas Content

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{t}) satisfy the exponential equation, and the gas content and K

_{t}are linear equations. The correlation coefficient of the fitting equation gradually decreases as the exposure time of the coal sample increases. Using the new method to measure and calculate the gas content of coal samples at two different working faces of the Lubanshan North mine (LBS), the deviation of the calculated coal sample gas content ranged from 0.32% to 8.84%, with an average of only 4.49%. Therefore, the new method meets the needs of field engineering technology.

## 1. Introduction

## 2. Experimental Study

#### 2.1. Experimental Apparatus

- (1)
- Vacuum system: This system consisted of a composite vacuum gauge, a vacuum pump, a vacuum tube, a vacuum gauge, and a glass three-way valve.
- (2)
- Constant temperature system: This system consisted of a constant temperature water bath, a coal sample tank, a diffusion tank, a precision pressure gauge, and a high-purity methane gas source.
- (3)
- Adsorption balance system: This system consisted of precision pressure gauges, methane gas sources, inflatable tanks, coal sample tanks, and valves.
- (4)
- Desorption measurement control system: This system consisted of a pressure control valve and a homemade gas desorption analyzer.

#### 2.2. Coal Sample Preparation

_{t}). Based on these indicators, the coal seam outburst risk assessment and coal seam classification could be carried out, and the index K

_{t}could be calculated.

#### 2.3. Experimental Procedure

_{t}is the total amount of gas desorption in the standard state (mL), W

_{t}’ is the total gas desorption measured in the experimental environment (mL), t

_{w}is the water temperature in the tube (°C), P

_{atm}is atmospheric pressure (Pa), h

_{w}is the height of the water column in the measuring tube (mm), and P

_{S}is the saturated water vapor pressure (Pa).

## 3. Experimental Results

#### 3.1. Related Parameter

_{ac}and b

_{ac}were measured using a high-pressure volumetric method to determine the coalbed methane adsorption constants a

_{ac}and b

_{ac}. The adsorption constants a

_{ac}and b

_{ac}are calculated from the Langmuir adsorption equation [32,33] as follows:

_{ac}and b

_{ac}are the Langmuir adsorption constants.

_{ac}and b

_{ac}are determined by the amount of coal gas sample adsorbed under different pressures. Therefore, the gas adsorption constant of the coal is an indicator of coal gas adsorption capacity. The physical meaning of a

_{ac}is the maximum gas adsorption capacity of coal.

#### 3.2. Gas Desorption Process

^{0.5}and 4.5 min

^{0.5}; since the start of desorption, the slope of the line gradually increased and then decreased. The square root of the gas desorption time exceeds 4.5 min

^{0.5}. The slope of the straight line is less than the slope of the straight line at the initial stage and gradually decreases; the square root of the gas desorption time falls between 1 min

^{0.5}and 4.5 min

^{0.5}. As the gas pressure in the coal seam increases, the slope of the straight line increases. According to the calculation model of Winter [29], the change in the gas desorption rate with time can be expressed by an exponential equation [31] for certain other conditions as follows:

_{t}is the gas desorption characteristic coefficient whose exposure time ranges from 1 min to 5 min (mL/(g·min

^{0.5})). V

_{t}and V

_{a}are the gas desorption speed of coal samples with unit mass at the time t and t

_{a}, respectively (cm

^{3}/min). t and t

_{a}are the gas desorption time and time in min, respectively.

_{t}) was determined by the least squares method. The results are listed in Table 7.

_{1}to K

_{5}with the exposure time of the experimental coal sample; that is, K

_{1}> K

_{2}> K

_{3}> K

_{4}> K

_{5}. First, this result is attributed to the gradual decrease of adsorbed gas and the decrease of the amount of available desorption gas. Second, with the accumulation of the amount of desorption gas in fixed space, the gas pressure in the fixed space and the pressure gradient in the coal gas gradually decrease. For the same gas desorption characteristic coefficient, K

_{t}gradually increases with an increase in the adsorption equilibrium gas pressure. The larger the adsorption equilibrium gas pressure, the larger the amount of gas adsorbed by the coal sample under the larger adsorbed gas pressure gradient. When the gas is desorbed into the fixed space, the larger the gas pressure gradient between the fixed space and the coal sample, the larger the amount of gas desorption per unit time.

_{t}can be considered to be a reflection of the physical quantity of the gas desorption speed at different times.

## 4. Discussion

#### 4.1. Relationship between Gas Pressure and K_{t}

_{t}) also increases, and the increase in amplitude is gradually increased with gas pressure. Because coal is a natural adsorbent, the larger the adsorption pressure, the larger the amount of gas adsorption and the larger the amount of gas that is desorbed [31]. For the same gas desorption characteristic coefficient, the index (K

_{t}) gradually increases with an increase in the adsorption equilibrium gas pressure. According to the adsorption theory of Langmuir [33], under the action of the larger adsorption equilibrium gas pressure, the coal sample absorbs a larger amount of gas. When the gas is desorbed into the fixed space, a larger pressure gradient of desorption gas is generated between the fixed space and the coal sample to promote coal adsorption equilibrium gas desorption.

_{t}respectively, trend fitting is available. The adsorption equilibrium gas pressure and the different K

_{t}are exponential equation relations and have good correlation, the coefficient of determination (R

^{2}) being higher than 0.97.

_{t}at different exposure times is shown in Figure 8. The results indicate that R

^{2}decreases to a minor extent with the exposure time of the coal sample due to the deviation of the gas desorption amount error caused by the increase in the exposure time [16,40]. However, the R

^{2}of the coal sample gas desorption regression fitting curve remains greater than 0.97, the correlation of regression fitting curve is higher, and the result is reliable. Therefore, the gas pressure can be expressed as follows:

_{c}and B

_{c}are the constants that correspond to different desorption times, which are dimensionless; P is the adsorption equilibrium gas pressure (MPa); and K

_{t}is the gas desorption characteristic coefficient that corresponds to different desorption times (mL/(g·min

^{0.5})).

#### 4.2. Relationship between Gas Content and K_{t}

_{t}increases. Coal is a natural adsorbent with double pores and fissures. The larger the gas content, the larger K

_{t}is. According to the adsorption theory equation of Langmuir [32], the larger the gas content, the larger the gas pressure, and the larger the amount of adsorbed coal gas. The larger the amount of adsorption gas in the coal sample, the larger the index K

_{t}.

_{t}have a linear equation relationship and an excellent correlation. The correlation coefficient of the regression fitting curve showed a slight decrease with the exposure time. With an increase in desorption time, the deviation of the desorption amount of the coal sample gas gradually increases. However, R

^{2}remains greater than 0.98, which means the regression fitting curve has higher correlation and the result is reliable. Therefore, the relationship between the gas content and K

_{t}can be expressed by Equation (6) as follows:

_{t}+ β

_{t}is the gas desorption characteristic coefficients that correspond to different desorption times (mL/(g·min

^{0.5})).

_{t}for different exposure times, R

^{2}at different times is compared and listed in Table 8.

^{2}, the K

_{t}used to describe the coal sample gas content and gas pressure at different exposure times can reach a high accuracy, especially when K

_{t}is used to describe the gas content. The maximum R

^{2}is 0.99146.

_{t}to describe coal gas pressure and gas content has a certain decrease; the decrease range is very small within 5 min, and the effect on the accuracy of the results is negligible.

#### 4.3. Technical Verification

#### 4.3.1. Experimental Verification

#### 4.3.2. Field Verification

_{5}calculated from the desorption law is also smaller than the actual K

_{5}, which directly causes the calculated gas content of the new method to be smaller than the real gas content. When the indirect method is used to determine the gas content, the desorption rate that is measured at the site is less than the real desorption rate and will only affect the calculation of the loss and a part of the desorption amount, and the influence on the gas content of the raw coal is small.

## 5. Conclusions

- (1)
- The gas desorption amount and the square root of the gas desorption time are linear, and the slope of the straight line will slightly decrease with the extension of the exposure time. The slope of the straight line is less than the slope of the straight line at the initial stage and gradually decreases; the square root of the gas desorption time falls between 1 min
^{0.5}and 4.5 min^{0.5}. As the gas pressure increases, the slope of the straight line increases. - (2)
- Simulation and verification of the on-site gas desorption law verified that the gas pressure and gas content of coal seams and K
_{t}have an exponential equation and a linear equation relationship, respectively. Using this equation relationship, a new method for accurately calculating the gas content of underground coal seams is constructed. - (3)
- Simulation experiments determined that the exposure time of the coal sample should be controlled within 5 min when using the new method to calculate gas content in a coal seam. The calculation equations at 1 min, 2 min, 3 min, and 5 min were given. The method can be used to calculate the coal seam gas content, and the deviation is within the allowable range of the project. Thus, this method can satisfy the needs of rapid gas content estimation at the site.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Q_{t} | cumulative amount of desorbed gas from time t = 0 to time t, mL/g |

Q_{∞} | ultimate adsorption-desorption gas amount, mL/g |

S | unit mass sample outer surface area, cm^{2}/g |

V | unit mass volume of coal sample, mL/g |

D | diffusion coefficient, cm^{2}/min |

v_{1} | gas desorption speed at t = 1 min, mL/(g·min) |

k_{1} | characteristic coefficient of gas desorption speed change |

v_{0} | gas desorption speed at t = 0 min, mL/(g·min) |

A | cumulative gas desorption amount from start to time t, mL/g |

B | desorption constant, dimensionless |

a, i | constants related to the gas content and structure of coal, dimensionless |

b | gas desorption speed decay coefficient with time, dimensionless |

W_{t} | total amount of gas desorption in the standard state, mL/g |

W_{t}’ | total gas desorption measured in the experimental environment, mL/g |

t_{w} | water temperature in the tube, °C |

P_{atm} | atmospheric pressure, MPa |

h_{w} | height of the water column in the measuring tube, mm |

P_{S} | saturated water vapor pressure, MPa |

V_{t}, V_{a} | gas desorption speeds of the coal samples with unit mass at time t and t_{a} |

t, t_{a} | gas desorption time and time in min |

K_{t} | gas desorption characteristic coefficient whose exposure time ranges from 1 min to 5 min |

M_{ad} | air dry basis moisture, % |

A_{ad} | air dry basis ash, % |

V_{daf} | dry ash-free basis of volatile content, % |

S_{t,d} | true relative density, g/cm^{3} |

Q_{b,d} | calorific value, MJ/kg |

G_{R,I} | clean coal bond index, dimensionless |

C_{daf} | fixed carbon content, % |

H_{daf} | dry ash-free basis hydrogen content, % |

O_{daf} | dry ash-free basis oxygen content, % |

N_{daf} | dry ash-free basis nitrogen content, % |

f | coal hardiness coefficient, dimensionless |

ΔP | initial velocity of diffusion of coal gas, mmHg |

D_{cf} | degree of coal fracturing, dimensionless |

P | measured coal seam gas pressure, MPa |

TRD | true relative density of the coal sample, g/cm^{3} |

ARD | apparent relative density of the coal sample, g/cm^{3} |

n | ratio of the total volume of tiny voids to the total volume of coal, % |

a_{ac} | maximum gas adsorption capacity, cm^{3}/g |

b_{ac} | adsorption constant, MPa^{−1} |

Q | adsorption gas quantity, mL/g |

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Equations | Q_{t} (mL/g) | Applicable Conditions |
---|---|---|

Barrer [28] | $\frac{{Q}_{\mathrm{t}}}{{Q}_{\infty}}=\frac{2s}{V}\sqrt{\frac{{D}_{\mathrm{t}}}{\pi}}$ | $0\le \sqrt{t}\le \frac{V}{2s}\sqrt{\frac{\pi}{D}}$ |

Winter [29] | ${Q}_{\mathrm{t}}=\frac{{v}_{1}}{1-{k}_{1}}{t}^{1-{k}_{1}}$ | $0<{k}_{\mathrm{t}}<1$ |

Wang [30] | ${Q}_{\mathrm{t}}=\frac{ABt}{1+Bt}$ | |

Sun [31] | ${Q}_{\mathrm{t}}=a{t}^{i}$ | $0<i<1$ |

Exponential [32] | ${Q}_{\mathrm{t}}=\frac{{v}_{0}}{b}\left(1-{e}^{-bt}\right)$ |

Term | Particle Size (mm) | Quality (g) | Quantity (parts) |
---|---|---|---|

Hardiness coefficient | 20~30 | 50 | 15 |

Proximate analysis | <0.2 | 50 | 3 |

Density | <0.2 | 2 | 3 |

Adsorption constant | 0.2~0.25 | 50 | 1 |

Desorption property | 1~3 | 200 | 1 |

Proximate Analysis Indexes | Elemental Analysis Indexes | ||||||||
---|---|---|---|---|---|---|---|---|---|

M_{ad} (%) | A_{ad} (%) | V_{daf} (%) | S_{t,d} (%) | C_{daf} (%) | Q_{b,d} (MJ/kg) | G_{R,I} | H_{daf} (%) | O_{daf} (%) | N_{daf} (%) |

1.15 | 17.67 | 16.12 | 0.31 | 65.06 | 29.41 | 11.2 | 4.30 | 2.53 | 1.50 |

_{ad}is the air dry basis moisture (%). A

_{ad}is the air dry basis ash (%). V

_{daf}is the dry ash-free basis of volatile content (%). S

_{t,d}is the true relative density (g/cm

^{3}). Q

_{b,d}is the calorific value (MJ/kg). G

_{R,I}is the clean coal bond index (dimensionless). C

_{daf}is the fixed carbon content (%). H

_{daf}is the dry ash-free basis hydrogen content (%). O

_{daf}is the dry ash-free basis oxygen content (%). N

_{daf}is the dry ash-free basis nitrogen content (%).

Outstanding Predictive Indicators | Characteristics Indicators | Adsorption Constants | ||||||
---|---|---|---|---|---|---|---|---|

f | ΔP (mmHg) | D_{cf} | P (MPa) | TRD (g/cm^{3}) | ARD (g/cm^{3}) | n (%) | a_{ac} (cm^{3}/g) | b_{ac} (MPa^{−1}) |

0.395 | 29.1 | IV | 1.20 | 1.32 | 1.23 | 6.8 | 29.6786 | 1.3236 |

_{cf}is the degree of coal fracturing (dimensionless), as shown in Table 5. P is the measured coal seam gas pressure (MPa). TRD is the true relative density of the coal sample (g/cm

^{3}). ARD is the apparent relative density of the coal sample (g/cm

^{3}). n is the ratio of the total volume of tiny voids to the total volume of coal (%). a

_{ac}and b

_{ac}are Langmuir adsorption constants; a

_{ac}is the maximum gas adsorption capacity (cm

^{3}/g) and b

_{ac}is the adsorption constant (MPa

^{−1}).

Class | I | II | III | IV | V |
---|---|---|---|---|---|

Degree of coal fracturing | Massive coal | Slightly fractured coal | Severely fractured coal | Pulverized coal | Completely pulverized coal |

Term | D_{cf} | ΔP (mmHg) | f | P (MPa) |
---|---|---|---|---|

Thresholds | III, IV, V | ≥10 | ≤0.5 | ≥0.74 |

P (MPa) | Q (mL/g) | K_{1} (mL/(g·min^{0.5})) | K_{2} (mL/(g·min^{0.5})) | K_{3} (mL/(g·min^{0.5})) | K_{5} (mL/(g·min^{0.5})) |
---|---|---|---|---|---|

0.131 | 4.72 | 0.1467 | 0.1380 | 0.1268 | 0.1202 |

0.296 | 6.92 | 0.2895 | 0.2644 | 0.2582 | 0.2292 |

0.420 | 8.20 | 0.3660 | 0.3568 | 0.3533 | 0.3274 |

0.604 | 9.70 | 0.4891 | 0.4434 | 0.4059 | 0.3852 |

0.653 | 10.04 | 0.5405 | 0.5067 | 0.4764 | 0.4326 |

1.410 | 13.40 | 0.7702 | 0.7176 | 0.6783 | 0.6283 |

1.720 | 14.20 | 0.8428 | 0.7897 | 0.7148 | 0.6470 |

2.238 | 15.19 | 0.9395 | 0.8846 | 0.8555 | 0.7991 |

_{t}is the gas desorption characteristic coefficient whose exposure time ranges from 1 min to 5 min (mL/(g·min

^{0.5})).

Term | P = A_{c}e^{B}^{cKt} | W = ∂K_{t} + β | Exposure Time (min) |
---|---|---|---|

R^{2} | 0.98079 | 0.99653 | 1 |

0.97922 | 0.99531 | 2 | |

0.97535 | 0.98858 | 3 | |

0.97140 | 0.98542 | 5 | |

average of R^{2} | 0.97669 | 0.99146 |

Gas Pressure (MPa) | Gas Content (mL/g) | Exposure Time (min) | K_{t} (mL/(g·min^{0.5})) | Calculated Gas Content (mL/g) | Deviation (%) |
---|---|---|---|---|---|

0.64 | 9.95 | 1 | 0.4634 | 9.18 | −7.73 |

2 | 0.4232 | 9.04 | −9.14 | ||

3 | 0.4114 | 9.22 | −7.33 | ||

5 | 0.3860 | 9.33 | −6.23 | ||

0.912 | 11.51 | 1 | 0.6309 | 11.39 | −1.04 |

2 | 0.5351 | 10.61 | −7.81 | ||

3 | 0.5137 | 10.74 | −6.68 | ||

5 | 0.5262 | 11.58 | 0.60 |

Number | K_{5} (mL/(g·min^{0.5})) | Calculated Values (mL/g) | Measured Values (mL/g) | Deviation (%) |
---|---|---|---|---|

1 | 0.4153 | 9.80 | 10.10 | −2.97 |

2 | 0.3925 | 9.43 | 9.40 | 0.32 |

3 | 0.3611 | 8.93 | 9.41 | −5.1 |

4 | 0.4385 | 10.17 | 10.71 | −5.0 |

5 | 0.5186 | 11.45 | 10.93 | 4.76 |

6 | 0.40225 | 9.59 | 10.52 | −8.84 |

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## Share and Cite

**MDPI and ACS Style**

Wang, F.; Zhao, X.; Liang, Y.; Li, X.; Chen, Y.
Calculation Model and Rapid Estimation Method for Coal Seam Gas Content. *Processes* **2018**, *6*, 223.
https://doi.org/10.3390/pr6110223

**AMA Style**

Wang F, Zhao X, Liang Y, Li X, Chen Y.
Calculation Model and Rapid Estimation Method for Coal Seam Gas Content. *Processes*. 2018; 6(11):223.
https://doi.org/10.3390/pr6110223

**Chicago/Turabian Style**

Wang, Fakai, Xusheng Zhao, Yunpei Liang, Xuelong Li, and Yulong Chen.
2018. "Calculation Model and Rapid Estimation Method for Coal Seam Gas Content" *Processes* 6, no. 11: 223.
https://doi.org/10.3390/pr6110223