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Fractal dimension of coal particles and their CH4 adsorption
International Journal of Mining Science and Technology 22 (2012) 855–858
Contents lists available at SciVerse ScienceDirect
International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Fractal dimension of coal particles and their CH4 adsorption Wang Chengyang a, Hao Shixiong a,b, Sun Wenjing a, Chu Wei a,⇑ a b
Department of Chemical Engineering, Sichuan University, Chengdu 610065, China Department of Chemical Engineering, Sichuan University of Science & Engineering, Zigong 643000, China
a r t i c l e
i n f o
Article history: Received 10 March 2012 Received in revised form 14 April 2012 Accepted 15 May 2012 Available online 11 January 2013 Keywords: Coal Fractal dimension Frenkel-Halsey-Hill Brunauer–Emmett–Teller Adsorption isotherm
a b s t r a c t We describe the fractal analysis of three differently sized coal samples (0.350–0.833 mm, 0.245– 0.350 mm, and 0.198–0.245 mm). The influence of fractal dimension on CH4 adsorption capacity is investigated. The physical parameters of the samples were determined via the Brunauer–Emmett–Teller (BET) theory. A CH4 adsorption study over the pressures range from 0 to 5 MPa was carried out with a new volumetric measurement system. The CH4 adsorption was measured using the differently sized coal. Two fractal dimensions, D1 and D2 were determined over the pressure ranges from 0 to 0.5 MPa and from 0.5 to 1 MPa, using the Frenkel-Halsey-Hill (FHH) method. We conclude that the two fractal dimensions correlate with the CH4 adsorption capacity of the coal: increasing CH4 adsorption capacity occurs with a corresponding increase in fractal dimension. Furthermore, D1 and D2 are positively correlated with surface area, pore volume, and samples size. The size distribution of the samples has fractal characteristics. Ó 2012 Published by Elsevier B.V. on behalf of China University of Mining & Technology.
1. Introduction Mandelbrot popularized the concept of a fractal in 1975 and since then the concept has been applied to the study of coal, which has a characteristic complex surface structure [1]. Avnir et al. introduced fractal geometry into the study of surface structure and it has been used to study the irregular shape of materials having no characteristic repeat length but yet having self-similar forms [2]. The fractal concept provides a quantitative description of an irregular shape and is a powerful tool. Coal is a complex black or dark brown material with a complicated porous structure that allows it to burn easily. The structure is closely related to the adsorption and mobility of methane [3]. The pore size distribution is the foundation of investigations into coal bed methane and coal, gas matrix interactions. This includes coal bed methane absorption, desorption, diffusion, and seepage [4]. Many studies report that spaces within coal particles show fractal characteristics on a length scale over the atomic to grain size range [5]. Moreover, coal is a porous medium with a large internal surface area that has the capacity for gas adsorption [6,7]. Thus, it is important to study the relationships between fractal dimension and adsorption capacity of coals. From this, the migration and accumulation of coal bed methane (CBM) could be understood. Most of the recent measurements of CBM adsorption studied the adsorption isotherm as it relates to the physical structure of coal. Éttinger ⇑ Corresponding author. Tel.: +86 28 85403836. E-mail address: [email protected] (C. Wei).
et al. showed that the CH4 adsorption capacity of coal is positively correlated with the metamorphic grade of the coal [8]. Rodrigues et al. examined the adsorption capacity of coal for different gases, including N2, CO2, and CH4, and concluded that the adsorption capacity increased with increasing coal porosity. They also showed that the adsorption capacity for these three gases fell in the order CO2 > CH4 > N2. Yao et al. analyzed the N2 adsorption isotherm to estimate the pore structure and surface fractal dimension with the fractal Frenkel-Halsey-Hill (FHH) method. The relationship between fractal dimension and CH4 adsorption capacity were discussed [9]. Sahouli et al. and Cai et al. calculated the fractal dimension of a solid from the N2 adsorption isotherm using the fractal FHH method and a thermodynamics method. The results showed that the coal pore structure had fractal characteristics and that the fractal dimension of the pores was controlled by the composition and pore parameters of the coal. In this study both fractal models appeared to give equivalent results [10,11]. Many researchers now apply the Langmuir monolayer adsorption model to coal as a way to explain the CH4 adsorption. The fractal dimension can be obtained from isotherm adsorption data based on the monolayer adsorption model. However, methane adsorption on coal does not seem a likely candidate for a monolayer model. This conundrum may be explained by noting the small outside surface area of coal compared to its internal surface area. The internal surface area plays a more important role in methane adsorption. The pore structure is very complicated and the distribution of pore sizes is quite wide. This means that the interaction between gas and coal is unusual. Previous studies have shown that the percentage of micro-pores and transition holes in
2095-2686/$ - see front matter Ó 2012 Published by Elsevier B.V. on behalf of China University of Mining & Technology. http://dx.doi.org/10.1016/j.ijmst.2012.11.003
856
C. Wang et al. / International Journal of Mining Science and Technology 22 (2012) 855–858
the coal exceeds the percentage of the macro- and meso-pores [12,13]. CH4 adsorption is considered a monomolecular adsorption within macro- and meso-pores but it is considered volume filling in the micro-pores and transitions holes. Hence a modified FHH equation is used to calculate the fractal dimension of CH4 adsorption capacity of a coal [14–16]. This method has practical significance for this study. As described herein, physical adsorption parameters of coal were determined by applying Brunauer–Emmett–Teller (BET) theory and analyzing the fractal dimension with the FHH method applied to CH4 gas adsorption isotherm data. The pore structure and surface fractal dimension is obtained from these efforts. The relationship between fractal dimension and CH4 adsorption capacity is also discussed. 2. Experimental 2.1. Sample preparation The coal was collected from Qinghua, Qinghai province, China. The samples were prepared by crushing and sieving into three sizes: a range from 0.350 to 0.833 mm, from 0.245 to 0.350 mm, and from 0.198 to 0.245 mm. The samples were then dried at 393 K for 12 h in an oven. The proximate analysis of the sample was: moisture, 0.68% (by weight); ash, 1.66% (by weight); volatile matter, 20.97% (by weight); and carbon, 76.7% (by weight). 2.2. N2 adsorption isotherms The N2 adsorption was measured with a NOVA 1000e instrument from the Quantachrome Company. The BET specific surface area and pore volume were obtained from these measurements. The samples were out gassed at 393 K for 16 h. After out gassing for this period the N2 gas isotherm adsorption measurements were carried out at 77 K. The relative pressure (P/P0) ranged from 0.001 to 0.99. 2.3. CH4 adsorption isotherms Auto-adsorption experiments, equipment designed by the Northwest Chemical Engineering Research Center, were used to obtain the CH4 adsorption isotherms using the volumetric method. The results were obtained with the Redlich–Kwong equation. The adsorption equipment is shown in Fig. 1. All samples were out gassed at 298 K for 16 h under vacuum condition and then measured over a pressure range from 0.1 to 5 MPa. The CH4 adsorption capacity was determined at various pressures. The adsorption equilibrium time was 4 h.
1
Adsorption equipment Pressure gage
3.2. An analysis of CH4 adsorption Fig. 2b shows the CH4 adsorption isotherms. The CH4 adsorption increases as the particle size becomes smaller. The physical adsorption mechanism implies that since the smaller particles have more specific surface area and pore volume the CH4 adsorption will increase as the particle size decreases. CH4 adsorption also increases with increasing pressure. This could be explained by noting that increased pressure gives the CH4 gas in the adsorption cylinder more energy, which makes the interaction between the coal and the gas more intensive. This enhanced interaction forces gas into the micro-pores. Increased pressure also might collapse the fragile structure of the coal. This would also lead to a larger specific surface area and pore volume and, thus, increased CH4 adsorption. Many researchers have applied the Langmuir equation to their investigations of CH4 adsorption on coal [17]. Gas adsorption into coal is not monolayer adsorption, however. The Langmuir model is used because the adsorption of CH4 onto coal is classified as a type I adsorption isotherm. An adsorption situation that appears to fit a type I definition may not be a monolayer adsorption, however. Adsorption into the micro-pores of coal (62–3 nm) ought to be multilayer adsorption, capillary pore condensation, or micro-pore filling but these always show the characteristic type I isotherm. Multilayer adsorption and capillary pore condensation occurred during the gas adsorption in this study. These will show the type I adsorption isotherm [18]. Thus, the Langmuir model is appropriate for this study. Fig. 2b shows the fit of the CH4 pressure to the adsorbed CH4 with this model: The correlation coefficient is R2 P0.996. 3.3. Fractal dimension from an analysis of the CH4 isotherms
6
Heated Thermostatic Water bath
Reference
Sample
Helium
The total surface area, pore volume, and average pore size reported in this study were obtained using the BET model. The physical parameters of the coals are shown in Table 1. The total surface area and the pore volume both increase with a decrease in the particle size while the average pore size shows no significant change. Existing literature suggests that the decrease in coal particle size should correlate with an increase in total surface area. During crushing the micro-porous interior of the coal is exposed, which is normally blocked by minerals and ash, so the pore volume also increases. Fig. 2a shows the N2 adsorption isotherms of the three samples at 77 K. The N2 adsorption capacity of the coal increases with a decrease in the particle size. The fact that adsorption onto coal is a physical adsorption and the total surface area and pore volume affect adsorption can explain this. Thus, the increase in specific surface area and pore volume could increase the N2 adsorption capacity. Furthermore, decreasing pore size is correlated with increased N2 adsorption capacity of coal.
3 Filter
Methane
3.1. Analysis of the N2 adsorption isotherm adsorption
5
4 2
Unloading
3. Results and discussion
Vacuum pump
Fig. 1. CH4 adsorption equipment.
Fractal FHH and thermodynamic methods have been used to measure fractal dimension on the basis of gas adsorption isotherms [9,19]. The fractal FHH method has been shown to be the most effective method. This method is used herein on theCH4 adsorption data. The FHH method allows the fractal dimension to be determined from Eqs. (1) and (2):
ln V ¼ A ln½lnðP0 =PÞ þ constant
ð1Þ
D¼Aþ3
ð2Þ
857
C. Wang et al. / International Journal of Mining Science and Technology 22 (2012) 855–858
pressure region was larger than D2. Fig. 2b also shows how the incremental increase in adsorption for an incremental increase in pressure over the region where P/P0 = 0.5–1 decreases. Hence, through D1 and D2 it appears that the adsorption capacity increases with an increase in the fractal dimension. The variation in fractal dimension for a given coal sample is also reflected in dA/dP. The fractal dimension is positively correlated with dA/dP.
Table 1 Physical parameters of the coal. Particle size (mm)
Total surface area (m2/g)
Pore volume (cm3/g)
Average pore diameter (nm)
0.350–0.833 0.245–0.350 0.198–0.245
3.29 3.75 4.69
3.82 4.46 5.21
2.28 2.56 2.27
where V is the amount of adsorbed CH4 at equilibrium pressure P, P0 the saturation pressure of CH4; A an exponent related to the fractal dimension; and D the mechanism of adsorption. A plot of ln V vs. ln[ln (P0/P)] gives a straight line with a slope equal to A. The fractal dimension D depends on the value of A. The FHH plots of the three coal samples are shown in Fig. 3. Two distinct linear segments appear, one over the range P/P0 = 0–0.5 and the other at P/P0 = 0.5–1. Both of these segments show good fits, suggesting that the fractal characteristics at these two intervals are different. Table 2 summarizes the slopes of the regression lines and the fractal dimension value (D1 and D2) calculated at the two relative pressure ranges. Both D1 and D2 increase with decreasing particle size but the variation of D1 in the lower relative
3.4. Relationship between fractal dimensions and coal adsorption capacity Tables 1 and 2 show the results that indicate that the total surface area and pore volume increase as the particle size decreases and that there is a positive correlation with the fractal dimension. By definition the fractal dimension characterizes the surface roughness [20]. It has been reported that the particle size of coal decreases with increasing surface roughness [21]. This is in accord with our experimental results. The larger the fractal dimension the larger the surface roughness. Hence, particles with a higher fractal dimension have bigger specific surface area, surface roughness, and fractal dimension.
1.2 0.350-0.833 mm 0.245-0.350 mm 0.198-0.245 mm
2.5 2.0
CH4 adsorption capcity (mmol/g)
Volume adsorbed (V, mL/g)
3.0
1.5 1.0 0.5 0
0.2
0.4 0.6 0.8 Relative pressure (P/P0 ) (a) 77 K
0.350-0.833 mm 0.245-0.350 mm 0.198-0.245 mm Langmuir fit
1.0 0.8 0.6 0.4
R2 0.350-0.833 mm = 0.996 R2 0.245-0.350 mm = 0.997 R2 0.198-0.245 mm = 0.997
0.2
1.0
0
1
2 3 P (MPa) (b) 298 K
4
5
Fig. 2. CH4 adsorption isotherms.
lnV
lnV
2.5 2.0 0.350-0.833 mm Linear fit
1.5 1.0
-2.5 -2.0 -1.5 -1.0 -0.5 0 ln[ln(p0 /p)]
0.5
1.0
3.0 2.8 2.6 2.4 2.2 2.0
3.2 3.0 2.8 0.245-0.350 mm Linear fit
1.8 1.6 1.4 -2.5 -2.0 -1.5 -1.0 -0.5 ln[ln(p0 /p)]
(a) Particle size 0.350-0.833 mm
lnV
3.0
2.6 2.4 2.2
0.198-0.245 mm Linear fit
2.0 1.8
0
0.5
1.0
-2.5 -2.0 -1.5 -1.0 -0.5 0 ln[ln(p0 /p)]
0.5 1.0
(c) Particle size 0.198-0.245 mm
(b) Particle size 0.245-0.350 mm Fig. 3. A plot of lnV vs. ln[ln(P0/P)].
Table 2 Fractal dimension derived using the fractal FHH model. Particle size (mm)
0.350–0.833 0.245–0.350 0.198–0.245
P/P0 = 0–0.5
P/P0 = 0.5–1
D1 = 3 + A1
FHH model
R21
1.85 2.04 2.16
y1 = 1.15x1 + 2 y1 = 0.96x1 + 2.32 y1 = 0.84x1 + 2.54
0.96 0.96 0.98
D2 = 3 + A2
FHH model
R22
2.80 2.82 2.84
y2 = 0.2x2+ 2.3 y2 = 0.18x2+ 2.6 y2 = 0.16x2 + 2.77
0.91 0.93 0.95
858
C. Wang et al. / International Journal of Mining Science and Technology 22 (2012) 855–858
4. Conclusions (1) The adsorption of CH4 and N2 increases with increasing pressure. The adsorption capacity and the particle size are negatively correlated. A smaller particle size has larger adsorption capacity and larger particles have less adsorption capacity. (2) The adsorption capacity of coal increases as the fractal dimension increases. The fractal dimension is positively correlated with adsorption capacity. The variation in fractal dimension is reflected in dA/dP: Higher fractal dimension is correlated with larger values. (3) The smaller the particle size of the coal the bigger the specific surface area, the surface roughness, and the fractal dimension.
Acknowledgments This research was funded by the State Key Basic Research Program of China (No. 2011CB201202). The authors also thank Dr. Sun Wenjing, Tang Min and Feng Yanyan for their valuable assistance in the preparation of the manuscript and its revision. References [1] Mandelbrot BB. Stochastic models for the earth’s relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. Proc Natl Acad Sci 1975;72(10):3825. [2] Avnir D. The fractal approach to heterogeneous chemistry: surfaces, colloids, polymers. New York: John Wiley & Sons; 1989.
[3] Meyers RA. Coal Structure. New York: Academic Press; 1982. [4] Rodrigues C, Lemos de Sousa M. The measurement of coal porosity with different gases. Int J Coal Geol 2002;48(3–4):245–51. [5] Xie HP. Fractal-Rock Mechanics Introduction. Beijing: Science Press; 1996. [6] Zhang TJ, Xu HJ, Li SG, Ren SX. The effect of particle size on adsorption of methane on coal. J Hunan Univ Sci Technol 2009;24(001):9–12. [7] Zhang XD, Sang SX, Qin Y, Tang JX. Isotherm adsorption of coal samples with different grain size. J China Univ Mining Technol 2005;34(4):427–32. [8] Éttinger I. Methane saturation of coal strata as methane–coal solid solution. J Mining Sci 1990;26(2):159–64. [9] Yao YB, Tang SH, Huang WH. Fractal characterization of adsorption-pores of coals from north China: an investigation on CH4 adsorption capacity of coals. Int J Coal Geol 2008;73(1):27–42. [10] Sahouli B, Blacher S, Brouers F. Fractal surface analysis by using nitrogen adsorption data: the case of the capillary condensation regime. Langmuir 1996;12(11):2872–4. [11] Cai YD, Li JQ, Liu JL. Fractal characteristics of coal pores based on classic geometry and thermodynamics models. Beijing Acta Geologica Sinica 2011;85(5):1150–62. [12] Li CM, Zhang WQ. China’s main coalfields of shallow coal-derived gas. Beijing: Science Press; 1990. [13] Zhang XM, Zhang SA, Zhong AL. China’s Coal Seam Methane. Xi’an: Shanxi Scientific and Technological Press; 1991. [14] Avnir D, Jaroniec M. An isotherm equation for adsorption on fractal surfaces of heterogeneous porous materials. Langmuir 1989;5(6):1431–3. [15] Pfeifer P, Avnir D. Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces. J Chem Phys 1983;79:3558. [16] Pfeifer P, Wu YJ. Multilayer adsorption on a fractally rough surface. Phys Rev Lett 1989;62(17):1997–2000. [17] Zhou YP, Zhou L. Fundamentals of high pressure adsorption. Langmuir 2009;3.898(23):13461–6. [18] Yan JM, Zhang QY. Adsorption and condensed-the surface of the solid with holes. Beijing: Science Press; 1986. [19] Friesen W, Mikula R. Fractal dimensions of coal particles. J Colloid Interface Sci 1987;120(1):263–71. [20] Zhao ZG. Adsorption Effect Application Principle. Beijing: Chemical Industry Press; 2005. [21] Zhang YY. Chemica. Wall friction characteristics of pulverized coal by experiment and numerical simulation. J Southeast Univ 2010;001:133–8.
Contents lists available at SciVerse ScienceDirect
International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Fractal dimension of coal particles and their CH4 adsorption Wang Chengyang a, Hao Shixiong a,b, Sun Wenjing a, Chu Wei a,⇑ a b
Department of Chemical Engineering, Sichuan University, Chengdu 610065, China Department of Chemical Engineering, Sichuan University of Science & Engineering, Zigong 643000, China
a r t i c l e
i n f o
Article history: Received 10 March 2012 Received in revised form 14 April 2012 Accepted 15 May 2012 Available online 11 January 2013 Keywords: Coal Fractal dimension Frenkel-Halsey-Hill Brunauer–Emmett–Teller Adsorption isotherm
a b s t r a c t We describe the fractal analysis of three differently sized coal samples (0.350–0.833 mm, 0.245– 0.350 mm, and 0.198–0.245 mm). The influence of fractal dimension on CH4 adsorption capacity is investigated. The physical parameters of the samples were determined via the Brunauer–Emmett–Teller (BET) theory. A CH4 adsorption study over the pressures range from 0 to 5 MPa was carried out with a new volumetric measurement system. The CH4 adsorption was measured using the differently sized coal. Two fractal dimensions, D1 and D2 were determined over the pressure ranges from 0 to 0.5 MPa and from 0.5 to 1 MPa, using the Frenkel-Halsey-Hill (FHH) method. We conclude that the two fractal dimensions correlate with the CH4 adsorption capacity of the coal: increasing CH4 adsorption capacity occurs with a corresponding increase in fractal dimension. Furthermore, D1 and D2 are positively correlated with surface area, pore volume, and samples size. The size distribution of the samples has fractal characteristics. Ó 2012 Published by Elsevier B.V. on behalf of China University of Mining & Technology.
1. Introduction Mandelbrot popularized the concept of a fractal in 1975 and since then the concept has been applied to the study of coal, which has a characteristic complex surface structure [1]. Avnir et al. introduced fractal geometry into the study of surface structure and it has been used to study the irregular shape of materials having no characteristic repeat length but yet having self-similar forms [2]. The fractal concept provides a quantitative description of an irregular shape and is a powerful tool. Coal is a complex black or dark brown material with a complicated porous structure that allows it to burn easily. The structure is closely related to the adsorption and mobility of methane [3]. The pore size distribution is the foundation of investigations into coal bed methane and coal, gas matrix interactions. This includes coal bed methane absorption, desorption, diffusion, and seepage [4]. Many studies report that spaces within coal particles show fractal characteristics on a length scale over the atomic to grain size range [5]. Moreover, coal is a porous medium with a large internal surface area that has the capacity for gas adsorption [6,7]. Thus, it is important to study the relationships between fractal dimension and adsorption capacity of coals. From this, the migration and accumulation of coal bed methane (CBM) could be understood. Most of the recent measurements of CBM adsorption studied the adsorption isotherm as it relates to the physical structure of coal. Éttinger ⇑ Corresponding author. Tel.: +86 28 85403836. E-mail address: [email protected] (C. Wei).
et al. showed that the CH4 adsorption capacity of coal is positively correlated with the metamorphic grade of the coal [8]. Rodrigues et al. examined the adsorption capacity of coal for different gases, including N2, CO2, and CH4, and concluded that the adsorption capacity increased with increasing coal porosity. They also showed that the adsorption capacity for these three gases fell in the order CO2 > CH4 > N2. Yao et al. analyzed the N2 adsorption isotherm to estimate the pore structure and surface fractal dimension with the fractal Frenkel-Halsey-Hill (FHH) method. The relationship between fractal dimension and CH4 adsorption capacity were discussed [9]. Sahouli et al. and Cai et al. calculated the fractal dimension of a solid from the N2 adsorption isotherm using the fractal FHH method and a thermodynamics method. The results showed that the coal pore structure had fractal characteristics and that the fractal dimension of the pores was controlled by the composition and pore parameters of the coal. In this study both fractal models appeared to give equivalent results [10,11]. Many researchers now apply the Langmuir monolayer adsorption model to coal as a way to explain the CH4 adsorption. The fractal dimension can be obtained from isotherm adsorption data based on the monolayer adsorption model. However, methane adsorption on coal does not seem a likely candidate for a monolayer model. This conundrum may be explained by noting the small outside surface area of coal compared to its internal surface area. The internal surface area plays a more important role in methane adsorption. The pore structure is very complicated and the distribution of pore sizes is quite wide. This means that the interaction between gas and coal is unusual. Previous studies have shown that the percentage of micro-pores and transition holes in
2095-2686/$ - see front matter Ó 2012 Published by Elsevier B.V. on behalf of China University of Mining & Technology. http://dx.doi.org/10.1016/j.ijmst.2012.11.003
856
C. Wang et al. / International Journal of Mining Science and Technology 22 (2012) 855–858
the coal exceeds the percentage of the macro- and meso-pores [12,13]. CH4 adsorption is considered a monomolecular adsorption within macro- and meso-pores but it is considered volume filling in the micro-pores and transitions holes. Hence a modified FHH equation is used to calculate the fractal dimension of CH4 adsorption capacity of a coal [14–16]. This method has practical significance for this study. As described herein, physical adsorption parameters of coal were determined by applying Brunauer–Emmett–Teller (BET) theory and analyzing the fractal dimension with the FHH method applied to CH4 gas adsorption isotherm data. The pore structure and surface fractal dimension is obtained from these efforts. The relationship between fractal dimension and CH4 adsorption capacity is also discussed. 2. Experimental 2.1. Sample preparation The coal was collected from Qinghua, Qinghai province, China. The samples were prepared by crushing and sieving into three sizes: a range from 0.350 to 0.833 mm, from 0.245 to 0.350 mm, and from 0.198 to 0.245 mm. The samples were then dried at 393 K for 12 h in an oven. The proximate analysis of the sample was: moisture, 0.68% (by weight); ash, 1.66% (by weight); volatile matter, 20.97% (by weight); and carbon, 76.7% (by weight). 2.2. N2 adsorption isotherms The N2 adsorption was measured with a NOVA 1000e instrument from the Quantachrome Company. The BET specific surface area and pore volume were obtained from these measurements. The samples were out gassed at 393 K for 16 h. After out gassing for this period the N2 gas isotherm adsorption measurements were carried out at 77 K. The relative pressure (P/P0) ranged from 0.001 to 0.99. 2.3. CH4 adsorption isotherms Auto-adsorption experiments, equipment designed by the Northwest Chemical Engineering Research Center, were used to obtain the CH4 adsorption isotherms using the volumetric method. The results were obtained with the Redlich–Kwong equation. The adsorption equipment is shown in Fig. 1. All samples were out gassed at 298 K for 16 h under vacuum condition and then measured over a pressure range from 0.1 to 5 MPa. The CH4 adsorption capacity was determined at various pressures. The adsorption equilibrium time was 4 h.
1
Adsorption equipment Pressure gage
3.2. An analysis of CH4 adsorption Fig. 2b shows the CH4 adsorption isotherms. The CH4 adsorption increases as the particle size becomes smaller. The physical adsorption mechanism implies that since the smaller particles have more specific surface area and pore volume the CH4 adsorption will increase as the particle size decreases. CH4 adsorption also increases with increasing pressure. This could be explained by noting that increased pressure gives the CH4 gas in the adsorption cylinder more energy, which makes the interaction between the coal and the gas more intensive. This enhanced interaction forces gas into the micro-pores. Increased pressure also might collapse the fragile structure of the coal. This would also lead to a larger specific surface area and pore volume and, thus, increased CH4 adsorption. Many researchers have applied the Langmuir equation to their investigations of CH4 adsorption on coal [17]. Gas adsorption into coal is not monolayer adsorption, however. The Langmuir model is used because the adsorption of CH4 onto coal is classified as a type I adsorption isotherm. An adsorption situation that appears to fit a type I definition may not be a monolayer adsorption, however. Adsorption into the micro-pores of coal (62–3 nm) ought to be multilayer adsorption, capillary pore condensation, or micro-pore filling but these always show the characteristic type I isotherm. Multilayer adsorption and capillary pore condensation occurred during the gas adsorption in this study. These will show the type I adsorption isotherm [18]. Thus, the Langmuir model is appropriate for this study. Fig. 2b shows the fit of the CH4 pressure to the adsorbed CH4 with this model: The correlation coefficient is R2 P0.996. 3.3. Fractal dimension from an analysis of the CH4 isotherms
6
Heated Thermostatic Water bath
Reference
Sample
Helium
The total surface area, pore volume, and average pore size reported in this study were obtained using the BET model. The physical parameters of the coals are shown in Table 1. The total surface area and the pore volume both increase with a decrease in the particle size while the average pore size shows no significant change. Existing literature suggests that the decrease in coal particle size should correlate with an increase in total surface area. During crushing the micro-porous interior of the coal is exposed, which is normally blocked by minerals and ash, so the pore volume also increases. Fig. 2a shows the N2 adsorption isotherms of the three samples at 77 K. The N2 adsorption capacity of the coal increases with a decrease in the particle size. The fact that adsorption onto coal is a physical adsorption and the total surface area and pore volume affect adsorption can explain this. Thus, the increase in specific surface area and pore volume could increase the N2 adsorption capacity. Furthermore, decreasing pore size is correlated with increased N2 adsorption capacity of coal.
3 Filter
Methane
3.1. Analysis of the N2 adsorption isotherm adsorption
5
4 2
Unloading
3. Results and discussion
Vacuum pump
Fig. 1. CH4 adsorption equipment.
Fractal FHH and thermodynamic methods have been used to measure fractal dimension on the basis of gas adsorption isotherms [9,19]. The fractal FHH method has been shown to be the most effective method. This method is used herein on theCH4 adsorption data. The FHH method allows the fractal dimension to be determined from Eqs. (1) and (2):
ln V ¼ A ln½lnðP0 =PÞ þ constant
ð1Þ
D¼Aþ3
ð2Þ
857
C. Wang et al. / International Journal of Mining Science and Technology 22 (2012) 855–858
pressure region was larger than D2. Fig. 2b also shows how the incremental increase in adsorption for an incremental increase in pressure over the region where P/P0 = 0.5–1 decreases. Hence, through D1 and D2 it appears that the adsorption capacity increases with an increase in the fractal dimension. The variation in fractal dimension for a given coal sample is also reflected in dA/dP. The fractal dimension is positively correlated with dA/dP.
Table 1 Physical parameters of the coal. Particle size (mm)
Total surface area (m2/g)
Pore volume (cm3/g)
Average pore diameter (nm)
0.350–0.833 0.245–0.350 0.198–0.245
3.29 3.75 4.69
3.82 4.46 5.21
2.28 2.56 2.27
where V is the amount of adsorbed CH4 at equilibrium pressure P, P0 the saturation pressure of CH4; A an exponent related to the fractal dimension; and D the mechanism of adsorption. A plot of ln V vs. ln[ln (P0/P)] gives a straight line with a slope equal to A. The fractal dimension D depends on the value of A. The FHH plots of the three coal samples are shown in Fig. 3. Two distinct linear segments appear, one over the range P/P0 = 0–0.5 and the other at P/P0 = 0.5–1. Both of these segments show good fits, suggesting that the fractal characteristics at these two intervals are different. Table 2 summarizes the slopes of the regression lines and the fractal dimension value (D1 and D2) calculated at the two relative pressure ranges. Both D1 and D2 increase with decreasing particle size but the variation of D1 in the lower relative
3.4. Relationship between fractal dimensions and coal adsorption capacity Tables 1 and 2 show the results that indicate that the total surface area and pore volume increase as the particle size decreases and that there is a positive correlation with the fractal dimension. By definition the fractal dimension characterizes the surface roughness [20]. It has been reported that the particle size of coal decreases with increasing surface roughness [21]. This is in accord with our experimental results. The larger the fractal dimension the larger the surface roughness. Hence, particles with a higher fractal dimension have bigger specific surface area, surface roughness, and fractal dimension.
1.2 0.350-0.833 mm 0.245-0.350 mm 0.198-0.245 mm
2.5 2.0
CH4 adsorption capcity (mmol/g)
Volume adsorbed (V, mL/g)
3.0
1.5 1.0 0.5 0
0.2
0.4 0.6 0.8 Relative pressure (P/P0 ) (a) 77 K
0.350-0.833 mm 0.245-0.350 mm 0.198-0.245 mm Langmuir fit
1.0 0.8 0.6 0.4
R2 0.350-0.833 mm = 0.996 R2 0.245-0.350 mm = 0.997 R2 0.198-0.245 mm = 0.997
0.2
1.0
0
1
2 3 P (MPa) (b) 298 K
4
5
Fig. 2. CH4 adsorption isotherms.
lnV
lnV
2.5 2.0 0.350-0.833 mm Linear fit
1.5 1.0
-2.5 -2.0 -1.5 -1.0 -0.5 0 ln[ln(p0 /p)]
0.5
1.0
3.0 2.8 2.6 2.4 2.2 2.0
3.2 3.0 2.8 0.245-0.350 mm Linear fit
1.8 1.6 1.4 -2.5 -2.0 -1.5 -1.0 -0.5 ln[ln(p0 /p)]
(a) Particle size 0.350-0.833 mm
lnV
3.0
2.6 2.4 2.2
0.198-0.245 mm Linear fit
2.0 1.8
0
0.5
1.0
-2.5 -2.0 -1.5 -1.0 -0.5 0 ln[ln(p0 /p)]
0.5 1.0
(c) Particle size 0.198-0.245 mm
(b) Particle size 0.245-0.350 mm Fig. 3. A plot of lnV vs. ln[ln(P0/P)].
Table 2 Fractal dimension derived using the fractal FHH model. Particle size (mm)
0.350–0.833 0.245–0.350 0.198–0.245
P/P0 = 0–0.5
P/P0 = 0.5–1
D1 = 3 + A1
FHH model
R21
1.85 2.04 2.16
y1 = 1.15x1 + 2 y1 = 0.96x1 + 2.32 y1 = 0.84x1 + 2.54
0.96 0.96 0.98
D2 = 3 + A2
FHH model
R22
2.80 2.82 2.84
y2 = 0.2x2+ 2.3 y2 = 0.18x2+ 2.6 y2 = 0.16x2 + 2.77
0.91 0.93 0.95
858
C. Wang et al. / International Journal of Mining Science and Technology 22 (2012) 855–858
4. Conclusions (1) The adsorption of CH4 and N2 increases with increasing pressure. The adsorption capacity and the particle size are negatively correlated. A smaller particle size has larger adsorption capacity and larger particles have less adsorption capacity. (2) The adsorption capacity of coal increases as the fractal dimension increases. The fractal dimension is positively correlated with adsorption capacity. The variation in fractal dimension is reflected in dA/dP: Higher fractal dimension is correlated with larger values. (3) The smaller the particle size of the coal the bigger the specific surface area, the surface roughness, and the fractal dimension.
Acknowledgments This research was funded by the State Key Basic Research Program of China (No. 2011CB201202). The authors also thank Dr. Sun Wenjing, Tang Min and Feng Yanyan for their valuable assistance in the preparation of the manuscript and its revision. References [1] Mandelbrot BB. Stochastic models for the earth’s relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. Proc Natl Acad Sci 1975;72(10):3825. [2] Avnir D. The fractal approach to heterogeneous chemistry: surfaces, colloids, polymers. New York: John Wiley & Sons; 1989.
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