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Gas diffusion behavior of coal and its impact on production from coalbed methane reservoirs
International Journal of Coal Geology 86 (2011) 342–348
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International Journal of Coal Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j c o a l g e o
Gas diffusion behavior of coal and its impact on production from coalbed methane reservoirs Mallikarjun Pillalamarry, Satya Harpalani ⁎, Shimin Liu Department of Mining and Mineral Resources Engineering, Southern Illinois University, Carbondale, Illinois 62901-6603, United States
a r t i c l e
i n f o
Article history: Received 4 January 2011 Received in revised form 25 March 2011 Accepted 25 March 2011 Available online 31 March 2011 Keywords: Methane diffusion Fick's law Unipore model Sorption isotherms
a b s t r a c t This paper discusses the results of an experimental study carried out to study and evaluate the sorption and diffusion properties of methane in Illinois basin coals. As a first step, sorption results were modeled using the Langmuir isotherm model and the Langmuir Constants were estimated. Next, the diffusion coefficient, D, was estimated by modeling experimental data using the unipore diffusion theory and Fick's law of diffusion. The results clearly indicated a negative correlation between D and pressure for pressures below 3.5 MPa. The overall trend of the variation was found to be bi-modal, its value remaining constant at high pressures, followed by a sharp increase below this critical pressure. Finally, a comparison of the sorption and diffusion results revealed that D depended on the surface coverage, which exhibits a positive relationship with pressure. The trend of diffusion variation with pressure appeared to be in good agreement with the results reported in the past studies using the bi-disperse diffusion model. The practical implication of the results is that the movement of methane is eased significantly at low pressures. Given the low in situ pressure typically encountered in the Illinois basin, this is a positive finding. Finally, this behavior may be responsible, at least in part, for the increased gas production rates encountered in the San Juan basin after several years of production. © 2011 Elsevier B.V. All rights reserved.
1. Introduction and background Coalbed methane is as an abundant, low cost, energy fuel that has significant long-term potential for discovery and development. Methane production from virgin coal seams in the US, almost zero in 1980, increased to 91 Bcf (billion cubic feet) in 1989 and 2 Tcf (trillion cubic feet) in 2008, contributing almost 10% of the US natural gas production (US EIA, 2009). The estimated gas-in-place in the US coals has increased from 400 Tcf (Bell and Rakop, 1986) to more than 700 Tcf (USGS, 2000). Coal has unique characteristics, such as, pore structure, gas storage and flow mechanisms that require a different production approach than that employed in conventional gas reservoirs. First, the pore structure of coal is highly heterogeneous, with pore size varying from a few Angstroms to frequently over a micrometer in size (IUPAC, 1982). Second, coal is characterized as a dual porosity system (Warren and Root, 1963), where the primary porosity consists of micropores associated with the coal matrix and secondary porosity system of macropores. The micropores occur as a part of the coal matrix, providing extremely large internal surface area with a strong affinity to certain gasses, like methane, ethane and CO2. The coal matrix stores ~ 95% of the total gas available in adsorbed form (Gray, 1987). The
⁎ Corresponding author. Tel.: +1 618 453 7918; fax: +1 618 453 7455. E-mail address: [email protected] (S. Harpalani). 0166-5162/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2011.03.007
secondary porosity system, on the other hand, consists of a naturally occurring network of closely spaced fractures, surrounding the matrix blocks of coal, called the cleat system, and provides the flow paths for gas and water. The cleat spacing is fairly uniform, ranging from a fraction of an inch to several inches (Rogers, 1994). Typically, virgin coalbeds in the US are saturated with water, that is, cleats are filled with water and water pressure holds the methane in place. De-pressurization of the coalbed by pumping out water from the cleats results in release of adsorbed methane. Subsequently, the released gas moves to the depressurized zone. Commonly, gas transport in coal is considered to occur in two stages: gas flow within the coal matrix and flow in the cleat system. Flow through the cleat system is believed to be pressure-driven, and described using Darcy's law. Flow through the matrix is assumed to be concentration gradient-driven and is usually modeled using Fick's Second Law of Diffusion (Harpalani and Chen, 1997). The general process of gas transport in coal is schematically shown in Fig. 1. Although micropore diffusion is considered a single process, it is usually a combination of three types of diffusion: Knudsen (where molecule–wall collisions dominate), surface (transport through physically adsorbed layer) and bulk (molecule–molecule collisions dominate) (Shi and Durucan, 2003). When the mean free path of the gas molecules is greater than the molecular diameter, or when the pressure is very low, Knudsen diffusion takes place, and gas molecules flow from higher to lower gas concentration (Collins, 1991; Zhao, 1991). In this mechanism, the gas molecules collide more frequently
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Fig. 1. Gas transport mechanisms in CBM reservoirs (King, 1985).
with the walls of the flow paths than with other molecules (Thorstenson and Pollock, 1989). Broadly, the resistance to flow is not due to the intermolecular collisions, but rather due to gas molecules colliding with pore walls. Bulk diffusion, on the other hand, is the opposite of Knudsen diffusion, occurring at higher pressures (Collins, 1991), or where the pore diameter is larger than the mean free path of gas molecules. The resistance to diffusion comes primarily from collision between gas molecules. Finally, surface diffusion of gas occurs when adsorbed gas molecules move along the micropore surface like a liquid (Collins, 1991). At room temperature, surface diffusion is much smaller than the Knudsen diffusion and is typically ignored in CBM production. Overall, the micropore diffusion can be a complex parameter, which often includes more than one type of diffusion. A significant amount of work has been completed in the area of modeling diffusion coefficient (D) for methane and CO2 in coal (Busch et al., 2004; Charrière et al., 2010; Clarkson and Bustin, 1999b; Cui et al., 2004; Kumar, 2007; Mavor et al., 1990; Nandi and Walker, 1970; Saghafi et al., 2007; Shi and Durucan, 2003; Siemons et al., 2007). Clarkson and Bustin (1999b) showed that the kinetics of adsorption at low and high pressures depends on the nature of the gas, moisture content, and temperature. Furthermore, diffusion of CO2 in coal is higher than methane and this is attributed to the physico-chemical properties of the molecules, such as, size and polarity as well as gas interaction in coal. Cui et al. (2004) used the bi-disperse diffusion model to calculate the diffusion coefficient for coal and methane, carbon dioxide and nitrogen systems at varying gas pressures and found a negative correlation between diffusion coefficient and reservoir pressure. Similar studies were conducted by Busch et al. (2004), Kumar (2007), Saghafi et al. (2007) and Shi and Durucan (2003). Both unipore and bi-disperse pore methods were used successfully to model diffusion in coal and it was concluded that both models can be used effectively for modeling of methane diffusion in coal. This paper describes a study carried out to characterize methane diffusion properties of coals in the Illinois basin. Since the primary objective of the study was to establish the variation trend in the diffusion coefficient with gas depletion, the unipore model was used rather than the bi-disperse model to avoid complex mathematical calculations. A comparison of the results obtained in this study, and the study carried out by Cui et al. (2004) using bi-disperse model, is presented at the end.
average radius of 0.0143 cm. Although crushing the coal changes the surface area for gas adsorption, the increase for 40–100 mesh coal size is between 0.1 and 0.3%, which is not believed to affect the accuracy of the experiment (Jones et al., 1988). Furthermore, the effect of grain size on diffusion was studied by Busch et al. (2004), Nandi and Walker (1970), and Siemons et al. (2003). The results showed that there is no effect of grain size when the particle radius is greater than 0.1 mm. In this study, the average particle radius was 0.143 mm. Moreover, the purpose of grinding the coal to this size is to reduce the diffusion time and to eliminate the effect of cleats on diffusion since, flow through the cleat system is believed to be pressure-driven. Prior to starting an experiment, approximately 90 g of pulverized sample was placed in environmental chamber for ~ 48 h at reservoir temperature (73 °F) and humid conditions (99%) for moisture equilibrium. Six grams of sample was used for moisture and ash analysis following the ASTM procedures (ASTM D3173-87, 1987; ASTM D3174-04, 2004), and the rest was used for the sorption/diffusion experiment. 2.2. Experimental setup and procedure The experimental setup consisted of a sample cylinder and a reference volume, both capable of withstanding high pressures. The sample cylinder was connected to the reference volume through a two-way valve and a micro-filter to prevent movement of coal particles with sudden changes in pressure. Since the diffusion/ sorption is extremely sensitive to temperature, the entire setup was placed in a constant-temperature bath, capable of maintaining the temperature to within 0.2 °C of the desired temperature. This not only ensured constant temperature throughout the experiment, but also allowed carrying out the experiment at in situ temperature. A schematic of the experimental setup is shown in Fig. 2. Precise
2. Experimental setup and procedure 2.1. Sample procurement and preparation Blocks of coal were obtained from two different seams in the Illinois basin. The most commonly used technique, particle method, was used to estimate the diffusion coefficient. This involves grinding the coal to eliminate the cracks and macropores completely, ensuring that the movement of gas is purely diffusive in nature. In order to prepare appropriate samples, coal was first broken into lumps approximately half-inch in size. These were then ground and sieved to obtain the desired sample size of 40–100 mesh (0.0425–0.0149 cm), giving an
Fig. 2. Schematic of experimental setup used for diffusion/sorption experiments.
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monitoring of pressure variation in the sample container is critical in order to calculate the amount of gas diffusing from within the coal matrix. Hence, a highly sensitive pressure transducer was connected to the reference volume which was subsequently connected to a data acquisition system (DAS), capable of recording pressure data at very short time intervals. Prior to starting a diffusion experiment, calibration of the setup was carried out. This involved determining the volume of the void space in the sample container using a non-adsorbing gas, like helium. Diffusion tests were performed for increasing and decreasing pressure steps and designated as adsorption/desorption steps. Initially, the pressure in the sample container was set to zero. The reference volume was subjected to a pressure of 1 MPa and allowed to equilibrate. The valve between the sample container and reference volume was then opened. The DAS was programmed to take readings at half-second intervals at this stage since methane adsorption rate is extremely high during the initial period. Acquiring data at this pace continued until the pressure variation became insignificant, in this case, 0.7 kPa/h. Readings were then taken at 50 s intervals and continued for approximately 20 h, after which, there was negligible change in the pressure and the sample was believed to have attained equilibrium. The coal sample was now believed to be fully saturated with methane at the equilibrium pressure. The procedure was repeated for a step-wise pressure increment of ~1 MPa, to a final pressure of ~7 MPa. Following this, the entire procedure was repeated for decreasing pressure steps of 1 MPa.
pore structure of coal, that have been successfully used in prior studies are the ‘unipore’ and ‘bi-disperse’ models (Busch et al., 2004; Nandi and Walker, 1970; Ruckenstein et al., 1971; Shi and Durucan, 2003). In this study, the data was modeled using the unipore approach, since most CBM/ECBM reservoir simulators are based on a single-step unipore diffusion model. As the name suggests, unipore model assumes that all the pores in the coal matrix are of the same size (Crank, 1975). The basis of this model is the Fick's Second Law of Diffusion for spherically symmetric flow. The model also assumes a constant gas concentration at the surface of the spheres throughout the sorption process. Although this method does not provide a perfect fit of the measured data, it is considered adequate as a first-order approximation for the purpose of making a first estimate of the sorption rates in a specific coal reservoir. For homogeneous spherical particles with a constant surface concentration and isothermal conditions, Fick's Second Law, is given as (Crank, 1975):
3. Measurement technique
" # Vt 6 ∞ 1 Dn2 π2 t = 1− 2 ∑ 2 exp − V∞ π n=1 n r2p
3.1. Ad/de-sorption isotherm The pressure data recorded during each step of the experiment was used to establish the adsorption isotherm, a natural by-product of the diffusion experiment. The amount of gas adsorbed at a given pressure was calculated using the Gibbs isotherm principle. Gibbs adsorption isotherm calculation assumes constant void volume within the coal throughout the pressure steps. It neglects the volume occupied by the adsorbed gas at each pressure step when calculating the amount of “free” gas. The difference between Gibbs and absolute adsorption is significant at high pressures, and the relationship used to calculate the absolute volume is given as (Sudibandriyo et al., 2003): Vabs =
VGibbs ρgas ρads
ð1Þ
1
" # 2 2 Mt 6 ∞ 1 Dn π t = 1− 2 ∑ 2 exp − M∞ π n=1 n r2p
ð3Þ
where, Mt is the total mass of the diffusing gas that has desorbed in time t, M∞ is the total desorbed mass in infinite time, and D is the diffusion coefficient, and rp is diffusion path length. After a step change in the surface concentration, the relationship for desorbed gas can be expressed as (Clarkson and Bustin, 1999b): ð4Þ
where, Vt is the total volume of gas ad/de-sorbed in time t and V∞ is the total gas adsorbed or desorbed after infinite time. For short times (t b 600 s) and when the fraction of gas desorbed (Vt/V∞) is less than 0.5, the Eq. (4) can be approximated to: sffiffiffiffiffiffiffiffiffi Vt Dt =6 : V∞ πr2p
ð5Þ
Several researchers have used the unipore approach to fit their experimental sorption data (Clarkson and Bustin, 1999b; Mavor, et al., 1990; Smith and Williams, 1984). They concluded that the unipore diffusion model is more applicable at high pressure steps of the isotherm rather than all of the steps. 4. Results and discussion
where, Vabs and VGibbs are the absolute and Gibbs sorption respectively, and ρgas and ρads are gas densities in gaseous and adsorbed phases respectively. The phase density for adsorbed methane used to calculate the absolute adsorption was 0.421 g/cm3 (Sudibandriyo et al., 2003). The isotherm was established using the Langmuir isotherm model, given as: V=
PVL P + PL
ð2Þ
where, P is the equilibrium gas pressure, V is the volume of gas adsorbed, VL is the Langmuir Volume representing the maximum volume that can be sorbed at infinite pressure, and PL is the Langmuir Pressure at which the sorbed volume is half the Langmuir Volume. 3.2. Estimation of diffusion coefficient Various approaches have been used by past researchers to model kinetics of gas sorption on coal. Two diffusion models, based on the
4.1. Ad/de-sorption isotherms The experiments were performed on both samples at in situ temperature of 73 °F and pressures up to 9 MPa. Experimental isotherms for adsorption and desorption steps are shown for the two coal types in Fig. 3 (Ref: Table 1). The isotherm shows that desorption hysteresis is insignificant. Ideally, desorption isotherm for coal and methane should not deviate from the adsorption isotherm since the sorption process is purely physical in nature and is reversible (Ruthven, 1984). Laboratory based isotherms typically exhibit some hysteresis due to the fact that the moisture content of the sample varies somewhat between the two isotherms (Dutta et al., 2008; Harpalani et al., 2006). A part of the sample moisture is removed during desorption every time gas is bled out. Another reason for the hysteresis, pointed out by previous researchers, is that there may be a change in the properties of the adsorbate. When the adsorbent/ adsorbate system is in a metastable state, a decrease in pressure does not release the gas as readily (Busch et al., 2003).
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12
12
Sorption, ml/g
16
Sorption, ml/g
16
8 Sample1-Adsorption Sample1-Desorption Sample2-Adsorption Sample2-Desorption
4
0
8
1
2
3
4
5
6
7
Sample1-Experimental Data Sample1-Langmuir Isotherm Sample2-Experimental Data Sample2-Langmuir Isotherm
4
0 0
345
8
0
1
2
3
4
5
6
7
8
Pressure, MPa
Pressure, MPa Fig. 3. Experimental absolute ad/de-sorption isotherms for methane.
Fig. 4. Langmuir isotherm models for desorption data.
Since it is the desorption part of the experiment that truly replicates the CBM operations, only desorption data was modeled using the Langmuir isotherm. Langmuir isotherms for the two coal types are shown in Fig. 4. The Langmuir parameters obtained for the samples, along with proximate analysis results, of the two coal types are presented in Table 1. It is apparent that all isotherms are of Type 1, according to Brunauer's classification (Brunauer et al., 1940). The relative errors of deviation of Langmuir-predicted values were calculated to be 2.5%. These levels of error are acceptable (Dutta et al., 2008). Gas sorption capacity of coal is typically influenced by pressure and temperature, the actual moisture content, composition of the organic material, mineral content, coal rank and meceral composition (Crosdale et al., 1998; Hildenbrand et al., 2006; Krooss et al., 2002). It is evident from Fig. 4 that Sample 1 has a higher sorptive affinity for methane than Sample 2 although the depth from which these were retrieved was almost the same. The volatile matter and fixed carbon content are also fairly close. Hence, the slight difference in the results obtained for the two samples may very well be the result of other controlling factors, such as, ash content, volatile matter and meceral composition.
Law, and described by Eq. (4), was used to calculate the diffusion coefficient for each step. The results depicting the variation in the value of diffusion coefficient for adsorption and desorption steps with pressure for the samples are shown in Fig. 6. The overall trend exhibited by all the results is very similar. It is apparent from the figures that there is a negative correlation between diffusion coefficient and pressure below 3.5 MPa, both for increasing as well as decreasing pressure steps. This suggests that the ease with which methane moves in the coal matrix improves with pressure reduction, or with continued gas production in the reservoir. However, since desorption part of the experiment truly replicates a CBM operation, the diffusion variation trend analysis was carried out for this alone. This is shown in Fig. 7. The diffusion variation trend is consistent with other diffusion results that have been reported by Clarkson and Bustin (1999a, 1999b), Cui et al. (2004), Wei et al. (2007) who studied the diffusion/adsorption of methane at different pressures using the bi-disperse model. Cui et al. (2004) observed that both micropore and macropore diffusions decrease with increasing adsorption. Reduction in diffusion coefficient with increased adsorption may be attributed to two reasons: (1) the effect of coal matrix swelling on pore size because adsorption swelling may narrow some micropore entrances and increase the resistance to diffuse the gas molecule through (Cui et al., 2004); and (2) strong repulsive force between adsorbed molecules with increase in surface coverage (Chen and Yang, 1991). However, a few researchers have reported that pressure is not directly related to the rate of adsorption or desorption for coals, Nandi and Walker (1970) for pressures below 2 MPa, and Sevenster (1959) for pressures below 0.1 MPa. Moreover, the results of this study contrast the observation made by Nandi and Walker (1970) stating that the diffusion coefficient increases with average methane concentration at high surface coverage. Finally, Charrière et al. (2010) and Nandi and Walker (1970) observed a surface cover dependency of the diffusion coefficient for methane and CO2 on coals. Their results showed a positive correlation between the diffusion coefficient and surface coverage (sorbed volume). To test this conclusion, desorption isotherm was plotted along with the variation in the value of diffusion coefficient for one of the samples. This is shown in Fig. 8. There is clear indication that the two are almost mirror images of each other. The observed trend was similar for the second coal type tested. Moreover, it is also apparent
4.2. Estimation of diffusion coefficient Compared to measurements for sorption isotherm, where only the final equilibrium pressure is required, measurement of diffusion coefficient requires precise and continuous change in pressure in the sample container over time, especially during the initial period of desorption when the rate of diffusion is extremely fast. This was repeated for every pressure step, that is, every time pressure in the sample container was changed to ad/de-sorb the gas. Decrease/ increase in the gas pressure of the sample container was converted to the amount of gas ad/de-sorbed. The frequency of data collection was decreased as equilibrium approached. Also, for calculation of the diffusion coefficient, only the initial sorption period (Vt/V∞ ~ 0.5) was considered, when the gas sorbs at a relatively fast pace. The change in gas content was calculated for each time interval during a pressure step. The fraction of gas (Vt/V∞) desorbed over time for the desorption steps of Sample 2 is shown in Fig. 5. The model, derived from Fick's
Table 1 Langmuir constants for desorption isotherms. Sample
Depth (m)
Volatile matter (%)
Fixed carbon (%)
Ash (%)
Moisture (%)
Temperature (°F)
Desorption VL (ml/g)
PL (MPa)
Sample 1 Sample 2
154 145
35 37
48 46
9.3 13
2.3 1.1
73 73
16.5 15.4
1.84 2.7
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Diffusion Coeffcient, x10-10 cm2/sec
1
Fraction Sorbed
0.8 0.6 38.2E-10 cm2/sec 26.7E-10 ,, 12.5E-10 ,, 4.70E-10 ,, 3.10E-10 ,, 2.40E-10 ,, 2.10E-10 ,,
0.4 0.2 0
10
0
20
30
40
45 40
Sample1 Sample2
35 30 25 20 15 10
50
5 0
0
1
2
3
4
5
6
7
8
Pressure, MPa
Time, Hours
Fig. 7. Variation of diffusion coefficient for desorption data (gray band is a free-plot trend line to emphasize the general trend).
Fig. 5. Fraction of gas desorbed with time for Sample 2.
from Fig. 6 that the diffusion coefficient for adsorption steps is slightly higher than for desorption steps. A similar observation was reported by other researchers (Dutta et al., 2008; Harpalani et al., 2006) during the sorption process, where adsorption isotherm was slightly higher than the desorption isotherm. Hence, this corroborates the findings that both diffusion and surface coverage are related, and in this case, negatively related below 3.5 MPa. The overall diffusion versus pressure trend established suggests that the variation in the value of diffusion coefficient with pressure is bi-modal in nature. At high pressures, its value remains fairly constant. However, after a certain pressure, the value of diffusion coefficient starts to increase, the rate of increase being almost exponential, suggesting that substantial desorption is responsible for the increase in the value of diffusion coefficient. Alternatively, desorption is the result of a significant increase in the value of the diffusion coefficient. This finding can have a significant impact on projecting methane production from coals at low pressures, that is, after substantial depletion. The finding would also have a significant impact on our understanding of the release of methane from abandoned mines and release of methane in worked out and sealed coal mining gob operations. As a final exercise to evaluate the difference between using the unipore versus the bi-disperse theory when estimating diffusion coefficient in the laboratory, results obtained by Cui et al. (2004) were compared with those obtained in this study. Fig. 9 shows the two trends together. It is apparent that, for the purpose of establishing variation trends, the two theories give almost identical results.
4.3. Effect of varying diffusion coefficient on gas production A preliminary and basic simulation study, using the simulator package COMET3, was carried out to investigate the effect of varying diffusion coefficient on continued gas production for a period of 10 years. Since the permeability and diffusion coefficient influence the gas transport in coal, both parameters were considered as variables. The simulation results are shown in Fig. 10. The results show that, for a high permeability reservoir (25 md), increase in diffusion coefficient from 2.4 × 10− 10 cm2/s to 38.2 × 10− 10 cm2/s resulted in increased production. The value of D remained constant throughout the period simulated since the simulator is not capable of handling a variable D. It is apparent from Fig. 10 that the increase in gas production is not significant for a low permeability reservoir (14 md), suggesting that diffusion is not the controlling mechanism in gas production for low permeability reservoirs. Nevertheless, this is inconclusive since the simulator used in the modeling exercise is not very sensitive to diffusion coefficient. This may very well be due to the well accepted belief in the past that production of methane in CBM reservoirs is permeability controlled rather than diffusion controlled. Although this is believed no longer to be the case, most simulators have not been modified to reflect this change. The ideal simulation would be possible only if a variable value of D could be used, perhaps something that the developers of the various simulator packages need to consider.
50
60 50 40
40
12
Sample1Adsorption Step Sample1 Desorption Step Sample2 Adsorption Step Sample2 Desorption Step
Sorption, ml/g
Diffusion Coeffcient, x10-10 cm2/sec
16
30
Desorption Data Points Langmuir Isotherm Diffusion Coefficient Data Points
8
30 20
4
20
10
10 0
0 0
0 0
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
Diffusion Coeffcient, x10-10 cm2/sec
346
8
Pressure, MPa
Pressure, MPa Fig. 6. Variation in the diffusion coefficient with pressure.
Fig. 8. Desorption isotherm and variation in D with pressure for one sample (gray band is a free-plot trend line to emphasize the general trend).
Apparent Diffusivity x10-6, Sec-1
M. Pillalamarry et al. / International Journal of Coal Geology 86 (2011) 342–348
9 8
Bi-disperse Model Unipore Model
7 6 5 4 3 2 1 0
0
1
2
3
4
5
6
7
8
9
Pressure, MPa Fig. 9. Comparison of results using the unipore and bi-disperse models (re-constructed after Cui et al., 2004) (gray band is a free-plot trend line to emphasize the general trend).
5. Summary and conclusions Methane adsorption and diffusion characteristics of Illinois basin coals were established using the volumetric method. The Langmuir equation was used to model sorption data and unipore model to estimate the behavior of diffusion coefficient. Based on the work completed, the following conclusions are made: • The value of diffusion coefficient is not constant over the life of a CBM reservoir. There is a negative correlation between diffusion coefficient and pressure in the low pressure range. This finding has a significant practical implication. First, since the pressures encountered in Illinois coals are typically low, this can have a positive impact on methane production from coals in the basin. Second, current simulators incorporate the diffusion parameter using the ‘sorption time’, which is considered to be constant for the entire production period and this is simply not the case. Therefore, sorption time should be treated as a variable when simulating long/ short-term production. Modification of the simulators to incorporate this change should not be much of a challenge since permeability is already considered a dynamic parameter in several simulators. In fact, using the diffusion coefficient as a direct input parameter would make more sense rather than impacting its impact using sorption time. • The value of diffusion coefficient can be represented by a dual model, its value remaining constant at high pressures, and increasing continuously when accompanied by substantial desorption of gas. An important extrapolation of this finding to other basins, particularly the San Juan, which is considered the most
Production per Well, MSCFD
50
25 md Permeability, 2.40E-10 cm2/sec DC 25 md Permeability, 38.2E-10 cm2/sec DC 2 14 md Permeability, 2.40E-10 cm /sec DC 2 14 md Permeability, 38.2E-10 cm /sec DC
40 30 20 10 0
0
500
1000
1500
2000
2500
3000
3500
4000
Time, Days Fig. 10. Effect of varying diffusion coefficient (DC) and permeability on gas production.
347
prolific basin in the world, is that diffusion might be playing a significant role in later stages of the life of a CBM reservoir and might even explain the increased production rates typically observed in the basin during the later part of the reservoir's life. • The analysis of the adsorption and diffusion results revealed that the diffusion coefficient also depends on adsorption or surface coverage. These results support the observations made by Clarkson and Bustin (1999a, 1999b), Cui et al. (2004) who used bi-disperse methods to model the experimental data. Since adsorption is different for different gasses, variation in the value of diffusion coefficient should be measured as a function of gas-in-place composition. For the same reason, the value of D should be measured for coal–CO2 system as well. In a scenario where CO2 is injected in coalbeds to enhance the CBM production, or CO2 sequestration, there is counter-diffusion in the matrix, with CO2 diffusing in to, and methane diffusing out of, the matrix. An effort was initiated by Wei et al. (2007) to develop this theoretically but no studies have been reported to date to do so effectively, nor have there been studies to validate any theoretical models. • The pore-size distribution within coal varies with coal type, basin, rank, etc. and is highly heterogeneous (Clarkson and Bustin, 1999a). Hence, no model can perfectly fit the experimental data unless it considers all pores of different sizes that exist in coal, which may not be possible due to mathematical complications. Although unipore method used in this study does not provide a perfect fit of the measured data, the results showed that it may be adequate for making a first-estimate of the trend of this gas transport phenomenon in CBM reservoirs. Hence, the use of the unipore model of diffusion is definitely justified even if the bi-disperse model of diffusion represents the coal particle properties better. The unipore model is simpler and easy to use and gives very similar results for the variability of diffusivity as a function of reservoir pressure. • Based on the preliminary simulation study, gas production from low permeability reservoirs is not controlled by diffusion although this may be due to the simulator algorithm, which underplays the importance of diffusion. However, for high permeability reservoirs, application of varying diffusion characteristics can become a controlling factor in methane production. The authors do believe that the philosophy that methane production from coalbeds is permeability-controlled should be re-evaluated.
Acknowledgments This study was carried out with support, in part by grants made possible by the Illinois Department of Commerce and Economic Opportunity (DCEO) through the Office of Coal Development and the Illinois Clean Coal Institute (ICCI). The authors wish to thank these organizations for the financial support. References ASTM D3173-87, 1987. Standard Test Method for Moisture in the Analysis Sample of Coal and Coke. ASTM International. ASTM D3174-04, 2004. Standard Test Method for Ash in the Analysis Sample of Coal and Coke from Coal. ASTM International. Bell, G.J., Rakop, K.C., 1986. Hysteresis of methane/coal sorption isotherms. SPE 15454. SPE 61st Annual Technical Conference. New Orleans, LA. Brunauer, S., Deming, L.S., Deming, W.E., Teller, E., 1940. On a theory of van der walls adsorption of gases. J. Chem. Soc. 62, 1723–1732. Busch, A., Gensterblum, Y., Krooss, B.M., 2003. Methane and CO2 sorption and desorption measurements on dry Argonne premium coals: pure components and mixtures. Int. J. Coal. Geol. 55, 205–224. Busch, A., Gensterblum, Y., Krooss, B.M., Littke, R., 2004. Methane and carbon dioxide adsorption–diffusion experiments on coal: upscaling and modelling. Int. J. Coal. Geol. 60, 151–168. Charrière, D., Pokryszk, Z., Behra, P., 2010. Effect of pressure and temperature on diffusion of CO2 and CH4 into coal from the Lorraine basin (France). Int. J. Coal. Geol. 81, 373–380.
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Chen, Y.D., Yang, R.T., 1991. Concentration dependence of surface diffusion and zeolitic diffusion. AIChE J. 37, 1579–1582. Clarkson, C.R., Bustin, R.M., 1999a. The effect of pore structure and gas pressure upon the transport properties of coal: a laboratory and modeling study 1. Isotherms and pore volume distributions. Fuel 78, 1333–1344. Clarkson, C.R., Bustin, R.M., 1999b. The effect of pore structure and gas pressure upon the transport properties of coal: a laboratory and modeling study 2. Adsorption rate modeling. Fuel 78, 1345–1362. Collins, R.E., 1991. New theory for gas adsorption and transport in coal. Int. Coalbed Methane Symp. Univ. of Alabama, Tuscaloosa, pp. 425–431. Crank, J., 1975. Mathematics of Diffusion. Oxford University Press, London. Crosdale, P.J., Beamish, B.B., Valix, M., 1998. Coalbed methane sorption related to coal composition. Int. J. Coal. Geol. 35, 147–158. Cui, X., Bustin, R.M., Dipple, G., 2004. Selective transport of CO2, CH4 and N2 in coals: insights from modeling of experimental gas adsorption data. Fuel 83, 293–303. Dutta, P., Harpalani, S., Prusty, B., 2008. Modeling of CO2 sorption on coal. Fuel 87, 2023–2036. Gray, I., 1987. Reservoir engineering in coal seams: part 1. The physical process of gas storage and movement in coal seams. SPE Res. Eng. 2, 28–34. Harpalani, S., Chen, G., 1997. Influence of gas production induced volumetric strain on permeability of coal. Geotech. Geol. Eng. 15, 303–325. Harpalani, S., Prusty, B.K., Dutta, P., 2006. Methane/CO2 sorption modeling for coalbed methane production and CO2 sequestration. Energy Fuel 20, 1591–1599. Hildenbrand, A., Krooss, B.M., Busch, A., Gaschnitz, R., 2006. Evolution of methane sorption capacity of coal seams as a function of burial history — a case study from the Campine Basin, NE Belgium. Int. J. Coal. Geol. 66, 179–203. IUPAC, 1982. Appendix 2, part 1, colloid and surface chemistry. Pure Appl. Chem. 52, 2201. Jones, A.H., Bell, G., Schraufnagel, R., 1988. A review of the physical and mechanical properties of coal with implications for coal-bed methane well completion and production. In: Fassett, J.E. (Ed.), Geological and Coal-bed Methane Resources of the Northern San Juan Basin, Colorado and New Mexico. Rocky Mountain Association of Geologists Guide Book, Denver, pp. 169–181. King, G.R., 1985. Numerical Simulation of the Simultaneous Flow of Methane and Water through Dual Porosity Coal Seams during the Degasification Process. Ph.D. Dissertation, Pennsylvania State University. Krooss, B.M., van Bergen, F., Gensterblum, Y., Siemons, N., 2002. High-pressure methane and carbon dioxide adsorption on dry and moisture-equilibrated Pennsylvanian coals. Int. J. Coal. Geol. 51, 69–92.
Kumar, A., 2007. Methane Diffusion Characteristics of Illinois Coals. MS Thesis. Southern Illinois University, Carbondale. Mavor, M.J., Owen, L.B., Pratt, T.J., 1990. Measurement and evaluation of coal sorption isotherm data. SPE 20728. SPE 65th Annual Technical Conference and Exhibition, New Orleans, LA. Nandi, S.P., Walker, P.L., 1970. Activated diffusion of methane in coal. Fuel 49, 309–323. Rogers, R.E., 1994. Coalbed Methane: Principles and Practices. Prentice Hall Inc, New Jersey. Ruckenstein, E., Vaidyanathan, A.S., Youngquist, G.R., 1971. Sorption by solids with bidisperse pore structure. Chem. Eng. Sci. 26, 1305–1318. Ruthven, D.M., 1984. Principles of Adsorption and Adsorption Processes. John Wiley & Sons Inc. Saghafi, A., Faiz, M., Roberts, D., 2007. CO2 storage and gas diffusivity properties of coals from Sydney basin Australia. Int. J. Coal. Geol. 70, 240–254. Sevenster, P.G., 1959. Diffusion of gases from coal. Fuel 38, 403–418. Shi, J.Q., Durucan, S., 2003. A bidisperse pore diffusion model for methane displacement desorption in coal by CO2 injection. Fuel 82, 1219–1229. Siemons, N., Busch, A., Bruining, H., Krooss, B.M., Gensterblum, Y., 2003. Assessing the kinetics and capacity of gas adsorption in coals by a combined adsorption/diffusion method. SPE 84340. Annual Technical Conference and Exhibition, 5–8 October, Denver. Siemons, N., Wolf, K.H., Bruining, J., 2007. Interpretation of carbon dioxide diffusion behavior in coals. Int. J. Coal. Geol. 72, 315–324. Smith, D.M., Williams, F.L., 1984. Diffusional effects in the recovery of methane from coalbeds. SPE 24, 529–535. Sudibandriyo, M., Fitzgerald, J.E., Pan, Z., Robinson Jr., R.L., Gasem, K.A.M., 2003. Adsorption of methane, nitrogen, carbon dioxide, and their binary mixtures on dry activated carbon at 318.2 K and pressures up to 13.6 MPa. Langmuir 19, 5323–5331. Thorstenson, D.C., Pollock, D.W., 1989. Gas transport in unsaturated porous media: the adequacy of Fick's Law. Reviews Geophysics 27, 61–78. US EIA, 2009. Natural Gas Gross Withdrawals and Production Released on 10/29/2010. US Energy Information Administration. USGS, 2000. Coal-bed methane: potential and concerns. USGS Fact Sheet FS 123–00, October 2000. Warren, J.E., Root, P.J., 1963. The behavior of naturally fractured reservoirs. SPE 426, 245–255. Wei, X.R., et al., 2007. Numerical simulation of multi-component gas diffusion and flow in coals for CO2 enhanced coalbed methane recovery. Chem. Eng. Sci. 62, 4193–4203. Zhao, X., 1991. An Experimental Study of Methane Diffusion in Coal using Transient Approach. Ph. D. Dissertation. University of Arizona.
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International Journal of Coal Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j c o a l g e o
Gas diffusion behavior of coal and its impact on production from coalbed methane reservoirs Mallikarjun Pillalamarry, Satya Harpalani ⁎, Shimin Liu Department of Mining and Mineral Resources Engineering, Southern Illinois University, Carbondale, Illinois 62901-6603, United States
a r t i c l e
i n f o
Article history: Received 4 January 2011 Received in revised form 25 March 2011 Accepted 25 March 2011 Available online 31 March 2011 Keywords: Methane diffusion Fick's law Unipore model Sorption isotherms
a b s t r a c t This paper discusses the results of an experimental study carried out to study and evaluate the sorption and diffusion properties of methane in Illinois basin coals. As a first step, sorption results were modeled using the Langmuir isotherm model and the Langmuir Constants were estimated. Next, the diffusion coefficient, D, was estimated by modeling experimental data using the unipore diffusion theory and Fick's law of diffusion. The results clearly indicated a negative correlation between D and pressure for pressures below 3.5 MPa. The overall trend of the variation was found to be bi-modal, its value remaining constant at high pressures, followed by a sharp increase below this critical pressure. Finally, a comparison of the sorption and diffusion results revealed that D depended on the surface coverage, which exhibits a positive relationship with pressure. The trend of diffusion variation with pressure appeared to be in good agreement with the results reported in the past studies using the bi-disperse diffusion model. The practical implication of the results is that the movement of methane is eased significantly at low pressures. Given the low in situ pressure typically encountered in the Illinois basin, this is a positive finding. Finally, this behavior may be responsible, at least in part, for the increased gas production rates encountered in the San Juan basin after several years of production. © 2011 Elsevier B.V. All rights reserved.
1. Introduction and background Coalbed methane is as an abundant, low cost, energy fuel that has significant long-term potential for discovery and development. Methane production from virgin coal seams in the US, almost zero in 1980, increased to 91 Bcf (billion cubic feet) in 1989 and 2 Tcf (trillion cubic feet) in 2008, contributing almost 10% of the US natural gas production (US EIA, 2009). The estimated gas-in-place in the US coals has increased from 400 Tcf (Bell and Rakop, 1986) to more than 700 Tcf (USGS, 2000). Coal has unique characteristics, such as, pore structure, gas storage and flow mechanisms that require a different production approach than that employed in conventional gas reservoirs. First, the pore structure of coal is highly heterogeneous, with pore size varying from a few Angstroms to frequently over a micrometer in size (IUPAC, 1982). Second, coal is characterized as a dual porosity system (Warren and Root, 1963), where the primary porosity consists of micropores associated with the coal matrix and secondary porosity system of macropores. The micropores occur as a part of the coal matrix, providing extremely large internal surface area with a strong affinity to certain gasses, like methane, ethane and CO2. The coal matrix stores ~ 95% of the total gas available in adsorbed form (Gray, 1987). The
⁎ Corresponding author. Tel.: +1 618 453 7918; fax: +1 618 453 7455. E-mail address: [email protected] (S. Harpalani). 0166-5162/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2011.03.007
secondary porosity system, on the other hand, consists of a naturally occurring network of closely spaced fractures, surrounding the matrix blocks of coal, called the cleat system, and provides the flow paths for gas and water. The cleat spacing is fairly uniform, ranging from a fraction of an inch to several inches (Rogers, 1994). Typically, virgin coalbeds in the US are saturated with water, that is, cleats are filled with water and water pressure holds the methane in place. De-pressurization of the coalbed by pumping out water from the cleats results in release of adsorbed methane. Subsequently, the released gas moves to the depressurized zone. Commonly, gas transport in coal is considered to occur in two stages: gas flow within the coal matrix and flow in the cleat system. Flow through the cleat system is believed to be pressure-driven, and described using Darcy's law. Flow through the matrix is assumed to be concentration gradient-driven and is usually modeled using Fick's Second Law of Diffusion (Harpalani and Chen, 1997). The general process of gas transport in coal is schematically shown in Fig. 1. Although micropore diffusion is considered a single process, it is usually a combination of three types of diffusion: Knudsen (where molecule–wall collisions dominate), surface (transport through physically adsorbed layer) and bulk (molecule–molecule collisions dominate) (Shi and Durucan, 2003). When the mean free path of the gas molecules is greater than the molecular diameter, or when the pressure is very low, Knudsen diffusion takes place, and gas molecules flow from higher to lower gas concentration (Collins, 1991; Zhao, 1991). In this mechanism, the gas molecules collide more frequently
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343
Fig. 1. Gas transport mechanisms in CBM reservoirs (King, 1985).
with the walls of the flow paths than with other molecules (Thorstenson and Pollock, 1989). Broadly, the resistance to flow is not due to the intermolecular collisions, but rather due to gas molecules colliding with pore walls. Bulk diffusion, on the other hand, is the opposite of Knudsen diffusion, occurring at higher pressures (Collins, 1991), or where the pore diameter is larger than the mean free path of gas molecules. The resistance to diffusion comes primarily from collision between gas molecules. Finally, surface diffusion of gas occurs when adsorbed gas molecules move along the micropore surface like a liquid (Collins, 1991). At room temperature, surface diffusion is much smaller than the Knudsen diffusion and is typically ignored in CBM production. Overall, the micropore diffusion can be a complex parameter, which often includes more than one type of diffusion. A significant amount of work has been completed in the area of modeling diffusion coefficient (D) for methane and CO2 in coal (Busch et al., 2004; Charrière et al., 2010; Clarkson and Bustin, 1999b; Cui et al., 2004; Kumar, 2007; Mavor et al., 1990; Nandi and Walker, 1970; Saghafi et al., 2007; Shi and Durucan, 2003; Siemons et al., 2007). Clarkson and Bustin (1999b) showed that the kinetics of adsorption at low and high pressures depends on the nature of the gas, moisture content, and temperature. Furthermore, diffusion of CO2 in coal is higher than methane and this is attributed to the physico-chemical properties of the molecules, such as, size and polarity as well as gas interaction in coal. Cui et al. (2004) used the bi-disperse diffusion model to calculate the diffusion coefficient for coal and methane, carbon dioxide and nitrogen systems at varying gas pressures and found a negative correlation between diffusion coefficient and reservoir pressure. Similar studies were conducted by Busch et al. (2004), Kumar (2007), Saghafi et al. (2007) and Shi and Durucan (2003). Both unipore and bi-disperse pore methods were used successfully to model diffusion in coal and it was concluded that both models can be used effectively for modeling of methane diffusion in coal. This paper describes a study carried out to characterize methane diffusion properties of coals in the Illinois basin. Since the primary objective of the study was to establish the variation trend in the diffusion coefficient with gas depletion, the unipore model was used rather than the bi-disperse model to avoid complex mathematical calculations. A comparison of the results obtained in this study, and the study carried out by Cui et al. (2004) using bi-disperse model, is presented at the end.
average radius of 0.0143 cm. Although crushing the coal changes the surface area for gas adsorption, the increase for 40–100 mesh coal size is between 0.1 and 0.3%, which is not believed to affect the accuracy of the experiment (Jones et al., 1988). Furthermore, the effect of grain size on diffusion was studied by Busch et al. (2004), Nandi and Walker (1970), and Siemons et al. (2003). The results showed that there is no effect of grain size when the particle radius is greater than 0.1 mm. In this study, the average particle radius was 0.143 mm. Moreover, the purpose of grinding the coal to this size is to reduce the diffusion time and to eliminate the effect of cleats on diffusion since, flow through the cleat system is believed to be pressure-driven. Prior to starting an experiment, approximately 90 g of pulverized sample was placed in environmental chamber for ~ 48 h at reservoir temperature (73 °F) and humid conditions (99%) for moisture equilibrium. Six grams of sample was used for moisture and ash analysis following the ASTM procedures (ASTM D3173-87, 1987; ASTM D3174-04, 2004), and the rest was used for the sorption/diffusion experiment. 2.2. Experimental setup and procedure The experimental setup consisted of a sample cylinder and a reference volume, both capable of withstanding high pressures. The sample cylinder was connected to the reference volume through a two-way valve and a micro-filter to prevent movement of coal particles with sudden changes in pressure. Since the diffusion/ sorption is extremely sensitive to temperature, the entire setup was placed in a constant-temperature bath, capable of maintaining the temperature to within 0.2 °C of the desired temperature. This not only ensured constant temperature throughout the experiment, but also allowed carrying out the experiment at in situ temperature. A schematic of the experimental setup is shown in Fig. 2. Precise
2. Experimental setup and procedure 2.1. Sample procurement and preparation Blocks of coal were obtained from two different seams in the Illinois basin. The most commonly used technique, particle method, was used to estimate the diffusion coefficient. This involves grinding the coal to eliminate the cracks and macropores completely, ensuring that the movement of gas is purely diffusive in nature. In order to prepare appropriate samples, coal was first broken into lumps approximately half-inch in size. These were then ground and sieved to obtain the desired sample size of 40–100 mesh (0.0425–0.0149 cm), giving an
Fig. 2. Schematic of experimental setup used for diffusion/sorption experiments.
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monitoring of pressure variation in the sample container is critical in order to calculate the amount of gas diffusing from within the coal matrix. Hence, a highly sensitive pressure transducer was connected to the reference volume which was subsequently connected to a data acquisition system (DAS), capable of recording pressure data at very short time intervals. Prior to starting a diffusion experiment, calibration of the setup was carried out. This involved determining the volume of the void space in the sample container using a non-adsorbing gas, like helium. Diffusion tests were performed for increasing and decreasing pressure steps and designated as adsorption/desorption steps. Initially, the pressure in the sample container was set to zero. The reference volume was subjected to a pressure of 1 MPa and allowed to equilibrate. The valve between the sample container and reference volume was then opened. The DAS was programmed to take readings at half-second intervals at this stage since methane adsorption rate is extremely high during the initial period. Acquiring data at this pace continued until the pressure variation became insignificant, in this case, 0.7 kPa/h. Readings were then taken at 50 s intervals and continued for approximately 20 h, after which, there was negligible change in the pressure and the sample was believed to have attained equilibrium. The coal sample was now believed to be fully saturated with methane at the equilibrium pressure. The procedure was repeated for a step-wise pressure increment of ~1 MPa, to a final pressure of ~7 MPa. Following this, the entire procedure was repeated for decreasing pressure steps of 1 MPa.
pore structure of coal, that have been successfully used in prior studies are the ‘unipore’ and ‘bi-disperse’ models (Busch et al., 2004; Nandi and Walker, 1970; Ruckenstein et al., 1971; Shi and Durucan, 2003). In this study, the data was modeled using the unipore approach, since most CBM/ECBM reservoir simulators are based on a single-step unipore diffusion model. As the name suggests, unipore model assumes that all the pores in the coal matrix are of the same size (Crank, 1975). The basis of this model is the Fick's Second Law of Diffusion for spherically symmetric flow. The model also assumes a constant gas concentration at the surface of the spheres throughout the sorption process. Although this method does not provide a perfect fit of the measured data, it is considered adequate as a first-order approximation for the purpose of making a first estimate of the sorption rates in a specific coal reservoir. For homogeneous spherical particles with a constant surface concentration and isothermal conditions, Fick's Second Law, is given as (Crank, 1975):
3. Measurement technique
" # Vt 6 ∞ 1 Dn2 π2 t = 1− 2 ∑ 2 exp − V∞ π n=1 n r2p
3.1. Ad/de-sorption isotherm The pressure data recorded during each step of the experiment was used to establish the adsorption isotherm, a natural by-product of the diffusion experiment. The amount of gas adsorbed at a given pressure was calculated using the Gibbs isotherm principle. Gibbs adsorption isotherm calculation assumes constant void volume within the coal throughout the pressure steps. It neglects the volume occupied by the adsorbed gas at each pressure step when calculating the amount of “free” gas. The difference between Gibbs and absolute adsorption is significant at high pressures, and the relationship used to calculate the absolute volume is given as (Sudibandriyo et al., 2003): Vabs =
VGibbs ρgas ρads
ð1Þ
1
" # 2 2 Mt 6 ∞ 1 Dn π t = 1− 2 ∑ 2 exp − M∞ π n=1 n r2p
ð3Þ
where, Mt is the total mass of the diffusing gas that has desorbed in time t, M∞ is the total desorbed mass in infinite time, and D is the diffusion coefficient, and rp is diffusion path length. After a step change in the surface concentration, the relationship for desorbed gas can be expressed as (Clarkson and Bustin, 1999b): ð4Þ
where, Vt is the total volume of gas ad/de-sorbed in time t and V∞ is the total gas adsorbed or desorbed after infinite time. For short times (t b 600 s) and when the fraction of gas desorbed (Vt/V∞) is less than 0.5, the Eq. (4) can be approximated to: sffiffiffiffiffiffiffiffiffi Vt Dt =6 : V∞ πr2p
ð5Þ
Several researchers have used the unipore approach to fit their experimental sorption data (Clarkson and Bustin, 1999b; Mavor, et al., 1990; Smith and Williams, 1984). They concluded that the unipore diffusion model is more applicable at high pressure steps of the isotherm rather than all of the steps. 4. Results and discussion
where, Vabs and VGibbs are the absolute and Gibbs sorption respectively, and ρgas and ρads are gas densities in gaseous and adsorbed phases respectively. The phase density for adsorbed methane used to calculate the absolute adsorption was 0.421 g/cm3 (Sudibandriyo et al., 2003). The isotherm was established using the Langmuir isotherm model, given as: V=
PVL P + PL
ð2Þ
where, P is the equilibrium gas pressure, V is the volume of gas adsorbed, VL is the Langmuir Volume representing the maximum volume that can be sorbed at infinite pressure, and PL is the Langmuir Pressure at which the sorbed volume is half the Langmuir Volume. 3.2. Estimation of diffusion coefficient Various approaches have been used by past researchers to model kinetics of gas sorption on coal. Two diffusion models, based on the
4.1. Ad/de-sorption isotherms The experiments were performed on both samples at in situ temperature of 73 °F and pressures up to 9 MPa. Experimental isotherms for adsorption and desorption steps are shown for the two coal types in Fig. 3 (Ref: Table 1). The isotherm shows that desorption hysteresis is insignificant. Ideally, desorption isotherm for coal and methane should not deviate from the adsorption isotherm since the sorption process is purely physical in nature and is reversible (Ruthven, 1984). Laboratory based isotherms typically exhibit some hysteresis due to the fact that the moisture content of the sample varies somewhat between the two isotherms (Dutta et al., 2008; Harpalani et al., 2006). A part of the sample moisture is removed during desorption every time gas is bled out. Another reason for the hysteresis, pointed out by previous researchers, is that there may be a change in the properties of the adsorbate. When the adsorbent/ adsorbate system is in a metastable state, a decrease in pressure does not release the gas as readily (Busch et al., 2003).
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12
12
Sorption, ml/g
16
Sorption, ml/g
16
8 Sample1-Adsorption Sample1-Desorption Sample2-Adsorption Sample2-Desorption
4
0
8
1
2
3
4
5
6
7
Sample1-Experimental Data Sample1-Langmuir Isotherm Sample2-Experimental Data Sample2-Langmuir Isotherm
4
0 0
345
8
0
1
2
3
4
5
6
7
8
Pressure, MPa
Pressure, MPa Fig. 3. Experimental absolute ad/de-sorption isotherms for methane.
Fig. 4. Langmuir isotherm models for desorption data.
Since it is the desorption part of the experiment that truly replicates the CBM operations, only desorption data was modeled using the Langmuir isotherm. Langmuir isotherms for the two coal types are shown in Fig. 4. The Langmuir parameters obtained for the samples, along with proximate analysis results, of the two coal types are presented in Table 1. It is apparent that all isotherms are of Type 1, according to Brunauer's classification (Brunauer et al., 1940). The relative errors of deviation of Langmuir-predicted values were calculated to be 2.5%. These levels of error are acceptable (Dutta et al., 2008). Gas sorption capacity of coal is typically influenced by pressure and temperature, the actual moisture content, composition of the organic material, mineral content, coal rank and meceral composition (Crosdale et al., 1998; Hildenbrand et al., 2006; Krooss et al., 2002). It is evident from Fig. 4 that Sample 1 has a higher sorptive affinity for methane than Sample 2 although the depth from which these were retrieved was almost the same. The volatile matter and fixed carbon content are also fairly close. Hence, the slight difference in the results obtained for the two samples may very well be the result of other controlling factors, such as, ash content, volatile matter and meceral composition.
Law, and described by Eq. (4), was used to calculate the diffusion coefficient for each step. The results depicting the variation in the value of diffusion coefficient for adsorption and desorption steps with pressure for the samples are shown in Fig. 6. The overall trend exhibited by all the results is very similar. It is apparent from the figures that there is a negative correlation between diffusion coefficient and pressure below 3.5 MPa, both for increasing as well as decreasing pressure steps. This suggests that the ease with which methane moves in the coal matrix improves with pressure reduction, or with continued gas production in the reservoir. However, since desorption part of the experiment truly replicates a CBM operation, the diffusion variation trend analysis was carried out for this alone. This is shown in Fig. 7. The diffusion variation trend is consistent with other diffusion results that have been reported by Clarkson and Bustin (1999a, 1999b), Cui et al. (2004), Wei et al. (2007) who studied the diffusion/adsorption of methane at different pressures using the bi-disperse model. Cui et al. (2004) observed that both micropore and macropore diffusions decrease with increasing adsorption. Reduction in diffusion coefficient with increased adsorption may be attributed to two reasons: (1) the effect of coal matrix swelling on pore size because adsorption swelling may narrow some micropore entrances and increase the resistance to diffuse the gas molecule through (Cui et al., 2004); and (2) strong repulsive force between adsorbed molecules with increase in surface coverage (Chen and Yang, 1991). However, a few researchers have reported that pressure is not directly related to the rate of adsorption or desorption for coals, Nandi and Walker (1970) for pressures below 2 MPa, and Sevenster (1959) for pressures below 0.1 MPa. Moreover, the results of this study contrast the observation made by Nandi and Walker (1970) stating that the diffusion coefficient increases with average methane concentration at high surface coverage. Finally, Charrière et al. (2010) and Nandi and Walker (1970) observed a surface cover dependency of the diffusion coefficient for methane and CO2 on coals. Their results showed a positive correlation between the diffusion coefficient and surface coverage (sorbed volume). To test this conclusion, desorption isotherm was plotted along with the variation in the value of diffusion coefficient for one of the samples. This is shown in Fig. 8. There is clear indication that the two are almost mirror images of each other. The observed trend was similar for the second coal type tested. Moreover, it is also apparent
4.2. Estimation of diffusion coefficient Compared to measurements for sorption isotherm, where only the final equilibrium pressure is required, measurement of diffusion coefficient requires precise and continuous change in pressure in the sample container over time, especially during the initial period of desorption when the rate of diffusion is extremely fast. This was repeated for every pressure step, that is, every time pressure in the sample container was changed to ad/de-sorb the gas. Decrease/ increase in the gas pressure of the sample container was converted to the amount of gas ad/de-sorbed. The frequency of data collection was decreased as equilibrium approached. Also, for calculation of the diffusion coefficient, only the initial sorption period (Vt/V∞ ~ 0.5) was considered, when the gas sorbs at a relatively fast pace. The change in gas content was calculated for each time interval during a pressure step. The fraction of gas (Vt/V∞) desorbed over time for the desorption steps of Sample 2 is shown in Fig. 5. The model, derived from Fick's
Table 1 Langmuir constants for desorption isotherms. Sample
Depth (m)
Volatile matter (%)
Fixed carbon (%)
Ash (%)
Moisture (%)
Temperature (°F)
Desorption VL (ml/g)
PL (MPa)
Sample 1 Sample 2
154 145
35 37
48 46
9.3 13
2.3 1.1
73 73
16.5 15.4
1.84 2.7
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Diffusion Coeffcient, x10-10 cm2/sec
1
Fraction Sorbed
0.8 0.6 38.2E-10 cm2/sec 26.7E-10 ,, 12.5E-10 ,, 4.70E-10 ,, 3.10E-10 ,, 2.40E-10 ,, 2.10E-10 ,,
0.4 0.2 0
10
0
20
30
40
45 40
Sample1 Sample2
35 30 25 20 15 10
50
5 0
0
1
2
3
4
5
6
7
8
Pressure, MPa
Time, Hours
Fig. 7. Variation of diffusion coefficient for desorption data (gray band is a free-plot trend line to emphasize the general trend).
Fig. 5. Fraction of gas desorbed with time for Sample 2.
from Fig. 6 that the diffusion coefficient for adsorption steps is slightly higher than for desorption steps. A similar observation was reported by other researchers (Dutta et al., 2008; Harpalani et al., 2006) during the sorption process, where adsorption isotherm was slightly higher than the desorption isotherm. Hence, this corroborates the findings that both diffusion and surface coverage are related, and in this case, negatively related below 3.5 MPa. The overall diffusion versus pressure trend established suggests that the variation in the value of diffusion coefficient with pressure is bi-modal in nature. At high pressures, its value remains fairly constant. However, after a certain pressure, the value of diffusion coefficient starts to increase, the rate of increase being almost exponential, suggesting that substantial desorption is responsible for the increase in the value of diffusion coefficient. Alternatively, desorption is the result of a significant increase in the value of the diffusion coefficient. This finding can have a significant impact on projecting methane production from coals at low pressures, that is, after substantial depletion. The finding would also have a significant impact on our understanding of the release of methane from abandoned mines and release of methane in worked out and sealed coal mining gob operations. As a final exercise to evaluate the difference between using the unipore versus the bi-disperse theory when estimating diffusion coefficient in the laboratory, results obtained by Cui et al. (2004) were compared with those obtained in this study. Fig. 9 shows the two trends together. It is apparent that, for the purpose of establishing variation trends, the two theories give almost identical results.
4.3. Effect of varying diffusion coefficient on gas production A preliminary and basic simulation study, using the simulator package COMET3, was carried out to investigate the effect of varying diffusion coefficient on continued gas production for a period of 10 years. Since the permeability and diffusion coefficient influence the gas transport in coal, both parameters were considered as variables. The simulation results are shown in Fig. 10. The results show that, for a high permeability reservoir (25 md), increase in diffusion coefficient from 2.4 × 10− 10 cm2/s to 38.2 × 10− 10 cm2/s resulted in increased production. The value of D remained constant throughout the period simulated since the simulator is not capable of handling a variable D. It is apparent from Fig. 10 that the increase in gas production is not significant for a low permeability reservoir (14 md), suggesting that diffusion is not the controlling mechanism in gas production for low permeability reservoirs. Nevertheless, this is inconclusive since the simulator used in the modeling exercise is not very sensitive to diffusion coefficient. This may very well be due to the well accepted belief in the past that production of methane in CBM reservoirs is permeability controlled rather than diffusion controlled. Although this is believed no longer to be the case, most simulators have not been modified to reflect this change. The ideal simulation would be possible only if a variable value of D could be used, perhaps something that the developers of the various simulator packages need to consider.
50
60 50 40
40
12
Sample1Adsorption Step Sample1 Desorption Step Sample2 Adsorption Step Sample2 Desorption Step
Sorption, ml/g
Diffusion Coeffcient, x10-10 cm2/sec
16
30
Desorption Data Points Langmuir Isotherm Diffusion Coefficient Data Points
8
30 20
4
20
10
10 0
0 0
0 0
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
Diffusion Coeffcient, x10-10 cm2/sec
346
8
Pressure, MPa
Pressure, MPa Fig. 6. Variation in the diffusion coefficient with pressure.
Fig. 8. Desorption isotherm and variation in D with pressure for one sample (gray band is a free-plot trend line to emphasize the general trend).
Apparent Diffusivity x10-6, Sec-1
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9 8
Bi-disperse Model Unipore Model
7 6 5 4 3 2 1 0
0
1
2
3
4
5
6
7
8
9
Pressure, MPa Fig. 9. Comparison of results using the unipore and bi-disperse models (re-constructed after Cui et al., 2004) (gray band is a free-plot trend line to emphasize the general trend).
5. Summary and conclusions Methane adsorption and diffusion characteristics of Illinois basin coals were established using the volumetric method. The Langmuir equation was used to model sorption data and unipore model to estimate the behavior of diffusion coefficient. Based on the work completed, the following conclusions are made: • The value of diffusion coefficient is not constant over the life of a CBM reservoir. There is a negative correlation between diffusion coefficient and pressure in the low pressure range. This finding has a significant practical implication. First, since the pressures encountered in Illinois coals are typically low, this can have a positive impact on methane production from coals in the basin. Second, current simulators incorporate the diffusion parameter using the ‘sorption time’, which is considered to be constant for the entire production period and this is simply not the case. Therefore, sorption time should be treated as a variable when simulating long/ short-term production. Modification of the simulators to incorporate this change should not be much of a challenge since permeability is already considered a dynamic parameter in several simulators. In fact, using the diffusion coefficient as a direct input parameter would make more sense rather than impacting its impact using sorption time. • The value of diffusion coefficient can be represented by a dual model, its value remaining constant at high pressures, and increasing continuously when accompanied by substantial desorption of gas. An important extrapolation of this finding to other basins, particularly the San Juan, which is considered the most
Production per Well, MSCFD
50
25 md Permeability, 2.40E-10 cm2/sec DC 25 md Permeability, 38.2E-10 cm2/sec DC 2 14 md Permeability, 2.40E-10 cm /sec DC 2 14 md Permeability, 38.2E-10 cm /sec DC
40 30 20 10 0
0
500
1000
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2500
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Time, Days Fig. 10. Effect of varying diffusion coefficient (DC) and permeability on gas production.
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prolific basin in the world, is that diffusion might be playing a significant role in later stages of the life of a CBM reservoir and might even explain the increased production rates typically observed in the basin during the later part of the reservoir's life. • The analysis of the adsorption and diffusion results revealed that the diffusion coefficient also depends on adsorption or surface coverage. These results support the observations made by Clarkson and Bustin (1999a, 1999b), Cui et al. (2004) who used bi-disperse methods to model the experimental data. Since adsorption is different for different gasses, variation in the value of diffusion coefficient should be measured as a function of gas-in-place composition. For the same reason, the value of D should be measured for coal–CO2 system as well. In a scenario where CO2 is injected in coalbeds to enhance the CBM production, or CO2 sequestration, there is counter-diffusion in the matrix, with CO2 diffusing in to, and methane diffusing out of, the matrix. An effort was initiated by Wei et al. (2007) to develop this theoretically but no studies have been reported to date to do so effectively, nor have there been studies to validate any theoretical models. • The pore-size distribution within coal varies with coal type, basin, rank, etc. and is highly heterogeneous (Clarkson and Bustin, 1999a). Hence, no model can perfectly fit the experimental data unless it considers all pores of different sizes that exist in coal, which may not be possible due to mathematical complications. Although unipore method used in this study does not provide a perfect fit of the measured data, the results showed that it may be adequate for making a first-estimate of the trend of this gas transport phenomenon in CBM reservoirs. Hence, the use of the unipore model of diffusion is definitely justified even if the bi-disperse model of diffusion represents the coal particle properties better. The unipore model is simpler and easy to use and gives very similar results for the variability of diffusivity as a function of reservoir pressure. • Based on the preliminary simulation study, gas production from low permeability reservoirs is not controlled by diffusion although this may be due to the simulator algorithm, which underplays the importance of diffusion. However, for high permeability reservoirs, application of varying diffusion characteristics can become a controlling factor in methane production. The authors do believe that the philosophy that methane production from coalbeds is permeability-controlled should be re-evaluated.
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