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Abstract

CO₂-enhanced coalbed methane (CO₂-ECBM) can improve coalbed methane production efficiency and simultaneously alleviate greenhouse gas emissions. In this paper, we integrated TOUGH2 and FLAC3D numerical simulation software to conduct hydro-mechanical coupling analysis for effects of hydrofracturing and secondary fracturing in CO₂-ECBM. The simulation results show that the hydrofracturing and secondary fracturing treatments significantly increase the coal seam interconnectivity, enhancing overall injection and production. The reduction of the pore pressure near injection wells can effectively reduce the damage of gas injection well. Moreover, secondary fracturing can even increase cumulative gas production up to 32.5%. In addition to rising fracture density, increasing the fracture length is also considered an efficacious procedure for enhancing permeability in the secondary fracturing process.

Keywords

thermo-hydro-mechanical TOUGH-FLAC reservoir fracturing coal seams

Introduction

CO₂-enhanced coalbed methane (CO₂-ECBM) not only improves the gas recovery ratio (Godec et al., 2014) but also realizes CO₂ emission reduction to ameliorate the greenhouse effect (Mazzotti et al., 2009; Pan et al., 2018; Reeves, 2010; Shen et al., 2018). It is therefore considered to be a win-win technology. CO₂ would displace coalbed methane due to the strong adsorption capacity of coal and improve the production of CBM (Kumar et al., 2014; White et al., 2005).

The simultaneous CO₂ injection and CH₄ extraction process is believed to be a complex hydro-mechanical coupling process. The changes in effective stress caused by variations of pore pressure and adsorption/desorption-induced strains result in the evolution of permeability (Bustin et al., 2008; Connell and Detournay, 2009; Gu and Chalaturnyk, 2005; Lin et al., 2008; Ma et al., 2020b; Pan et al., 2018; Wang et al., 2009). Generally, strain-based and stress-based permeability models have been widely used in CBM production and CO₂-ECBM. Pan et al. conducted a series of measurements about coal permeability for CO₂-ECBM, and the evolution of permeability under different stress conditions was illustrated (Pan et al., 2010). Fan et al. established a THM coupled model to study the gas migration during CO₂-enhanced coalbed methane recovery (Fan et al., 2019). The simulation shows that the injection of CO₂ has a significant influence on the permeability of the coal seam. Connell and Detournay investigated the coupled ﬂow and geomechanical processes CO₂-ECBM by linking gas reservoir simulator SIMED II with the geomechanical model FLAC3D (Connell and Detournay, 2009). Ma et al. modeled the process of CO₂-ECBM using the TOUGH-FLAC simulator, with consideration of the gas solubility. They revealed the impact of CO₂ injection on the mechanical behaviors of the coal seam. Mechanical failure was induced near the injection well in the case with a very unfavorable stress ﬁeld (Ma et al., 2017a).

As most of the coal reservoirs in China have low pressure and permeability, direct production is complicated and inefficient. The permeability of coal seam is one of the main parameters that affect gas production, and it is a controllable industry parameter that can be used to improve productivity. Hydrofracturing is a useful industrial technology for low permeability reservoir production. The fracture aperture is affected by normal stress and shear stress (Bai et al., 1999). Several numerical models have been developed to investigate the effects of fractures on flow patterns and gas production (Chen et al., 2017; Ma et al., 2020a; Wang, 2018). In these models, the geomechanical eﬀects on fracture permeability are ignored. According to the parallel plate flow experiment, the relationship between the permeability and the opening degree of fracture is cubic. A small change in the fracture aperture results in a significant variation in permeability (Yuan, 2002), which should be considered.

In this study, the effects of hydrofracturing and secondary fracturing in CO₂-enhanced coalbed methane with TOUGH-FLAC simulator with consideration of mechanical deformation on fracture permeability. Firstly, we perform a coupled THM simulation to investigate the influence of hydraulic fractures on fluid migration, stress evolution, and methane production. Then, we carry out a simulation case to examine the effect of secondary fracturing on injection and production efficiency. Finally, the influences of length and permeability of fractures are studied in a sensitivity analysis.

Mathematical model

Hydro-mechanical formulations

The general form of the fluid mass and energy balance equations is expressed as (Pruess et al., 1999)

\frac{d}{d t} \int_{V_{n}} M^{K} d V_{n} = \int_{Γ_{n}} F^{K} \cdot n d Γ_{n} + \int_{V_{n}} q^{K} d V_{n}

(1)

The equation of solid deformation is shown as follows

G \nabla^{2} u + \frac{G}{1 - 2 ν} \nabla u - α I p - K ε_{s} + F = 0

(2)

where

M^{K}

is the mass per unit volume,

F^{K}

is mass flux, and

q^{K}

is a source or sink per unit volume,

G

is shear modulus,

u

is displacement,

ν

is Poisson’s ratio,

α

is Biot’s coefficient,

I

is the unit tensor,

p

is phase-averaged pore pressure,

K

is bulk modulus,

ε_{s}

is adsorption/desorption-induced strains and

F

is the body force vector.

Porosity and permeability changes

For the coal reservoir, we use the following stress-dependent porosity and permeability models (Ma et al., 2017b)

ϕ_{m} = α + (ϕ_{m 0} - α) e xp (- \frac{Δ σ_{m}^{'}}{K_{m}})

(3)

\frac{k_{m}}{k_{m 0}} = {(\frac{ϕ_{m}}{ϕ_{m 0}})}^{3} = {[\frac{α}{ϕ_{m 0}} + \frac{(ϕ_{m 0} - α)}{ϕ_{m 0}} e xp (- \frac{Δ σ_{m}^{'}}{K_{m}})]}^{3}

(4)

where

ϕ_{m 0}

and

k_{m 0}

represent the initial porosity and permeability at initial stress for the simulation domains, respectively,

K_{m}

is the ‘drained’ bulk modulus, and

σ_{m}^{'}

is the effective mean stress.

Ignoring the influence of fracture connectivity, we decomposed fracture permeability into the superposition of permeability in the three directions of x, y, and z, as shown in Figure 1 (Yuan, 2002).

Figure 1.

The simplification of a fracture system with the parallel plate fracture flow model.

The permeability in a specific direction is determined by the opening degree of the vertical fracture and the matrix width. According to the cubic law, the expressions of permeability in all directions are obtained as follows

k_{f j} = \sum_{i = 1}^{3} \frac{{b_{i}}^{3}}{12 a_{i}} (i \neq j)

(5)

where

a

is the spacing of the fractures;

b

is the fracture aperture. The current effective normal stress mainly controls fracture aperture and they satisfy an exponential relationship (Rutqvist et al., 2002). The variation of the fracture aperture caused by normal stress can be calculated using the following formula

Δ b_{i n} = b_{\max} [e xp (d \times σ_{n i}) - \exp (d \times σ_{n 0})]

(6)

where,

b_{\max}

is the maximum fracture aperture;

σ_{n 0}

and

σ_{n i}

are the initial and current normal stresses respectively. The current fracture aperture is given by

{b = b}_{i n} + b_{\max} [\exp (d \times σ_{n i}) - \exp (d \times σ_{n 0})]

(7)

Equation (7) can be rewritten concerning the apertures of residual cracks

{b = b}_{r} + b_{\max} [\exp (d \times σ_{n i})]

(8)

where

d

is a parameter related to the radius of curvature in Figure 2.

Figure 2.

The relationship between fracture aperture and normal stress.

In the process of gas injection, the dilatancy effect caused by shear stress/strain affects the measurement of the fracture aperture (Bai et al., 1999)

Δ b_{ish} = \sum_{i \neq j} Δ e_{ijsh} (a_{i 0} + \frac{G}{K_{s h}}) \tan (Φ_{d})

(9)

where

Δ e_{ijsh}

G

K_{s h}

and

ϕ_{d}

are the shear strain, modulus, stiffness and expansion angle, respectively. Therefore, the total

Δ b_{i}

of fracture aperture is given by

Δ b_{i} = Δ b_{i n} + Δ b_{ish}

(10)

By introducing equation (10) into equation (5), we obtain

k_{f j} = \sum_{i = 1}^{3} \frac{{(b_{i 0} + Δ b_{i})}^{3}}{12 a_{i}}

(11)

Also, the porosity of the fracture can be calculated as (Gan and Elsworth, 2016)

Φ_{f} = 1 - (1 - Φ_{0}) e x p (- Δ ε_{υ}^{f})

(12)

where,

ϕ_{f 0}

is the initial fracture porosity. Equations 11 and 12 are the anisotropic permeability and porosity of fracture.

Geometric model and physical parameters

Figure 3 shows the description of a five-spot well distribution. The gas injection well is located in the middle, with four gas producing wells around it. Fractures generated by hydrofracturing are located in the horizontal direction of all the wells.

Figure 3.

Five-spot well distribution.

The schematic of the geometrical model within FLAC3D, involving coal seam, wells, and fractures are shown in Figure 4. The depth of coal seam is 1 km, and the average density of the upper rock is 2260 kg/m³. It can be calculated that the vertical stress $σ_{V}$ at the top of the coal seam equals –22.3 MPa. The crack length is 0.1 km and the horizontal stress $σ_{x} = σ_{Hmax} = 0.9 \times σ_{V}$ is greater than $σ_{y} = σ_{Hmin} = 0.5 \times σ_{V}$ . The initial pressure and temperature are 5 MPa and T = 30 $° C$ . It is assumed that there is no horizontal displacement at the boundary and the initial gas saturation $S_{g}$ =0.408. The gas injection rate is 0.20 kg/s, with temperature equal to 45 $° C$ . The initial temperature and pressure of the production wells are 15 $° C$ and 0.275 MPa. The coal seam and fracture parameters in the numerical simulation are shown in Table 1.

Figure 4.

Schematic of the geometrical model, involving coal seam, wells and fractures.

Table 1.

Parameters of coal seam and fractures for CO₂-ECBM simulation.

Variable	Value	Unit
Coal seam thickness	5.00	m
Initial coal porosity, $ϕ_{0}$	10%
Initial coal permeability, $k_{0}$	$1.00 \times 10^{- 14}$	$m^{2}$
Elastic modulus of coal, $E_{r}$	3.0	$GPa$
Poisson ratio of coal, $μ_{r}$	0.3
Fracture apertures, $b_{0}$	$1.8171 \times 10^{- 4}$	m
Side length of model	800	m
Elastic modulus of fracture, $E_{f}$	2.83	$GPa$
Poisson ratio of fracture, $μ_{f}$	0.30
Initial fracture porosity, $ϕ_{f}$	0.50
Initial fracture permeability, $k_{f}$	$1.00 \times 10^{- 13}$	$m^{2}$
Curvature parameter, $d$	$1.10 \times 10^{- 6}$	${Pa}^{- 1}$

The elastic modulus of the fracture element $E_{f}$ in Figure 4 can be calculated using the following formula (Figueiredo et al., 2017)

\frac{1}{E_{f}} = \frac{1}{E_{r}} + \frac{1}{k_{n} a}

(13)

where the fracture normal stiffness is 5 GPa/m and the spacing of the fractures is a = 10 m.

E_{f}

= 2.83 GPa can be obtained from equation (13).

Simulation result and analysis

The influence of fracturing

Figure 5 shows the distribution of the pore pressure (A) to (C) and CO₂ mass fraction $X_{{gCO}_{2}}$ (a) to (c) in the early (10 days), middle (100 days) and late (1 year) stages of injection and production. With the injection of CO₂, the pore pressure and CO₂ content near the gas injection well increase continuously. The change of pore pressure and CO₂ content is more evident in the direction of fracture extension. To gain an intuitive understanding of the effect of fractures on gas injection and production, Figure 6 shows the distribution of pore pressure and CO₂ mass fraction $X_{{gCO}_{2}}$ along the horizontal monitoring line y = 5 in the fracture direction.

Figure 5.

The distribution of pore pressure in 10 days (A), 100 days (B), 1 year (C), and the distribution of CO₂ mass fraction in 10 days (a), 100 days (b), 1 year (c).

Figure 6.

Pore pressure and CO₂ mass fraction after 10 days, 100 days and 1 year of injection and production.

As shown in Figure 6(a), the changes in the pore pressure with time ( $d P / d t$ ) and with length ( $d P / d x$ ) in the fracture are more significant than the changes in coal. This is because of the larger initial fracture permeability and the omission of CH₄ adsorption capacity in the fracture. Both of these factors can improve the injection efficiency of CO₂. After injection for 10 days, 100 days and 1 year, the pore pressure of the fracture near the injection well are 7 MP, 10 MPa and 14.5 MPa, respectively.

In Figures 5(a) to (c) and 6(b), the migration distance of CO₂ in the horizontal direction is more considerable compared to the vertical direction. Compared with CH₄, CO₂ has a stronger adsorption capacity. Without considering the time effect of desorption and adsorption, CO₂ completely displaced free and adsorbed CH₄. In the early, middle and late stages of injection, CO₂ flows to 100 m, 150 m and 240 m away from the wellhead in the horizontal direction.

Figure 7 shows the methane production rate is attributable to the fracture and coal elements and the ratio between them. During the entire injection and production process, gas in the production well originates from adjacent fracture elements and coal elements. The flow rate from the fracture elements to the well is faster. According to Figure 7, the maximum production of fracture element F2 and coal element C2 is 1.48 kg/s and ${1.48 \times 10}^{- 2}$ kg/s, respectively, and their ratio is 100, which is equal to the initial permeability ratio. Subsequently, CO₂ is fully adsorbed by the coal wall and flows steadily, and the injection efficiency decreases to $5.36 \times 10^{- 3} kg / s$ and $5.36 \times 10^{- 4} kg / s$ .

Figure 7.

The methane production rate comes from the fracture and coal element (a) and their ratio (b).

Figure 8 shows the temporal evolution of pore pressure, temperature, and CO₂ mass fraction at fracture and coal elements near the injection well. Given that the fracture and coal elements are adjacent to the injection well, the variation trend with time and the value of the pore pressure of the two elements are similar. The model doesn’t consider the adsorption of fracture and the strong adsorption of the coal elements for CO₂. Therefore, CO₂ can be quickly stored in the coal matrix by replacing CH₄ (Figure 8(c)), thus enabling the $X_{{gCO}_{2}}$ in the coal, element to promptly reach a peak value (Figure 8(b)).

Figure 8.

The temporal evolution of (a) pore pressure, (b) temperature, and (c) CO₂ mass fraction at fracture and coal elements near the injection well.

The temporal evolution of the total and effective maximum and minimum stress at C1 and F1 is shown as Figure 9. In Figure 9(a), the trend of the stress change of C1 and F1 are similar. An increase is initially observed followed by a steady trend, and the value is different. The initial maximum principal stress $σ_{1}$ is in the vertical direction, equaling $σ_{z}$ , and is set as a stress boundary condition. Therefore, the main factors that affect the first principal stress of C1 are the thermal expansion and the adsorption expansion/desorption contraction; the first principal stress of F1 is only affected by the temperature. Fifty days after gas injection, according to Figure 8(b), the temperature of C1 and F1 is approximately 44 $° C$ , and the variation is 14 $° C$ .

Figure 9.

Temporal evolution of (a) total and (b) effective maximum and minimum stress at C1 and F1.

The elastic modulus of C1 and F1 is 3.0 GPa and 2.83 GPa, respectively, and their Poisson's ratios are 0.3. Thus, the corresponding bulk modulus are 2.500 GPa and 2.358 GPa. Assuming that fixed displacements around them constrain the C1 and F1 elements, the maximum extremes of the temperature-induced stress change are calculated to be 3.465 GPa and 3.268 GPa, respectively. Considering the stress change caused by the adsorption of C1, the variation of $σ_{1}$ at C1 is larger than that at F1. According to the theory of porous elasticity, the maximum and minimum effective stresses can be calculated. As shown in Figure 9(b), unlike the variation tendency of the total stress, the maximum and minimum effective stresses exhibit a downtrend under the influence of increasing pore pressure.

Figure 10 shows the temporal evolution of the pore pressure and gas saturation at C2 and F2. With the development of production, pore pressure decreases rapidly. There is a rapid pressure drop in fractures, which promotes more gas flow into the production well so that the change of gas saturation in fractures is more prominent.

Figure 10.

Temporal evolution of the (a) pore pressure and (b) gas saturation at C2 and F2.

The temporal evolution of the total maximum and minimum stresses and effective stresses at coal and fracture elements near the production well is shown in Figure 11. In the exploitation process, the reduction of pressure increases the shear stress in the reservoir, causing the difference between the maximum and minimum principal stresses. The shear stress increase is mainly due to the different mechanical boundaries in different directions and the different variations of stress caused by the pressure drop. In Figure 11(a), the shear stress in the fracture element advances more conspicuously. Subsequently, due to pore pressure reduction, the maximum and minimum effective stresses rise rapidly and remain stable.

Figure 11.

Temporal evolution of (a) total and (b) effective maximum and minimum stresses at C2 and F2.

Based on the maximum and minimum effective stress in Figure 9(b), the corresponding stress path is drawn as Figure 12(a). Initially, to ensure that C1 and F1 are in a relatively safe state (without damage), it is assumed that the coal and fracture element's internal friction angle $ϕ_{f}$ is 50 $°$ in this investigation. After 300 days of injection, the coal elements reach the submitted status. During the entire injection process, the fracture elements are in a relatively safe state. Due to the difference of stress change caused by heat/adsorption in the coal and fracture, the stress state between them is different. Figure 12(b) shows the stress path of the fracture element F2 and the coal element C2 near the production well. During the 500-day production process, F2 and C2 are slowly moving away from the yield surface, causing the production to be relatively safe.

Figure 12.

Effective stress paths at (a) C1, F1 and (b) C2, F2.

The influence of secondary fracturing

Figure 13 shows the distribution of the horizontal stress $σ_{x}$ . Due to the existence of fracture elements, the $σ_{x}$ near wells vary significantly in the x- and y-directions, which leads to the rotation of stress and the possibility of damage or new fracture. The process is usually known as secondary fracturing or refracturing treatment. This section will focus on the impact of secondary fracturing on the efficiency of injection and production.

Figure 13.

Distribution of horizontal stress $σ_{x}$ . (x, y/m).

Figure 14 shows the geometry of the secondary fracturing model and the initial stress state. Figure 15 shows the distributions of the pore pressure and CO₂ mass fraction $X_{{gCO}_{2}}$ after 10 days, 100 days and 1 year of injection and production in the case of secondary fracturing. From Figure 15(A) to (C), it is evident that the change of pore pressure near the injection and production wells is obvious. The CO₂ near the injection well extends along the fracture to the coal seam because of the high porosity and permeability of the fracture.

Figure 14.

The geometry of secondary fracturing model and initial stress state.

Figure 15.

In the case of secondary fracturing, the distribution of pore pressure in 10 days (A), 100 days (B), 1 year (C), and the distribution of CO₂ mass fraction in 10 days (a), 100 days (b), 1 year (c).

Figure 16 Figure 16 shows the distributions of pore pressure and CO₂ mass fraction along the vertical monitoring line (x = 2.5) in the early (10 days), middle (100 days), and late (1 year) of injection and production. Free CO₂ can displace methane and water more quickly in the coal seam because of the higher permeability and porosity of the fractures. In the early, middle and late stages of injection, secondary fracturing results show that gaseous CO₂ can reach 100 m, 150 m and 250 m away from the well. Figure 17 shows the production rate and cumulative production of coalbed methane. With the other parameters unchanged, the cracks of secondary fracturing help improve the production efficiency and cumulative production of coalbed methane in the entire production process. The cumulative production increased from ${4.0 \times 10}^{4}$ kg of hydrofracturing to ${5.37 \times 10}^{4}$ kg of secondary fracturing, an increase of nearly 32.5%.

Figure 16.

The distributions of pore pressure and CO2 mass fraction along the vertical monitoring line after 10 days, 100 days and 1 year of injection and production.

Figure 17.

(a) Production rate and (b) cumulative production of coalbed methane.

This section presents sensitivity analyses on the effects of increasing/decreasing length and permeability of fracture caused by secondary fracturing (‘refracture’ for short) by 20% on the injection and production. The basic value of fracture length is 100 m, the decreasing and increasing values are 80 m and 120 m, respectively; the basic value of permeability is ${1.0 \times 10}^{- 13} m^{2}$ , the decreasing and increasing values are ${8 \times 10}^{- 14} m^{2}$ and ${1.2 \times 10}^{- 13} m^{2}$ , while the other variables remain unchanged. Figures 18 and 19 show the effect of refracture length and permeability on CO₂ mass fraction and pore pressure along the vertical monitoring line. Figure 20 shows the effect of length and permeability of refracture on the cumulative production of coalbed methane.

Figure 18.

Effect of refracture length on (a) CO₂ mass fraction and (b) pore pressure along the vertical monitoring line.

Figure 19.

Effect of refracture permeability on (a) CO₂ mass fraction and (b) pore pressure along the vertical monitoring line.

Figure 20.

Effect of (a) length and (b) permeability of refracture on cumulative production of coalbed methane.

From Figures 18 and 19, it is evident that the increase of refracture length and opening contributes to the rapid flow of CO₂ to the coal seam, thereby effectively reducing the pore pressure near the well. The pressure drop can reduce the probability of damage near wells. As shown in Figure 20, when the length of refracture changes by $\pm$ 20%, the production increases and decreases to ${5.54 \times 10}^{4}$ kg and ${5.21 \times 10}^{4}$ kg, respectively, from ${5.37 \times 10}^{4}$ kg in the basic simulation, changing by 3.17% and –2.98%; when the fracture permeability increases and decreases by 20%, the cumulative production is ${5.43 \times 10}^{4}$ kg and ${5.30 \times 10}^{4}$ kg respectively, changing by 1.12% and –1.30%. Compared with the permeability, the length of refracture has a more significant influence on the CO₂-ECBM. In the practical process of CO₂-ECBM, increasing the fracture ratio to improve the coal seam penetration is more conducive to improving production efficiency.

Conclusions

In this study, the influence of hydrofracturing and secondary fracturing in CO₂-enhanced coalbed methane was studied using a coupled THM model with consideration of a stress-dependent reservoir permeability model and an anisotropic fracture permeability model. The variation in fracture permeability is affected by fracture normal stress and dilatancy effect, and the basic mechanical properties of fracture were calculated using the equivalent continuity method. We conclude as follows:

Hydrofracturing and secondary fracturing help improve the permeability of coal seam, thus effectively improving the injection efficiency, causing CO₂ to flow and rapidly displace CH₄. Also, the pore pressure near the well is effectively suppressed, which reduces the probability of damage in this region.

The maximum production of the fracture adjacent to the production well is 100 times that of the intact coal, which are 1.48 kg/s and ${1.48 \times 10}^{- 4}$ kg/s, respectively. Secondary fracturing can further enhance the recovery efficiency of CBM, and the cumulative production increased from ${4.0 \times 10}^{5}$ kg of primary fracturing to ${5.37 \times 10}^{5}$ kg, increasing by 32.5%.

In addition to continued fracturing, increasing the fracture length is also a meaningful way to increase permeability by secondary fracturing. The fracture length increases by 20%, and the cumulative production of coalbed methane increases by approximately 3.17%.

Footnotes

Acknowledgments

This study was supported by National Science and Technology Major (No. 2016ZX05043), National Natural Science Foundation of China (No. 42002255 and 41902310), Chinese Geological Survey (No. DD20201165), Natural Science Foundation of Jiangsu Province (BK20180636), Natural Science Foundation of Liaoning Province (2020KF2303), and Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX1052).

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Tianran Ma

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Coupled flow-geomechanics studies on the role of hydrofracturing and secondary fracturing in CO 2 -enhanced coalbed methane

Abstract

Keywords

Introduction

Mathematical model

Hydro-mechanical formulations

Porosity and permeability changes

Geometric model and physical parameters

Simulation result and analysis

The influence of fracturing

The influence of secondary fracturing

Conclusions

Footnotes

Acknowledgments

Declaration of conflicting interests

Funding

ORCID iD

References