Numerical Study on the Evolution of Reservoir Pressure and CBM Concentration Considering Hydraulic Fractures

Abstract

Based on the theories of mass conservation and coalbed methane (CBM) adsorption/desorption, this paper first establishes a novel reservoir pressure model for CBM production, following which, the CBM concentration and production models are also proposed. Then, these models are programmed and solved by means of the finite element method. Taking the Hunchun CBM field in Jilin province, China, as an example, the reservoir pressure, gas concentration, and production characteristics under different hydraulic fracture forms are simulated and investigated. In conclusion, the reservoir pressure decreases very rapidly in a small region near the fracture tip, which we called the “reservoir pressure singularity”. The existence of a hydraulic fracture greatly reduces the reservoir pressure in the process of CBM exploitation. The permeability sensitivity coefficient of reservoir pressure, R_pk, is defined to quantitatively describe the influence of coal seam permeability on the evolution of reservoir pressure. R_pk decreases logarithmically as the distance from the CBM extraction well increases. The reservoir pressure and CBM recovery rate characteristics in the presence of multiple hydraulic fractures are also investigated. We believe these results could contribute to the design of hydraulic fracturing wells and the evaluation of gas production in a CBM reservoir.

1. Introduction

As a type of unconventional natural gas, CBM has huge reserves in China. The shallow CBM resources of 42 major coal-bearing basins in China with a depth less than 2000 m are about 36.8 × 10¹² m³ (see Figure 1). However, CBM recovery is limited due to the extremely low porosity and permeability of some CBM reservoirs [1]. Low average single well production has become the main bottleneck problem for the development of China’s CBM industry. Hydraulic fracturing technology could effectively enhance the permeability of CBM reservoirs and has been widely used in CBM extraction engineering [2,3]. As a porous adsorption medium, coal is both the source rock and reservoir rock for Coalbed methane (CBM). To exploit CBM, water in a reservoir is first drained to reduce the reservoir pressure. After the fluid pressure decreases below the critical desorption pressure level, CBM begins to desorb and diffuse into cleats or fractures and then penetrates into the shaft. Permeability is a key controlling factor of gas transport in coal and gas production, through which CBM recovery rates and economic benefits are influenced.

CBM mainly exists in the form of adsorbed gas in coal reservoirs. During the CBM exploitation, methane can be desorbed and penetrates towards the wellbore only when the reservoir pressure sufficiently depletes below the critical desorption pressure [5,6]. The traditional approaches and developed models for in-place natural gas resource and reserve estimation calculations suitable for reservoir rocks displaying a wide range of permeability and porosity distributions are described by Radwan et al. (2022) [7]. The reservoir pressure is one of the most important parameters that affect CBM exploitation, and directly controls the content and saturation of adsorbed gas in coal reservoirs. The reservoir pressure may change dynamically as CBM is extracted. A pressure drop funnel will be formed around the drainage well to rapidly reduce the reservoir pressure [8]. With the progress of CBM exploitation, the reservoir pressure decreases continuously from the near field to the far, and the range of the pressure drop funnel continues to expand [9,10]. When the reservoir pressure after drainage is reduced to the critical desorption pressure, the methane adsorbed in the coal seam is gradually desorbed and penetrates to hydraulic fractures and wellbore. With the expansion of the range of the pressure drop funnel, the desorption radius of CBM also becomes larger. The schematic diagram of coal seam pressure drop propagation is shown in Figure 2. Accurate determination of the spatiotemporal dynamic evolution of reservoir pressure is the key to effectively assessing desorption intensity, cross-well interference, and gas production [6,11]. Clarkson et al. (2007 [12], 2009 [13]) investigated the reservoir pressure evolution in a CBM reservoir in Canada and concluded that the average reservoir pressure could be obtained from the material balance equation. Based on Chen et al. (2015) [14], the reservoir pressure could directly affect coal intrinsic permeability, thus determining the output of CBM. Li et al. (2016) [15] investigated the influence of fracture distribution on reservoir pressure depletion, and summarized the depressurization transferring modes. In addition, they proposed a theoretical model to calculate the reservoir depressurization for bounded drainage. In short, numerous researchers have investigated the evolution of reservoir pressure in CBM extraction. Among them, few studies have considered the influence of hydraulic fracture morphology and distribution.

CBM production is determined by many factors, including the reservoir pressure [2], gas concentration [16] (Ma et al., 2017), and extraction measures, e.g., hydraulic fracturing [3]. After hydraulic fracturing, the production of coalbed methane will increase by 5–20 times [17,18]. Complex fractures within a complex system of joints, natural fractures, and cleats can be created by hydraulic fracturing [19,20]. The newly generated fractures enhance the permeability of the coal seam [21]. Many classic fracture models have been proposed, including PKN, KGD, and penny-shaped crack models, to investigate fracture propagation during fluid injection (Nordgren, 1972; Geertsma and Klerk, 1969) [22,23]. In fractured rocks, the coupling of the mechanical–hydrologic processes, including stress-induced changes in fracture apertures and poroelastic effects, exert a significant influence on a reservoir’s properties. Zhi et al. (2018) found that the hydraulically stimulated fracture pathways, especially when connecting with a natural fracture network, optimally improve methane production and potential recovery [3]. To better enhance the reservoir permeability, the reservoir is often perforated in different directions from the pumping well, resulting in multiple hydraulic fracture networks. In recent years, significant progress has been made in modelling complex hydraulic fracture networks (Tomac and Gutierrez, 2017; Peshcherenko and Chuprakov, 2021; Li et al., 2021) [24,25,26]. Zou et al. (2021) [27] simulated the propagation of complex hydraulic fracture networks by means of the cohesive element method, and the interaction of multiple fractures and the interference effect among adjacent hydraulic fracture branches are also interpreted. However, there are few studies on the superposition of reservoir pressure among multiple fractures and the influence of multiple hydraulic fractures on CBM recovery rate.

In this paper, a reservoir pressure model for CBM production is first derived. The model is then programmed and solved by means of multi-field coupling analysis software (COMSOL Multiphysics). In Chapter 2, the reservoir pressure evolution model for CBM production is derived, by which, the reservoir CBM concentration, Q, could also be calculated. In Chapter 3, Taking the Hunchun coalbed methane field in Jilin province, China, as an example, the built numerical simulation model, including the initial condition and boundary condition, is introduced. In Chapter 4, the reservoir pressure and CBM production under the influence of hydraulic fractures are investigated. Chapter 5 gives the obtained main conclusions.

2. Reservoir Pressure Model for CBM Production

According to the conservation of mass, the continuity equation of CBM flow in the reservoir can be expressed as

$$\frac{\partial ({\rho }_g{q}_x)}{\partial x}+\frac{\partial ({\rho }_g{q}_y)}{\partial y}+\frac{\partial ({\rho }_g{q}_z)}{\partial z}=-\frac{\partial Q}{\partial t}$$

(1)

where ρ_g is the flowing methane concentration (kg/m³); q_x, q_y, q_z are the CBM flow rates in the x, y, and z directions, respectively (m/s); and Q is the mass concentration of CBM in the reservoir (kg/m³).

Assuming that the effect of temperature on the adsorption constant is ignored, and CBM in the reservoir consists of two parts, i.e., adsorbed gas and free gas, the adsorbed CBM concentration can be described by the Langmuir equation $Q_a=\frac{v_{l}p}{p_l+p}\cdot {\rho }_n$ [28,29]. Based on the equation of state for real gas, the free gas concentration can be written as $Q_f=\frac{\varphi p}{Z\cdot p_n}\cdot {\rho }_n$ [1]. Therefore, the equation of whole CBM concentration is

$$Q=Q_a+Q_f=(\frac{v_{l}p}{p_l+p}+\varphi \frac{p}{Z\cdot p_n})\cdot {\rho }_n$$

(2)

where $v_l$ is the Langmuir volume (m³/kg); $p_l$ is the Langmuir pressure (MPa); $\varphi$ is the porosity; $p$ represents the reservoir pressure (MPa); $p_n$ is the gas pressure in the standard state, which takes 0.10325 MPa in this paper; ${\rho }_n$ is the methane density in the standard state (kg/m³); and Z is the compression factor, which is approximately 1.0 when the temperature changes are not obvious.

It is assumed that the seepage of coalbed methane in the reservoir conforms to Darcy’s Law:

$$q=-\frac{k}{\mu }\frac{\partial p}{\partial n}$$

(3)

where k is the permeability of coal (m²); μ is the methane viscosity (mPa·s); and $\frac{\partial p}{\partial n}$ is the gas pressure gradient in the coal seam (MPa/m).

The state equation of coal seam gas can be expressed as

$${\rho }_g=\frac{{\rho }_{n}p}{p_{n}Z}$$

(4)

Combining Equations (3) and (4) results in

$${\rho }_{g}q=-\frac{k{\rho }_{n}p}{\mu p_{n}Z}\frac{\partial p}{\partial n}$$

(5)

The coal permeability decreases exponentially with the increase in effective stress [30,31,32]. A coal permeability model considering fracture compressibility is proposed by Seidle (1992) [33], which has been widely used in both laboratory permeability tests and in situ permeability analysis. The model can be expressed as Equation (5).

In recognizing the strains of a matrix block as the change in dimension divided by the original dimension, strains can also be expressed as

$$k=k_0\exp (-3C_f\Delta \sigma )$$

(6)

where $\Delta \sigma =\sigma -{\sigma }_0$ is the change in the effective stress, $C_f$ represents the coal cleat compressibility, and $k_0$ is the permeability when the effective stress is ${\sigma }_0$. The effective stress, σ, is equal to the total stress, ${\sigma }_t$, minus the pore pressure, $p$. Therefore, the change in the effective stress $\Delta \sigma =\sigma -{\sigma }_0={\sigma }_t-p-{\sigma }_0$. Notice that Equation (6) has a negative sign ‘−’ in bracket, i.e., $-\Delta \sigma ={\sigma }_0+p-{\sigma }_t$.

Combining Equations (5) and (6) produces

$${\rho }_g{q}_x=-\frac{k_0{\rho }_{n}p}{\mu p_{n}Z}\exp \left[3C_f\left({\sigma }_0+p-{\sigma }_t\right)\right]\frac{\partial p}{\partial x}$$

(7)

The methane viscosity, μ, under different pressures and temperatures has been tested by numerous researchers. Figure 3 shows the methane viscosity testing results by Lee (1965) [34], Diehl et al. (1970) [35], and Stephan and Lucas (1979) [36], respectively. When the pressure rises from 0 MPa to 12 MPa, the methane viscosity, μ, changes within the small region of 0.011~0.015 mPa. The methane viscosity is not sensitive to changes in pressure when the pressure is low. Therefore, in this paper, to simplify the calculation, the methane viscosity, μ, is assumed to be a constant value, which does not change with the pressure.

Taking the derivative of (7), we can obtain

$$\frac{\partial ({\rho }_g{q}_x)}{\partial x}=-\frac{k_0{\rho }_n}{\mu p_{n}Z}\exp \left[3C_f\left(p+{\sigma }_0-{\sigma }_t\right)\right]\left(3C_f+\frac{\partial p}{\partial x}+\frac{{\partial }^{2}p}{\partial x^2}\right)\frac{\partial p}{\partial x}$$

(8)

Similarly,

$$\left\{\begin{array}{c}\frac{\partial ({\rho }_g{q}_y)}{\partial y}=-\frac{k_0{\rho }_n}{\mu p_{n}Z}\exp \left[3C_f\left(p+{\sigma }_0-{\sigma }_t\right)\right]\left(3C_f+\frac{\partial p}{\partial y}+\frac{{\partial }^{2}p}{\partial y^2}\right)\frac{\partial p}{\partial y}\\ \frac{\partial ({\rho }_g{q}_z)}{\partial z}=-\frac{k_0{\rho }_n}{\mu p_{n}Z}\exp \left[3C_f\left(p+{\sigma }_0-{\sigma }_t\right)\right]\left(3C_f+\frac{\partial p}{\partial z}+\frac{{\partial }^{2}p}{\partial z^2}\right)\frac{\partial p}{\partial z}\end{array}\right.$$

(9)

Therefore, the following partial differential equation can be obtained

$$\begin{array}{l}\frac{\partial ({\rho }_g{q}_x)}{\partial x}+\frac{\partial ({\rho }_g{q}_y)}{\partial y}+\frac{\partial ({\rho }_g{q}_z)}{\partial z}\\ =\lambda \left[{\left(\frac{\partial p}{\partial x}\right)}^2+{\left(\frac{\partial p}{\partial y}\right)}^2+{\left(\frac{\partial p}{\partial z}\right)}^2+\frac{{\partial }^{2}p}{\partial x^2}\frac{\partial p}{\partial x}+\frac{{\partial }^{2}p}{\partial y^2}\frac{\partial p}{\partial y}+\frac{{\partial }^{2}p}{\partial z^2}\frac{\partial p}{\partial z}+3C_f\left(\frac{\partial p}{\partial x}+\frac{\partial p}{\partial y}+\frac{\partial p}{\partial z}\right)\right]\end{array}$$

(10)

where λ is a parameter that we set to simplify the formula and has no actual physical meaning. It is a function of the pore pressure, p:

$$\lambda =-\frac{k_0{\rho }_n}{\mu p_{n}Z}\exp \left[3C_f\left(p+{\sigma }_0-{\sigma }_t\right)\right]$$

(11)

We take the time derivative of Equation (2), resulting in

$$-\frac{\partial Q}{\partial t}=-(\frac{v_l{p}_l}{{(p+p_l)}^2}+\frac{{\rho }_n\varphi }{p_{n}Z})\frac{\partial p}{\partial t}$$

(12)

The reservoir pressure equation for CBM production is finally obtained, combining with Equations (1), (10), and (12).

$$\begin{array}{l}\lambda \left[{\left(\frac{\partial p}{\partial x}\right)}^2+{\left(\frac{\partial p}{\partial y}\right)}^2+{\left(\frac{\partial p}{\partial z}\right)}^2+\frac{{\partial }^{2}p}{\partial x^2}\frac{\partial p}{\partial x}+\frac{{\partial }^{2}p}{\partial y^2}\frac{\partial p}{\partial y}+\frac{{\partial }^{2}p}{\partial z^2}\frac{\partial p}{\partial z}+3C_f\left(\frac{\partial p}{\partial x}+\frac{\partial p}{\partial y}+\frac{\partial p}{\partial z}\right)\right]\\ =-(\frac{v_l{p}_l}{{(p+p_l)}^2}+\frac{{\rho }_n\varphi }{p_{n}Z})\frac{\partial p}{\partial t}\end{array}$$

(13)

Combining Equation (2), the reservoir CBM concentration, Q, can also be calculated.

3. Numerical Simulation Model

3.1. Engineering Background

The CBM reservoir is situated is the Hunchun low-rank coalfield in Jilin Province, China. With developed multi-minable thin coal seams, the regional structural characteristics of the Hunchun coalfield are relatively simple and clear. The largest proportion of coal in the coal seam is semi-bright coal, which is followed by semi-dark type. The average bulk density is 1340 kg/m³. The majority of macerals is vitrinite, at 78.59%, while the proportions of inertinite and exinite are 4.21% and 1.25%, respectively; the maximum vitrinite reflectance is 0.567%. The seam’s existing occurrence depth increases with distance, with the vitrinite reflectance rising 0.05% every 100 m.

Based on microseismic monitoring results during field hydraulic fracturing, when the injection rate is 0.117 m³/s, the half-length of the hydraulic fracture on one side of the borehole is about 130 m. Figure 4 shows the in-situ curve of CBM production of well #BLCX-1005. The average daily gas production decreases exponentially with the production time, and the average gas production over the five years is 1058 m³/day.

According to the physical and mechanical test results, the main model parameters are shown in

Table 1. Main model parameters.

Elastic Modulus (GPa)	Poisson’s Ratio	Cleat Compressibility (MPa−1)	Initial Permeability (mD)	Porosity/%
4.71	0.26	0.16	0.704	11
Coal density (kg/m3)	Methane density (kg/m3)	Gas pressure in standard state Pn (MPa)	Compression factor Z	Methane viscosity $\mu$ (mPa·s)
1340	0.716	0.10325	1	0.011

.

3.2. Numerical Model

A finite element numerical model of the CBM reservoir was established by means of COMSOL Multiphysics software. The calculation of reservoir pressure in the process of gas production is reduced to the problem of solving partial differential equations. The size of the simulated reservoir area is 2000 × 2000 m, and the schematic diagram of the model is shown in Figure 5. To obtain more accurate simulation results, the grid size is extremely small. The grid refinement is carried out near the production well.

Initial condition setting: in situ stress σ_x = σ_y = 7.17 MPa; reservoir pressure p₀ = 2.0 MPa. The first derivative of the initial reservoir pressure with respect to time is 0, i.e.,

$$\frac{\partial p}{\partial t}\left|{}_{t=0}=0\right.$$

(14)

Boundary condition setting: the gas flow pressure at the bottom of the well is 0.4 MPa, i.e.,

$$p\left|{}_{\mathsf{\Omega }}=0.4\right.$$

(15)

4. Reservoir Pressure and CBM Production under the Influence of Hydraulic Fractures

4.1. Constant Hydraulic Fracture Length

Hydraulic fracturing utilizes the high injection water pressure to destroy the rock and generate a fracture with a certain length, and a pressure relief zone is formed around the fracture. After desorption of the reservoir CBM, it seeps into hydraulic fracture, and then drains along the fractures. The existence of a hydraulic fracture greatly increases the permeability of coal seams.

Figure 6 shows the calculated results of reservoir pressure after 5 years. The reservoir pressure is distributed symmetrically in an elliptical shape with the hydraulic fracture direction as the long axis. The reservoir pressure contour distribution at the fracture tip is the densest, and the farther from the crack tip, the sparser the contour distribution. Similar to the concept of stress singularity of fracture tip, we believe that the phenomenon of “reservoir pressure singularity” exists near the fracture tip. We mean that the reservoir pressure decreases very rapidly in a small region near the fracture tip. In addition, the results of our simulation are related to the boundary conditions set. In this paper, we give a constant gas flow pressure at the bottom of the well of 0.4 MPa, which refers to the in situ measured values. However, with the continuous extraction of CBM, the reservoir pressure distribution changes dynamically.

To visualize the evolution of reservoir pressure, we set up two section lines that pass through the production well and are perpendicular to each other, as shown in Figure 7. The reservoir pressures on section lines 1 and 2 after CBM exploitation at different times are shown in Figure 8. The area where the reservoir pressure drops by more than 0.5 MPa after 5 years of mining is an elliptical area with a short axis of 130 m and a long axis of 190 m. The area with a drop of more than 0.2 Mpa is an elliptical area with a short axis of 270 m and a long axis of 310 m. The existence of a hydraulic fracture greatly reduces the reservoir pressure in the process of CBM exploitation, significantly increases the influence range of single-well extraction, and greatly rises the permeability of coal seams.

CBM production in the presence of a hydraulic fracture with the half-length of 130 m is calculated. Figure 8 shows the relationship between the daily gas production and the extraction time. As the CBM is extracted, the daily gas production gradually decreases. The average CBM production rate calculated by our model fits well with the in situ gas production within 5 years, and the maximum error is just 0.092, by which the accuracy of the numerical calculation has been verified. After 738 days of extraction, the gas production of a single well drops below 1000 m³/day, and the average daily gas production within 5 years is 1156 m³/day. The gas adsorption capacity of low-rank coal is generally low. For the Hunchun low-rank coalfield, the results of maintaining an average daily gas production above 1000 m³/day is quite impressive.

4.2. Permeability Sensitivity Analysis of the Reservoir Pressure

We know that permeability is a key controlling factor of gas transport in coal and gas production through which CBM recovery rates and economic benefits are influenced (Zou et al., 2016 [21], 2020 [37]). The CBM recovery rate is defined as the percentage of the produced CBM to CBM reserves in the reservoir. It can be calculated by the change of gas concentration in the reservoir:

$$\eta =\left(Q_0-Q_t\right)/Q_0$$

(16)

where, Q₀ is the initial reservoir CBM concentration, and Q_t is the average gas concentration of the reservoir at the extraction time of t.

Coal is a weak rock with cleat apertures, and thus permeability is sensitive to effective stress (Pan et al., 2012) [38]. As effective stress increases, permeability decreases exponentially; this relationship is supported by extensive laboratory studies [31,33]. Conversely, the permeability also affects reservoir pressure, which in turn affects the CBM recovery rate.

Figure 9 shows that he reservoir pressure evolution varies with permeability after 5 years of CBM extraction. Permeability has a significant effect on the reservoir pressure at different times during CBM extraction, especially near the well. The farther away from the well, the less reservoir pressure is affected. To quantitatively describe the influence of coal seam permeability on the evolution of reservoir pressure, we define the permeability sensitivity coefficient of reservoir pressure, R_pk:

$$R_{pk}=(p_1-p_2)/(k_2-k_1)\times 100\%$$

(17)

where R_pk is the permeability sensitivity coefficient of reservoir pressure, and p₂ and p₁ are the reservoir pressure when reservoir permeability is k₁ and k₂, respectively. The unit of p is MPa, and that of k is mD.

According to Equation (17), we calculated the permeability sensitivity coefficient of reservoir pressure, R_pk, at different distances from the CBM well, and the calculation results are shown in Figure 10. The permeability sensitivity coefficient of reservoir pressure, R_pk, decreases logarithmically as the distance from the CBM extraction well increases. This indicates that the influence range of the pressure drop funnel in the CBM extraction process is limited, and CBM adsorbed in the coal seam far away from the extraction well is difficult to be extracted. The permeability sensitivity coefficient of the reservoir pressure, R_pk, could contribute to optimizing the spacing of the CBM group wells.

4.3. Influence of a Hydraulic Fracture

The reservoir pressure for different hydraulic fracture morphologies is calculated, and those on profile line 1 (see Figure 7) after 5 years are shown in Figure 11, and those on profile line 2 are shown in Figure 12. The reservoir pressure drop of CBM exploitation with hydraulic fractures is much higher than that without hydraulic fractures, indicating that the effect of hydraulic fracturing is significant. With the increase in the hydraulic fracture length, the reservoir pressure drops after the CBM being extracted for the same time increases. The pressure drop difference along the fracture length is more significant than that perpendicular to the fracture.

The CBM concentrations for different hydraulic fracture lengths are also calculated, and those on profile lines 1 and 2 (see Figure 5) after 5 years of extraction are shown in Figure 13. When there is a hydraulic fracture, the CBM extraction volume is much larger than that without a hydraulic fracture. Figure 14 shows the average CBM production rate and CBM recovery rate of the reservoir with different fracture morphologies. With the increase in fracture length, the gas production rate at the same time gradually increases; the average daily gas production at the same time of extraction also increases gradually. Calculated over a five-year period, the average daily gas production of fractures with a half-length of 70–190 m is 792.9–1514.1 m³/day. Calculated based on the reservoir area of 4.0 km², the recovery rate of single well extraction is shown in Figure 14b. The CBM recovery rate is basically proportional to the fracture length. However, the recovery curve flattens out as the extraction progresses. The maximum recovery rate for a single well without a hydraulic fracture is just 0.0031, while for a hydraulic fracture half-length of 130 m, the recovery rate could reach 0.0169 after 5 years. However, due to the limitations of the physical and mechanical properties of the reservoir itself, construction equipment, and methods, the hydraulic fractures could not grow indefinitely. Considering the construction cost, there must be an optimal hydraulic fracture shape and gas production, which is not the focus of this paper.

4.4. Influence of Multiple Hydraulic Fractures

As shown in Figure 15, a CBM extraction numerical model with different hydraulic fracture morphologies is established, and the half-length of a single hydraulic fracture is 130 m. The reservoir pressure distribution after one month is calculated when one, two, three, and four hydraulic fractures exist, respectively. The superposition effect of reservoir pressure among multiple hydraulic fractures can be clearly seen. When multiple hydraulic fractures exist, CBM near fracture intersections can be fully desorbed, and the influence range of the pressure drop funnel formed in the CBM extraction process is also significant.

The CBM recovery rate results of the reservoir with different hydraulic fracture morphologies are shown in Figure 16. As the number of hydraulic fractures increases, CBM recovery rate increases in a quadratic function. This indicates that the formation of hydraulic fracture networks could greatly improve reservoir permeability, and CBM within the affected area of hydraulic fractures could be extracted in a short time. However, the impact of fracturing is limited, and the production of CBM will gradually plateau as the extraction proceeds.

The limitations of this paper are mainly reflected in the following three aspects. Firstly, we know that the CBM reservoir is generally anisotropic. However, this paper does not consider the anisotropic characteristics of the reservoir in the calculation of CBM permeability and migration process. Secondly, for low permeability CBM reservoirs, the gas slippage effect could be significant, and the influence of the gas slippage effect is assumed to be ignored. Thirdly, in the actual process of CBM extraction, the hydraulic fractures gradually close and even fill with impurities, which affects the gas production, which is not considered in this paper. In future work, the anisotropy characteristics of reservoir and gas slippage effects will be taken into account in the reservoir pressure model for CBM production. In addition, the proppant within multiple fractures will be considered in the numerical calculation model.

5. Conclusions

(1)

Based on the theories of mass conservation and CBM adsorption/desorption, this paper first established a novel reservoir pressure model for CBM production, following which, the CBM concentration and production models are proposed. Then, these models are programmed and solved by means of multi-field coupling analysis software (COMSOL Multiphysics). Taking the Hunchun CBM field in Jilin province, China, as an example, the reservoir pressure, gas concentration, and production characteristics under different hydraulic fracture forms are simulated and investigated.

(2)

The permeability sensitivity coefficient of reservoir pressure, R_pk, is defined. R_pk decreases logarithmically as the distance from the CBM extraction well increases. Permeability has a significant effect on the reservoir pressure at different times during CBM extraction, especially near the well. The farther away from the well, the less the reservoir pressure is affected.

(3)

The reservoir pressure is distributed symmetrically in an elliptical shape, with the hydraulic fracture direction as the long axis. The phenomenon of “reservoir pressure singularity” exists near the fracture tip, which means that the reservoir pressure decreases very rapidly in a small region near the fracture tip. The existence of a hydraulic fracture greatly reduces the reservoir pressure in the process of CBM exploitation, significantly increases the influence range of single-well extraction, and greatly rises the permeability of coal seams.

(4)

The reservoir pressure, CBM concentration, and production for different hydraulic fracture morphologies are calculated. With the increase in the hydraulic fracture length, the reservoir pressure drops, and gas production rate after the CBM being extracted for the same time increase. The pressure drop difference along the fracture length is more significant than that perpendicular to the fracture.

(5)

The evolution of reservoir pressure and CBM recovery rate are investigated in the presence of multiple hydraulic fractures. As the number of hydraulic fractures increases, CBM recovery rate increases in a quadratic function. The superposition effect of reservoir pressure among multiple hydraulic fractures is significant. When multiple hydraulic fractures exist, CBM near fractures’ intersection can be fully desorbed, and the influence range of the pressure drop funnel formed in the CBM extraction process is large.