Modeling and Simulation of Moisture Effect on Gas Storage and

Article pubs.acs.org/EF

Modeling and Simulation of Moisture Effect on Gas Storage and Transport in Coal Seams Dong Chen,†,‡ Zhejun Pan,*,‡ Jishan Liu,† and Luke D. Connell‡ †

School of Mechanical and Chemical Engineering, The University of Western Australia, WA 6009, Australia CSIRO Earth Science and Resource Engineering, Private Bag 10, Clayton South, VIC 3169, Australia

‡

ABSTRACT: It has been observed in a series of experiments that the presence of moisture in the coal matrix has profound influences on the gas storage and transport in coal seams by reducing the gas adsorption capacity of the coal, decreasing the gas effective diffusivity through the coal matrix, and varying the coal swelling strain. A striking piece of evidence of the loss of moisture content in field is the increasing dustiness during the ventilation in coal mining, and this may definitely affect the gas production. However, the combined effect of these processes on coalbed methane production has not been studied in previous works. Therefore, an initial reservoir simulation model has been constructed to investigate the magnitude and interplay of the moisture effect on coalbed methane production. To develop the aforementioned model, approximate relationships have been built to quantify the moisture effect on the gas adsorption capacity, the gas effective diffusivity and the coal swelling strain. These relationships have been validated by comparison with a selection of literature data. The results of the reservoir model show that the combined moisture effect can significantly affect the overall gas storage and transport behavior. For the reservoir simulation conducted in this work, the gas production is enhanced as a result of the moisture loss by the ventilation air in the underground coal mining. The magnitude of this effect is sufficient to warrant additional research and modeling studies on the effect of moisture on coalbed methane drainage and production.

1. INTRODUCTION Coal seams are naturally fractured rocks that consist of cleats and porous coal matrix. Water is normally associated with coal as inherent moisture in the coal matrix and free phase water in the cleat networks.1 Water/moisture has multiple effects on the overall gas storage and flow behavior in coal. First, the water in the coal cleats affects the gas flow through relative permeability effect.2 Second, the moisture in the coal matrix can significantly reduce gas adsorption capacity by blocking the coal pore structure and limiting the accessibility of adsorbing gas.3,4 Third, the moisture in the coal matrix also has significant impact on the gas diffusivity in the matrix, as well as the coal permeability in the cleat system.5 Although the effects of the matrix moisture on gas storage and transport in coal seams have been recognized in experiments, they are often ignored in the reservoir simulations, and thereby, the combined effect of matrix moisture on coalbed methane production is still not well understood. A reservoir simulation model with the consideration of moisture effect is important to investigate the combined effect of the matrix moisture on gas transport processes in coal seams. To construct such a reservoir simulation model, proper relationships to quantify the moisture effect on the gas adsorption capacity, the gas effective diffusivity, and the coal swelling strain are required. It has been well acknowledged that the coal moisture affects the gas adsorption capacity and several models have been proposed in literature to quantify this behavior. Ettinger6 introduced a linear relationship between the moisture content and the gas adsorption capacity. The linear model was further validated by Joubert et al.7 and Levy et al.8 with different moisture effect coefficients. However, Ozdemir and Schroeder9 stated that it was difficult to obtain a coal sample totally free of © 2012 American Chemical Society

moisture required by the Ettinger’s model. So, they modified the Ettinger’s equation and applied it to describe the moisture effect on the gas adsorption capacity for both high and low rank coals. Nevertheless, a nonlinear relationship was observed in the laboratory for some low-rank coals.5,10 Hence, Crosdale et al.10 utilized a power law equation to describe the moisture effect for their experimental measurements. The study of the moisture effect on gas effective diffusivity and coal permeability is rare in the literature. Pan et al.5 published experimental data of the moisture effect on the gas adsorption capacity and diffusivity. Their results show that the moisture in the coal matrix significantly reduces the gas diffusivity. They also measured the coal swelling strain in water vapor and the magnitude of the swelling is similar to that induced by gas adsorption. Moisture adsorption induced swelling has also been reported by Fry et al.,11 and the results are similar to those by Pan et al.2 Although there was no measurement of permeability change with respect to moisture content in the coal matrix, the effect of matrix moisture on coal permeability change can be expected as mixed: on one hand, coal swells when it adsorbs water; on the other hand, coal shrinks due to the reduction of gas adsorption capacity and the resulting reduction of gas adsorption induced swelling strain when the water is adsorbed. The magnitude of the moisture induced swelling strain is comparable to the gas adsorption induced swelling strain, and thus, the coal may either swell or shrink when the water is adsorbed.5 Received: September 20, 2011 Revised: January 21, 2012 Published: January 23, 2012 1695

dx.doi.org/10.1021/ef2014327 | Energy Fuels 2012, 26, 1695−1706

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close to 0.10 The adsorbed gas amount may reach infinite for dry coal using eq 2. This is problematic and thus limits its application. Hence, to represent the moisture effect on both high and low rank coals with one model, we propose an exponential decay equation, as expressed in eq 3:

There are a few pieces of evidence that moisture content changes in the field. For instance, the relative humidity may change during the coal mining.12 The variation of the relative humidity may dynamically change the moisture content in the coal. Another piece of evidence for the lowering of the matrix moisture content is increasing dustiness during coal mining.1 The matrix moisture content may also change during the CO2 sequestration in coal seams for enhanced coalbed methane production, because the wettability of coal may change from water wet to CO2 wet.13 Nevertheless, the quantitative dynamic moisture effect on gas storage and production is still not well studied. Especially, little has been done to incorporate moisture effect into existing simulation models. A possible reason may be the lack of the proper models that can be easily coupled into the existing numerical simulation models to quantitatively describe the moisture effects. In this paper, models are proposed to quantify the moisture effect on gas adsorption capacity, gas diffusivity in the coal matrix, and the coal swelling strain and permeability. With these models, the moisture effect is incorporated into the reservoir simulation model to investigate the gas transport process in coal seams under different moisture content levels. Furthermore, the effect of dynamically changing moisture content on the methane production is studied at field conditions.

Vw = Vd exp( −λm)

(0 ≤ m ≤ mc)

(3)

where Vw and Vd are the adsorbed amount on the wet and dry coals, respectively, m is the moisture content in weight percentage, mc is the equilibrium moisture content of the coal in weight percentage, and λ is the adsorption capacity decay coefficient, which can be determined from matching the experimental data. To validate the proposed exponential model, available experimental data from literature are used: (1) a high rank Permian coal from the Bowen Basin of Queensland;7 (2) a low rank coal from the Huntly Coalfield, New Zealand;10 and (3) a subbituminous Bulli seam coal from Sydney basin.5 These data cover a good range of coal ranks, and all the three models, as described by eqs 1−3, are applied to represent the experimental data. The methane adsorption at 5 MPa on the high rank Permian coal with respect to the moisture content is shown in Figure 1.

2. MODELING OF MOISTURE EFFECT ON GAS STORAGE AND TRANSPORT IN COAL The modeling of matrix moisture effect on gas adsorption, diffusivity, and permeability are described in this section. It should be noted that the effect of water in the coal cleat networks, the relative permeability effect, is not the topic of this work and thus not considered in this study. 2.1. Moisture Effect on Gas Adsorption. 2.1.1. New Model for Moisture Effect on Gas Adsorption Capacity. The first step to model gas adsorption on coal at different moisture contents is to evaluate the adsorption capacity with respect to moisture content. Ettinger6 proposed a linear relationship between the gas adsorption capacity and the moisture content, as expressed in eq 1: Vw 1 = Vd 1 + Am

Figure 1. Data match of moisture effect (at 5 MPa) on methane adsorption capacity of Permian coal from Bowen Basin at 30 °C (Levy et al.8) with exponential, linear, and power law models.

(1)

where Vw and Vd are the adsorbed amount of gas on the wet and dry coal, respectively, m is the moisture content in weight percentage, and A is moisture effect coefficient. The value of m is between 0 and equilibrium moisture content, which is coal dependent. There is no further reduction in gas adsorption capacity with moisture content above equilibrium moisture content.8 The linear model is valid for high rank coals, but it may not be applicable for some low rank coals. Crosdale et al.10 observed a nonlinear relationship between the moisture content and the gas adsorption capacity for a low rank coal from Huntly Coalfield in the North Island of New Zealand. A power law equation, as expressed in eq 2, was used to describe the experimental data.10 V = cmd

For this coal sample, all the three models can represent the experimental data at moisture content greater than 1% with reasonable accuracy. However, the power law model predicts the gas adsorption capacity poorly at moisture content less than 1%. All the model representations are shown in Figure 1 as well. The experimental adsorption data for the low rank Huntly Coalfield coal are shown in Figure 2. The modeling results, also plotted in Figure 2, show that the linear model is not able to represent the experimental data. The power law model can accurately represent the experimental data. However, as discussed earlier, it is limited in predicting the gas adsorption capacity at the dry coal condition. Nevertheless, the proposed exponential equation can reasonably represent the experimental data for the full range with slight underestimation at low moisture content region. The experimental data for the subbituminous Bulli seam coal are shown in Figure 3. Because the experimental data include measurement on dry coal, the power law equation cannot model the data with accuracy. Thus, only the linear and exponential models are applied to represent the experimental

(2)

where V is the adsorbed gas amount, m is the moisture content in weight percentage, and c and d are constants determined by fitting the experimental data. Equation 2 can accurately describe the experimental data except for those at moisture content 1696


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Figure 2. Data match of moisture effect on methane adsorption capacity of coal from Huntly Coalfield at 32 °C (Crosdale et al.10) with exponential, linear, and power law models.

Figure 3. Data match of moisture effect on methane adsorption capacity of coal from Bulli seam at 26 °C (Pan et al.5) with exponential and linear models.

Table 1. Average Relative Error for Gas Adsorption Capacity Modeling coal high rank Permian

8

subbituminous Bulli seam coal5

low rank coal from Huntly Coalfield10

models

5 MPa

1 MPa

8 MPa

0.6 MPa

1.1 MPa

2.06 MPa

4 MPa

linear power law exponential (this work)

3.2% 4.4% 2.7%

49.0% 6.0% 16.3%

29.9% 3.1% 14.8%

23.1%

10.4%

16.2%

8.4%

10.7%

8.6%

7.4%

6.6%

describes gas adsorption amounts at a fixed pressure with respect to different moisture contents. To apply this in reservoir simulation, an isotherm model incorporating both gas pressure and moisture content is required. In this work, the Langmuir isotherm model is extended to a binary function of both pressure and moisture content. The Langmuir isotherm model can be expressed as

data. Figure 3 shows that the exponential model is able to represent the experimental data more accurately than the linear model. The average relative error of the three models for matching the experimental data are calculated and listed in Table 1. The results show that the exponential model has lower average relative error than the linear model. Although the average relative error is the lowest for the Power law model for the low rank coal from Huntly Coalfield, the application of the Power law is limited near the dry coal condition. Hence, all the above modeling results demonstrate that, overall, the exponential model is able to describe the experimental data better than the linear and the power law models. 2.1.2. Extending the Langmuir Equation as a Binary Function of Pressure and Moisture Content. Equation 3

V=

VLp p + PL

(4)

where V is the gas adsorption amount, p is the pressure, VL is the Langmuir volume constant, and PL is the Langmuir pressure constant. 1697


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Figure 4. Matching isothermal (26 °C) methane adsorption data under different moisture content levels and pressures of coal from Bulli seam (Pan et al.5) with unary Langmuir equation.

Figure 5. Matching isothermal (26 °C) methane adsorption data under different moisture content levels and pressures of coal from Bulli seam (Pan et al.5) with binary Langmuir equation.

Figure 6. Matching isothermal (32 °C) methane adsorption data under different moisture content levels and pressures of coal from Huntly Coalfield (Crosdale et al.10) with binary Langmuir equation.

tightly bound “unfreezable” water through thermal drying at higher temperatures may alter the coal structure and then the adsorption capacity.9 Thus, a more reliable measurement can be achieved by using low temperature with a vacuum.5 The experimental data on the Bulli seam coal5 is used to validate the extended Langmuir isotherm model. As a comparison, eq 4 is first applied to each adsorption isotherm with independent Langmuir constants regressed, and the modeling results are shown in Figure 4. The modeling results

Combining eqs 3 and 4, the Langmuir isotherm model can be extended to Vw = Vd exp( −λm) = (0 ≤ m ≤ mc)

VLp exp( −λm) p + PL (5)

In eq 5, the Langmuir constants, VL and PL, are for the adsorption on dry coal. It is worth noting that removing the 1698


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Figure 7. Matching isothermal (22 °C) CO2 adsorption data under different moisture content levels and pressures of Illinois No. 6 coal (Ozdemir and Schroeder9) with binary Langmuir equation.

Figure 8. Data match of moisture effect on gas diffusivity in macropores and micropores of coal from Bulli seam (Pan et al.5) with linear model.

Equation 6 can be further extended for the multiphase diffusion in porous media as

using eq 5 are shown in Figure 5. It can be seen from Figure 5 that the modeling results using eq 5 are comparable to those shown in Figure 4, but they require fewer parameters. To further validate the developed model, experimental data of methane adsorption at 32 °C on a coal from Huntly Coalfield10 and CO2 adsorption at 22 °C on an Illinois No. 6 coal9 are also used. The modeling results for the Huntly and Illinois coals are shown in Figures 6 and 7, respectively. In both measurements, no adsorption on dry coal is available. So, the Langmuir constants, VL and PL, for the dry coal and the adsorption capacity decay coefficient, λ, are obtained via fitting all the experimental data simultaneously. From Figures 6 and 7, it can be seen that eq 5 is able to describe all the data accurately. 2.2. Moisture Effect on Gas Diffusivity. The gas diffusion can be represented by either the unipore or bidisperse model based on the type of coal.14,15 Effective diffusion coefficient is the key parameter in either the unipore model or the bidisperse model, and it is used instead of the diffusion coefficient to describe the diffusivity in porous media.16 For the fluid diffusion in porous media, the effective diffusion coefficient can be expressed as17,18 De =

ϕD δ τ

De, i =

ϕDi δSi τ

(7)

where De,i, Di, and Si are the effective diffusion coefficient, the diffusion coefficient, and the saturation of phase i (water or gas), respectively. The diffusion coefficient (D) is constant for the same type of fluid under isothermal condition. The constrictivity (δ) and the tortuosity (τ) can be assumed as constants for the same coal sample. Therefore, the reduction of the effective gas diffusivity due to the moisture effect can be attributed to two factors: (1) the porosity (ϕ) change due to the moisture effect and (2) the decrease of the gas saturation (Sg). Because the porosity change is negligible, the diffusivity decrease is mainly caused by the gas saturation change. The gas saturation in the coal matrix, Sg, can be calculated as Sg = 1 − S w V =1− w Vv m w ms =1− ρw Vt ϕms ms =1− m ρw Vt ϕ

(6)

where De is the effective diffusion coefficient, ϕ is the porosity, D is the diffusion coefficient, δ is the constrictivity, and τ is the tortuosity. 1699

(8)


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where mw is the mass of moisture in coal matrix, ms is the mass of the coal solid, ρw is the density of water, Vw is the volume of water, Vv is the matrix pore volume of coal, and Vt is the volume of the coal bulk. The relationship between the diffusivity ratio and the moisture content can be expressed by combining eqs 7 and 8: Deg Degdry

=

Sg Sgdry

=

Sg 1

=1−

ms m = 1 − αm ρw Vt ϕ

(0 ≤ m ≤ mc)

(9)

where Deg is the effective gas diffusion coefficient on the wet coal with moisture content of m, Degdry is the effective gas diffusion coefficient on the dry coal, Sgdry is the gas saturation on the dry coal and is equal to 100%, α is a decline coefficient, and mc is the equilibrium moisture content in weight percentage. Because the mass of the coal solid, the density of water, the volume, and the porosity of the coal are all constant, the decline coefficient, α, is constant. Equation 9 is applied to both the macropore and micropore diffusivity data for CH4 and CO2 by Pan et al.5 As presented in Figure 8, eq 9 is able to represent the experimental data. Furthermore, the results show that the diffusivity decline coefficient, α, for both gases and both macropore and micropore diffusivities are similar. The values of the decline coefficient are summarized in Table 2. However, it should be

Figure 9. Data match of moisture effect on swelling strain of coal from Bulli seam (Pan et al.5) with Langmuir type model.

Table 2. Summary of Diffusivity Decline Coefficient for Bulli Seam Coal5 modeling results diffusivity decline coefficient (α)

CH4 diffusivity in macropore

CO2 diffusivity in macropore

CH4 diffusivity in micropore

CO2 diffusivity in micropore

0.100

0.087

0.115

0.112

Figure 10. Data match of methane sorption induced swelling strain of dry coal from Bulli seam (Pan et al.5) with Langmuir type model.

example of matching coal swelling strain using eq 11 and the experimental data are also for a Bulli seam coal from Australia.21 The moisture in coal affects the gas adsorption capacity, which is described in eq 3, and it will, in turn, change the gas sorption induced coal swelling strain. Similar to eq 5, eq 11 can be written as eq 12, with the consideration of the moisture effect.

noted that more experimental measurements are required for a better understanding of the moisture effect on matrix diffusivity. 2.3. Moisture Effect on Coal Permeability. The effect of matrix moisture on permeability is through the gas and moisture sorption induced coal swelling. In this section, gas and moisture sorption induced coal swelling is modeled first and then incorporated in to the coal permeability model. Figure 9 shows that the moisture sorption induced swelling strain can be fit with the Langmuir type model as expressed in eq 10: ε m εm = Lm (0 ≤ m ≤ mc) m + mL (10)

εs =

εLp exp( −λm) p + Pε

(0 ≤ m ≤ mc )

(12)

The total coal swelling strain should include both the gas sorption-induced strain and the moisture induced strain. Combining eqs 10 and 12, the total coal swelling strain (εst) can be calculated by εst = εs + εm =

where εm is the moisture sorption induced swelling strain, εLm is the maximum moisture sorption induced swelling strain, and mL is the Langmuir strain constant for moisture sorption. It is usually considered that the coal swelling strain is proportional to the amount of gas adsorbed.19,20 The gas sorption induced swelling strain (εs) is often modeled by a Langmuir type equation, as expressed in eq 11. ε p εs = L p + Pε (11)

(0 ≤ m ≤ mc)

εLp ε m exp( −λm) + Lm p + Pε m + mL (13)

According to eq 13 and the parameters obtained from Figures 5, 9, and 10, the total coal swelling strain at 5 MPa gas pressure and different moisture content levels is presented in Figure 11. The results show that the moisture induced swelling strain increases as the moisture content increases, and at the same time, the gas sorption induced swelling strain decreases. For this coal sample, the total coal swelling strain increases significantly when a small amount of moisture uptake due to the significant increase of the moisture induced swelling strain. When the moisture content is greater than 5%, the total

where εL is the maximum gas sorption induced swelling strain and Pε is the Langmuir strain constant. Figure 10 shows an 1700


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Figure 11. Effect of moisture content on coal swelling strain at 5 MPa.

Figure 12. Effect of moisture effect on coal permeability change as a function of gas pressure.

swelling strain becomes almost unchanged, because the moisture induced swelling strain is comparable to the shrinkage strain due to the gas adsorption amount decrease. Although the modeling results suggest an overall strain increase for CH4 adsorption at 5 MPa on the Bulli seam coal with moisture content increase, this does not mean other gas and other coal will exhibit the same behavior. Thus, measurement of strain for the gas and coal of interest with respect to moisture content must be conducted. To include the moisture effect on the permeability, the Shi and Durucan model,22 one of the widely used permeability models for coal seams, is considered: σ − σ0 = −

EΔεs ν (p − p0 ) + 1−ν 3(1 − ν)

3. MATHEMATICAL RESERVOIR SIMULATION MODEL To investigate the moisture effect on the gas storage and transport in coal seams, reservoir simulations are performed. To focus our analyses on matrix moisture, it is assumed that the water in the coal cleats has been drained. Thus, the relative permeability effect is not considered. The models of the moisture effect developed in section 2 are coupled into the reservoir simulation model. The mass conservation equation for gas in the coal cleats is expressed as eq 16, and the gas diffusion in the coal matrix is described by a quasi-steady-state equation, as expressed in eq 17.23,24

(14)

∂ρgϕ

where σ is the effective horizontal stress, σ0 is the effective horizontal stress at the initial reservoir pressure, and εs is the volumetric swelling/shrinkage strain change. Permeability is related to stress by k f = k f0 exp( −3c f (σ − σ0))

∂t

⎛ k ⎞ − ∇⎜ρg ∇p⎟ = qd ⎝ μ ⎠

dV 1 = − [V − VE(p)] dt τ

(16)

(17)

where ρg is the gas density in the coal cleats, which is calculated by eq 18, according to the gas equation of state (EOS), t is the time, μg is the dynamic viscosity of gas, k is permeability and is calculated by eqs 14 and 15, V (m3/kg) is the average remaining gas content in the coal matrix, VE (m3/kg) is the gas content in equilibrium with cleat gas pressure calculated by eq 5, τ is a diffusion-time constant of the coal matrix given by eq 19,23 and qd is the gas mass transfer rate between the matrix blocks and cleats, given by eq 20.

(15)

where cf is the cleat volume compressibility with respect to change in the effective horizontal stress normal to the cleat. Equation 13 is used to account for the swelling strain in eq 14. It is worth noting that the pressure used in eq 13 is the equivalent equilibrium gas pressure for the gas adsorption in the coal matrix, while the pressure in eq 14 is the gas pressure in the coal cleats. They become the same when gas adsorption reaches equilibrium. It is assumed in this work that the gas adsorption in the matrix and gas in the cleats are in equilibrium to demonstrate the impact of moisture content on permeability change. Based on eqs 14 and 15, the permeability change with different pressures and moisture content levels are calculated and shown in Figure 12. The parameters used are obtained from the experiments.5,21 The results show that moisture can significantly change the coal permeability, not only by the magnitude but also by the shape of the permeability curves. The permeability of the dry coal decreases with the gas pressure increasing from 0 to about 4 MPa, where the coal swelling strain dominates the permeability change. Permeability rebounds with gas pressure increase (>4 MPa), indicating that the effective stress decrease dominates that permeability change. However, permeability reduction at the low pressure region is weakened due to the less gas sorption induced strain at the high moisture condition, as can be seen from Figure 12.

ρg =

Mg

p ZRT g

(18)

where Mg is the molar mass of the gas, Z is the compressibility factor of the gas, which is a function of pressure under isothermal condition, R is the universal gas constant, T is the temperature, and pg is the gas pressure in the coal cleats.

τ=

1 aD

(19)

where D is the diffusion coefficient of gas in the coal matrix and a is a shape factor discussed by Warren and Root.25 dV qd = − ρgaρc dt

(20)

where ρga is the gas density at standard conditions and ρc is the density of coal. 1701


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parameters, as listed in Table 3, are obtained from fitting the experimental data in section 2 or are reasonably assumed. The gas properties such as viscosity and density are obtained from the NIST Web site http://webbook.nist.gov/chemistry/fluid/. According to eq 18, the gas compressibility factor is calculated through the relation between the gas pressure and gas density, which is also available at the NIST Web site. 4.2. Simulation Results and Discussion. Scenario 1. (1) Moisture Effect on Gas Production. The gas production rate and the cumulative gas production under different moisture content levels are shown in Figures 14 and 15,

The equivalent equilibrium gas pressure in the coal matrix is calculated by

pm =

VP L VL − V

(21)

We used a commercial PDE solver, COMSOL Multiphysics, to solve those PDE equations.

4. SIMULATION OF MOISTURE EFFECT ON GAS PRODUCTION Two simulation scenarios are considered in the work: (1) comparison of the gas drainage performance under different moisture content levels with the moisture content considered as unchanged during the gas production and (2) the gas drainage behavior with moisture content changing with time. Scenario 1 is sensitivity analyses to investigate the impact of moisture on gas production. Scenario 2 is to investigate the gas production behavior when matrix moisture content changes over time, for instance, during gas drainage in underground coal mining. 4.1. Model Description. A 200 × 200 m area is considered with a 150 m horizontal gas drainage borehole in the middle, as shown in Figure 13. The mechanical, sorption, and permeability

Figure 14. Evolution of gas production rate under different equilibrium moisture content levels.

Figure 13. Geometry of gas drainage model.

Table 3. Parameters Used in Reservoir Simulation param

Figure 15. Cumulative gas production under different equilibrium moisture content levels.

value 3

Langmuir volume constant, VL (m /kg) Langmuir pressure constant, PL (MPa) Langmuir strain constant, Pε (MPa) Langmuir strain constant for moisture sorption, mL (%) maximum moisture sorption induced swelling strain, εLm (%) maximum gas sorption induced swelling strain, εL (%) Young’s modulus, E (MPa) Poisson’s ratio, ν coal cleats compressibility, cf (MPa−1) coal density, ρc (kg/m3) initial coal porosity, ϕ (%) initial coal cleats permeability, kf0 (m2) diffusion-time constant of coal matrix, τ (day) diffusivity decline constant, α temp., T (K) coal seam thickness, h (m)

0.025 1.59 7.6 3.5 2.2 2.5 791 0.418 0.05 1250 1 1e-14 9 0.1 299.15 1

respectively. The moisture content of 0, 1, 3, and 7% are considered. The results show that the gas production rate is highest for the dry coal and it decreases with the increase of moisture content. This is due to the permeability, and the diffusivity decreases with the increase of moisture content, as discussed in section 2. In addition, the cumulative gas production reduces with the increase of moisture content, because the initial gas in place in coal seams, mainly determined by the gas adsorption capacity, decreases with the increase of moisture content. (2). Sensitivity of Gas Adsorption Capacity Decay Coefficient. According to the results in section 2, the gas adsorption capacity decay coefficient (λ) is an important parameter. The value of λ is coal dependent: λ is 0.244 for the high rank Permian coal from the Bowen Basin of Queensland at 1702


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pressure of 5 MPa; λ is 0.145 for the Bulli seam coal from Sydney basin at pressures from 0.4 to 6 MPa; and λ is 0.084 for the low rank coal from the Huntly Coalfield in New Zealand at pressures from 1 to 8 MPa. These results indicate that the gas adsorption capacity reduction is greater for higher rank coal than lower rank coal for the same increment in moisture content. This may be because the low rank coal has greater capacity to uptake water (higher equilibrium moisture content) due to the increasing of the hydrophilic groups as the coal rank decreases.26,27 Thus, the gas adsorption capacity reduction for low rank coal is less sensitive than that for the high rank coal with the same amount of moisture change. The sensitivity analysis for the gas adsorption capacity decay coefficient is shown in Figures 16 and 17, with the moisture contents all at

value and artificially vary the diffusivity decline coefficient to analyze the sensitivity of this coefficient on gas production. Similar to the sensitivity study of the gas adsorption decay coefficient, we keep the moisture content level at 5% for all cases and only change the diffusivity decline coefficient. Figures 18 and 19 present the effect of diffusivity decline coefficient on

Figure 18. Effect of diffusivity decline coefficient (α) on evolution of gas production rate.

Figure 16. Effect of gas adsorption capacity decay coefficient (λ) on evolution of gas production rate.

Figure 19. Effect of diffusivity decline coefficient (α) on cumulative gas production rate.

gas production rate and cumulative gas production. The results show that the gas production is enhanced with low diffusivity decline coefficient as expected, because the diffusivity is greater under the low diffusivity decline coefficient. The impact of diffusivity decline coefficient is more evident at early production stages and becomes less evident at later stages. 4.2.2. Scenario 2. (1) Moisture Content as Function of Temperature and Relative Humidity. Moisture in the coal matrix is adsorbed to the coal; thus, it is directly related to partial water vapor pressure or relative humidity of the air. The relationship between relative humidity (RH) and equilibrium moisture content (m) for both the thermally dried and air-dried samples can be described by28

Figure 17. Effect of gas adsorption capacity decay coefficient (λ) on cumulative gas production rate.

5% for different coals. The results show that both the gas production rate and the cumulative gas production increase significantly with respect to the gas adsorption capacity decay coefficient, indicating that moisture content has a different impact on coals with different rank and adsorption behavior. (3). Sensitivity of Diffusivity Decline Coefficient. The value of the diffusivity decline coefficient (α) is only available for the Bulli seam coal, and it remains nearly constant (0.1) for both macro/micropores and CH4/CO2. Diffusivity decline coefficients may vary for different coals. However, because of the limited experimental data available, we take the 0.1 as the base

1 − RH = exp( − K mTmn)

(21)

where T is temperature in Kelvin and Km and n are material specific factors. (2). Moisture Content Model Validation. The experimental data of three different coal samples from Tavistock coal in South Africa,29 Huntly Coalfield coal in New Zealand,10 and 1703


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Bulli seam coal in Australia5 are used to validate eq 21. It is shown in Figure 20 that the equilibrium moisture content

Figure 21. Calculation of moisture content change of three different coal samples from Tavistock coal in South Africa (van der Merwe and Campbell29), Huntly Coalfield coal in New Zealand (Crosdale et al.10), and Bulli seam coal in Australia (Pan et al.5), with moisture content model as a function of relative humidity (Henderson28), which decreases from 99% to 73% based on field observations (Su et al.12).

Figure 20. Validation of moisture content model as a function of relative humidity (Henderson28) against experimental data of three different coal samples from Tavistock coal in South Africa (van der Merwe and Campbell29), Huntly Coalfield coal in New Zealand (Crosdale et al.10), and Bulli seam coal in Australia (Pan et al.5).

(4). Simulation of Dynamic Moisture Effect on Gas Production. To investigate the impact of the dynamic moisture effect on the gas production, several cases are studied on the basis of the simulation model and the parameters used in scenario 1: case 1, RH maintains at the initial value of 99%; case 2, RH is at 73%; case 3, RH decreases at a rate of 1% for every 10 days; and case 4, RH decreases at a rate of 1% for every 100 days. Figure 22 shows that the gas production rate for constant

increases with the relative humidity and eq 21 can reasonably represent the experimental data. The model parameters are listed in Table 4. Table 4. Parameters Used for Validating Moisture Content Model (eq 21) as a Function of Relative Humidity coals

T (K)

Km

n

Tavistock Huntly Coalfield Bulli seam

301.15 (28 °C) 305.15 (32 °C) 299.15 (26 °C)

8.71 0.25 3.48

2.25 2.03 2.28

(3). Effect of Relative Humidity on Moisture Content. The coal matrix moisture can be removed through ventilation air in underground coal mining by reducing the relative humidity. In addition, the carbon sequestration in coal seams may also change the moisture content by CO2 acting as drying medium. Su et al.12 measured the relative humidity of the ventilation air for four Australian coal mines, as listed in Table 5. According to Table 5. Relative Humidity of Ventilation Air (VA) Flows at Four Australian Coal Mines mine A: Bulli seam B: Central Queensland C: Central Bowen Basin D: Hunter Valley

Figure 22. Evolution of gas production rate with constant and variable relative humidity.

avg VA flow rate (m3/s) relative humidity (%) 250 200 385 210

RH cases decrease with time, which is consistent with the simulation results in scenario 1. However, the gas production rate in case 3 increases initially with the loss of matrix moisture, indicating combined moisture effect in the gas transport process. Then, the gas production rate decreases as the constant RH cases. This behavior is not obvious in case 4. However, the gas production rate enhanced compared with case 1 as a result of the combined moisture effect on gas diffusion and flow. Figure 23 shows that the gas production is underestimated or overestimated by using the initial RH value (99%) or the ultimate value (73%). A more realistic result can be obtained by using the variable RH. However, this requires the knowledge of how the relative humidity changes during the gas production.

100 85−100 74−84 73−100

their field observations, the maximum change of the relative humidity was from 100% to 73%. However, the relative humidity may be further reduced by the ventilation air flow, depending on the inflow ventilation air humidity. Based on the experimental data of the three types of coal listed in Table 4, the moisture content at two relative humidity levels (73% and 99%) are compared in Figure 21. The results show that the moisture content drops nearly 50% from relative humidity of 99% to 73% for all three coals, which may significantly affect the gas production. 1704


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AUTHOR INFORMATION

Corresponding Author

*Tel.: +61 3 9545 8394. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by CSC-UWA scholarship and CSIRO Earth Science and Resources Engineering top-up scholarship. Their support is gratefully appreciated. Special thanks to the anonymous reviewers for their valuable suggestions.

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Figure 23. Cumulative gas production with constant and variable relative humidity.

REFERENCES

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5. CONCLUSION The matrix moisture can significantly affect the gas storage and transport behavior in coal seams. In this study, matrix moisture effects on gas adsorption capacity, gas diffusivity, and coal swelling strain and permeability are modeled. Gas adsorption capacity shows a declining trend when gaining moisture. While previous models are only applicable with limitations, the proposed exponential decay model is able to describe the gas adsorption capacity reduction with respect to the matrix moisture for both high and low rank coals. Moreover, experimental results from literature show a strong dependence of gas diffusivity on moisture. The developed linear model is able to describe the diffusivity reduction with respect to moisture content. The modeling results shows that the diffusivity decline coefficient is similar for the CH4 and CO2 diffusivity on the Bulli seam coal, although more experiential measurements are required to validate this behavior. Furthermore, the extended coal swelling strain model shows that there are two competing effects: the moisture induced swelling strain increases with the moisture content increase and the gas sorption induced swelling strain decreases with the moisture content increase. Thus, the overall swelling strain will depend on the gas, moisture, and coal interactions, and measurement is required to quantify the swelling behavior for the particular coal interested. The extended coal swelling strain model is able to be coupled with the existing permeability models, and the permeability results show that moisture effect on permeability change is significant and thus critical to be included in the reservoir simulation models. All these models are then coupled into the reservoir simulation model to investigate the impact of moisture on gas production. The gas production rate and the cumulative gas production under different equilibrium moisture content levels are compared. The results show that the gas production significantly increases with the reduction of moisture content. This suggests that reducing the moisture in the coal matrix has important implications for gas transport in coal seams. The reservoir simulation results also show that changing moisture content may have significant impact on gas production predictions. Thus, incorporating moisture effect on the reservoir simulation will lead to more accurate gas production prediction when the moisture content change in the coal matrix is evident. 1705


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(27) Švábová, M.; Weishauptová, Z.; Přibyl, O. Fuel 2011, 90, 1892− 1899. (28) Henderson, S. M. Agric. Eng. 1952, 1, 29−32. (29) van der Merwe, D.; Campbell, Q. P. J. South. Afr. Inst. Min. Metall. 2002, 417−420.

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Modeling and Simulation of Moisture Effect on Gas Storage and

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