_{2}Sequestration in Coal Seam: the Roles of Multiphase Flow and Gas Dynamic Diffusion on Fluid Transfer and Coal Behavior

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CO_{2} sequestration in coal seam has proved to be an effective way for reducing air pollution caused by greenhouse gases. A study on the rules of fluid transfer and reliability of CO_{2} storage during gas injection is necessary for the engineering application. However, the clarification of multifield coupling in long-term CO_{2} sequestration is the difficulty to solve the aforementioned problem. Previous investigations on the coupled model for CO_{2} storage in coal seam were not exactly comprehensive; for example, the multiphase flow in the fracture and the nonlinear behavior of gas diffusion were generally neglected. In this paper, a new multistage pore model of the coal matrix and the corresponding dynamic diffusion model were adopted. Meanwhile, the CO_{2}-induced coal softening and the CO_{2}-water two-phase flow in coal fracture were also taken into account. Subsequently, all the mentioned mechanisms and interactions were embedded into the coupled hydromechanical model, and this new fully coupled model was well verified by a set of experimental data. Additionally, through the model application for long-term CO_{2} sequestration, we found that the stored CO_{2} molecules are mainly in an adsorbed state at the early injection stage, while with the continuous injection of gas, the stored CO_{2} molecules are mainly in a free state. Finally, the roles of multiphase flow and gas dynamic diffusion on fluid transfer and coal behavior were analyzed. The results showed that the impact of multiphase flow is principally embodied in the area adjacent to the injection well and the coal seam with lower initial water saturation is more reliable for CO_{2} sequestration, while the impact of gas dynamic diffusion is principally embodied in the area far away from the injection well, and it is safer for CO_{2} sequestration in coal seam with greater attenuation coefficient of CO_{2} diffusion.

With the rapid development of human society industrialization, the anthropogenic emissions of greenhouse gases (GHG) such as CO_{2} are escalating, which is believed as a primary cause for global climate change [_{2} storage have been proposed, including geological sequestration [_{2} sequestration in unminable coal seams is the most concerned one worldwide because of its multiple benefits [_{2} injection is urgently needed.

The process of CO_{2} sequestration in coal seam can be described as follows: firstly, the CO_{2} discharged from industry is cooled and compressed into liquid or supercritical state; then, the processed CO_{2} is transported and injected into deep coal seam through a pipeline; and finally, the injected CO_{2} is stored in the coal seam under adsorbed state or free state after multiple mechanisms of migration, such as Darcy’s flow, diffusion, and adsorption [_{2} transfer and storage in coal seam [_{2} also has a strong feedback on coal mechanical behavior [_{2} sequestration in the coal seam. To date, there are various models that have been proposed under different assumptions. Wu et al. [_{2} injection. They viewed the coal seam as a dual-porosity dual-permeability media and found that the interactions between the fracture system and matrix system are crucial for analyzing the CO_{2} migration in coal seam. Qu et al. [_{2} sequestration. Additionally, several models for CO_{2} geological sequestration with different coupling relations have also been proposed in recent years. Masoudian et al. [_{2} storage. Fan et al. [_{2} storage efficiency. Further, Zhang et al. [_{2} injection rate and studying the mechanical behavior of coal.

Although considerable models have been proposed, there are still two imperfections in the recent studies. The first is that the effect of groundwater is usually neglected. Based on Fan et al.’s [_{2} sequestration or CO_{2} enhanced coalbed methane recovery. The preexisting water can complicate the fluid flow during CO_{2} sequestration in coal as a result of the interaction between the gas phase and liquid phase, which is mainly reflected by relative permeability [_{2} storage rate grossly.

Results of relative permeability from Watanabe et al. [

The second imperfection is that the prior models did not address the complex dynamic diffusion of CO_{2} in coal. But in fact, the nonlinear diffusion process of gas in coal matrix pore has been widely reported in previous investigations [_{2} diffusivities in coal under different pore structure and gas pressure. The results indicated that the CO_{2} diffusion in the coal matrix may not be a steady-state process and is largely dependent upon the pore structure and distribution. Therefore, to analyze the fluid flow in coal seam during CO_{2} geological sequestration and reveal the mechanical characteristic alterations induced by CO_{2} injection, an applicable coupled model, which considers multiphase flow and dynamic diffusion of gas, must be developed first.

This paper establishes a fully coupled CO_{2}-water-coal multiphase model in which the CO_{2} diffusion coefficient is dependent on the pore size of the coal and diffusion time. Young’s modulus and Poisson’s ratio of coal are also varied with the amount of the adsorbed CO_{2} in coal according to a set of experimental results. In addition, the impacts of multiphase flow and gas dynamic diffusion on CO_{2} storage efficiency and coal behavior were analyzed accordingly. Our investigation can improve the understanding of gas-water-coal interactions under complex coupling and better evaluate the reliability of storage conditions after CO_{2} injection.

Aiming at comprehensively clarifying the complex coupled process during CO2 geological sequestration, in this section, four governing equations and a set of coupling relations are developed, including coal deformation, gas diffusion in coal matrix, two-phase flow in coal fracture, CO2-indeced softening in coal, adsorption-induced coal swelling and stress-induced permeability alternations in coal fracture.

The diffusion and adsorption of gas in coal is the main reason why coal seam can capture and store CO_{2}. Thus, describing the diffusion behavior of CO_{2} in the coal matrix accurately is vitally important in making exactly the prediction of CO_{2} geosequestration. Typically, the unipore diffusion model is adopted to express the gas diffusion in porous media, as shown in Figure _{2} storage (see in Figure _{2} diffusion coefficient varies with time because of the narrowing diffusion path (see in Figure _{2}, and _{2} diffusion [_{2} pressure in the matrix, _{2} pressure in fracture, _{2}, _{2} under standard condition, _{2} diffusion between the coal matrix and fracture, which is defined as a nonlinear process in this paper.

Two different models for CO_{2} diffusion in coal matrix pore.

As a result of initial water saturation, the fluid flow in coal fracture should be regarded as a two-phase flow process during CO_{2} injection. Based on a previous study [_{2} or water, respectively),

In this paper, we assume that the water only exists in the fracture system, while the CO_{2} exists in both the fracture system and the matrix system, and the CO_{2} in the fracture can further diffuse into the coal matrix. Therefore, the flow sinks for gas and water in the fracture can be expressed as:

Substituting Eqs. (_{2}-water two-phase flow in fracture:

As mentioned in the Introduction section, the relative permeability is the key factor for controlling the two-phase flow behavior. Several relative permeability curves have been proposed over the last two decades. In this study, the following equations are adopted to describe the relationship between relative permeability and water saturation [

Relative permeability curves for two-phase flow.

The alternations of mechanical properties in coal induced by CO_{2} injection are another process which is usually neglected in modeling long-term CO_{2} sequestration in the coal seam. And considerable reports have shown that the coal properties, such as Young’s modulus and Poisson’s ratio, are not negligible for analyzing fluid migration and evaluating the reliability of CO_{2} storage. Therefore, embedding the CO_{2}-induced coal softening into the coupled model is much-needed.

Aiming to clarify the impact of CO_{2} pressure on coal mechanical behavior, Ma et al. [_{2} contents. The laboratory data indicates that the sample with high CO_{2} pressure exhibits lower Young’s modulus and higher Poisson’s ratio, as shown in Figure _{2} overpressure, we propose an exponential equation to fit the experimental results (see in Figure _{2} injection,

Experimental data of Young’s modulus and Poisson’s ratio at different CO_{2} pressures.

Similarly, another exponential equation is introduced to quantify the alternation of Poisson’s ratio (see in Figure

Based on our previous study [_{2}-induced softening can be described as:
_{2} adsorption, which is defined as:
_{2} pressure in the coal matrix.

The interactions between fluid transport and coal deformation are the primary reason why it is difficult to model long-term CO_{2} geological sequestration. Fluid transfer in coal seam during CO_{2} injection involves multiple mechanisms, such as two-phase flow, gas diffusion, and gas adsorption. All of these processes can cause alternations of stress and strain in the coal seam. In this paper, the change of porosity is adopted to reflect the main impact of the fluid transfer on the mechanical properties of coal. And mutually, the change of porosity also has a strong feedback on coal permeability. According to cubic law and the investigation of Ma et al. [

Thus, the fully coupled hydromechanical model for CO_{2} sequestration in the coal seam is established, and the corresponding cross-couplings between the fluid transfer and coal deformation are illustrated in Figure _{2} injection, the increasing fluid pressure in fracture causes the opening of coal fracture and further leads to the increase of the fracture porosity, the increasing CO_{2} pressure in the coal matrix softens the coal seam and makes the coal easier to deform, and the CO_{2} adsorption results in obvious coal swelling, which can induce the decrease of fracture porosity. All the alternations on the mechanical field will have a substantial feedback on the hydraulic field, which is mainly reflected in coal permeability. In the next sections, the proposed model is implemented into COMSOL multiphysics software to have further validation and analysis.

Cross-couplings between fluid transfer and coal deformation.

In this section, to verify the reliability and accuracy of the new proposed model, we match the experimental data derived by Robertson and Christiansen [_{2} injection was performed at the other end of the sample. In the numerical simulation, a 2-D geometry model is developed to restore the real experimental conditions, which is illustrated in Figure

The model used in the validation.

Experimental conditions in the laboratory

2-D model for simulation

Figure _{2} sequestration.

Results of coal permeability obtained by the experiment and simulation during CO_{2} injection.

In order for the proposed theoretical model to account for the long-term CO_{2} sequestration in the coal seam, a 3-D geometry model with a vertical well is assumed, which is illustrated in Figure _{2} injection.

Schematic of the simulation model for long-term CO_{2} sequestration.

In this paper, the complex coupled model is handled by a finite element method using COMSOL multiphysics software. And the essence of dealing with this problem is to solve the partial differential equations. Therefore, defining the boundary conditions of different variables is the major step in solving the provided equations. For coal deformation, the boundary conditions are shown in Figure _{2} diffusion in the coal matrix, the boundary condition is unavailable because the corresponding governing equation does not involve the derivative of position. While for the two-phase flow in fracture, the top, bottom, and right boundaries are set with no-flow boundary, and the flux boundary condition (Neumann boundary condition) is adopted on the left side of the model, which can be written as:
_{2} and water per unit time, respectively. Additionally, some key parameters used in the numerical simulation are listed in Table

Parameters implemented in the simulator.

Valuable (parameter) | Value | Units |
---|---|---|

_{2} diffusion coefficient) | m^{2}/s | |

- | ||

293 | K | |

1650 | kg/m^{3} | |

0.045 | m^{3}/kg | |

0.6 | MPa | |

0.005 | m | |

0.2 | - | |

0.1 | - | |

0.65 | - | |

4 | GPa | |

0.285 | - | |

0.03 | - | |

0.03 | - | |

m/s | ||

0.01 | - | |

0.6 | - | |

_{2} injection rate) | m^{2}/s | |

m^{2}/s |

Figure _{2} accumulative storage versus time during the CO_{2} injection. It can be found that because the CO_{2} injection rate is constant, the CO_{2} accumulative storage is directly proportional to the injection time. But at the early injection stage, the stored CO_{2} is mainly in an adsorbed state, while at the later injection stage, the stored CO_{2} is mainly in the free state due to the attenuation of CO_{2} diffusion in the coal matrix. Also, the decrease in diffusion coefficient blocks the gas transfer from coal fracture into the inner of the coal seam and further limits the rise of gas matrix pressure. This mechanism is more nonnegligible when it is far away from the wellhead. For instance, after a 500-day CO_{2} injection, the value of gas pressure in the matrix is 98.86% of that in fracture at MA, while at MB, this number decreases to 53.96%, as shown in Figure

The variation of (a) cumulative CO_{2} injection and (b) gas pressure of matrix and fracture at MA and MB during 500 days of injection.

Coal permeability and water saturation are the two most essential parameters in controlling the two-phase flow behavior. Figures

The spatial distribution of (a) permeability ratio, (b) water saturation, (c) Young’s modulus, and (d) Poisson’s ratio after 1 day, 20 days, 100 days, and 500 days of injection.

Young’s modulus and Poisson’s ratio are the two most essential parameters in controlling coal behavior during CO_{2} injection. Figures

Figure _{2} injection, which further induces the lower Young’s modulus and higher Poisson’s ratio for coal seam. In addition, due to the difference of Young’s modulus, the coal permeability calculated by the two-phase model is higher than the single-phase model. All the mentioned rules are more notable near the injection well. This conclusion also indicates that the impact of multiphase flow on fluid transfer and coal behavior is principally reflected in the area adjacent to the wellbore.

Impact of multiphase flow on fluid transfer and coal behavior.

Figure _{2} injection, which further induces the greater coal permeability, higher Young’s modulus, and lower Poisson’s ratio for coal seam. Additionally, as shown in Figure _{2} molecules are allowed to diffuse into the coal matrix, and more CO_{2} molecules are stranded in the coal fracture. The figure also indicates that the impact of the gas dynamic diffusion on fluid transfer and coal behavior is principally reflected in the area far away from the wellhead.

Impact of dynamic diffusion on fluid transfer and coal behavior.

In this paper, we numerically studied the fluid transfer and coal behavior during CO_{2} sequestration in an unminable coal seam. To comprehensively describe the whole process, a multistage CO_{2} diffusion model is adopted and a fully coupled hydromechanical model is developed. In the proposed models, the two-phase flow in fracture, the multistage pore structure of the coal matrix, the adsorption-induced coal swelling, and the CO_{2}-induced coal softening are also considered, which is controlled by four governing equations and several cross-coupling equations. These equations are solved by COMSOL multiphysics software with the finite element method. In addition, through the model validation, application, and analysis, the following conclusions can be drawn:

Our new proposed model is well varied by the experimental data. It is more applicable and accurate in modeling long-term CO_{2} sequestration in coal seam

At the early injection stage, the stored CO_{2} in the coal seam is mainly in an adsorbed state, while at the later injection stage, the stored CO2 is mainly in a free state. After 500 days of injection, the value of gas pressure in the matrix is only about 54% of that in fracture, which is attributed to the decrease in the diffusion coefficient. Additionally, during CO_{2} injection, the increasing distance from the injection well corresponds to greater water saturation, higher Young’s modulus, and lower Poisson’s ratio, while the coal permeability decreases firstly and then increases with the distance from the wellhead

The impact of multiphase flow on fluid transfer and coal behavior is principally embodied in the area adjacent to the injection well. Further, the model considering the multiphase flow shows a greater permeability, a lower Young’s modulus, and a higher Poisson’s ratio for coal seam. That also means the coal seam with lower water content is more reliable for long-term CO_{2} sequestration

The impact of the gas dynamic diffusion on fluid transfer and coal behavior is principally embodied in the area far away from the injection well. Further, the model considering gas dynamic diffusion shows a greater permeability, a higher Young’s modulus, and a lower Poisson’s ratio for coal seam. That also means the coal seam with greater attenuation coefficient of CO_{2} diffusion is more reliable for long-term CO_{2} sequestration

Additionally, the temperature of injection CO_{2} also has a significant impact on fluid flow and coal behavior, which needs to be investigated in the future.

Data are available on request.

The authors declare that they have no conflicts of interest.

This study was supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX20_1980) and the Future Scientists Program of China University of Mining and Technology (No. 2020WLKXJ055).