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Fuel 233 (2018) 816–824
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Full Length Article
Dynamic behavior of gas pressure and optimization of borehole length in
stress relaxation zone during coalbed methane production
Chaolin Zhanga,b,c, , Jiang Xua,b,c, Shoujian Penga,b,c, Qixian Lia,b,c, Fazhi Yana,b,c,
Yuexia Chena,b,c
State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400030, China
State and Local Joint Engineering Laboratory of Methane Drainage in Complex Coal Gas Seam, Chongqing University, Chongqing 400030, China
College of Resources and Environmental Science, Chongqing University, Chongqing 400030, China
Coalbed methane (CBM)
Borehole length
Stress relaxation zone (SRZ)
Gas production
Physical simulation
Although coalbed methane (CBM) poses potential safety hazards in coal mines, it can also be used as a clean
energy source. Optimization of the borehole length to maximize gas drainage and efficient use of human and
material resources are key factors that determine the feasibility and cost of CBM production. In addition, three
geo-stress zones are commonly formed in front of the working face due to underground mining activities, namely
the stress relaxation zone (SRZ), stress concentration zone (SCZ), and original stress zone (OSZ). In this study, we
conducted gas drainage experiments in a simulated SRZ to investigate gas pressure dynamic behavior and optimize the borehole length. The gas pressure gradient in the direction perpendicular to the borehole was greater
than that in the direction parallel to the borehole, and the SCZ showed significant hindrance to gas seepage into
the borehole. Longer boreholes resulted in higher gas production; however, the gas production increasing rate
was not stable over time as the borehole length increased. The relationship between gas production and borehole
length is a logarithmic function, which was used to further optimize the borehole length taking mine safety and
economic factors into consideration. The following optimized borehole lengths were obtained under experimental conditions: 155.6–262.5 mm, 129.7–155.6 mm, and 24.5–129.7 mm for short-term, medium-term, and
long-term gas drainage, respectively.
1. Introduction
Coalbed methane (CBM) is a methane-rich gas present in coal seams
and is a source of clean energy that can be exploited either by drilling
boreholes from the surface or from underground coal mines workings
[1,2]. With the commercial development of CBM in the USA in the early
1980s, CBM extraction has received increasing interest from many
countries, including Australia, Canada, India, and China [3,4]. Global
CBM reserves have been estimated to be 84–262 trillion m3, while
China ranks third in the world after Russia and Canada [5–7]. In China,
CBM development can be divided into two classes, surface extraction
and underground gas drainage [8]. To accelerate the development of
the CBM industry in China, a target production of 24 billion m3
(10 billion m3 for surface production and 14 billion m3 for underground
production) has been proposed by the National Energy Administration
in the 13th Five Year Plan for National Energy Development [9,10].
CBM reservoirs in China are characterized by low gas saturation,
low permeability, low reservoir pressure, and a relatively high
metamorphic grade [11]. For example, the permeability of most coal
seams in China ranges from 10−4 to 10−1 mD, which is three to four
orders of magnitude lower than that of most countries in the world
[12,13]. Meanwhile, as coal mining depths increase at an annual rate of
10–50 m in China, both the gas pressure and gas content increase along
with much more complex geological coal structures and geo-stress
states [14,15]. All these factors result in increasingly challenging CBM
production in China.
Although CBM is a clean energy source, it poses potential risks and
hazards in the coal mining process owing to the risk of fire and explosion [16–19]. Fig. 1 shows statistics of the causes of different coal
mine accidents (i.e., gas, roof, flood, fire, electromechanical, transportation, blasting, and others) between 2011 and 2016 in China. It can be
observed that gas-related accidents accounted for approximately 50%
of the incidents, although the total number of accidents decreased every
year this percentage increased slightly. To ensure the health and safety
of coal miners, and improve CBM production, various methods have
been employed to improve the efficiency of CBM extraction, including
Corresponding author at: State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400030, China.
E-mail address: (C. Zhang).
Received 17 April 2018; Received in revised form 17 June 2018; Accepted 30 June 2018
Available online 03 July 2018
0016-2361/ © 2018 Elsevier Ltd. All rights reserved.
Fuel 233 (2018) 816–824
C. Zhang et al.
Fig. 1. Statistics of Chinese coal mine accidents (death of more than 3 people) between 2011 and 2016.
made of metal foam, which allows fast gas adsorption.
CO2-enhanced CBM recovery (CO2-ECBM) [20–22], hydraulic technology for seam permeability enhancement (HTSPE; including hydraulic fracturing [23], hydraulic slotting [24], hydraulic flushing [25],
waterjet technique [26]), deep-hole pre-split blasting [27,28], highvoltage electrical pulse (HVEP) [29], and multi-branched horizontal
wells (MBHWs) technology [17,30]. In addition, gas drainage borehole
patterns were optimized by field tests and numerical simulations
These past developments have shown an increase in CBM yields and
decrease in coal mining accident frequency. Meanwhile, three geostress zones are commonly formed in front of the working face due to
underground mining activities, namely, the stress relaxation zone
(SRZ), stress concentration zone (SCZ), and original stress zone (OSZ)
[34,35]. Gas drainage boreholes are usually positioned in the SRZ
where the permeability is high [36]. However, few studies have focused
on optimizing the borehole length, which is a key factor affecting CBM
production and cost. Improper borehole length will lead to unsatisfactory gas drainage or inefficient use of human and material resources. Considering that field research is usually expensive and timeconsuming, physical simulations are a suitable alternative [37,38]. This
study conducted three gas drainage experiments with different borehole
lengths. Three geo-stress zones were physically simulated and the gas
pressure was measured. The dynamic behavior of the gas pressure was
analyzed and the relationship between the borehole length and gas
production was discussed. In addition, a method for optimizing the
borehole length was proposed.
2.2. Experimental scheme
Fig. 3(a) shows the SRZ, SCZ, and OSZ in front of the working face.
In the OSZ the stress δH equals γH, where γ is the average unit weight of
the overburden and H is the mining depth. In the SCZ, the stress is
higher than δH, while in the SRZ, the stress is lower than δH. A schematic diagram of the stress loading experiments is shown in Fig. 3(b);
σ11, σ12, σ13, and σ14 were 0.9 MPa, 2.6 MPa, 2.6 MPa, and 1.8 MPa,
respectively in the X direction, σ2 was 2.2 MPa in the Z direction, and
σ31, σ32, σ33, and σ34 were 0.7 MPa in the Y direction. The gas pressure
was 0.7 MPa at equilibrium. The values of the in-situ stress and gas
pressure were in accordance with the previous study [39]. The in-situ
stress was loaded throughout the duration of the experiment after vacuum pumping for 8 h, then the coal specimen was saturated by applying injection gas pressure of 0.7 MPa. The gas adsorption time required to saturate the coal specimen was approximately 48 h [40,41].
The gas inlet was closed after the adsorption equilibrium of the coal
specimen, and the gas outlet was opened to initiate the gas production
2.3. Sensor arrangement
The raw coal samples were sourced from the Songzao coal mine,
Chongqing Province, China. Proximate analysis of the coal sample was
carried out according to the Chinese National Standard GB/T212-2008
guidelines [42], which is presented in Table 1. To facilitate the installation of gas pressure sensors within the coal, reconstituted coals
were used to simulate a coal seam. It has been confirmed through laboratory experiments that raw coal and reconstituted coal have similar
geomechanical properties and permeability [40,41,43–46]. Raw coal
was first crushed and then shaped using a pressing machine. The reconstituted coal were divided into four layers, and each layer was
pressed for 1 h under a shaping stress of 7.5 MPa. During the shaping
stage, 32 gas pressure sensors (labeled P1–P32) and a borehole were
placed in the simulated coal seam, as shown in Fig. 4. The gas pressure
sensors were distributed in seven planes perpendicular to the borehole.
For example, P1–P7 were in the z = 919 mm plane, while the x values of
P2–P5 and y values of P1, P4, P6, and P7 were each 205 mm. The z values
of the other six planes were 133, 264, 395, 526, 657, and 788 mm. The
2. Material and methods
2.1. Experimental setup
Fig. 2 shows the photograph and schematic diagram of the experimental setup used in this study, which was developed in our laboratory;
and it consists of the control and data acquisition system, coal specimen
box, loading system, reaction frame, borehole, drainage pipe, flowmeter, gas cylinder, and vacuum pump. The effective dimensions of the
coal specimen box were 1050 mm × 410 mm × 410 mm. The loading
system consists of nine oil cylinders in three directions, which were
used to simulate the three geo-stress zones (SRZ, SCZ, and OSZ). We
used three boreholes with lengths of 45 mm, 90 mm, and 180 mm, each
having a diameter of 6 mm. The bottom of the coal specimen box was
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C. Zhang et al.
Fig. 2. Experimental setup. (a) Photograph, and (b) schematic diagram.
gas pressure values of sensors P1–P32 were numbered P1–P32. For
convenience, Pn (x, y, z) refers to the coordinate of sensor Pn, and Pn (l)
refers to the gas pressure value of sensor Pn at the borehole length of l.
longest borehole (180 mm) and at the lowest rate in the shortest
borehole (45 mm). At the end of the gas drainage period, P1 (90) and
P1 (180) were all approximately 0.02 MPa, while P1 (45) was slightly
higher (0.04 MPa). In addition, P4 (205, 205, 919), P10 (290, 205, 657),
and P19 (290, 205, 395) exhibited a similar trend as P1 (290, 205, 919),
as shown in Fig. 5(b)–(d).
Fig. 6 shows spatial gas pressure plots over time for the 45 mm
borehole. The four gas pressure sensors labeled P1, P4, P6, and P7 were
located parallel to the X axis (see Fig. 4) with X coordinates of 290, 205,
134, and 85, respectively. Fig. 6(a) shows data for P1, P4, P6, and P7 at
1, 10, 30, 60, 120, and 360 min; it can be observed that P7 recorded the
highest pressure, while P4 recorded the lowest pressure over the entire
measurement period. As P7 was located farthest from the borehole and
P4 was the closest sensor, it was concluded that low gas pressures
3. Results and discussion
3.1. Dynamic gas pressure behavior
A total of three tests were conducted using borehole lengths of
45 mm, 90 mm, and 180 mm. The total drainage time was 360 min, as
shown in Fig. 5. Fig. 5(a) shows data for P1 (290, 205, 919) versus time
for different borehole lengths. It can be observed that the gas pressure
decreased rapidly in the initial period, and then decreased slowly in the
later period. The gas pressure decreased at the highest rate in the
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Fig. 3. Experimental scheme. (a) The three geo-stress zones, and (b) stress loading scheme.
zones, the parameter ∇P (the gas pressure gradient between sensors Pm
and Pn) is defined as follows:
Table 1
Proximate analysis result of the coal sample.
Coal source
Songzao coal mine
Proximate analysis (wt%)
∇P =
Note: Mad is the moisture content, Aad is the ash yield, Vad is the volatile matter,
and FCad is the fixed carbon. Subscript “ad” means air-dry basis.
P m−Pn
Pm (x m , ym , z m)−Pn (x n , yn , z n )
|P m−Pn|
(x m−x n )2 + (ym −yn )2 + (z m−z n )2
where Pm and Pn are the gas pressures of two adjacent gas pressure
sensors located parallel to one coordinate axis. Pm (x m , ym , z m) and
Pn (x n , yn , z n ) are the coordinates of sensors Pm and Pn, respectively.
Fig. 7(a) and (b) show the values of ∇P in the X direction (P1, P4, P6,
and P7) and Y direction (P2, P3, P4, and P5), respectively. The seven
gas pressure points were all in the SRZ and showed similar gas pressure
gradient behavior. The ∇P values in the X and Y directions all decreased
from 2.5 MPa/m to 0.1 MPa/m with increasing drainage time. Moreover, for 0 < y < 102.5 mm (Fig. 7(b)), ∇P was significantly smaller
than the values in the other areas, probably due to boundary effects.
Fig. 7(c) shows gas pressure gradients in the Z direction (P1, P8,
P10, P17, P19, P25 and P27). The trend of ∇P in the Z direction was
more complicated than the behavior in the X and Y directions as the gas
pressure sensors were located in three different geo-stress zones. In
(σ11 = 0.9 MPa,
788 < y < 1050 mm) were the highest, followed by those in the SCZ
(σ12 = σ13 = 2.6 MPa, 264 < y < 788 mm), and then the OSZ
occurred close to the borehole in the X direction. Fig. 6(b) shows data
for P2, P3, P4, and P5 sensors located parallel to the Y axis, where the
sensor closest to the borehole also showed the lowest gas pressure.
Fig. 6(c) shows line data for P1, P8, P10, P17, P19, P25, and P27 sensors
located parallel to the Z axis, and with Z coordinates of 919, 788, 657,
526, 395, 264, and 133, respectively. The gas pressure in the SRZ was
slightly lower than the values in the other zones, while the gas pressures
in the OSZ and SCZ were similar. In summary, in the plane perpendicular to the borehole, lower gas pressures were observed close to the
borehole. However, in the plane parallel to the borehole, the gas
pressure variation was not as distinct as in the X and Y directions.
3.2. Evolution of gas pressure gradient
To further elucidate the gas pressure behavior in different stress
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Fig. 4. Schematic diagram of the positions of the gas pressure sensors and borehole in the coal seam.
Consequently, ∇P was higher in this zone than in the other zones in the
early stages. After 60 min of gas drainage, the gas content in the SRZ
decreased, resulting in a lower gas pressure gradient. Nevertheless, the
SCZ had a small permeability, making gas flow in this region difficult
and further preventing gas seepage from the OSZ to the borehole.
(σ14 = 1.8 MPa, 0 < y < 264 mm) before 60 min. Afterwards, the
values of ∇P in the SRZ decreased, while high values were maintained
in the 526 < y < 657 mm area. This is because the permeability in
the SRZ was greater than that in the other zones, thereby creating favorable conditions for gas desorption, diffusion, and seepage [47].
Fig. 5. Gas pressure vs. time for different borehole lengths (45, 90, and 180 mm) measured using sensors. (a) P1, (b) P4, (c) P10, and (d) P19.
Fuel 233 (2018) 816–824
C. Zhang et al.
Fig. 7. Gas pressure gradient vs. distance for the 45 mm borehole measured
using sensors. (a) P1, P4, P6, and P7 in the X direction, (b) P2, P3, P4, and P5 in
the Y direction, and (c) P1, P8, P10, P17, P19, P25, and P27 in the Z direction.
Fig. 6. Gas pressure vs. distance for the 45 mm borehole measured using sensors. (a) P1, P4, P6, and P7 in the X direction, (b) P2, P3, P4, and P5 in the Y
direction, and (c) P1, P8, P10, P17, P19, P25, and P27 in the Z direction.
and 180 mm boreholes, which all decreased to approximately 3.84 L/
min at 73 min, and finally to 0.59 L/min, 0.30 L/min, and 0.08 L/min,
respectively. Compared to the other boreholes, the longer borehole
showed higher q values before 73 min and then lower values after this
point. It was also observed that the longer borehole had higher Q values; Fig. 8(c) shows Q values of 931.93 L, 957.70 L, and 990.72 L after
gas drainage for the 45, 90, and 180 mm boreholes, respectively.
In general, the coal seam is considered to be homogeneous and
isotropic and the gas is extracted through a borehole in the shortest
flow paths during CBM production [48]. The length of the shortest flow
paths would decrease when the length of a borehole increases, leading
to high gas flow rate. At the same time, gas pressure in the coal wall
exposed area of a borehole would immediately decrease to the internal
pressure in the borehole [49]. Hence, the gas flow rate increases as the
length of a borehole increases because of improvement in the coal wall
exposed area. As a result, increasing the borehole length can increase
the gas flow rate and increase in the degree of gas production varies
dynamically as shown in Fig. 8(c). Hence, two parameters were defined
to determine variation in the gas production for different borehole
lengths, as given in Eqs. (2) and (3).
Hence, a local area of high ∇P was formed in the SCZ with slightly
higher values than those in the SRZ. In addition, the ∇P values in the Z
direction were significantly smaller than those in the X and Y directions
(compare Fig. 7(a)–(c)). Therefore, it can be concluded that ∇P in the
direction perpendicular to the borehole was greater than that in the
direction parallel to the borehole, where the SCZ hindered gas seepage
into the borehole.
3.3. Comparison of gas production
Gas production is an important index for measuring gas drainage. It
can be observed from Fig. 8(a) that the gas flow rate q was initially very
high, and then decreased over the drainage time; these data showed a
similar trend to the gas pressure. Consequently, gas production Q first
increased significantly, then became increasingly stable. Fig. 8(b)
compares the values of q for different borehole lengths, showing initial
values of 15.11 L/min, 20.99 L/min, and 24.79 L/min for the 45, 90,
Fuel 233 (2018) 816–824
C. Zhang et al.
Fig. 8. Comparison of gas production. (a) Flow rate q and gas production Q for the 45 mm length borehole, (b) q values for different borehole lengths, (c) Q values for
different borehole lengths, and (d) gas production ΔQ and gas production increase ratio ŋ.
at 85.2 L after 35 min, and decreased to 33.2 L at 360 min. It is clear
that ΔQ (90–45) was the same as ΔQ (180–90) before 20 min, then
became higher between 20 min and 257 min, and lower after 257 min.
In addition, ŋ (90–45) was consistently higher than ŋ (180–90) until
286 min.
We can conclude that the ΔQ and ŋ values were higher when the
borehole length increased from 45 mm to 90 mm than when it increased
from 90 mm to 180 mm in the early and middle stages of gas drainage,
and were only surpassed in the later stage of gas drainage, although the
borehole length doubled in both cases. In other words, a longer borehole yields a higher gas production but does not necessarily yield a
higher production increase ratio; therefore, in terms of economic cost, a
borehole with longer length is not necessarily the best choice.
Fig. 9. Fitting of gas production and borehole length.
ΔQ (l2−l1) = Q (l2)−Q (l1)
η (l2−l1) =
Q (l2)−Q (l1)
× 100%
Q (l1)
3.4. Optimization of borehole length
To quantitatively analyze the relationship between gas production
and borehole length, experimental data for different drainage times
were fitted using a logarithmic function, Q = a × ln(l) + b, as shown in
Fig. 9, where a and b are fitting parameters. All determined coefficients
(R2) were above 0.98 (as presented in Table 2), indicating that the
logarithmic function accurately fits the gas production data. The
parameter a is given by the slope of the curve, which first increased and
then decreased with increasing l, indicating that the gas production
growth rate was not stable over time as the borehole length increases.
From the perspective of coal mine safety, gas pre-drainage efficiency
should not be < 30% [50], while maximum gas drainage is preferable
considering resource development. Therefore, this study proposes a
where l2 and l1 are the lengths of boreholes 2 and l, respectively, while
Q (l2) and Q (l1) are the corresponding gas production. ΔQ (l2-l1) denotes the change in Q when the borehole length changes from l1 to l2,
while ŋ (l2-l1) represents increase in the ratio of Q (l2) compared to Q
(l1). Fig. 8(d) shows ΔQ (90–45) and ΔQ (180–90), along with ŋ
(90–45) and ŋ (180–90). ΔQ (90–45) initially showed a sharp increase,
then peaked at 110.1 L after 73 min, and decreased to 25.8 L at
360 min, while ΔQ (180–90) initially showed a sharp increase, peaked
Fuel 233 (2018) 816–824
C. Zhang et al.
measured, while longer boreholes resulted in faster gas pressure drops
during CBM production. The gas pressure gradient in the direction
perpendicular to the borehole was greater than that in the direction
parallel to the borehole, where the SCZ significantly hindered gas flow
into the borehole. Longer boreholes resulted in higher gas production,
where the gas production increment first increased and then decreased
with increasing borehole length. A method for optimizing the borehole
length was proposed which considered both mine safety and economic
factors. The following optimized results were obtained under experimental conditions using the proposed method: 155.6–262.5 mm,
129.7–155.6 mm, and 24.5–129.7 mm for short-term, medium-term,
and long-term gas drainage, respectively.
It should be noted that the specific optimization results of the
borehole lengths presented in this paper were obtained from the tested
coal sample and under the test conditions in this study. However, the
optimization method can be applied to various experimental conditions
and coal fields, and optimization experiments using different coal
samples and field application should be investigated in the future.
Table 2
Fitting function and fitting parameters.
Fitting function
Time (min)
a (L)
b (L)
Q = a × ln(l) + b
This work was supported by the National Science and Technology
Major Project of China [No. 2016ZX05044-002]; the National Natural
Science Foundation of China [No. 51434003]; the Basic and Frontier
Research Projects of Chongqing [No. cstc2016jcyjA0117]; and the
Fundamental Research Funds for the Central Universities [No.
106112017CDJQJ248825]. The authors would like to thank Editage for
English language editing.
Fig. 10. Optimization diagram of borehole length.
method to optimize the borehole length taking both safety and economic factors into consideration. As stated above, the gas production
growth rate and borehole lengths depend on the gas drainage time.
Hence, three different gas drainage periods were defined; namely, short
term, medium term, and long term, corresponding to 0–60 min,
60–120 min, and 120–360 min, respectively, as shown in Fig. 10. Different borehole length ranges were proposed based on various criteria
of the optimization method. Initially, the maximum borehole length
was equal to the width of the SRZ (i.e., 262.5 mm) taking the boundary
condition into considering. The minimum gas drainage efficiency was
30% taking safety criteria into considering, and the maximum gas
drainage efficiency was 90% taking economic factors into considering
because increasing the borehole length considerably was uneconomical.
In the experiments, the original gas volume in the coal seam was
1075.1 L; thus, the minimum gas drainage production was 322.5 L. The
line Q = 322.5 in Fig. 10 was labeled “safety line”, where gas production must be above this line regardless of the borehole length. Gas
production from the longest borehole (262.5 mm) was approximately
324.3 L after 15 min, which was close to the safety line value, that is,
the minimum drainage time was 15 min. In addition, for the three gas
production curves of 60 min, 120 min, and 360 min, the 90% drainage
efficiency points were A (155.6, 619.9), B (129.7, 784.0), and C (24.5,
904.9), respectively. Therefore, we recommend the following optimized
borehole lengths: 155.6–262.5 mm for short-term gas drainage
(15–60 min); 129.7–155.6 mm for medium-term gas drainage
(60–120 min); and 24.5–129.7 mm for long-term gas drainage
(120–360 min).
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