Characterization of Permeability Changes in Coal of High Rank during the CH 4-CO 2 Replacement Process

The influences of coal matrix expansion/contraction and effective stress on the permeability of coal with different thermal maturities are different during the CH4-CO2 replacement process due to different mechanical properties and gas adsorption capacities. To accurately predict the variation law of coal permeability during the CH4-CO2 replacement process, it is critical to understand how the matrix expansion/contraction and effective stress affect the permeability of coal at different thermal maturities during the CH4-CO2 replacement. In this study, the permeability of two coal specimens with anthracite and high-rank bituminous coal during the CH4-CO2 replacement process under different confining and injection pressures was tested using a CBM replacement testing machine. The results demonstrate that with decreasing gas injection pressure, the permeability of the two coal specimens exhibited a U-shaped correlation under different confining pressures. Under the same gas injection pressure, with increasing effective stress, the permeability presented a negative exponential decrease and the permeability of the anthracite decreased more significantly. Moreover, under the same confining pressure, with increasing gas injection pressure, the decreasing permeability agreed with Langmuir curve and the permeability of high-rank bituminous coal was more significantly reduced.


Introduction
Coal has a greater adsorption capacity for CO 2 compared to CH 4 under the same conditions [1,2].It has been shown to be feasible to replace CH4 from coal seams by means of competitive adsorption of CO 2 [3][4][5].However, due to gas adsorption/desorption and gas pressure changes during the replacement process, the permeability of the coal always undergoes complex changes due to the synergetic effects of coal matrix expansion/contraction and effective stress.Extensive studies have been made aiming at understanding how the matrix expansion/contraction and effective stress impact the permeability during the replacement.
Many studies have shown that as the amount of swelling of coal adsorbed with CO 2 is greater than that of CH 4 under the same conditions [6][7][8], the permeability of coal specimens decreases during the CH 4 -CO 2 replacement process [5,[9][10][11].To investigate the amount of swelling of coal after absorbing gas, a number of approaches including probe test methods [12][13][14], stress detectors [15][16][17], and fiber optic cameras [18][19][20][21] have been adopted by some researchers.Data from these studies show that the amount of swelling and adsorption capacity are in close agreement with the results of the Langmuir adsorption isotherm.Some applied theories including adsorption isotherms, surface free energy, elastic-plastic mechanics, and the stress-strain relationship of coal rock have been used to construct mathematic models of swelling and shrinkage for coal matrix after adsorbing/ desorbing gas [22,23].The effective stress during the gas injection process has also been shown to change.
To investigate the impact of varying effective stresses on the permeability of coal, studies have suggested improved rock mechanics and servo-controlled testing systems to conduct pressure and flow tests.The study results have indicated that as effective stress increases, permeability shows a negative exponential decay [24][25][26][27].Each of the previously mentioned studies analyzed coal matrix expansion/contraction or effective stress and did not comprehensively consider the relationship between the two.Hence, previous studies are limited in revealing the impact of effective stress and matrix expansion/contraction on the permeability of coal during the CH 4 -CO 2 replacement process.
This research aimed at testing the contribution of matrix expansion and effective stress changes on the permeability of coal with different metamorphic degrees during the CH 4 -CO 2 replacement process.For this purpose, the change laws of permeability of anthracite and high-rank bituminous coal specimens during the replacement process were analyzed under varying confining and gas injection pressures.The results provide a theoretical foundation for in situ CO 2 injection.

Preparation of Coal Specimens and Experimental Device.
Coal specimens with different thermal maturities were obtained from the Sihe and Tunliu coal mines in the Qinshui Basin of Shanxi Province of China.Location of coal specimens is shown in Figure 1.Prior to the experiment, the vitrinite reflectance, proximate analysis, adsorption constant, and elastic modulus of the coal specimens were determined, and the results are summarized in Tables 1 and 2. Cylindrical core specimens 50 mm in diameter and 100 mm in length were specimend from the coal block in the direction parallel to the bedding planes, as shown in Figure 2. According to Table 1, the vitrinite reflectance of the specimens from the Sihe and Tunliu coal mines were 3.07% and 1.96%, respectively.
Based on the classification of ISO 11760 Classification of coal, the coal specimens from the Sihe and Tunliu mines were anthracite and meager lean coal.In the following statement, the Sihe and Tunliu specimens are, respectively, represented by anthracite (HA) and high-rank bituminous coal (HB).As shown in Table 2, when the temperature of the test was set to 298.15 K, the adsorption capability and elastic modulus of the coal specimens from the Sihe coal mine were both greater than those from the Tunliu mine.
The CBM replacement testing machine in the National Engineering Research Center of Coalbed Methane Development & Utilization, Beijing, was used as the experimental device.This device was used to test the change in permeability of the specimens under different stresses and gas injection pressures.The working mechanism can be described as (1) a stress-loading device was used to apply confining pressure and axial compression on the coal specimens by simulating stress states of the specimens; (2) gas pipes on both ends of the specimens were connected to the devices including a metering pump, a flow rate controller, a flow meter, and a pressure gauge.Gas was injected with the coal specimens under different pressures.The corresponding data were collected and used to calculate the permeability, as shown in Figure 3.
The parameters in the experiment included as follows: the dimension was set to be ¢50 × 100 mm or ¢25 × 50 mm, the temperature ranged between 173.15~373.15K with a  a M ad = moisture content (wt.%, air dry basis), A ad = ash yield (wt.%, air dry basis), and V ad = volatile matter (wt.%, air dry basis).
2 Geofluids precision of ±0.1 K, and the confining pressure was in the range of 0~30 MPa with a precision of ±0.5%.The gas injection pressure ranged between 0~20 MPa with a precision of ±0.5% FS, and the axial stress was in the range of 0~150 MPa with a precision of ≤±1%.Permeability ranged between 0.001~100 mD.  3 Geofluids

Experimental Procedure
(1) The gas pipelines were connected to examine the closure of the system, and the volume of the pipelines was tested.The HA coal specimen was dried and installed within a heat-shrinkable sleeve before being precisely put into the coal specimen chamber.Finally, the experimental system was performed by a vacuum pump (2) After placing the specimens in a designed location as described, axial compression was applied to the specimen.Axial compression and confining pressure were alternatively loaded on the specimen until the confining pressure reached up to 6 MPa.To prevent coal specimen from damage, the stress-loading speed was less than or equal to 0.2 MPa/s (3) CH 4 was injected at a constant pressure of 1 MPa.As the adsorption of CH 4 reached equilibrium, CO 2 was injected at a higher pressure of 1.25 MPa to induce competitive adsorption.When the adsorption and desorption for both types of gas reached equilibrium, the pressure and gas flow rates on both ends of the specimen were recorded.The permeability of the coal specimens was calculated based on equation (1).Afterwards, gas injection was ceased.The experimental system has undergone sufficient vacuum-pumping.
where K ge is the effective permeability, mD; p u and p d are the fluid pressure on both ends of each specimen, MPa.q ge refers to fluid velocity, cm 3 /s; μ g is the fluid viscosity, mPa ⋅ s; h is the length of the specimens, cm; and A represents the cross-section area of each specimen, cm 2 Figure 4 shows that under different confining pressures and with decreasing gas injection pressure, the permeability of the two coal specimens all exhibited a U-shaped correlation.The greater the confining pressure, the lower the permeability of the same coal specimen.In the anthracite specimen, when the gas injection pressures were 1.3 and 6.25 MPa, the permeability values were equal.In the high-rank bituminous coal specimen, when the gas injection pressures were and 6.25 MPa, the permeability values were equal.

The Influence of Effective Stress on Permeability during
the CH 4 -CO 2 Replacement Process.According to the experimental design, the permeability of the two specimens was, respectively, tested during the CH 4 -CO 2 replacement process under different confining and gas injection pressures.Under the same confining pressure, the effective stress changes with changing injection pressure, which leads to failure to apply the variable selective control method to derive the relationships between effective stress and permeability.However, under the same gas injection pressure, the effect of gas adsorption on permeability could be considered equal.Based on these observations, the permeability data of the same gas injection pressure and different confining pressures were selected to obtain the variation law of permeability.

Geofluids
Figure 5 shows the variation of permeability with increasing effective stresses during the CH 4 -CO 2 replacement process at different gas injection pressures.
As can be seen in Figure 5, under different injection pressures, with increasing effective stress, the permeability of the HA coal decreases in a negative exponential manner and each of the correlation coefficients exceeds 0.9.
With increasing the effective stress, the permeability of the HB coal first slowly decreases and then presents a sharp decrease under the four gas injection pressures of 3.25, 4.25, 5.25, and 6.25 MPa.This indicates that the influence of effective stress on the permeability of HB coal exists at an abrupt turning point, after reaching a certain amount of adsorption; the greater the amount of gas adsorption, the earlier the turning point that permeability shows a sharp decrease.This may be related to the heterogeneity of the distribution of pores and fissures in coal.
To further study the change laws of permeability of the two specimens with a variation of effective stress, the decreased permeability caused by increased effective stress under the six injection gas balanced pressures was calculated, and the results are shown in Table 3.
As can be seen in Table 3, when the gas injection pressures are between 1.25 and 6.25 MPa, the decreasing values of permeability due to the increase of effective stress of HA coal range from 0.119 to 0.180 mD.For the HB coal, the values range from 0.067 to 0.107 mD, indicating that the permeability of the HA coal is more sensitive to effective stress.

Influence of Gas Adsorption/Desorption on Permeability
during the CH 4 -CO 2 Replacement Process.As the gas injection pressure changes, the permeability of the coal specimens also changed due to the gas adsorption/desorption.To study the change in permeability caused by gas adsorption as injection pressure increases, the value of permeability under the effect of gas adsorption was calculated.The calculation process is shown in equation 2.  where K a is the permeability under the effect of gas adsorption, which can be seen as the original permeability of coal specimens plus the permeability change caused by effective stress gas and adsorption/desorption, mD; K b is the permeability under the effect of gas adsorption and effective stress, which can be seen as the original permeability of coal specimens plus the permeability change caused by effective stress, mD; K c is the permeability under the effect of effective stress, which can be seen as the original permeability of coal specimens plus the permeability change caused by effective stress gas and adsorption/desorption, mD; K e is the original permeability of coal specimens.As the experiment did not use inert gas to test the original permeability of the coal specimens, the permeability under an injection pressure of 1.25 MPa and the confining pressure of 0 MPa (calculated by the formula in Table 3) was considered as the original permeability.The permeability under the effects of gas adsorption was calculated, and the results are shown in Table 4.
According to the results shown in Table 4, the change in permeability under the effect of gas adsorption can be shown in Figure 6.
From Figure 6, it can be seen that under the different confining pressures, the permeability of both coal specimens showed a decreasing trend with increasing gas injection pressure.The shape of the permeability change curves are similar to that of the Langmuir adsorption, thus based on the calculated data in Table 4, the relationship between gas adsorption and permeability can be fitted by the following equation: According to the Langmuir equation, K is the permeability of coal specimen, mD; P is the gas injection pressure, MPa; a is the lower boundary of permeability under the effect of gas adsorption, mD; b is the gas injection pressure on the half lower boundary, MPa.
Table 5 shows the fitting and the calculated results of permeability decrements under the effect of gas adsorption.
The a value represents the lower boundary of permeability under the effect of gas adsorption, as can be seen in Table 5; the a values in HA coal are smaller than those in the HB coal as a whole.On one hand, the original permeability   6 Geofluids of the coal specimen is one of the most important reasons that led to the results.On the other hand, the differences of adsorption capacity are one of the important reasons; the greater the Langmuir volume, the lower the a values.The b values show no obvious regularity.Comparing the decrease of the permeability values caused by the gas adsorption of HA and HB coal, it can be concluded that in the replacement process, the effect of gas adsorption on the permeability of HB coal is greater than that of HA coal.

Figure 1 :
Figure 1: Location of coal specimens studied in this paper.

( 4 )( 5 )( 6 ) 2 replacement process was tested by repeating the above procedures 3 .
The permeability of HA coal specimen under different injection pressures (1.25, 2.25, 3.25, 4.25, and 5.25 MPa) under a confining pressure of 6 MPa was tested by repeating procedure (3) The permeability of the HA coal specimen under different confining pressures (6, 8, 10, 12, and 14 MPa) and different injection pressures (1.25, 2.25, 3.25, 4.25, 5.25, and 6.25 MPa) during the CH 4 -CO 2 replacement process was tested by repeating procedures (2)~(4) The HA coal specimen was replaced by the HB coal specimen after the gas injection was ceased and stress was unloaded (7) The permeability of the HB coal specimen under different confining pressures (8, 12, 16, and 20 MPa) and different injection pressures (1.25, 2.25, 3.25, 4.25, 5.25, and 6.25 MPa) during the CH 4 -CO Results and Discussion 3.1.Experimental Results.The change in permeability of coal specimens during the CH 4 -CO 2 replacement process under different confining pressures is shown in Figure 4.

Confining pressure 8 Figure 4 :
Figure 4: Permeability variation of the HA and HB coal specimens under different confining and injection pressures.
gas balanced pressure 1.25 MPa Injection gas balanced pressure 2.25 MPa Injection gas balanced pressure 3.25 MPa Injection gas balanced pressure 4.25 MPa Injection gas balanced pressure 5.25 MPa Injection gas balanced pressure 6HA coal Injection gas balanced pressure 1.25 MPa Injection gas balanced pressure 2.25 MPa Injection gas balanced pressure 3.25 MPa Injection gas balanced pressure 4.25 MPa Injection gas balanced pressure 5.25 MPa Injection gas balanced pressure 6

Figure 5 :
Figure 5: The change of permeability with a variation of effective stress.

Figure 6 :
Figure 6: Permeability change characteristics due to gas desorption under different confining pressures.

Table 1 :
Results of vitrinite reflectance and proximate analysis.

Table 2 :
Testing results of isothermal adsorption experiments about CO 2 and CH 4 .

Table 4 :
Calculated results of permeability influenced by coal matrix shrinkage under different confining pressures.

Table 5 :
Fitting and the calculated results of permeability increments under the effect of gas adsorption.