Full Paper Volumetric Effects in Coal Sorption Capacity Measurements By Vyacheslav Romanov*, Yee Soong, and Karl Schroeder DOI: 10.1002/ceat.200500242 Many types of materials e.g., rubber, polymer, coal, change their volume and structure after absorption of gaseous and liquid substances. Various kinds of volume changes affect the accuracy of absorption measurements by gravimetric and manometric methods, the two major techniques currently employed. The errors associated with the volumetric effects, specifically, the case of carbon dioxide sorption on coal, were investigated. It was demonstrated that the resulting error in the buoyancy correction in the gravimetric method is equivalent to the corresponding error in the assumed void volume in the manometric method. It is suggested that the integration of the two methods, combined with the binary gas mixture technique of in-situ volume measurement, will contribute to dramatically improve the accuracy of absorption measurements for plastic materials. 1 Introduction Sequestration of CO2 in deep unmineable coal seams has been identified as one of the technologically feasible options to reduce atmospheric carbon dioxide emissions. However, there is a fundamental lack of understanding of the physical, chemical, and thermodynamic phenomena that occur when CO2 is injected into a coal seam [1]. Being able to reliably predict carbon dioxide injectivity is an important prerequisite to large-scale project investment. High precision sorption data are required to accurately forecast the performance of such projects. There are two main methods currently employed for measuring adsorption isotherms on coal: the manometric and the gravimetric technique. A manometric apparatus consists of a cell containing the coal sample, a system for controlled admission of the adsorbate gas, and manometers. As the gas is adsorbed, the pressure in the sample cell decreases. The quantity of the gas is determined by the void volume within the cell and the density of the gas that is estimated by using an equation of state (EOS) or the tables of compressibility factors (z). The uncertainty in adsorbate compressibility value complicates the analysis of the experimental data, especially, for real gas mixtures or gases near the critical point. In gravimetric systems, the adsorbed amount is measured by a microbalance. Before the adsorption isotherm procedure, the sample volume is measured with a helium pycnometer to determine the buoyancy. By direct gravimetric gas density measurements, the problems associated with the equation of state are eliminated but the implicit assumption that the sample volume remains constant seems absolutely unwarranted for many types of materials (rubber, polymer, coal, etc.). Similarly, the manometric method relies on assumptions about the errors associated with the sample – [*] 368 V. Romanov (author to whom correspondence should be addressed, Romanov@or.netl.doe.gov), Y. Soong, K. Schroeder, U.S. Department of Energy – National Energy Technology Laboratory, Pittsburgh, P.O. Box 10940, Pennsylvania 15236-0940, USA. volume changes. In fact, this is the key problem of these methods [2]. In either gravimetric or manometric apparatus, swelling of the coal sample and the corresponding volume changes cannot be directly measured during the test. A recent interlaboratory comparison of CO2 isotherms measured on Argonne Premium Coal samples showed very large divergence in the experimental results [3]. In order to better understand the variability of experimental observations, the assumptions behind the main test methods will be analyzed: – Sorption of CO2 on coal reduces the gas pressure and increases the mass of the coal sample. – Sample mass changes are measured by the gravimetric isotherm method. – Pressure changes are used in a volumetric isotherm method to derive the corresponding changes in gaseous mass. – Compressibility values are tabulated (equation of state) and/or measured directly. – Traditional methods assume homogeneous properties of the sorbate and constant volume of the sample and usually are limited to single gas sorption. Coal is known to swell in the presence of CO2 and this may be significant with respect to interpreting experimental data. Until recently, very limited investigations have been conducted on the adsorption of CO2 on coal beyond the critical point. At pressures above the critical point, the measured data deviate strongly from the Langmuir model of monolayer-type filling of micropores, in both manometric and gravimetric systems. The manometric approach often results in bimodal behavior observed in the vicinity of the critical point, with an apparent local minimum (sometimes even negative, especially for moisture-equilibrated coals [4, 5]) around 7–9 MPa, followed by an abrupt rise in the amount of absorbed CO2. This was interpreted as a swelling effect caused by supercritical CO2 and enhanced by water. The gravimetric results [6] also confirm that absorption by coal under supercritical conditions is in excess of what is predicted using the Langmuir adsorption isotherms based on adsorption at lower pressures, indicating that a greater amount of carbon dioxide can be sequestered by coal than © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eng. Technol. 2006, 29, No. 3 Full Paper previously estimated. However, density-gravimetric measurements reportedly show no evidence of peculiar changes in adsorption with pressure observed in volumetric systems at ∼ 8 MPa. Microbalance (gravimetric) measurements as well as manometric (volumetric) measurements of the gas (fluid) sorption equilibrium only allow the excess (apparent) mass, Dam, to be determined, that is the difference of the mass adsorbed on a porous solid, Dgm, and the product of the buoyancy related volume, VS, of the sorbent/sorbate system and the density of the sorbate. While this can be seen directly from the formula for excess sorption calculation in the gravimetric method (Eq. (1))1), m

g nex ˆ
a m
g m q
Vs ˆ l l 1† where Dgnex is the excess sorption, m is the mass of the sample, q is the average fluid density, l is the molar mass of the sorbate, it will be shown that the manometric method measures the same physical property, barring the physical changes other than due to the sample-sorbate interaction. The combination of the volumetric and gravimetric techniques, on the other hand, utilizes the advantages of both and gives a very accurate direct method of adsorption measurement [7]. 2 Theory – Interlaboratory comparison [3] has demonstrated a wide variability of the data for the same coal observed for the CO2 pressures about the critical point. The Langmuir model is questioned in the supercritical region, due to coal swelling [2]. – The Palmer-Mansoori equation does not match historical data [9]. – Coal swelling/shrinkage is treated within a rock mechanics model, ignoring the polymer-like behavior. If the pressure, temperature, temporal, etc., conditions are reproduced, the excess sorption isotherms should be the same, regardless of the technique (gravimetric or volumetric) employed, as long as the volume is determined by the same gas. It turns out that VS can depend on the adsorptive gas mixture [7]. Various types of hidden volumes are depicted in Fig. 1. It should be noted that the accessible pore volume is not directly associated with the apparent dimensions of the sample. Should the volume V be inaccessible to helium, for instance, but become partly permeable to CO2, then it is treated as the envelope volume of the sample in either adsorption measurement method. Any amount of CO2 making its way to this volume is missing from the void volume in the manometric/volumetric method and is erroneously attributed to excess adsorption. By the same amount the gravimetric buoyancy is overcorrected and is still attributed to excess adsorption. Vice versa, if this volume is accessible to helium but not to CO2, then the difference between the adsorbate density inside of it and the quasiequilibrium density in the void volume of the sample cell results in equal understatement of the excess adsorption in both methods. Conventional theoretical models used for analysis of sorption isotherms are the Langmuir theory and the PalmerMansoori equation [8]. – Langmuir equation: V = V∞ · Ka · Pe/(1 + Ka · Pe) (2) where Pe is the equilibrium pressure, Ka is the absorption equilibrium constant (1/Ka is the Langmuir pressure), V∞ is the CO2 sorption capacity (Langmuir volume), and V is the equilibrium volume of adsorbed gas. – The Palmer-Mansoori model relates matrix shrinkage to porosity and uses elastic moduli to describe the effect of changing pressure on the coal volume. The problems arising with supercritical carbon dioxide injection are: – The volume of the coal sample is measured only before and/or after the test. During the test it is an unknown variable and is assumed to fit a certain model behavior. – 1) List of symbols at the end of the paper. Chem. Eng. Technol. 2006, 29, No. 3 Figure 1. Illustration of the open and closed voids in the coal network. This can be shown precisely by the mathematical equations for volumetric (see schematic diagram shown in Fig. 2) and gravimetric methods. The excess sorption, Dvnex, on the sample of mass, m, is calculated in the manometric method (sorption isotherm at temperature T) as a difference between the CO2 molar amount decrease in a reference cell (volume VR) and the molar amount increase in the void volume of a sample cell (volume Vo), according to Eq. (2). Compressibility z can be estimated from the equation of state. The underlying assumption is that the void volume before and after CO2 injection is the same. Similarly, the buoyancy correction in the gravimetric method relies on the assumption that the envelope volume of the sample does not change (Eq. (1)). Eq. (3) shows that the errors in excess © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com 369 Full Paper sorption determination by volumetric and gravimetric techniques caused by the uncertainty of the sample volume are identical. m

v nex ˆ PRi zRi PRf zRf !
VR RT 0 B PS B f B @ zSf |{z} error 1 PSi C C Vo C
zSi A RT ! PSf PSf PSv q

Vs V ˆ

Vs 
o l RT zSv RT
zSf zSf |‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚{z‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚‚} 3† 4†
Vs 
Vo where the subscripts Ri and Rf refer to the initial and final (equilibrium) conditions of the reference cell and Si and Sf to the sample cell respectively, while Sv represents a virtual state of no volume change with the same amount sorbed as in the final state of equilibrium; DVS is the change in buoyancy associated volume, VS, and DVo is the change in the void volume, Vo. The error in Eq. (2) is due to the fact that the pressure and density of the “free” (nonsorbed) fluid in the equilibrium state are different from their respective values in the virtual state, Sv, because the same number of sorbate molecules occupies a different void volume, Vo. The transformation in Eq. (3) follows from the EOS and the assumption that both VS and Vo change primarily due to the changes in the envelop volume of the sample. 3 Experimental Sorption and desorption behavior of carbon dioxide has been studied on a set of well-characterized coals from the Argonne Premium Coal (Argonne National Laboratory, USA): a low volatile bituminous (Pocahontas #3), a high volatile bituminous (Illinois #6), and a lignite (Beulah Zap) coal. All sorption experiments were performed on approximately 0.5–2.5 g of the powdered (100 mesh), dried (in vacuum, at 130 °C for 24 h) and moisture equilibrated (at 96 % relative humidity and 55 °C for 48 h) coal samples. The modified version of the ASTM moisture equilibration procedure D 1412–99 (55 °C instead of 30 °C) was adopted for all moist coal tests: the lignite sample that usually requires 72 hours to reach equilibrium was also equilibrated for 48 hours. This procedure was recommended in order to reproduce the moisture content under the reservoir conditions [10]. The sample handling was performed in a positive pressure (dry nitrogen) glove bag to prevent surface oxidation. The NETL-built [2] high-pressure manometric/volumetric apparatus (see Fig. 2) was used to collect the CO2 (99.999 % purity, Valley Co., Pittsburgh, PA, USA) adsorption isotherm data at 55 °C (± 0.1 °C) and the pressures up to 16 MPa. Gases were pressurized by the ISCO syringe pump 370 http://www.cet-journal.com Figure 2. Schematic diagram of the manometric/volumetric apparatus: R = reference cell, S = sample cell, B = constant temperature bath, T = thermocouple, P = pressure transducer, V = mechanical vacuum pump, G = gas regulator, D = data logger. (Model 500D). The sample and cells volume determination was done with helium (99.997 % purity, Valley Co., Pittsburgh, PA, USA). Evacuation of the gas line and the reference and sample cells was done by the HayVac-2 (HayVac Products Co.) mechanical vacuum pump. Temperature was stabilized by the constant temperature bath from NesLab (Model RTE-111). Additionally, the gravimetric adsorption isotherm measurements for the dry Pocahontas #3 sample under the same conditions have been done with a magnetic suspension balance of the Rubotherm GmbH at the Leipzig University, Germany. The excess (or Gibbs) absorption was used to interpret the observations made, because at high pressures, where the density of the supercritical fluid approaches the density of the adsorbed phase, it is more appropriate than the absolute adsorption [11, 12]. 4 Results and Discussion The gravimetric measurements gave a surprising result: negative adsorption values at the pressures above 10 MPa (see Fig. 3). This was explained by the estimated 45 % swelling of the coal sample (Argonne Premium Pocahontas #3 coal powder) during the test, which resulted in an erroneous buoyancy term based on the He volume measurements prior to the test. The new volume that was determined immediately after the CO2 adsorption measurements showed some residual swelling (∼ 20 %). After correction, the excess adsorption plot strongly deviates from the Langmuir model at pressures above 8 MPa. Obviously, the above buoyancy corrections are very tentative since the volume measurements were done only before and after the test, rather than during the test. This is a common problem of pure gravimetric and pure volumetric techniques. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eng. Technol. 2006, 29, No. 3 Full Paper Figure 3. Gravimetric vs. volumetric data. After the volume correction (based on the “after-the-test” residual volume), the gravimetric isotherm is similar to the volumetric data. Gravimetric-1 is based on the volume measured before the test. Gravimetric-2 is based on the corrected volume. The above gravimetric data were compared to the results of the volumetric measurements (see Fig. 3) for the powdered sample of the same Argonne Premium Coal (Pocahontas #3). The volumetric adsorption plots exhibit a typical mesoporous adsorbent behavior [13], similar to the corrected gravimetric data, except for a minor dip at the onset of the supercritical CO2 pressures, at around 7–9 MPa. Desorption of CO2 was done in a three-step catastrophic expansion mode (into vacuum), similar to the comminution process. After each step, the pressure was stabilized for an hour before the data were collected. The sample volume measured after desorption was ∼ 6 % smaller than the original volume, which is usually interpreted as shrinkage due to extraction of the volatile matter. The apparent sorption capacity of the coal has increased dramatically in the above procedure, which could also be attributed to either accessible surface area increase or the void volume increase or both, since the breaking of the coal particles into smaller pieces may decrease the “dead” (envelope) volume of the sample and thus increase the accessible surface area. Repeated adsorption measurements confirmed the correlation between the temporal sample volume changes and adsorption capacity, especially for the CO2 pressures less than 8 MPa (see Fig. 4). The second and third adsorption isotherms were run immediately after the first desorption and were consistent with the first desorption data. The fourth adsorption experiment was run six weeks later, when the envelope volume of the sample measured by helium pycnometry almost relaxed to its original value. It caused the gas phase excess adsorption return to the original values as well. However, the subsequent injection of supercritical CO2 caused the adsorption trend to break off from the original plot (first adsorption) half way to the post-comminution isotherms. It is suggested that after six weeks the structural relaxation of coal was still incomplete. Partial restoration of the hydrogen-bond cross-links that contribute to elastic forces opposing the swelling of coal was sufficient to prevent carbon diChem. Eng. Technol. 2006, 29, No. 3 Figure 4. Effects of coal volume changes on sorption capacity. After the first (catastrophic) desorption, the envelop volume decreased by 5.6 % and the sorption capacity increased by 50 to 150 %. Six weeks later (fourth absorption), the coal properties partly returned to the original values. oxide molecules from reaching the excess adsorption sites. However, the supercritical carbon dioxide fluid is capable of reaching some of the hidden adsorption sites by exerting additional osmotic pressure due to a thermodynamically nonequilibrium condition inherent in the injection process around the critical pressures. This can also increase the pores interconnectivity and void volume. For the volumetric study of the effects of moisture on adsorption capacity, three types of Argonne Premium Coal powders representing a wide range of carbon content and corresponding degrees of hydrophobicity were selected (see Tab. 1). An additional small sample of Pocahontas #3 was used to validate the method by distinguishing between the sample-specific and the instrument-specific effects. Unlike the previous study, the bath temperature oscillated between 54 °C and 56 °C with a period of one hour. Table 1. Volume changes of the moisture equilibrated Argonne Premium Coal samples. Pocahontas #3 Pocahontas #3 (small) Illinois #6 Beulah Zap Mass 473 mg 2.197 g 2.164 g 2.615 g H2O – 2 wt % 4 wt % 20 wt % Shrink – < 1 vol.-% 6 vol.-% 2 vol.-% Desorption of the Illinois #6 sample was conducted by the three-step catastrophic expansion, but the Pocahontas #3 and Beulah Zap samples were brought to zero CO2 pressure by more gradual decompression. The resulting changes in the envelope volume are consistent with the nonequilibrium excessive surface area hypothesis. The moisture level does not seem to have any significant effect on the volume changes, but it does affect the sorption capacity to the gas phase CO2 (see Fig. 5). © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com 371 Full Paper Figure 5. Gas phase CO2 sorption on moisture equilibrated coals. The only coal that showed a dip near the critical pressure was Pocahontas #3 (both samples). This dip was more significant than the one previously observed for dry Pocahontas #3 at nearly constant bath temperature (see Fig. 6). At the same time, the following rise in the excess adsorption after transition to the supercritical phase was also much steeper during the test with the larger bath temperature swings. This is another indication of the nonequilibrium nature of the adsorption process. Figure 7. Development of the volume-gravimetric technique. the sample can be computed by the standard volumetric procedure. Since the sampled pressure and density have to be representative of the entire void volume, the volume-gravimetric apparatus inevitably requires a static mixer incorporated into the gas lines of the traditional volumetric apparatus (see Fig. 8). The mass measurements have to be done during shut-off periods of the mixer to avoid buoyancy errors related to the flow of the CO2/He mixture. Figure 8. Schematic diagram of the volume-gravimetric apparatus. The reference and the sample cells should be separated by 0.5 m to minimize magnetic interference. The mixer is required for homogeneous mixing of the fluids. Figure 6. Anomalous sorption behavior of the Pocahontas #3 coal powder near the critical pressure: A/C = absorption/desorption isotherms, B = sorption under the oscillating temperature conditions. The “dip” and rise become more prominent as the temperature oscillations increase. In order to eliminate this error, the volume changes need to be continuously monitored during the test. This can be done by combining the two techniques into the volumegravimetric method and using a binary gas mixture of CO2 and helium (see Fig. 7). By using the simultaneous pressure and density measurements one can determine the partial pressures of the two components as long as their molar masses are very different [14]. Once the helium pressure is known, the void volume and hence the envelope volume of 372 http://www.cet-journal.com The common issue of the volumetric techniques is the need for a very accurate EOS application to analysis of the experimental data. This becomes a problem if the physical properties of the adsorbate are not uniform or far from the equilibrium state. It is suggested that the samples with significantly differing masses be used to calibrate the method. In the experiments with oscillating temperature, the excess adsorption isotherms of the typical (2.197 g) and small (473 mg) samples were compared to filter out the signal contribution that was not proportional to the sample size. The corresponding equation of state was compared to Span and Wagner [15] EOS (see Fig. 9). © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eng. Technol. 2006, 29, No. 3 Full Paper the Langmuir-type behavior (without hysteresis) can be observed at very high CO2 pressures [3]. 5 Summary Coal swelling becomes a major factor at supercritical CO2 conditions. Various types of accessible volume changes affect the accuracy of absorption measurements by gravimetric and manometric (volumetric) methods. The resulting error is invariant of the test method and is not directly related to apparent changes in the sample dimensions. Swelling kinetics can be quantified experimentally by the volumegravimetric technique. Acknowledgements Figure 9. Experimentally determined effective equations of state corresponding to uneven size sample calibration of the system with oscillating temperature: dashed line; Span and Wagner EOS: 55 °C (circles) and 56 °C (solid line). A possible explanation of the observed deviation from the equilibrium EOS is that, at pressures above 10 MPa, the lower temperature entropic equilibrium (for simplicity, it is called “condensation”) is reached slower than at higher temperatures (“evaporation”), resulting in effective compressibility values slightly higher than expected. Application of the effective EOS to Illinois #6 and Beulah Zap isotherms was not successful, which may indicate that the sample properties such as heat capacity, swelling, etc., are important as well. The corrected absorption isotherm for Pocahontas #3 is very similar to the corrected gravimetric isotherm for the same coal powder (see Fig. 10), which confirms that the supercritical CO2 region strongly deviates from the Langmuir-type isotherm. Still, some research groups report that Figure 10. Volume-corrected gravimetric and temperature-corrected volumetric data versus Langmuir-type (enhanced form) isotherm [12], Volumetric-2. Chem. Eng. Technol. 2006, 29, No. 3 The authors thank Dr.-Ing. Frieder Dreisbach (Rubotherm GmbH, Germany) for providing the interpretation of the gravimetric data. Thanks are given to Dr. Curt White (NETL) and Dr. Angela Goodman (NETL) for discussion of advantages and disadvantages of the volumetric and gravimetric techniques and the volume-gravimetric method. Received: July 19, 2005 Symbols used Ka m Pe PRf PRi PSf PSi Ru T V Vo VR VS V∞ z zRf [Pa–1] [kg] [Pa] [Pa] [Pa] [Pa] [Pa] [J/(mol·K)] [K] [m3] [m3] [m3] [m3] [m3] [–] [–] zRi [–] zSf [–] zSi [–] Dam [kg] Dgm [kg] Dg nex [mol/kg] absorption equilibrium constant mass of the sample equilibrium pressure final pressure in reference cell initial pressure in reference cell final pressure in sample cell initial pressure in sample cell universal gas constant temperature pore volume void volume of sample cell void volume of reference cell volume of the sample (inaccessible) Langmuir volume (sorption capacity) gas compressibility gas compressibility in reference cell, final gas compressibility in reference cell, initial gas compressibility in sample cell, final gas compressibility in sample cell, initial excess (apparent) mass of adsorbed molecules actual mass of adsorbed molecules excess sorption (gravimetric) © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com 373 Full Paper Dv nex [mol/kg] l [kg/mol] q [kg·m–3] excess sorption (volumetric) molecular weight average fluid density References [1] [2] [3] [4] [5] [6] C. M. White, in Proc. of the Int. ECBM/Sequestration Consortium (Coal-Seq II), Washington, DC, March 2003. E. Ozdemir, B. I. Morsi, K. Schroeder, Langmuir 2003, 19, 9764. A. L. Goodman et al., Energy Fuels 2004, 18, 1175. B. Krooss et al., Int. J. Coal Geology 2002, 51, 69. M. M. Toribio, Y. Oshima, S. Shimada, in Proc. of the 7th Int. Conf. Greenhouse Gas Control Technologies, Vancouver, Canada, September 2004. S. J. Day, G. J. Duffy, A. Saghafi, R. Sakurovs, in Proc. of the 7th Int. Conf. Greenhouse Gas Control Technologies, Vancouver, Canada, September 2004. [7] M. Tomalla, R. Staudt, J. U. Keller, in Microbalance Techniques (Eds: J. U. Keller, E. Robens) Multi-Science Publishing, Brentwood 1994. [8] I. Palmer, J. 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R. Clarkson, R. M. Bustin, J. H. Levy, Carbon 1997, 35, 1689. ______________________ 374 http://www.cet-journal.com © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eng. Technol. 2006, 29, No. 3