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Enhanced storage of hydrogen at the temperature of liquid nitrogen
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International Journal of Hydrogen Energy 29 (2004) 319 – 322
www.elsevier.com/locate/ijhydene
Enhanced storage of hydrogen at the temperature of liquid nitrogen Li Zhoua;∗ , Yaping Zhoub , Yan Suna a High
b Group
Pressure Adsorption Laboratory, School of Chemical Engineering, Tianjin 300072, People’s Republic of China of Physical Chemistry, Department of Chemistry, Tianjin University, Tianjin 300072, People’s Republic of China Accepted 3 June 2003
Abstract Storage of hydrogen in activated carbon at liquid nitrogen temperature is considerably enhanced in terms of compression and adsorption on activated carbon. To reach the capacity of 4:1 kg per 100 l of storage vessel, it needs to compress the gas to as high a pressure as 75 MPa at 298 K, but only to 15 MPa if compressed at 77 K. The pressure is reduced to 6 MPa if the container is 6lled with pellets of activated carbon AX-21. Liquid nitrogen is cheap in cost and widely available. Therefore, storing hydrogen on activated carbon cooled by liquid nitrogen seems feasible for the hydrogen vehicle programs. ? 2003 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Enhanced storage; Hydrogen; Compression; Adsorption; Liquid nitrogen
1. Introduction Fueling vehicles with hydrogen is the core of hydrogen economy and has attracted research interest all round the world. It is not only for protecting the atmosphere from polluting by the emission of toxic gases from conventional vehicles, but also for developing a renewable energy source. Fueling cars with hydrogen is feasible either by using an internal combustion engine or electric motor coupled with fuel cells. The bottleneck is the onboard storage of hydrogen to satisfy the demand of energy density and cost competition. Several ways of storage, including liquid hydrogen, compressed hydrogen, decomposed in situ from methanol or from metal hydride, could not be proven as a practical method to compete with conventional cars. Therefore, searching for a new way to store hydrogen is an urgent task and, therefore, major research budget was put on hydrogen storage [1]. Storage of compressed hydrogen at ambient temperature and very high pressures was proposed again recently, but the target pressure that satis6es practical constraints could not be reached at the present level of technology. Adsorptive storage of hydrogen on activated carbon ∗
Corresponding author. Tel.: +86-22-8789-1466. E-mail address: [email protected] (L. Zhou).
was proposed previously [2,3], yet it did not receive much attention from the industry, especially when carbon nanotubes were claimed to possess abnormal performance as a hydrogen carrier [4]. However, there is a big controversy on this claim both experimentally and theoretically. The others could not repeat the high-storage capacity claimed by some authors. The enhanced storage of hydrogen, either by compression or by adsorption on activated carbon, at the temperature of liquid nitrogen is presented. It takes advantage of the eCect of temperature on adsorption and hydrogen density as well as of the low cost and widespread availability of liquid nitrogen to intensify the storage of hydrogen. The storage capacity and the cost of hydrogen stored could meet the criterion of commercialization. 2. A comparison of compression storage at 77 and 298 K High-pressure compression has been considered again as an option of storage method recently, and one expects to gain about 20% savings in cost compared to liquid hydrogen. However, compression at ambient temperature is not eCective compared to compression at the temperature of liquid nitrogen (77 K). As shown in Fig. 1, which is drawn based on the p–V –T data of hydrogen [5], the pressure of
0360-3199/03/$ 30.00 ? 2003 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S0360-3199(03)00155-1
320
L. Zhou et al. / International Journal of Hydrogen Energy 29 (2004) 319 – 322
35
90 77 K
80
298 K
30 25
60 n/mmol.g-1
Capacity/g.L-1
70
50 40
20 15
30 10
20 10
powder pellets
5
0 0
10
20
30
40
50
60
70
80
90 100
p/MPa Fig. 1. Storage of H2 by compression.
hydrogen must reach 75 MPa at 298 K to store 41 g H2 in a 1 l container, but only 15 MPa is required at 77 K. Storage of hydrogen at as high a pressure as 75 MPa is presently not technically feasible. 3. Storing H2 on activated carbon cooled by liquid nitrogen Adsorption increases the density of hydrogen near the surface of carbon and, hence was applied to enhance the storage of hydrogen or natural gas in the container. However, only physical adsorption is feasible for the use of hydrogen in motor vehicles. As a fundamental feature of physical adsorption, the amount adsorbed depends strongly on temperature. An eCective way of enhancing the storage is to reduce the temperature of storage if the amount stored at ambient temperature could not meet the criterion of quali6cation. Liquid nitrogen is cheap in cost and widely available, and therefore, is a practical cooling media. Adsorption isotherms of H2 at 77 K on powder and pellets of activated carbon AX-21 were measured in our laboratory by an accurate volumetric apparatus. Details of the measurement technique were given previously [6]. The isotherms obtained are shown in Fig. 2, where symbols indicate the experimentally measured amount adsorbed, but they are not the real quantity of hydrogen 6xed on the carbon surface. Either volumetric or gravimetric method can only measure adsorption through the diCerence or change in pressure or weight readings, and give the quantity of excess adsorption. The total quantity of hydrogen contained in the adsorbed phase is the so-called absolute adsorption, which equals the sum of the
0 0
1
2
3
4
5
6
7
8
p/MPa Fig. 2. Adsorption isotherm on AC AX-21 at 77 K. Points: the excess; Curves: the absolute.
excess adsorption plus the product of gas phase density and the volume of the adsorbed phase. How to estimate the total adsorption from the excess adsorption data was regarded as a major challenge in high-pressure adsorption [7]. Based on the principle that excess and absolute adsorption are equal provided the surface concentration of adsorbate is dilute, the authors proposed a method to calculate the absolute adsorption isotherm from the excess adsorption data [8,9]. Shown as solid lines in Fig. 2 are the isotherms of absolute adsorption determined by the proposed method. The isotherms of absolute adsorption always increase with pressure, although the isotherms of the excess adsorption may decrease with pressure or even show negative values [10]. The storage capacity in a given volume is the capacity of adsorbed molecules on the carbon surface plus the volumetric capacity due to compression in the void space. The volume of the void space before adsorption, Vtv , is the sum of pore volume inside adsorbent particles and the volume outside the particles. This volume is experimentally determined by the helium expansion method, provided helium does not adsorb. Care must be exercised in terms of adsorbents containing extremely 6ne pores, where adsorption of helium might be possible. However, the volume of the void space is decreased to Vg after adsorption since a space of Va was occupied by the adsorbed phase and Vtv = Va + Vg :
(1)
Multiplying both sides of Eq. (1) by the gas phase density, g , we obtain g Vtv = g Va + g Vg :
(2)
L. Zhou et al. / International Journal of Hydrogen Energy 29 (2004) 319 – 322
50
12 77 K
45
11 77 K
10
40
5
9
35
der pow
8 4
30 25
3
wt % stored
Gram of H2 stored in 1 L
321
1
20
2
7
pellets
6 5 4
15
3
10
2 5
1
0 0
1
2
3
4 5 p/MPa
6
7
8
0 0
1
2
3
4 p/MPa
5
6
7
8
Fig. 3. Storage capacity on AC AX-21 and by compression. (1) Compressed; (2) Fixed on powder surface; (3) Total quantity stored in unit volume of powder; (4) Fixed on pellets surface; (5) Total quantity stored in unit volume of pellets.
Fig. 4. Weight percentage of H2 stored on AC AX-21 powder and pellets.
Adding the excess adsorption, n, to both sides of Eq. (2), we have
adsorption data on powder and pellets, respectively, based on the mass of carbon contained in the 1 l container; curves 3 and 5 are the total storage capacity of a 1 l container 6lled with carbon powder and carbon pellets, respectively (the bulk density of carbon powder is 0:3 kg=dm3 , and that of carbon pellets is 0:72 kg=dm3 ). For example, 19:6 g hydrogen could be stored at 6 MPa in a vacant 1 l container, 32:5 g hydrogen stored in the same container 6lled with 0:3 kg of carbon powder, and 41 g hydrogen could be stored if the container was 6lled with 0:72 kg of pellets. The Department of Energy, USA set up a criterion of 6:5 wt% for any potential hydrogen carrier. The value of such an index is 10:8 wt% for carbon powder at 6 MPa, and even higher at higher pressures as shown in Fig. 4. However, the storage capacity expressed by weight percentage is not a proper index since much more hydrogen can be stored per unit volume of container 6lled with carbon pellets as shown in Fig. 3, although the weight percentage of H2 is less than that when the container was 6lled with carbon powder. This fact may be explained by the changes of the bulk density and the speci6c surface area in making pellets. The loss in surface area leads to the decrease of gravimetric storage capacity, but the increase in bulk density leads to more adsorbent being 6lled in a given volume, which results in the increase in the volumetric storage capacity. Based on the above information, it is concluded that storage of hydrogen at 77 K achieves considerable enhancement due to both compression and adsorption. The pressure needed for storing 4:1 kg hydrogen in a container of 100 l
n + g Vtv = (n + g Va ) + g Vg = n s + g Vg = Ctot ;
(3)
where Ctot is the total capacity of storage. Therefore, neither Va nor Vg is needed for the evaluation of Ctot . Suppose the bulk density and the skeleton density of adsorbent is, respectively, b and s , then the volume occupied by “solid” or “skeleton” part of adsorbent is Vs =b =s , and the void space Vtv = 1 − b =s . Determination of b is a common practice of the laboratory, but that of s requires a special technique. The density of graphite was usually taken for the skeleton density of activated carbon. But this may not be correct because the existence of closed pores or small pores that are inaccessible to helium molecules makes the skeleton density of activated carbon smaller than that of graphite. The volume of the skeleton part of activated carbon was determined as the diCerence between the volumes of adsorption cell without and with loading adsorbent, and the density of the skeleton carbon was calculated based on such a volume. The “volumetric” storage capacity of activated carbon AX-21 for hydrogen at 77 K is shown in Fig. 3 on the basis of a 1 l container. Curve 1 is the quantity of hydrogen stored just by compression; curves 2 and 4 are the excess
322
L. Zhou et al. / International Journal of Hydrogen Energy 29 (2004) 319 – 322
by compression is decreased by a factor of 5 if the temperature is reduced from 298 to 77 K. The pressure is decreased further by two and half times if the container is 6lled with carbon pellets. Such a method of storage provides important practical implications. First, the storage capacity is acceptable for driving practice and the reported data can be repeated in any laboratory equipped with an accurate apparatus for adsorption measurement and operated by quali6ed personnel. Charging and discharging of hydrogen in activated carbon is reversible, since no hysterisis was observed at any temperature tested [6]. The adsorption of hydrogen on activated carbon, as a typical physical adsorption, reaches equilibrium fast. Second, activated carbon of a high speci6c surface area can be produced at a large scale with reasonable cost. Third, hydrogen is stored in gas state, therefore, is much cheaper than liquid hydrogen, and cleaner and safer than methanol. The storage facility is much simpler than that for on-board producing hydrogen. Fourth, instead of hydrogen, nitrogen is lost as evaporation loss; therefore, is safe and cheap. Fifth, liquid nitrogen is widely available at low cost. It does not need a nitrogen cylinder on board, but is required to add some into the insulation jacket periodically, usually once a week due to the large heat capacity of the fuel tank.
Acknowledgements This work is subsidized by the Special Funds of Major State Basic Research Projects (G2000026404) and supported by the National Natural Science Foundation of China (#29936100). References [1] Cannon JS. Int J Hydrogen Energy 1994;19(11):905–9. [2] Noh JS, Agarwal RK, Schwarz JA. Int J Hydrogen Energy 1987;12:693–700. [3] Zhou L. Sci Technol Rev 1999;12:11–3 [in Chinese]. [4] Dillon AC, Jones KM, Bekkedahl TA, Kiang CH, Bethune DS, Heben MJ. Nature 1997;386:377–9. [5] Vargaftik NB. Handbook of physical properties of liquids and gases, pure substances and mixtures, 2nd ed. New York: Hemisphere Publishing Corporation; 1975. [6] Zhou YP, Zhou L. Sci China Ser B 1996;39(6):598–607. [7] Humayun R, Tomasko DL. AIChE J 2000;46:2065–75. [8] Zhou L, Zhou YP. Chem Eng Sci 1998;53:2531–6. [9] Zhou L, Zhou YP. Chin J Chem Eng 2001;9:110–5. [10] Zhou L. Adsorption isotherms for the supercritical region. In: Toth J, editor. Adsorption: theory, modeling & analysis. New York: Marcel Dekker; 2002.
International Journal of Hydrogen Energy 29 (2004) 319 – 322
www.elsevier.com/locate/ijhydene
Enhanced storage of hydrogen at the temperature of liquid nitrogen Li Zhoua;∗ , Yaping Zhoub , Yan Suna a High
b Group
Pressure Adsorption Laboratory, School of Chemical Engineering, Tianjin 300072, People’s Republic of China of Physical Chemistry, Department of Chemistry, Tianjin University, Tianjin 300072, People’s Republic of China Accepted 3 June 2003
Abstract Storage of hydrogen in activated carbon at liquid nitrogen temperature is considerably enhanced in terms of compression and adsorption on activated carbon. To reach the capacity of 4:1 kg per 100 l of storage vessel, it needs to compress the gas to as high a pressure as 75 MPa at 298 K, but only to 15 MPa if compressed at 77 K. The pressure is reduced to 6 MPa if the container is 6lled with pellets of activated carbon AX-21. Liquid nitrogen is cheap in cost and widely available. Therefore, storing hydrogen on activated carbon cooled by liquid nitrogen seems feasible for the hydrogen vehicle programs. ? 2003 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Enhanced storage; Hydrogen; Compression; Adsorption; Liquid nitrogen
1. Introduction Fueling vehicles with hydrogen is the core of hydrogen economy and has attracted research interest all round the world. It is not only for protecting the atmosphere from polluting by the emission of toxic gases from conventional vehicles, but also for developing a renewable energy source. Fueling cars with hydrogen is feasible either by using an internal combustion engine or electric motor coupled with fuel cells. The bottleneck is the onboard storage of hydrogen to satisfy the demand of energy density and cost competition. Several ways of storage, including liquid hydrogen, compressed hydrogen, decomposed in situ from methanol or from metal hydride, could not be proven as a practical method to compete with conventional cars. Therefore, searching for a new way to store hydrogen is an urgent task and, therefore, major research budget was put on hydrogen storage [1]. Storage of compressed hydrogen at ambient temperature and very high pressures was proposed again recently, but the target pressure that satis6es practical constraints could not be reached at the present level of technology. Adsorptive storage of hydrogen on activated carbon ∗
Corresponding author. Tel.: +86-22-8789-1466. E-mail address: [email protected] (L. Zhou).
was proposed previously [2,3], yet it did not receive much attention from the industry, especially when carbon nanotubes were claimed to possess abnormal performance as a hydrogen carrier [4]. However, there is a big controversy on this claim both experimentally and theoretically. The others could not repeat the high-storage capacity claimed by some authors. The enhanced storage of hydrogen, either by compression or by adsorption on activated carbon, at the temperature of liquid nitrogen is presented. It takes advantage of the eCect of temperature on adsorption and hydrogen density as well as of the low cost and widespread availability of liquid nitrogen to intensify the storage of hydrogen. The storage capacity and the cost of hydrogen stored could meet the criterion of commercialization. 2. A comparison of compression storage at 77 and 298 K High-pressure compression has been considered again as an option of storage method recently, and one expects to gain about 20% savings in cost compared to liquid hydrogen. However, compression at ambient temperature is not eCective compared to compression at the temperature of liquid nitrogen (77 K). As shown in Fig. 1, which is drawn based on the p–V –T data of hydrogen [5], the pressure of
0360-3199/03/$ 30.00 ? 2003 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S0360-3199(03)00155-1
320
L. Zhou et al. / International Journal of Hydrogen Energy 29 (2004) 319 – 322
35
90 77 K
80
298 K
30 25
60 n/mmol.g-1
Capacity/g.L-1
70
50 40
20 15
30 10
20 10
powder pellets
5
0 0
10
20
30
40
50
60
70
80
90 100
p/MPa Fig. 1. Storage of H2 by compression.
hydrogen must reach 75 MPa at 298 K to store 41 g H2 in a 1 l container, but only 15 MPa is required at 77 K. Storage of hydrogen at as high a pressure as 75 MPa is presently not technically feasible. 3. Storing H2 on activated carbon cooled by liquid nitrogen Adsorption increases the density of hydrogen near the surface of carbon and, hence was applied to enhance the storage of hydrogen or natural gas in the container. However, only physical adsorption is feasible for the use of hydrogen in motor vehicles. As a fundamental feature of physical adsorption, the amount adsorbed depends strongly on temperature. An eCective way of enhancing the storage is to reduce the temperature of storage if the amount stored at ambient temperature could not meet the criterion of quali6cation. Liquid nitrogen is cheap in cost and widely available, and therefore, is a practical cooling media. Adsorption isotherms of H2 at 77 K on powder and pellets of activated carbon AX-21 were measured in our laboratory by an accurate volumetric apparatus. Details of the measurement technique were given previously [6]. The isotherms obtained are shown in Fig. 2, where symbols indicate the experimentally measured amount adsorbed, but they are not the real quantity of hydrogen 6xed on the carbon surface. Either volumetric or gravimetric method can only measure adsorption through the diCerence or change in pressure or weight readings, and give the quantity of excess adsorption. The total quantity of hydrogen contained in the adsorbed phase is the so-called absolute adsorption, which equals the sum of the
0 0
1
2
3
4
5
6
7
8
p/MPa Fig. 2. Adsorption isotherm on AC AX-21 at 77 K. Points: the excess; Curves: the absolute.
excess adsorption plus the product of gas phase density and the volume of the adsorbed phase. How to estimate the total adsorption from the excess adsorption data was regarded as a major challenge in high-pressure adsorption [7]. Based on the principle that excess and absolute adsorption are equal provided the surface concentration of adsorbate is dilute, the authors proposed a method to calculate the absolute adsorption isotherm from the excess adsorption data [8,9]. Shown as solid lines in Fig. 2 are the isotherms of absolute adsorption determined by the proposed method. The isotherms of absolute adsorption always increase with pressure, although the isotherms of the excess adsorption may decrease with pressure or even show negative values [10]. The storage capacity in a given volume is the capacity of adsorbed molecules on the carbon surface plus the volumetric capacity due to compression in the void space. The volume of the void space before adsorption, Vtv , is the sum of pore volume inside adsorbent particles and the volume outside the particles. This volume is experimentally determined by the helium expansion method, provided helium does not adsorb. Care must be exercised in terms of adsorbents containing extremely 6ne pores, where adsorption of helium might be possible. However, the volume of the void space is decreased to Vg after adsorption since a space of Va was occupied by the adsorbed phase and Vtv = Va + Vg :
(1)
Multiplying both sides of Eq. (1) by the gas phase density, g , we obtain g Vtv = g Va + g Vg :
(2)
L. Zhou et al. / International Journal of Hydrogen Energy 29 (2004) 319 – 322
50
12 77 K
45
11 77 K
10
40
5
9
35
der pow
8 4
30 25
3
wt % stored
Gram of H2 stored in 1 L
321
1
20
2
7
pellets
6 5 4
15
3
10
2 5
1
0 0
1
2
3
4 5 p/MPa
6
7
8
0 0
1
2
3
4 p/MPa
5
6
7
8
Fig. 3. Storage capacity on AC AX-21 and by compression. (1) Compressed; (2) Fixed on powder surface; (3) Total quantity stored in unit volume of powder; (4) Fixed on pellets surface; (5) Total quantity stored in unit volume of pellets.
Fig. 4. Weight percentage of H2 stored on AC AX-21 powder and pellets.
Adding the excess adsorption, n, to both sides of Eq. (2), we have
adsorption data on powder and pellets, respectively, based on the mass of carbon contained in the 1 l container; curves 3 and 5 are the total storage capacity of a 1 l container 6lled with carbon powder and carbon pellets, respectively (the bulk density of carbon powder is 0:3 kg=dm3 , and that of carbon pellets is 0:72 kg=dm3 ). For example, 19:6 g hydrogen could be stored at 6 MPa in a vacant 1 l container, 32:5 g hydrogen stored in the same container 6lled with 0:3 kg of carbon powder, and 41 g hydrogen could be stored if the container was 6lled with 0:72 kg of pellets. The Department of Energy, USA set up a criterion of 6:5 wt% for any potential hydrogen carrier. The value of such an index is 10:8 wt% for carbon powder at 6 MPa, and even higher at higher pressures as shown in Fig. 4. However, the storage capacity expressed by weight percentage is not a proper index since much more hydrogen can be stored per unit volume of container 6lled with carbon pellets as shown in Fig. 3, although the weight percentage of H2 is less than that when the container was 6lled with carbon powder. This fact may be explained by the changes of the bulk density and the speci6c surface area in making pellets. The loss in surface area leads to the decrease of gravimetric storage capacity, but the increase in bulk density leads to more adsorbent being 6lled in a given volume, which results in the increase in the volumetric storage capacity. Based on the above information, it is concluded that storage of hydrogen at 77 K achieves considerable enhancement due to both compression and adsorption. The pressure needed for storing 4:1 kg hydrogen in a container of 100 l
n + g Vtv = (n + g Va ) + g Vg = n s + g Vg = Ctot ;
(3)
where Ctot is the total capacity of storage. Therefore, neither Va nor Vg is needed for the evaluation of Ctot . Suppose the bulk density and the skeleton density of adsorbent is, respectively, b and s , then the volume occupied by “solid” or “skeleton” part of adsorbent is Vs =b =s , and the void space Vtv = 1 − b =s . Determination of b is a common practice of the laboratory, but that of s requires a special technique. The density of graphite was usually taken for the skeleton density of activated carbon. But this may not be correct because the existence of closed pores or small pores that are inaccessible to helium molecules makes the skeleton density of activated carbon smaller than that of graphite. The volume of the skeleton part of activated carbon was determined as the diCerence between the volumes of adsorption cell without and with loading adsorbent, and the density of the skeleton carbon was calculated based on such a volume. The “volumetric” storage capacity of activated carbon AX-21 for hydrogen at 77 K is shown in Fig. 3 on the basis of a 1 l container. Curve 1 is the quantity of hydrogen stored just by compression; curves 2 and 4 are the excess
322
L. Zhou et al. / International Journal of Hydrogen Energy 29 (2004) 319 – 322
by compression is decreased by a factor of 5 if the temperature is reduced from 298 to 77 K. The pressure is decreased further by two and half times if the container is 6lled with carbon pellets. Such a method of storage provides important practical implications. First, the storage capacity is acceptable for driving practice and the reported data can be repeated in any laboratory equipped with an accurate apparatus for adsorption measurement and operated by quali6ed personnel. Charging and discharging of hydrogen in activated carbon is reversible, since no hysterisis was observed at any temperature tested [6]. The adsorption of hydrogen on activated carbon, as a typical physical adsorption, reaches equilibrium fast. Second, activated carbon of a high speci6c surface area can be produced at a large scale with reasonable cost. Third, hydrogen is stored in gas state, therefore, is much cheaper than liquid hydrogen, and cleaner and safer than methanol. The storage facility is much simpler than that for on-board producing hydrogen. Fourth, instead of hydrogen, nitrogen is lost as evaporation loss; therefore, is safe and cheap. Fifth, liquid nitrogen is widely available at low cost. It does not need a nitrogen cylinder on board, but is required to add some into the insulation jacket periodically, usually once a week due to the large heat capacity of the fuel tank.
Acknowledgements This work is subsidized by the Special Funds of Major State Basic Research Projects (G2000026404) and supported by the National Natural Science Foundation of China (#29936100). References [1] Cannon JS. Int J Hydrogen Energy 1994;19(11):905–9. [2] Noh JS, Agarwal RK, Schwarz JA. Int J Hydrogen Energy 1987;12:693–700. [3] Zhou L. Sci Technol Rev 1999;12:11–3 [in Chinese]. [4] Dillon AC, Jones KM, Bekkedahl TA, Kiang CH, Bethune DS, Heben MJ. Nature 1997;386:377–9. [5] Vargaftik NB. Handbook of physical properties of liquids and gases, pure substances and mixtures, 2nd ed. New York: Hemisphere Publishing Corporation; 1975. [6] Zhou YP, Zhou L. Sci China Ser B 1996;39(6):598–607. [7] Humayun R, Tomasko DL. AIChE J 2000;46:2065–75. [8] Zhou L, Zhou YP. Chem Eng Sci 1998;53:2531–6. [9] Zhou L, Zhou YP. Chin J Chem Eng 2001;9:110–5. [10] Zhou L. Adsorption isotherms for the supercritical region. In: Toth J, editor. Adsorption: theory, modeling & analysis. New York: Marcel Dekker; 2002.