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Injection of high-temperature water or steam into low-permeability coalbed for efficient and rapid extraction of coalbed methane has been studied by our university for many years and will soon be implemented in the field. With comprehensive consideration of coupling of heat transfer, water seepage, desorption of coalbed methane, and coal-rock mass deformation, the paper establishes a more comprehensive mathematical model of the coupling effect of deformation-seepage-heat transfer on coalbed methane transport. Compared with the previous studies, this theoretical model considers the change of adsorbed and free coalbed methane at high temperature and the coalbed methane transport caused by a high-temperature gradient. Using the Tunlan Coal Mine of Shanxi Coking Coal Group to conduct the numerical simulations on the coalbed methane extraction project using heat injection technology, results show that (1) high-temperature water flowed towards the extraction hole along fractured fissures, with seepage towards the coal mass on both sides of the fissure at the same time, gradually heating the coalbed and forming an arcuate distribution of temperature from high to low for an area from the fractured fissure to the coalbed upper and lower boundaries. On the thirtieth day of heat injection, the temperature of the coalbed in the heat injection area ranged from 140°C to 260°C. (2) Under high temperatures, desorption of the coalbed gas was quick, and the adsorption gas content formed an oval funnel from the heat injection hole towards the extraction hole, centered by the fractured fissure, and migrating towards the coalbed upper and lower boundaries. Along with heat injection and extraction, the absorbed gas content rapidly decreased, and on the thirtieth day of injection, the absorbed gas content of the entire heat injection area decreased to 1.5 m^{3}/

Understanding the controls and influences on coalbed methane transportation is an important problem in production and safety technology related to safe and efficient coalbed methane and coal mining. Therefore, scholars continue to perform extensive studies from various angles. As the leader in coal production, China has also led in studies for extraction of coalbed methane and safety of coal mines. Zhao et al. [

First, heat injection wells and gas extraction wells are drilled in the coal seam. Then, by injecting superheated steam into the heat injection well, the temperature of the coal body may rise rapidly due to the effect of heat conduction and convection heat transfer, which will promote the desorption of adsorbed gas. At the same time, from the heat injection well to the extraction well, the gas seepage pressure gradient will increase. Hence, the permeability of the coal seam is greatly improved, thereby greatly enhancing the efficiency of gas extraction. Studies on the extraction theory and technology of coalbed methane on heating have been rapidly promoted and implemented in China [

Extraction of coalbed methane using heat injection not only involves the adsorption and desorption of coal and coalbed methane, heat convection, conduction and transmission, changes in the solid stress field, and several other processes but also involves changes in the permeability coefficient, adsorption constant, and other physical parameters related to the coal mass. To make the model better reflect these essential laws, the following basic assumptions are proposed:

With the increase of temperature, some adsorbed coalbed methane is instantaneously desorbed and converted to free coalbed methane.

The coalbed methane, water, and the solid matrix of coal mass can instantly reach local thermal equilibrium.

The coalbed methane in coal seams is reserved in free and adsorbed states, in which coalbed methane in a free state can be regarded as an ideal gas, with the content of

The content of the absorbed coalbed methane, along with the temperature variation law, is subordinated to the Langmuir adsorption equation:

According to the experimental results of [

The total content of the coalbed methane in the coal mass can be determined by

The volumetric strain caused by adsorbed coalbed methane of the coal mass conforms to the exponential law [

The seepage law of coalbed methane and water in coal seams conforms to the linear Darcy’s law at the microsegment pressure gradient [

The entire interval conforms to the following formula [

The pressure of water and coalbed methane is always consistent throughout the entire seepage field; that is, the effect of surface tension is not considered at the gas-liquid interface, and the pressure of coalbed methane is the same as that of water; therefore,

Pores and fissures within the coal mass are saturated by coalbed methane and water; therefore,

The coal and rock mass in the elastic deformation stage obeys the generalized Hooke’s law:

Under the action of coalbed methane, the effective stress state of the coal mass follows the modified Biot effective stress law [

The effective stress coefficient

The volume deformation of coal and rock mass consists of two parts, the deformation of the solid matrix of coal and rock mass, and the deformation of pores and fissures:

It is assumed that

The density of the water is no longer a constant but a function of pressure and temperature

Study on mass conservation of any representative elementary volume (REV) can refer to the following equation:

The component form is written as follows:

Darcy’s law (

The following can be obtained with the integration of formulas (

These equations are the general transport and seepage equations of coalbed methane considering solid deformation, temperature action, adsorption parameter variations, and several other factors.

The following formulas can be obtained from partial derivative of time from formula (

Equation (

The mass conservation of water in any representative elementary volume can be expressed by the following formula:

With respect to the saturation of coalbed methane and water in the pores, then

According to assumption (

Assumption (

This formula is the water seepage equation considering the deformation of coal and rock mass. As seen from the right side of the equation, the distribution of seepage pressure is affected by the solid matrix deformation, saturation, fluid pressure changing with time, and several other factors.

During the heat injection and extraction of coalbed methane, the fluid undergoes heat transfer by convection, and the coal and rock mass matrix undergoes heat transfer by heat conduction, with different heat transfer characteristics between the two materials, so the heat transfer equations need to be established, respectively, for analysis.

Heat conduction equation of a solid matrix is as follows:

Fluid convective heat transfer equation is as follows:

Formulas for specific heat, heat conductivity, and density of the mixed fluid are shown as follows:

Combined with assumption (

According to assumption (

In the formulas above,

According to the elasticity theory, the static equilibrium equation of coal and rock mass is

According to assumptions (

Equation (

Combined with the coalbed methane seepage equation considering the temperature action, the water seepage equation considering rock deformation, the temperature field control equation considering gas-water convective heat transfer and heat conduction of coal and rock mass, and related coupling equations, the solid-fluid-heat coupling control equation for coalbed methane extraction using heat injection technology can then be established and expressed as

The above equations, containing eight unknowns and eight variables and supplemented by initial and boundary value conditions, form the complete mathematical model of coalbed methane extraction using heat injection technology. The model is extremely nonlinear and unable to obtain its analytical solutions directly but can have approximate solutions determined by numerical methods.

Liang et al. [

The mathematical model of heat-fluid-solid coupling effect considering effect of temperature on coalbed methane seepage, gas-water coexistence, and many other factors in the paper, compared with the existing mathematical models [

Term I,

Terms II and III at the right end of the equation, respectively, consider the actions of solid deformation and gas-water relative saturation.

Terms IV and V at the right end of the equation refer to the effect of pore pressure variation of free and absorbed coalbed methane on the seepage process, respectively.

Term VI at the right end of the equation refers to the effect of temperature variation on free coalbed methane transport, while terms VII and VIII refer to the effect of temperature on adsorbed-phase coalbed methane, further affecting the mechanisms of seepage process:

Terms X and XI in the solid deformation equation of the model refer to the action of pore pressure on solid deformation and the action of adsorbed-phase coalbed methane on solid deformation, respectively.

From the analysis of the mathematical model of the solid-fluid-heat coupling effect on coalbed methane transport proposed in the paper, the distinctive characteristics and developments mentioned above are not included in existing mathematical models, which is another important progress in the theoretical model of coalbed methane transport.

The main idea of program design is to perform time loops on various physics fields (see Figure _{0}, so as to obtain the relative saturation of two-phase gas-liquid fluid. At the same time, according to the temperature value at this time, the physical parameters of fluid and coal matrix are reassigned, and the above parameters are substituted into the seepage equation. ② The pressure and velocity of the fluid are calculated based on the seepage equation, and then the calculated values are substituted into the seepage equation of coalbed methane. ③ Calculate the pore pressure of each node on coal seam, and obtain the gas content of each unit. Correspondingly, the expansion stress of coal and rock mass caused by adsorption can be obtained. ④ Calculate the stress field distribution of coal mass under the coupled process of coalbed methane adsorption, geostatic stress, pore pressure, thermal stress, and expansion stress. ④ When _{1} = _{0} +

The block diagram of program design in this study.

The mining area, Tunlan Coal Mine, is a modern superhuge coal mine operated by the Xishan Coal Electricity Group Co., Ltd. of the Shanxi Coking Coal Group, with an annual production capacity of 5 million tons. The mining area is 6 km south of Gujiao City, Shanxi Province, with a minefield area of 73.33 m^{2}, industrial reserves of 1,028 million tons, and recoverable reserves of 628 million tons. Main coal types in production include coking coal, fat coal, and a small amount of lean coal. The minefield contains 13 layers of coal in total, and the total thickness of the coal-bearing strata is 161.59 m, while the actual total thickness of the coal seams is 17.64 m, with a coal-bearing coefficient of 10.92%. There are six minable seams, No.2, No. 3, No. 6, No. 7, No. 8, and No. 9, with a total minable seam of 15.08 m and a mineable coal-beating coefficient of 9.33%. The thickness of the 2# coal seam used here as an example is 6°m. In the crossheading of the working face, the horizontal drilling was taken with an interval of 100 m, to form drilling holes for heat injection and production.

Hexahedron isoparametric elements were used to divide the area into 2,448 nodes and 1,650 units.

According to the mathematical model of the “solid-fluid-heat” coupling effect on coalbed methane extraction using heat injection technology proposed in formula (

The schematic diagram of gas extraction by heat injection.

Mechanical model of the XZ plane.

Initial and boundary conditions.

Equation category | Initial conditions | Boundary conditions |
---|---|---|

Gas seepage equation | All sides of the model are airtight boundaries (except the extraction hole): | |

Extraction hole: | ||

Temperature field control equation | Initial temperature of primitive coalbed: | Front, rear, left, and right boundaries: adiabatic boundaries, |

Upper and lower boundary conditions: | ||

Temperature of water injection well: | In the formula, | |

Solid stress equation | Displacement boundaries: lower boundary, | |

Stress boundaries on the top and right side: uniform load boundaries, | ||

Fluid seepage field equation | Water injection well: |

Modeling parameters for the numerical simulation.

Parameter name | Numerical value | Unit |
---|---|---|

Young’s modulus of coal seams, | ||

Poisson’s ratio of coal seams, | — | |

Aerodynamic viscosity of coal seam, | ||

Unit weight of coal mass, | ||

Porosity, | — | |

Coalbed methane density, | ||

Adsorption constant of coalbed methane, | ||

Coefficient of adsorption constant, | 0.003 | — |

Adsorption constant of coalbed methane, | ||

Coefficient of adsorption constant, | 0.003 | — |

Water permeability coefficient, | ||

Fissure permeability coefficient, | ||

Heat conductivity coefficient of coal, | ||

Heat capacity coefficient of coalbed methane, | 2.16 | |

Heat capacity coefficient of water, | 4.117 |

This paper establishes a numerical model based on the 2# coal seam of Tunlan Coal Mine, with the heat injection hole set on the left of the model and the drainage hole set on the right, and conducts numerical simulation calculation with the consideration of “solid-fluid-heat” coupling.

This model took time as the loop variable and calculated numerical solutions of the heat transfer equation, coalbed methane seepage equation, solid deformation equation, and other coupling equations at different times, respectively. According to the calculation results, the temperature field variations of the coal mass and the variations of coalbed methane content in coal seams during heat injection of coal seams are analyzed, respectively. The results are potted for 3 days, 10 days, 20 days, and 30 days in Figures

Simulation results of temperature: (a) 3 days, (b) 10 days, (c) 20 days, and (d) 30 days.

The temperature distribution in the section along the drill hole: (a) 3 days, (b) 10 days, (c) 20 days, and (d) 30 days.

Simulation results of adsorbed gas content (unit: m^{3}/t_{coal}): (a) 3 days, (b) 10 days, (c) 20 days, and (d) 30 days.

Simulation results of gas adsorption amount of section ^{3}/t_{coal}): (a) 3 days, (b) 10 days, (c) 20 days, and (d) 30 days.

Variation of the total gas content of coal mass with heat injection and drainage time (unit: m^{3}/t_{coal}): (a) 3 days, (b) 10 days, (c) 20 days, and (d) 30 days.

Variation trends of the total gas content of coal mass with heat injection and drainage time (unit: m^{3}/t_{coal}): (a) 3 days, (b) 10 days, (c) 20 days, and (d) 30 days.

Simulation results of pore pressure: (a) 3 days, (b) 10 days, (c) 20 days, and (d) 30 days.

Sectional view of pore pressure: (a) 3 days, (b) 10 days, (c) 20 days, and (d) 30 days.

Simulation results of volume stress: (a) 3 days, (b) 10 days, (c) 20 days, and (d) 30 days.

Sectional view of volume stress: (a) 3 days, (b) 10 days, (c) 20 days, and (d) 30 days.

Figure

Figure

Figures

As seen from Figure ^{3}/^{3}/^{3}/^{3}/

Figure

Figure ^{3}; after heat injection for 3 days, the total gas content of the fissure zone decreased rapidly, with a minimum value of 1.2 m^{3}/t_{coal}. After 10 days, the total gas content of the coal seams continuously decreased, with the total content at top beds down to 17.3 m^{3}/t_{coal} and the minimum near the extraction holes. After 30 days, the maximum gas content of the coal seams reached 6.1 m^{3}/t_{coal}, with a minimum value of 1.2 m^{3}/t_{coal}. According to the area weighted average, the total gas content reached 3.5 m^{3}/t_{coal}, and the mining rate reached 85% within one month in the heat injection and extraction area of coalbed methane, which is an effect that has not been achieved by single extraction technology to date.

Figure ^{3}/t_{coal}.

As seen in Figure

As seen from Figure

As seen from Figure ^{2} to 170 kg/cm^{2}.

As seen from Figure

To sum up, the results of the simulation show extreme nonlinearity, which is closely related to the extreme nonlinearity of the mathematical model, and there is square term

Through in-depth analysis on the mechanisms of coalbed methane extraction using heat injection in coal seams and industrial schemes, this paper analyzed the complex coupling process of temperature field, gas-water seepage field, and coal mass deformation field for desorption and seepage of coalbed methane using heat injection. The following can be concluded:

A solid-fluid-heat coupling mathematical model of coalbed methane extraction using heat injection was established, with distinctive characteristics that the right end of the coalbed methane equation contained the pore variation action term

Under water pressure, the temperature of coal seams increased rapidly along the fissure zone. After 30 days, the temperature reached 260°C within 2°m of the fissure zone outwards vertically. The minimum temperature of coal seams on both sides of the fissure zone reached 140°C.

The pore pressure of the coal seams gradually increased with the increase of temperature. After heat injection for 10 days, the pore pressure of the coal seams in the heat injection area increased to 5.5 MPa, and after 30 days, the pressure remained constant at 3.5 Mpa. Such a high fracturing gradient promoted the rapid flow and drainage of gas. The coalbed methane mainly took seepage in the direction parallel to the fissures, forming a pressure decrease round funnel near the drainage holes. This funnel area gradually expanded along with heat injection and extraction.

Under high temperature, the coalbed gas was desorbed quickly, the absorbed gas content formed an oval funnel from the heat injection hole towards the extraction hole, centered by the fractured fissure and outwards vertically towards the coalbed upper and lower boundaries. Along with heat injection and extraction, the absorbed gas content rapidly decreased. On the 30th day, the absorbed gas content of the entire heat injection area decreased to 1.5 m^{3}/

Physical meaning (dimension of physical parameters)

Content of coalbed methane adsorbed in the coal body ([ML^{−3}])

Content of coalbed methane adsorbed in the coal body ([ML^{−3}])

Content of free coalbed methane in the coal body ([ML^{−3}])

Porosity (1)

Density of water ([ML^{−3}])

Density of gas ([ML^{－3}])

Density of gas-liquid two-phase mixed fluid ([ML^{－3}])

Density of the rock matrix ([ML^{−3}])

Gas density at normal temperature and one atmosphere ([ML^{−3}])

Pore gas pressure ([ML^{−1}T^{−2}])

Pore water pressure ([ML^{−1}T^{−2}])

Molar mass ([

Gas constant ([ML^{2}T^{−2}n^{−1}^{−1}])

Time ([T])

Temperature of the rock matrix ([

Water temperature ([

Absolute temperature ([

Langmuir adsorption constant ([ML^{−3}])

Langmuir adsorption constant (dimensionless)

Langmuir adsorption constant of coal at normal temperature ([ML^{−3}])

Langmuir adsorption constant of coal at normal temperature (dimensionless)

Exponential decay coefficient of adsorption constant with respect to temperature (dimensionless)

Total content of coalbed methane in the coal body ([ML^{−3}])

Volumetric strain (1)

Deformation coefficient of coal caused by gas adsorption (dimensionless)

Gas specific flux ([LT^{−1}])

Water specific flux ([LT^{−1}])

Volume stress ([ML^{−1}T^{−2}])

Effective stress coefficient (dimensionless)

_{1,}

_{2,}

_{3,}

_{4}:

The experimental constant of the effective stress coefficient obeying the bilinear law (dimensionless)

Relative saturation of gas and water in coal pore/fissures (1)

_{i}:

Permeability of fluid in a certain direction ([L^{2}])

Dynamic viscosity coefficient of coalbed methane ([ML^{−1}T^{−1}])

_{s}:

Specific heat capacity of coal ([L^{2}T^{−2}^{−1}])

_{p}:

Specific heat capacity of gas-liquid two-phase mixed fluid ([L^{2}T^{−2}^{−1}])

_{z}:

Thermal conductivity of gas-liquid two-phase mixed fluid ([LMT^{−3}^{−1}])

_{s}:

Thermal conductivity of the rock matrix ([LMT^{−3}^{−1}])

_{w}:

Thermal conductivity of water ([LMT^{−3}^{−1}])

_{g}:

Thermal conductivity of coalbed methane ([LMT^{−3}^{−1}])

Poisson’s ratio (1)

_{C}:

Coefficient of volume expansion stress of the coal matrix caused by adsorbing coalbed methane (dimensionless)

Coefficient of volume expansion stress of the coal matrix caused by thermal stress ([ML^{−1}T^{−2}])

One of the lame constants ([ML^{−1}T^{−2}])

One of the lame constants ([ML^{−1}T^{−2}])

_{i}:

Solid displacement component ([L])

_{i}:

Applied to rock mass body force component ([ML^{−1}T^{−2}])

Elastic modulus ([ML^{−1}T^{−2}])

_{0}:

Source sink term of heat ([ML^{-1}T^{−3}])

_{ij}:

Kronecker symbol (dimensionless)

_{w}:

Related to the density of water, not exceed 6% of 1/_{w} (dimensionless)

_{pr}:

Specific heat of the coal matrix ([L^{2}T^{−2}^{−1}])

_{pw}:

Specific heat of water([L^{2}T^{−2}^{−1}])

The velocity of flow in three directions ([LT^{−1}]).

All the data used to support this study are present within the article as figures and tables.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This paper was supported by the Key Research and Development (R&D) Projects of Shanxi Province (Grant no. 201603D121031), Applied Basic Research Programs of Shanxi Province (201801D121278; 201801D221357; 201901D211294; 201901D211300), and Natural Science Funds for Young Scholar (Grant no. 51904195).

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