- Email: [email protected]
Determination method of initial gas desorption law of coal based on flow characteristics of convergent nozzle
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Contents lists available at ScienceDirect
Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
Determination method of initial gas desorption law of coal based on flow characteristics of convergent nozzle
T
Yujia Chena,b,c, Dingding Yanga,b,c,∗, Jun Tanga,b,c, Xiaowei Lia,b,c, Chenglin Jianga,b,c a
Key Laboratory of Gas and Fire Control for Coal Mines, Xuzhou, Jiangsu 221116, China National Engineering Research Center of Coal Gas Control, Xuzhou, Jiangsu 221116, China c School of Safety Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221116, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Coal and gas outburst Initial desorption Flow characteristics Convergent nozzle Pneumatic component
The amount of initial gas release after the destruction of coal by ground stress relates closely to the outburst danger. In this paper, the following method was proposed to accurately determine the initial gas desorption law of coal. First, real-time temperature and pressure data of sealed coal sample tank after the sudden exposure of coal that had reached adsorption equilibrium within the tank were collected first via a high-precision, highfrequency response sensor. Then, the mass flow of gas passing through the pneumatic component at different times was calculated according to flow rate characteristics of pneumatic component that communicated with the atmosphere on the tank. In this process, it is determined that a convergent nozzle with a larger contraction ratio should be used as the channel for gas desorption and release. Moreover, in light of the characteristics of the testing process, the existing parameters that characterize the flow characteristics of pneumatic component were optimized and measured. Finally, the initial gas desorption laws of two coal samples with different metamorphic degrees were measured and analyzed under two pressures using three different-sized convergent nozzles.
1. Introduction The gas desorption law of coal is one of the important subjects for studying coal bed methane exploitation and coal and gas disaster prevention and control. By using a diffusion equation to describe gas desorption process of coal (Kissell and Meculloch, 1973), United States Bureau of Mines (USBM) found that the amount of gas accumulated in the early desorption process was proportional to the square root of time. Based on this finding, Kissell then established the industry standard for the determination of coal seam gas content, namely, the USBM desorption method, which has been widely used in various countries. In addition, this method is the basis for studying methods and indicators of coal and gas outburst prediction (Alexeev et al., 2007). According to the spherical shell instability mechanism of coal and gas outburst, the amount of initial gas release after the destruction of coal by ground stress relates closely to the outburst danger (Jiang et al., 2015). When the coal containing high-pressure gas is suddenly exposed to atmospheric environment, the high-pressure gas within it gets released and desorbed outwards. With large amounts of gas desorbed and released at the initial stage of coal exposure, the gas desorption rate and amount both drop rapidly. During the process, the rapid gas release in a short period of time and the sharp drop of gas pressure bring huge
∗
difficulties to the determination. Considering the important role of initial gas desorption law of coal, scholars at home and abroad have conducted in-depth laboratorial studies on its determination methods which, according to the principle of determination, can be divided into volumetric method, gravimetric method, etc. (Busch et al., 2003; Gruszkiewicz et al., 2009; Li et al., 2010; Pillalamarry et al., 2011). Among these methods, the volumetric method mostly determines the change of desorption amount over time via a gas gathering system after the release of gas pressure in the coal sample tank (Saghafi et al., 2007; Ma et al., 2008). However, this method can hardly obtain the gas desorption law during the initial seconds of sample exposure, yet this part of gas release is often closely related to gas disasters. The gravimetric method which determines the variation of gas content in coal samples via a microbalance (Guan et al., 2009; Jian et al., 2012) is unable to determine gas desorption law at the initial sudden gas pressure release of coal exposure, either. In this paper, real-time temperature and pressure data of sealed coal sample tank after the sudden exposure of coal that had reached adsorption equilibrium within the tank were collected first via a highprecision, high-frequency response sensor. Then, the mass flow of gas passing through the pneumatic component at different times was calculated according to flow rate characteristics of pneumatic component
Corresponding author. Key Laboratory of Gas and Fire Control for Coal Mines, Xuzhou, Jiangsu 221116, China. E-mail address: [email protected] (D. Yang).
https://doi.org/10.1016/j.jlp.2018.04.002 Received 5 December 2017; Received in revised form 19 March 2018; Accepted 3 April 2018 Available online 06 April 2018 0950-4230/ © 2018 Elsevier Ltd. All rights reserved.
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
Fig. 1. Schematic diagram of experimental device: 1-gas cylinder, 2-pressure-reducing valves, 3-pipeline, 4, 5, 9, 10-valves, 6-vacuum pump, 7-pressure gauge, 8low-pressure sensor, 10-solenoid valve, 12-high-pressure sensor, 13-pneumatic valve, 14-convergent nozzle, 15-filter, 16-thermostatic bath.
that communicated with the atmosphere on the tank. Furthermore, the problems existing therein were studied. In this way, the initial gas release law of coal containing high-pressure gas can be obtained scientifically and accurately.
⎧ ⎪ ⎪ qm = ⎨ ⎪S ⎪ ⎩
2.1. Experimental principle The core of the proposed determination method lies in the selection of pneumatic component on the coal sample tank and the determination of flow characteristics. Considering characteristics of determination process, a convergent nozzle with a larger contraction ratio was chosen as the channel for gas desorption and release. The specific reasons are as follows: When a convergent nozzle is used, the one-dimensional compressible unsteady flow field can be maintained within the nozzle after the valve is suddenly opened. The large contraction ratio means that the nozzle is very short, so the high-speed airflow has no time to exchange heat with the outside world when it flows within the nozzle. Moreover, since the frictional resistance is negligible, the gas flow within the nozzle can be approximately regarded as an isentropic flow with constant total pressure of gas flow line along the nozzle. According to the Bernoulli equation of isentropic airflow, the mass flow of gas passing through the convergent nozzle (Sullivan, 1981; Zhang, 1999) can be obtained, as shown in Eq. (1):
qm = S
2k P − ⎛ 1⎞ P0 ρ ⎜ ⎜ ⎝ P0 ⎠ k−1 ⎝ P0 ⎠ ⎝ ⎜
⎟
⎜
⎟
( ) −( ) ⎝ P1 P0
k+1 k ⎞ ⎟
⎠
P1 > P ∗ (2)
2.2. Experimental device Independently developed by China University of Mining and Technology, the experimental device was equipped with several major functions, including adsorption and desorption, data acquisition and temperature control, as shown in Fig. 1. A convergent nozzle was connected above the coal sample tank made of stainless steel, and its switch was controlled by a pneumatic valve that would be smoothly connected with the nozzle when the valve opened. A filter was arranged between the coal sample within the tank and the convergent nozzle to prevent the pulverized coal from blocking the pipe during the sudden pressure relief in the tank. Two pressure sensors and a temperature sensor were connected to the tank to acquire the total pressure and total temperature within the tank. Due to the wide range of pressure changes in the determination process, the pressure data were acquired in segments via high-pressure and low-pressure sensors. When the total pressure got below 2 KPa, the low-pressure channel was switched on through the electromagnetic
k+1 k ⎞
⎟⎟ ⎠
2 P 2k P ρ⎛ 1 k k − 1 0 ⎜ P0
P1 ≤ P ∗
kρP0
At the same time, the flow velocity in the tank can be minimized by the convergent nozzle due to its large contraction ratio, so that the total pressure and total temperature of gas flow can be measured directly by the pressure and temperature sensors on the tank. In the whole flowing process, the pressure outside the nozzle remains constant at atmospheric pressure P1, while the total gas pressure P0 in the tank decreases gradually over time. By setting up the above experimental device in the laboratory, the relation curves of total pressure and total temperature in the tank over time under different conditions can be measured. The attenuation law of mass flow of gas passing through the nozzle over time can be obtained by combining the flow characteristics at the convergent nozzle. Furthermore, the initial gas desorption law of coal can be acquired. The flow characteristic here refers to the relationship between the pressure drop from the nozzle inlet to outlet and the flow passing through the pneumatic element when the fluid flows from the nozzle inlet to the outlet (Liu and Liu, 2001).
2. Experimental
2 ⎛ P1 k ⎛ ⎞
k+1 2 2(k − 1) S k+1
( )
(1)
When the external pressure P1 is lower than the critical pressure P ∗, the flow velocity at the convergent nozzle reaches the sound velocity, making the pressure wave velocity still relative to the nozzle. Consequently, the pressure difference cannot be transmitted to the inside of the tank nozzle, so the flow remains critical and constant. Eq. (1) can be converted to Eq. (2), where k is the adiabatic index and S is the effective cross-sectional area of the nozzle.
223
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
experimental device shown in Fig. 1, the mass flow of gas flowing through the nozzle at different time points can be calculated based on the flow characteristics of convergent nozzle. The flow characteristics of pneumatic component can be characterized by many parameters. Usually, countries will make their own corresponding regulations of pneumatic component parameters (ISO6358:1989; GB/T14513:1993; FESTO942029:1997; JISC9312:2005; ISO6358–1:2013). Table 3 lists the characteristics and applicable conditions of flow characteristic parameters specified in different standards, and Table 4 gives the meanings and units of the parameters involved in this study. Based on the results of comparative analysis of various methods, it was determined that the sonic conductance C, the critical back-pressure ratio b and the subsonic index m in ISO6358–1:2013 were adopted to comprehensively express the flow characteristics of the convergent nozzle. Besides, they were taken as the basis for the determination of initial gas desorption law of coal, as shown in Eq. (3).
Table 1 Sensor parameters. Sensor type
Range
Accuracy
Model
Origin
High-pressure Low-pressure Temperature
2 MPa 2 KPa 0–60 °C
< 0.04% FS < 0.25% FS < 0.2% FS
PMP4070 HM26-2-V1-F0-W1 A12
United States Germany United States
valve, so as to ensure the accuracy of pressure data acquisition. To precisely reflect the rapid changes of gas pressure in the early stage of coal exposure within the tank, the data acquisition interval of sensors was set to 1.6 ms which was far smaller than the data acquisition interval adopted by previous determinations (Busch et al., 2003; Gruszkiewicz et al., 2009; Li et al., 2010; Pillalamarry et al., 2011). The models and accuracies of the selected sensors are listed in Table 1. 2.3. Experimental process
⎧ P1/ P0 ≤ b: qm∗ = CρP0 293.15 T0 ⎪ ⎨ b < P / P ≤ 1: q = q ∗ 1 − P1 / P0 − b 1 0 m ⎪ m 1−b ⎩
( (
For determining the initial gas desorption law of coal, the prepared coal sample was firstly weighed and then loaded into the sample tank. Next, air tightness of the device was checked. After the device passed the check, the vacuum pump was started to vacuumize the coal sample for 8 h. When pressure within the tank was reduced to lower than 10 Pa, high-pressure CH4 was then injected into the tank to allow it to adsorb on the coal sample for 24 h. While the adsorption equilibrium was reached, the pneumatic valve was opened, and meanwhile the data acquisition program started to acquire the data. Then, the coal sample was removed from the tank and steel balls of the same volume were loaded in the tank to repeat the above procedure. After the test program was started, the computer would automatically record and save parameters including the total pressure and total temperature in the tank, acquisition time, acquisition frequency etc. In this way, the change laws of acquired pressure and temperature over time under the same pressure and two different conditions (coal samples and dead space, dead space) were obtained. The experimental coal samples included anthracite with high metamorphic degree from WS coal mine in Guizhou Province, China and gas coal with low metamorphic degree from KZD mine in Anhui Province, China. Basic parameters of the samples are listed in Table 2. Since the determination process not only requires repeated experiments and vacuum pumping but also lasts for a long time, it may be affected by changes in factors such as the pore structure, mass loss, temperature and moisture of coal. To address this issue, the following measures were taken: First, the sample taken on site was screened, after which about 300 g of coal particles with sizes of 3–5 mm was chosen as the experimental object. Second, a thermostatic bath was employed to keep constant temperature of the sample tank. Third, the sample was continuously vacumized for 48 h before the experiment, so that its internal moisture would no longer decrease under the effect of vacuum pumping.
3.1. Determination flow characteristic parameters of the convergent nozzle In order to determine flow characteristic parameters of the convergent nozzle, this study built an experimental platform according to the requirements of ISO6358–1:2013 for measuring the sonic conductance C, the critical back-pressure ratio b and the subsonic index m. The schematic diagram of the system is presented in Fig. 2 (ISO6358–1:2013). Before the test started, the circuit system should be connected to the power supply first to preheat the sensors for at least 10 min, so as to ensure the stability of the output voltage and reduce measurement error. Furthermore, it is necessary to detect the air tightness of the testing system and calibrate the sensors. During the test, the high-pressure gas passed successively through the gas filter, the pressure relief valve, the flow sensor, the temperature measuring tube, the pressure measuring tube and other components before it flowed to atmosphere through the convergent nozzle. Among these components, the filter was used for removing water vapor, small particles, oil and other impurities from the gas; the pressure relief valve for adjusting the upstream gas flow of the nozzle; the flow sensor for measuring the flow rate in the gas channel; the temperature sensor in the temperature measuring tube for measuring the temperature of gas flow; the downstream throttle valve for adjusting both the gas flow rate through the nozzle and the pressure; the upstream and downstream pressure sensors for measuring the pressure change during the experiment. The filter, pressure relief valve, precise pressure regulating valve and flow sensor used in the laboratory were all produced by FESTO Company in Germany. The high-precision pressure sensor was produced by GE Company in the United States. The temperature sensor which was made in China was characterized by high frequency and high precision. The switch actuator of convergent nozzle was manufactured by OMAL Company in Italian. The real testing system is exhibited in Fig. 3. According to the requirements of ISO6358–1:2013, with the upstream absolute pressure set at about 6 × 105 Pa, the downstream
After total temperature and total pressure of gas in the sample tank during gas desorption of coal samples were measured using the Table 2 Coal sample parameters. Coal rank
Ash
Moisture
Volatile matter
Adsorption constant a
Adsorption constant b
WS KZD
Anthracite Gas coal
26.71 25.92
1.86 2.17
10.49 30.36
25.58 16.54
1.43 0.917
(3)
There are two benefits for this choice. First, based on Sanville's assumption that the flow characteristic curve approximates a 1/4 ellipse, the flow characteristic curve can be expressed only by using several characteristic parameters. In addition, different from standards like ISO6358, FESA20942029 and GB/T14513, ISO6358–1:2013 introduces the subsonic index m to describe the effect of flow channel changes within the pneumatic component on determination results in the determination process (Zhang and Xu, 2015).
3. Data processing and analysis
Coal sample
2 m
))
224
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
Table 3 Characteristics and application conditions of determination standard for flow characteristic parameters. Standard
Organization/ nation
Convergent nozzle, flow-rate characteristic index
ISO6358:1989
ISO
C, b
Mass flow calculation formula
Characteristics and applicable conditions
∗ ⎧ P1/ P0 ≤ b: = CρP0 293.15 qm T0 ⎪ ⎨ P1 / P 0 − b ∗⎛ ⎪ b < P1/ P0 ≤ 1: qm = qm 1 − 1−b ⎝ ⎩
(
GB/T14513:1993
FESTO942029:1997
China
Germany
B, S
P
∗ = 0.0404 0 S qm ⎧ P1/ P0 ≤ b: T0 ⎪ P1 / P 0 − b ⎨ ∗⎛ ⎪ b < P1/ P0 ≤ 1: qm = qm 1 − 1−b ⎝ ⎩
C, b
⎧ P1/ P0 ≤ b: ⎪
) ⎞⎠
∗ qm = CP0total
293.15 T0
⎜
Japan
S
2 0.5
(
⎨ ∗⎛ ⎪ b < P1/ P0 ≤ 1: qm = qm 1 − ⎝ ⎩ JISC9312:2005
2 0.5
) ⎞⎠
(
0.5 P1total / P0total − b 2⎞ 1−b
)⎠ ⎟
k+1 2 2(k − 1) P0 S k+1 T0
1
⎧ P S k 2 ∗ qm =C 0 = ⎪ P1/ P0 ≤ b: R T0 ⎪ ⎨ 2k ⎡ ∗ P0 S ⎪ b < P1/ P0 ≤ 1: qm = qm RT0 k − 1 ⎢ ⎪ ⎢ ⎣ ⎩
()( ) 2 P1 k P0
( ) −( )
ISO6358–1:2013
ISO
C, b, m
∗ ⎧ P1/ P0 ≤ b: = CρP0 293.15 qm T0 ⎪ ⎨ P1 / P 0 − b ∗⎛ ⎪ b < P1/ P0 ≤ 1: qm = qm 1 − 1−b ⎝ ⎩
(
Symbols
SI unit
Critical back-pressure ratio Conductance Sonic conductance Subsonic index Downstream absolute static pressure Downstream absolute total pressure Upstream absolute static pressure Upstream absolute total pressure Critical absolute static pressure Critical absolute total pressure Mass flow rate Choked mass flow rate Gas constant (for a perfect gas) Absolute stagnation temperature Mass density Effective cross-sectional area of the nozzle Adiabatic index
b Ce C m P1 P1total P0 P0total P∗ P∗total qm q*m R T0 ρ S k
– m3/(s·Pa) (ANR) m3/(s·Pa) (ANR) m3/(s·Pa) (ANR) Pa Pa Pa Pa Pa Pa kg/s kg/s J/(kg·K) K kg/m3 m2 –
k+1 k ⎤
⎥ ⎥ ⎦
pressure, temperature, mass flow and downstream pressure after stabilization. The relationship between the back-pressure ratio P1/ P0 and the conductance Ce during the gradual reduction of mass flow rates of three different-sized nozzles is shown in Fig. 4, where the abscissa and the ordinate represent back-pressure ratio and conductance, respectively. As can be seen from Fig. 4, as gas pressure in the tank decreases, the back-pressure ratios grow gradually, while the conductance of nozzles fall. The flow characteristic curve of the 1 mm-diameter convergent nozzle is given in Fig. 4a, where the left side of coordinate area is the chocked flow region while the right side is the subsonic flow area. The critical back-pressure ratio refers to the back-pressure ratio at the turning point of gas flow state at the nozzle from the chocked flow region to the subsonic flow region. The conductance which is theoretically constant in the chocked flow region is called the sound conductance. The flow characteristic curves of three different-sized convergent nozzles were presented in Fig. 4b, in which the larger the conductance value, the greater the flow capacity of the nozzle. Based on these data, the flow characteristic parameters of three different-sized convergent nozzles were obtained, as listed in Table 5 (ISO6358–1:2013). It can be seen from Table 5 that with the rise of nozzle diameter, its sound conductance increases correspondingly, that is, the flow capacity of the nozzle is gradually enhanced. The critical back-pressure ratio of
Table 4 Symbols and units of the flow-rate characteristic parameters. Description
2 m
) ⎞⎠
P1 P0
This method calculates the mass flow based on the pressure drop using the sound conductance C and the critical back-pressure ratio b. The method treats the subsonic flow curve at the convergent nozzle as a 1/ 4 ellipse. This method measures the effective cross-sectional area S in the critical state according to the constant volume sound velocity deflation method and then calculates the critical mass flow based on the S value obtained. Its subcritical mass flow is the same as that of ISO6358:1989. This method is essentially the same as ISO6358:1989; the sound conductance C and the critical back-pressure ratio b measured by the two methods can be interconverted. However, the corresponding test environment is the reference state, and in addition, the density is absent. This method measures the effective cross-sectional area S of the nozzle according to the constant volume sound velocity deflation method and then calculates the critical mass flow on the basis of S. However, the S value obtained, which is constant in both critical and subcritical states, cannot reflect the change of effective cross-sectional area in the subcritical state; thus, this approach is not suitable for testing conditions crossing critical and subcritical states. This method adds subsonic velocity index m on the basis of ISO6358:1989 and corrects the flow curve in the subcritical state.
throttle valve was adjusted to first raise and then lower the mass flow rate of gas that passed through the measuring components. Meanwhile, three points in the chocked flow region and five points in the subsonic state were selected in the process to determine parameters of upstream
Fig. 2. Schematic diagram of the testing system: 1-compressed gas source, 2-filter, 3-adjustable pressure regulator, 4 -valve, 5-flow sensor, 6temperature measuring tube, 7-temperature sensor, 8-upstream pressure-measuring tube, 9pressure sensor, 10- convergent nozzle, 11downstream pressure-measuring tube, 12-flow control valve. 225
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
Fig. 3. Physical diagram of testing system. Table 5 Determination results of the flow-rate characteristic parameters. Nozzle diameter
1 mm 2 mm 3 mm
Gas type
CH4
10−9m3/(s·Pa)
Critical backpressure ratio b
Subsonic index m
1.70 7.17 12.57
0.552 0.551 0.550
0.5 0.5 0.5
Sound conductance C
nozzles are all 0.5 which is the same as the expression in ISO6358:1989, indicating that the flow curve at the convergent nozzle adopted in this testing system follows the 1/4 ellipse distribution in subsonic state. 3.2. Processing of gas desorption data of coal According to the variation curves of total pressure and total temperature in the tank over time during desorption of coal sample, the attenuation law of mass flow passing through the nozzle over time can be obtained based on the flow characteristic expression of convergent nozzle given in ISO6358–1:2013. Then, the initial gas desorption law of coal can be acquired. Fig. 5a shows the change curves of desorbed gas flow rates of coal sample and dead space and dead space with time for the WS coal sample charged with 6.0 × 105 Pa CH4. Of the two curves, the desorbed gas flow curve of coal sample and dead space was obtained after the sample was loaded into the sample tank, while that of dead space was measured after steel balls with the same volume of coal sample were loaded into the tank. It can be observed from Fig. 5a that in the two cases, the mass flow rates of gas passing through the nozzle both decline gradually over time, which corresponds to decrease of gas pressure in the tank over time. In Fig. 5a, the width of the curve, which represents the fluctuation of data, gradually widens with the lowering of gas pressure, indicating the gradually growing relative error of data collected by the high-pressure sensor. At this time, the low-pressure sensor starts to collect pressure parameters in the tank in place of the highpressure sensor. As can be found from Fig. 5a, due to the switchover between the two pressure sensors, the mass flow rates in both curves undergo slight drops when they fall to the same value. Fig. 5b shows the gas desorption curve of coal over time, which is obtained by subtracting the data in the dead space curve from those in the coal sample and dead space curve at the same time points. From the perspective of curve shape, a flow peak appears at the initial stage of coal sample exposure. This is because the concentrated gas release from the dead space in the tank postpones the gas desorption and release in the sample to some extent. Besides, some fluctuation occurs before the
Fig. 4. Relationship curve between back-pressure ratio and conductance.
ideal gas is merely related to the physical parameters of gas. However, the actual measured critical pressure is usually smaller than the theoretical value, and both values are particularly close, because the gas will undergo a certain energy loss while flowing through the pneumatic component. The subsonic index is used to correct the flow curve in subsonic flow region. The results obtained at the three different-sized 226
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
Fig. 6. Gas desorption law of coal sample at three nozzles with different diameters.
durations for the influences of dead space are both reduced to shorter than 1 s whose impact on the determination results is negligible compared with other determination methods. 3.4. Influence of metamorphic degree and experimental pressure on determination results of gas desorption law For coal, the higher the metamorphic degree, the stronger the gas adsorption capacity, and thus the larger the gas adsorption amount under the same pressure. With the rise of experimental pressure, the amounts of gas in dead space and gas adsorbed in coal will both increase. These variations will also affect the determination of initial gas desorption law. To investigate whether the laws and conclusions obtained in this study are applicable to the coal sample of other metamorphic degree under various experimental pressures, the KZD coal sample with a low metamorphic degree from Anhui Province was selected for performing a comparative experiment under different gas pressures. Fig. 7 exhibits the appearance times for flow peaks of three nozzle diameters for WS and KZD coal samples under 0.6 MPa and 1.1 MPa, respectively. It can be seen from Fig. 7 that both the metamorphic degree of coal and the experimental gas pressure have an impact on the peak appearance time. The decline of either the metamorphic degree of
Fig. 5. Determination data of gas desorption law of WS coal sample.
appearance of flow peak, which is caused by the same reason for the occurrence of slight drops in Fig. 5a. The left side of the peak can be regarded as the dead space influence zone, whereas the right side represents the normal desorption zone. In the dead space influence zone, the gas desorption flow of coal exhibits a gradual ascending trend, because the gas in the dead space can be released directly outside upon the opening of the nozzle while the gas in the coal cannot be released outside until it undergoes a transition from the adsorption state to the free state. The earlier the peak appearance time, the smaller the influence of dead space on the determination results. 3.3. Influence of nozzle size on determination results of gas desorption law The time needed for the release of the dead space can be shortened by raising the nozzle diameter, so that its influence on the gas determination results of initial gas desorption law of coal can be weakened. To this end, in addition to 1 mm-diameter nozzle adopted previously, this study also used 2 mm and 3 mm nozzles to determine the desorption law of WS coal sample under 6.0 × 105 Pa, so as to investigate the effect of nozzle size on determination results of gas desorption law, as shown in Fig. 6. For the convenience of observation, the curves of the first 6 s were acquired. It can be seen from Fig. 6 that the larger the nozzle diameter, the shorter the appearance time of flow peak. The flow peaks of nozzles with diameters of 3 mm, 2 mm and 1 mm appear for 0.44 s, 0.81 s and 3.64 s, respectively. This suggests that the rise of nozzle size can indeed reduce the effect of dead space on the gas desorption of coal and thus improve the accuracy of determination results. A further analysis of the data shows that when the nozzle diameters are 2 mm and 3 mm, the
Fig. 7. Flow peak appearance times of three nozzle diameters for the two coal samples. 227
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
ISO 6358–1:2013 can correct the flow curve in subsonic region, which can improve the accuracy of determination results. 2) When the method proposed in this paper is applied to the determination of initial gas desorption law of coal, a flow peak appears in each desorption curve at the early stage of coal sample exposure. This is because after the sudden opening of the valve on the coal sample tank, the concentrated release of compressed gas from the dead space in the tank postpones gas desorption in the coal to some extent. 3) The earlier the flow peak appearance time, the smaller the influence of gas release from dead space on the determination results. Nozzle diameter, experimental pressure and metamorphic degree will all affect the peak appearance time, and nozzle diameter is the most influential factor. 4) When the nozzle diameter rises to 2 mm, the flow peak appearance times of coal samples with different metamorphic degrees measured under the pressures of 0.6 MPa and 1.1 MPa have been reduced to shorter than 1 s, suggesting that the present testing method and system are fully applicable to the determination of initial gas desorption law of coal under various conditions.
Fig. 8. Relationship between difference in peak appearance times and nozzle diameter under different experimental gas pressures.
Acknowledgments coal or the experimental gas pressure can advance the appearance of flow peak, but their influences are almost negligible compared with that of nozzle diameter. When the nozzle diameter rises to 3 mm, the peak appearance time depends only on the experimental gas pressure rather than the metamorphic degree, because the coal with a higher metamorphic degree can adsorb a larger amount gas under the same pressure. When the valve on the tank is suddenly opened, the gas adsorbed in coal and the gas in the dead space scramble to be released to the outside, eventually postponing the appearance of flow peak. However, this influence will gradually weaken with the rise of nozzle diameter, and consequently the peak appearance time depends only on the amount of gas in dead space, namely, the experimental gas pressure. To further investigate the effect of gas pressure on the flow peak appearance time, the differences in peak appearance times of three nozzle diameters for the two samples under different gas pressures were tested, as shown in Fig. 8, where ΔT reflects the effect of gas pressure on the peak appearance time. Fig. 8 suggests the negative exponential distribution between ΔT and the nozzle diameter. In addition, as the metamorphic degree of coal grows, the effect of gas pressure on the peak appearance time becomes smaller. Based on the above analyses of Figs. 7 and 8, the three factors that affect the determination results can be ranked according to the weights of their influences: nozzle diameter > experimental pressure > metamorphic degree. Among the three factors, the nozzle diameter exerts far more influence than the other two factors. By raising the nozzle diameter, the flow peak appearance time can be shortened, and the influence of concentrated gas release in the dead space on the determination results can be reduced. However, as the nozzle diameter increases, the peak appearance time reduces at a lower rate, while the requirement for pressure sensor grows exponentially. That is, under certain conditions of sensor accuracy and acquisition frequency, the reduction of the influence of dead space gas on the determination results by raising the nozzle diameter is not limitless. For the present testing system, when the nozzle diameter is 2 mm, the peak appearance times of coal samples with different metamorphic degrees measured under the pressures of 0.6 MPa and 1.1 MPa have been reduced to shorter than 1 s. Compared with previous determination methods, the method proposed in this paper has achieved much more accurate results.
The authors are grateful to the Natural Science Foundation of Jiangsu Province (BK20150180), the Natural Science Foundation of Jiangsu Province (BK20150195), and the Natural Science Foundation of Jiangsu Province (BK20150181). The authors would like to thank the editor and the anonymous reviewers for their careful review of this paper. References Alexeev, A.D., Feldman, E.P., Vasilenko, T.A., 2007. Methane desorption from a coal-bed. Fuel 86, 2574–2580. Busch, A., et al., 2003. Methane and CO2 sorption and desorption measurements on dry Argonne premium coals: pure components and mixtures. Int. J. Coal Geol. 55 (2e4), 205–224. FESTO 942029, 1997. Flow Rate Measurement. GB/T14513, 1993. Pneumatic Fluid Power-determination of Flowrate Characteristics of Pneumatic Components. Gruszkiewicz, M.S., et al., 2009. Adsorption kinetics of CO2, CH4, and their equimolar mixture on coal from the Black Warrior Basin, West-Central Alabama. Int. J. Coal Geol. 77 (1e2), 23–33. Guan, P., Wang, H.Y., Zhang, Y.X., 2009. Mechanism of instantaneous coal outbursts. Geology 37, 915–918. ISO/DIS 6358, 1989. Pneumatic Fluid Power-components Using Compressible FluidsDetermination of Flow-rate Characteristics. ISO 6358–1, 2013. Pneumatic Fluid Power-Determination of Flow-rate Characteristics of Using Compressible Fluids. Jian, X., Guan, P., Zhang, W., 2012. Carbon dioxide sorption and diffusion in coals: experimental investigation and modeling. Sci. China Earth Sci. 55, 633–643. Jiang, C.L., Xu, L.H., Li, X.W., Tang, J., Chen, Y.J., Tian, S.X., Liu, H.H., 2015. Identification model and indicator of outburst-prone coal seams. Rock Mech. Rock Eng. 48, 409–415. JISC 9312, 2005. Japanese Industrial Standards. Kissell, F.N., Meculloch, 1973. The Direct Method of Determining Methane Content of Coalbeds for Ventilation Design. U.S. Bureau of Mines Report of Investigations RI7767. Li, D., et al., 2010. High-pressure sorption isotherms and sorption kinetics of CH4and CO2 on coals. Fuel 89 (3), 569–580. Liu, O., Liu, L.H., 2001. Interchangeability and Measurement Technology Foundation. Harbin Institute of Technology Press. Ma, D.M., Wei, B., Cai, Z.Y., 2008. Experimental study of coalbed methane desorption. Acta Geol. Sin. 82 (10), 1432–1436. Pillalamarry, M., et al., 2011. Gas diffusion behavior of coal and its impact on production from coalbed methane reservoirs. Int. J. Coal Geol. 86 (4), 342–348. Saghafi, A., Faiz, M., Roberts, D., 2007. CO2 storage and gas diffusivity properties of coals from Sydney Basin, Australia. Int. J. Coal Geol. 70, 240–254. Sullivan, D.A., 1981. Historical review of real-fluid isentropic flow models. J. Fluid Eng. 103, 258–267. Zhang, Y.Y., 1999. Fluid Mechanics, second ed. Higher Education Press. Zhang, S.H., Xu, W.C., 2015. Comments and proposals on ISO6358-1 in-line test. Hyd. Pneum. Seals (6), 75–80.
4. Conclusions 1) Compared with other methods of characterizing flow characteristics,
228
Contents lists available at ScienceDirect
Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
Determination method of initial gas desorption law of coal based on flow characteristics of convergent nozzle
T
Yujia Chena,b,c, Dingding Yanga,b,c,∗, Jun Tanga,b,c, Xiaowei Lia,b,c, Chenglin Jianga,b,c a
Key Laboratory of Gas and Fire Control for Coal Mines, Xuzhou, Jiangsu 221116, China National Engineering Research Center of Coal Gas Control, Xuzhou, Jiangsu 221116, China c School of Safety Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221116, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Coal and gas outburst Initial desorption Flow characteristics Convergent nozzle Pneumatic component
The amount of initial gas release after the destruction of coal by ground stress relates closely to the outburst danger. In this paper, the following method was proposed to accurately determine the initial gas desorption law of coal. First, real-time temperature and pressure data of sealed coal sample tank after the sudden exposure of coal that had reached adsorption equilibrium within the tank were collected first via a high-precision, highfrequency response sensor. Then, the mass flow of gas passing through the pneumatic component at different times was calculated according to flow rate characteristics of pneumatic component that communicated with the atmosphere on the tank. In this process, it is determined that a convergent nozzle with a larger contraction ratio should be used as the channel for gas desorption and release. Moreover, in light of the characteristics of the testing process, the existing parameters that characterize the flow characteristics of pneumatic component were optimized and measured. Finally, the initial gas desorption laws of two coal samples with different metamorphic degrees were measured and analyzed under two pressures using three different-sized convergent nozzles.
1. Introduction The gas desorption law of coal is one of the important subjects for studying coal bed methane exploitation and coal and gas disaster prevention and control. By using a diffusion equation to describe gas desorption process of coal (Kissell and Meculloch, 1973), United States Bureau of Mines (USBM) found that the amount of gas accumulated in the early desorption process was proportional to the square root of time. Based on this finding, Kissell then established the industry standard for the determination of coal seam gas content, namely, the USBM desorption method, which has been widely used in various countries. In addition, this method is the basis for studying methods and indicators of coal and gas outburst prediction (Alexeev et al., 2007). According to the spherical shell instability mechanism of coal and gas outburst, the amount of initial gas release after the destruction of coal by ground stress relates closely to the outburst danger (Jiang et al., 2015). When the coal containing high-pressure gas is suddenly exposed to atmospheric environment, the high-pressure gas within it gets released and desorbed outwards. With large amounts of gas desorbed and released at the initial stage of coal exposure, the gas desorption rate and amount both drop rapidly. During the process, the rapid gas release in a short period of time and the sharp drop of gas pressure bring huge
∗
difficulties to the determination. Considering the important role of initial gas desorption law of coal, scholars at home and abroad have conducted in-depth laboratorial studies on its determination methods which, according to the principle of determination, can be divided into volumetric method, gravimetric method, etc. (Busch et al., 2003; Gruszkiewicz et al., 2009; Li et al., 2010; Pillalamarry et al., 2011). Among these methods, the volumetric method mostly determines the change of desorption amount over time via a gas gathering system after the release of gas pressure in the coal sample tank (Saghafi et al., 2007; Ma et al., 2008). However, this method can hardly obtain the gas desorption law during the initial seconds of sample exposure, yet this part of gas release is often closely related to gas disasters. The gravimetric method which determines the variation of gas content in coal samples via a microbalance (Guan et al., 2009; Jian et al., 2012) is unable to determine gas desorption law at the initial sudden gas pressure release of coal exposure, either. In this paper, real-time temperature and pressure data of sealed coal sample tank after the sudden exposure of coal that had reached adsorption equilibrium within the tank were collected first via a highprecision, high-frequency response sensor. Then, the mass flow of gas passing through the pneumatic component at different times was calculated according to flow rate characteristics of pneumatic component
Corresponding author. Key Laboratory of Gas and Fire Control for Coal Mines, Xuzhou, Jiangsu 221116, China. E-mail address: [email protected] (D. Yang).
https://doi.org/10.1016/j.jlp.2018.04.002 Received 5 December 2017; Received in revised form 19 March 2018; Accepted 3 April 2018 Available online 06 April 2018 0950-4230/ © 2018 Elsevier Ltd. All rights reserved.
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
Fig. 1. Schematic diagram of experimental device: 1-gas cylinder, 2-pressure-reducing valves, 3-pipeline, 4, 5, 9, 10-valves, 6-vacuum pump, 7-pressure gauge, 8low-pressure sensor, 10-solenoid valve, 12-high-pressure sensor, 13-pneumatic valve, 14-convergent nozzle, 15-filter, 16-thermostatic bath.
that communicated with the atmosphere on the tank. Furthermore, the problems existing therein were studied. In this way, the initial gas release law of coal containing high-pressure gas can be obtained scientifically and accurately.
⎧ ⎪ ⎪ qm = ⎨ ⎪S ⎪ ⎩
2.1. Experimental principle The core of the proposed determination method lies in the selection of pneumatic component on the coal sample tank and the determination of flow characteristics. Considering characteristics of determination process, a convergent nozzle with a larger contraction ratio was chosen as the channel for gas desorption and release. The specific reasons are as follows: When a convergent nozzle is used, the one-dimensional compressible unsteady flow field can be maintained within the nozzle after the valve is suddenly opened. The large contraction ratio means that the nozzle is very short, so the high-speed airflow has no time to exchange heat with the outside world when it flows within the nozzle. Moreover, since the frictional resistance is negligible, the gas flow within the nozzle can be approximately regarded as an isentropic flow with constant total pressure of gas flow line along the nozzle. According to the Bernoulli equation of isentropic airflow, the mass flow of gas passing through the convergent nozzle (Sullivan, 1981; Zhang, 1999) can be obtained, as shown in Eq. (1):
qm = S
2k P − ⎛ 1⎞ P0 ρ ⎜ ⎜ ⎝ P0 ⎠ k−1 ⎝ P0 ⎠ ⎝ ⎜
⎟
⎜
⎟
( ) −( ) ⎝ P1 P0
k+1 k ⎞ ⎟
⎠
P1 > P ∗ (2)
2.2. Experimental device Independently developed by China University of Mining and Technology, the experimental device was equipped with several major functions, including adsorption and desorption, data acquisition and temperature control, as shown in Fig. 1. A convergent nozzle was connected above the coal sample tank made of stainless steel, and its switch was controlled by a pneumatic valve that would be smoothly connected with the nozzle when the valve opened. A filter was arranged between the coal sample within the tank and the convergent nozzle to prevent the pulverized coal from blocking the pipe during the sudden pressure relief in the tank. Two pressure sensors and a temperature sensor were connected to the tank to acquire the total pressure and total temperature within the tank. Due to the wide range of pressure changes in the determination process, the pressure data were acquired in segments via high-pressure and low-pressure sensors. When the total pressure got below 2 KPa, the low-pressure channel was switched on through the electromagnetic
k+1 k ⎞
⎟⎟ ⎠
2 P 2k P ρ⎛ 1 k k − 1 0 ⎜ P0
P1 ≤ P ∗
kρP0
At the same time, the flow velocity in the tank can be minimized by the convergent nozzle due to its large contraction ratio, so that the total pressure and total temperature of gas flow can be measured directly by the pressure and temperature sensors on the tank. In the whole flowing process, the pressure outside the nozzle remains constant at atmospheric pressure P1, while the total gas pressure P0 in the tank decreases gradually over time. By setting up the above experimental device in the laboratory, the relation curves of total pressure and total temperature in the tank over time under different conditions can be measured. The attenuation law of mass flow of gas passing through the nozzle over time can be obtained by combining the flow characteristics at the convergent nozzle. Furthermore, the initial gas desorption law of coal can be acquired. The flow characteristic here refers to the relationship between the pressure drop from the nozzle inlet to outlet and the flow passing through the pneumatic element when the fluid flows from the nozzle inlet to the outlet (Liu and Liu, 2001).
2. Experimental
2 ⎛ P1 k ⎛ ⎞
k+1 2 2(k − 1) S k+1
( )
(1)
When the external pressure P1 is lower than the critical pressure P ∗, the flow velocity at the convergent nozzle reaches the sound velocity, making the pressure wave velocity still relative to the nozzle. Consequently, the pressure difference cannot be transmitted to the inside of the tank nozzle, so the flow remains critical and constant. Eq. (1) can be converted to Eq. (2), where k is the adiabatic index and S is the effective cross-sectional area of the nozzle.
223
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
experimental device shown in Fig. 1, the mass flow of gas flowing through the nozzle at different time points can be calculated based on the flow characteristics of convergent nozzle. The flow characteristics of pneumatic component can be characterized by many parameters. Usually, countries will make their own corresponding regulations of pneumatic component parameters (ISO6358:1989; GB/T14513:1993; FESTO942029:1997; JISC9312:2005; ISO6358–1:2013). Table 3 lists the characteristics and applicable conditions of flow characteristic parameters specified in different standards, and Table 4 gives the meanings and units of the parameters involved in this study. Based on the results of comparative analysis of various methods, it was determined that the sonic conductance C, the critical back-pressure ratio b and the subsonic index m in ISO6358–1:2013 were adopted to comprehensively express the flow characteristics of the convergent nozzle. Besides, they were taken as the basis for the determination of initial gas desorption law of coal, as shown in Eq. (3).
Table 1 Sensor parameters. Sensor type
Range
Accuracy
Model
Origin
High-pressure Low-pressure Temperature
2 MPa 2 KPa 0–60 °C
< 0.04% FS < 0.25% FS < 0.2% FS
PMP4070 HM26-2-V1-F0-W1 A12
United States Germany United States
valve, so as to ensure the accuracy of pressure data acquisition. To precisely reflect the rapid changes of gas pressure in the early stage of coal exposure within the tank, the data acquisition interval of sensors was set to 1.6 ms which was far smaller than the data acquisition interval adopted by previous determinations (Busch et al., 2003; Gruszkiewicz et al., 2009; Li et al., 2010; Pillalamarry et al., 2011). The models and accuracies of the selected sensors are listed in Table 1. 2.3. Experimental process
⎧ P1/ P0 ≤ b: qm∗ = CρP0 293.15 T0 ⎪ ⎨ b < P / P ≤ 1: q = q ∗ 1 − P1 / P0 − b 1 0 m ⎪ m 1−b ⎩
( (
For determining the initial gas desorption law of coal, the prepared coal sample was firstly weighed and then loaded into the sample tank. Next, air tightness of the device was checked. After the device passed the check, the vacuum pump was started to vacuumize the coal sample for 8 h. When pressure within the tank was reduced to lower than 10 Pa, high-pressure CH4 was then injected into the tank to allow it to adsorb on the coal sample for 24 h. While the adsorption equilibrium was reached, the pneumatic valve was opened, and meanwhile the data acquisition program started to acquire the data. Then, the coal sample was removed from the tank and steel balls of the same volume were loaded in the tank to repeat the above procedure. After the test program was started, the computer would automatically record and save parameters including the total pressure and total temperature in the tank, acquisition time, acquisition frequency etc. In this way, the change laws of acquired pressure and temperature over time under the same pressure and two different conditions (coal samples and dead space, dead space) were obtained. The experimental coal samples included anthracite with high metamorphic degree from WS coal mine in Guizhou Province, China and gas coal with low metamorphic degree from KZD mine in Anhui Province, China. Basic parameters of the samples are listed in Table 2. Since the determination process not only requires repeated experiments and vacuum pumping but also lasts for a long time, it may be affected by changes in factors such as the pore structure, mass loss, temperature and moisture of coal. To address this issue, the following measures were taken: First, the sample taken on site was screened, after which about 300 g of coal particles with sizes of 3–5 mm was chosen as the experimental object. Second, a thermostatic bath was employed to keep constant temperature of the sample tank. Third, the sample was continuously vacumized for 48 h before the experiment, so that its internal moisture would no longer decrease under the effect of vacuum pumping.
3.1. Determination flow characteristic parameters of the convergent nozzle In order to determine flow characteristic parameters of the convergent nozzle, this study built an experimental platform according to the requirements of ISO6358–1:2013 for measuring the sonic conductance C, the critical back-pressure ratio b and the subsonic index m. The schematic diagram of the system is presented in Fig. 2 (ISO6358–1:2013). Before the test started, the circuit system should be connected to the power supply first to preheat the sensors for at least 10 min, so as to ensure the stability of the output voltage and reduce measurement error. Furthermore, it is necessary to detect the air tightness of the testing system and calibrate the sensors. During the test, the high-pressure gas passed successively through the gas filter, the pressure relief valve, the flow sensor, the temperature measuring tube, the pressure measuring tube and other components before it flowed to atmosphere through the convergent nozzle. Among these components, the filter was used for removing water vapor, small particles, oil and other impurities from the gas; the pressure relief valve for adjusting the upstream gas flow of the nozzle; the flow sensor for measuring the flow rate in the gas channel; the temperature sensor in the temperature measuring tube for measuring the temperature of gas flow; the downstream throttle valve for adjusting both the gas flow rate through the nozzle and the pressure; the upstream and downstream pressure sensors for measuring the pressure change during the experiment. The filter, pressure relief valve, precise pressure regulating valve and flow sensor used in the laboratory were all produced by FESTO Company in Germany. The high-precision pressure sensor was produced by GE Company in the United States. The temperature sensor which was made in China was characterized by high frequency and high precision. The switch actuator of convergent nozzle was manufactured by OMAL Company in Italian. The real testing system is exhibited in Fig. 3. According to the requirements of ISO6358–1:2013, with the upstream absolute pressure set at about 6 × 105 Pa, the downstream
After total temperature and total pressure of gas in the sample tank during gas desorption of coal samples were measured using the Table 2 Coal sample parameters. Coal rank
Ash
Moisture
Volatile matter
Adsorption constant a
Adsorption constant b
WS KZD
Anthracite Gas coal
26.71 25.92
1.86 2.17
10.49 30.36
25.58 16.54
1.43 0.917
(3)
There are two benefits for this choice. First, based on Sanville's assumption that the flow characteristic curve approximates a 1/4 ellipse, the flow characteristic curve can be expressed only by using several characteristic parameters. In addition, different from standards like ISO6358, FESA20942029 and GB/T14513, ISO6358–1:2013 introduces the subsonic index m to describe the effect of flow channel changes within the pneumatic component on determination results in the determination process (Zhang and Xu, 2015).
3. Data processing and analysis
Coal sample
2 m
))
224
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
Table 3 Characteristics and application conditions of determination standard for flow characteristic parameters. Standard
Organization/ nation
Convergent nozzle, flow-rate characteristic index
ISO6358:1989
ISO
C, b
Mass flow calculation formula
Characteristics and applicable conditions
∗ ⎧ P1/ P0 ≤ b: = CρP0 293.15 qm T0 ⎪ ⎨ P1 / P 0 − b ∗⎛ ⎪ b < P1/ P0 ≤ 1: qm = qm 1 − 1−b ⎝ ⎩
(
GB/T14513:1993
FESTO942029:1997
China
Germany
B, S
P
∗ = 0.0404 0 S qm ⎧ P1/ P0 ≤ b: T0 ⎪ P1 / P 0 − b ⎨ ∗⎛ ⎪ b < P1/ P0 ≤ 1: qm = qm 1 − 1−b ⎝ ⎩
C, b
⎧ P1/ P0 ≤ b: ⎪
) ⎞⎠
∗ qm = CP0total
293.15 T0
⎜
Japan
S
2 0.5
(
⎨ ∗⎛ ⎪ b < P1/ P0 ≤ 1: qm = qm 1 − ⎝ ⎩ JISC9312:2005
2 0.5
) ⎞⎠
(
0.5 P1total / P0total − b 2⎞ 1−b
)⎠ ⎟
k+1 2 2(k − 1) P0 S k+1 T0
1
⎧ P S k 2 ∗ qm =C 0 = ⎪ P1/ P0 ≤ b: R T0 ⎪ ⎨ 2k ⎡ ∗ P0 S ⎪ b < P1/ P0 ≤ 1: qm = qm RT0 k − 1 ⎢ ⎪ ⎢ ⎣ ⎩
()( ) 2 P1 k P0
( ) −( )
ISO6358–1:2013
ISO
C, b, m
∗ ⎧ P1/ P0 ≤ b: = CρP0 293.15 qm T0 ⎪ ⎨ P1 / P 0 − b ∗⎛ ⎪ b < P1/ P0 ≤ 1: qm = qm 1 − 1−b ⎝ ⎩
(
Symbols
SI unit
Critical back-pressure ratio Conductance Sonic conductance Subsonic index Downstream absolute static pressure Downstream absolute total pressure Upstream absolute static pressure Upstream absolute total pressure Critical absolute static pressure Critical absolute total pressure Mass flow rate Choked mass flow rate Gas constant (for a perfect gas) Absolute stagnation temperature Mass density Effective cross-sectional area of the nozzle Adiabatic index
b Ce C m P1 P1total P0 P0total P∗ P∗total qm q*m R T0 ρ S k
– m3/(s·Pa) (ANR) m3/(s·Pa) (ANR) m3/(s·Pa) (ANR) Pa Pa Pa Pa Pa Pa kg/s kg/s J/(kg·K) K kg/m3 m2 –
k+1 k ⎤
⎥ ⎥ ⎦
pressure, temperature, mass flow and downstream pressure after stabilization. The relationship between the back-pressure ratio P1/ P0 and the conductance Ce during the gradual reduction of mass flow rates of three different-sized nozzles is shown in Fig. 4, where the abscissa and the ordinate represent back-pressure ratio and conductance, respectively. As can be seen from Fig. 4, as gas pressure in the tank decreases, the back-pressure ratios grow gradually, while the conductance of nozzles fall. The flow characteristic curve of the 1 mm-diameter convergent nozzle is given in Fig. 4a, where the left side of coordinate area is the chocked flow region while the right side is the subsonic flow area. The critical back-pressure ratio refers to the back-pressure ratio at the turning point of gas flow state at the nozzle from the chocked flow region to the subsonic flow region. The conductance which is theoretically constant in the chocked flow region is called the sound conductance. The flow characteristic curves of three different-sized convergent nozzles were presented in Fig. 4b, in which the larger the conductance value, the greater the flow capacity of the nozzle. Based on these data, the flow characteristic parameters of three different-sized convergent nozzles were obtained, as listed in Table 5 (ISO6358–1:2013). It can be seen from Table 5 that with the rise of nozzle diameter, its sound conductance increases correspondingly, that is, the flow capacity of the nozzle is gradually enhanced. The critical back-pressure ratio of
Table 4 Symbols and units of the flow-rate characteristic parameters. Description
2 m
) ⎞⎠
P1 P0
This method calculates the mass flow based on the pressure drop using the sound conductance C and the critical back-pressure ratio b. The method treats the subsonic flow curve at the convergent nozzle as a 1/ 4 ellipse. This method measures the effective cross-sectional area S in the critical state according to the constant volume sound velocity deflation method and then calculates the critical mass flow based on the S value obtained. Its subcritical mass flow is the same as that of ISO6358:1989. This method is essentially the same as ISO6358:1989; the sound conductance C and the critical back-pressure ratio b measured by the two methods can be interconverted. However, the corresponding test environment is the reference state, and in addition, the density is absent. This method measures the effective cross-sectional area S of the nozzle according to the constant volume sound velocity deflation method and then calculates the critical mass flow on the basis of S. However, the S value obtained, which is constant in both critical and subcritical states, cannot reflect the change of effective cross-sectional area in the subcritical state; thus, this approach is not suitable for testing conditions crossing critical and subcritical states. This method adds subsonic velocity index m on the basis of ISO6358:1989 and corrects the flow curve in the subcritical state.
throttle valve was adjusted to first raise and then lower the mass flow rate of gas that passed through the measuring components. Meanwhile, three points in the chocked flow region and five points in the subsonic state were selected in the process to determine parameters of upstream
Fig. 2. Schematic diagram of the testing system: 1-compressed gas source, 2-filter, 3-adjustable pressure regulator, 4 -valve, 5-flow sensor, 6temperature measuring tube, 7-temperature sensor, 8-upstream pressure-measuring tube, 9pressure sensor, 10- convergent nozzle, 11downstream pressure-measuring tube, 12-flow control valve. 225
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
Fig. 3. Physical diagram of testing system. Table 5 Determination results of the flow-rate characteristic parameters. Nozzle diameter
1 mm 2 mm 3 mm
Gas type
CH4
10−9m3/(s·Pa)
Critical backpressure ratio b
Subsonic index m
1.70 7.17 12.57
0.552 0.551 0.550
0.5 0.5 0.5
Sound conductance C
nozzles are all 0.5 which is the same as the expression in ISO6358:1989, indicating that the flow curve at the convergent nozzle adopted in this testing system follows the 1/4 ellipse distribution in subsonic state. 3.2. Processing of gas desorption data of coal According to the variation curves of total pressure and total temperature in the tank over time during desorption of coal sample, the attenuation law of mass flow passing through the nozzle over time can be obtained based on the flow characteristic expression of convergent nozzle given in ISO6358–1:2013. Then, the initial gas desorption law of coal can be acquired. Fig. 5a shows the change curves of desorbed gas flow rates of coal sample and dead space and dead space with time for the WS coal sample charged with 6.0 × 105 Pa CH4. Of the two curves, the desorbed gas flow curve of coal sample and dead space was obtained after the sample was loaded into the sample tank, while that of dead space was measured after steel balls with the same volume of coal sample were loaded into the tank. It can be observed from Fig. 5a that in the two cases, the mass flow rates of gas passing through the nozzle both decline gradually over time, which corresponds to decrease of gas pressure in the tank over time. In Fig. 5a, the width of the curve, which represents the fluctuation of data, gradually widens with the lowering of gas pressure, indicating the gradually growing relative error of data collected by the high-pressure sensor. At this time, the low-pressure sensor starts to collect pressure parameters in the tank in place of the highpressure sensor. As can be found from Fig. 5a, due to the switchover between the two pressure sensors, the mass flow rates in both curves undergo slight drops when they fall to the same value. Fig. 5b shows the gas desorption curve of coal over time, which is obtained by subtracting the data in the dead space curve from those in the coal sample and dead space curve at the same time points. From the perspective of curve shape, a flow peak appears at the initial stage of coal sample exposure. This is because the concentrated gas release from the dead space in the tank postpones the gas desorption and release in the sample to some extent. Besides, some fluctuation occurs before the
Fig. 4. Relationship curve between back-pressure ratio and conductance.
ideal gas is merely related to the physical parameters of gas. However, the actual measured critical pressure is usually smaller than the theoretical value, and both values are particularly close, because the gas will undergo a certain energy loss while flowing through the pneumatic component. The subsonic index is used to correct the flow curve in subsonic flow region. The results obtained at the three different-sized 226
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
Fig. 6. Gas desorption law of coal sample at three nozzles with different diameters.
durations for the influences of dead space are both reduced to shorter than 1 s whose impact on the determination results is negligible compared with other determination methods. 3.4. Influence of metamorphic degree and experimental pressure on determination results of gas desorption law For coal, the higher the metamorphic degree, the stronger the gas adsorption capacity, and thus the larger the gas adsorption amount under the same pressure. With the rise of experimental pressure, the amounts of gas in dead space and gas adsorbed in coal will both increase. These variations will also affect the determination of initial gas desorption law. To investigate whether the laws and conclusions obtained in this study are applicable to the coal sample of other metamorphic degree under various experimental pressures, the KZD coal sample with a low metamorphic degree from Anhui Province was selected for performing a comparative experiment under different gas pressures. Fig. 7 exhibits the appearance times for flow peaks of three nozzle diameters for WS and KZD coal samples under 0.6 MPa and 1.1 MPa, respectively. It can be seen from Fig. 7 that both the metamorphic degree of coal and the experimental gas pressure have an impact on the peak appearance time. The decline of either the metamorphic degree of
Fig. 5. Determination data of gas desorption law of WS coal sample.
appearance of flow peak, which is caused by the same reason for the occurrence of slight drops in Fig. 5a. The left side of the peak can be regarded as the dead space influence zone, whereas the right side represents the normal desorption zone. In the dead space influence zone, the gas desorption flow of coal exhibits a gradual ascending trend, because the gas in the dead space can be released directly outside upon the opening of the nozzle while the gas in the coal cannot be released outside until it undergoes a transition from the adsorption state to the free state. The earlier the peak appearance time, the smaller the influence of dead space on the determination results. 3.3. Influence of nozzle size on determination results of gas desorption law The time needed for the release of the dead space can be shortened by raising the nozzle diameter, so that its influence on the gas determination results of initial gas desorption law of coal can be weakened. To this end, in addition to 1 mm-diameter nozzle adopted previously, this study also used 2 mm and 3 mm nozzles to determine the desorption law of WS coal sample under 6.0 × 105 Pa, so as to investigate the effect of nozzle size on determination results of gas desorption law, as shown in Fig. 6. For the convenience of observation, the curves of the first 6 s were acquired. It can be seen from Fig. 6 that the larger the nozzle diameter, the shorter the appearance time of flow peak. The flow peaks of nozzles with diameters of 3 mm, 2 mm and 1 mm appear for 0.44 s, 0.81 s and 3.64 s, respectively. This suggests that the rise of nozzle size can indeed reduce the effect of dead space on the gas desorption of coal and thus improve the accuracy of determination results. A further analysis of the data shows that when the nozzle diameters are 2 mm and 3 mm, the
Fig. 7. Flow peak appearance times of three nozzle diameters for the two coal samples. 227
Journal of Loss Prevention in the Process Industries 54 (2018) 222–228
Y. Chen et al.
ISO 6358–1:2013 can correct the flow curve in subsonic region, which can improve the accuracy of determination results. 2) When the method proposed in this paper is applied to the determination of initial gas desorption law of coal, a flow peak appears in each desorption curve at the early stage of coal sample exposure. This is because after the sudden opening of the valve on the coal sample tank, the concentrated release of compressed gas from the dead space in the tank postpones gas desorption in the coal to some extent. 3) The earlier the flow peak appearance time, the smaller the influence of gas release from dead space on the determination results. Nozzle diameter, experimental pressure and metamorphic degree will all affect the peak appearance time, and nozzle diameter is the most influential factor. 4) When the nozzle diameter rises to 2 mm, the flow peak appearance times of coal samples with different metamorphic degrees measured under the pressures of 0.6 MPa and 1.1 MPa have been reduced to shorter than 1 s, suggesting that the present testing method and system are fully applicable to the determination of initial gas desorption law of coal under various conditions.
Fig. 8. Relationship between difference in peak appearance times and nozzle diameter under different experimental gas pressures.
Acknowledgments coal or the experimental gas pressure can advance the appearance of flow peak, but their influences are almost negligible compared with that of nozzle diameter. When the nozzle diameter rises to 3 mm, the peak appearance time depends only on the experimental gas pressure rather than the metamorphic degree, because the coal with a higher metamorphic degree can adsorb a larger amount gas under the same pressure. When the valve on the tank is suddenly opened, the gas adsorbed in coal and the gas in the dead space scramble to be released to the outside, eventually postponing the appearance of flow peak. However, this influence will gradually weaken with the rise of nozzle diameter, and consequently the peak appearance time depends only on the amount of gas in dead space, namely, the experimental gas pressure. To further investigate the effect of gas pressure on the flow peak appearance time, the differences in peak appearance times of three nozzle diameters for the two samples under different gas pressures were tested, as shown in Fig. 8, where ΔT reflects the effect of gas pressure on the peak appearance time. Fig. 8 suggests the negative exponential distribution between ΔT and the nozzle diameter. In addition, as the metamorphic degree of coal grows, the effect of gas pressure on the peak appearance time becomes smaller. Based on the above analyses of Figs. 7 and 8, the three factors that affect the determination results can be ranked according to the weights of their influences: nozzle diameter > experimental pressure > metamorphic degree. Among the three factors, the nozzle diameter exerts far more influence than the other two factors. By raising the nozzle diameter, the flow peak appearance time can be shortened, and the influence of concentrated gas release in the dead space on the determination results can be reduced. However, as the nozzle diameter increases, the peak appearance time reduces at a lower rate, while the requirement for pressure sensor grows exponentially. That is, under certain conditions of sensor accuracy and acquisition frequency, the reduction of the influence of dead space gas on the determination results by raising the nozzle diameter is not limitless. For the present testing system, when the nozzle diameter is 2 mm, the peak appearance times of coal samples with different metamorphic degrees measured under the pressures of 0.6 MPa and 1.1 MPa have been reduced to shorter than 1 s. Compared with previous determination methods, the method proposed in this paper has achieved much more accurate results.
The authors are grateful to the Natural Science Foundation of Jiangsu Province (BK20150180), the Natural Science Foundation of Jiangsu Province (BK20150195), and the Natural Science Foundation of Jiangsu Province (BK20150181). The authors would like to thank the editor and the anonymous reviewers for their careful review of this paper. References Alexeev, A.D., Feldman, E.P., Vasilenko, T.A., 2007. Methane desorption from a coal-bed. Fuel 86, 2574–2580. Busch, A., et al., 2003. Methane and CO2 sorption and desorption measurements on dry Argonne premium coals: pure components and mixtures. Int. J. Coal Geol. 55 (2e4), 205–224. FESTO 942029, 1997. Flow Rate Measurement. GB/T14513, 1993. Pneumatic Fluid Power-determination of Flowrate Characteristics of Pneumatic Components. Gruszkiewicz, M.S., et al., 2009. Adsorption kinetics of CO2, CH4, and their equimolar mixture on coal from the Black Warrior Basin, West-Central Alabama. Int. J. Coal Geol. 77 (1e2), 23–33. Guan, P., Wang, H.Y., Zhang, Y.X., 2009. Mechanism of instantaneous coal outbursts. Geology 37, 915–918. ISO/DIS 6358, 1989. Pneumatic Fluid Power-components Using Compressible FluidsDetermination of Flow-rate Characteristics. ISO 6358–1, 2013. Pneumatic Fluid Power-Determination of Flow-rate Characteristics of Using Compressible Fluids. Jian, X., Guan, P., Zhang, W., 2012. Carbon dioxide sorption and diffusion in coals: experimental investigation and modeling. Sci. China Earth Sci. 55, 633–643. Jiang, C.L., Xu, L.H., Li, X.W., Tang, J., Chen, Y.J., Tian, S.X., Liu, H.H., 2015. Identification model and indicator of outburst-prone coal seams. Rock Mech. Rock Eng. 48, 409–415. JISC 9312, 2005. Japanese Industrial Standards. Kissell, F.N., Meculloch, 1973. The Direct Method of Determining Methane Content of Coalbeds for Ventilation Design. U.S. Bureau of Mines Report of Investigations RI7767. Li, D., et al., 2010. High-pressure sorption isotherms and sorption kinetics of CH4and CO2 on coals. Fuel 89 (3), 569–580. Liu, O., Liu, L.H., 2001. Interchangeability and Measurement Technology Foundation. Harbin Institute of Technology Press. Ma, D.M., Wei, B., Cai, Z.Y., 2008. Experimental study of coalbed methane desorption. Acta Geol. Sin. 82 (10), 1432–1436. Pillalamarry, M., et al., 2011. Gas diffusion behavior of coal and its impact on production from coalbed methane reservoirs. Int. J. Coal Geol. 86 (4), 342–348. Saghafi, A., Faiz, M., Roberts, D., 2007. CO2 storage and gas diffusivity properties of coals from Sydney Basin, Australia. Int. J. Coal Geol. 70, 240–254. Sullivan, D.A., 1981. Historical review of real-fluid isentropic flow models. J. Fluid Eng. 103, 258–267. Zhang, Y.Y., 1999. Fluid Mechanics, second ed. Higher Education Press. Zhang, S.H., Xu, W.C., 2015. Comments and proposals on ISO6358-1 in-line test. Hyd. Pneum. Seals (6), 75–80.
4. Conclusions 1) Compared with other methods of characterizing flow characteristics,
228