The Inﬂuence of Fracturing Fluid Volume on the Productivity of Coalbed Methane Wells in the Southern Qinshui Basin

: Hydraulic fracturing is the main technical means for the reservoir stimulation of coalbed methane (CBM) vertical wells. The design of fracturing ﬂuid volume (FFV) is mainly through numerical simulation, and the numerical simulation method does not fully consider the water block damage caused by the leakage of fracturing ﬂuid into the reservoir. In this work, the variance analysis method was used to analyze the production data of 1238 CBM vertical wells in the Fanzhuang block and Zhengzhuang block of the Qinshui Basin, to clarify the relationship between the FFV and the peak gas production (PGP) under the different ratios of critical desorption pressure to reservoir pressure (R c/r ), and to reveal the controlling mechanism of fracturing ﬂuid on CBM migration. The results show that both the FFV and R c/r have a signiﬁcant impact on gas production. When R c/r < 0.5, the PGP decreases with the increase of the FFV, and the FFV that is beneﬁcial to gas production is 200–500 m 3 . When R c/r > 0.5, the PGP increases ﬁrst and then decreases with the increase of FFV. Speciﬁcally, the FFV that is favorable for gas production is 500–700 m 3 . Excessive FFV does not signiﬁcantly increase the length of fractures due to leaks in the coal reservoir. Instead, it is more likely to invade and stay in smaller pores, causing water block damage and reducing gas production. Reservoirs with high R c/r have larger displacement pressure, which can effectively overcome the resistance of liquid migration in pores, thereby reducing the damage of the water block. Therefore, different reservoir conditions need to match the appropriate fracturing scale. This study can provide guidance for the optimal design of hydraulic fracturing parameters for CBM wells.


Introduction
Hydraulic fracturing is one of the important reservoir stimulations of coalbed methane (CBM) wells, and its main purpose is to form efficient conductivity fractures and improve coal seam permeability [1,2]. However, while hydraulic fracturing improves the permeability of coal seams, tons of fracturing fluid are injected into the coal seam [3,4], and a large amount of fracturing fluid is leaked into the coal reservoir, which also brings many adverse effects to the development of coalbed methane, such as water block damage [5][6][7][8], clay swelling [9,10], and consequently increased difficulty in methane desorption, etc. [11,12].
In view of the adverse effects of fracturing fluid leakage, a large number of scientific research and experiments have been carried out on the influencing factors of the leakage. Yuan et al. [4] and Chang et al. [10] studied the self-absorption process and microscopic migration mechanism of coal reservoirs after hydraulic fracturing and evaluated the effect of this process on permeability. Wang et al. [13] expounded the influence of the wettability of coal on the irreducible water content from a microscopic point of view, and discussed In this paper, we aim to better clarify whether different FFVs have an impact on gas production, and design the amount of fracturing fluid that matches the geological conditions. By analyzing the production data of 1238 wells in the Fanzhuang (FZ) block and ZZ block, the influence of different FFV on the gas production was studied, the FFV for optimal gas production under the different ratios of critical desorption pressure to the reservoir pressure (R c/r ) was discussed, and the effect of water block damage caused by fluid leakage on gas production was clarified. The research results can provide some insights into the optimal design of hydraulic fracturing parameters for CBM reservoirs.

Geological Setting
The Qinshui Basin, located in southeastern Shanxi Province (Figure 1a), is a typical example of the successful development of high-rank coal in China [23]. The FZ block and ZZ block are located in the southern Qinshui Basin (Figure 1b). The study area consists of the Pennsylvanian Benxi (C 2 b) and Taiyuan (C 2 t) Formations, the Permian Shanxi the No.3 coal seam of the Shanxi Formation is stably distributed in the whole area and is the main layer for CBM development in the study area [24][25][26].
The FZ block and ZZ block are bounded by the Sitou Fault. The ZZ block is situated west of the fault, and the FZ block is located east of the fault [27][28][29]. The stratigraphic structure of the study area is relatively complex. Local folds and faults are relatively developed, and the regional structural form is mainly distributed in the north-northeast, and the stratigraphic dip is 3° to 8°. The thickness of the No. 3 coal seam ranges from 5 to 7 m, and its burial depth varies between 300 and 1200 m (Figure 1c). The vitrinite reflectance (Ro,max, %) varies between 3.1% and 3.9%, and the gas content is between 14 and 30 m 3 /t. The reservoir permeability is generally lower than 1 mD, with an average of 0.27 mD [30][31][32].  The FZ block and ZZ block are bounded by the Sitou Fault. The ZZ block is situated west of the fault, and the FZ block is located east of the fault [27][28][29]. The stratigraphic structure of the study area is relatively complex. Local folds and faults are relatively developed, and the regional structural form is mainly distributed in the north-northeast, and the stratigraphic dip is 3 • to 8 • . The thickness of the No. 3 coal seam ranges from 5 to 7 m, and its burial depth varies between 300 and 1200 m (Figure 1c). The vitrinite reflectance (R o,max , %) varies between 3.1% and 3.9%, and the gas content is between 14 and 30 m 3 /t. The reservoir permeability is generally lower than 1 mD, with an average of 0.27 mD [30][31][32].

Methods
In order to analyze the influence of FFV on gas production in the southern Qinshui Basin, the production data of 1238 CBM wells in FZ block and ZZ block since 2006 were collected and analyzed. These wells all use conventional hydraulic fracturing fluid. The fracturing fluid is potassium chloride solution with a concentration of 1%, and the FFV is between 200-1000 m 3 . After the fracturing operation, the well is shut in, and the fracturing fluid is almost completely leaked into the reservoir. The basic data collected include FFV, critical desorption pressure, reservoir pressure, R c/r , and peak gas production (PGP). Among them, the critical desorption pressure is the bottom hole flow pressure at the initial gas desorption during the CBM drainage process; the R c/r is the ratio of the critical desorption pressure to the reservoir pressure; the PGP is the maximum daily production after the first hydraulic fracturing stimulation.
In this work, one-way analysis of variance (ANOVA) was used to analyze the influence of FFV and R c/r on gas production. First, as many as possible FFV and R c/r are grouped, and then the least-significant difference (LSD) method is used to test the significant differences between the different groups, and the adjacent and insignificant groups are merged [33]. The grouping level of FFV and R c/r is actually obtained, which is convenient for multiway ANOVA. Then, the multiway ANOVA on the significant effect of gas production is carried out using the R c/r and FFV grouping level determined after one-way ANOVA, and then the optimal combination that beneficial to gas production is found [34].
In this work, SPSS software is used for ANOVA, the system default significance level α is set at 0.05 and compared with p-value of the test statistic. If the p-value < 0.05, it is considered that the different grouping levels of the independent variable have a significant impact on the dependent variable. F ratio is the test statistic, the F ratio is the between-group variance divided by the within-group variance in a data set. If F > 1, there are statistically significant differences between groups, a high F ratio indicates the greater likelihood of statistically significant differences between groups [34]. Table 2 shows the results of one-way ANOVA on the PGP when the FFV is divided into 8 groups (200-300 m 3 , 300-400 m 3 , 400-500 m 3 , 500-600 m 3 , 600-700 m 3 , 700-800 m 3 , 800-900 m 3 , and 900-1000 m 3 ). The results show that the amount of fracturing fluid has a significant effect on PGP (F = 20.35, p = 0.000). Analysis of the pairwise comparison between different groups by the LSD method shows that the difference between the 300-400 m 3 and 400-500 m 3 groups is not significant, and they are combined into a group of 300-500 m 3 . Similarly, the 700-800 m 3 , 800-900 m 3 , and 900-1000 m 3 were combined into a group of 700-1000 m 3 . The differences between other adjacent groups are significant, and the results show that the effects of different FFV groups on PGP are significantly different. The average PGP when the FFV is divided into 8 groups is shown in Figure 2a.   Table 3 shows the results of one-way ANOVA on the PGP when the FFV is divided into 5 groups (200-300 m 3 , 300-500 m 3 , 500-600 m 3 , 600-700 m 3 , and 700-1000 m 3 ). The results show that the amount of fracturing fluid has a significant effect on the PGP (F = 35.1, P = 0.000). Figure 2b shows that with the increase of FFV, the average PGP first increases and then decreases. When the FFV is 500-600 m 3 , the average PGP is the largest, and when the FFV exceeds 500-600 m 3 , the average PGP shows a rapid downward trend.  Table 4 shows the results of one-way ANOVA on the PGP when the FFV is divided into 3 groups (200-500 m 3 , 500-700 m 3 , and 700-1000 m 3 ). The results show that the amount of fracturing fluid has a significant effect on PGP (F = 54.6, P = 0.000). The LSD method analyzes the pairwise comparison between the three different grouping levels, and the results show that the differences between the groups are significant. It can be known from Figure 2c that when the FFV is 200-500 m 3 , the average PGP is 2136 m 3 ; when the FFV is 500-700 m 3 , the average PGP is 2795 m 3 ; and when the FFV is 700-1000 m 3 , the average PGP dropped rapidly to only 1121 m 3 .  Table 3 shows the results of one-way ANOVA on the PGP when the FFV is divided into 5 groups (200-300 m 3 , 300-500 m 3 , 500-600 m 3 , 600-700 m 3 , and 700-1000 m 3 ). The results show that the amount of fracturing fluid has a significant effect on the PGP (F = 35.1, p = 0.000). Figure 2b shows that with the increase of FFV, the average PGP first increases and then decreases. When the FFV is 500-600 m 3 , the average PGP is the largest, and when the FFV exceeds 500-600 m 3 , the average PGP shows a rapid downward trend.  Table 4 shows the results of one-way ANOVA on the PGP when the FFV is divided into 3 groups (200-500 m 3 , 500-700 m 3 , and 700-1000 m 3 ). The results show that the amount of fracturing fluid has a significant effect on PGP (F = 54.6, p = 0.000). The LSD method analyzes the pairwise comparison between the three different grouping levels, and the results show that the differences between the groups are significant. It can be known from Figure 2c that when the FFV is 200-500 m 3 , the average PGP is 2136 m 3 ; when the FFV is 500-700 m 3 , the average PGP is 2795 m 3 ; and when the FFV is 700-1000 m 3 , the average PGP dropped rapidly to only 1121 m 3 . The one-way ANOVA process of R c/r on gas production is shown in Table 5, which shows that R c/r has a significant impact on gas production when R c/r is divided into 10, 7, and 6 groups. Table 6 shows the results of one-way ANOVA on PGP when the R c/r is divided into 4 groups (0-0.3, 0.3-0.5, 0.5-0.8 and 0.8-1). The results showed that the R c/r had a significant impact on the PGP (F = 111.53, p = 0.000). The results of pairwise comparison between different groups by the LSD method showed that the differences in PGP between the four different grouping levels were significant. Figure 2d shows that the average PGP is positively correlated with the R c/r . Table 5. F and p-value of one-way ANOVA for different groups of R c/r .

Number of Grouping Levels
Grouping One-way ANOVA shows that both the FFV and R c/r have a significant impact on the gas production. Combined with the actual situation, the FFV is divided into 3 groups and the R c/r is divided into 4 groups for multiway ANOVA, as shown in Table 7. homogeneous, which meets the precondition of the variance test. Table 8 shows that the model used for the multiway ANOVA was statistically significant (F = 40.2, p = 0.000). The interaction between R c/r and FFV had a very significant impact on PGP (F = 7.42, p = 0.000). The multiway ANOVA shows that when the FFV is constant, the larger the R c/r , the better the gas production, and the R c/r have a significant contribution to the gas production. When the R c/r is constant, the amount of fracturing fluid is different, and the gas production is also different. The specific performance is as follows: (a) when R c/r < 0.5, the gas production is negatively correlated with the amount of fracturing fluid. when R c/r is 0-0.3, the FFV is 700-1000 m 3 and the gas production decreases rapidly; when R c/r is 0.3-0.5, the FFV is 500-700 m 3 and the gas production decreases rapidly. (b) when R c/r > 0.5, the gas production increases first and then decreases with the increase of the FFV, but there are differences. When R c/r is 0.5-0.8, the gas production when the FFV is 700-1000 m 3 is less than that when the FFV is 200-500 m 3 . When R c/r is 0.8-1, the gas production when the FFV is 700-1000 m 3 is greater than that when the FFV is 200-500 m 3 . In short, the gas production decreases when the FFV is 700-1000 m 3 , indicating that excessive FFV is not conducive to the increase of gas production ( Figure 3). The interaction between Rc/r and FFV had a very significant impact on PGP (F = 7.42, P = 0.000). The multiway ANOVA shows that when the FFV is constant, the larger the Rc/r, the better the gas production, and the Rc/r have a significant contribution to the gas production. When the Rc/r is constant, the amount of fracturing fluid is different, and the gas production is also different. The specific performance is as follows: (a) when Rc/r < 0.5, the gas production is negatively correlated with the amount of fracturing fluid. when Rc/r is 0-0.3, the FFV is 700-1000 m 3 and the gas production decreases rapidly; when Rc/r is 0.3-0.5, the FFV is 500-700 m 3 and the gas production decreases rapidly. (b) when Rc/r > 0.5, the gas production increases first and then decreases with the increase of the FFV, but there are differences. When Rc/r is 0.5-0.8, the gas production when the FFV is 700-1000 m 3 is less than that when the FFV is 200-500 m 3 . When Rc/r is 0.8-1, the gas production when the FFV is 700-1000 m 3 is greater than that when the FFV is 200-500 m 3 . In short, the gas production decreases when the FFV is 700-1000 m 3 , indicating that excessive FFV is not conducive to the increase of gas production ( Figure 3).

Intrusion and Retention of Fracturing Fluid
The process of hydraulic fracturing of CBM wells is the process of intrusion of fracturing fluid into pores and fractures of coal seams. The schematic diagram of fluid distribution in pores and fractures before hydraulic fracturing is shown in Figure 4a. The water intrusion process is mainly affected by injection pressure (P ), imbibition capillary force (P ), viscous resistance (P ), fluid resistance (P ), and gas pressure (P ) in the coal seam. It is generally considered that P and P are the main driving forces [35,36]. When the coal reservoir is saturated with gas and contains more free methane gas, P is also a

Intrusion and Retention of Fracturing Fluid
The process of hydraulic fracturing of CBM wells is the process of intrusion of fracturing fluid into pores and fractures of coal seams. The schematic diagram of fluid distribution in pores and fractures before hydraulic fracturing is shown in Figure 4a. The water intrusion process is mainly affected by injection pressure (P d ), imbibition capillary force (P c ), viscous resistance (P n ), fluid resistance (P f ), and gas pressure (P g ) in the coal seam. It is generally considered that P d and P c are the main driving forces [35,36]. When the coal reservoir is saturated with gas and contains more free methane gas, P g is also a non-negligible resistance to prevent water migration in pores [37,38]. Therefore, for the fluid migrating in the pores and fractures of coal seams during the water invasion process, the pressure difference (∆P i ) across the pores is: where σ is the interfacial tension between the solution and the air, N/m; θ is the contact angle between the solution and coal, ( • ); r is the radius of the pore, m. non-negligible resistance to prevent water migration in pores [37,38]. Therefore, for the fluid migrating in the pores and fractures of coal seams during the water invasion process, the pressure difference (∆P ) across the pores is: where σ is the interfacial tension between the solution and the air, N/m; θ is the contact angle between the solution and coal, (°); r is the radius of the pore, m. When ∆P is >0, water intrusion occurs. The water retained in the pores may fill the pores, or may form multi-level and intermittent water columns (Figure 4b). The water intrusion experiments in coal pillars show that water intrusion occurs simultaneously in micropore-transition pores, mesopores, macropores and fractures, and the water intrusion rate decreases sequentially. The speed of water intrusion in the micropore-transition pore is mainly determined by the capillary force of imbibition; the more complex the pore structure, the smaller the degree of water intrusion, and the more difficult it is to flow back after water intrusion. The water saturation of pores and fractures increased with the increase of injection time and inlet pressure during the water invasion process [39].
In the practice of hydraulic fracturing, with the increase of the fracturing scale, the injection rate and pressure need to be increased accordingly. In this way, the amount of fracturing fluid invading into the pores also increases, and the radius of the pores that can be invaded is smaller, and more fracturing fluid enters the complex pores and micropores. Therefore, if the scale of hydraulic fracturing is too large, the more fracturing fluid that is leaked and retained in the pores and fractures, and the residual fracturing fluid will affect the gas production [40]. As shown in Figure 3, when the amount of frac- When ∆P i is >0, water intrusion occurs. The water retained in the pores may fill the pores, or may form multi-level and intermittent water columns (Figure 4b).
The water intrusion experiments in coal pillars show that water intrusion occurs simultaneously in micropore-transition pores, mesopores, macropores and fractures, and the water intrusion rate decreases sequentially. The speed of water intrusion in the microporetransition pore is mainly determined by the capillary force of imbibition; the more complex the pore structure, the smaller the degree of water intrusion, and the more difficult it is to flow back after water intrusion. The water saturation of pores and fractures increased with the increase of injection time and inlet pressure during the water invasion process [39].
In the practice of hydraulic fracturing, with the increase of the fracturing scale, the injection rate and pressure need to be increased accordingly. In this way, the amount of fracturing fluid invading into the pores also increases, and the radius of the pores that can be invaded is smaller, and more fracturing fluid enters the complex pores and micropores. Therefore, if the scale of hydraulic fracturing is too large, the more fracturing fluid that is leaked and retained in the pores and fractures, and the residual fracturing fluid will affect the gas production [40]. As shown in Figure 3, when the amount of fracturing fluid is 700-1000 m 3 , the average PGP decreases compared with that when the amount of fracturing fluid is 500-700 m 3 , and more external liquid stays in the pores and fractures of the coal.

Fluid Migration and Water Block Damage during Drainage
At the early stage of CBM well drainage, there is saturated water in the pores and fissures. As the water in the fracture is drained first, the fluid pressure in the fracture will decrease and the gas begins to desorb (Figure 4c). After the water in the fracture is drained out, some of the water in the pore does not migrate with the water in the fracture, but stays in the pore (Figure 4d). According to the principle of gas-liquid two-phase fluid flow, it can be known that the fluid in the pore mainly considers the two-phase flow driven by the pressure difference [41]. The pressure difference for liquid column migration in the pore is [13,42]: where P g is the gas pressure in the pore; P w is the fluid pressure in the fracture; and G is the gravity of the liquid column in the pore. P g is the main driving force for the liquid column migration in the pore, and P c and P w are the main resistances. When the pore radius is small enough and the liquid column is short enough, P f and G can be ignored. When ∆P o = 0, the fluid in the pore does not migrate ( Figure 5a). As the fluid in the fracture migrates out, P w will decrease, the pressure drop will be transferred to the pore, and part of the adsorbed gas will be desorbed from the pore, and P g will increase. When ∆P o > 0, the liquid column migrates to the fracture. At this time, the fluid pressure balance in the pore is destroyed, and the gas at the bottom of the pore will push the liquid column at the bottom upward until a new balance is reached (Figure 5b). With the progress of drainage, the pressure drop is effectively transferred to the internal pores, and more gas is desorbed. When the flow resistance of the liquid column can be overcome, the gas will break through the constraints of the liquid and migrate out. At this time, the pores and fractures are fully connected (Figure 5c). In this process, the part of the liquid column that cannot overcome its flow resistance is bound in the pores, blocking the pores, affecting the migration of gas, and forming water block damage. turing fluid is 700-1000 m 3 , the average PGP decreases compared with that when the amount of fracturing fluid is 500-700 m 3 , and more external liquid stays in the pores and fractures of the coal.

Fluid Migration and Water Block Damage during Drainage
At the early stage of CBM well drainage, there is saturated water in the pores and fissures. As the water in the fracture is drained first, the fluid pressure in the fracture will decrease and the gas begins to desorb (Figure 4c). After the water in the fracture is drained out, some of the water in the pore does not migrate with the water in the fracture, but stays in the pore (Figure 4d). According to the principle of gas-liquid two-phase fluid flow, it can be known that the fluid in the pore mainly considers the two-phase flow driven by the pressure difference [41]. The pressure difference for liquid column migration in the pore is [13,42]: where P is the gas pressure in the pore; P is the fluid pressure in the fracture; and G is the gravity of the liquid column in the pore. P is the main driving force for the liquid column migration in the pore, and P and P are the main resistances. When the pore radius is small enough and the liquid column is short enough, P and G can be ignored. When ∆P = 0, the fluid in the pore does not migrate ( Figure 5a). As the fluid in the fracture migrates out, P will decrease, the pressure drop will be transferred to the pore, and part of the adsorbed gas will be desorbed from the pore, and P will increase. When ∆P > 0, the liquid column migrates to the fracture. At this time, the fluid pressure balance in the pore is destroyed, and the gas at the bottom of the pore will push the liquid column at the bottom upward until a new balance is reached (Figure 5b). With the progress of drainage, the pressure drop is effectively transferred to the internal pores, and more gas is desorbed. When the flow resistance of the liquid column can be overcome, the gas will break through the constraints of the liquid and migrate out. At this time, the pores and fractures are fully connected (Figure 5c). In this process, the part of the liquid column that cannot overcome its flow resistance is bound in the pores, blocking the pores, affecting the migration of gas, and forming water block damage. The gas flooding experiment also showed that the water block damage of macropores and fractures can be relieved, and the water block of mesopores can be partially relieved, while the water in micropores and transition pores was difficult to displace [39,43,44]. In actual production, a large amount of fracturing fluid invades into the pores, and there is no additional driving force during the drainage process, and it will be The gas flooding experiment also showed that the water block damage of macropores and fractures can be relieved, and the water block of mesopores can be partially relieved, while the water in micropores and transition pores was difficult to displace [39,43,44]. In actual production, a large amount of fracturing fluid invades into the pores, and there is no additional driving force during the drainage process, and it will be more difficult for the fracturing fluid to be completely discharged from the micropores and transition pores. Therefore, this part of water must rely on the driving force of the gas in the pores to be discharged.

Mechanism of FFV Affecting Gas Production
It can be seen from the above analysis that water block mainly comes in two ways: (1) during the fracturing process, a large amount of fracturing fluid intrudes into the pores and fractures, and is trapped by capillary force; (2) in the process of drainage, the driving force of the gas in the pore is not enough to overcome the resistance of its migration, and the fracturing fluid retained in the pore cannot be discharged back. According to the Hagen-Poiseuille law, the volume of the fracturing fluid discharged from the pores against the capillary resistance is [45]: where Q is the volume of fracturing fluid discharged, m 3 ; r is the radius of the pore, m; µ is the dynamic viscosity, Pa s; L is the length of the liquid column, m. Take the derivative of Equation (4) as By the integral of Equation (5), it can be obtained that the time (t) for the liquid column of length (L) to flow back from the pores is Substitute Equation (3) into Equation (6): When the scale of hydraulic fracturing fluid increases, the amount of invading fluid in pores increases, the length of the liquid column (L) increases, and the radius (r) of the pores that can be invaded becomes smaller; at the same time, the P and G of the liquid column will have to be considered, increasing the resistance and time for the fluid to move out, making it easier to cause water block [37].
According to the analysis of the microseismic fracture monitoring report of CBM wells in the study area, the FFV has no significant effect on the length of the fracture, and the length of the fracture does not increase with the increase of the FFV ( Figure 6). The correlation between gas production and fracture length is also not obvious (Figure 7). It can be seen that increasing the scale of fracturing has not always brought positive effects on gas production [22]. From the one-way ANOVA of FFV and PGP (Figure 2), it can be seen that with the increase of FFV, the PGP increases first and then decreases. Within a certain scale, increasing the amount of fracturing fluid has a positive effect on gas production. When it exceeds a certain scale, it will have a negative effect on gas production. This is because excess fracturing fluid does not play a role in creating fractures and increasing reservoir connectivity. The excess fracturing fluid is leaked into the coal reservoir or surrounding rock along the pore and fracture channels, and the positive effect is not as great as the negative effect of water block caused by excessive fracturing fluid staying in the reservoir [46]. Therefore, the negative impact of FFV on gas production is mainly reflected in the water block damage caused to the reservoir.  It can be seen from Equation (7) that the greater the ∆P , the greater the fluid resistance that can be overcome. Therefore, under different reservoir conditions, the degree of difficulty in releasing the water block is also different. Lyu et al. [38] and Lu et al. [42] showed that water block did not occur when the differential pressure driving force was greater than the resistance. The larger the Rc/r value, the better the fluid drainage index of the reservoir, which was more conducive to the desorption of gas, resulting in high production [47]. The Rc/r value can represent the gas saturation to a certain extent. Higher gas saturation leads to higher desorption pressure and is beneficial for early gas production, leading to greater total gas production [48,49]. It can be seen that the larger the Rc/r value, the easier the gas desorption, the greater the pressure of gas in the pore, and the greater the driving force of liquid migration in the pore. Therefore, when the Rc/r increases, it becomes easier for the water in the pores to be displaced out.
As shown in Figure 3, when Rc/r > 0.5, the gas production with the FFV of 500-700 m 3 is better than that with the FFV of 200-500 m 3 , indicating that the positive effect of increasing the FFV on the reservoir is greater than the water block damage to the reservoir. When the amount of fracturing fluid increases to 700-1000 m 3 , the gas production decreases, indicating that the damage of the water block caused by increasing the volume of fracturing fluid is greater than the positive effect caused by increasing the volume of fracturing fluid. In particular, when Rc/r is 0.5-0.8, the gas production with the FFV of 700-1000 m 3 is smaller than that with the FFV of 200-500 m 3 , implying that the negative effect of excessively increasing the amount of fracturing fluid is greater, and more water blocks are not released. When Rc/r is 0.8-1, the gas production with the FFV of 700-1000m 3 is higher than that of the FFV of 200-500m 3 , indicating that the positive effect brought by the large FFV is greater than the negative effect. The water block is easier to be eliminated  It can be seen from Equation (7) that the greater the ∆P , the greater the fluid resistance that can be overcome. Therefore, under different reservoir conditions, the degree of difficulty in releasing the water block is also different. Lyu et al. [38] and Lu et al. [42] showed that water block did not occur when the differential pressure driving force was greater than the resistance. The larger the Rc/r value, the better the fluid drainage index of the reservoir, which was more conducive to the desorption of gas, resulting in high production [47]. The Rc/r value can represent the gas saturation to a certain extent. Higher gas saturation leads to higher desorption pressure and is beneficial for early gas production, leading to greater total gas production [48,49]. It can be seen that the larger the Rc/r value, the easier the gas desorption, the greater the pressure of gas in the pore, and the greater the driving force of liquid migration in the pore. Therefore, when the Rc/r increases, it becomes easier for the water in the pores to be displaced out.
As shown in Figure 3, when Rc/r > 0.5, the gas production with the FFV of 500-700 m 3 is better than that with the FFV of 200-500 m 3 , indicating that the positive effect of increasing the FFV on the reservoir is greater than the water block damage to the reservoir. When the amount of fracturing fluid increases to 700-1000 m 3 , the gas production decreases, indicating that the damage of the water block caused by increasing the volume of fracturing fluid is greater than the positive effect caused by increasing the volume of fracturing fluid. In particular, when Rc/r is 0.5-0.8, the gas production with the FFV of 700-1000 m 3 is smaller than that with the FFV of 200-500 m 3 , implying that the negative effect of excessively increasing the amount of fracturing fluid is greater, and more water blocks are not released. When Rc/r is 0.8-1, the gas production with the FFV of 700-1000m 3 is higher than that of the FFV of 200-500m 3 , indicating that the positive effect brought by the large FFV is greater than the negative effect. The water block is easier to be eliminated It can be seen from Equation (7) that the greater the ∆P o , the greater the fluid resistance that can be overcome. Therefore, under different reservoir conditions, the degree of difficulty in releasing the water block is also different. Lyu et al. [38] and Lu et al. [42] showed that water block did not occur when the differential pressure driving force was greater than the resistance. The larger the R c/r value, the better the fluid drainage index of the reservoir, which was more conducive to the desorption of gas, resulting in high production [47]. The R c/r value can represent the gas saturation to a certain extent. Higher gas saturation leads to higher desorption pressure and is beneficial for early gas production, leading to greater total gas production [48,49]. It can be seen that the larger the R c/r value, the easier the gas desorption, the greater the pressure of gas in the pore, and the greater the driving force of liquid migration in the pore. Therefore, when the R c/r increases, it becomes easier for the water in the pores to be displaced out.
As shown in Figure 3, when R c/r > 0.5, the gas production with the FFV of 500-700 m 3 is better than that with the FFV of 200-500 m 3 , indicating that the positive effect of increasing the FFV on the reservoir is greater than the water block damage to the reservoir. When the amount of fracturing fluid increases to 700-1000 m 3 , the gas production decreases, indicating that the damage of the water block caused by increasing the volume of fracturing fluid is greater than the positive effect caused by increasing the volume of fracturing fluid. In particular, when R c/r is 0.5-0.8, the gas production with the FFV of 700-1000 m 3 is smaller than that with the FFV of 200-500 m 3 , implying that the negative effect of excessively increasing the amount of fracturing fluid is greater, and more water blocks are not released. When R c/r is 0.8-1, the gas production with the FFV of 700-1000 m 3 is higher than that of the FFV of 200-500 m 3 , indicating that the positive effect brought by the large FFV is greater than the negative effect. The water block is easier to be eliminated when the R c/r is 0.8-1 than when the R c/r is 0.5-0.8. When R c/r < 0.5, the gas production will be less when the FFV is increased, which indicates that the fracturing fluid enters the pores and is difficult to be displaced, which is more likely to cause water block damage to the reservoir. Therefore, the smaller the R c/r value, the larger the FFV, and the more serious the water block damage.

The Uncertainty or Limitation of This Study
There are many factors affecting the production of CBM [32,[50][51][52][53]. This paper illustrates that the amount of fracturing fluid is also one of the factors affecting the production of gas through the ANOVA of production data. This paper selects the R c/r and FFV for multivariate ANOVA, and proposes that the design of FFV can be based on the R c/r in the study area. The combination of other geological factors and FFV may also affect gas production and multivariate ANOVA of other geological parameters, and FFV may be attempted later. In this paper, the coal samples in the study area are not used for the analysis of water intrusion, drainage, and water block in pores and fractures, and the experiment of Li et al. [40] is cited for illustration. The data in this paper are from the FZ block and ZZ block in Qinshui Basin, which is a high-rank coal, so the applicability of the optimal combination and the reference of FFV parameter design are only applicable to this block.

Conclusions
(1) One-way ANOVA shows that FFV has a significant effect on gas production. In particular, with the increase of FFV, the gas production increases first and then decreases, and the best gas production is when the FFV is 500-600 m 3 in the study area. (2) When the R c/r < 0.5 (0-0.3 and 0.3-0.5), the gas production is negatively correlated with the FFV. When the R c/r > 0.5 (0.5-0.8 and 0.8-1), the gas production increases first and then decreases with the increase of FFV. The best combination for gas production is the R c/r of 0.8-1 and the FFV of 500-700 m 3 . (3) It is found that too much injected fracturing fluid will increase the fluid leakage and lead to the water block damage of coal reservoir, and the increase of the R c/r is conducive to removing the water block damage. Therefore, it is necessary to adapt the optimal amount of fracturing fluid according to the condition of the R c/r in the study area, so as to achieve the best fracturing effect.