Numerical simulation of CO₂-ECBM for deep coal reservoir with strong stress sensitivity

Abstract

CH₄ production rate of coalbed methane (CBM) well decreases rapidly during primary recovery in the deeply buried coal seam, resulting in a lot of CH₄ residues. CO₂ pour into deep coal seam with high stress sensitivity is available for enhancing CH₄ recovery by improving permeability for reservoir fracture and displacing CH₄ adsorbed in matrix. A coupled adsorp-hydro-thermo-mechanical (AHTM) model for deep methane development is established by considering the coupling relationships of non-isothermal and non-constant pressure competitive adsorption between CO₂ and CH₄, multi-phase flow, unsteady diffusion, heat transmission and in-situ stress variety. The model is verified by historical production and then used for CO₂ enhanced CBM (CO₂-ECBM) of deep coal reservoir in a sedimentary basin in Northwest China. The simulation results show that: (1) For primary recovery, permeability in coal reservoir drops rapidly with the development of CBM, which seriously restricts the production of CH₄. The permeability of the reservoir decreases from 7.89 × 10⁻¹⁶ m² to less than 1.50 × 10⁻¹⁶ m², CH₄ production rate in CBM well reduces to below 2000 m³/d, and the average total CH₄ content of coal reservoir is reduced by 5.49 m³/t with the decrease of only 1.12 m³/t of average adsorbed CH₄ in a production duration of 2000 d (2) With 10 MPa CO₂ continuous injection into coal seam after 700d of primary, the permeability for reservoir and CH₄ production rate increase while the total CH₄ content and adsorption CH₄ content in reservoir decrease compared with the primary recovery. (3) CO₂ pouring into coal reservoir increases the CH₄ production time and rate, which improves CH₄ recovery of coal reservoir. And it increases by 23.36 %, 23.07 % and 22.46 % with shut-in thresholds of CH₄ production rate of 1000 m³/d, 800 m³/d and 600 m³/d, respectively. The investigation is of great significance for the development of deep coalbed methane.

1. Introduction

Coalbed methane (CBM), a high-quality clean energy mainly composed of methane, resides within the pore, fissure and water of coal reservoir in the phase for adsorption, freedom and dissolution, respectively. As the country with the third largest coalbed methane reserves in the world, China in which most coal-bearing basins store abundant oil and gas resources has over 3.6 billion cubic meters of methane in coal reservoirs shallower than 2000 m [1]. After many years of exploration, CBM in shallow coal seams has entered full development, and the development of CBM in deep coal seams has attracted more and more attention [[2], [3], [4]]. Nevertheless, the exploitation of CBM is limited to a certain extent due to the special geological conditions of formidable tectonic stress, scorching temperatures and minuscule permeability for the deep coal reservoir [5,6]. The in-situ stress has an extremely significant impact on the fluid transport capacity within the coal reservoir in this area [7]. The raise of coal skeleton effective stress due to the induction of the diminishment for reservoir fluid pressure leads to a fact that permeability of the deep coal reservoir with strong stress sensitivity reduces rapidly during CBM production, which seriously restricts the development of CBM in this area.

As an efficient method to improve the methane recovery, injecting gas into coal seam for enhancing coalbed methane has been implemented in engineering [8]. These projects are mainly focused on CO₂ injection, which has the advantage of improving methane recovery and sequestering CO₂ to obtain economic environmental benefits, especially suitable for high rank coal reservoirs with strong gas adsorption capacity [9,10]. By injecting CO₂ into the coal reservoir, CO₂ contends with CH₄ for the gas adsorption sites on the inner surface of micropores in coal matrix, which promotes methane desorption from the inner surface of the pores [[11], [12], [13], [14], [15]]. At the same time, the injection of excessive CO₂ increases the pore pressure for deep coal reservoir with strong stress sensitivity, which may induce an improvement in the reservoir permeability according to the principle of effective stress, thereby increasing the methane production rate of coalbed methane wells.

During CO₂ enhanced coalbed methane, complex reactions occurred within the coal reservoir, including geochemical reactions and matrix shrinkage/expansion [[16], [17], [18]]. On the one hand, the CO₂ injected into the coal reservoir dissolves in the water of fracture and undergoes ionization to generate H⁻, HCO₃⁻, and CO₃²⁻ [19,20]. These ions react chemically with other ions in the water, promoting the precipitation and dissolution of minerals such as calcite, dolomite, gypsum, montmorillonite, illite [21,22]. However, the geochemical reaction for CO₂-water-coal has an extremely small impact on the various properties of reservoir due to the small mineral content in coal. On the other hand, CO₂ injected into coal reservoirs will adsorb onto the inner surface of the pores, promoting the expansion of the coal matrix, which may seriously affect the permeability and mechanical properties of the reservoir [[23], [24], [25]], especially in coal reservoirs with strong anisotropy [26].

Numerical simulation is a relatively advanced research method that can intuitively depict the changes in reservoir properties during deep coalbed methane primary recovery and CO₂-ECBM recovery [[27], [28], [29]]. One of the core issues is the construction of a multi field coupled mathematical model in the numerical simulation. Some multi physical field coupling mathematical models have been constructed to investigate the effect of injecting gas enhanced coalbed methane [[30], [31], [32]]. In these models, a good many classic theories and equations are widely applied. Langmuir's theory and Fick's law are often used to explain the adsorption and diffusion of gases in coal matrix [33,34], the linear flow law and gas slip effect are often used to describe the flow of fluids in reservoir fracture [35], the theory of porous media elasticity is often used to characterize the strain and stress changes in coal reservoir [36], Newton's cooling law is often used to analyze the transfer of energy within the reservoir [37]. These mathematical models make it easier to understand the process of injecting CO₂ enhanced CBM and provide a good basis for numerical simulation, whereas some key processes are ignored, including but not limited to energy exchange between the coal reservoir and adjacent strata, dissolution of gas in fracture water, unsteady diffusion coefficient of Fick diffusion, stress sensitive permeability.

In this paper, we establish an improved adsorp-hydro-thermo-mechanical (AHTM) mathematical model including the coupling relationships of non-isothermal and non-constant pressure rivalry sorption for mixed gas, free-dissolved gas and water for multicomponent-multiphase flow, unsteady diffusion for gas, heat transmission and reservoir stress evolution. Meanwhile, the changes in porosity and permeability of coal reservoir are derived from the perspectives of formation strain and stress in the model. The mathematical model covers the vast majority of processes involved in deep coalbed methane development and has broad application prospects. Combined with the geological properties for deep coal reservoir of a basin in Northwest China, the AHTM model is validated through methane production data of coalbed methane engineering field, then we simulate CH₄ production for coal reservoir and discuss changes of CH₄ content, permeability, CH₄ production rate and CH₄ recovery in coal reservoir of primary recovery and CO₂-ECBM. These investigations help to better understand the material transfer during CO₂-ECBM process and lead to some recommendations for the exploitation of CBM in deep coal seams.

2. Coupled model for multiple physical fields

In the following, some equations are constructed to describe transformation for adsorption field, hydrological field, thermal field and mechanical field of coal reservoir during primary recovery and CO₂-ECBM recovery. For the purposes of this investigation, the field equations are in line with the postulated conditions: (1) Compared to the size of coal reservoir, the coal deformation caused by methane production and CO₂ injection is extremely tiny and the reservoir is considered as a double-porosity/single-permeability medium. (2) In matrix, CH₄ and CO₂ are primarily resident in the micropores, following extended Langmuir adsorption equation. (3) In fracture, CH₄ and CO₂ are stored and transported in free and dissolved states, following Darcy's law, Klingberg effect and Henry's law. (4) CH₄ and CO₂ are transferred between the matrix and fracture through diffusion, following Fick's first diffusion law and Arrhenius equation. (5) The energy exchange between solids, liquids, and gases is instantaneous, which means that the temperature of the matrix block, water, CH₄, and CO₂ in a matrix-fracture unit is the same. Fig. 1 shows the simplified physical model for the deep coal reservoir and the occurrence status of gas and water inside.

Fig. 1.

The physical model of coal reservoir and its internal fluid occurrence.

2.1. Adsorption field

The adsorption content for CH₄ and CO₂ in matrix is controlled by the natural physical environment in which deep coal reservoir are located. The combined effect of pressure and temperature on gas adsorption can be expressed as Eq (1) [37]:

$$V_{Tj}=\frac{V_{Lj}{P}_{mj}\exp \left[-\frac{d_2\left(T-T_0\right)}{1+d_1{P}_m}\right]}{P_{Lj}\left(1+\frac{P_{m1}}{P_{L1}}+\frac{P_{m2}}{P_{L2}}\right)}$$ (1)

where the subscript $j=1,2$ represents CH₄ and CO₂, respectively; $V_L$ and $P_L$ represent the Langmuir constants of volume and pressure, respectively; $T_0$ represents the original temperature for coal reservoir, and $T$ represents coal reservoir temperature during the coalbed methane primary or CO₂-ECBM recovery; $d_1$ and $d_2$ represent the pressure and temperature coefficients that affect gas adsorption, respectively.

In line with Fick diffusion equation and Arrhenius equation, the transport for CH₄ and CO₂ between matrix and fracture can be described as Eqs (2), (3) [33,38]:

$$\frac{\partial \left({\rho }_{sj}{V}_{Tj}{\rho }_c\right)}{\partial t}=-\sigma D_{Tj}\left({\rho }_{mj}-{\rho }_{fj}\right)$$ (2)

$$\sigma D_{Tj}=\frac{1}{{\tau }_{j0}}\exp \left[Q_j/\left(R{T}_0\right)-Q_j/\left(RT\right)\right]$$ (3)

Where ${\rho }_s$, ${\rho }_c$, ${\rho }_m$ and ${\rho }_f$ respectively represent gas density under standard conditions, coal skeleton density, adsorbed gas concentration and free gas concentration; and except for ${\rho }_c$, $\rho =M_{g}P/\left(RT\right)$ which means they follow the ideal gas equation; ${\tau }_0$ is gas adsorption time at initial reservoir temperature; $Q$ is gas diffusion activation energy.

Plugging (1), (3) into formula (2), the equation for adsorption field is determined as Eq (4):

$$\frac{\partial }{\partial t}\left\{\frac{M_{gj}{P}_s}{R{T}_s}\frac{V_{Lj}{P}_{mj}\exp \left[-\frac{d_2\left(T-T_0\right)}{1+d_1{P}_m}\right]}{P_{Lj}\left(1+\frac{P_{m1}}{P_{L1}}+\frac{P_{m2}}{P_{L2}}\right)}{\rho }_s\right\}=\frac{M_{gj}\left(P_{fj}-P_{mj}\right)\exp \left[Q_j/\left(R{T}_0\right)-Q_j/\left(RT\right)\right]}{RT{\tau }_{j0}}$$ (4)

2.2. Hydrological field

Fracture in coal reservoir is the migration channel of gas and water. The gas not only exist and migrate in a free state, but also dissolve in trace amounts in water. The transport of movable fluids within fracture can be described as Eq (5):

$$\{\begin{array}{c}\frac{\partial \left({\rho }_{gj}{S}_g\varphi \right)}{\partial t}+\nabla \bullet \left({\rho }_{gj}{v}_{gj}\right)+\frac{\partial \left({\rho }_{dgj}{S}_w\varphi \right)}{\partial t}+\nabla \bullet \left({\rho }_{dgj}{v}_w\right)=\frac{M_{gj}\left(P_{mj}{-P}_{fj}\right)\exp \left[Q_j/\left(R{T}_0\right)-Q_j/\left(RT\right)\right]}{RT{\tau }_{j0}}\\ \frac{\partial \left({\rho }_w{S}_w\varphi \right)}{\partial t}+\nabla \bullet \left({\rho }_w{v}_w\right)=0\end{array}$$ (5)

where the subscript $w$, $dg$ and $g$ represent water, gas and dissolved gas, respectively; $S$ is fluid saturation, $S_w+S_g=1$; $\varphi$ is porosity and $v$ is transport rate of fluid. ${\rho }_{dg}=H_g{\rho }_g$, where $H_g$ is the Henry's coefficient.

According to Darcy's law and Klinberg effect, transport velocities for fluids in fracture can be expressed as Eq (6):

$$\{\begin{array}{c}{v}_{gj}=-\frac{k{k}_{rg}}{{\mu }_{gj}}\left(1+\frac{b_k}{P_{fj}}\right)\nabla P_{fj}\\ v_w=-\frac{k{k}_{rw}}{{\mu }_w}\nabla P_w\end{array}$$ (6)

where $k$, $k_{rg}$ and $k_{rw}$ represent absolute permeability, gas relative permeability and water relative permeability, respectively. $u$ is dynamic viscosity of fluid and $b_k$ is Klinkenberg factor.

In general, coal is a hydrophilic substance. The Brooks-Corey model is often used to describe the water pressure and fluid relative permeability in fracture, which can be expressed as Eq (7) [39]:

$$\{\begin{array}{c}{P}_w=P_f-P_c\\ P_f=P_{f1}+P_{f2}\\ P_c=P_e{\left[\left(S_w-S_{wr}\right)/\left(1-S_{wr}\right)\right]}^{-1/\eta }\\ k_{rg}={\left(\frac{S_g}{1-S_{wr}}\right)}^2\left[1-{\left(1-\frac{S_g}{1-S_{wr}}\right)}^{\frac{2+\eta }{\eta }}\right]\\ k_{rw}={\left(\frac{S_w-S_{wr}}{1-S_{wr}}\right)}^{\frac{2+3\eta }{\eta }}\end{array}$$ (7)

where the subscript $wr$ represents immovable water within the fracture; $\eta$ is pore size distribution index.

2.3. Thermal field

The main factors affecting temperature of coal reservoirs are thermal conduction, thermal convection, coal deformation and gas adsorption/desorption and dissolution/precipitation. The variation for temperature in coal reservoir is gradually continuous as Eq (8) [40,41]:

$$\frac{\partial \left[{\left(\rho C_P\right)}_{eff}T\right]}{\partial t}+{\eta }_{eff}\nabla T-\nabla \bullet \left({\lambda }_{eff}\nabla T\right)+K{a}_{T}T\frac{\partial {\epsilon }_{\nu }}{\partial t}=\sum _{j=1}^2{q}_{sti}\frac{{\rho }_s{\rho }_{gj}}{M_{gj}}\frac{\partial V_{Tj}}{\partial t}+\sum _{j=1}^2\frac{q_{dgj}{\rho }_{dgj}}{M_{gi}}$$ (8)

where the subscript $eff$ represents the effective synthesis of parameters; $K$, $a_T$ and ${\epsilon }_{\nu }$ are bulk modulus, thermal expansion coefficient and volumetric strain of coal, respectively; $q_{sti}$ and $q_{dgj}$ are gas adsorption heat and gas dissolution heat, respectively.

${\left(\rho C_P\right)}_{eff}$, ${\eta }_{eff}$ and ${\lambda }_{eff}$ are effective comprehensive parameters of coal, CH₄, CO₂, and water, which is characterized as Eq (9):

$$\{\begin{array}{c}{\left(\rho C_P\right)}_{eff}=\left(1-\varphi \right){\rho }_c{C}_c+\sum _{j=1}^2\left(\varphi S_g{\rho }_{gj}+\varphi S_w{\rho }_{dgj}\right)C_{gj}+\varphi S_w{\rho }_w{C}_w\\ {\eta }_{eff}=-\sum _{j=1}^2\left[\frac{{\rho }_{gj}{C}_{gj}k{k}_{rg}}{{\mu }_{gj}}\left(1+\frac{b_k}{P_{fj}}\right)\nabla P_{fj}+{\rho }_{dgj}{v}_w\right]C_{gj}-{\rho }_w\frac{k{k}_{rw}}{{\mu }_w}\nabla P_w{C}_w\\ {\lambda }_{eff}=\left(1-\varphi \right){\lambda }_c+\varphi \left(S_g{\lambda }_g+S_w{\lambda }_w\right)\\ {\lambda }_g=\left[{\chi }_{g1}{\lambda }_{g1}+{\chi }_{g2}{\lambda }_{g2}+{\left({\chi }_{g1}/{\lambda }_{g1}+{\chi }_{g2}/{\lambda }_{g2}\right)}^{-1}\right]/2\end{array}$$ (9)

where $C$ and $\lambda$ are specific heat capacity and heat conduction coefficient, respectively; $\chi$ is molar volume fraction.

2.4. Mechanical field

According to the porous isotropic elastic assumption, the reservoir stress field is significantly affected by gas adsorption, fluid pressure and temperature. The total stress for deep coal reservoir is confirmed as Eq (10) [[41], [42], [43]]:

$${\sigma }_{kl}=2G{\epsilon }_{kl}+\frac{2G\nu }{1-2\nu }{\epsilon }_{cc}{\delta }_{kl}-\alpha \left(S_w{P}_w+\sum _{j=1}^2{S}_g{P}_{fj}\right){\delta }_{kl}-K{\alpha }_{T}T{\delta }_{kl}-\sum _{j=1}^2{\alpha }_s{V}_{Tj}K{\delta }_{kl}$$ (10)

where $G$, $\alpha$ and ${\alpha }_s$ are shear modulus, Biot effective stress coefficient and adsorption expansion coefficient, respectively.

The equations for stress balance and strain-displacement for deep coal reservoir are written as Eq (11):

$$\{\begin{array}{c}{\sigma }_{kl,l}+F_k=0\\ {\epsilon }_{kl}=\frac{1}{2}\left(u_{kl}+u_{lk}\right)\end{array}$$ (11)

where $F$ and $u$ are volumetric force and displacement, respectively; $k$ and $l$ represent the directions of $x$, $y$, and $z$.

Substituting formula (11) into formula (10) results in the equation for mechanical field as Eq (12):

$$G{u}_{k,ll}+\frac{G}{1-2\nu }{u}_{l,lk}+F_k=\alpha \left(S_w{P}_{w,k}+\sum _{j=1}^2{S}_g{P}_{fj,k}\right)+K{\alpha }_T{T}_{,k}+K{\left(\sum _{j=1}^2{\alpha }_s{V}_{Tj}\right)}_{,k}$$ (12)

2.5. Coupling equations

• (1)Porosity of fracture

Porosity, a numerical representation of the fracture space in coal reservoir, is constantly changing during primary and CO₂-ECBM recovery. In general, the variation in porosity is controlled by fluid pressure, CH₄ and CO₂ adsorption and thermal strain, which can be written as Eq (13) [34]:

$$\{\begin{array}{c}\varphi =\frac{1}{1+S}\left[\left(1+S_0\right){\varphi }_0+\alpha \left(S-S_0\right)\right]\\ S_0={\epsilon }_{v0}+P_{f0}/K_s-{\epsilon }_{s0}-{\alpha }_T{T}_0\\ S={\epsilon }_v+P_f/K_s-{\epsilon }_s-{\alpha }_{T}T\end{array}$$ (13)

where $K_s$ is bulk modulus of coal matrix.

• (2)Permeability of fracture

Permeability, the ability of reservoir to allow fluids to pass through, is extremely important for primary recovery and CO₂-ECBM recovery. For stress sensitive coal reservoir, its permeability is exponentially related to effective stress, which can be expressed as Eq (14) [[44], [45], [46]]:

$$\{\begin{array}{c}k=k_0\mathit{exp}\left[-3C_f\left(\Delta \bar{\sigma }-\alpha \left(S_w{P}_w+\sum _{j=1}^2{S}_g{P}_{fj}\right)\right)\right]\\ \bar{\sigma }=\left({\sigma }_1+{\sigma }_2+{\sigma }_3\right)/3\end{array}$$ (14)

where $k_0$ and $C_f$ are initial permeability and compressibility factor of fracture, respectively; ${\sigma }_1$, ${\sigma }_2$ and ${\sigma }_3$ are first, second and third primary stress.

(4), (5), (8), (12)-(14) together form an multi physics field coupled model, including Adsorption field (A), Hydrological field (H), Thermal field (T) and Mechanical field (M). The intercoupling among various physical fields within the model is mostly bidirectional (Fig. 2). It can be described as: (1) for Adsorption field, the free gas content in fracture is controlled by the gas pressure in matrix, the change in reservoir temperature is influenced by the heat release/absorption caused by gas adsorption/desorption, and the expansion/contraction deformation of the coal matrix caused by gas adsorption/desorption affects the reservoir stress; (2) for Hydraulic field, the adsorbed gas content in matrix is controlled by the gas pressure in fracture, the reservoir temperature is affected by thermal conduction and convection caused by fluid flow, and the change in reservoir stress is controlled by fluid pressure in fracture; (3)for thermal field, temperature change affects the gas adsorption capacity and gas diffusion rate within the matrix, controls gas pressure in fracture by ideal gas state equation, and transforms reservoir stress through thermal strain; (4) for Mechanical field, reservoir temperature is affected by changes in strain energy, fluid pressure and flow velocity in fracture are controlled by variation for porosity and permeability of fracture caused by changes in strain and stress, respectively. Based on the numerical simulation platform of COMSOL Multiphysics 5.6, the partial differential equations for Adsorption field, Hydrological field, and Thermal field are defined in the mathematical module, the partial differential equations for Mechanical field are defined in the solid mechanics module, and the numerical analysis (FEM) can be used to calculate the governing equations of physical fields. In addition, the porosity and permeability of coal reservoir were defined as variables in the form of expressions.

Fig. 2.

Coupling relationships among AHTM model.

3. Geological model, key parameters, simulation scheme and boundary conditions

3.1. Geometric model and critical parameter

As a representative, a deep coal seam with a thickness of about 8.5 m located in a basin in Northwest China is selected for investigation. Considering the huge amount of simulation calculations and the single well drainage radius of about 150m, a quarter of the single well control area is selected to define the size of the geological model as 150m × 150m × 8.5m (Fig. 3a). The green columnar IW represents the gas injection well with a diameter of 0.1m, and the black columnar PW1 represents a fluid production well with a diameter of 0.1m. Point P1, P2 and P3 and line L (red line) are available for monitoring the variation of reservoir permeability for methane primary and CO₂-ECBM. The geological model is divided into 482 grid edge elements, 7206 boundary elements and 3484 domain elements with the minimum grid quality for 0.6212 and the average grid quality for 0.9286 (Fig. 3b).

Fig. 3.

Geometric model and element division for simulation.

The critical parameters in the investigation are mainly derived from engineering testing, laboratory experiments, and a small number of parameters are sourced from previous research results [37,47], as shown in Table 1.

Table 1.

Key parameters for numerical simulation.

Parameter	Value	Parameter	Value
$P_{m10}$, MPa	18.53	${\mu }_{g2}$, Pa·s	1.84 × 10−5
$P_{f10}$, MPa	18.53	${\mu }_w$, Pa·s	1.01 × 10−3
$P_{m20}$, MPa	0.01	$b_k$, MPa	0.75
$P_{f20}$, MPa	0.01	$G$, MPa	1153.85
$S_{w0}$, 1	0.228	$K$, MPa	2500
${\varphi }_0$, 1	0.12	$C_{g1}$, kJ/(kg·K)	2.22
$k_0$, m2	7.89 × 10−16	$C_{g2}$, kJ/(kg·K)	0.84
$T_0$, K	353.15	$C_w$, kJ/(kg·K)	4.187
$V_{L1}$, m3/t	8.77	$C_c$, kJ/(kg·K)	1.35
$P_{L1}$, MPa	6.69	${\lambda }_{g1}$, W/(m·K)	0.0301
$V_{L2}$, m3/t	11.24	${\lambda }_{g2}$, W/(m·K)	0.0137
$P_{L2}$, MPa	5.76	${\lambda }_w$, W/(m·K)	0.5985
$d_1$, MPa−1	0.071	${\lambda }_c$, W/(m·K)	0.1913
$d_2$, K−1	0.021	${\alpha }_s$, kg/m3	0.1
${\tau }_{10}$, d	10	${\alpha }_T$, K−1	2.4 × 10−5
${\tau }_{20}$, d	12.70	$q_{st1}$, kJ/mol	16.40
$Q_1$, kJ/mol	34	$q_{st2}$, kJ/mol	19.20
$Q_2$, kJ/mol	18	$P_e$, kPa	10
${\rho }_c$, kg/m3	1350	$\eta$, 1	1
${\rho }_w$, kg/m3	1000	$S_{wr}$, 1	0.05
${\mu }_{g1}$, Pa·s	1.34 × 10−5	$C_f$, MPa−1	0.05

3.2. Simulation scheme and boundary conditions

The research of this paper includes three parts as shown in Table 2: (1) Production history fitting. Combined with the production data of a CBM well drilled into the deep coal seam of a certain basin in Northwest China, the accuracy of AHTM model is verified. (2) Methane primary recovery. The time covers 5000d with 2 MPa of bottom hole pressure in PW1. The simulation results from 0 to 2000d are available for analysis of CH₄ gas content, permeability and CH₄ gas production rate of primary recovery, and the results from 700d to 5000d were selected for comparison with CO₂-ECBM recovery. (3) CO₂-ECBM recovery. Considering that initial coal reservoir pressure is too high to be unfavorable for CO₂ injection, it is after 700 days of primary recovery that CO₂ is injected from the IW well with 10 MPa of pressure and 288.15K of temperature. Based on the in-situ stress state, direction and magnitude for the deep coal reservoir in the basin, the bottom surface for geometric model is defined as a fixed boundary, the compressive stresses for the top, back and right surfaces of geometric model are 82.32 MPa (vertical stress), 63.2 MPa (minimum principal stress) and 114.21 MPa (maximum principal stress), respectively. Furthermore, in thermal field, the energy conduction rate between the surfaces for coal reservoir and its surrounding strata is $Q_b=h\left(T-T_0\right)$, where h = 91.5 mW/m² is thermal conductivity of coal reservoir boundary.

Table 2.

Simulation scheme.

Stage	Objective	Time/d
(1) Production history fitting	Verify the accuracy of AHTM model based on geological conditions of deep coal reservoir	0–120
(2) Methane Primary recovery	Investigate the evolution of CH4 content and permeability in the deep coal reservoir and CH4 production rate of well	0–2000
(3) CO2-ECBM recovery	Analyze the impact of CO2 injection into deep coal reservoir with strong stress sensitivity on methane development	700–5000

4. Results and discussion

4.1. Model validation

A CBM well of a certain basin in Northwest China produces continuously for about 4 months after drilling. Fig. 4 shows the results of gas production rates for field measurement data and numerical simulation of this well. Similar to the variation trend of CH₄ production rate of field, a gradual decline in CH₄ production rate of simulation has been maintained during primary recovery except a initial short period of time. The substantially consistent CH₄ production rate results from field and simulation indicate that AHTM model is credible and can be popularized to CO₂-ECBM recovery.

Fig. 4.

Measurement and simulation of methane production.

4.2. Primary recovery

• (1)CH₄ content in coal reservoir

Fig. 5, Fig. 6 show the change in CH₄ content distribution and the variety for average CH₄ content in reservoir during 2000 days of primary recovery, respectively. It's extremely significant that total CH₄ content, adsorbed CH₄ content and the percentage of free CH₄ in total CH₄ content in coal reservoir decrease continuously with the prolongation of production time, which is particularly evident near the production well (Fig. 5). Correspondingly, the average values of total CH₄ content, adsorbed CH₄ content and free CH₄ concentration in total CH₄ content of coal reservoir reduce with the drainage of CBM well (Fig. 6). Compared with the declines of average total CH₄ content and average free CH₄ concentration, the reduction of average adsorbed CH₄ content in reservoir is minor. Initially, total CH₄ content and the CH₄ adsorption content are 16.15 m³/t and 6.44 m³/t, respectively. Total CH₄ content ranges from 5.5 to 11.5 m³/t with a mean value for 10.66 m³/t, adsorbed CH₄ content ranges from 4.0 to 5.6 m³/t with a mean value for 5.32 m³/t after 2000 days of primary recovery. The reduction of average adsorbed CH₄ (1.12 m³/t) accounts for 20.40 % of reduction of the average total CH₄ (5.49 m³/t), which suggests that only a little of adsorbed CH₄ in matrix has been recovered and the main source of CH₄ production from CBM well is free CH₄ in fracture of coal reservoir with high stress sensitivity.

• (2)Reservoir permeability

Fig. 5.

Changes in CH₄ content for primary recovery.

Fig. 6.

The variations of average content and concentration of CH₄ in coal reservoir for primary recovery.

Permeability of coal reservoir is constantly varying with continuous production of CBM well. Fig. 7, Fig. 8 show the varieties of permeability ratio (calculate based on the ratio for permeabilities at present and original reservoir, $k/k_0$) for monitoring points P1, P2 and P3 and permeability for monitoring line L during primary recovery. The overall performance for the permeability of coal reservoir is characterized by significant reduction. With the extension of methane development time and the diminishment of distance from extraction well, reservoir permeability is continuously decreasing. Since the CBM well initiates production, the permeability ratios of the three monitoring points have fallen rapidly and dropped below 0.2 at 2000 days. Due to the proximity of the production well, the permeability ratio of P3 has dropped by more than 0.10 in the first 10 days (Fig. 7). Furthermore, permeability varieties of monitoring line L demonstrate that reservoir permeability is affected by the control range and assignment duration of methane development well (Fig. 8). Permeability which represents the property of allowing fluid flow in coal reservoir have a huge impact on CBM production. The speedy decline in reservoir permeability would reduce the flow speed for coalbed methane, which is very unfavorable for CBM production during primary recovery.

• (3)Methane production

Fig. 7.

Permeability ratio of monitoring points.

Fig. 8.

Permeability of monitoring line L.

Fig. 9 shows the methane production rate of PW well during primary recovery. Under the discharge pressure of 2 MPa, the production rate of CH₄ initially exceeds 5000 m³/d and reduce rapidly with the increase of production time, which decreases by more than 1500 m³/d in the initial 200 days, reduces to less than 2000 m³/d after 700d and drops below 1000 m³/d by 2000d. It is indisputable that total methane content in coal reservoir is very sufficient (Fig. 4, Fig. 5) and permeability for coal reservoir is continuously decreasing (Fig. 6, Fig. 7) during primary recovery, which implies that the methane production rate is predominantly regulated by the permeability for coal reservoir.

Fig. 9.

CH₄ production rate of CBM well PW1.

4.3. CO₂-ECBM recovery

• (1)CH₄ content in coal reservoir

Fig. 10 displays the changes for total CH₄ content, adsorbed CH₄ content and free CH₄ concentration of coal reservoir during primary recovery and CO₂-ECBM recovery with 10 MPa, 288.15K CO₂ injection starting from the 700th day. In the initial time for CO₂ injection, the CH₄ contents for total and adsorption in coal reservoir increase firstly and then decrease significantly in the direction from the lower left corner to the upper right corner of the geological model of coal reservoir, which is different from those of primary recovery gradually decrease (Fig. 10a and b). In addition, they are higher in the lower left corner than the periphery of reservoir, as the temperature for reservoir near CO₂ injection well (IW) is reduced through heat conduction and convection during low-temperature CO₂ injection, which improves the adsorption capacity of coal matrix for CH₄. The free CH₄ concentration in coal reservoir with CO₂ injection is always higher than that of primary recovery (Fig. 10c). A number of CO₂ pouring into reservoir spreads into micropore and competes with CH₄ for adsorption, which accelerates the relocation for CH₄ from adsorption into freedom and increases the CH₄ content in the fracture. Contrary to the characteristics of total CH₄ content and adsorbed CH₄ content, free CH₄ concentration in the lower left corner of coal reservoir is slightly less than that in surrounding area due to the high adsorption capacity of coal for CH₄ at low temperature (Fig. 10c).

Fig. 10.

Variation in CH₄ content for primary and CO₂-ECBM.

Fig. 11 shows the changes of the averages of total CH₄ content, adsorbed CH₄ content and free CH₄ concentration in reservoir during primary and CO₂-ECBM recovery. The averages of total and adsorbed CH₄ content for CO₂ injection are less than those for primary recovery, while the average of free CH₄ concentration is just the opposite. At the beginning stage for CO₂-ECBM, the average of total CH₄ content of coal reservoir has barely budged, the average of adsorbed CH₄ content speedily declines and the average of free CH₄ concentration increases sharply relative to those of primary recovery, which indicates that CO₂ displaces a large amount of CH₄ adsorbed in matrix into fracture during CO₂-ECBM. By 5000 days, average CH₄ total content and average adsorbed CH₄ content of primary recovery decrease to 8.88 m³/t and 4.78 m³/t, and those of CO₂-ECBM recovery reduce to 5.30 m³/t and 2.55 m³/t which are reduced by 3.58 m³/t and 2.23 m³/t, respectively. And it shows that injecting CO₂ increases the recoveries of adsorbed CH₄ and free CH₄ in coal reservoir.

• (2)Reservoir permeability

Fig. 11.

Variation of average CH₄ content and its proportion for primary and CO₂-ECBM.

Fig. 12, Fig. 13 show the varieties of permeability ratio for monitoring points P1, P2, P3 and the permeability for monitoring line L of methane primary and CO₂-ECBM. The permeability ratios of CO₂-ECBM increase swiftly to the summit and then decrease slowly compared to those which reduce slowly for primary recovery. The permeability ratio of monitoring points P1, P2 and P3 peak at 1.51, 1.29, and 1.12 at 1060th, 1140th and 1160th day, respectively. And by the end of 5000 days of production, the permeability ratios of the three monitoring points are still higher than 0.35 for CO₂-ECBM recovery, while those of the primary recovery are about 0.10 (Fig. 12). Similar to the permeability ratio characteristics of monitoring points, the permeability of monitoring line L for CO₂-ECBM recovery continuously exceeds that of primary recovery (Fig. 13), which means that CO₂-ECBM can effectively improve the permeability or slow down the decrease in permeability for coal reservoir with a strong stress sensitivity. On the whole, it shows that a successive reduction in the reservoir permeability occurs with the enhancement for the distance from CO₂ injection well and the extension of implementation time. The permeability of monitoring line L where is more than 116.5 m away from injection well at 900 d is lower than that in the same point at 1800 d, as the influence of CO₂ injection in a short time (only 200 days) on permeability has not yet spread to this area.

• (3)Methane production

Fig. 12.

Permeability ratio of monitoring points.

Fig. 13.

Permeability of monitoring line L.

Fig. 14 displays the comparison for CH₄ production rate between primary and CO₂-ECBM (CO₂ injection from the 700th day). After a brief decrease, the gas manufacture rate for CO₂-ECBM rises rapidly to the peak and then drops progressively, which is distinct from that of primary recovery. It diminishes to 492.2 m³/d which is the same as that of primary recovery at the 4360th day, then lower than that of primary recovery. During practical production, CH₄ production rate is available as shut-in condition for CBM well, which means CBM well would be shut down as it is below a certain value, such as 1000, 800 or 600 m³/d. It's extremely obvious that the CO₂-ECBM prolongs the production time of CBM well when the shut-in threshold is higher than 492.2 m³/d. For the shut-in threshold of 1000, 800 and 600 m³/d, the discharge time of CBM well are extended by 632.6, 503.2 and 234.1 days, respectively. The characteristic for gas manufacture suggests that improving gas production rate and extending production time of CBM well are the advantages of CO₂-ECBM relative to methane primary.

• (4)CH₄ recovery

Fig. 14.

CH₄ production rate of CBM well PW1 during primary and CO₂-ECBM recovery.

Fig. 15 shows the variety of CH₄ recovery of coal reservoir during primary and CO₂-ECBM (CO₂ injection from the 700th day). CH₄ recovery increases totally with the extension of production time. In contrast with CH₄ recovery for primary, that of CO₂-ECBM improves rapidly during CO₂ injection for effluxion of time. CH₄ recovery varies with different shut-in thresholds of CH₄ production rate. For the shut-in thresholds of 1000, 800 and 600 m³/d, the CH₄ recoveries of primary are 33.60 %, 36.81 % and 40.74 %, and those of CO₂-ECBM are 56.99 %, 59.89 % and 63.20 %, which the CH₄ recoveries enhance by 23.36 %, 23.07 % and 22.46 %, respectively. For the shut-in threshold of 492.2 m³/d which is the intersection point for gas production rates of both primary and CO₂-ECBM, CH₄ recovery for primary is 43.36 %, and that of CO₂-ECBM is 65.34 % which is increased by 22.02 % relative to primary's. In conclusion, the variation characteristics of CH₄ recoveries indicate that CH₄ recovery of coal reservoir can be increased by more than 20 % by CO₂-ECBM with injection pressure 10 MPa from the 700th day when CH₄ production rate of CBM well shut-in is between 492.2 m³/d and 1000 m³/d.

Fig. 15.

Changes in CH₄ recoveries for primary and CO₂-ECBM.

5. Conclusion

In this paper, a multi-physical fields coupling model is proposed on the basis of Langmuir monolayer adsorption mode, mass conservation law, Fick diffusion, Darcy equation, energy conservation law and elastic mechanics of porous media. It is verified by historical fitting according to field data. Then the model is available for simulation of CH₄ primary recovery and CO₂-ECBM recovery of a deep coal seam of a sedimentary basin in Northwest China. The main conclusions are as follows.

• (1)A fully coupled model of AHTM suitable for exploitation of CBM in coal reservoir buried deep underground with high in-situ stress and temperature is established. The model is proved to be accurate by historical fitting, which considers anisothermal competitive adsorption for CH₄ and CO₂, non-stationary diffusion for gas, multicomponent-multiphase flow, thermal field including heat exchange with surrounding strata, matrix deformation induced by adsorption/desorption, reservoir pressure and temperature and variable permeability on the basis of effective stress principle of porous media.
• (2)For primary recovery, total CH₄ content, adsorbed CH₄ content, free CH₄ concentration, permeability in coal reservoir and CH₄ production rate in CBM well decrease with the extension of drainage time. By 2000 day, produced coalbed methane in CBM well mainly stems from free CH₄ in fracture, for average total CH₄ content and average of adsorbed CH₄ content decrease by 5.49 and 1.12 m³/t, respectively. However, CH₄ production rate of CBM well has been lower than 1000 m³/d with a decrease in permeability ratio exceeding 0.8 at this time.
• (3)For CO₂-ECBM recovery, average total CH₄ content and average adsorbed CH₄ content in coal reservoir decrease rapidly, while average free CH₄ concentration, permeability of coal reservoir and CH₄ production rate increase rapidly compared with primary recovery. Injecting CO₂ into the coal reservoir would enhances recoveries of adsorbed CH₄ and free CH₄ of coal reservoir through competitive adsorption in matrix and permeability improvement of fracture. It increases CH₄ production rate and time for CBM well, which the CH₄ recovery is increased by more than 20 % at the same shut-in threshold with 10 MPa CO₂ injection from the 700th day.

Ethics approval

Review and/or approval by an ethics committee was not needed for this study because our investigation does not involve humans or animals.

Funding

This work was funded by the Fellowship Plan Program of EnerTech-Drilling & Production Co., China National Offshore Oil Corporation (HFKJYC-GY202109) and Engineering application research project of China National Offshore Oil Corporation (GCJSXMHT-2319).

Nomenclature

0	Initial situation of coal reservoir	k	Permeability of fracture
g	Gas in coal reservoir	T	Reservoir temperature
w	Water in fracture	VL	Langmuir volume for coal
m	Coal matrix	PL	Langmuir pressure for coal
f	Coal fracture	τ	Gas adsorption time
P	Fluid pressure	q	Absorb/release heat
S	Fluid saturation in fracture	ρ	Density for gas, water and coal
P	Gas pressure	μ	dynamic viscosity for fluid
Q	Gas diffusion activation energy	dg	dissolved gas
ϕ	Porosity for coal	st	sorption heat
bk	Klinkenberg factor	C	Specific heat volume
λ	Thermal conductivity	η	Pore size distribution index

Data availability statement

No data was used for the research described in the article.

CRediT authorship contribution statement

Shengli Gong: Writing – original draft, Conceptualization. Lu Zhang: Writing – original draft, Conceptualization. Tongyao Zhang: Investigation. Wei He: Formal analysis. Weiqiang Hu: Data curation. Hongchao Yin: Data curation. Liangshuai Ma: Investigation. Xin Hong: Formal analysis. Wei Zhang: Writing – original draft. Bo Zhang: Writing – original draft.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.