Energy Fuels 2009, 23, 4688–4695 Published on Web 07/24/2009
: DOI:10.1021/ef9003158
Sorption Capacity and Sorption Kinetic Measurements of CO2 and CH4 in Confined and Unconfined Bituminous Coal J. Denis N. Pone,* Phillip M. Halleck, and Jonathan P. Mathews Department of Energy and Mineral Engineering and The EMS Energy Institute, The Pennsylvania State University, University Park, Pennsylvania 16802 Received April 8, 2009. Revised Manuscript Received July 8, 2009
Carbon dioxide injection into coal formations provides an opportunity to sequester carbon while simultaneously enhancing methane recovery. Although powdered coal samples provide a quick indication of the gas sorption capacity, underground storage takes place within compact coal monoliths, and therefore, it may be necessary to account for in situ conditions, specifically confining stress, for meaningful estimates. This study presents the sorption rates and sorption capacities of CO2 and CH4 for a bituminous coal sample in a whole sample and in pulverized form. The impact of confining stress on these sorption capacities of coal cores is evaluated with a multiple-point isotherm over a prolonged time period. The kinetics of the complex, heterogeneous processes occurring in a bituminous coal sample are quantified while under confining stress. Sorption capacities for a powdered sample are 1.17 and 0.66 mmol/g for CO2 and CH4, respectively. The application of 6.9 and 13.8 MPa of confining stress contributed to 39 and 64% CO2 sorption capacity reduction. Similarly, 85 and 91% CH4 uptake capacity reduction is observed at those confining stresses. The time-dependent gas diffusion parameters are quantified using the volumetric method with a mathematical analysis of the pressure-decay data. Carbon dioxide diffused through the coal faster than CH4. Initial exposure over a few days showed a rapid reduction in diffusion presumably as the macro- and mesopores filled. With longer exposure, 10 additional days, a steady slower diffusion is observed for CO2. The steady-state slower diffusion is achieved within a few days for CH4. It was found that the overall gas movement, specifically diffusion, is hindered by confining stresses and takes place at rates significantly less than in unconfined powder coal.
and kinetics of CO2 and CH4 transport through the coal structure at in situ stress conditions. The heterogeneous nature of coal introduces a number of complex factors into the various processes involved in the retention of gas, its release, and subsequent flow through the coal seam. Gas uptake capacities and transport rates are based on simple calculations. However, the interplay of different in situ processes and conditions makes this evaluation challenging. Existing CO2 storage capacity estimates in coal are highly scattered and sometimes contradictory.4,5 Some of the inconsistencies are consequences of using inappropriate methodology to derive rough estimates or due to the desire to make quick assessments with limited or no data, as noted by Bradshaw et al.2 Also, current capacity estimates for CO2 sequestration in coal are uncertain because of limited field experience and few experiments at in situ conditions. These limitations, because of the challenges of applying the scientific approach to such a variant material and complex set of competing processes, restrict the knowledge base necessary for sequestration. Although crushed coal provides useful information for coal characterization, underground storage takes place within compact coal monoliths. There is evidence
1. Introduction Injecting carbon dioxide into coalbed reservoirs for sequestration and enhanced coalbed methane recovery (ECBM) purposes is one of the climate-change mitigation options. Globally, there is an estimated potential of about 2000 GtCO2 of CO2 capacity in geological formations, with at least 15 GtCO2 in unmineable coal formations.1 Because ECBM could make a substantial greenhouse gas reduction strategy, policy makers and potential investors are in need of reliable estimates for storage capacities and an indication of long-term sustainability. Valuable resources could be wasted if sorption capacities are based on unreliable data.2 Carbon dioxide injection into coal formations provides the ability to sequester CO2 while simultaneously enhancing methane recovery. The characterization of sorption capacity and gas transport is required for successful implementation of CO2 sequestration in coal. Despite extensive research, there are gaps in our fundamental understanding concerning aspects of CO2 interactions with coal.3 Among these are the sorption capacities *To whom correspondence should be addressed: 133 GB, Bartlesville Technology Center, ConocoPhillips, OK 74002. Telephone: 1-918-6610805. Fax: 1-918-662-2047. E-mail:
[email protected]. (1) Intergovernmental Panel on Climate Change (IPCC). Carbon Dioxide Capture and Storage: Special Report of the Intergovernmental Panel on Climate Change; Cambridge University Press: New York, 2005. (2) Bradshaw, J.; Bachu, S.; Bonijoly, D.; Burruss, R.; Holloway, S.; Christensen, N. P.; Mathiassen, O. M. Int. J. Greenhouse Gas Control 2007, 1, 62–68. (3) Majewska, Z.; Zietek, J. Int. J. Coal Geol. 2007, 70, 305–312. r 2009 American Chemical Society
(4) Goodman, A. L.; Busch, A.; Duffy, G. J.; Fitzgerald, J. E.; Gasem, K. A. M.; Gensterblum, Y.; Krooss, B. M.; Levy, J.; Ozdemir, E.; Pan, Z.; Robinson, R. L.; Schroeder, K.; Sudibandriyo, M.; White, C. M. Energy Fuels 2004, 18, 1175–1182. (5) Yu, H. G.; Guo, W. J.; Cheng, J. L.; Hu, Q. T. Int. J. Coal Geol. 2008, 74, 250–258.
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investigation over the years. Although the coal structure presents challenging scientific questions, the general understanding is clear.20 Interaction of the coal structure with some gases and liquids leads to a chain of physical and chemical reactions. Among these are adsorption, absorption, persorption, and chemisorption. All of these processes are often designated, without distinction, as sorption. Different conditions, such as pressure, temperature, physical nature of the coal, and sorbate, influence the extent to which each of these interactions can occur. Additional factors affecting the sorption characteristics of coal are the presence of pores with highly polar surfaces and its nonrigid structure when exposed to certain sorbates.21 One of the characteristics deserving attention is the extent of microstructural changes in the coal pore system that occurs during the sorption processes because of its impact on porosity and, hence, capacity. These variations have a strong influence on the kinetics of gas uptake or desorption. The swelling behavior of the cross-linked macromolecular network, when exposed to certain gases or liquid sorbates, has been observed.22-37 However, swelling data characterizing coal under stress are limited. Compression/compaction as well as regional swelling is expected from the coal structure under in situ stresses.38 In a key contribution describing a novel technique for the removal of methane from coal, Every and Dell’osso39 demonstrated that, under laboratory conditions, it was possible to displace 90% of the residual CH4 from crushed coal at ambient temperature, within 1 week, by CO2 sorption. They also showed that CO2 had high affinity with the coal structure, displacing 3 times more CH4 than air and 5 times more than helium, as demonstrated earlier by Graham.40 These two observations are some of the earliest investigations into industrial ECBM and can be applied to CO2 sequestration in coal seams.
that in situ stress conditions affect coal uptake capacity, influence strain distribution,8 and consequently, impact gas transport in coal. Characterizations of coal and appropriate interpretations of laboratory results are prerequisites for the generation of reliable estimates of CO2 and CH4 sorption capacities and diffusion rates in coal. This paper focuses on the characterization of the coal-gas system dynamic behavior during CO2 and CH4 sorption under in situ confining stress conditions. The effect of confining stress on sorption capacity, gas transport rates, and their variation at a constant effective stress is evaluated in this study. The rank of the coal, the temperature, and the confining stresses used in this work are consistent with potential ECBM sites in the eastern United States. The relationship between sorption rates of CH4 and CO2 and the confining stress is evaluated with a descriptive mathematical model developed on the basis of experimental data. Information collected from the same coal samples, unconfined crushed to -60 mesh yet unconfined, allows for comparison between powder sorption capacities and sorption rates obtained for nonpowder confined samples. Sorption and transport rates obtained in this study can be used in reservoir simulations of ECBM and CO2 sequestration in unmineable coal seams. 2. Background Sorption and diffusivity are primary characteristics required for evaluation and predictive modeling of coal reservoirs.9 Nonpowdered coal is viewed as a heterogeneous porous medium consisting of a matrix system with mostly microporosity and low permeability located within a system of fractures of high permeability. The bulk matrix of coal consists of micropores on the order of 5-10 A˚, while the cleat and fracture systems are characterized by pores ranging from micropore dimensions to several micrometers in sizes.10 Cleats with dimensions as large as micrometers to several centimeters have also been reported.11 The cleat frequency is dependent upon the rank, lithography, and geological history of the coal. According to Marsh,12 the microporous texture of coal accounts for the observed high CO2-determined surface area ranging from 200 to 300 m2/g and contributes, depending upon experimental conditions, rank, and physical characteristics, to more than 95% of the gas uptake capacity.13 The permeability of the seam is highly influenced by the cleat size distribution.14,15 2.1. Gas Sorption in Coal. The complexity of the coal structure, because of the mixture of organic and inorganic matter, has made fundamental sorption studies an ongoing
(17) Airey, E. M. Int. J. Rock Mech. Min. Sci. 1968, 5, 475. (18) Bertard, C.; Bruyet, B.; Gunther, J. Int. J. Rock Mech. Min. Sci. 1970, 7, 43–65. (19) Vinokurova, E. B. Khim. Tverd. Topl. 1978, 12, 132–139. (20) Berkowits, N. Coal Science and Technology 7;The Chemistry of Coal; Elsevier Science: London, U.K., 1985. (21) Mahajan, O. P. Carbon 1991, 29, 735–742. (22) Ceglarska-Stefanska, G.; Czaplinski, A. Fuel 1993, 72, 413–417. (23) Czaplinski, A. Arch. Gorn. 1986, 31, 591–598. (24) Czaplinski, A. Arch. Gorn. 1986, 31, 563–568. (25) Czaplinski, A. Arch. Gorn. 1986, 31, 581–589. (26) Goodman, A. L.; Favors, R. N.; Hill, M. M.; Larsen, J. W. Energy Fuels 2005, 19, 1759–1760. (27) Gorucu, F. B.; Jikich, S. A.; Bromhal, G. S.; Sams, W. N.; Ertekin, T.; Smith, D. H. Matrix shrinkage and swelling effects on economics of enhanced coalbed methane production and CO2 sequestration in coal. In Proceedings of the Eastern Regional Meeting of the Society of Petroleum Engineers, Morgantown, WV, Sept 14-16, 2005; SPE Paper 97963, pp 137-151. (28) Hall, P. J.; Marsh, H.; Thomas, K. M. Fuel 1988, 67, 863–866. (29) Larsen, J. W. Int. J. Coal Geol. 2004, 57, 63–70. (30) Nelson, J. R.; Mahajan, O. P.; Walker, P. L. Jr. Fuel 1980, 59, 831–837. (31) Nelson, J. R.; Mahajan, O. P.; Walker, P. L. Jr. Prepr. Pap.;Am. Chem. Soc., Div. Org. Coat. Plast. Chem. 1980, 43, 337–340. (32) Nishioka, M. Fuel 1993, 72, 997–1000. (33) Nishioka, M. Fuel 1993, 72, 1001–1005. (34) Reucroft, P. J.; Patel, H. Fuel 1986, 65, 816–820. (35) Reucroft, P. J.; Patel, K. B. Fuel 1983, 62, 279–284. (36) Sethuraman, A. R.; Reucroft, P. J. Prepr. Pap.;Am. Chem. Soc., Div. Fuel Chem. 1987, 32, 259–264. (37) Strezov, V.; Lucas, J. A.; Wall, T. F. Fuel 2005, 84, 1238–1245. (38) Pone, J. D. N.; Halleck, P. M.; Mathews, J. P. Energy Procedia 2009, 1, 3121–3128. (39) Every, R. L.; Dell’osso, L. J. Can. Min. Metall. Bull. 1972, 65, 143–150. (40) Graham, I. J. Trans. Inst. Min. Eng. 1919, 58 (1), 32–38.
(6) Hile, L. M. Master’s Thesis, The Pennsylvania State University, University Park, PA, 2006. (7) Smith, D. H.; Jikich, S. A.; Seshadri, K. Carbon dioxide sorption isotherms and matrix transport rates for non-powdered coal. In Proceedings of the International Coalbed Methane Symposium, University of Alabama, Tuscaloosa, AL, May 21-25, 2007. (8) Pone, J. D. N.; Hile, L. M.; Halleck, P. M.; Mathews, J. P. Int. J. Coal Geol. 2009, 77, 103–108. (9) Saghafi, A.; Faiz, M.; Roberts, D. Int. J. Coal Geol. 2007, 70, 240–254. (10) Van Krevelen, D. W. Coal: Topology;Physics;Chemistry; Constitution; Elsevier: Amsterdam, The Netherlands, 1993; p 979. (11) McCulloch, C. M.; Deul, M.; Jeran, P. W. Cleat in Bituminous Coalbeds; U.S. Bureau of Mines: Washington, D.C., 1974; p 25. (12) Marsh, H. Fuel 1965, 44, 253–260. (13) Shi, J. Q.; Durucan, S. Oil Gas Sci. Technol. 2005, 60, 547–558. (14) Karn, F. S.; Friedel, R. A.; Sharkey, J. A. G. Fuel 1975, 54, 279– 282. (15) Karn, F. S.; Friedel, R. A.; Thames, B. M.; Sharkey, J. A. G. Fuel 1970, 49, 249–256. (16) Harpalani, S.; Prusty, B. K.; Dutta, P. Energy Fuels 2006, 20, 1591–1599.
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Table 1. Proximate and Ultimate Analyses of the Four Samples sample ID
% moisture
% ash
% VM
% FC
carbon
hydrogen
nitrogen
sulfur
oxygen
A B C D
1.80 ( 0.03 1.70 ( 0.01 1.55 ( 0.00 1.82 ( 0.00
5.72 ( 0.05 3.12 ( 0.01 4.71 ( 0.12 2.99 ( 0.01
37.46 ( 0.19 39.31 ( 0.06 37.72 ( 0.02 37.94 ( 0.06
56.82 57.57 57.57 59.07
80.24 ( 0.20 82.66 ( 0.15 80.90 ( 0.15 82.55 ( 0.05
5.25 ( 0.06 6.05 ( 0.08 5.95 ( 0.03 6.01 ( 0.01
1.48 ( 0.06 1.66 ( 0.02 1.58 ( 0.01 1.60 ( 0.03
2.38 ( 0.07 1.59 ( 0.00 1.53 ( 0.00 1.46 ( 0.01
4.92 4.93 5.32 5.4
2.2. Gas Transport in Coal. Gas sorption kinetics in coal is important.41 The movement of gas in the pore networks occurs as a result of both pressure and concentration gradients.42 It can also be explained by the energy fluctuation because of the sorption processes. The mechanism of gas transport may be molecular diffusion through the micropores, bulk diffusion through the macro/mesopores, or permeation through the cleats.13 Transport of gas in coalbeds takes place in a multiscale system, often characterized by a distinctive matrix structure involving a simplified bimodal pore size distribution.43 The interplay of the highflow rate of the macroscopic fracture network and the lowflow rate of the matrix during adsorption or desorption in coals needs to be well-characterized to allow for management of injection and production processes. Existing models used for coalbed simulators assume gas sorption or desorption as being controlled by a constant diffusivity coefficient from spherical objects or “matchstick” sets connected by a relatively large fracture network.44 An application of this general model may result in the introduction of large errors in the estimation of sorption capacity and the prediction of flow behavior. Rigorous predictive models should encompass all forms of gas transport mechanisms. The process of gas injection and production of CH4 from coal seam faces a number of challenges.45 The application of analytical approaches developed for conventional reservoir characterization has been unsuccessful in evaluating sorption and transport of gas in coal. A recent study compared the accuracy of three popular field-permeability models when applied to laboratory-generated, sorption-affected permeability data and found poor agreement.46 Much of this has to do with the complex structure of coal that has a continuum of pores varying from nanometer to micrometer size.47 Furthermore, many ECBM reservoir simulators operate with either a single-step unipore48 or bimodal pore diffusion model, which, although are useful approximations, is a simplistic representation of the transport process in coal.
Table 2. Comparison of the Maceral Composition of the Four Samples (Vol %, Mineral Matter Free) maceral
A
B
C
D
total vitrinite sporinite resinite cutinite liptodetrinite total liptinite fusinite semifusinite macrinite micrinite inertodetrinite total inertinite total
66.0 5.2 1.6 0.4 0.5 7.7 2.7 9.1 0.4 9.9 4.2 26.3 100.0
66.4 5.1 0.5 0.7 0.5 6.8 2.8 8.9 0.3 11.4 3.4 26.8 100.0
65.1 5.2 0.6 0.5 0.9 7.2 4.0 9.8 0.4 10.8 2.7 27.7 100.0
64.6 3.8 0.7 0.6 0.8 5.9 3.8 13.6 0.4 9.2 2.5 29.5 100.0
This is further complicated by various sorption types and mechanisms that can occur, the different time frames, and the different physical states in which the CO2 might occur.2 Many of the discrepancies between the various sorption rates reported can be attributed to the dynamic pore structure variation and different diffusion lengths.49,50 3. Experimental Procedures 3.1. Sample Preparation. Coal samples used for this study were prepared from a single block collected from the Hazard No. 9 coal seam, Perry County of the Western Kentucky Coalfield. The highwall overburden, mostly sandstone, was estimated to be 200 m thick, and the seam was estimated to be 2 m thick. The block was removed and coated with a waterbased polycrylic protective finish to prevent any further oxidation and dehydration of the sample. The block was cast in plaster to give it some rigidity during the coring process. Multiple side-by-side cores were cut from the block parallel to the bedding plane. The cores were preserved in a sealed container under a nitrogen environment. The end surfaces of the cores were polished to produce a flat and parallel surface for the application of uniform stress. Core samples of 2.5 cm in diameter and 6.3 cm in average length were hydraulically confined to replicate the in situ conditions during sorption experiments. Some of the cores obtained were cut using a diamond saw to produce (∼2 1 1 cm) rectangular shape samples used for sorption measurements with and without confining stress. The remaining pieces were crushed to -60 mesh and used for sorption measurements on powder samples. Petrographic, proximate and ultimate analyses of the sample were determined to verify the similarity of the samples. Results presented were obtained using four samples, as indicated in Tables 1 and 2. 3.2. Isotherm Measurement Method. Measurements were made using the volumetric gas adsorption apparatus shown schematically in Figure 1. Briefly, the system consisted of a sample cell and a reference cell, both of which have accurately known volumes determined by Boyle’s law. All cells are contained in a temperature-controlled environment ((0.1 C).
(41) Walker, P. L.; Austin, L. G.; Nandi, S. P. Activated diffusion of gases in molecular-sieve materials. In The Chemistry and Physics of Carbon; Walker, P. L., Ed.; Marcel Dekker: New York, 1966; Vol. 2, pp 257271. (42) Gilman, A.; Beckie, R. Transp. Porous Media 2000, 41, 1–16. (43) Yi, J.; Chongqing, U.; Akkutlu, I. Y.; Deutsch, C. V. Gas sorption and transport in poroelastic coals. In Proceeding of the Rocky Mountain Oil and Gas Technology Symposium, Society of Petroleum Engineers, Denver, CO, 2007; SPE Paper 103180. (44) King, G. R.; Ertekin, T. M. A survey of mathematical models related to methane production from coal seams. In Proceedings of the International Coalbed Methane Symposium, University of Alabama, Tuscaloosa, AL, 1989; pp 125-155. (45) Reeves, S.; Harpalani, S.; Gasem, K. Results, status and future activities of the Coal-Seq Consortium. In Proceedings of the International Coalbed Methane Symposium, University of Alabama, Tuscaloosa, AL, 2008. (46) Robertson, E. P.; Christiansen, R. L. Modeling permeability in coal using sorption induced strain data. In Proceedings of the Annual Technical Conference of the Society of Petroleum Engineers, Dallas, TX, Oct 10-12, 2005; SPE Paper 97068. (47) Gamson, P. D.; Beamish, B. B.; Johnson, D. P. Fuel 1993, 72, 87– 99. (48) Busch, A.; Gensterblum, Y.; Krooss, B. M.; Littke, R. Int. J. Coal Geol. 2004, 60, 151–168.
(49) Olague, N. E.; Smith, D. M. Fuel 1989, 68, 1381–1387. (50) Mathews, J. P.; Karacan, O.; Halleck, P.; Mitchell, G. D.; Grader, A. Storage of pressurized carbon dioxide in coal observed using X-ray tomography. In Proceedings of the First National Conference on Carbon Sequestration, Washington, D.C., May 14-17, 2001.
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Figure 1. Experimental setup for the measurement of sorption and kinetics of gases in coal (HP, hydraulic pump; P, pressure transducers; G, gas supply; R, reference cell; Data, data acquisition system; Vac, vacuum pump).
Measurements were performed in small time increments, where the gas sorption volumes were high, but these increments were lengthened as the sorbed volume rate decreased. The gas pressure readings were continued for several days or weeks until the gas pressure change in the sample cell became too small to measure. The gas injection pressure was kept constant at 3.1 MPa for all sorption cycles. Confining stresses of 6.9 or 13.8 MPa were used during measurements. The sorption of gases as a function of time was obtained on the basis of the difference between the initial amount of gas introduced into the cell and the amount of the gas remaining in the dead space of the cell at any given time ti from t = 0 to teq (apparent equilibrium), as shown in eq 1. Pressure decreases in the system were measured and recorded automatically as a function of time. The injection pressure was 3.1 MPa in all of the sorption cycles. Capacity values reported were not corrected for mineral matter content. Adsorption isotherms were plotted as the total amount of excess adsorbed gas versus elapsed time steps. An error analysis similar to that reported by Odzemir52 indicated that the error associated with each data point could be as high as 2%. A detailed mathematical description of the volumetric method is provided by Mavor et al.53 and Odzemir et al.54 3.3. Mathematical Modeling of Sorption Kinetics. Sorption kinetic data were obtained by monitoring the rate of pressure equilibration during individual steps of the volumetric sorption experiments. Pressure decay data were used to compute diffusion coefficients. For diffusion in a system, such as that used in the present work, the differential equation, as written by Fourier,55 or commonly known as Fick’s second law is valid provided that diffusion occurs primarily in the radial direction Dc 1 D Dc ¼ rD ð2Þ Dt r Dr Dr
Two distinct system configurations were designed to accommodate measurements with and without stress. A Temco-designed pressure vessel was used for measurements under stress, while a customized high-pressure chamber was used for measurements at zero-confining stress. The apparatus consisted of a reference cell of approximately 10 mL and a sample cell of about 3 mL. Core samples were evacuated for 48 h, and powder samples were evacuated for 24 h to remove any residual gases and weakly bond water molecules before the measurements were performed. The gas-accessible void volume in the sample cell was calculated using helium displacement. After the helium was removed under vacuum, the reference cell was pressurized with CH4 or CO2. After thermal equilibrium was achieved, a portion of the gas (CH4 or CO2) was transferred from the reference cell into the sample cell. Pressure and temperature were monitored in both cells using high-precision pressure transducers. Sorption was rapid for the powdered coals, but long equilibration times were allowed for solid cores of coal. A few hours were sufficient for the sorption on powdered coal samples to establish a trend. At an arbitrary equilibrium point, the amounts of gas within both the reference and sample cells were calculated using the real gas law and the Span and Wagner51 values for the gas compressibility factor. From the mass balance, the difference between the moles of gas transferred from the reference cell and the moles of gas calculated to be present in the He-estimated free-gas phase in the sample cell was considered to be the Gibbs excess adsorption. The reference cell was then pressurized with additional gas, and the process was repeated. The incremental Gibbs excess adsorption (Δnex i ) at the end of ith step was determined from eq 1, as described by Yu et al.5 0 ! !1 PiS, Eq PiS-1 PiR, I PiR, F 1 , Eq A ex @ Δni ¼ - i -V0 VR i RTm ZR ZSi , Eq ZSi -1 , I ZR, F , Eq
with boundary conditions C ¼ 0 at t ¼ 0
ð1Þ where the subscripts I, F, and Eq refer to the initial conditions in the cell, final gas expansion, and adsorption apparent equilibrium or steady state, respectively, the subscripts R and S represent the reference and sample cells, respectively, the superscripts, i and (i - 1) represent the ith and (i - 1)th steps, respectively, P is the pressure, Z is the compressibility factor of the gas, T is the temperature, R is the molar gas constant, m is the mass of the coal sample, and VR and V0 are the volume of the reference cell and the void volume in the sample cell, respectively.
ð3Þ
It was also assumed that there were no angular concentration gradients and that the diffusion coefficient was isotropic and (52) Ozdemir, E. Ph.D. Dissertation, University of Pittsburgh, Pittsburgh, PA, 2004. (53) Mavor, M. J.; Owen, L. B.; Pratt, T. J. Measurement and evaluation of coal sorption isotherm data. In Proceedings of the 65th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, LA, Sept 23-26, 1990; SPE Paper 20728, pp 157-170. (54) Ozdemir, E.; Morsi, B. I.; Schroeder, K. Langmuir 2003, 19, 9764–9773. (55) Fourier, J. The Analytical Theory of Heat; Dover: New York, 1955.
(51) Span, R.; Wagner, W. J. Phys. Chem. Ref. Data 1996, 25, 1509– 1596.
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independent of the concentration at the gas concentration used. In eqs 2 and 3, C is the concentration, t is the time, r is the radial distance, and D is the diffusion coefficient. Fourier,55 Carman and Haul,56 and later Crank57 solved the above diffusivity equations for the case where diffusion occurs from a solution of limited volume, i.e., when the concentration of gas or the total amount of gas is changing at the surface of the sample. The solution was written in a more convenient form by Carman and Haul56 as ! ¥ X Mt 4Rð1þRÞ -qn 2 Dt 1¼ exp ð4Þ 4 þ 4R þ R2 qn 2 a2 M¥ n ¼1 where Mt is the total amount of gas sorbed after time t, M¥ is the amount after infinite time, and qn values are the nonzero roots of the equation Rqn J0 ðqn Þ þ 2J1 ðqn Þ ¼ 0 ð5Þ
Figure 2. Methane (O) and carbon dioxide (b) excess sorption on powder (-60 mesh) coal at 20 C for a short exposure time.
where Jn values are the Bessel function of nt order. In Crank’s solution,57 the diffusivity equations reflect the condition in which the total amount of gas in a limited volume changes at the surface of the sample. When the sorbate is a pure gas, the concentration is measured by the pressure, p; i.e., the initial pressure is p1, the pressure at t = 0 is p2, and at t = ¥, it is p¥. It then follows that Mt p -p¥ ¼ ð6Þ 1M¥ p2 -p¥ R ¼
p¥ -p1 p2 -p¥
ð7Þ
This method is particularly well-suited for gas diffusion estimation, because measurement of a sorption isotherm by the volumetric method is normally carried out in steps. The p¥ attained in one step becomes p1 for the next. The six roots of qn for different values of R are given by Crank57 to assist the evaluation of eq 5. The convergence of the series in eq 4 becomes inconveniently slow for numerical evaluation when Dt/a2 is small. An alternative solution was proposed by Carman and Haul,56 which is accurate up to considerably higher values of Mt/M¥. Considering the non-ideality of the gas, the pressure values were corrected using the compressibility factor51 and the Carman and Haul56 equation, rewritten as follows: ( ) p=z -p¥ =z¥ γ3 2γ3 Dt 1=2 2 2 2 ¼ expf4γ3 Dt=ða R Þgerfc p2 =z2 -p¥ =z¥ γ3 þγ4 R a2 ( ) γ4 2γ4 Dt 1=2 2 2 2 þ expf4γ4 Dt=ða R Þgerfc ð8Þ γ3 þγ4 R a2 where 1 ð9Þ γ3 ¼ fð1þRÞ1=2 þ1g, γ4 ¼ γ3 -1 2 Effective diffusivity (D/a2) values were calculated from the experimental pressure-time data using eqs 6-9. The raw pressure decay data were corrected for the non-ideality of the gas using the compressibility factor from Span and Wagner.51 From the knowledge of the initial and final pressure values, R was established. Then, a model pressure-decay curve was generated. Experimental Mt/M¥ values were then plotted against time t and compared to the predicted Mt/M¥ versus time generated by applying an estimated diffusivity value. The minimum deviation from the experimental Mt/M¥ versus time curve was obtained through an iterative least-squares method in
Figure 3. Methane (O) and carbon dioxide (b) excess sorption on powder (-60 mesh) coal at 20 C for a long exposure time.
fitting the best diffusivity value. Finally, a value of diffusivity was chosen, which gave the best fit of the model pressure-decay curve with the experimental pressure-decay curve, in the same manner as Durrill and Griskey,58 Singh et al.,59 Chen and Rizvi,60 and Li et al.61
4. Results and Discussion 4.1. Sorption Capacity. The CO2 and CH4 uptake capacities on a powdered sample for short (t e 0.1 day) and long (t f eq) coal-gas contact times at 20 C are showed on Figures 2 and 3, respectively. It can be seen that the sorption of CO2 occurred rapidly, achieving more than 95% of the total capacity during the first few hours of the experiment. The sorption of CH4 occurred relatively slowly, achieving almost 75% of the total capacity at the same period. Similar sorption studies on powder coal have shown that CO2 is preferentially sorbed in comparison to CH4. Cui et al.62 indicated that, because of its relatively smaller kinetic diameter, CO2 can permeate not only macropores but also ultramicropores. According to Mastalerz et al.,63 this difference in the sorption of CO2 and CH4 is justified by sorption into (58) Durrill, P. L.; Griskey, R. G. AIChE J. 1966, 12, 1147–1151. (59) Singh, B.; Rizvi, S. S. H.; Harriott, P. Ind. Eng. Chem. Res. 1996, 35, 4457–4463. (60) Chen, K. H. J.; Rizvi, S. S. H. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 607–621. (61) Li, Z. W.; Dong, M. Z.; Li, S. L.; Dai, L. M. J. Porous Media 2006, 9, 445–461. (62) Cui, X.; Bustin, R. M.; Dipple, G. Fuel 2004, 83, 293–303. (63) Mastalerz, M.; Gluskoter, H.; Rupp, J. Int. J. Coal Geol. 2004, 60, 43–55.
(56) Carman, P. C.; Haul, R. A. W. Proc. Phys. Soc. London, Sect. A 1954, 222, 109–118. (57) Crank, J. The Mathematics of Diffusion; Clarendon Press: Oxford, U.K., 1975.
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Figure 4. Carbon dioxide excess sorption on nonpowder coal cores at 13.8 MPa (b) and 6.9 MPa (4) confining stresses and nonpowder unconfined (O).
Figure 6. Carbon dioxide diffusivity coefficient variation as a function of the time and physical state of the sample: (0) the powder sample, (O) solid unconfined, and (4) 6.9 MPa and (b) 13.8 MPa confining stresses.
Figure 5. Methane excess sorption on nonpowder coal cores at 13.8 MPa (b) and 6.9 MPa (4) confining stresses and nonpowder unconfined (O).
Figure 7. Methane diffusivity coefficient variation as a function of the time and physical state of the sample: (0) powder sample, (O) solid unconfined, and (4) 6.9 MPa and (b) 13.8 MPa confining stresses.
the micropores being the major mechanism for CH4, whereas both adsorption into the micropores and absorption (imbibed) into the organic matrix of coal were dominant for CO2. Milewska-Duda et al.64 based on modeling data suggested that, for CO2, absorption and adsorption contributions are comparable, whereas for CH4, the absorption is much lower. Walker et al.65 stated that CO2 dissolution into the organic structure of coal contributed up to half of the total uptake. For sequestration of CO2 in coal seams, attention must be paid to the possible effects of dissolved CO2 on the structure and its impacts of the coal behavior, as suggested by Larsen.29 Data shown in Figures 3 and 4 indicate that the CO2 sorption capacity of about 1.2, 1.4, 0.9, and 0.5 mmolCO2/ gcoal was reached for powder, nonpowder unconfined, confined at 6.9 MPa, and confined at 13.8 MPa, respectively. All four samples had similar levels of mineral matter (3-5.7% by mass), similar maceral compositions, and similar moisture levels, as presented in Tables 1 and 2. Similarly with CH4, a sorption capacity of about 0.7, 0.6, 0.1, and 0.06 mmolCH4/ gcoal was measured for powder, nonpowder unconfined, confined at 6.9 MPa, and confined at 13.8 MPa, respectively. The results depicted in Figures 4 and 5 show that the uptake of CO2 and CH4 varied with the physical state and compression of the sample. Specifically, the uptake capacities decreased with increasing stress conditions. The sorption process under confining stress was very slow in comparison to the powdered coal sample. The nonpowder unconfined
coal sample sorbed more CO2 compared to the powdered sample. This may be an indication that the pulverization of coal generated new porosity or surface area or that the dispersion of different lithotypes does not resemble the property of the banded coal.50 Therefore, the transfer of sorption capacities obtained from crushed unconfined coal samples to studies based upon solid confined coal is not justified. Sorption studies of CO2 and CH4 on nonpowder confined coal samples are limited. Hile6 analyzed the impacts of confining stress on the CO2 uptake capacity of Pittsburgh No. 8 coal and reported 80% sorption capacity reduction compared to the sorption capacity of a powdered sample. Studying the sorption of CO2 on nonpowder unconfined coal samples, Smith et al.7 and Kelemen and Kwiatek66 also reported a sorption capacity reduction. In general, results provided in Tables 1 and 2 suggest that coal samples used are relatively the same and can be classified as high-volatile A bituminous coal. In addition, each of these samples had a similar distribution of minerals. Proximate analysis presented in Table 1 shows that ash values for these samples ranged from 3 to 5.7%. At the end of the experiments, proximate analysis of the samples revealed an average moisture content of 1.72%. Although all samples were evacuated before the experiment, it is possible that residual moisture content may have impacted the sorption capacity. 4.2. Sorption Kinetics. The uptake of organic molecules, methane and carbon dioxide, into the coal structure may be accompanied by the physical softening of the structure, which induced compression/compaction and swelling of the coal matrix. Non-uniform swelling in turn could give
(64) Milewska-Duda, J.; Duda, J.; Nodzenski, A.; Lakatos, J. Langmuir 2000, 16, 5458–5466. (65) Walker, P. L.; Verma, S. K.; Rivera-Utrilla, J.; Khan, M. R. Fuel 1988, 67, 719–726.
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Table 3. Variation of the Diffusivity Coefficient with Time and Stress State of the Sample sample state
initial diffusivity coefficient (s-1)
A B C D
-60 mesh powder solid unconfined 6.9 MPa confining 13.8 MPa confining
2.10 10-3 1.40 10-3 4.36 10-4 1.15 10-4
A B C D
-60 mesh powder solid unconfined 6.9 MPa confining 13.8 MPa confining
1.70 10-3 1.25 10-3 3.93 10-4 1.14 10-4
sample ID
final diffusivity coefficient (s-1) CO2
CH4
time (days)
cumulative uptake (mmol/g)
1.00 10-9 1.01 10-9 1.00 10-8 2.79 10-8
6 25 30 20
1.17 1.39 0.85 0.50
1.92 10-8 2.54 10-8 1.00 10-9 2.20 10-8
5 9 23 7
0.66 0.57 0.10 0.06
transport mechanism of CH4 and CO2 in coal. Additionally, confining stress contributed to the closure of pores or pore throats, impacting the sorption process further. Results presented in Figures 2-8 and Table 3 demonstrate that confining stresses influence gas uptake capacity. The sorption of gas by coal under stress leads to a non-uniform deformation of the coal matrix, which consequently impacts the pore volume. Although the effects of any macropore volume changes because of stresses on the overall gas uptake may be negligible as reported by Soeder,67 they promoted a considerable retardation effect on flow and diffusion in the matrix. As a result, a substantial uptake capacity reduction was noted. Figure 8. Comparison of CO2 (b) and CH4 (O) diffusivity coefficient variation in a 6.9 MPa confined coal core as a function of the time.
5. Conclusions
rise to differential stresses, while the visco-elastic response of the structure to these stresses may exert a critical influence on the transport within the matrix of the coal.8 The resulting kinetics of penetration may vary widely, and their interpretation requires information obtained on the particular coalgas system. Figures 6 and 7 show the variation of the diffusivity constant as a function of time for CO2 and CH4, respectively. Table 3 is a compilation of diffusivity coefficients obtained. Initial and final values of the diffusivity coefficient for both CO2 and CH4 are reported. Additionally, these figures illustrate the impacts of the physical state of the samples on the diffusion processes. Diffusivity constants for CO2 and CH4 decrease with time. The early stage of the transport of gas in coal is dominated by Darcy’s type flow and, dependent upon the stress state of the sample, the process becomes diffusion-controlled later. Diffusion plays a more important role for CO2 flow into the coal compared to CH4. Different gas sorption rates corresponding to different stages of the experiment are evident in Figures 6 and 7. The final diffusivity coefficients for the confined cores are higher because they are less saturated at the stop of the experiments compared to the powder or nonpowder unconfined sample. This process is also influenced by the interaction of CO2 with the coal pores network. It is important to note that all of these processes overlap. Hence, a constant diffusion coefficient might not be accurate for CO2 transport characterization in nonpowder confined coals. Figures 3-8 describe the contrast between CO2 and CH4 sorption rates in a coal core under confining stresses. These figures show that the imbibitions and dissolution of CO2 in the coal matrix, which has been reported previously, lead to a different
Gas sorption and transport behavior in a powder and nonpowder confined coal sample was quantified for CO2 gas uptake capacity. A method based on pressure decay was adapted to characterize the transport behavior of CH4 and CO2 in coal. The sorption capacity and the kinetics of gas in coal are both influenced by the stress state of the sample. The application of 6.9 and 13.8 MPa of confining stress contributed to 39 and 64% of CO2 sorption capacity reductions, respectively, in comparison to powder coal. Similarly, 85 and 91% CH4 uptake capacity reductions because of 6.9 and 13.8 MPa of confining stress in comparison to powder coal were recorded. Carbon dioxide diffused through the coal at a faster rate than methane, as expected. The initial exposure over a few days showed a rapid reduction in diffusion presumably as the macroand mesopores filled. With longer exposure, 10 additional days, a steady slower diffusion was observed for CO2. The steadystate slower diffusion was achieved within a few days for CH4. It was found that the overall gas movement, specifically diffusion, was hindered by confining stresses and takes place at rates significantly less than in unconfined powder coal. These observations emphasize that it is necessary to use coal samples confined at representative in situ confining stress for reliable evaluation of the sorption capacities and sorption rates. Investigation of sorption and diffusion of gases in coal at in situ stress conditions are limited and should be investigated further across the rank range and with inclusion of other competing processes. The difference in sorption and flow behavior observed from the coal samples at different physical state of stress can best be explained in terms of macro- and micropore and matrix components of the coal. These components are affected differently by the confining stress and the subsequent deformation induced by exposure to gas.
(66) Kelemen, S. R.; Kwiatek, L. M. Physical properties of dry block argonne premium bituninous coal related to CO2, CH4, and N2 adsorption. In Proceedings of the International Coalbed Methane Symposium, University of Alabama, Tuscalosa, AL, 2007.
(67) Soeder, D. The effects of overburden stress on coalbed methane production. In Geology in Coal Resource Utilization; Peters, D. C., Ed.; American Association of Petroleum Geologists, Energy Minerals Division: Fairfax, VA, 1991; pp 125-135.
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Equally significant, it also suggests that the connectivity of the microstructures of the coal and the continuity of the pore network that is influenced by the minerals distribution will play a significant role on the overall gas sorption and are likely to contribute significantly to the flow of gas through coal during sequestration or methane production. Not accounting for decreasing CO2 storage potential and permeability reduction at increasing depth, temperature, moisture content, and the presence of methane and other gases existing in unmineable coal seams are erroneous. Future work should focus on
these issues, better quantifying the capacity of whole coals under stress, and the interplay of the competing processes to enable meaningful predictions. Acknowledgment. We thank Glenn Stracher and Jim Hower for coal collection, Gary Mitchell for providing petrographic analysis, and Ron Wasco for the proximate and ultimate analyses. We appreciate the constructive comments and suggestions from the reviewers. We are thankful to James Howard who reviewed the manuscript before final submission.
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