Numerical study on injection of flue gas as a heat carrier into coal reservoir to enhance CBM recovery

Journal Pre-proof Numerical study on injection of flue gas as a heat carrier into coal reservoir to enhance CBM recovery Yongliang Mu, Yongpeng Fan, Jiren Wang, Nan Fan PII:

S1875-5100(19)30269-0

DOI:

https://doi.org/10.1016/j.jngse.2019.103017

Reference:

JNGSE 103017

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 8 June 2019 Revised Date:

22 July 2019

Accepted Date: 29 September 2019

Please cite this article as: Mu, Y., Fan, Y., Wang, J., Fan, N., Numerical study on injection of flue gas as a heat carrier into coal reservoir to enhance CBM recovery, Journal of Natural Gas Science & Engineering, https://doi.org/10.1016/j.jngse.2019.103017. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier B.V. All rights reserved.

Coal skeleton

CO2 molecule

N2 molecule

CH4 molecule

Numerical study on injection of flue gas as a heat carrier into coal reservoir to enhance CBM recovery Yongliang Mua, Yongpeng, Fana, Jiren Wangb, Nan Fana a College of Mining Engineering, Liaoning Technical University, Fuxin, China; b College of Safety Science & Engineering, Liaoning Technical University, Fuxin, China

Corresponding author: Yonglinag Mu, PhD College of Mining Engineering, Liaoning Technical University No.47, Zhonghua Road, Fuxin, Liaoning, 123000, China Tel: +86 18341893669 E-mail: [email protected] Keywords: Multiphysics; Power plant flue gas; Heat injection; Enhanced CBM recovery; CO2 sequestration; Reservoir permeability

Disclosure Statement: The authors have nothing to disclose

1

Abstract A hydraulic-mechanical-thermal coupled numerical model for enhanced CBM recovery by injecting the flue gas(flue gas ECBM) is established, which fully couples the gas-water two-phase flow, competitive adsorption and temperature change as well as coal deformation. The model is first validated, then used to analyze the effects of different injectant components and temperature on CH4 production, CO2 storage and the evolution of permeability. The mechanism that enhanced CBM recovery and CO2 sequestration by injecting flue gas is discussed from the perspective of competitive adsorption and selective diffusion in the molecule scale as well as the permeability evolution. CO2 can be competitively adsorbed on the surface of coal pores to desorb adsorbed CH4, while N2 desorbs adsorbed CH4 by effectively reducing the CH4 partial pressure in the pores, enhanced CBM recovery by injection of flue gas is the result of the combination of these two effects. During the flue gas ECBM process, the permeability first decreases under the coaction of coal matrix expansion and effective stress increase; subsequently, the desorption of adsorbed CH4 induced by the N2 component is dominant, which leads to a significant increase in permeability. Appropriately increasing the injection temperature of flue gas is conducive to the desorption of CH4 adsorption, and thus beneficial to the permeability and CO2 sequestration. Before the arrival of CO2, some adsorbed CH4 can be desorbed first under the action of N2, which is not only beneficial to permeability, but also provides more adsorption sites for CO2 adsorption. However, the strategies for managing N2 breakthroughs are needed to achieve an optimal balance between CH4 production, CH4 purity and CO2 sequestration over the entire project period.

2

1. Introduction Current commercial production of CBM is primarily through the depletion of reservoir pressure(Syed et al. 2013). However, this production technology has been recognized as inefficient(Durucan and Shi 2009; Zhou et al. 2013). Therefore, the stimulation treatments are required to effectively and economically recover CBM. Gas and heat injection into the coal seam are two potential ways to enhance CBM recovery(Teng et al. 2016). Enhanced coalbed methane recovery by injecting CO2(CO2-ECBM), especially unminable coal seams, not only recovers additional CBM, but also effectively reduces anthropogenic CO2 emissions(Pan and Connell 2009; Liu and Mostaghimi 2017; Fang et al. 2019). However, injection of CO2 can cause a net swelling of coal matrix, which has a severe detrimental impact on reservoir permeability(Busch and Gensterblum 2011; Liu et al. 2017a). The coal-fired power plants are the largest sources of anthropogenic CO2(Durucan and Shi 2009), and CO2 in power plant flue gas, mainly composed of N2 and CO2, accounts for 30% of total carbon emissions(Aaron and Tsouris 2005). The injection of power plant flue gas can mitigate the reduction of reservoir permeability and significantly enhance CBM recovery(Mazumder et al. 2008; Shi et al. 2008). The desorption of CH4 from the coal surface is an endothermic process, and the heat treatment of the coal can contribute to gas desorption(Salmachi and Haghighi 2012). Thermal stimulation techniques have been successfully applied to enhance CBM recovery(Wang et al. 2015; Shahtalebi et al. 2016). For mixed gases injection, previous studies have focused on the sorption and swelling characteristics of coal, the comparison of CH4 production under pure or mixed gases injection, and the optimization of injected gas components(Durucan and Shi 2009; Syed et al. 2013; Liu et al. 3

2015a; Sayyafzadeh and Keshavarz 2016; Zhang et al. 2016a). In terms of heat injection, scholars mainly studied the effect of heat injection on CH4 seepage velocity, and compared the CH4 production under different temperature environments (Yasunami et al. 2010; Vilarrasa and Rutqvist 2017; Qu et al. 2017; Fang et al. 2019). Previous works have shown that injection of flue gas and heat, individually, can enhance CBM recovery, but few scholars have used flue gas as a heat carrier to enhance CBM recovery. Moreover, the effect of hydraulic-mechanical-thermal coupled action on enhanced CBM recovery by injecting flue gas(flue gas ECBM) is not well understood so far. Numerical simulation is an important research method for complicated problems of coal reservoir. In recent years, many mathematical models have been established to provide the necessary physics-based insight into CBM recovery(Zhou et al. 2012; Gong et al. 2014; Xia et al. 2014a; Liu et al. 2017b). In addition, Fan et al. (Fan et al. 2019a; 2019b; 2019c) have done a great deal of wonderful works in establishing multi-physical coupled mathematical model for enhanced CBM recovery. In this work, hydraulic-mechanical-thermal coupled equations are established based on the previous work, which includes two-phase flow, competitive adsorption of ternary gases (CH4, CO2 and N2) and temperature change as well as coal deformation, in order to address enhanced CBM recovery by injecting flue gas. The flue gas ECBM recovery processes under different injected gas components and injection temperatures are simulated numerically by COMSOL Multiphysics. The effects of injected gas components and temperature on CH4 production and CO2 storage as well as the permeability evolution are quantitatively analyzed by control variate method. It is of great theoretical significance to carry out the numerical study of injecting flue gas into coal seam as a heat carrier for improving resource recovery and reducing carbon emissions. 4

2 Establishment of coupled equations The coupled equations for gas and water migration, competitive adsorption and coal deformation as well as heat conduction are established based on the following hypotheses(Xia et al. 2015; Li et al. 2016; Fan et al. 2018a): (1) The coal reservoir is homogeneous isotropic media; (2) The elastic deformation of coal is infinitesimal; (3) The pores of the coal reservoir are saturated with gas and water, the gas and water are evenly distributed in the reservoir; (4) The gas is agreed with the ideal state equation; (5) The influence of temperature change on dynamic viscosity and the dissolution of CO2 by water is not considered; (6) Tensile stress is positive, while pore pressure is negative.

2.1 Governing equation of hydraulic field The mass of coalbed water mw can be expressed as: mw = sw ρ wϕ

(1)

where, sw is the water saturation; ρw is the density of coalbed water; φ is the porosity of coal reservoir. The density of water is a function of temperature and can be expressed as(Li et al. 2016):

ρ w = c∆T + ρ ws

(2)

where, c is temperature coefficient of water, kg·m-3·K-1; △T is the change in temperature; ρws is the density of water under standard condition, kg·m-3. Therefore, the mass conservation equation of coalbed water is(Fan et al. 2018b):

∂mw + ∇ ( ρ wuw ) = Qw ∂t

(3)

where, t is the time; uw is the velocity of water flow, m·s; Qw is the quality source of water. Flue gas ECBM involves the competitive adsorption of ternary gases(CH4, CO2 and N2). The 5

adsorption volume of component i per unit mass of coal can be described by the modified extended Langmuir equation(Chaback et al. 1996; Zhu et al. 2011): Vi =

where, VLi = VLi 0 exp[−

(

VLi Ci RT

PLi 1 + ∑ i =1 ( Ci RT PLi ) 3

)

(4)

d2 C 1 1 ∆T ] , PLi = PLi 0 exp[ Li ( − )] ; subscript i (i=1,2,3) refers to the 1 + d1Ci RT R T Tt

different gas components (components 1, 2, and 3 refer to CO2, CH4 and N2, respectively); d1 and d2 are the pressure correction factor, Pa−1, and the temperature correction factor, K−1, respectively; VLi and PLi are the modified Langmuir volume constant, m3·kg-1, and the pressure constant, Pa, respectively; Ci is the gas concentration, mol·m-3; R is universal gas constant, J·mol-1·K-1; T is the coalbed temperature, K; Tt is the laboratory reference temperature, K; CLi is the heat capacity at constant pressure, J·kg-1·K-1. The gas in the coal reservoir has both free and adsorbed phases, and the total mass of component i can be expressed as(Liu et al. 2015b): mi = M i sgϕ Ci + (1 − ϕ ) ρ s ρ gaiVi

(5)

where, sg is the gas saturation, expressed as sg=1-sw; Mi is the gas molar mass, kg·mol-1; ρs is the density of coal skeleton, kg·m-3; ρgai is the density of gas under standard condition, kg·m-3. The mass conservation equation of gas component i can be expressed as(Qu et al. 2012):

∂mi + ∇( ρ gi ui ) + ∇(− M i Di∇ϕ Ci ) = Qi ∂t

(6)

where, ρgi is the gas density, kg·m-3, expressed as ρgi=MiCi; ui is the gas migration velocity, m·s-1; Di is the hydrodynamic dispersion coefficient, m2·s-1; Qi is the quality source of gas, kg·m-3·s-1. According to the generalized Darcy's law of gas-water two-phase flow, the gas and water 6

velocities can be expressed as(Li et al. 2016):

kkrw  uw = − µ ∇pw w   u = − kkrg RT ∇C i  i µ gi

(7)

where, pw is the pore water pressure, expressed as pw=RT(C1+C2+C3)-pcgw, C1, C2 and C3 are the concentration of CO2, CH4 and N2, mol·m-3, respectively; pcgw is the capillary pressure, Pa; k is the absolute permeability of the reservoir, m2, µw and µgi are the dynamic viscosity of water and gas, respectively, Pa·s; krw and krg are the relative permeability of water and gas, respectively. The relative permeability model developed by Corey is the most widely used model for multiphase relative permeability in porous media, and it is found to be capable of modeling gas and water relative permeability curves in coals with high accuracy(Xu et al. 2014). This model is described as(Clarkson et al. 2011): 4   sw − swr  krw =     1 − swr     s −s  w wr krg = 1 −  1 − s − s wr gr   

    

2

  s − s 2  1 −  w wr     1 − swr  

(8)

where, swr is the irreducible water saturation, sgr is the irreducible gas saturation. By substituting Eq.(1), Eq.(2) and Eq.(7) into Eq.(3), the mass conservation equation of water in coal reservoirs can be derived as:

  ∂ ( sw ρ wϕ ) kk + ∇  −(c∆T + ρ ws ) rw ∇pw  = Qw µw ∂t  

(9)

By substituting Eq.(4), Eq.(5) and Eq.(7) into Eq.(6), the mass conservation equation of gas in coal reservoirs can be derived as: 7

kk RT   ∂  M i sgϕ Ci + M i (1 − ϕ ) ρ s ρ gaiVi  + ∇  − M iCi rg ∇Ci  + ∇(− M i Di ∇ϕ Ci ) = Qi µi ∂t  

(10)

2.2 Governing equation of mechanical field The establishment of coal constitutive relation is based on the hypotheses of linear thermoelasticity, that is, the total strain of the coal is the sum of thermal strain, the strain induced by gas desorption/adsorption, pore pressure, and surrounding. The total strain εij of coal can be expressed as(Xia et al. 2014b; Liu et al. 2015b):

ε ij =

α  sg ∆pg + sw ∆pw  ∆ (ε1 + ε 2 + ε 3 ) 1 1  α ∆T  1 − − σ ij −  σ δ δ ij + T δ ij + δ ij kk ij  2G 3K s 3 3  6G 9 K 

(11)

where, G=E/(2+2ν),K=E/(1-2ν),α=1-K/Ks,△pg= RT△(C1+C2+C3), △pw=△pg - pcgw, ε1 =αg1V1, ε2 =αg2V2, ε3 =αg3V3; G is the shear modulus, Pa; E is the Young's modulus of coal, Pa; K is the bulk modulus of coal, Pa; Ks is the bulk modulus of coal skeleton, Pa; ν is Poisson's ratio; Es is the Young's modulus of coal skeleton, Pa; α is the Biot coefficient

αT is the thermal expansion

coefficient, K-1; ∆T is the coalbed temperature change, K; ε1, ε2 and ε3 are the strain induced by adsorption of CO2, CH4 and N2, respectively; αg1, αg2 and αg3 are the coefficient adsorption induced strain of CO2, CH4 and N2, kg·m-3. The relationship between coal deformation and displacement can be expressed by the Cauchy equation(Chen et al. 2018; Fan et al. 2018b):

1 2

ε ij = (ui , j + u j ,i )

(i, j = 1, 2,3)

(12)

where, uij is the displacement component, m. The Navier equation of coal reservoir is expressed as(Fan et al. 2018b):

σ ij , j + Fi = 0

(i, j = 1, 2,3) 8

(13)

Combining Eqs.(11)-(13), the governing equation of mechanical field can be derived:

Gui , jj +

G u j , ji − K s ( ε1,i + ε 2,i + ε 3,i ) − K sαT T,i + α  RT (C1,i + C2,i + C3,i ) − sw pcgw  + F,i = 0 1 − 2ν

(14)

2.3 Governing equation of thermal field The coal skeleton and the fluid exist together in the same volume space. Based on the assumption of thermal equilibrium between the fluid and solid phases, the heat conservation equation over a representative element volume without considering the conversion of heat and mechanical energy can be expressed by a single equation(Lin et al. 2017; Wang et al. 2017).

ρ ρ ∂V ∂ ∂ 3 3 ( ρ C p )eff T  + ηeff ∇T − ∇(λeff ∇T ) + ∑ i =1 qi s gai i + KαT T (∑ i =1 ε i ) = 0 Mi t ∂t ∂t

(15)

( ρ C p ) eff = (1 − ϕ ) ρ s C s + s g ϕ ∑ i =1 M i C i C Li + s wϕρ w C w 3

ηeff = −∑ i =1 3

kk rg RT

µ gi

M i Ci C Li ∇Ci −

kk rw

µw

ρ wC w∇pw

λeff = (1 − ϕ ) λ s + s g ϕ ∑ i =1 λ gi + s wϕλ w 3

where, (ρCp)eff is the effective heat capacity, J·m-3·K-1; ηeff is the effective heat convection transfer coefficient, W·m-2·K-1; λeff is the effective coefficient of isotropic thermal conductivity, W·m-1·K-1; Cs, CLi and Cw are the specific heat capacity of the coal skeleton, gas component i and water, respectively, J·kg-1·K-1; λs, λgi, and λw are the heat conductivity of the coal skeleton, gas component i and water, respectively, W·m-1·K-1; qi is the isosteric heat of adsorption of

gas component i,

J·mol-1.

2.4 Cross coupling According to previous works(Kong et al. 2017), the relationship between reservoir porosity and coal skeleton strain can be expressed as: 9

ϕ = 1−

1 − ϕ0  ∆Vs  1 +  1+ εe  Vs 0 

(16)

where, subscript “0” refers to the initial state; φ0 is the initial porosity; εe is the volumetric strain of coal; △Vs is the change of coal skeleton volume, m3; Vs0 is the initial volume of coal skeleton, m3. The change in coal skeleton volume is caused by pore pressure, gas adsorption/desorption and temperature change, which can be expressed as follows(Fan et al. 2018a):

(

)

∆Vs α 3 3 =− ∆ RT ∑ i =1 Ci − sw pcgw + ∆ ∑ i =1 ε i + α T ∆T Vs 0 Ks

(17)

Bringing Eq. (17) into Eq. (16), the porosity model is expressed as:

ϕ = 1−

(

)

 1 − ϕ0  α 3 3 ∆ RT ∑ i =1 Ci − sw pcgw + ∆ ∑ i =1 ε i + αT ∆T  1 − 1 + ε e  Ks 

(18)

According to the cubic theorem between permeability and porosity(Wu et al. 2010), the absolute permeability of the reservoir can be expressed as follows:  1  1 − ϕ0    3 3 α k = k0   1 − ∆ RT ∑ i =1 Ci − sw pcgw + ∆ ∑ i =1 ε i + α T ∆T    1 −  ϕ0  1 + ε e  K s   

(

)

3

(19)

where, k0 is the initial permeability of reservoir, m2.

3 Model validation Shaqu Coal Mine is located in the middle section of Hedong Coalfield in Shanxi Province, China. The 3# and 4# coal seams being mined have high gas pressure, threatening the safety of coal mine production. To ensure production safety, two horizontal wells, XC01 and XC02, were constructed in the 24307 working face area of Shaqu Coal Mine to pre-extract coal seam gas(Fig.1). The length of XC01 horizontal well is 1027m. The XC02 well is a multi-branch horizontal well with

10

four branches, the length of its trunk is 1056m, and the lengths of its branches are 272m, 272m, 273m and 797m respectively. All extraction wells are 152.4mm in diameter. The XC02 multi-branch horizontal well was put into operation on December 17, 2012, and the XC01 horizontal well was put into operation 159 days later.

400

The 24307 working face area

300

XC01 horizontal well

200 100

XC02 multi-branch horizontal well 100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

Fig.1 Geological model for model validation

In order to validate the numerical model established in this paper, the numerical model is used to simulate the gas extraction project in the 24307 working face area of Shaqu Coal Mine, and the modelling results are compared with the field data. The size of geological model for model validation is 1300m×425m, which is divided into 3926 units by triangular grid. The numerical simulation parameters are set according to the geological data of the coal seam. The average thickness and the temperature of the coal seam are 4.5m and 299.5K, respectively; the average gas pressure in the coal seam is 1.4MPa. The other key parameters used in modelling are listed in table 1. Tab.1 Key parameters used in model validation. Parameter Value Young’s modulus of coal, E 2713 MPa Young’s modulus of coal skeleton, Es 8160 MPa Poisson’s ratio of coal, ν 0.35 Initial porosity, φ0 0.027 Initial permeability of coal, k0 9.5×10−17 m2 Thermal expansion coefficient, αT 2.4×10−5 1/K 1350 J/(kg·K) Specific heat capacity of coal skeleton, Cs Thermal conductivity of the coal skeleton, λs 0.191 W/(m·K) 11

0.02873 m3/kg 1.75 MPa 0.6 13 kPa

Langmuir volume constant of CH4, VL0 Langmuir pressure constant CH4, PL0 Initial water saturation Extraction negative pressure

Figure 2 shows the match between measured and modeled CH4 production rate. Two peak production rates are typically in simulation, the first may result from the rapid release of free gas in the coal seam near the production well with the second liberated by dewatering and the work of XC01 well. The average relative error of CH4 production rate is ~13.4%. Although there is a slight deviation, the modeled CH4 production rate is generally consistent with the measured CH4 production rate. This indicates that the numerical model established in this paper can be used to simulate the primary CBM recovery, as well as extended to flue gas ECBM recovery.

CH 4 production rate (×10 4 m3/day)

3.5

Field data Modelling results

3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

200

400

600

800

1000

Time (day)

Fig.2 Comparison of modeled and measured CH4 production rate.

4 Numerical simulation for flue gas ECBM 4.1 Model description The three-dimensional process of flue gas ECBM can be simplified into a two-dimensional process by considering the feasibility and effectiveness of numerical calculation(Sang et al. 2016). The geological model adopts the typical 5-point well layout, with only a quarter is taken as the simulation object, given its symmetry. The model size is 150m×150m and is divided into 2330 cells 12

by triangular (Fig.3). The lower left corner of the region is the injection well, the upper right corner of the region is the production well. The radii of both injection well and production well are 0.1m. For the convenience of observing the simulation effect, the reference point A and the reference line BC are set. The coordinates of the point A, B, C are (80, 80), (0,0) and (150,150), respectively. 150 Production well

C

100

A(80,80)

50

B

Injection well 50

100

150

Fig.3 Geological model for flue gas ECBM

3.2 Simulation scheme and physical parameters The control variate method is adopted to carry out the simulation schemes as follows (Tab.2). The first set of simulation schemes is designed to investigate the effect of injected gas components on CBM recovery; the second set is to investigate the effect of the presence of N2 component(or N2 partial pressure) in injectant on CO2 storage; the third set is to investigate the effect of injection temperature on CBM recovery as well as CO2 storage. Scheme sets

Tab.2 Numerical simulation schemes Injected gas components Injected gas temperature

Injected gas pressure

No injection 300K 6MPa Pure CO2 300K 6MPa First set Pure N2 300K 6MPa Flue gas 300K 6MPa Pure CO2 300K 0.9MPa Second set Flue gas 300K 6MPa Flue gas 300K 6MPa Third set Flue gas 320K 6MPa Flue gas 340K 6MPa Caption: The partial pressures of N2 and CO2 in injected flue gas(15% CO2, 85% N2) are 5.1MPa and 0.9MPa, 13

respectively.

The physical parameters of the numerical model are set according to the geological data of No. 3 coal reservoir in Qinshui Basin Fanzhuang Block and the experimental results, and they are listed in table 3. Symbol E Es ν ρs φ0 k0 αT PL10 PL20 PL30 VL10 VL20 VL30 d1 d2 αg1 αg2 αg3 D1 D2 D3 µg1 µg2 µg3 µw q1 q2 q3 Cs CL1 CL2 CL3 Cw λs λg1 λg2 λg3 λw swr

Parameter

Tab.3 Physical parameters of the numerical model Value

Young's modulus of coal Young's modulus of coal skeleton Poisson's ratio Density of coal skeleton Initial porosity Initial permeability of coal reservoir Thermal expansion coefficient Langmuir pressure constant of CO2 Langmuir pressure constant of CH4 Langmuir pressure constant of N2 Langmuir volume constant of CO2 Langmuir volume constant of CH4 Langmuir volume constant of N2 Pressure correction factor Temperature correction factor Adsorption strain constant of CO2 Adsorption strain constant of CH4 Adsorption strain constant of N2 Hydrodynamic dispersion coefficient of CO2 Hydrodynamic dispersion coefficient of CH4 Hydrodynamic dispersion coefficient of N2 Dynamic viscosity coefficient of CO2 Dynamic viscosity coefficient of CH4 Dynamic viscosity coefficient of N2 Dynamic viscosity coefficient of water Isosteric heat of adsorption of CO2 Isosteric heat of adsorption of CH4 Isosteric heat of adsorption of N2 Specific heat capacity of coal skeleton Specific heat capacity of CO2 Specific heat capacity of CH4 Specific heat capacity of N2 Specific heat capacity of water Heat conductivity of coal skeleton Heat conductivity of CO2 Heat conductivity of CH4 Heat conductivity of N2 Heat conductivity of water Irreducible water saturation 14

2710 8469 0.35 1470 0.037 5.14×10-16 2.4×10-5 1.71 3.44 18.02 0.06 0.02882 0.0203 0.071 0.021 0.063 0.058 0.044 5.8×10-12 3.6×10-12 4.1×10-12 2.22×10-5 1.84×10-5 1.7805×10-5 1.01×10-3 35 33.4 32 1250 651 1624 1038 4200 0.191 0.015 0.031 0.02475 0.598 0.05

Unit MPa MPa kg·m-3 m2 1·K-1 MPa MPa MPa m3·kg-1 m3·kg-1 m3·kg-1 MPa-1 K-1 kg·m-3 kg·m-3 kg·m-3 m2·s m2·s m2·s Pa·s Pa·s Pa·s Pa·s kJ·mol-1 kJ·mol-1 kJ·mol-1 J·kg-1·K-1 J·kg-1·K-1 J·kg-1·K-1 J·kg-1·K-1 J·kg-1·K-1 W·m-1·K-1 W·m-1·K-1 W·m-1·K-1 W·m-1·K-1 W·m-1·K-1

sgr pcgw c Tt

Irreducible gas saturation Capillary pressure Temperature coefficient of water Laboratory reference temperature

0.05 0.05 0.0228 300

MPa kg·m-3·K-1 K

3.3 Initial condition and boundary setting All sides of the model are fixed. The initial pressures of CH4, CO2 and N2 in coal reservoir are 5.24MPa, 0MPa and 0MPa, respectively. The initial temperature and initial water saturation of coal reservoir are 300K and 0.8, respectively. The extraction negative pressure in the CH4 production well is 13kPa. The gas injection pressure is constant, as shown in Table 2. The boundary condition of water saturation in the CH4 production well is set to 0.1. The sides other than the injection well and the producer well are zero flux boundaries.

4 Results and analysis 4.1 Effect of different injectant on CBM recovery and CO2 sequestration (1) CH4 production As shown in Figure 4, the CH4 production rates all show a trend of rising first and then decreasing with a peak. At the beginning of CBM recovery, due to the sealing of coalbed water to coal pores, the fluidity of gas is poor, resulting in a small amount of CH4 production. As the coalbed water is continuously discharged, the gas saturation increases gradually, and the gas fluidity is enhanced, which leads to the rise of CH4 production rates. Subsequently, the CH4 production rates begin to decrease from the peak due to the decreasing gas pressure gradient and content of CH4 in the coal reservoir. The enrichment of N2 component can significantly enhance CBM recovery. In the cases of injection of CO2, flue gas and N2, the peak values of CH4 production rate are 483.5m3/day, 581.2 15

m3/day, 733.0 m3/day, respectively, while in the absence of injection, the peak value is only 249.2m3/day (Fig.4 (a)). Making the case of no injection as a reference, by the 2000th day, the CH4 cumulative productions under the injection of CO2, flue gas, N2 are increased by 90.3%, 116.0%, 147.8%, respectively; by the 4000th day, they are increased by 73.6%, 64.1%, 71.8%, respectively (Fig.4(b)). For CO2, CH4 and N2, the adsorption capacity of coal for CO2 is the largest, followed by CH4 and finally N2. As a result, N2 gas is easier to pass through the coal seam, and CH4 production rises rapidly under its sweep action. But also due to the strong passing ability of N2 gas, the pressure gradient in the reservoir will decline rapidly over time, which leads to the decline of CH4 gas production rate. In contrast, although CO2 has a weak passing ability, it is more effective in replacing CH4, and this effect is relatively stable over time. As shown in Figure 4(b), CH4 cumulative production under flue gas injection is slightly lower than that under N2 injection, and that under CO2 injection after 3316 days, but the production cost of pure CO2 and N2 is very high. Therefore, it is economical to use power plant flue gas to enhance CBM recovery. 800

(a)

CH4 production rate (m3/day)

700 600 500 400

(b)

300 200 100

CH4 cumulative production (×106 m3)

1.4

No injection CO2 injection N2 injection Flue gas injection

No injection CO2 injection N2 injection FLue gas injection

1.2 1.0 0.8 0.6 0.4 0.2

2000 day

3316 day

0.0

0 0

1000

2000

3000

0

4000

1000

2000

3000

4000

Time (day)

Time (day)

Fig.4 CH4 production under different injection gas components. (a) Production rate; (b) Cumulative production

(2) CO2 storage Figure 5 shows the maximum transport distances of CO2 along the reference line BC under pure 16

CO2 injection(the pressure of CO2 is 0.9MPa) and flue gas injection(the partial pressures of CO2 and N2 are 0.9MPa and 5.1MPa, respectively).

Maximum transport distance of CO2 (m)

80

Pure CO2 FLue gas

70 60 50 40 30 20 10 0

1000th day

0

1000

2000th day

2000

3000th day

3000

4000

Time (day)

Fig.5 The maximum transport distances of CO2 along the reference line BC with time.

By the 1000th day, the 2000th day, the 3000th day and the 4000th day, in the case of pure CO2 injection, the maximum transport distances of CO2 are 31.8m, 44.9m, 55.3m and 62.6m, respectively; in the case of flue gas injection, the maximum transport distances of CO2 are 35.6m, 51.0m, 62.7m and 72.1m, respectively. In both cases, although the amounts of CO2 in the injectants are the same, the maximum transport distance of CO2 under flue gas injection is always greater than that under pure CO2 injection, due to the effect of N2 component (or N2 partial pressure). The greater the transport distance of CO2 means that CO2 can be in contact with more coal, which is conducive to CO2 sequestration. The comparison of CO2 storage under the injection of pure CO2 and flue gas is shown in Figure 6. Since the presence of N2 component (or N2 partial pressure) in the injectant promotes the migration of CO2 in the coal(Fig.5), the CO2 storage under the flue gas injection is obviously larger than that under the pure CO2 injection, even if the amounts of CO2 in the injectants are identical. The 17

CO2 storage rates first rise with the dewatering of the coal seam. Subsequently, the changes of storage rates are relatively gentle. The maximum CO2 storage rates under the injection of pure CO2 and flue gas are 17.8m3/day, 21.4m3/day, respectively (Fig.6(a)). By the 4000th day, CO2 cumulative storage under flue gas injection is increased by 15.4% compared to that under pure CO2 injection(Fig.6(b)). From the perspective of CO2 storage, in the case where the CO2 injection pressure is the same as the CO2 partial pressure in the injected flue gas, it is more effective and economical to use power plant flue gas as injectant for CO2 storage. 8

(a)

CO2 storage rate (m3/day)

20

15

Pure CO2 injection Flue gas injection

10

(b)

5

CO2 cumulative storage (×104 m3)

25

Pure CO2 injection Flue gas injection 6

4

2

0

0 0

1000

2000

3000

0

4000

1000

2000

3000

4000

Time (day)

Time (day)

Fig.6 The comparison of CO2 storage under the injection of pure CO2 and flue gas. (a) Storage rate; (b) Cumulative storage

4.2 Effect of injection temperature on CBM recovery and CO2 sequestration (1) CH4 production Since the increase in temperature facilitates the desorption of adsorbed CH4, the increase of flue gas injection temperature is advantageous to enhance CBM recovery. The peak values of CH4 production rate with flue gas injection temperature Tinj=300K, 340K, 380K are 582.1m3/day, 655.2 m3/day and 724.0 m3/day, respectively (Fig.7(a)). Making the case of Tinj=300K as a reference, by the 2000th day, the CH4 cumulative productions with Tinj=340K, 380K are increased by 9.1×104 m3, 5.6×104 m3, respectively; by the 4000th day, they are increased by 2.0×104 m3 and 3.4×104 m3, 18

respectively(Fig.7(b)).

(2) CO2 storage The storage rates under different Tinj first rise with the dewatering of the coal seam, then the change of storage rate is relatively gentle. The maximum values of the CO2 storage rate with Tinj=300K, 340K, 380K are 21.4m3/day, 29.2m3/day and 34.9 m3/day, respectively(Fig.8(a)). After

injection for 2000 days, making the case of Tinj=300K as a reference, the CO2 cumulative storages with Tinj=340K, 380K are increased by 41.2%, 69.0%, respectively(Fig.8(b)). CO2 storage is positively correlated with flue gas injection temperature Tinj, because the fact that the increase of temperature is conducive to promoting the desorption of CH4, which provides more adsorption sites for CO2 adsorption. 800

Tinj=300K Tinj=340K Tinj=380K

(a)

CH4 production rate (m3/day)

700 600 500 400

(b) 300 200 100

Cumulative CH4 production (×106 m3)

1.4

0

Tinj=300K Tinj=340K Tinj=380K

1.2 1.0 0.8 0.6 0.4

2000 day

0.2 0.0

0

1000

2000

3000

4000

0

1000

Time (day)

2000

3000

4000

Time (day)

Fig.7 CH4 production under different injected gas temperature. (a) Production rate; (b) Cumulative production 14

30

20

(b) Tinj=300K Tinj=340K Tinj=380K

10

CO2 cumulative storage (×104 m3)

(a)

CO2 storage rate (m3/day)

40

Tinj=300K Tinj=340K Tinj=380K

12 10 8 6 4 2 0

0 0

1000

2000

3000

4000

0

1000

2000

3000

Time (day)

Time (day)

Fig.8 CO2 storage under different injection temperature. (a) Storage rate; (b) Cumulative storage. 19

4000

5. Discussion 5.1 Selective transport of CO2, CH4, and N2 in coals Coal, by nature, is a heterogeneous porous solid material(Zhao et al. 2016; Song et al. 2016) and thus has a great adsorption capacity to gases(Clarkson and Bustin 1999). The nanopores (0.1−100 nm) are primarily where gases are adsorbed on the coal surface, especially the pores having a size of <8 nm(Song et al. 2017). Flue gas ECBM involves competitive adsorption and selective diffusion of CO2, N2 and CH4. The adsorption energies(the negative minimum potential of the adsorbate–wall interaction) of CO2, N2 and CH4 molecules in the slit-shape pore with different widths can be obtained through the Steele potential function(Cui et al. 2004), as shown in figure 9. 25

Adsorption energy (kJ/mole)

~0.32nm

0.36nm 0.46nm

CO2 N2 CH4

20

15

10

0.289 nm(CO2 ) 0.305 nm(N2 ) 0.310 nm(CH4)

5 0.2

0.3

0.4

0.5

0.6

0.7

0.8

Half width of slit-shape pore (w, nm)

Fig.9 Adsorption energy of CO2, CH4, and N2 in slit-shape pores with different widths. The kinetic diameters of CO2, N2 and CH4 have the relation: CO2 (0.33 nm)
The adsorption energy of CO2 is larger than that of CH4 in the pores with w<0.36nm and w>0.46nm, and larger than that of N2 in the pores at all sizes; the adsorption energy of CH4 is larger

than that of N2 in the pores with w>~0.32nm. When the half width of the pore is close to the dynamic diameter of the gas molecule, the adsorption energy is the highest, indicating that the gas molecules 20

are preferentially adsorbed in these smaller pores. Furthermore, the pores with w<~0.29 nm will inhibit penetration of all three gases under the repulsive forces of both walls; the pores with half width w between ~0.29nm and ~0.31nm are accessible for CO2, but CH4 and N2 are excluded; the pores with w>~0.31nm are accessible for all three gas molecules. Enhanced CBM recovery is the result of coaction of CO2 and N2 in the flue gas ECBM project. The studies (Zhao et al. 2016; Song et al. 2018) have shown that CO2 has a faster diffusion rate than CH4 in coal, due to its kinetic diameter less than CH4. Hence, there is a strong selective diffusion of CO2 over CH4(Cui et al. 2004). When CO2 is injected into the coal seam, since CO2 has a higher diffusion rate and adsorption energy than CH4, CO2 can be competitively adsorbed onto the inner surface of the coal micropores or even the ultra-micropores by desorbing the pre-adsorbed CH4. Although the kinetic diameter of N2 is smaller than that of CH4, the adsorption energy of N2 is obviously smaller than that of CH4. Due to the weaker van der Waals force between the pore walls and N2, N2 has a faster transport rate in the micropores than CH4 and CO2(Song et al. 2018). When the N2 stream enters the coal fracture system, the CH4 partial pressure in the fracture system is reduced to a low level, which promotes the desorption of adsorbed CH4. Then, the CH4 is swept along with the N2 stream through the coal fracture system to the production wells(Law et al. 2003). When the flue gas is injected into the coal seam, since the transport rate of N2 in the coal micropores is faster than that of CO2 and CH4, some CH4 will desorption first under the action of N2 before the arrival of CO2, which increases reservoir permeability and also provides more adsorption sites for CO2, thereby contributing to CO2 sequestration. As the van der Waals force between CH4 and coal is weaker than that between CO2 and coal, an appropriate increase in temperature of flue gas 21

can enhance the desorption of CH4 and thus further provide more adsorption sites for CO2 adsorption.

5.2 Permeability variation characteristics under different injection conditions There is a close relationship between permeability and porosity, that is, the higher the porosity, the higher the permeability. Since the swelling and shrinkage of the coal skeleton plays a decisive role in the change of porosity, the evolution of permeability can be discussed from the perspective of the volumetric strain of the coal skeleton.

(1) Evolution of permeability without injection The volumetric strain of coal skeleton, △Vs , is mainly the result of the combined action of these four parts: the strain induced by pore pressure compressing, △Vp; the strain induced by adsorption/desorption of gases, △Va; and the strain induced by thermoelastic expansion, △VT; as well as the strain induced by confining stress, △Vc. According to the hypotheses of linear thermoelasticity, the relationship of these four can be expressed as △Vs=△Vp+△Va+△VT+△Vc. In the absence of an injection, the permeability evolution at the reference point is shown in figure 10. In the process of drainage and recovery, free water and CH4 in coal pores are first discharged. At this stage, the reduction of the pore pressure causes the expansion of the coal skeleton, and thus the increase of the effective stress causes the coal to be compacted, so the absolute permeability first shows a downward trend. With the recovery operation going on, the shrinkage of coal skeleton, which is caused by CH4 desorption and thus temperature drop induced by desorption, begins to dominate and in turn leads to an increase in permeability. 22

(2) Evolution of permeability under pure CO2 injection The evolution of the permeability at the reference point under pure CO2 injection is shown in figure 11. Before CO2 gas is migrated to the reference point, the evolution law of permeability under pure CO2 injection is the same as that without injection, that is, first down and then up. In addition, permeability begins to rise earlier, because CO2 injection accelerates CH4 desorption. On the 2187th day, CO2 gas is migrated to the reference point, after which the permeability begins to drop dramatically. The dramatic decline in permeability is dominated by coal skeleton swelling induced by CO2 adsorption and the resulting increase in temperature. As of the 4000th day, the permeability is 17.2% lower than its initial value. 1.02

1.005

300

Permeability ratio (k/k0)

Permeability ratio (k/k0)

0.98

1.000

0.995

0.990

0.96

200

0.94

Permeability ratio CO2 concentration

0.92 0.90

100

0.88 0.86 0.84

0.985

0 2187 day

0.82

0

1000

2000

3000

4000

0

1000

Time (day)

Fig.10 Variation of permeability ratio without injection at reference point

CO2 concentration (mol/m3)

1.00

2000

3000

4000

Time (day)

Fig.11 Variation of permeability ratio under pure CO2 injection at reference point

(3) Evolution of permeability under pure N2 and flue gas injection The evolutions of permeability under pure N2 and flue gas injection are shown in figure 12. The time required for the N2 gas to be migrated to the reference point is much less than the CO2 gas, only 278 days for pure N2 injection and 311 days for flue gas injection. Before N2 gas is migrated to the reference point, the permeability decreases under the domination of the reduction of pore pressure as well as the increase of effective stress. After the N2 gas being transported to the reference point, a 23

rapid rise in the permeability at the reference point is induced(Fig.12). This is because the desorption of adsorbed CH4 induced by N2 is dominant. Moreover, the higher the N2 concentration, the more favorable it is to induce an increase in permeability. As of the 4000th day, the permeability under pure N2 injection increased by 40.2% and that under flue gas injection increased by 32.7% compared with the initial permeability.

(4) Evolution of permeability under different injection temperature The increase of flue gas injection temperature is beneficial to permeability(Fig.13). The temperature plays an important role in gas activation. and the increase of flue gas injection temperature, on the one hand, can accelerate the free gas migration in pore space, which is conducive to reduce CH4 partial pressure; on the other hand, the CH4 molecules can get more energy to conquer the adsorption of coal. During the flue gas injection process, the deformation of the coal skeleton is still dominated by the shrinkage induced by CH4 desorption, which is beneficial for permeability. 3

1.35

1.4

278 311 day day

2

1.2

1.1 1 1.0

Permeability ratio with pure N2 injection Permeability ratio with flue gas injection

0.9

N2 concentration with pure N2 injection N2 concentration with flue gas injection 1000

2000

3000

1.25 1.20 1.15 1.10

300K 340K 380K

1.05 1.00

0

0.8 0

Permeability ratio (k/k0)

1.3

N2 concentration (×103 mol/m3)

Permeability ratio (k/k0)

1.30

4000

Time (day)

Fig.12 Variation of permeability ratio under pure N2 and flue gas injection at reference point

0.95 0

1000

2000

3000

4000

Time (day)

Fig.13 Variation of permeability ratio under different injection temperature at reference point

The above analysis shows that the injection of flue gas into the coal seam can increase the permeability duo to the action of N2, which is beneficial for CBM recovery and CO2 sequestration. 24

Therefore, it is technically feasible to use power plant flue gas as injectant to achieve enhanced CBM recovery and CO2 sequestration, and it also saves the production cost of pure N2 or CO2. However, the injection of flue gas causes an early breakthrough of N2(Sun et al. 2016; Zhang et al. 2016b), which deteriorates the quality of the produced gas. Hence, a trade-off is required between incremental CH4 recovery and produced CH4 purity. One strategy for managing the N2 breakthrough is to introduce the flue gas ECBM in stages, so that the produced gas containing N2 impurity may be merged into the high quality gas stream from primary production wells. When N2 mole fraction in the produced gas is too high to allow mixing, the technologies for generating electricity using low concentration methane may be considered (Farzaneh et al. 2016). Moreover, the pure CO2 stream can also be used to regulate the CO2 mole fraction in the power plant flue gas to achieve an optimised balance between CH4 production, CH4 purity and CO2 sequestration over the entire project period.

6 Conclusion A fully coupled thermal-hydraulic-mechanical model is established for flue gas ECBM recovery. The model is first validated, then applied to quantitatively compare and analyze CH4 production, CO2 storage and the evolution of permeability under different injectants and injection temperature by control variate method. Based on these modeling results and observations, following conclusions can be drawn: (1) CO2 can be competitively adsorbed on the surface of coal pores to desorb adsorbed CH4, while N2 desorbs adsorbed CH4 by effectively reducing the CH4 partial pressure in the pores, enhanced CBM recovery by injection of flue gas is the result of the combination of these two effects.

25

(2) The evolution of reservoir permeability is the competitive result of coal matrix shrinkage/swelling caused by ternary gases (CO2, N2, CH4) desorption/adsorption, compaction leaded by effective stress increase and expansion caused by the increase of temperature. During the flue gas ECBM process, the permeability first decreases under the combined action of coal matrix expansion and effective stress increase; subsequently, the desorption of adsorbed CH4 induced by the N2 component is dominant, which leads to a significant increase in permeability. (3) Appropriately increasing the injection temperature of flue gas is conducive to the desorption of CH4 adsorption, and thus beneficial to the permeability of coal reservoir and the sequestration of CO2. (4) Before the arrival of CO2, some adsorbed CH4 can be desorbed first under the action of N2, which is not only beneficial to permeability, but also provides more adsorption sites for CO2 adsorption. However, the strategies for managing N2 breakthroughs are needed to achieve an optimal balance between CH4 production, CH4 purity and CO2 sequestration over the entire project period.

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Tab.2 Numerical simulation schemes Injected gas Scheme sets Injected gas components Injected gas pressure temperature No injection 300K 6MPa Pure CO2 300K 6MPa First set Pure N2 300K 6MPa Flue gas 300K 6MPa Pure CO2 300K 0.9MPa Second set Flue gas 300K 6MPa Flue gas 300K 6MPa Flue gas 320K 6MPa Third set Flue gas 340K 6MPa Caption: The partial pressures of N2 and CO2 in injected flue gas(15% CO2, 85% N2) are 5.1MPa and 0.9MPa, respectively.

1. A multi-physical coupled model was established for flue gas ECBM. 2. The presence of N2 component is conducive to permeability and CO2 storage. 3. Increased flue gas temperature can enhance CH4 recovery and CO2 storage.