# Numerical simulation of enhancing coalbed methane recovery by injecting CO_{2} with heat injection

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## Abstract

The technology used to enhance coalbed methane (CBM) recovery by injecting CO_{2} (CO_{2}-ECBM) with heat, combining heat injection with CO_{2} injection, is still in its infancy; therefore, theoretical studies of this CO_{2}-ECBM technology should be perused. First, the coupling equations of the diffusion–adsorption–seepage–heat transfer fields of gas are established. The displacement processes under different pressures and temperatures are simulated by COMSOL. Finally, the displacement effects, a comparison of the CO_{2} storage capacity with the CH_{4} output and the effective influencing radius of CO_{2} injection are analyzed and discussed. The results show that (1) the displacement pressure and temperature are two key factors influencing the CH_{4} output and the CO_{2} storage capacity, and the increase in the CO_{2} storage capacity is more sensitive to temperature and pressure than the CH_{4} output. (2) The gas flow direction is from the injection hole to the discharge hole during the displacement process, and the regions with high velocity are concentrated at the injection hole and the discharge hole. (3) A reduction in the CH_{4} concentration and an increase in the CO_{2} concentration are obvious during the displacement process. (4) The effective influencing radius of injecting CO_{2} with heat increases with the increase in time and pressure. The relationship between the effective influencing radius and the injection time of CO_{2} has a power exponential function, and there is a linear relationship between the functional coefficient and the injection pressure of CO_{2}. This numerical simulation study on enhancing CBM recovery by injecting CO_{2} with heat can further promote the implementation of CO_{2}-ECBM project in deep coal seams.

## Keywords

CO_{2}-ECBM Numerical simulation Displacement effect COMSOL CO

_{2}storage capacity Effective influencing radius

## 1 Introduction

Enhancing coalbed methane (CBM) recovery by injecting CO_{2} (CO_{2}-ECBM) is a new technology used to increase CBM production (Pan et al. 2017; Ranathunga et al. 2017a, b), indicating that CO_{2} can be permanently sequestered in unmineable coal seams and thus increase CBM production (Li et al. 2017). The adsorption capacity of CO_{2} in coal is better than that of CH_{4} in high-temperature and pressure environment (Andreas and Yves 2011). Therefore, when CO_{2} is injected and adsorbed on a matrix in coal, it can improve not only the CO_{2} storage capacity, but also the CH_{4} output (Pratama et al. 2018).

The injected CO_{2} has a supercritical state and a normal state (Yasunami et al. 2010; Vanelle and Gajewski 2011). Although supercritical CO_{2} has excellent enhancement effects on increasing the CH_{4} output compared to normal CO_{2} (Ranathunga et al. 2017a, b), the requirement for normal CO_{2} to reach supercritical CO_{2} (pressure > 7.38 MPa, temperature > 31.1 °C) is relatively stringent (Zhang et al. 2011a, 2013). Therefore, increasing attention has been paid to the displacement process of enhancing CBM recovery by injecting CO_{2} with heat in deep coal seams in geological environments that cannot reach supercritical conditions due to the influence of the thermal environment on the pore structures and adsorption behavior (Mandadige 2017; Feng et al. 2017; Zhang et al. 2017).

The numerical simulation to enhance CBM recovery can be divided into heat injection and gas injection (Wei et al. 2007; Zhou et al. 2013). For heat injection, scholars mainly carry out studies based on the experimental simulation and mainly discuss the influences of heat injection on CH_{4} seepage velocity and compare CBM production in thermal or nonthermal environments (Yasunami et al. 2010; Vilarrasa and Rutqvist 2017; Qu et al. 2017). Gas injection simulation is more systematic than heat injection simulation (Vishal et al. 2013; Ma et al. 2017). Scholars mainly focus on analyzing and deriving numerical models (i.e., multi-gas adsorption model, heat transfer model and fluid–solid coupled model; Liu and Smirnov 2008; Vishal et al. 2013; Sun et al. 2016), which have been successfully applied to the numerical software (i.e., COMSOL, COMET and SIMEDWin). Previous studies have shown that the injection of heat and CO_{2}, individually, into coal can enhance CBM production. However, there are few publications on how to combine heat injection and CO_{2} injection. Few people are involved in the field of CO_{2} with heat injection, and few scholars have considered using CO_{2} as a heat-carrying medium.

To improve theoretical studies on technologies to displace CBM by injecting CO_{2} with heat, the coupling equations of gas diffusion–adsorption–seepage–heat transfer fields are established, and the displacement processes at different pressures and temperatures are simulated by COMSOL in this research. The displacement effect, the comparison of the CO_{2} storage capacity with CH_{4} output and the effective influencing radius of CO_{2} injection under different pressures and temperatures are analyzed and discussed. Carrying out the numerical simulation of enhancing CBM recovery by injecting CO_{2} with heat under the geological conditions of the Qinshui Basin has important practical value and theoretical significance for promoting the implementation of this technology.

## 2 Theoretical analysis

In this study, COMSOL software (www.comsol.com), based on the finite element method, was used to carry out the numerical simulation analysis of enhancing CBM recovery by injecting CO_{2} with heat (Taheri et al. 2017; Liu et al. 2017a, b). COMSOL has been widely used to solve problems in the geosciences (i.e., element migration, fluid migration and heat transfer), and the widely used partial differential equation module has a strong capability of coupling physical fields (Ni et al. 2017; Ma et al. 2017).

### 2.1 Governing equations

There are several assumptions applied to establish governing equations (Wei et al. 2007; Vishal et al. 2013): (a) Coal is a dual and isotropic porous medium containing both pores and fractures; (b) there is only CO_{2} and CH_{4} in the coal seam without water, and the adsorption and desorption of multiple gases is in accordance with the extended Langmuir model; (c) the gas in pore is free, conforming to the ideal gas equation; (d) the migration of gas in pores obeys Fick’s law, and the transport of gas in fractures obeys Darcy’s law; and (e) there is a mass exchange between the diffusion and percolation processes of gas.

#### 2.1.1 Mass conservation equation for gas diffusion motion

_{4}and CO

_{2}in coal follows the Fick’s diffusion law (Eq. 1; Sampath et al. 2017; Liu et al. 2018).

*C*

_{1}and

*C*

_{2}are the mole concentration of CH

_{4}and CO

_{2},

*D*

_{1}and

*D*

_{1}are the gas diffusion coefficient of CH

_{4}and CO

_{2}and

*S*

_{1}and

*S*

_{2}denote the source terms, which reflect the mass exchange between adsorption phase and free phase.

#### 2.1.2 Mass conservation equation of gas seepage motion

_{4}and CO

_{2}in coal follows Darcy’s law based on the analysis of the mass conservation equation (Eq. 2; Xu et al. 2017; Li et al. 2016; Zhong et al. 2016; Le et al. 2017).

*φ*denotes the porosity of coal,

*M*

_{1}

*and M*

_{2}are the mole mass of CH

_{4}and CO

_{2},

*R*is the gas constant,

*T*denotes the gas temperature,

*P*

_{1}and

*P*

_{2}represent the pressure of CH

_{4}and CO

_{2},

*K*

_{1}and

*K*

_{2}are the permeabilities of CH

_{4}and CO

_{2},

*μ*

_{1}and

*μ*

_{2}represent the dynamic viscosity of CH

_{4}and CO

_{2}and

*S*

_{1}and

*S*

_{2}are the source term in the seepage field.

#### 2.1.3 Multi-gas adsorption equations

*S*

_{1}

*and S*

_{2}in the seepage equation can be derived according to Eq. 3.

*ρ*

_{c}is the density of the coal,

*ρ*

_{1a}and

*ρ*

_{2a}are the density of CH

_{4}and CO

_{2}under standard conditions,

*a*

_{1}and

*a*

_{2}are the Langmuir volume parameter of CH

_{4}and CO

_{2},

*b*

_{1}and

*b*

_{2}are the Langmuir pressure parameter of CH

_{4}and CO

_{2}and

*τ*denotes the desorption diffusion coefficient, which reflects the difficulty of desorption of the adsorbed gas and diffusion to the fracture system.

#### 2.1.4 Heat transfer equation

*C*

_{c,p}denotes the specific heat capacity of coal,

*C*

_{mix,p}denotes the ratio heat capacity of mixed gas,

*β*

_{c}denotes the thermal conductivity of coal,

*β*

_{mix}is the thermal conductivity of mixed gas and

*Q*

_{TS}is the source terms in the heat transfer field.

#### 2.1.5 Relationship between porosity, permeability and in situ stress

_{2}with heat is also affected by the in situ stress environment, which further affects the porosity of coal. The expression is as follows:

*φ*

_{0}denotes the initial porosity of coal,

*φ*

_{r}denotes the porosity of coal in a high-pressure stress state,

*α*

_{φ}denotes the stress sensitivity coefficient of permeability and

*σ*

_{v}denotes average effective stress. The expression is as follows:

*α*denotes the effective stress coefficient of Biot and

*σ*

_{1},

*σ*

_{2}and

*σ*

_{3}denote the minimum, intermediate and maximum principal stress, respectively.

*k*denotes the permeability after stress action and

*k*

_{0}denotes the initial permeability.

### 2.2 Coupling of equations

The processes of enhancing CBM recovery by injecting CO_{2} with heat include the processes of gas seepage–adsorption–diffusion–heat transfer in a porous medium. The seepage field, coupled with the diffusion field through flow velocity and with the adsorption field through source terms, is coupled with the heat transfer field by controlling convection heat transfer. The multiple gas adsorption field, coupled with the diffusion field through the concentration distribution and the seepage field through the partial pressure, is coupled with the heat transfer field by the relationship between the adsorption constant and temperature. When the heat transfer field is influenced by the seepage velocity, the temperature distribution will also affect the permeability distribution, gas density and gas viscosity in the seepage field. Meanwhile, it will also affect the adsorption constant in the adsorption field, so that it can be coupled with the multiple gas adsorption field. The porosity and permeability will also be affected by the in situ stress environment.

## 3 Model description and model validation against experimental data

### 3.1 Model description

_{2}and heat is a three-dimensional process that can be simplified to a two-dimensional (2D) process by considering the feasibility and effectiveness of numerical calculation (Sang et al. 2016). The geological model is a square area of 20 m, one-fourth region of which is selected as the numerical simulation area considering the symmetry of the affected area (Fig. 1). The upper right corner of the region is the CO

_{2}injection hole (

*H*

_{in}), and the lower left corner is the CH

_{4}discharge hole (

*H*

_{out}). The centerline,

*L*, connecting the CO

_{2}injection hole and the CH

_{4}discharge hole, is selected as a 2D transversal (Fig. 1).

### 3.2 Simulation schemes and physical parameters

_{2}with heat, the simulation schemes can be carried out as follows (Table 1). By changing the injection pressure or temperature, this paper carries out a comparative study of displacement effect with different displacement pressures at the same injection temperature and different injection temperatures at the same displacement pressure.

Numerical simulation scheme of enhancing CBM recovery by injecting CO_{2} with heat

Injection pressure, MPa | Injection temperature, K |
---|---|

3 | 293.15 |

5 | 293.15 |

7 | 293.15 |

5 | 313.15 |

5 | 333.15 |

_{2}-ECBM process in the southern Qinshui Basin is the first technical well in China (Zhang et al. 2011b). For the numerical simulation of enhancing CBM recovery by injecting CO

_{2}and heat, all parameters concerning coal are derived from the experimental results of the same samples collected from No. 3 coal seams in the TL-003 well (i.e., mercury injection experiments, liquid nitrogen experiment, adsorption experiments, nuclear magnetic resonance and displacement experiment). Other parameters needed for the numerical simulation are derived from other scholars’ research results in the same research area (Ye et al. 2007, 2012, 2016). The relevant parameters are given in Table 2.

Physical parameters of numerical simulation for enhancing CBM recovery by injecting CO_{2} with heat injection

Symbol | Parameter | Value | Unit |
---|---|---|---|

| Density of coal | 1.38 × 10 | kg/m |

| Initial porosity of coal | 0.084 | – |

| Initial permeability of coal | 2.6 × 10 | m |

| Mole mass of CH | 16 | g/mol |

| Langmuir parameter of CH | 0.03832 | m |

| Langmuir parameter of CH | 0.51 | 1/MPa |

| Dynamic viscosity of CH | 1.03 × 10 | Pa s |

| Mole mass of CO | 44 | g/mol |

| Langmuir parameter of CO | 0.06329 | m |

| Langmuir parameter of CO | 1.92 | 1/MPa |

| Dynamic viscosity of CO | 1.38 × 10 | Pa S |

| Gas constant | 8.314 | J/(mol K) |

| Thermal conductivity of coal | 0.2 | W/(m K) |

| Specific heat capacity of coal | 1.25 × 10 | J/(kg K) |

| Stress sensitivity coefficient of permeability | 5.0 × 10 | Pa |

| Effective stress coefficient of Biot | 1 | – |

| Desorption diffusion coefficient | 1.42 | ms |

### 3.3 Boundary setting and initial conditions

#### 3.3.1 Seepage field

According to the simulation scheme, the boundary condition of the CO_{2} injection hole is constant pressure, and the *p*_{in} is 3 MPa, 5 MPa and 7 MPa, respectively. The boundary condition of the CH_{4} discharge hole is connected to the bottom hole flow pressure; thus, the *p*_{out} is set to 0.5 MPa. The condition of the other boundaries is set to zero flow. It is assumed that the initial pressure of the coal seams is 2.5 MPa, the free gas pressure is 2.5 MPa, and the adsorbed gas is a saturated adsorption state at 2.5 MPa.

#### 3.3.2 Diffusion field

According to the simulation scheme, the boundary condition of the CO_{2} injection hole is a constant concentration, and the concentration of CO_{2} is 820 mol/m^{3}, 1641 mol/m^{3} and 2462 mol/m^{3}, respectively. The boundary condition of the CH_{4} discharge hole is connected to the export. The condition of the other boundaries is set to zero flow. It is assumed that CH_{4} at a concentration of 451.7 mol/m^{3} in the coal is saturated at 2.5 MPa in the original condition, and there is no CO_{2} in the coal.

#### 3.3.3 Heat transfer field in a porous medium

According to the simulation scheme, the boundary condition of the CO_{2} injection hole is a constant temperature, and the *T*_{in} is 293.15 K, 313.15 K or 333.15 K, respectively. The boundary condition of the CH_{4} discharge hole is connected with the atmosphere. It is defined as the constant temperature boundary, and the *T*_{out} is 293.15 K. The condition of the other boundaries is set to a constant temperature. It is assumed that the initial temperature of the coal seam is 293.15 K.

### 3.4 Model validation against experimental data

Some laboratory experiments can be carried out to verify the accuracy of the coupling models. The setting of the required parameters and boundary conditions are consistent with the numerical simulation conditions. The laboratory experiments maintain the isothermal process, which means that the displacement mole fraction of CO_{2} (i.e., injection of CO_{2} mol number/initial CH_{4} mol number) and the displacement efficiency of CH_{4} (i.e., output of CH_{4} mol number/initial CH_{4} mol number) in the numerical simulation results can be better compared to those in the laboratory experiment results without considering the influence of temperature.

_{2}, a large amount of CH

_{4}was displaced from the coal seam, and CO

_{2}was sequestered in the coal seam. At the initial stage of CO

_{2}injection, the output rate of CH

_{4}was high. With the continuous injection of CO

_{2}, the permeability of the coal seam decreased as a result of the adsorption deformation of coal, and the injectivity of CO

_{2}was reduced. It can also be seen that the experimental and simulation results are consistent. The maximum error is less than 10%, which proves the rationality of the coupling models by injecting CO

_{2}. Therefore, the coupling models with multi-physical fields can be used to simulate the displacement process by injecting CO

_{2}with a heat injection.

## 4 Results and analysis

In this study, the displacement effect of enhancing CBM recovery by injecting heat and CO_{2} can be analyzed from gas injection, different displacement pressures and different displacement temperatures.

### 4.1 Displacement process of gas injection and the analysis of this effect

The displacement effect of gas injection can be analyzed according to the pressure distribution, the temperature distribution and the concentration distribution.

_{2}at high pressure moves from the CO

_{2}injection hole toward the middle of the coal seam as time goes on. On the 10th day, the pressure distribution reached 7 m. On the 50th day, the influencing range of gas pressure has nearly covered the entire coal seam. The gas pressure in coal changes obviously when the time of the gas injection lasts for less than 40 days. The gas pressure changes slowly as the displacement time increases, especially after the 60th day. The partial pressure of CH

_{4}increases due to the energy caused by CO

_{2}. The highest point of the pressure moves to the CH

_{4}discharge hole based on the fact that the injection pressure of CO

_{2}is higher than that of CH

_{4}in the original formation.

_{2}injection process (Fig. 4). In the early stage of CO

_{2}injection, the ranging radius of the temperature obviously changes, but the increase in the radius decreases.

_{4}concentration around the injection hole varies significantly. The reducing range of concentration increases as time passes, and there is an area with a CH

_{4}concentration near 0 mol/m

^{3}. The influencing radius of CO

_{2}concentration expands, which is in accordance with the changing range of CH

_{4}concentration. Therefore, it can be seen that the CO

_{2}injection has a significant effect on the displacement of CH

_{4}in coal (Figs. 5, 6). The changing range of CH

_{4}and the CO

_{2}concentration has a strong correspondence. The lowest concentration of CH

_{4}can reach 0 mol/m

^{3}, that is, CH

_{4}has been completely displaced. The highest concentration of CO

_{2}can reach 1750 mol/m

^{3}, which shows that coal has a strong carbon sequestration capacity.

### 4.2 Analysis of the displacement effect under different displacement pressures

The displacement effect under different displacement pressures can be analyzed according to gas pressure and concentration distribution with the same displacement time.

_{2}injection, the increase in the displacement pressure can increase the gas pressure in coal over a short time (Fig. 7), which improves the gas energy in the coal seam and allows CH

_{4}to be easily produced.

_{4}being driven out of coal is (Fig. 8), which shows that the increase in the displacement pressure can effectively remove the CH

_{4}from the original position and leave the coal seam in a short time, thus improving the CBM production. The greater the displacement pressure is, the greater the migration range of CO

_{2}in the same time is, and the difference of the influencing scope increases with time (Fig. 9). It is indicated that increasing displacement pressure can store more CO

_{2}in coal at the same time.

### 4.3 Analysis of the displacement effect under different displacement temperatures

The displacement effect analysis under different temperatures is mainly based on temperature distribution in the same displacement time.

## 5 Discussions

### 5.1 Comparative analysis of CO_{2} storage capacity and CH_{4} output

_{2}storage capacity and CH

_{4}output increase as time passes within the simulating timescale. With the increase in displacement pressure, there is a significant difference between the CO

_{2}storage capacity and the CH

_{4}output (Fig. 11a). When displacement pressure increases from 3 MPa to 7 MPa, the CH

_{4}output and the CO

_{2}storage capacity increase from 753.36 mol and 1610.78 mol to 2250.31 mol and 15,032.29 mol, respectively. On the 100th day, the CH

_{4}output and the CO

_{2}storage capacity at the displacement pressure of 5 MPa and 7 MPa are 2.00 times, 2.99 times and 4.21 times, 9.33 times that of 3 MPa (Fig. 11a). The displacement ratio is 2.14, 4.49 and 6.69, respectively, when displacement pressure is 3 MPa, 5 MPa and 7 MPa, which shows that the increase in displacement pressure can increase not only the CH

_{4}output and the CO

_{2}storage capacity but also the displacement ratio.

There is also a difference between the CH_{4} output and the CO_{2} storage capacity under different displacement temperatures. With the increase in the displacement temperature, the CH_{4} output and the CO_{2} storage capacity increase from 1638.32 mol and 6751.13 mol to 1732.11 mol and 6832.32 mol, respectively, on the 100th day. It can be seen that the increase in displacement temperature can increase the CH_{4} output and the CO_{2} storage capacity at the same time. The increase in the CO_{2} storage capacity is more sensitive to temperature than the CH_{4} output (Fig. 11b).

The increase in the displacement pressure increases the activation energy of the surface for the matrix in the coal during the displacing process. CO_{2} has more contact collisions with CH_{4} and will produce more CH_{4}. The increase in temperature plays a significant role in activating the gas. By heating the coal, the CH_{4} adsorbed on the coal surface is more easily desorbed, which moves more CH_{4} away from the matrix surface in the coal and provides more adsorption sites for CO_{2}. Because of the increase in temperature, the coal will produce a new fracture structure due to thermal action, which makes more CO_{2} adsorption space in coal. The above aspects cause an increase in the CO_{2} volume stored in coal, and the difference between the CH_{4} output and the CO_{2} storage capacity will become small as the temperature increases. Analyzing the relationship between CH_{4} output, CO_{2} storage capacity and time, temperature and pressure of gas injection can guide the development and implementation of the CO_{2}-ECBM project.

### 5.2 Analysis of the effective influencing radius of gas injection

The effective influencing radius of gas injection refers to the distance between the point with the lowest effective pressure, which can effectively displace the CH_{4} in coal, and the CO_{2} injection hole. The minimum distance that conforms to the condition is the effective influencing radius of gas injection (Wang et al. 2012). The author proposes that the radial distance between the point when the CH_{4} pressure is reduced to 0.1 MPa in coal and the CO_{2} injection hole is the effective influencing radius of the gas injection during the gas injection.

_{2}with heat injection. Therefore, the first 10 days are chosen to analyze the effective influencing radius of enhancing CBM recovery by injecting CO

_{2}with heat injection with different injection pressures and times. Table 3 shows that the effective influencing radius of gas injection increases with the increase in injection time and injection pressure, the increase in which is gradually reduced.

Effective influencing radius of enhancing CBM recovery by injecting CO_{2} with heat injection with different injection pressures and injection times

Injection time, days | Effective influencing radius with different injection pressures, m | ||
---|---|---|---|

3 MPa | 5 MPa | 7 MPa | |

1 | 1.0 | 1.9 | 2.9 |

2 | 1.8 | 3.1 | 4.4 |

4 | 2.5 | 4.4 | 5.6 |

6 | 3.1 | 5.7 | 6.3 |

8 | 3.6 | 6.4 | 7.0 |

10 | 4.0 | 6.9 | 7.6 |

*R*, and the gas injection time,

*t*,

*R*=

*At*

^{B}. According to regression analysis, there is a linear relationship among the coefficients,

*A*and

*B*, and the gas injection pressure,

*P*(Fig. 13), where

*A*= 0.47

*P*+ 0.22,

*B*= − 0.02

*P*+ 0.63 and

*R*= (0.47

*P*+ 0.22)

*t*

^{(−0.02P+0.63)}(3 ≤

*P*≤ 7 MPa). Analyzing the relationships among the effective influencing radius of gas injection and the gas injection pressure and time, it is beneficial to guide the development and implementation of the CO

_{2}-ECBM project.

## 6 Conclusion

_{2}with heat injection, the coupling equations of gas diffusion–adsorption–seepage–heat transfer fields are established, and the displacement processes under different pressures and temperatures are simulated by COMSOL. The displacement effect, the comparison of the CO

_{2}storage capacity with the CH

_{4}output, and the effective influencing radius of CO

_{2}injection under different pressures and temperatures are emphatically analyzed and discussed. The main conclusions are as follows.

- (1)
The displacement pressure and temperature are the key factors influencing the CH

_{4}output and the CO_{2}storage capacity, which can be significantly increased by improving the displacement pressure and temperature. The displacement ratio can also be improved. The CO_{2}storage capacity is more sensitive to temperature and pressure than the CH_{4}output. - (2)
The decrease in the CH

_{4}concentration and the increase in the CO_{2}concentration are obvious during the displacement process of injecting CO_{2}with heat injection. The coal seams have a high storage capacity for CO_{2}, and the increase in the displacement radius decreases as time passes. - (3)
The effective influencing radius of injecting CO

_{2}with heat injection is increased with the increase in time and pressure, but the increase in the radius is gradually reduced. The relationship between the effective influencing radius and the time of gas injection has a power exponential function, and there is a linear relationship between the function coefficient and the gas injection pressure. It is beneficial to guide the development and implementation of the CO_{2}-ECBM project by analyzing the relationship between the effective influencing radius and injection pressure with injection time.

## Notes

### Acknowledgements

We would like to express our gratitude to the two anonymous reviewers for offering their constructive suggestions and comments which improved this manuscript in many aspects. The work was financially supported by the National Natural Science Foundation of China (No. 41330638).

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