Modeling the selectivity of activated carbons for efficient separation of hydrogen and carbon dioxide

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1 Carbon 3 (5) Modeling the selectivity of activated carbons for efficient separation of hydrogen and carbon dioxide Dapeng Cao, Jianzhong Wu * Department of Chemical and Environmental Engineering, University of California, Riverside, CA 95, United States Received June ; accepted January 5 Available online March 5 Abstract Grand canonical Monte Carlo simulations (GCMC) are carried out to investigate the separation of hydrogen and carbon dioxide via adsorption in activated carbons. In the simulations, both hydrogen and carbon dioxide molecules are modeled as Lennard-Jones spheres, and the activated carbons are represented by a slit-pore model. At elevated temperatures (T = 55 and 93 K), the activated carbons exhibit essentially no preference over the two gases and the selectivity of carbon dioxide relative to hydrogen falls monotonically as the pore size increases. At room temperature, however, the selectivity of carbon dioxide relative to hydrogen reaches up to 9, indicating that hydrogen and carbon dioxide can be efficiently separated. Furthermore, the optimized pore sizes, of width H =. nm for the bulk mole fraction ratio of x CO =x H ¼ : and H =. nm for x CO =x H ¼ :, are identified in which the activated carbons show the highest selectivity for the separation of hydrogen and carbon dioxide. Ó 5 Elsevier Ltd. All rights reserved. Keywords: Activated carbons; Adsorption separation; Molecular simulation. Introduction Hydrogen is expected to be a primary energy source in the st century for automobiles and other energy applications []. A primary current technology [ ] for hydrogen generation is by coal gasification that produces synthesis gases containing mainly CO and H. After the pyrolysis, CO is converted into H and CO by water-gas-shift reaction. In a conventional process, coal gasification occurs at a temperature of approximately 73 K, and the water-gas-shift reaction is performed at a temperature below 73 K. Very recently, direct H production by coal/cao pyrolysis has been reported at a temperature of about 9 K and pressure * Corresponding author. Tel.: ; fax: address: jwu@engr.ucr.edu (J. Wu). about MPa [3,5]. By fixing CO into CaCO 3 and completely converting CO to H, this new process yields nearly.5 times more H in comparison with the conventional method. Moreover, the gases produced from the new method contain up to 5% H, nearly six folds higher than that from the conventional method [3]. A common challenge in both conventional and more recent technologies is, however, the purification of hydrogen by efficient removal of CO and other contaminants from the mixture without significantly lowing the temperature and pressure. Most previous investigations for CO and H separation are focused on membrane technologies [ ] with few exceptions using alternative methods such as hydrate process or adsorption using porous materials. These methods are most suitable for operation at conditions remote from the hostile temperature and pressure used during coal gasification. Application of novel nanoporous materials, such as activated carbons -3/$ - see front matter Ó 5 Elsevier Ltd. All rights reserved. doi:./j.carbon.5..

2 D. Cao, J. Wu / Carbon 3 (5) [,], MCM- [3,] or sorbents with alkali metals, as a means of CO separation from the flue gas by adsorption represents a more recent development [,5]. Motivated by the accuracy of molecular simulations for predicting the adsorption of gas molecules in porous materials, we intend to investigate the efficiency of nanoporous materials for the separation of hydrogen and carbon dioxide at room and higher temperatures by using the grand canonical Monte Carlo (GCMC) simulations. The simulation results will provide useful insights for the design and selection of porous materials for hydrogen production and purification. Activated carbons have excellent chemical stability and mechanical performance promising for gas separation at extreme conditions. These materials are relatively inexpensive and have been extensively used for separations, natural gas storage and removal of various pollutants. Depending on the activation process, activated carbons possess pores ranging from a few Angströms up to hundreds of nanometers, and exhibit large Brunauer Emmett Teller (BET) specific surface areas and pore volumes [,,7]. The geometrical heterogeneity of the activated carbons is often represented by the pore-size distribution. Some previous investigations show that activated carbons are promising for the efficient separation of gas mixtures such as H /CO [], N /CH [], and CO /CH [5]. With the right pore size, activated carbons may also provide a convenient yet inexpensive medium for the removal of CO and other gas contaminants for H purification. The rest of this paper is organized as the following. Section briefly introduces the molecular models used in this work and justifications of the model parameters. The details of GCMC simulations and the relationship between chemical potential, pressure and gas-phase composition are presented in Section 3. Section gives the simulation results for the relative selectivity and adsorption isotherms of carbon dioxide and hydrogen in activated carbons of various geometries. The main findings of this work are summarized in Section 5 along with some remarks for practical applications.. Molecular models In this work, both carbon dioxide and hydrogen molecules are represented by spherical Lennard-Jones particles, and the geometry of activated carbon is assumed as slit pores. For carbon dioxide, Vishnyakov et al. [9] made a comprehensive comparison between the spherical Lennard-Jones (SLJ) model and the three-center Lennard-Jones (TCLJ) plus qudrupolar moment model. Apparently, the two models yield entirely different density profiles for the confined carbon dioxide because the TCLJ model entails the orientation of gas molecules while the SLJ model does not. However, it was found that the two models are of excellent agreement for the calculation of adsorption isotherms of carbon dioxide in slit pores [9]. Because the later is of key concern in this work, the SLJ model is adopted for numerical simplicity. As reported earlier [], hydrogen molecules is assumed as spherical LJ particles, and the activated carbon is assumed to have slit pores. The cut-shifted potential is used to represent the pair interaction between fluid molecules [,] / ff ¼ / LJðrÞ / LJ ðr c Þ r < r c ðþ r P r c where r denotes the intermolecular distance, r c =5r ff is the cutoff radius with r being the Lennard-Jones diameter and the subscribe f standing for a fluid molecule. In Eq. (), / LJ represents the full LJ potential r ff r ff / LJ ðrþ ¼e ff ðþ r r where e ff and r ff are the energy and size parameters respectively. The interaction between a fluid molecule and the wall of the activated carbon is represented by the SteeleÕs - -3 potential: " / fw ðzþ ¼pq w e fw r fw D : r fw r fw z z!# r fw ð3þ 3Dð:D þ zþ 3 where q w = nm 3 is the number density of the activated carbons, and the subscript ÔwÕ represents the carbon wall. Other parameters in Eq. (3) are defined as follows: D =.335 nm is the distance between the lattice planes of the carbon wall, z is the normal distance between a gas molecule and one of the carbon walls, and e fw and r fw are the cross interaction parameters obtained from the Lorentz Berthelot combining rules. For a slit pore of fixed width H, the total potential / T can be calculated by summation of fluid-fluid and fluid-wall interactions [7] / T ¼ / ff þ / fw ðzþþ/ fw ðh zþ ðþ Table gives the energy and size parameters of carbon dioxide, hydrogen, and carbon walls. The hydrogen parameters used in this work yield accurate P-V-T behavior over a broad range of temperatures and pressures [], and have been extensively used in the calculation of hydrogen adsorption [,3,]. Based on the SLJ parameters of carbon dioxide molecules, the adsorption isotherms and diffusion coefficient of carbon dioxide in activated slit pores have been accurately predicted [5]. Recently, the SLJ model for carbon dioxide is also applied to the separation of carbon dioxidealkane mixtures in nanopores [].

3 3 D. Cao, J. Wu / Carbon 3 (5) 3 37 Table Molecular parameters for hydrogen, carbon dioxide and activated carbons Hydrogen [,] a Carbon dioxide [5] Carbon [] r H ðnmþ e H =k ðkþ r CO ðnmþ e CO =k ðkþ r CO ðnmþ e CO =k ðkþ a It has been shown that these parameters yield accurate P-V-T behavior of hydrogen over a broad range of temperatures and pressures []. 3. Simulation details The standard grand canonical Monte Carlo simulation (GCMC) is employed to calculate the adsorption of hydrogen and carbon dioxide gases in carbon slit pores. The GCMC consists of three types of Monte Carlo moves, all following the Metropolis algorithm: an attempted displacement of a molecule, an attempted deletion of a randomly selected molecule, and an attempted insertion of a molecule at a random position []. For each simulation run, the system temperature, the chemical potentials of gases and the micropore volume are specified in advance. Because the carbon walls are located in the z-direction, the periodic boundary condition was imposed only in the x and y directions. In our simulations, all variables were reduced with respect to hydrogen parameters, and the displacement, insertion and deletion moves were chosen with equal probability. At adsorption equilibrium, the chemical potentials of the confined gases are the same as those in the bulk fluid, which can be calculated from an equation of state. At low pressure, we assume that the gas mixture is an ideal gas. At higher pressures, a second virial correction is added to the ideal-gas law and the pressure can be calculated via the following equation of state [9] P ¼ RT ðq þ q i B ii þ q i q j B ij þ q j B jjþ ð5þ where i =H and j =CO, R is the gas constant, q is the molar density, and the second virial coefficients are related to the pair intermolecular forces [3] Z B ij ¼ pn A ½ expð u ij ðrþ=kt ÞŠr dr ðþ where N A is AvogadroÕs constant. Accordingly, the bulk chemical potential is given by a i ¼ RT ðq i B ii þ q j B ij ÞþRT lnðq i =q Þ; i ¼ H or CO ð7þ where q is the molar density of a reference ideal-gas state [9]. For each simulation run, 7 configurations were generated with the first half discarded to equilibrate the system and the second half used for the calculation of the ensemble averages as well as thermodynamic properties. The uncertainty for the ensemble averages of the number of adsorbate molecules in the simulation box and the total potential energy was estimated to be less than % [3].. Results and discussion The efficiency of separation may be represented by selectivity defined as [3] S ¼ ð xpore H Þ=x pore H ð x bulk H Þ=x bulk H ¼ q pore CO =q bulk CO q pore H =q bulk H ðþ where the superscripts ÔporeÕ and ÔbulkÕ denote the pore and the bulk phase, and x pore i and x bulk i are the average mole fractions of species i in the pore and in the bulk respectively. We first explore the separation of hydrogen and carbon dioxide in activated carbons at high temperatures as of interest in H production via coal gasification. Because hydrogen represents the main component in the gas mixture, two mole fraction ratios x CO =x H ¼ : and :are investigated in the work. Fig. shows the selectivity of carbon dioxide relative to hydrogen in activated carbon at T = 93 K corresponding to that used for the production of H by coal/cao pyrolysis [3]. The top panel corresponds to the mole fraction of x CO =x H ¼ : and the bottom panel is for x CO =x H ¼ :. For the pore of width H =.9 nm, the selectivity drastically decreases as the pressure increase. Around. MPa, the selectivity is approximately the same as the Knudsen separation factor []. For the activated carbons with the pore width H >., however, the selectivity is essential invariant with pressure. Furthermore, the selectivity is near unity, indicating that the activated carbons exhibit no preference over the two gases. This is understandable because at high temperatures, the gas mixture is essentially ideal and there is essentially no interaction between the gas and carbon molecules. Fig. shows the dependence of the selectivity on pore size. With the increase in pore size, the selectivity of carbon dioxide falls monotonically. In addition, one may observe that at high pressure, the selectivity is insensitive to the pore width. At low pressure, however, the selectivity drastically falls as the pore width increases. Fig. 3 shows the selectivity of activated carbons of different pore widths for the separation of carbon dioxide and hydrogen at T = 55 K. Basically, the behavior

4 D. Cao, J. Wu / Carbon 3 (5) T=93 K, xco =: H=.9 nm T=55 K, x CO /x H =: H=.9 nm 3 H=.9 nm T=55 K, x CO /x H =: H=.9 nm T=93 K, xco =: Fig.. of carbon dioxide relative to hydrogen on activated carbons of different pore sizes at T =93K. Fig. 3. of carbon dioxide relative to hydrogen on activated carbons of different pore sizes at T = 55 K T=93 K, xco =: T=93 K, xco =: P=.53 MPa P=3.7 MPa P=. MPa P=.5 MPa P=7.7 MPa P=9. MPa P=. MPa H (nm) P=.5 MPa P=.3 MPa P=3. MPa P=. MPa P=5.79 MPa P=.9 MPa P=.3 MPa P=9.3 MPa Fig.. of carbon dioxide relative to hydrogen at various pore sizes of activated carbons at T =93K (a) (b) T=9 K, xco =: T=9 K, xco =: P=. MPa P=. MPa P=.99 MPa P=3.75 MPa P=.7 MPa P=5.7 MPa P=. MPa P=7. MPa H (nm) H=.9 nm H=. nm H=.7 nm Fig.. of carbon dioxide relative to hydrogen changing with (a) pressure and (b) pore size of activated carbons at T = 9 K and x CO =x H ¼ :.

5 3 D. Cao, J. Wu / Carbon 3 (5) 3 37 is the same as that at T = 93 K. The only difference is the magnitude of selectivity. The activated carbon of pore of H =.9 nm exhibits the adsorption preference to carbon dioxide. In particular, at the low pressures the selectivity is greater than, which is about.5 times of the ideal separation factor (=.9) of Knudsen [9]. The selectivity of activated carbon over hydrogen and carbon dioxide increases as the temperature falls. Fig. shows the selectivity isotherms of carbon dioxide at T =9 K and x CO =x H ¼ :. As expected, at room temperature, the activated carbon exhibits a strong adsorption preference over carbon dioxide. Furthermore, the pore size has a significant effect on the selectivity of carbon dioxide. Fig. suggests that the activated carbon with pore of H =. nm has an optimal selectivity of carbon dioxide at all pressures. In particular, at P =. MPa, the selectivity of carbon dioxide reaches 9, indicating that hydrogen can be efficiently purified from the binary mixture of hydrogen and carbon dioxide. Fig. 5 shows the selectivity of carbon dioxide at T = 9 K and x CO =x H ¼ :. Interestingly, the mole fraction appears to have a significant effect on the selectivity of carbon dioxide. In the case of x CO =x H ¼ :, the activated carbon with pore of H =. nm rather than H =. nm presents a maximum selectivity for the separation of carbon dioxide and hydrogen. Apparently, the pore width corresponding to the maximum selectivity becomes larger as the mole fraction of hydrogen in the binary mixture becomes smaller. To provide further insights on the selectivity of activated carbons for the separation of carbon dioxide and hydrogen, we have also calculated the adsorption isotherms of hydrogen and carbon dioxide mixtures in activated carbons at room temperature (Fig. ). For all the activated carbons investigated in this work, the adsorption of carbon dioxide is relatively insensitive to the pressure changes whereas hydrogen adsorption significantly increases with pressure. As a result, the selectivity of carbon dioxide decreases as the pressure rises. In addition, we observed that at T =9 K and x CO =x H ¼ :, the adsorption of hydrogen exhibits a minimum in activated carbons of pore widths between H =. nm and H =. nm; because the amount of adsorption is monotonic for carbon dioxide, the selectivity shows a maximum at H =. nm. At higher temperature (T = 55 K), the adsorption of hydrogen increases with the pore size (Fig. 7). Furthermore, the adsorption of carbon dioxide shows similar behavior as that for hydrogen, in contrast to that at room temperature. Therefore, for the separation of hydrogen and carbon dioxide at room temperature, there is an optimal pore (a) T=9 K, xco =: (b) T=9 K, xco =: H=.9 nm H=. nm H=.7 nm P=.3 MPa P=. MPa P=3. MPa P=3.95 MPa P=. MPa P=5.7 MPa P=. MPa P=7.5 MPa Adsorption of H (mmol/cm 3 ) Adsorption of CO (mmol/cm 3 ) H=.9 nm H=. nm H=.7 nm H=.9 nm H=. nm H=.7 nm H (nm) Fig. 5. of carbon dioxide relative to hydrogen changing with (a) pressure and (b) pore sizes of activated carbons at x CO =x H ¼ :. Fig.. Adsorption isotherms of hydrogen and carbon dioxide in activated carbons with different pore sizes at room temperature and x CO =x H ¼ :.

6 D. Cao, J. Wu / Carbon 3 (5) adsorption of CO (mmol/cm 3 ) adsorption of H (mmol/cm 3 ) H=.9 nm H=.9 nm H=.7 5. Conclusions Separation of hydrogen and carbon dioxide via activated carbons is investigated using grand canonical Monte Carlo simulations. The selectivity of carbon dioxide relative to hydrogen in activated carbons of different pore sizes is obtained at room (9 K) and higher temperatures (T = 55 K, 93 K). At T = 55 and 93 K, the activated carbons show virtually no adsorption preference over carbon dioxide. This is because at high temperature, the properties of two gases are very similar (both are essentially ideal gases). At room temperature, however, the activated carbon exhibits strong adsorption preference to carbon dioxide. For x CO =x H ¼ :, there is an optimum pore size of H =. nm in which the activated carbons show maximum selective adsorption of carbon dioxide. This optimum pore size is sensitive to gas composition; for instance, it is H =. nm for the case of x CO =x H ¼ :. Although the gas composition has no significant effect on the selectivity of carbon dioxide relative to hydrogen at high temperatures (T = 55, 93 K), it significantly affects the optimal pore size corresponding to the maximum selectivity at room temperature. Fig. 7. Adsorption isotherms of hydrogen and carbon dioxide in activated carbons with different pore sizes at T = 55 K and x CO =x H ¼ :. 5 3 xco =: xco =: Temperature (K) Fig.. Dependence of the selectivity on temperature at H =. nm and P =. MPa. size of H =. nm. However this optimum does not show up at higher temperatures (e.g., T = 55 K). Fig. presents the dependence of the selectivity of carbon dioxide on temperature at H =. nm and. MPa. Apparently, the selectivity of carbon dioxide is very sensitive to temperature at the range of T < 5 K. The higher temperature is, the smaller is the selectivity for the separation of carbon dioxide and hydrogen. References [] Brumfiel G. Hydrogen cars fuel debate on basic research. Nature 3;(9):. [] Kuramoto K, Furuya T, Suzuki Y, Hatano H, Kumabe K, Yoshiie R, et al. Coal gasification with a subcritical steam in the presence of a COsorbent: products and conversion under transient heating. Fuel Proc Technol 3;(): 73. [3] Lin SY, Harada M, Suzuki Y, Hatano H. Hydrogen production from coal by separating carbon dioxide during gasification. Fuel ;():79 5. [] Lin SY, Harada M, Suzuki Y, Hatano H. Continuous experiment regarding hydrogen production by coal/cao reaction with steam (I) gas products. Fuel ;3(7 ):9 7. [5] Lin SY, Suzuki Y, Hatano H, Harada M. Hydrogen production from hydrocarbon by integration of water-carbon reaction and carbon dioxide removal. Energy Fuels ;5(): [] Yoo SJ, Lee JW, Hwang UW, Park HS, Park DR, Jang HD, et al. H /CO separation characteristics of gamma-al O 3 membrane by aging stage in sol-gel process. Korean J Chem Eng ;7():3 3. [7] Yang J, Han S, Cho C, Lee CH, Lee H. Bulk separation of hydrogen mixtures by a one-column PSA process. Sep Technol 995;5():39 9. [] Timpe RC, Kulas RW, Hauserman WB, Sharma RK, Olson ES, Willson WG. Catalytic gasification of coal for the production of fuel cell feedstock. Inter J Hydrogen Energy 997;(5): 7 9. [9] Ahmad AL, Othman MR, Mukhtar H. H separation from binary gas mixture using coated alumina-titania membrane by sol-gel technique at high-temperature region. Inter J Hydrogen Energy ;9():7. [] Gu YF, Kusakabe K, Morooka S. The separation of hydrogen from carbon dioxide using platinum-loaded zirconia membranes. J Chem Eng Jpn ;35(5): 7.

7 37 D. Cao, J. Wu / Carbon 3 (5) 3 37 [] Lopez MCB, Martinez-Alonso A, Tascon JMD. N and CO adsorption on activated carbon fibres prepared from Nomex chars. Carbon ;3():77. [] Lozano-Castello D, Cazorla-Amoros D, Linares-Solana A, Quinn DF. Activated carbon monoliths for methane storage: influence of binder. Carbon ;(5):7 5. [3] Cao DP, Shen ZG, Chen JF, Zhang XR. Experiment, molecular simulation and density functional theory for investigation of fluid confined in MCM-. Micropor Mesopor Mater ;7( 3): 59. [] Yun JH, Duren T, Keil FJ, Sexton NA. Adsorption of methane, ethane, and their binary mixtures on MCM-: Experimental evaluation of methods for the prediction of adsorption equilibrium. Langmuir ;(7):93 7. [5] Heuchel M, Davies GM, Buss E, Seaton NA. Adsorption of carbon dioxide and methane and their mixtures on an activated carbon: Simulation and experiment. Langmuir 999;5(5): [] Zhou L, Zhou YP, Li M, Chen P, Wang Y. Experimental and modeling study of the adsorption of supercritical methane on a high surface activated carbon. Langmuir ;(): [7] Zhou L, Li M, Sun Y, Zhou YP. Effect of moisture in microporous activated carbon on the adsorption of methane. Carbon ;39(5):773. [] Gu C, Gao GH, Yu YX, Nitta T. Simulation for separation of hydrogen and carbon monoxide by adsorption on single-walled carbon nanotubes. Fluid Phase Equilibria ;9: [9] Vishnyakov A, Ravikovitch PI, Neimark AV. Molecular level models for CO sorption in nanopores. Langmuir 999;5(5): 73. [] Gordon PA, Saeger PB. Molecular modeling of adsorptive energy storage: Hydrogen storage in single-walled carbon nanotubes. Ind Eng Chem Res 999;3():7 55. [] Cao DP, Zhang XR, Chen JF, Wang WC, Yun J. Optimization of single-walled carbon nanotube arrays for methane storage at room temperature. J Phys Chem B 3;7():3 9. [] Wang QU, Johnson JK, Broughton JQ. Thermodynamic properties and phase equilibrium of fluid hydrogen from path integral simulations. Mol Phys 99;9():5 9. [3] Cao DP, Wu JZ. Molecular simulaion of novel carbonaceous materials for hydrogen storage. Nano Lett ;(): 9 9. [] Zhang XR, Cao DP, Chen JF. Hydrogen adsorption storage on single-walled carbon nanotube arrays by a combination of classical potential and density functional theory. J Phys Chem B 3;7():9 5. [5] Zhou J, Wang WC. Adsorption and diffusion of supercritical carbon dioxide in slit pores. Langmuir ;():3 7. [] Firouzi M, Nezhad KM, Tsotsis TT, Sahimi M. Molecular dynamics simulations of transport and separation of carbon dioxide-alkane mixtures in carbon nanopores. J Chem Phys ;(7):7 5. [7] Cao DP, Wang WC, Shen ZG, Chen JF. Determination of pore size distribution and adsorption of methane and CCl on activated carbon by molecular simulation. Carbon ;(3): [] Frenkel D, Smit B. Understanding molecular simulation: from algorithms to applications, nd ed. San Diego: Academic Press;. [9] Shevade AV, Jiang SY, Gubbins KE. Molecular simulation study of water-methanol mixtures in activated carbon pores. J Chem Phys ;3():933. [3] Prausnitz JM, Lichtenthaler RN, de Azevedo EG. Molecular thermodynamics of fluid-phase equilibria. 3rd ed. New Jersey: Prentice Hall PTR; 999. p. 33. [3] Cao DP, Wu JZ. Self-diffusion of methane in single-walled carbon nanotubes at sub- and supercritical conditions. Langmuir ;(9): [3] Tan Z, Gubbins KE. Selective adsorption of simple mixtures in slit pores a model of methane ethane mixtures in carbon. J Phys Chem 99;9():5 5.

Self-Diffusion of Methane in Single-Walled Carbon Nanotubes at Sub- and Supercritical Conditions

Langmuir 2004, 20, 3759-3765 3759 Self-Diffusion of Methane in Single-Walled Carbon Nanotubes at Sub- and Supercritical Conditions Dapeng Cao and Jianzhong Wu* Department of Chemical and Environmental