ARTICLE pubs.acs.org/EF
Solvent Swelling Extent of Permian-Aged Vitrinite- and Inertinite-Rich Coals: Experiments and Modeling Using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) Daniel Van Niekerk,*,† Fidel Castro-Marcano,†,‡ Coray M. Colina,‡ and Jonathan P. Mathews*,† †
John and Willie Leone Department of Energy & Mineral Engineering, The EMS Energy Institute, The Pennsylvania State University, Hosler Building, University Park, Pennsylvania 16802, United States ‡ Department of Materials Science and Engineering, The Pennsylvania State University, Steidle Building, University Park, Pennsylvania 16802, United States ABSTRACT: The perturbed-chain statistical associating fluid theory (PC-SAFT) was used to predict the solvent swelling extent of vitrinite- and inertinite-rich coals. These two maceral different coals yet similar in rank and carbon content were modeled as a mixture of pseudo-components according to molecular-weight fractions (obtained from laser desorptionionization time-of-flight mass spectrometry). The pure-component parameters for the solvents used for solvent swelling (pyridine, N-methylpyrrolidone, and the binary mixture of carbon disulfide and N-methylpyrrolidone) were determined by simultaneous fitting to experimental vapor pressure and liquid density data. The predicted swelling trends obtained from the PC-SAFT were comparable to experimental swelling extents. This approach may be a promising tool for solventcoal interaction predictions.
’ INTRODUCTION Bituminous coal is a three-dimensional macromolecular network structure consisting of polyaromatic and alkyl-substituted aromatic units linked by covalent and noncovalent bonds (hydrogen bonds, van der Waals interactions, electrostatic interactions, and ππ interactions).13 It is generally accepted that the structure of bituminous coal is similar to that of glassy polymers, because of its behavior in solvents. Bituminous coals exhibit swelling when exposed to solvents, resulting in a glassrubber transition (viscoelastic character).46 An effective method to model rubbery polymeric systems is the statistical associating fluid theory (SAFT). The SAFT equation of state (EoS) has been broadly used to describe the thermodynamic properties and phase equilibria behavior of a variety of highly asymmetric and associating mixtures.7,8 This approach was developed by Chapman et al.9,10 and is based on the thermodynamic perturbation theory of Wertheim11,12 to describe both associating fluids and long-chain molecules (including polymers). The general basis underlying SAFT is that the residual Helmholtz energy is given by a sum (a perturbation method) of different terms: (1) the repulsiondispersion term to account for the van der Waals interactions, (2) the chain term to consider the chain formation through covalent bonding, and (3) the association term to take into account associating interactions (e.g., hydrogen bonding between molecules). Polar interactions can also be taken into account by including an additional polar term. An example of the process to form chains and the subsequent association of these chains from a pure component in SAFT is shown in Figure 1. Initially, a reference fluid consists of identical “beads” (e.g., hard spheres) interacting through repulsion forces. In the first step, intermolecular dispersion forces are taken into account. Bonding sites are then simulated in such a manner that the beads r 2011 American Chemical Society
can be linked together through covalent bonds to form chains. Finally, associating sites are introduced into the chain such that two chains may associate through specific interactions, such as hydrogen bonding and polar interactions. Each of these steps provides a contribution to the residual Helmholtz energy. One of the most widely used versions of the SAFT approach is the perturbed-chain SAFT (PC-SAFT) model by Gross and Sadowski.13,14 In the original version of SAFT, the adopted reference fluid is the hard-sphere fluid, while in PC-SAFT, the reference fluid used is the hard-chain fluid. The methodology and applications of SAFT EoS were reviewed by Muller et al.,8 Economou,15 and Tan et al.,7 among others. SAFT has been used to model various fossil fuel hydrocarbon systems, e.g., crude oil, petroleum fluids, and asphaltenes.1622 Asphaltene phase behavior (precipitation, stability, etc.) has been modeled under a wide range of conditions extensively using SAFT.1618 Joule Thomson curves relevant in petroleum and gas reservoirs at extremely high pressures and temperatures have also been modeled using the SAFT approach.23 SAFTliquid crystal (LC) EoS have been developed and used to predict mesophase formation of carbonaceous oligomeric pitches over a range of conditions.24 PC-SAFT has also been used to calculate the Hildebrand solubility parameter of n-alkanes and 1-alcohols over a wide range of conditions (temperature and pressure).25 The extractive binary solvent N-methyl-2-pyrrolidone and carbon disulfide was investigated using PC-SAFT.26 Despite several applications of SAFT to fossil fuels and related systems, it has yet to be applied to coal. Received: January 26, 2011 Revised: May 4, 2011 Published: May 06, 2011 2559
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The goal of this paper was to evaluate PC-SAFT EoS as a modeling tool to predict the solvent swelling extent in a bituminous coal. Here, coal was modeled as a polydisperse polymer; therefore, its parameters were obtained by regressing experimental binary mixture data as proposed by Gross and Sadowski.13,14 Coal macromolecules were assumed to be chains of identical spheres, with the number of spheres in the chain being proportional to the molecular weight. Experimental solvent swelling data were compared to PC-SAFT results for several solvents.
’ EXPERIMENTAL SECTION Coal Samples. Run-of-mine inertinite-rich Highveld coal and commercial density separated vitrinite-rich Waterberg coal were collected in South Africa. The coal samples were demineralized to reduce the mineral matter for pack-bed solvent swelling. The demineralization method is described elsewhere.27 The maceral composition, elemental, and proximate analyses were determined and are summarized in Table 1. Waterberg coal is vitrinite-rich (92%), and Highveld is inertinite-rich (88%). Both coals were high-volatile bituminous rank according to vitrinite reflectance (0.75% for Waterberg and 0.71% for Highveld). The two coals were similar in rank and carbon content yet very different in maceral composition. Previous work found that these coals, although different in maceral composition, H/C ratio, aromaticity, and depositional basin, are similar in their base structural composition.27,28 Pack-Bed Solvent Swelling. The traditional approach was used for pack-bed swelling.29,30 Dried, demineralized coal samples (0.03 g of
200 mesh) were placed in a nuclear magnetic resonance (NMR) spectroscopy sample tube (8 mm diameter) and centrifuged at 3000 rpm for 10 min. The height of coal was measured, and the solvent (10 times the amount by volume) was added and mixed. The sample was left for 24 h and then again centrifuged, and the height was recorded. The swelling ratio (Q) of the coals was determined using eq 1. Q ¼
ð1Þ
A value of Q = 1.00 corresponds to zero swelling, and a value of Q = 2.00 corresponds to swelling of 100%. The solvents used were methanol, pyridine, N-methylpyrrolidone (NMP), and a 1:1 ratio of carbon disulfide and N-methylpyrrolidone (CS2/NMP). SAFT Modeling. The description of coal solvent swelling was performed by modeling coal as a polydisperse polymer using PC-SAFT. Previous works have modeled other fossil fuels as mono- and polydisperse pseudo-components.1619 The formation of associating complexes between coal and solvent molecules was modeled through hydrogen bonding. These associating interactions can be explicitly accounted for using the associating term in eq 2. The estimation of the molecular parameters for coal requires specifying the number of associating sites in the coal molecule. It has been recognized that the bituminous coal structure is heterogeneous and consists of a complex mixture of hydrocarbons. Therefore, a polymer repeat unit for coal cannot be defined. It is, however, possible to assume an average unit or segment per associating group for coal as proposed by Painter et al.31 when determining the effect of hydrogen bonds on coal solubility and solvent swelling. They also postulated that the majority of the hydrogen bonds occur because of the presence of hydroxyl groups (OH).31 Therefore, an average unit was defined containing an OH group and assigned three associating sites (two sites for oxygen and one site for hydrogen). With SAFT, associating fluids are treated as chains of covalently bonded spherical segments. Polymeric structures are modeled as chains of identical spheres, in which the number of spheres in the chain is proportional to the molecular weight.13 The PC-SAFT model assumes molecules to be chains formed by m spherical segments of identical diameter σ and characteristic energy ε/k. The residual Helmholtz free energy, aRES, is shown in eq 2 aRES
Figure 1. Schematic representation of the formation of chain molecules and association complexes in SAFT. The reference fluid consists of hard spheres that form chain molecules through covalent bonding. Specific interactions (e.g., polar and hydrogen bonding) between different chains results in association complexes.
final height of coal initial height of coal
ARES ¼ aREF þ aCHAIN þ aDISP þ aASSOC NkT
ð2Þ
where aREF is the contribution of the hard-sphere chain reference system, aCHAIN is the additional Helmholtz energy because of the formation of chains, aDISP is the dispersion contribution, aASSOC is the contribution because of the effect of molecular association, N is the number of molecules, k is the Boltzmann constant, and T is the temperature. The hard-sphere chain reference term is given by 2 3 ! m 4 ξ2 3 3ξ1 ξ2 ξ2 3 REF 5 ¼ ξ0 lnð1 ξ3 Þ þ þ a ð1 ξ3 Þ ξ3 ð1 ξ3 Þ2 ξ0 ξ3 2 ð3Þ with di = σi[1 0.12 exp(3εi/kT)], and where ξn = m = ∑iximi. The chain term is written as (π/6)F∑iximidin,
Table 1. Ultimate, Proximate, and Maceral Analysis for Waterberg and Highveld Coals (%)a coal
C
H
O
N
S
ash
volatile matter
fixed carbon
vitrinite
Waterberg
84.07
6.23
7.61
1.58
1.13
0.83
38.02
61.15
Highveld
83.72
4.53
8.89
1.97
1.99
2.14
27.67
70.19
inertinite
liptinite
91.8
5.8
2.4
11.2
87.7
1.1
a
Elemental data are presented on a dry and mineral-matter-free basis, and proximate analysis data are presented on a dry basis. Maceral composition consists of vitrinite, inertinite, and liptinite. 2560
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Table 2. Molecular Parameters of the PC-SAFT Model for the Systems Studied in This Worka m
σ (Å)
ε/k (K)
εHB/k (K)
kHB
pyridine
2.0352
3.8066
250.65
1890.3
0.189332
NMP carbon disulfide
2.7708 1.7699
3.6871 3.6124
282.81 304.69
2072.4 716.2
0.222645 0.039668
methanol
1.5255
3.2300
188.90
2899.5
0.035176
component
Table 3. Molecular-Weight Fractions of Vitrinite- and Inertinite-Rich Coals Determined from LDTOFMS mass fraction
Highveld coal
2051.3
4.0021
351.91
2443.4
0.000884
Waterberg coal
2327.8
4.0031
352.01
2446.3
0.000893
m, spherical segments; σ, diameter of the spheres; ε/k, interaction energy; εHB/k, association energy; and kHB, volume available for bonding. a
aCHAIN ¼
n
∑ xi ð1 mi Þln giiHS ðσii Þ i¼1
ð4Þ
where gHS ii is the radial distribution function of the hard-sphere fluid. The dispersion contribution to the Helmholtz free energy is given by aDISP ¼ aDISP þ aDISP 1 2
ð5Þ
where aDISP 1
n n εij σij 3 ¼ 2πFI1DISP ðξ3 , mÞ xi xj mi mj kT i¼1 j¼1
aDISP ¼ πFmC1 I2DISP ðξ3 , mÞ 2
∑∑ n
n
∑ ∑ xi xj mi mj i¼1 j¼1
εij kT
ð6Þ
2 σ ij 3
ð7Þ
where εij = (1 kij)(εiεj)1/2 and σij = (σi þ σj)/2 correspond to the interaction energy and the temperature-independent diameter between molecules of types i and j (BerthelotLorentz combining rules), respectively, and kij is the binary interaction parameter. Expressions , and IDISP as well as for the association term and definitions for C1, IDISP 1 2 (aASSOC) can be found in the work by Gross and Sadowski.13,14 As previously mentioned, there are three molecular parameters, m, σ, and ε/k, within the PC-SAFT EoS. In addition to these three parameters, the PC-SAFT model requires two further parameters for associating molecules, the association energy (εHB/k) and the volume available for bonding (kHB). Solvent molecules (pyridine, methanol, NMP, and CS2) used in this study were modeled as associating components with two association sites (often referred to as the 2B model32). The purecomponent parameters for pyridine, NMP, and CS2 were determined by simultaneous fitting to experimental vapor pressure and liquid density data,33 while parameters for methanol were taken from the literature.14 Coal was modeled as a polydisperse polymer; therefore, its molecular parameters were obtained by regressing experimental binary mixture data as proposed by Gross and Sadowski.13,14 Recently, an alternative approach based on FloryHuggins and Hildebrand solubility parameters has been proposed for estimation of PC-SAFT polymer parameters.34 The molecular parameters of the PC-SAFT model for the coal samples and solvents investigated in this study are listed in Table 2. The molecular-weight distribution of the two maceral different coals was modeled as a mixture of pseudo-components according to the algorithm suggested by Tork et al.35 (Table 3). The molecular-weight distributions were obtained from earlier work using laser desorptionionization time-of-flight mass spectrometry (LDTOFMS) data of these two maceral different coals.27 According to LDTOFMS data, both coals has a molecular-weight distribution ranging from m/z 80 to 1700.27
Mw (g/mol)
vitrinite-rich coal
inertinite-rich coal
100
0.02841
0.02222
200
0.06818
0.03407
300 400
0.11553 0.16288
0.07111 0.11852
500
0.16288
0.14370
600
0.13447
0.14370
700
0.09659
0.12148
800
0.06818
0.09333
900
0.04735
0.07407
1000
0.03409
0.05630
1100 1200
0.02273 0.01705
0.04148 0.02370
1300
0.01136
0.01778
1400
0.00947
0.01185
1500
0.00758
0.01037
1600
0.00758
0.00889
1700
0.00568
0.00741
’ RESULTS AND DISCUSSION Solvent swelling was conducted on the two maceral different coals using methanol, pyridine, NMP, and the binary solvent CS2/NMP. Figure 2 shows that the two coals reacted differently to the solvents; the vitrinite-rich coal swelled significantly greater in the solvents than the inertinite-rich coal, as expected. The only exception was for methanol, where both coals exhibited a small swelling extent (Q = 1.2 or 20%). The binary solvent CS2/NMP yielded the greatest swelling extent in both coals (Q = 2.6 or 160% for vitrinite and Q = 1.7 or 70% for inertinite). The inertinite-rich coal had similar Q values for pyridine, NMP, and CS2/NMP (Q = 1.6 or 160% in pyridine, Q = 1.6 or 160% in NMP, and Q = 1.7 or 70% in CS2/NMP). The vitrinite-rich coal had similar Q values for pyridine and NMP (Q = 2.1 or 110% in pyridine and Q = 2.2 or 120% in NMP). These swelling trends were consistent with the literature; vitrinite-rich coal swells to a greater extent than inertinite-rich coal, and binary solvent CS2/ NMP results in the greatest swelling extent.36,37 PC-SAFT calculations were performed using the VLXE Thermodynamic Software38 with the required molecular parameters (Table 2) and a mixture of pseudo-components (Table 3). The kij parameter is typically adjusted to obtain a better description of the experimental mixture data. This parameter accounts for the effect that differences in the dispersion energy of the molecules have on the Helmholtz free energy of the system. However, for associating systems, as investigated in this work, kij parameters are expected to affect slightly on free energy calculations because dispersion forces are not dominant (Figure 3). Thus, all binary interaction parameters between coal and solvent molecules were set to zero. Within the PC-SAFT framework, solvent swelling (Sw) of the coal matrix was determined by Sw = coal coal V0coal)/V0coal, where V0coal and Vswollen are the initial (Vswollen and swollen volume of the coal, respectively. Values for V0coal and Vcoal swollen were calculated from the PC-SAFT EoS. The solvent swelling extent predicted by PC-SAFT was compared to the experimental swelling extent (Figure 2). 2561
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Figure 2. Correlation between experimental solvent swelling and PC-SAFT prediction (note that the scale of the two graphs is different for better comparison and visualization).
Figure 3. Comparison of the different contributions to the residual Helmholtz energy as calculated from PC-SAFT for the (left) vitrinite-rich model and (right) inertinite-rich model with various solvents.
The PC-SAFT results exhibited the same trends as the experimental swelling. PC-SAFT predicted that the vitrinite-rich coal swells to a greater extent than the inertinite-rich coal in accordance with the experimental data. In addition, PC-SAFT also predicted that methanol has the lowest swelling extent and that CS2/NMP has the greatest swelling extent. However, the results obtained from PC-SAFT underestimated the experimental values. Although the trends were captured, PC-SAFT predictions (with kij = 0) were lower than the experimental values (for example, experimentally, the vitrinite-rich coal swelled to Q = 2.6 in CS2/NMP, but PCSAFT predicted a swelling of Q = 1.35). This behavior may be due to contributions from other hydrogen bonds in coal not taken into account in the simplified PC-SAFT calculation (hydrogen bonds from aliphatic and aromatic ethers and NH groups in coal). These groups were neglected in the current implementation (only the coal OH groups were taken into account). It can be seen that the PC-SAFT model is capable of predicting reasonably well the experimental swelling data trend, especially considering that these are very challenging systems. The solvent extraction mechanism of the binary solvent CS2/NMP in bituminous coals has been investigated by various groups.26,3941 Previous studies found that the extent of extraction by CS2/NMP is partially due to the
breaking of hydrogen bonds in the coal structure. CS2 prevents the formation of associated NMP/NMP complexes, thus leading to a high volume of NMP monomers that can penetrate the coal structure and break strong coalcoal interactions, thereby increasing solvent extraction. The mechanism of CS2/NMP in the solvent extraction of coal was elucidated using various experimental techniques (e.g., Fourier transform infrared spectroscopy) and computational methods (density functional theory, molecular dynamics, and PC-SAFT).26,3941 The separate contributions (repulsion, dispersion, chain, and association) to the residual Helmholtz energy from the PCSAFT model were also calculated, and the results are presented in Figure 3. Methanol is not an adequate solvent for coalsolvent swelling and was therefore not included. Calculations were performed for both solvent-swelled coals with pyridine, NMP, and CS2/NMP at 25 °C and 0.0001 GPa. As expected, the major contribution to the residual Helmholtz energy arises from the association term. For both coals, the absolute value of association contribution increased from the original coal via NMP swelled, pyridine swelled, to CS2/NMP swelled. This result is mainly due to the various hydrogen-bond associations in the swelled system: combination of coalcoal 2562
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Energy & Fuels hydrogen bonding, coalsolvent hydrogen bonding, and solvent solvent hydrogen bonding. PC-SAFT predicted that the original coals exhibit a larger residual Helmholtz energy value than the corresponding swelled coals, in agreement with experimental results obtained by Larsen et al.,42 where coal swelling was demonstrated to enable structural rearrangements to a lower free-energy configuration.
’ CONCLUSION SAFT modeling was explored to test whether this method could predict the swelling extent using current data. The PCSAFT results exhibited the same trends as the experimental swelling; vitrinite-rich coal swelled to a greater extent than the inertinite-rich coal. In addition, PC-SAFT also predicted that methanol has the lowest swelling extent and that CS2/NMP has the greatest swelling extent. Although the swelling trends were the same, PC-SAFT predictions were lower than the experimental values. Therefore, PC-SAFT seems to be a promising tool for solventcoal interaction predictions. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (D.V.);
[email protected] (J.P.M.).
’ ACKNOWLEDGMENT CMC and FCM acknowledge the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research (grant number 48570-AC7). ’ REFERENCES (1) Larsen, J. W.; Green, T. K.; Kovac, J. The nature of the macromolecular network structure of bituminous coals. J. Org. Chem. 1985, 50, 4729–4735. (2) Painter, C. P.; Graf, J.; Coleman, M. M. Coal solubility and swelling. 3. A model for coal swelling. Energy Fuels 1990, 4, 393–397. (3) van Krevelen, D. W. Coal: Typology, Chemistry, Physics, Constitution, 3rd ed.; Elsevier Science: Amsterdam, The Netherlands, 1993. (4) Cody, G. D.; Davis, A.; Hatcher, P. G. Physical structural characterization of bituminous coals: Stressstrain analysis in the pyridine-dilated state. Energy Fuels 1993, 7, 455–462. (5) Gao, H.; Nomura, M.; Murata, S.; Artok, L. Statistical distribution characterization of pyridine transport in coal particles and a series of new phenomenological models for overshoot and nonovershoot solvent swelling of coal particles. Energy Fuels 1999, 13, 518–528. (6) Ndaji, F. E.; Thomas, K. M. The kinetics of coal solvent swelling using pyridine as solvent. Fuel 1993, 72, 1525–1530. (7) Tan, S. P.; Adidharma, H.; Radosz, M. Recent advances and applications of statistical associating fluid theory. Ind. Eng. Chem. Res. 2008, 47, 8063–8082. (8) Muller, E. A.; Gubbins, K. E. Molecular-based equations of state for associating fluids: A review of SAFT and related approaches. Ind. Eng. Chem. Res. 2001, 40, 2193–2211. (9) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. SAFT equation-of-state solution model for associating fluids. Fluid Phase Equilib. 1989, 52, 31–38. (10) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. New reference equation of state for associating liquids. Ind. Eng. Chem. Res. 1990, 29, 1709–1721. (11) Wertheim, M. S. Fluids of dimerizing hard-spheres and fluid mixtures of hard-spheres and dispheres. J. Chem. Phys. 1986, 85, 2929–2936.
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