Article pubs.acs.org/EF
Cite This: Energy Fuels XXXX, XXX, XXX−XXX
Modeling CH4 Displacement by CO2 in Deformed Coalbeds during Enhanced Coalbed Methane Recovery Quanshu Zeng,† Zhiming Wang,*,† Liangqian Liu,† Jianping Ye,‡ Brian J. McPherson,§ and John D. McLennan§ †
State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China ‡ Exploration Department of CNOOC Ltd., Beijing 100010, China § Energy & Geoscience Institute at the University of Utah, Salt Lake City, Utah 84108, United States ABSTRACT: Gas adsorption and desorption and displacement has a significant effect on coal deformation and permeability evolution during the primary recovery of coalbed methane (CBM) and enhanced coalbed methane recovery (ECBM). The objectives are to (1) quantify the coal deformation and permeability change caused by methane (CH4) displacement with carbon dioxide (CO2) and (2) model the transportation of CH4 and CO2 in deformed coalbed. In this study, the gas adsorption and desorption and displacement, coal deformation, and permeability evolution during CBM and ECBM recovery were described by an internally consistent adsorption-strain-permeability model, of which the simplified local density (SLD) adsorption theory, a theoretical strain model, and a matchstick-based permeability model were rigorous coupled. The coupled model was then verified with all of the CH4 and CO2 measured gas adsorption and desorption and coal strain data published in the past 60 years. Next, sensitivity analysis was further conducted on the coupled model to highlight and calibrate its performance. Finally, the coupled model was integrated into the Transport of Unsaturated Groundwater and Heat Simulator (TOUGH2) to simulate the ECBM process. The results show that the coupled model can simultaneously describe gas adsorption and desorption and displacement, coal deformation, and permeability evolution during ECBM recovery with only six parameters, including slit width, solid−solid interaction potential energy parameter, surface areas of CH4 and CO2, adsorption expansion modulus, and initial porosity. The coupled model can predict both CH4 and CO2 adsorption and the induced coal deformation fairly accurately at a pressure up to 20 MPa, and the average relative errors are within 9.76% and 9.14%, respectively. The results also suggest that the adsorption capacity of CO2 is 2−5 times as large as that of CH4, and the volumetric strain induced by CO2 adsorption is 2−8 times as large as that caused by CH4 adsorption. While the stronger adsorption capacity of CO2 on coal offers an option for CO2-ECBM, matrix swelling due to CH4 displacement with CO2 may narrow down or even close the cleat, significantly reducing the permeability and thus impacting the injection efficiency. Last but not least, the original TOUGH2 simulator predicts similar results with several other CBM simulators. However, it is impossible that 90% of CH4 can be displaced within 90 days. Considering the coal deformation and permeability change due to CH4 displacement with CO2, the modified TOUGH2 simulator shows that only 24% of CH4 is displaced in the first 90 days, and it takes about 1800 days to displace 90% or more. Advances in the understanding of CH4 displacement by CO2 and their transportation mechanisms in coal seams suggests that the success of CO2-ECBM depends on the optimal management of matrix swelling.
1. INTRODUCTION Increasing atmospheric carbon dioxide (CO2) concentrations are believed to be the major cause of global warming. Several ways to reduce CO2 emissions include improving power generation efficiency by upgrading existing plants or building new plants, relying more on renewable energy and nuclear-generated power, and, finally, carbon capture and storage (CCS). Of all emissionreduction mechanisms, CCS is projected to provide the largest contribution to emission reduction in the coming decade.1,2 Carbon capture and storage is a process of capturing waste CO2 from large point sources, transporting it to storage sites, and depositing it where it will not enter the atmosphere, normally an underground geological formation. The geological sequestration of CO2 offers several options, including deep saline reservoirs, oil and gas fields, and unminable coal seams. Of these options, only enhanced oil recovery (EOR) and enhanced coalbed methane recovery (ECBM) provide a value-adding byproduct to CO2 injection, offsetting the sequestration cost or, in some cases, © XXXX American Chemical Society
making CO2 injection profitable. This economic benefit is particularly important in the absence of regulatory controls and financial incentives for CCS.3,4 CO2-EOR is a relatively mature technology; however, ECBM is still in its infancy, with most of the pilot projects not to be successful.5,6 Understand the processes of methane (CH4) displacement by CO2 and their transport mechanisms in coal seams may help to improve the ECBM technology. Existing coalbed methane (CBM) simulators, which are developed for primary CBM recovery, have considered many important features, such as (1) a dual porosity system, (2) a water and gas two-phase fluid, (3) Darcy flow in the cleat system, (4) pure gas desorption in the matrix system, and (5) coal deformation due to both reservoir compaction and gas desorption. However, Received: September 19, 2017 Revised: January 10, 2018 Published: January 17, 2018 A
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 1. Slit pore characterization in SLD theory.
Figure 2. Schematic diagram of CH4 and CO2 mixture adsorption on carbonaceous adsorbent.
concise purposes, both the equation of state and the potential function are omitted in this section but detailed in the Supporting Information. Several assumptions were made for SLD theory,7,9−12 including that: (1) the chemical potential of any point above adsorbent surface is equal to the bulk-phase chemical potential; (2) the chemical potential of any point above adsorbent surface is the sum of adsorbate−adsorbate and adsorbate−adsorbent interactions; (3) the adsorbate−adsorbent interaction of any point above adsorbent surface is independent of temperature or molecule number; (4) coal pores are considered as perfect slits with temperature and pressure distributed uniformly; and (5) all adsorbate and adsorbent molecules are spherical, except for the adsorbate molecules touching slit walls. As mentioned, the chemical potential of any point above adsorbent surface should be the same:
the recovery process becomes more complex with CO2 injection. Several additional features should be considered, including: (1) CH 4 /CO 2 mixture adsorption and desorption, (2) CH 4 displacement by CO2, and (3) the induced coal deformation and permeability evolution. This paper is aimed at developing an internally consistent adsorption-strain-permeability model to simultaneously quantify gas adsorption and desorption and displacement, coal deformation, and permeability change during ECBM recovery. The remainder of this paper is organized as follows: section 2 presents the modeling and coupling details of gas adsorption and desorption and displacement, coal deformation, and permeability evolution; section 3 presents the validation and sensitivity analysis of the coupled model; section 4 presents the application of the coupled model in an ECBM simulation.
2. MODELING In this section, the coupled adsorption-strain-permeability model is detailed. Gas adsorption and desorption and displacement, coal deformation, and cleat permeability evolution characteristics are described using the simplified local density theory, a theoretical strain model, and a matchstick-based permeability model, respectively. 2.1. Simplified Local Density Theory. Rangarajan7 first proposed the simplified local density (SLD) theory by combining mean-field approximation theory and density functional theory, believing that gas adsorption and desorption and displacement are the resultant effects of adsorbate−adsorbate and adsorbate−adsorbent molecule interactions, as shown in Figure 1. In this theory, the adsorbate−adsorbate interaction can be represented by a fluid equation of state,8 while the adsorbate− adsorbent interaction is described by the potential function.9 For
μ(z) = μ bulk = μff (z) + μfs (z)
(1)
where the chemical potentials of bulk and adsorption phases can be represented in fugacity forms: ⎛f ⎞ μ bulk = μref + RT ln⎜⎜ bulk ⎟⎟ ⎝ fref ⎠
(2)
⎡ f (z ) ⎤ μff (z) = μref + RT ln⎢ ads ⎥ ⎢⎣ fref ⎥⎦
(3)
and coal matrix pores can be effectively characterized by slits10,11 while adsorbate molecules locate between the parallel slit walls and have interactions with both walls (Figure 1): B
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels μfs (z) = NA[Ψfs(z) + Ψfs(W − z)]
walls exist in each slit pore (Figure 1), half of the surface area is considered for adsorption calculation:
(4)
where NA is the Avogadro constant, 6.02 × 1023 mol−1. Therefore, the adsorption equilibrium criteria can be obtained by substituting eqs 2, 3, and 4 into eq 1: ⎡ Ψ (z) + Ψfs(W − z) ⎤ fads (z) = fbulk exp⎢ − fs ⎥ kBT ⎦ ⎣
fibulk xip
=
bi̅
bulk
ρbulk
1 − b bulk ρbulk
W − 3d f /8
∫3d /8
[ρads (z) − ρbulk ]dz
f
(6)
For CH4/CO2 mixture adsorption on coal, the adsorbate− adsorbate interactions become more complex, including CH4− CH4, CH4−CO2, and CO2−CO2 (Figure 2). A fluid mixing rule11,13 was then implemented in the fluid equation of state to describe these interactions; thus, the fugacity of CH4 and CO2 in both phases can be rewritten as:
(5)
where kB is the Boltzmann constant, 1.38 × 10−23 J/K. According to SLD theory, the Gibbs excess adsorption can be obtained by integrating the density difference between adsorption and bulk phases along the slit width. Because two
ln
A 2
nGibbs =
⎛ p pb ⎞ abulk − ln⎜⎜ − bulk ⎟⎟ + 2 2 ρ RT RT ⎠ ⎝ RT b bulk + 6b bulk cbulk + cbulk bulk
bulk bulk ⎡ a bulk b b̅ + 3b bulk c i̅ bulk + 3bi̅ cbulk + cbulk c i̅ bulk ⎤⎥ × ⎢ i̅ + 1 − bulk i 2 2 ⎢⎣ abulk ⎥⎦ b bulk + 6b bulk cbulk + cbulk
⎡ 2 + ρbulk (b bulk + cbulk − × ln⎢ ⎢ 2 + ρ (b + cbulk + ⎣ bulk bulk
⎤ 2 2 b bulk + 6b bulk cbulk + cbulk )⎥ 2 2 b bulk + 6b bulk cbulk + cbulk ) ⎥⎦
bulk bulk ⎡ p b bulk bi̅ + 3b bulk c i̅ bulk + 3bi̅ cbulk + cbulk c i̅ bulk +⎢ 2 2 ⎢⎣ RTρbulk b bulk + 6b bulk cbulk + cbulk
+
⎛ cbulk − b bulk c i̅ bulk) ⎤⎥⎜ ⎜1 − 2 + 6b bulk cbulk + cbulk ⎦⎥⎜⎝
(− b bulk + cbulk )(bi̅ 2 b bulk
bulk
⎞ ⎟ pb bulk ⎟ ⎟ − RT ⎠
1 p RTρ bulk
(7)
and
ln
f iads (z) yi (z)p
⎡ pb ⎤ aads(z) p − ln⎢ − ads ⎥ + 2 2 ⎢⎣ RTρads (z) 1 − badsρads (z) RT ⎥⎦ RT bads + 6badscads + cads ads
=
bi̅ ρads (z)
ads ads ⎡ a ads(z) b b ̅ + 3bads c i̅ ads + 3bi̅ cads + cads c i̅ ads ⎤ ⎥ × ⎢ i̅ + 1 − ads i 2 2 ⎥⎦ ⎢⎣ aads(z) bads + 6badscads + cads
⎡ 2 + ρads (z)(bads + cads − × ln⎢ ⎢ 2 + ρ (z)(b + c − ⎣ ads ads ads
⎤ 2 2 bads )⎥ + 6badscads + cads 2 2 bads ) ⎥⎦ + 6badscads + cads
ads ads ⎡ bads bi̅ + 3bads c i̅ ads + 3bi̅ cads + cads c i̅ ads p +⎢ 2 2 ⎢⎣ RTρads (z) bads + 6badscads + cads
⎡ ads (− bads + cads)(bi̅ cads − bads c i̅ ads) ⎤⎢ ⎥ + ⎢1 − 2 2 bads + 6badscads + cads ⎦⎥⎢⎣
∑ ∑ xixj i
aads(z) =
bads =
j
∑ xibi̅ bulk
∑ yi (z)bi̅ ads i
(9)
∑ ∑ yi (z)yj (z)
⎤ ⎥ pbads ⎥ − RT ⎥ ⎦
i
ai̅ bulk a ̅jbulk
j
i
p RTρads (z)
b bulk =
where attraction terms are determined by quadratic mixing rules while repulsion and polarity terms are determined by linear mixing rules: abulk =
1
ai̅ ads(z)a ̅jads(z)
cbulk =
(10)
∑ xi c i̅ bulk i
C
(8)
(11)
(12)
(13) DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
cads =
Δε = Δεrc + Δεms
∑ yi (z) c i̅ ads
(14)
i
On the one hand, the effective stress will increase as the pore pressure decreases, resulting in the compaction of coal and the closure of cleats. The volumetric strain change due to reservoir compaction may be described by linear elastic theory and is three times as large as linear strain because isotropy is assumed:16−18
and ⎛ ∂nabulk ⎞ ai̅ bulk = ⎜ ⎟ ⎝ ∂ni ⎠θ , V , n
(15)
j
⎛ ∂nb bulk ⎞ =⎜ ⎟ ⎝ ∂ni ⎠θ , V , n
(16)
⎛ ∂nc ⎞ c i̅ bulk = ⎜ bulk ⎟ ⎝ ∂ni ⎠θ , V , n
(17)
bi̅
bulk
Δεrc = −
j
j
⎡ ∂naads(z) ⎤ ai̅ ads(z) = ⎢ ⎥ ⎣ ∂ni ⎦θ , V , n
j
j
(19)
⎛ ∂nc ⎞ c i̅ ads = ⎜ ads ⎟ ⎝ ∂ni ⎠θ , V , n
j
(20)
bi̅
ads
Δεms =
=
⎡ Ψ fs(z) + Ψ fs(W − z) ⎤ i i ⎥ ⎥⎦ k T ⎣ B
fibulk exp⎢ − ⎢
∑ yi = 1
(23)
p(n)
∑ niGibbs
Δεms =
Ai 2
W − 3/8dif
∫3/8d
f i
(24)
[ρads (z)yi (z) − ρbulk xi]dz
(28) 2
∫p(0)
nGibbs d(ln p) A spe
(29)
3Mcoaρcoa RT K ms
p(n)
∫p(0)
nGibbs dp p
(30)
2.3. Coal Permeability Model. As mentioned, reservoir compaction and matrix shrinkage have just the opposite effects on cleat deformation and associated permeability evolution.14,15 Note that the matrix pore contribution to fluid mobility is assumed to be small, and all permeability mentioned hereinafter refers to the cleat permeability. Several cleat permeability models for coal reservoirs have been developed and widely used, including the Shi−Durucan (S & D) model,20−23 the Cui−Bustin (C & B) model,24,25 and the Palmer−Mansoori (P & M) model26,27 (and its improved version).28 These models share several assumptions: (1) matchstick geometry, (2) uniaxial strain, (3) constant overburden stress, and (4) competing reservoir compaction and matrix shrinkage effects. Among these models, the improved P & M model was found to have the best performance. The following section provides a brief review of the improved P & M model. Palmer and Mansoori26,27 derived a permeability model accounting for both reservoir compaction and matrix shrinkage, stating that the cleat permeability ratio is three times the porosity ratio. The P & M model was derived from the strain change of a linear thermos-elastic porous medium, ignoring the grain compressibility:
where, niGibbs =
ΔΨ
Combining eqs 28 and 29, the volumetric strain change due to gas adsorption and desorption or displacement may be expressed as:
Then, the Gibbs excess adsorption of the mixture is shown as: nGibbs =
K ms
ΔΨ = RT
In addition, both phases should satisfy the mole fraction constraints: (22)
3A speMcoaρcoa
where Aspe is the specific surface area of adsorbent, m /m . According to the Gibbs adsorption equation, the surface free energy change of adsorbent can be also characterized as:
(21)
∑ xi = 1
(27)
2
To implement the CH4/CO2 mixture adsorption model, each component should satisfy the adsorption equilibrium criterion: f iads (z)
3(1 − 2v) Δp E
On the other hand, the adsorbate will desorb as the pore pressure reduces, causing coal matrix shrinkage and cleat opening. In addition, the adsorbate component difference due to CH4 displacement by CO2 may also cause a phenomenon referred to as matrix swelling, the opposite of matrix shrinkage. Base on the research results of Bangham and Fakhoury,19 the deformation induced is proportional to the surface free energy change:
(18)
⎛ ∂nb ⎞ = ⎜ ads ⎟ ⎝ ∂ni ⎠θ , V , n
(26)
(25)
and the adsorption difference due to gas adsorption and desorption or CH4 displacement by CO2 can be effectively described by subtraction from one another. 2.2. Coal Strain Model. Coal is known as a dual porosity media composed of cleat and matrix pore.14,15 In the process of CBM and ECBM recoveries, both reservoir compaction and matrix shrinkage will occur and have opposite effects on coal deformation. Note that the cleat deformation due to reservoir compaction is 2 or 3 orders of magnitude larger than the reservoir compaction induced matrix deformation, and only cleat deformation is considered for reservoir compaction. Because matrix pores form the major share of the porous structure and are more responsible for gas storage, adsorption difference mainly results in matrix deformation. Moreover, the strains induced are assumed to be independent but superposed:
⎡ ϕ ⎤3 ⎡ Δϕ ⎤3 k =⎢ + 1⎥ ⎥ =⎢ ⎣ ϕ(0) ⎦ k(0) ⎣ ϕ(0) ⎦
(31)
where D
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 3. Solution procedure for coupled adsorption−strain−permeability model.
Δϕ = ϕ − ϕ(0) (1 + v)(1 − 2v) 2(1 − 2v) Δεms Δp − = 3(1 − v) E(1 − v)
Δϕ = ϕ − ϕ(0) g (1 + v)(1 − 2v) 2(1 − 2v) Δεms = Δp − 3(1 − v) E(1 − v)
(32)
However, the P & M model did not match well with the permeability evolution trend observed in the field, and then a suppression factor (g = 0.3) was introduced into the compaction term to eliminate or somewhat offset the anisotropy effect:28
(33)
Note that permeability evolution is a result of cleat deformation combining matrix deformation, eq 33 has inherently considered the interactions among gas adsorption and E
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels Table 1. Model Fitting Results for Coal Strain Induced by CH4 and CO2 Adsorption coal 16
Fruitland Ardley25 Wolf Mountain25 Sulcis30 San Juan31 Illinois31
p(0), MPa
T, °C
ρc, m3/kg
E, MPa
v, no unit
W, nm
εss/kB, K
ACH4, m2/g
ACO2 m2/g
Kss, MPa
6 8 8
35 25 25
1400 1500 1340
4400 3000 3000
0.32 0.30 0.30
1.50 2.59 1.19
19.5 12.6 21.5
104.2 19.8 49.3
137.3 64.8 53.2
1665 559 823
1.43 1.96 5.39
20 8 6
45 35 35
1400 1400 1400
2400 3500 2100
0.48 0.37 0.40
1.80 1.14 2.08
66.7 22.6 18.1
83.9 71.6 51.2
96.7 61.0 97.2
1812 1484 816
2.21 − −
δnCH4, % δnCO2, %
δεCH4, %
δεCO2, %
4.11 5.77 4.50
5.41 3.78 2.07
3.50 4.49 8.46
9.76 − −
8.31 3.37 7.07
5.06 7.61 9.14
Figure 4. Adsorption isotherms of CH4 and CO2.
properties of coal were measured directly from coal samples, and adsorption, strain, and cleat parameters were obtained by fitting the adsorption isotherm, strain, and permeability data. Specifically, these data are first used to calculate the density, fugacity, and chemical potential of both components in the bulk phase. Then, divide the slit pores into n intervals, initialize the adsorption-phase densities of CH4 and CO2 with those in the bulk phase, calculate the chemical potential induced by adsorbate−adsorbent and adsorbate−adsorbate interactions,
desorption and displacement, coal deformation, and cleat permeability evolution during CBM and ECBM recoveries. 2.4. Model Solution. The solution procedure for the coupled adsorption-strain-permeability model is depicted in Figure 3. Input data include pressure, temperature, physical properties, and bulk-phase mole fraction of CH4 and CO2, as well as the physical and elastic properties, adsorption, strain, and cleat parameters of coal. The physical properties of CH4 and CO2 were extracted from the NIST database,29 while physical and elastic F
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 5. Volumetric strain with pressure.
3. RESULTS 3.1. Validation of the Coupled Model. All publicly available adsorption and desorption and coal strain data measured with CH4 and CO2 at one time during the past 60 years16,25,30−32 were assembled to evaluate the performance of the coupled model. Input parameters required prior to the model calculation were summarized in Table 1. The former five parameters were directly from the literature, while the latter five were obtained by fitting experimental data with the coupled model. Based on these parameters, adsorption and strain results were predicted and plotted in Figures 4 and 5, respectively. For comparison purpose, the Langmuir predictions were also plotted in Figure 4. Note that no experimental data for San Juan coal (Figure 4e) and Illinois coal (Figure 4f) is available in the original literature, and the Langmuir predictions are considered as reference values. These results suggest that both Langmuir and the coupled models can describe CH4 adsorption and desorption fairly accurately at a pressure up to 20 MPa, and the average relative errors between measured and predicted results are all within 5.39%. Langmuir model assumes that CH4 adsorption
and loop the adsorption-phase densities of CH4 and CO2 until the adsorption equilibrium criterion is met for each interval. Next, calculate the adsorption amount by integrating density differences between bulk and adsorption phases along slit width, and loop the adsorption parameters of coal until the predicted isotherm coincides with the adsorption data. The adsorption parameters include slit width, solid−solid interaction potential energy parameter, and surface areas of CH4 and CO2. Note that the surface area does not affect the adsorption-phase density distribution, and the former two parameters are determined by fitting the shape of both isotherms, while the surface area of each component is regressed with its isotherm magnitude. Based on adsorption isotherm predicts, coal strain due to reservoir compaction and matrix shrinkage is further calculated, with adsorption expansion modulus of coal iterated until the predicted results satisfy the strain data. Finally, coal cleat permeability evolution is predicted on adsorption isotherm and strain results, with the initial porosity updated until the predictions meet the permeability data. G
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels Table 2. Sensitivity Research Projects of the Coupled Model p(0), MPa
T, K
ρcoa, kg/m3
E, MPa
v, no unit
W, nm
ess/kB, K
ACH4, m2/g
ACO2, m2/g
Kss, MPa
ϕi, %
5−20 10 10 10 10 10 10 10 10 10 10
313.15 303.15−323.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15
1300 1300 800−1800 1300 1300 1300 1300 1300 1300 1300 1300
3000 3000 3000 1000−5000 3000 3000 3000 3000 3000 3000 3000
0.3 0.3 0.3 0.3 0.2−0.4 0.3 0.3 0.3 0.3 0.3 0.3
1.5 1.5 1.5 1.5 1.5 1−2 1.5 1.5 1.5 1.5 1.5
60 60 60 60 60 60 20−100 60 60 60 60
70 70 70 70 70 70 70 20−120 70 70 70
100 100 100 100 100 100 100 100 40−160 100 100
1200 1200 1200 1200 1200 1200 1200 1200 1200 400−2000 1200
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.1−1
cleat porosity ranges from 0.1% to 1%. For a typical coal,14,35−40 its density is usually within 800−1300 kg/m3, Young’s modulus is between 1000 and 5000 MPa, and Poisson’s ratio ranges from 0.2 to 0.4. For CH4 and CO2 adsorption on coals,41−45 slit width is between 1 to 2 nm, solid−solid interaction potential energy parameter ranges from 20 to 100 K, surface area of methane is within 20−120 m2/g, the surface area of carbon dioxide is located between 40 and 160 m2/g, and the adsorption expansion modulus ranges from 400 to 2000 MPa. The influence of these parameters mentioned above on adsorption, strain, and permeability changes were all predicted and plotted in Figure 6. Figure 6 suggests that both CH4 and CO2 adsorption first increase then decrease with pore pressure, and their maximum value occurs at approximately 6 and 13 MPa pressure, respectively. In addition, the adsorption capacity of both components decrease with temperature but increase with slit width, solid−solid interaction potential energy parameter, and surface area. It should be also noted that CO2 adsorption with temperature may reverse at the pressure exceeds 7.5 MPa. Figure 6 also shows that surface area has the greatest influence on CH4 and CO2 adsorption, initial pore pressure the second-most, solid−solid interaction potential energy parameter the thirdmost, and slit width and temperature the least. In fact, the impact of slit width and temperature on CH4 adsorption are assumed to be small and can be neglected. In general, the sensitivity results further illustrate that CO2 adsorption is larger than that of CH4 given the typical coal properties considered and then offers the possibility to sequester CO2 and displace CH4 in unminable coal seams. Figure 6 also suggests that the volumetric strains induced by both CH4 and CO2 decrease with temperature, slit width, and adsorption expansion modulus but increase with initial pore pressure, coal density, Young’s modulus, Poisson’s ratio, solid− solid interaction potential energy parameter, and surface area. The influence of these factors on volumetric strain may be sorted by initial porosity, slit width, Poisson’s ratio, temperature, Young’s modulus, coal density, solid−solid interaction potential energy parameter, initial pore pressure, surface area, and adsorption expansion modulus. The impacts of the former four parameters are assumed to be small, while Young’s modulus has little effect on volumetric strain change once it reaches 3000 MPa. Within the coal property range studied, the volumetric strains are always larger than zero and increase monotonously with pressure, indicating that matrix shrinkage dominates during the CBM recovery. In addition, the strain change due to adsorption component variation is much more dramatic than that due to the pressure change, this will result in matrix swelling instead of matrix shrinkage during the ECBM recovery.
increases monotonically with pressure; however, the experimental data (Figure 4d) shows that CH4 adsorption first increases then decreases with pressure, and the largest adsorption occurs at around 13 MPa pressure. Similarly, the Langmuir predictions for CO2 may deviate from the experimental data (Figure 4) obviously at the pressure exceeds 6 MPa, while the coupled model can effectively predict CO2 adsorption and desorption at a pressure up to 20 MPa, and the average relative errors for the coupled model are within 9.76%. In general, both CH4 and CO2 adsorption on coal can be better described by the coupled model, especially in the situation when the pressure exceeds its reversal value. Figure 4 also suggests that the adsorption capacity of CO2 is 2−5 times as large as that of CH4, indicating that coal has a stronger interaction with CO2. In addition, the presence of CO2 in the coal cleat system reduces the partial pressure to CH4, further enhancing CH4 desorption. Both characteristics mentioned above jointly offer the possibility to deposit CO2 in unminable coal seams and increase CBM recovery without excessively lowering the pressure. To be specific, the CO2 diffuses into the coal matrix upon injection and displaces CH4 from some of the adsorption sites, and the CH4 then diffuses into the cleat system, where it ultimately migrates via Darcy flow to the production wells. Figure 5 suggests that the strain model can predict coal deformation fairly accurately at a pressure up to 20 MPa; the average relative errors between measured and predicted results are all within 9.14%. For all plotted results (Figure 5), positive results express expansion, while negative results express shrinkage. Because the total volumetric strains increase monotonically with pressure and are always larger than zero, matrix shrinkage dominates and will lead to a monotonic increase of permeability during the primary recovery of coalbed methane. Figure 5 also suggests that CO2 adsorption induced volumetric strain is almost 2−8 times as large as that caused by CH4 adsorption at a given pressure; thus, the strain difference between CH4 and CO2 is even more dramatic than that due to the pressure change. During the ECBM recovery, the dominant matrix deformation will swell instead of shrinkage, and thus significantly reduce the permeability and injectivity. 3.2. Sensitivity Analysis of Coupled Model. Sensitivity analysis was further conducted on the coupled model to highlight and calibrate its performance. The parameters studied were summarized in Table 2, including reservoir environment, and physical and elastic properties, as well as adsorption, strain, and cleat parameters of coal. For a typical coal seam33,34 within 2000 m, its initial pore pressure is usually between 5 and 20 MPa, the temperature is located between 303.15 and 323.15 K, and initial H
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 6. continued
I
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 6. Parameter sensitivity analysis of the coupled model.
Figure 7. Schematic diagrams of the well pattern and grid system used.
Last but not least, Figure 6 illustrates that the permeability ratio decreases with Poisson’s ratio, adsorption expansion modulus, and initial porosity but increases with initial pore pressure, temperature, coal density, Young’s modulus, Poisson’s ratio, slit width, solid−solid interaction potential energy parameter, and surface area. In addition, the influence of these parameters on permeability ratio may be in the order of slit width,
temperature, Young’s modulus, initial pore pressure, Poisson’s ratio, coal density, solid−solid interaction potential energy parameter, surface area, adsorption expansion modulus, and initial porosity. Similarly, the former two parameters have little impact on permeability ratio and can be ignored. The influence of Young’s modulus on permeability ratio is assumed to be small if it is larger than 3000 MPa. Figure 6 also indicates that the J
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels Table 3. Coal Seam Properties Ac, m2
tc, m
kCH4(0), mD
kCO2(0), mD
ϕ(0), no unit
T, K
pinj, MPa
ppro, MPa
ρcoa, kg/m3
ρwater, kg/m3
Swater, no unit
SCH4, no unit
647 497
9
3.65
0.91
0.001
318.15
12.5
0.275
1434
990
0.592
0.408
desorption and displacement instead of the extend Langmuir model, a rigorous coupled adsorption−strain−permeability model for permeability prediction instead of the Verma permeability model,57 considering the interactions among these three processes. The ECBM process was then resimulated with the modified EOS7C-ECBM module. After 30, 60, 90, 180, 360, and 1800 days of injection, CH4 and CO2 mole fraction distributions in the coal seam were also shown in Figure 8. Taking into consideration the adsorption difference between CH4 and CO2, and the induced strain and permeability change, only 24% of the CH4 is displaced in the first 90 days, and it takes about 1800 days to displace 90% or more. This indicates that the injectivity decreases significantly with continued CO 2 injection. This phenomenon was interpreted to matrix swelling caused by the adsorption differences between CH4 and CO2. Although the matrix swell increment is usually within 6% or less, the narrow cleats with width at the micron order are easy to narrow down or even close, thus reducing the permeability near the injection well significantly and impacting the injection efficiency. This suggests that a key challenge to the success of CO2-ECBM may be the optimal management of coal swelling with CO2 injection.
permeability of both components decreases monotonously with pressure, of which CO2 permeability evolution is much more obvious. This, in turn, suggests that although a coal seam may start out with a high permeability for CO2, the permeability may be significantly reduced due to the matrix swelling caused by CH4 displacement with CO2.
4. DISCUSSION The Transport of Unsaturated Groundwater and Heat Simulator (TOUGH2) has multidimensional numerical models for simulating the coupled transport of water, vapor, noncondensible gas, and heat in porous and fractured media. EOS7C-ECBM, an equation-of-state module for the TOUGH2 program, is developed for simulating nitrogen (N2) or CO2 ECBM process.46 A typical CO2-ECBM case with an inverted five-spot pattern47 was then selected to test its performance. In this case, the coal seam is assumed homogeneous and isotropic. No heat transfer exists between the injected gas and coal seam, and the system remains isothermal. The injection well has a constant bottom hole flowing pressure of 12.5 MPa, while the bottom hole flowing pressure of producing well is constant at 0.275 MPa. Because the entire seepage field remains symmetrical, only a quarter is selected and divided into 11 × 11 × 1 grids, as illustrated in Figure 7. The properties of coal seam were summarized in Table 3, and coal properties were summarized in Table 4.
5. CONCLUSIONS In this paper, a rigorous coupled adsorption-strain-permeability model was developed to quantify the coal deformation and permeability change caused by CH4 displacement with CO2 and to reveal their transportation mechanisms in deformed coalbed. The following conclusions and recommendations can be suggested based on the results of this study. (1) With coal deformation due to matrix shrinkage calculated with the simplified local density adsorption theory and permeability evolution calculated with a theoretical strain model, these processes were rigorous coupled. The coupled model can simultaneously quantify gas adsorption and desorption and displacement, coal deformation, and permeability evolution during ECBM recovery with only six parameters. (2) The coupled model can predict both CH4 and CO2 adsorption and the induced coal deformation fairly accurately at a pressure up to 20 MPa, and the average relative errors between the measured and predicted results are within 9.76% and 9.14%, respectively. While solid− solid interaction potential energy parameter and surface area have a great influence on gas adsorption and desorption and the associated coal deformation and permeability evolution, coal density and the adsorption expansion modulus also contribute a lot to coal deformation and permeability evolution, and initial porosity has a significant effect on permeability evolution. (3) The adsorption capacity of CO2 is 2−5 times as large as that of CH4, and the volumetric strain induced by CO2 adsorption is 2−8 times as large as that caused by CH4 adsorption. While the stronger adsorption capacity of CO2 on coal offers an option for CO2-ECBM, this technology is yet to be successful due to matrix swelling induced by adsorption difference between CH4 and CO2. A key
Table 4. Coal Properties W, nm εss/kB, K 2.63
16.7
ACH4, m2/g
ACO2, m2/g
E, MPa
v, no unit
Kss, MPa
46.4
70.2
3450
0.37
1295
With the help of the EOC7C-ECBM module, CH4 and CO2 distributions in the coal seam after 30, 60, and 90 days of CO2 injection were shown in Figure 8. It can be observed that 90% of methane or more was displaced and produced within 90 days. The result is consistent with those obtained by the other coalbed methane reservoir simulators,47 also illustrated in Figure 8. This indicates that TOUGH2 EOC7C-ECBM has a comparable performance with GEM, ECLIPSE, COMET 2, and SIMED II. However, the results are not consistent with the field test48−53 and may be too optimistic. Injectivity reduction with continued CO2 injection was found common in the pilot tests, including the Allison unit CO2-ECBM pilot in the San Juan Basin,48 the Tanquary well project in the Illinois Basin,49 the RECOPOL project in the upper Silesian basin of Poland,50 the Yubari project in the Ishikari Basin of Japan,51 the ARC ECBM project in the Fenn Big Valley site of Canada,52 and the ECBM micropilot test in the Quinshi basin of China.53 In general, this injectivity reduction has been widely recognized as a result of coal swelling and permeability reduction; however, current simulators fail to simultaneously quantify the gas adsorption and desorption, coal deformation, and permeability change, and coal swelling due to CH4 displacement by CO2 is ignored.54−56 The proposed coupled model was then integrated into the EOC7C-ECBM module to overcome current problems during ECBM simulation. Modifications have been made to include the SLD adsorption theory for CH4/CO2 mixture adsorption and K
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 8. continued
L
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 8. CO2 mole fraction distributions predicted.
■
(9) Hasanzadeh, M.; Alavi, F.; Feyzi, F.; Dehghani, M. R. Simplified local density model for adsorption of pure gases on activated carbon using Sutherland and Kihara potentials. Microporous Mesoporous Mater. 2010, 136 (1−3), 1−9. (10) Fitzgerald, J. E.; Sudibandriyo, M.; Pan, Z. J.; Robinson, R. L.; Gasem, K. A. M. Modeling the adsorption of pure gases on coals with the SLD model. Carbon 2003, 41 (12), 2203−2216. (11) Fitzgerald, J. E.; Robinson, R. L.; Gasem, K. A. M. Modeling highpressure adsorption of gas mixtures on activated carbon and coal using a simplified local-density model. Langmuir 2006, 22 (23), 9610−9618. (12) Zeng, Q. S.; Wang, Z. M.; McPherson, B. J.; McLennan, J. D. Theoretical approach to model gas adsorption/desorption and the induced coal deformation and permeability change. Energy Fuels 2017, 31 (8), 7982−7994. (13) Zeng, Q. S.; Wang, Z. M.; McPherson, B. J.; McLennan, J. D. Modeling Competitive Adsorption between Methane and Water on Coals. Energy Fuels 2017, 31 (10), 10775−10786. (14) Seidle, J. Fundamentals of coalbed methane reservoir engineering; PennWell Corp: Tulsa, OK, 2011. (15) Zeng, Q. S.; Wang, Z. M. A New Cleat Volume Compressibility Determination Method and Corresponding Modification to Coal Permeability Model. Transp. Porous Media 2017, 119 (3), 689−706. (16) Levine, J. R. Model study of the influence of matrix shrinkage on absolute permeability of coal bed reservoirs. Geol. Soc. Spec. Publ. 1996, 109, 197−212. (17) Megson, T. H. G. Structural and stress analysis; Elsevier Butterworth-Heinemann: Oxford, Britain, 2014. (18) Robertson, E. P. Improvements in measuring sorption-induced strain and permeability in coal. In Proceedings of the Society of Petroleum Engineers - SPE Eastern Regional/AAPG Eastern Section Joint Meeting; Society of Petroleum Engineers: Pittsburgh, PA, 2008. (19) Bangham, D. H.; Fakhoury, N. J. The translation motion of molecules in the adsorbed phase on solids. J. Chem. Soc. 1931, 0, 1324− 1333. (20) Shi, J. Q.; Durucan, S. Drawdown induced changes in permeability of coalbeds: A new interpretation of the reservoir response to primary recovery. Transp. Porous Media 2004, 56 (1), 1−16. (21) Shi, J. Q.; Durucan, S. A model for changes in coalbed permeability during primary and enhanced methane recovery. SPE Reserv. Eval. Eng. 2005, 8 (4), 291−299. (22) Shi, J. Q.; Durucan, S. Exponential growth in San Juan Basin Fruitland coalbed permeability with reservoir drawdown: Model match and new insights. SPE Reserv. Eval. Eng. 2010, 13 (6), 914−925.
challenge to the success of CO2-ECBM is the optimal management of coal swelling with CO2 injection.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: +86-108-973-4958. ORCID
Zhiming Wang: 0000-0002-9301-1942 Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS Financial support from the Science Foundation of China University of Petroleum, Beijing (no. 2462017YJRC058), National Science and Technology Major Project of China (no. 2016ZX05044005-001), and High School Subject Innovation Engineering Plan of China (111 Project B12033) is gratefully acknowledged.
■
REFERENCES
(1) Advanced Resources International Inc. Enhanced coalbed methane recovery: Worldwide application and CO2 sequestration potential; International Energy Agency: Paris, France, 1999. (2) Godec, M.; Koperna, G.; Gale, J. CO2-ECBM: A review of its status and global potential. Energy Procedia 2014, 63 (3−4), 5858−5869. (3) Reeves, S. An overview of CO2-ECBM and sequestration in coal seams. AAPG Studies in Geology 2009, 17−32. (4) Sloss, D. L. L. Potential for enhanced coalbed methane recovery; International Energy Agency: Paris, France, 2015. (5) Reeves, S.; Taillefert, A.; Pekot, L.; Clarkson, C. The Allison Unit CO2 - ECBM pilot: A reservoir modeling study; U.S. Department of Energy: Washington, DC, 2004. (6) Li, X. C.; Fang, Z. M. Current status and technical challenges of CO2 storage in coal seams and enhanced coalbed methane recovery: An overview. Int. J. Coal Sci. Technol. 2014, 1 (1), 93−102. (7) Rangarajan, B.; Lira, C. T.; Subramanian, R. Simplified local density model for adsorption over large pressure ranges. AIChE J. 1995, 41 (4), 838−845. (8) Valderrama, J. O. A generalized Patel-Teja equation of state for polar and non-polar fluids and their mixtures. J. Chem. Eng. Jpn. 1990, 23 (1), 87−91. M
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels (23) Shi, J. Q.; Durucan, S. Modelling laboratory horizontal stress and coal permeability data using S&D permeability model. Int. J. Coal Geol. 2014, 131 (1), 172−176. (24) Cui, X.; Bustin, R. M.; Chikatamarla, L. Adsorption-induced coal swelling and stress: Implications for methane production and acid gas sequestration into coal seams. J. Geophys. Res. 2007, 112 (B10202), 1− 16. (25) Bustin, R. M.; Cui, X. J.; Chikatamarla, L. Impacts of volumetric strain on CO2 sequestration in coals and enhanced CH4 recovery. AAPG Bull. 2008, 92 (1), 15−29. (26) Palmer, I.; Mansoori, J. How permeability depends on stress and pore pressure in coalbeds: A new model. In Proceedings of the SPE Annual Technical Conference and Exhibition; Society of Petroleum Engineers: Denver, CO, 1996. (27) Palmer, I.; Mansoori, J. How permeability depends on stress and pore pressure in coalbeds: A new model. SPE Reserv. Eng. 1998, 1 (6), 539−543. (28) Palmer, I. Permeability changes in coal: Analytical modeling. Int. J. Coal Geol. 2009, 77 (1−2), 119−126. (29) National Institute of Standards and Technology. Thermophysical properties of fluid systems.; http://webbook.nist.gov/chemistry/fluid/. (30) Ottiger, S.; Pini, R.; Storti, G.; Mazzotti, M. Competitive adsorption equilibria of CO2 and CH4 on a dry coal. Adsorption 2008, 14 (4), 539−556. (31) Harpalani, S.; Mitra, A. Impact of CO2 injection on flow behavior of coalbed methane reservoirs. Transp. Porous Media 2010, 82 (1), 141− 156. (32) Pan, Z. J.; Connell, L. D. Modelling of anisotropic coal swelling and its impact on permeability behaviour for primary and enhanced coalbed methane recovery. Int. J. Coal Geol. 2011, 85 (3−4), 257−267. (33) Xu, H.; Tang, D. Z.; Tang, S. H.; Zhang, W. Z.; Meng, Y. J.; Gao, L. J.; Xie, S. Z.; Zhao, J. L. Geologic and hydrological controls on coal reservoir water production in marine coal-bearing strata: A case study of the Carboniferous Taiyuan Formation in the Liulin Area, Eastern Ordos Basin, China. Mar. Pet. Geol. 2015, 59, 517−526. (34) Pashin, J. C.; McIntyre, M. R. Temperature-pressure conditions in coalbed methane reservoirs of the Black Warrior basin: Implications for carbon sequestration and enhanced coalbed methane recovery. Int. J. Coal Geol. 2003, 54 (3−4), 167−183. (35) Gray, I. Reservoir engineering in coal seams: Part 1-the physical process of gas storage and movement in coal seams. SPE Reservoir Eng. 1987, 2 (1), 28−34. (36) Xie, K. C. Structure and reactivity of coal; Springer-Verlag Berlin Heidelberg: New York, NY, 2015. (37) Jones, A. H.; Ahmed, U.; Bush, D. D.; Holland, M. T.; Kelkar, S. M.; Rakop, K. C.; Bowman, K. C.; Bell, G. J. Methane production characteristics for a deeply buried coalbed reservoir in the San Juan basin. In Proceedings of the SPE Unconventional Gas Recovery Symposium; Society of Petroleum Engineers: Pittsburgh, PA, 1984. (38) Bell, G. J.; Seccombe, J.; Rakop, K. C.; Jones, A. H. Laboratory characterization of deeply buried coal seams in the western U.S. In Proceedings of the SPE Annual Technical Conference and Exhibition; Society of Petroleum Engineers: Las Vegas, NV, 1985. (39) Gu, F.; Chalaturnyk, J. Analysis of coalbed methane production by reservoir and geomechanical coupling simulation. J. Can. Petrol. Technol. 2005, 44 (10), 33−42. (40) Gentzis, T.; Deisman, N.; Chalaturnyk, R. J. Geomechanical properties and permeability of coals from the Foothills and Mountain regions of western Canada. Int. J. Coal Geol. 2007, 69 (3), 153−164. (41) Mohammad, S. A. Adsorption modeling of coalbed gases and the effects of water on their adsorption behavior. Ph.D. Thesis, Oklahoma State University, Stillwater, OK, 2009. (42) Liu, S. M.; Harpalani, S. Permeability prediction of coalbed methane reservoirs during primary depletion. Int. J. Coal Geol. 2013, 113, 1−10. (43) Mohammad, S. A.; Sudibandriyo, M.; Fitzgerald, J. E.; Liang, X.; Robinson, R. L.; Gasem, K. A. M. Measurements and modeling of excess adsorption of pure and mixed gases on wet coals. Energy Fuels 2012, 26 (5), 2899−2910.
(44) Mohammad, S. A.; Arumugam, A.; Robinson, R. L.; Gasem, K. A. M. High-pressure adsorption of pure gases on coals and activated carbon: Measurements and modeling. Energy Fuels 2012, 26 (1), 536− 548. (45) Liu, S. M.; Harpalani, S. A new theoretical approach to model sorption-induced coal shrinkage or swelling. AAPG Bull. 2013, 97 (7), 1033−1049. (46) Stephen, W. W. Modification of TOUGH2 for enhanced coal bed methane simulations; Sandia National Laboratories: Washington, DC, 2003. (47) Law, D. H. S.; Van der Meer, L. G. H.; Gunter, M. D. Numerical Simulator Comparison study for enhanced coalbed methane recovery processes, part I: Pure carbon dioxide injection. In Proceedings of the SPE Gas Technology Symposium; Society of Petroleum Engineers: Calgary, Alberta, 2002. (48) Reeves, S. R.; Oudinot, A. The Allison unit CO2-ECBM pilot - A reservoir and economic analysis. In Proceedings of the 2005 International Coalbed Methane Symposium; University of Alabama: Tuscaloosa, AL, 2005. (49) Finley, R.; Moulton, S. Sequestration and enhanced coal bed methane: Tanquary farms test site, Wabash County, Illinois; U.S. Department of Energy: Washington, DC, 2012. (50) van Bergen, F.; Pagnier, H.; Krzystolik, P. Field experiment of enhanced coalbed methane-CO2 in the upper Silesian basin of Poland. Environ. Geosci. 2006, 13 (3), 201−224. (51) Yamaguchi, S.; Ohga, K.; Fujioka, M.; Nako, M.; Muto, S. Field experiment of Japan CO2 geosequestration in Coal Seams Project (JCOP). In Proceedings of the 8th International Conference on Greenhouse Gas Control Technologies; GHGT: Trondheim, Norway, 2006. (52) Mavor, M. J.; Gunter, W. D.; Robinson, J. R. Alberta multiwell micro-pilot testing for CBM properties, enhanced methane recovery and CO2 storage potential. In Proceedings of the SPE Annual Technical Conference and Exhibition; Society of Petroleum Engineers: Houston, TX, 2004. (53) Wong, S.; Law, D.; Deng, X.; Robinson, J.; Kadatz, B.; Gunter, W. D.; Ye, J. P.; Feng, S. L.; Fan, Z. Q. Enhanced coalbed methane-micropilot test at south Qinshui, Shanxi, China. In Proceedings of the 8th International Conference on Greenhouse Gas Control Technologies; GHGT: Trondheim, Norway, 2006. (54) Wu, K.; Chen, Z. X.; Li, X. F.; Xu, J. Z.; Li, J.; Wang, K.; Wang, H.; Wang, S. H.; Dong, X. H. Flow behavior of gas confined in nanoporous shale at high pressure: Real gas effect. Fuel 2017, 205, 173−183. (55) Wu, K. L.; Chen, Z. X.; Li, X. F. Real gas transport through nanopores of varying cross-section type and shape in shale gas reservoirs. Chem. Eng. J. 2015, 281, 813−825. (56) Wu, K. L.; Chen, Z. X.; Li, X. F.; Guo, C. H.; Wei, M. Z. A model for multiple transport mechanisms through nanopores of shale gas reservoirs with real gas effect-adsorption-mechanic coupling. Int. J. Heat Mass Transfer 2016, 93, 408−426. (57) Verma, A.; Pruess, K. Thermohydrological conditions and silica redistribution near high-level nuclear wastes emplaced in saturated geological formations. J. Geophys. Res. 1988, 93 (B2), 1159−1173.
N
DOI: 10.1021/acs.energyfuels.7b02830 Energy Fuels XXXX, XXX, XXX−XXX
