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Energy & Fuels 2009, 23, 342–348
An Improved Three-Dimensional Microscope Image Analysis Method for Studying Solvent Swelling of Single Coal Particles Hong Gao,*,† Jicheng He,‡ Jiuju Cai,‡ Masahiro Ishigaki,§ and Masakatsu Nomura⊥ Department of Thermal Energy and Power Engineering, Vehicle and Energy College, Yanshan UniVersity, 438 West Hebei AVenue, Qinhuangdao, Hebei, 066004, China, Department of Thermal Energy Engineering, Northeastern UniVersity, 11-Alley 3, Wenhua Road, Heping District, Shenyang, Liaoning, 110004, China, Center for Interdisciplinary Research, Tohoku UniVersity, 2-2-1 Aramaki, Aoba-ku, Sendai 980-77, Japan, and Department of Applied Chemistry, Faculty of Engineering, Osaka UniVersity, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan ReceiVed August 6, 2008. ReVised Manuscript ReceiVed October 14, 2008
An improved three-dimensional microscope video camera system coupled with an image system and a quantitative method was developed to observe and evaluate dynamic swelling behavior of coal particles, and to study kinetics of solvent diffusion in coal particles. The proposed system and method were proved to be more effective, more compact, and more economical than the previous proposed orthogonal microscope system. The new system can finally solve the problem of a one-microscope system and an orthogonal two-microscope system caused by orientation of the anisotropic swelling of coal particles with respect to some known frames of reference not being measured. Using the proposed system and quantitative method, it is possible to obtain the solvent swelling data and kinetics data more accurately. Moreover, the proposed system can be used in dynamically observing and evaluating solvent swelling and diffusion kinetics of any samples with an anisotropic feature, three-dimensionally.
Introduction Coal is a complex and heterogeneous material. However, it appears to have been accepted that coal consists of alkyl chainsubstituted aromatic and hydroaromatic units linked by covalent bonds and noncovalent bonds with entanglements of skeletal chain structure to form a three-dimensional network structure.1 In addition, coal is viscoelastic and partially dissolves in and swells when exposed to some kinds of solvents. The extent of swelling is thought to be controlled by the cross-link density and the magnitude of interaction of coal macromolecules with the solvent.2 An understanding of the knowledge about the nature and density of cross-links is important for effective utilization of coal resources. In general, cross-link density is evaluated in terms of volumetric swelling ratio (Qv), defined simply as the swollen sample volume divided by the unswollen sample volume. Four kinds of measurement methods have been adopted in evaluating coal swelling: (1) volumetric measurement based on a packed bed,3-5 (2) gravimetric measurement using solvent sorption from the vapor phase,6 (3) Malvern laser diffraction method based * To whom correspondence should be addressed. E-mail: gao_hong_05@ yahoo.com.cn. † Yanshan University. ‡ Northeastern University. § Tohoku University. ⊥ Osaka University. (1) Van Krevelen, D. W. Coal; Elsevier: New York, 1994. (2) Mastral, A. N.; Izquierdo, M. T.; Rubio, B. Fuel 1990, 69, 892. (3) Liotta, R.; Brons, G.; Isaacs, J. Fuel 1983, 62, 781. (4) Larsen, J. W.; Green, T. K. Fuel 1984, 63, 1538. (5) Ndaji, F. E.; Thomas, K. M. Fuel 1993, 72, 1525. (6) Hsieh, S. T.; Duda, J. L. Fuel 1987, 66, 170.
on the measurement of particle size distribution,7,8 (4) a microscopic observation coupled with image analysis.9-14 Gao et al.15-17 proposed a novel orthogonal microscopic video camera image analysis method to measure dynamical volumetric solvent-swelling of single coal particles from two orthogonal directions. However, the method is not three-dimensional and leads to a partial loss of information from one direction of the particles; therefore, it is important to advance this new method and finally solve the problem incurred with the one-microscope method and the orthogonal two-microscope method. In this study, an improved three-dimensional microscopic video camera image analysis system and quantitative method were developed to dynamically observe and quantitatively evaluate solvent swelling and the solvent diffusion mechanism in two kinds of Chinese coal particles. The experimental results indicate that the solvent-swelling behavior and characteristics
(7) Turpin, M.; Rand, B.; Ellis, B. Fuel 1996, 75, 107. (8) Milligan, J. B.; Thomas, K. M.; Crelling, J. C. Energy Fuels 1997, 11, 364. (9) Shibaoka, M.; Stephens, J. F.; Russell, N. J. Fuel 1979, 58, 515. (10) Brenner, D. Fuel 1984, 63, 1324. (11) Brenner, D. Fuel 1985, 64, 167. (12) Cody, G. D.; Larsen, J. W.; Siskin, M. Energy Fuels 1988, 2, 340. (13) Gao, H.; Nomura, M.; Murata, S. Prepr. Pap.-Am. Chem. Soc., DiV. Fuel Chem. 1997, 298. (14) French, D. C.; Dieckman, S. L.; Botto, R. E. Energy Fuels 1993, 7, 90. (15) Gao, H.; Artok, L.; Kidena, K.; Murata, S.; Miura, M.; Nomura, M. Energy Fuels 1998, 12, 881. (16) Gao, H.; Nomura, M.; Murata, S.; Artok, L. Energy Fuels 1999, 13, 518. (17) Murata, S.; Sako, T.; Yokoyama, T.; Gao, H.; Kidenab, K.; Nomura, M. Fuel Process. Technol. 2008, 89, 434.
10.1021/ef8006454 CCC: $40.75 2009 American Chemical Society Published on Web 12/11/2008
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Table 1. Ultimate and Proximate Analysis of Two Coals ultimate analysis wt%, daf
proximate analysis wt%, db
coal
C
H
N
S
Oa
VM
ash
D Z
85.41 93.38
4.92 3.84
0.87 0.90
0.37 0.27
8.43 1.61
29.45 10.19
3.04 7.96
a
Difference.
Figure 3. Three-dimensional images of a Z coal particle in pyridine at 0 and 500 min from three microscopic video cameras.
Figure 1. Three-dimensional microscopic video camera image analysis system for observing and evaluating solvent swelling of coal particles.
system (ICAS 5.2, Beijing Focus Instrument Co., Ltd., China). Magnification from 0.68 to 4.5 of the objective lens was used with the microscopes and image analysis system, providing a 200-2800× objective at the analyzer monitor. Under the conditions of atmospheric pressure and ambient temperature (28 °C), 5 mL of pyridine (reagent grade) was injected into the reaction cell, coal particles were placed into pyridine, and multichannel sampling was started until a quasiequilibrium state of swelling (generally 24 h) was achieved. The recorded images were examined and analyzed with the image analysis system. The time-resolved volumetric swelling ratio of a coal particle at t time (Qv,t) was defined as the average calculated with the equivalent volume converted from the three projection areas of the particles measured with three microscopic video cameras using the following equations. As shown in eq 1, the volume of a coal particle (V) defined as the average of the volume of the coal particle measured based on three projection areas from three microscopic video cameras.
4 3⁄2 3⁄2 (F1P3⁄2 1 + F2P2 + F3P3 ) 3√π V) 3
Figure 2. Three-dimensional images of a D coal particle in pyridine at 0 and 180 min from three microscopic video cameras.
of coal particles and kinetics data can be more effectively and accurately obtained using the proposed system and method. Experimental Section Samples. Two Chinese coals, Datong bituminous coal (D) and Zhangjiakou anthracite coal (Z), were selected. The coal samples were ground into 0.2-1.0 mm and vaccuum-dried at 110 °C for 24 h. The ultimate analysis and proximate analysis of the coals are given in Table 1. Experimental Apparatus and Procedure. As shown in Figure 1, the experimental apparatus developed in this study consists of three sets of microscopic video cameras, which are set orthogonally to three-dimensionally monitor the behavior of coal particles in a sealed solvent cell (made from transparent quartz glass, diameter 23 mm, height 40 mm). An image analysis system was used for multichannel sampling of the time-resolved images and quantitatively evaluating the time-resolved swelling ratios and shape factors of coal particles in solvent. Three microscopes (Model SZ66 TB-S, Beijing Focus Instrument Co., Ltd., China) fitted with three color video cameras (Model TKC1481BEC, JVC, Japan) provide input to a color image analysis
(1)
where P1, P2, and P3 are three projection areas of one coal particle measured from three microscopic video cameras. Fi (i ) 1, 2, 3) are the shape factors for the images of the coal particle obtained from three cameras. The time-resolved volumetric swelling ratio of a coal particle at t time (Qv,t) was defined as the ratio of volume of coal particle at t time (Vt) and zero time (V0), as shown in eq 2.
Qv,t )
Vt V0
(2)
Qv,t was defined as the average of three swelling ratios (Qvi,t, i ) 1, 2, 3) measured from three microscopic video cameras, as shown in eqs 3 and 4.
1 Qv,t ) (Qv1,t + Qv2,t + Qv3,t) 3
1 Qv,t ) 3
{ [ ] [ ] [ ]} F1,tP3/2 1,t
F1,0P3⁄2 1,0
+
F2,tP3/2 2,t
F2,0P3/2 2,0
+
F3,tP3/2 3,t
F3,0P3/2 3,0
(3) (4)
where Pi,t and Pi,0 (i ) 1, 2, 3) are the projection areas of a coal particle obtained from three microscopic video cameras at t time and zero time, respectively. Fi,t and Fi,0 (i ) 1, 2, 3) are the shape factors for the images of the coal particle obtained from three cameras at t time and zero time, respectively. In general, Fi,t is not a constant during swelling because of the anisotropic swelling features of coal particles in solvent. However, we have observed that some of coal particles have a tendency to maintain their initial shape during swelling in solvent. It seems to be reasonable to assume shape factors as constants during swelling; therefore, the
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shape factors for a given sample in one direction are assumed to be constant, that is Fi,t ) Fi,0 (i ) 1, 2, 3). As a result, eq 4 becomes eq 5.
Qv,t )
1 3
{ [ ] [ ] [ ]} P3/2 1,t
P3/2 1,0
+
P3⁄2 2,t
P3/2 2,0
+
P3/2 3,t
(5)
P3/2 3,0
The mineral matter would presumably be unswellable, and its contribution to the dry and swollen volumes should be subtracted. The correction is given in eq 6 from careful work.18
Qdmmf ) y)
(Qmeasured - y) (1 - y)
(6)
Fdry coal × ash Fminerals
(7)
Figure 4. A typical dynamical volumetric swelling process of a D coal particle in pyridine from three microscopic video cameras.
where Fdry coal and Fminerals are the densities of dry coal and minerals, and ash is the mass fraction of minerals in coal. Consequently, eqs 3 and 5 become eqs 8 and 9.
1 (Q [ 3 )
]
v1,t + Qv2,t + Qv3,t) - y
Qv,t
(8)
(1 - y)
{ [( ) ( ) ( )] }
3/2 P3/2 P3/2 1 P1,t 2,t 3,t + + 3/2 3/2 3 P3/2 P P 1,0 2,0 3,0 Qv,t ) (1 - y)
-y
(9)
In addition, considering the changes of the shape factors during swelling for most coal samples, eq 10 derived from eq 4 was also used.
{ [( ) ( ) ( )] }
3⁄2 F2,tP3⁄2 F3,tP3⁄2 1 F1,tP1,t 2,t 3,t + + 3⁄2 3⁄2 3 F P3⁄2 F P F P 1,0 1,0 2,0 2,0 3,0 3,0 Qv,t ) (1 - y)
Figure 5. A typical dynamical volumetric swelling process of a Z coal particle in pyridine from three microscopic video cameras.
-y
(10)
where the shape factor F is defined as follows.
F ) 4π(projection area)/(perimeter)2
(11)
Since Fdry coal/Fminerals is around 0.5,18 then the values of y are 0.0152 for D coal, and 0.0398 for Z coal, respectively.
Results and Discussions Three-Dimensional Images of Two Types of Chinese Coal Particles in Pyridine at Ambient Temperature. The images of a D coal particle in pyridine at 0 and 180 min from three cameras are shown in Figure 2. The images of a Z coal particle in pyridine at 0 and 500 min from three cameras are shown in Figure 3. As shown in these images, the shape features of the images from three directions are distinctive. Because of the anisotropic swelling features of coal particles in solvent, in general, the shapes of the coal
particles deform to some extent during swelling, and therefore the shape factors are not constant during swelling. Nevertheless, as shown in these images, the main shape features of the particles change little. These results indicate that the coal particles seem to have a tendency to maintain their initial shapes during swelling in solvent; it is reasonable to assume shape factors as constants during swelling. Another important feature is the anisotropic swelling of the coal particles displayed in Figures 2 and 3. As for the anisotropic swelling of coal, Cody et al.12 had made pioneer quantitative observations; Gao et al.15 had carefully discussed characteristic distributions of anisotropic swelling of coal particles, which are prepared by the density gradient centrifugation (DGC) method, based on their quantitative observation using the orthogonal two microscopic video camera image analysis method. In the first paper of this series, we focus on the measurement method itself and do not discuss anisotropic
Table 2. An Example of Measurement Analysis of Swelling Ratios for a D Coal Particle (Figure 4) microscope Qvi,max (Qvi,max - Qva,max)/Qva,max (%) Qev,i (Qev,a - Qev,a)/Qev,a (%)
average
1
2
3
(1 + 2 + 3)/3
(1 + 2)/2
(1 + 3)/2
(2 + 3)/2
2.979 6.32 2.840 6.37
2.953 5.39 2.771 3.78
2.393 -14.60 2.323 -13.00
2.802 0 2.670 0
2.966 5.85 2.806 5.09
2.686 -4.14 2.582 -3.30
2.673 -4.60 2.547 -4.61
Table 3. An Example of Measurement Analysis of Swelling Ratios for a Z Coal Particle (Figure 5) microscope Qev,i (Qev,i - Qev,a)/Qev,a (%)
average
1
2
3
(1 + 2 + 3)/3
(1 + 2)/2
(1 + 3)/2
(2 + 3)/2
2.735 -7.63
2.710 -8.48
3.203 8.17
2.961 0
2.722 -8.07
2.956 -0.17
3.082 4.09
Three-Dimensional Microscope Image Analysis Method
Figure 6. An example of analyzing n and k of a D coal particle in pyridine at ambient temperature using one- and three-microscopic camera data.
features of the two Chinese coals deeply; further studies will be presented in a subsequent paper. Typical Dynamic Swelling Processes of Particles from Two Chinese Coals in Pyridine at Ambient Temperature. Typical dynamic volumetric swelling ratios of a D coal particle and a Z coal particle in pyridine at ambient temperature are shown in Figures 4 and 5, in which the shape factors are assumed as constants. Anisotropic swelling is a general feature of the D coal particle and Z coal particle, which reflects the distinction of swelling ratios from three cameras. It is clear that if using only one microscope, the method would overestimate swelling ratios or underestimate swelling ratios. For example, as shown in Figure 4 and Table 2, maximum volumetric swelling ratios measured from three microscopes are Qv1, max ) 2.979, Qv2, max ) 2.953, Qv3, max ) 2.393, respectively, and their average is Qva, max ) 2.802; the maximum volumetric swelling ratios measured from two microscopes are Qv12, max ) 2.966, Qv13, max ) 2.686, Qv23, max ) 2.673, respectively. If Qva, max is a comparison standard, the measurement errors of using only one microscope are 6.32%, 5.39%, and -14.60%, respectively; the measurement errors of using two microscopes are 5.85%, -4.14%, and -4.60%, respectively. The equilibrium volumetric swelling ratios measured from three microscopes are Qev,1 ) 2.840, Qev,2 ) 2.771, and Qev,3 ) 2.323, respectively, and their average is Qev,a ) 2.670; the equilibrium volumetric swelling ratios measured from two microscopes are Qev,12 ) 2.806, Qev,13 ) 2.582, and Qev,23 ) 2.547, respectively; if Qev,a is a comparison standard, the measurement errors of using only one microscope are 6.37%, 3.78%, and -13.00%, respectively; the measurement errors of using two microscopes are 5.09%, -3.30%, and -4.61%, respectively. Another measurement analysis of equilibrium swelling ratios of a Z coal particle is
Energy & Fuels, Vol. 23, 2009 345
Figure 7. An example of analyzing n and k of a D coal particle in pyridine at ambient temperature using two- and three-microscopic camera data.
shown in Figure 5 and Table 3. The equilibrium volumetric swelling ratios measured from three microscopes are Qev,1 ) 2.735, Qev,2 ) 2.710, and Qev,3 ) 3.203, respectively, and their average is Qev,a ) 2.961; the equilibrium volumetric swelling ratios measured from two microscopes are Qev,12 ) 2.722, Qev,13 ) 2.956, and Qev,23 ) 3.082, respectively. The measurement errors of using only one microscope are -7.63%, -8.48%, and 8.17%, respectively; and the measurement errors of using two microscopes are -8.07%, -0.17%, and 4.09%, respectively. These results clearly indicate that orthogonal microscope method15 can well improve the estimation of swelling ratios of coal particles in solvent, and the three-dimensional microscope method proposed in this study can finally solve the problem of overestimation and underestimation from the one-microscope and two-microscope methods, respectively. In addition, for the two types of Chinese coal particles, there are two typical swelling processes: nonovershoot process and overshoot process. In the present state, although the nonovershoot phenomenon of coal particles in solvent, such as shown in Figures 5, 8b, and 10b, can be well modeled, modeling the overshoot phenomenon, as shown in Figures 4, 6b and 11b, remains a challenge, which motivates our group to work further. Examples of Analyzing Kinetics Parameters n and k of Two Types of Chinese Coal Particles. Another aim of coal swelling studies is to obtain kinetics data that can be used to analyze the interaction between coal macromolecules and solvents, and the solvent diffusion mechanism in coal macromolecules. Diffusion limitations are of concern in virtually all aspects of coal utilization. There have been quite a few of studies about (18) Green, T. K.; Larsen, J. W. Fuel 1984, 63, 1538.
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Figure 8. An example of analyzing n and k of a Z coal particle in pyridine at ambient temperature using one- and three-microscopic camera data.
the factors that influence solvent diffusion in coal macromolecules.15-17,19-28 Solvent uptake follows the generalized simple semiempirical expression (eq 12).20 Since the extent of solvent swelling is linearly related to mass uptake (eq 13), it is possible to relate two equations into one (eq 14).24 Mt ⁄ Me ) ktn
(12)
Mt ⁄ Me ) (Qv,t - 1) ⁄ (Qv,e - 1)
(13)
(Qv,t - 1) ⁄ (Qv,e - 1) ) ktn
(14)
where Mt and Qv,t are the mass uptake of solvent and volumetric swelling ratio at time t, Me and Qv,e are the mass uptake of solvent and volumetric swelling ratio at equilibrium state, n is the diffusion exponent which is indicative of the solvent transport mechanism, and k is relaxation constant. Ritger and Peppas20 determined that for a spherical geometry, Fickian diffusion has n ) 0.43, which is dependent upon the diffusion coefficient across a concentration gradient. Case II diffusion has n ) 0.85, in which a solvent uptake process is controlled by the relaxation of the macromolecular network structure, as opposed to diffusion itself. It is characterized by a sharp front separating the swollen and unswollen regions of coal. Interme(19) Lynch, L. J.; Peppas, Nikolaos, A. Fuel 1987, 66, 803. (20) Ritger, Philip, L.; Peppas, Nikolaos, A. Fuel 1987, 66, 815. (21) Ritger, Philip, L.; Peppas, Nikolaos, A. Fuel 1987, 66, 1379. (22) Hall, Peter, J.; Thomas, K. M.; Marsh, H. Fuel 1988, 67, 863. (23) Barton, W. A.; Lynch, L. J. Energy Fuels 1989, 3, 402. (24) Hall, Peter, J.; Thomas, K. M.; Marsh, H. Fuel 1992, 72, 1271. (25) Ndaji Francis, E.; Thomas, K. M. Fuel 1992, 72, 1531. (26) Motsegood, A. G. W.; Clarkson, R. B. Fuel 1993, 72, 1235. (27) Suuberg, E. M.; Otake, Y.; Langner, M. J.; Leung, K. T.; Milosavljevic, I. Energy Fuels 1994, 8, 1247. (28) Ndaji Francis, E.; Thomas, K. M. Fuel 1995, 74, 842.
Figure 9. An example of analyzing n and k of a Z coal particle in pyridine at ambient temperature using two- and three-microscopic video data.
diate values correspond to an anomalous diffusion mechanism in which diffusion and relaxation rates are comparable. Values above n ) 0.85 are possible and are termed supercase II. Values of n and k obtained by analyzing the initial linear part of the graph of ln [(Qv,t-1)/(Qv,e - 1)] ) n ln t + ln k of a D coal particle and a Z coal particle are shown in Figures 6-11. It should be noted that the best linear relationship seems to be in the initial part before ln t ) 4.5 because there is a definite change of slope after ln t ) 4.5, which suggests a change in the diffusion mechanism. Figures 6 and 7 are examples of analyzing n and k of a D coal particle in pyridine at ambient temperature using one-, two-, and three-camera data. Figures 8 and 9 are examples of analyzing n and k of a Z coal particle in pyridine at ambient temperature using one-, two-, and three-camera data. The swelling ratios used in the measurement analyses for the kinetics parameter data of n and k in Figures 6-9 used eq 5, which assume shape factors as constant. The analyzed results are summarized in Tables 4 and 5. As shown in Table 4 (Figures 6 and 7), the exponents n of the D coal particle in pyridine measured from three microscopes are n1 ) 0.823, n2 ) 0.727, and n3 ) 0.978, respectively, the average of three is na ) 0.805, and the average values of any two among three are n12 ) 0.764, n13 ) 0.880, and n23 ) 0.796. If na is a comparison standard, the measurement analysis errors of n using one-microscope data are 2.24%, -9.69%, and 21.49%, respectively, and the measurement analysis errors of n using two-camera data are -5.09%, 9.32%, and -1.12%, respectively. The natural logarithms of k (ln k) for the D coal particle in pyridine at ambient temperature from three microscopes are (ln k)1 ) -4.20, (ln k)2 ) -3.787, (ln k)3 ) -4.909, respectively, the average of three is (ln k)a ) -4.130, and the
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Energy & Fuels, Vol. 23, 2009 347
Table 4. An Example Measurement Analysis of Kinetics Data for a D Coal Particle (Figures 6 and 7) microscope n ln k (ni - na)/na (%) [(ln k)i - (ln k)a]/(ln k)a (%)
average
1
2
3
(1 + 2 + 3)/3
(1 + 2)/2
(1 + 3)/2
(2 + 3)/2
0.823 -4.20 2.24 1.69
0.727 -3.787 -9.69 -8.31
0.978 -4.909 21.49 18.86
0.805 -4.130 0 0
0.764 -3.942 -5.09 -4.55
0.880 -4.458 9.32 7.94
0.796 -4.093 -1.12 -0.90
Table 5. An Example of Measurement Analysis of Kinetics Data for a Z Coal Particle (Figures 8 and 9) microscope n ln k (ni - na)/na (%) [(ln k)i - (ln k)a]/(ln k)a (%)
average
1
2
3
(1 + 2 + 3)/3
(1 + 2)/2
(1 + 3)/2
(2 + 3)/2
0.810 -4.160 -16.92 -14.44
1.098 -5.549 12.62 14.13
1.056 -5.060 8.31 4.07
0.975 -4.862 0 0
0.941 -4.794 -3.49 -1.40
1.068 -5.261 9.54 8.21
1.013 -4.949 3.90 1.79
average values of any two among three are (ln k)12 ) -3.942, (ln k)13 ) -4.458, (ln k)23 ) -4.093, respectively. If (ln k)a is a comparison standard, the measurement analysis errors of ln k using one microscope are 1.69%, -8.31%, and 18.86%, respectively, and the measurement analysis errors of ln k using two microscopes are -4.55%, 7.94%, and -0.90%, respectively. As shown in Table 5 (Figures 8 and 9), the exponents n of the Z coal particle in pyridine measured from three microscopes are n1 ) 0.810, n2 ) 1.098, and n3 ) 1.056, respectively, the average of three is na ) 0.975, and the average values of any two among three are n12 ) 0.941, n13 ) 1.068, and n23 ) 1.013. The measurement analysis errors of n using one microscope are -16.92%, 12.62%, and 8.31%, respectively, and the measurement analysis errors of n using two microscopes are -3.49%, 9.54%, and 3.90%, respectively. The natural logarithms of k (ln k) for the Z coal particle in pyridine at ambient temperature from three microscopes are (ln k)1 ) -4.794, (ln k)2 ) -5.261, (ln k)3 ) -4.949, the average value of three is (ln k)a ) -4.862, and the average values of any two among
three are (ln k)12 ) -4.794, (ln k)13 ) -5.261, (ln k)23 ) -4.949, respectively. The measurement analysis errors of ln k using one microscope are -16.92%, 12.62%, and 8.31%, respectively, and the measurement analysis errors of ln k using two microscopes are -1.40%, 8.21%, and 1.79%, respectively. In terms of above measurement analysis results, it is clear that orthogonal microscope method15 using two microscopes could improve the estimation of n and k of solvent swelling of coal particles, and the three-dimensional microscope method proposed in this study can solve the problem of overestimation and underestimation of n and k, respectively, caused by orientation of anisotropic swelling of coal particles with respect to a known frame of reference not being measured in the orthogonal microscope method. Effect of Shape Factor on the Swelling Ratios and Kinetics Parameters of Two Types of Chinese Coal Particles in Pyridine. Generally, the shape of a coal particle in solvent changes with the anisotropic swelling of the coal particle. The shape factor of a coal particle certainly affects the volume
Figure 10. Effect of shape factor on swelling ratios and kinetics parameters of a D coal particle in pyridine at ambient temperature using three-microscopic video camera data.
Figure 11. Effect of shape factor on swelling ratios and kinetics parameters of a Z coal particle in pyridine at ambient temperature using three-microscopic video camera data.
348 Energy & Fuels, Vol. 23, 2009
estimation based on measuring the projection area and perimeter of the particle. Therefore, the shape factors accompanying coal swelling in solvent should be measured. In this study, the shape factor F is defined as F ) 4π(projection area)/(perimeter)2, which was calculated using measurements of projection area and perimeter of each particle from three directions with the image analysis software. Circles have the greatest area to perimeter ratio, and this formula will approach a value of 1 for a perfect circle. Squares are around 0.78. A thin thread-like object would have the lowest shape factor approaching 0. The effect of shape factors on swelling ratios and kinetics parameters of a D coal particle in pyridine at ambient temperature using three-camera data are shown in Figure 10. The shape factors of the D coal particle measured from three directions are different and change with time, especially during the initial stage. The shape factors from microscope 1 (F1,t) change from 0.784 to 0.762, and the average is 0.777. The shape factors from microscope 2 (F2,t) change from 0.669 to 0.571, and the average is 0.595. The shape factors from microscope 3 (F3,t) change from 0.739 to 0.661, and the average is 0.683. In addition, the measurement errors of swelling ratios calculated with [(Qvt,a Qvt,af)/Qvt,af] × 100 change from 0.00% to 9.75%. As for the kinetics parameters of solvent swelling, measured n with and without shape factor correction, naf and na are 0.418 and 0.467, respectively. The measurement error of n calculated with [(na - naf)/naf] × 100 is 11.72%. Measured ln k with and without shape factor correction, (ln k)af and (ln k)a are -1.979 and -2.201, respectively. The measurement error of ln k calculated with {[(ln k)a - (ln k)af]/(ln k)af} × 100 is 11.22%. The effect of shape factors on swelling ratios and kinetics parameters of a Z coal particle in pyridine at ambient temperature using three-camera data are shown in Figure 11. The shape factors from microscope 1 (F1,t) change from 0.755 to 0.715, and the average is 0.724. The shape factors from microscope 2 (F2,t) change from 0.758 to 0.580, and the average is 0.671. The shape factors from microscope 3 (F3,t) change from 0.654 to 0.617, and the average is 0.634. The measurement errors of swelling ratios calculated with [(Qvt,a - Qvt,af)/Qvt,af] × 100 change from 0.00% to 13.92%. The measured n with and without shape factor correction, naf and na, are 0.943 and 0.955, respectively. The measurement error calculated with [(na - naf)/ naf] × 100 is 1.27%. The measured ln k with and without shape factor correction, (lnk)af and (ln k)a are -4.924 and -4.826, respectively. The measurement error of ln k calculated with {[(ln k)a - (ln k)af]/(ln k)af} × 100 is -1.99%. From the above results, it is clear that the shape factors of coal particles in solvent change with time, especially during the initial stage of swelling. Shape factors affect the measurement precision of swelling ratios and kinetics parameters. Sometimes the effect might be large; therefore, shape factors should be considered and measured when using the threedimensional microscope method proposed in this paper. Summary and Conclusions An improved three-dimensional microscopic video camera system coupled with an image system and a quantitative method were developed to observe and evaluate the dynamic swelling behavior of coal particles in solvent and to study kinetics of solvent diffusion in one bituminous coal particle and one
Gao et al.
anthracite coal particle. The proposed system and methodology were proved to be more effective, more compact, and more economical than the previous proposed orthogonal microscope system. This system finally solved the problem of the onemicroscope system and the orthogonal two-microscope system caused by orientation of the anisotropic swelling of coal particles with respect to known frames of reference not being measured. Using the proposed system and quantitative method, it is possible to obtain the dynamic solvent swelling data and kinetics data more accurately. The proposed system can also be used to dynamically observe and evaluate any samples with anisotropic features, three-dimensionally. Some important results for two Chinese coals obtained using the three-dimensional microscopic video camera system and quantitative method are as follows. (1) Using three-dimensional data as the comparison standard, the measurement results indicate that the orthogonal twomicroscope system can decrease maximum measurement error of solvent swelling ratios from -14.60% to 5.85% for a D coal particle, and from 8.48% to -8.07% for a Z coal particle. The maximum measurement error of exponent n is from 21.49% to 9.32% for the D coal particle and from 16.92% to 9.54% for the Z coal particle. The maximum measurement error of relaxation constant ln k is from 18.86% to 7.94% for the D coal particle, and from 14.44% to 8.21% for the Z coal particle, respectively. (2) Using the three-dimensional microscope method, the measured na ) 0.805 (Figures 6 and 7) for a D coal particle shows that solvent diffusion and relaxation of the macromolecular structure of the D coal in pyridine seems to be comparable; the measured naf ) 0.418 (Figure 10) for another D coal particle shows a different solvent diffusion mechanism from well-known mechanisms. The measured na ) 0.975 (Figures 8 and 9) and naf ) 0.943 (Figure 11) for two Z coal particles indicate that superrelaxation of the macromolecular structure of Z coal in pyridine seems to be dominant. (3) The best linear relationship seems to be in the initial part before ln t ) 4.5 because there is a definite change of slope after ln t ) 4.5, which suggests a change in the diffusion mechanism. (4) The effect of shape factors on the measurement accuracy of swelling ratios and kinetics parameters might be large; therefore, shape factors should be considered and measured when using the three-dimensional microscope method proposed in this paper. (5) The experimental data have shown that equilibrium solvent swelling ratios, diffusion mechanism exponents, and relaxation constants of D coal particles and Z coal particles have distinctive distribution characteristics. Results will be presented in subsequent papers. (6) In the present state, modeling the overshoot phenomenon, as shown in Figures 4, 6b, and 11b, remains a challenge and motivates our group to work further. Acknowledgment. The experiments were performed in Yanshan University. We take this opportunity to sincerely thank Yanshan University for its financial support (B255) and for experimental apparatus. EF8006454
