Adsorption and Diffusion of H2, CO, CH4, and CO2 in BPL Activated

Article pubs.acs.org/IECR

Adsorption and Diffusion of H2, CO, CH4, and CO2 in BPL Activated Carbon and 13X Zeolite: Evaluation of Performance in Pressure Swing Adsorption Hydrogen Purification by Simulation José A. Delgado,*,† V. I. Á gueda,† M. A. Uguina,† J. L. Sotelo,† P. Brea,† and Carlos A. Grande‡ †

Department of Chemical Engineering, Universidad Complutense de Madrid, 28040, Madrid, Spain SINTEF Materials and Chemistry, Forskningsveien 1, 0373, Oslo, Norway

‡

S Supporting Information *

ABSTRACT: Hydrogen is an important energetic vector nowadays. The most common industrial method to produce ultrapure hydrogen is by steam methane reforming (SMR), where hydrogen is first produced as a mixture mainly composed of hydrogen, carbon monoxide, methane, and carbon dioxide. A purification step by pressure swing adsorption (PSA) is carried out usually using activated carbon and 5A zeolite as adsorbents. The design of this process requires fundamental information about the adsorption and diffusion of the components of SMR-off gas, which is only available in the literature for a limited number of adsorbents. In this work, adsorption Henry’s law constants and reciprocal diffusion time constants have been measured for hydrogen, carbon monoxide, methane, and carbon dioxide on BPL 4X10 activated carbon and 13X zeolite pellets from pulse experiments. Adsorption isotherms of these gases in both adsorbents at temperatures between 298 and 338 K, up to pressures of 20 bar for hydrogen and 2−5 bar for the other gases, have also been measured volumetrically. A PSA cycle for hydrogen purification using BPL activated carbon and 13X zeolite has been designed introducing the measured adsorption and diffusion data in a simulation tool. The process can yield 99.99+% hydrogen with 90% recovery and 7.2 mol H2 kg−1 h−1. If 13X zeolite is replaced by 5A zeolite with the same operating conditions, the hydrogen purity falls down to 99.81%.

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different affinities for each impurity.9,10 The first layer in contact with feed usually removes water vapor. For this purpose, a hydrophilic adsorbent such as alumina or silica gel is commonly employed. The next layer acts as a filter for other impurities with high adsorption affinity (such as carbon dioxide), which is often composed of activated carbon. The last layer (usually composed of 5A zeolite) removes the lighter impurities (such as methane and carbon monoxide).11−14 Design parameters such as the adsorbents used, the relative length and position of the different adsorbent layers, and the composition of the feed mixture have an important effect on the separation performance.15−17 Although the kind of adsorbents used in industrial units are usually known (such as activated carbons and zeolites), specific details about its properties (which can have a key effect on the process performance) are often not available for industrial property protection reasons. Most of the studies in the literature about SMR hydrogen purification consider the use of 5A zeolite in the last bed layer. Despite the growth of the industrial applications of the PSA processes, the design of commercial units and their optimization still requires an important experimental effort. Adsorption equilibrium data (adsorption isotherms of the main components in the gas mixture and adsorption heats), together

INTRODUCTION The use of hydrogen as a means to transport energy has become increasingly more widespread, among other reasons, due to the increased use of fuel cells.1,2 Moreover, oil refineries have found the need to increase the number of hydrotreating processes to remove sulfur compounds in fuels.3 For this reason, hydrogen production at the global level has increased greatly in recent years. The availability of hydrogen from natural sources is scarce, so its industrial production is very important. One of the routes to produce hydrogen more cheaply is by steam methane reforming (SMR).4 In this process, hydrogen is obtained mixed with a high proportion of impurities, such as water vapor, carbon dioxide, methane, carbon monoxide, and in some cases, nitrogen.5 Hydrogen is also obtained mixed with impurities in off-gases from many processes, such as catalytic reforming of naphta, ethylene production, and ammonia production. Reducing the content of impurities in hydrogen is essential for its applications. Thus, for use in fuel cells, hydrogen purity must be typically greater than 99.99%. In some fuel cell applications, more than 10 ppm of carbon monoxide are not allowed.6 The purity required in other applications is variable, as in the steel industry, where the required purity ranges from 90 to 99+%.7 The hydrogen purification is usually performed on an industrial scale by a PSA process (pressure swing adsorption).8 Industrial PSA processes typically include the use of several beds operating simultaneously in an adsorption/regeneration cycle, in such a way that each bed undergoes the same sequence of stages, but at different times. Each bed is made up of a series of layers of different adsorbents (up to 3 normally), with © XXXX American Chemical Society

Special Issue: Alirio Rodrigues Festschrift Received: November 5, 2013 Revised: January 8, 2014 Accepted: January 10, 2014

A

dx.doi.org/10.1021/ie403744u | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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Table 1. Adsorbent Properties adsorbent BPL 4X10 activated carbon 13X zeolite pellets

particle density (g cm−3)

particle size (mm)

particle porosityb

micropore volume (cm3 g−1)c

average pore diameter (nm)c

BET surface (m2 g−1)c

0.916

1.3

0.35

0.36

0.64

859

1.357

1.5

0.47

0.17

0.87

392

a

Excluding the Hg intrusion volume from the particle density. bConsidering the void volume estimated by Hg porosimetry only. cMeasured by nitrogen porosimetry.

with adsorption kinetics data are required. This information must be incorporated into an appropriate theoretical model to design and optimize the process.18−20 Fundamental studies about the adsorption of the main components of SMR off-gases (hydrogen, carbon monoxide, methane, and carbon dioxide) are scarce in the literature.21 The objectives of this work are the following: (i) To measure the adsorption Henry’s law constants and reciprocal diffusion time constants of hydrogen, carbon monoxide, methane, and carbon dioxide on BPL activated carbon (BPL 4X10) and 13X zeolite. This activated carbon has been chosen for this study because it is designed for use in gas applications and it has rapid adsorption kinetics.22−24 There are little data in the open literature about the adsorption of SMR off-gases in this particular adsorbent. 13X zeolite has been selected because it is a commercially available zeolite which has been successfully used in PSA processes for air separation25 and helium purification.26 Application of 13X zeolite exchanged with Ca to hydrogen purification by PSA has been studied recently.21,27 However, the adsorption of SMR-off gases on 13X zeolite in its commercial form (containing Na) is less known than on 5A zeolite. (ii) To evaluate the performance of BPL activated carbon and 13X zeolite in hydrogen purification of SMR offgases by PSA introducing the measured parameters in a PSA model. (iii) To compare the simulated performance using 13X zeolite and 5A zeolite in the second adsorbent layer, introducing in the PSA model equilibrium and kinetic parameters available in the literature for 5A zeolite.28

Figure 1. Scheme of the setup for pulse measurements.

reduce the dead volume outside the bed, through which two thermocouples are inserted. The gas flow rate at the bed exit was measured with a bubble meter. In each pulse experiment, a small loop volume placed in a rotary valve is filled with the studied gas (helium, carbon monoxide, carbon dioxide, or methane), which is swept by the carrier gas during the experiment (nitrogen or helium). The bed properties and the loop volume used in the different experiments are presented in Table 2. For the case of carbon dioxide pulses in 13X zeolite, it was necessary to increase the loop volume and to reduce the bed mass substantially to increase the signal-to-noise ratio and to reduce the time required to recover the baseline in the pulse experiments. The pulse responses are recorded by a mass spectrometer (Balzers ThermoStar). Each pulse was repeated three times to check the reproducibility, and the pulse resulting from averaging them (with Origin program) was used in the measurements. Pressure drop along the bed was not detectable in the pulse experiments. Prior to the pulse experiments, BPL activated carbon and 13X zeolite pellets were regenerated overnight at 423 and 623 K, respectively, under helium flow. Nitrogen was used as carrier gas for helium pulses only. As helium is used as a nonadsorbing tracer, the presence of nitrogen in the system does not affect to the nonadsorbing character of helium, because adsorbed nitrogen hinders the weak adsorption of helium. For the rest of adsorbing gases (hydrogen, carbon monoxide, carbon dioxide, and methane), helium was used as a carrier. The adsorption isotherms of hydrogen, carbon monoxide, carbon dioxide, and methane on both adsorbents have been measured in a volumetric equipment (BELSORP HP). Prior to the experiments, BPL activated carbon and 13X zeolite pellets were regenerated under vacuum for 10 h at 423 and 593 K, respectively.

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EXPERIMENTAL SECTION BPL 4X10 activated carbon was supplied by Calgon. 13X zeolite in the form of cylindrical pellets was supplied by Union Carbide. The properties of these adsorbents are presented in Table 1. The size of the crystals in the 13X zeolite pellets was determined from SEM photographs of the crushed pellets, with sizes ranging between about 2−4 μm (Figure 2). The textural properties were measured by mercury porosimetry (Thermo Finnigan Pascal 140 model). All the gases in this study had purities higher than 99.999% supplied by Praxair. Pulse experiments were carried out in a fixed bed installation, where the adsorbent bed is placed inside a stainless-steel column (i.d. = 9 mm, 25 cm long), surrounded by two stainless-steel spiral tubes (1/8 in.), used to preheat the feed gas and control the bed temperature with a thermostatted bath. A schematic drawing of the installation is shown in Figure 1. The column and the surrounding spiral tubes are covered by an electrical coaxial furnace, so that the bed temperature can be controlled between 25 and 600 °C. The bed temperature is measured with two thermocouples. Two glass hollow sticks B



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carrier) have been used to take into account the dead volume in the installation and to model the effect of the overall dispersion on the experimental pulse signal, caused by the void volume outside the bed and the mass spectrometer detector. The first moment of the pulse responses is used to calculate the adsorption Henry’s law constants.29 The pulses have been normalized by setting the area below the pulse to 1. For a given gas, the dimensionless Henry’s law constant is calculated as (mgas3 msolid−3), K=

Table 2. Bed Properties and Loop Volume in the Pulse Experiments adsorbent

gases

BPL 4X10 activated carbon

He, H2, CO, CO2 and CH4 He, H2, CO, and CH4 He and CO2

13X zeolite pellets 13X zeolite pellets

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bed length (cm)

bed mass (g)

porosity between particles

bed diameter (cm)

20

2.84

0.83

0.498

0.9

20

2.38

1.07

0.477

0.9

100

0.22

0.10

0.477

0.9

(1)

where v0 is the interstitial velocity, L is the bed length, ε is the bed void fraction between particles (Table 2), and εp is the particle porosity (Table 1). The values of μHe (for a helium pulse) and μgas correspond to the first moment of pulses with the same carrier flow rate and temperature. A theoretical model has been used to extract the reciprocal diffusion time constants from the experimental pulse responses, considering a flow pattern which consists of a portion of void volume with plug flow, followed by three perfectly mixed tanks in series (Tanks 1, 2, 3), connected to the bed, which is connected to other three perfectly mixed tanks in series (Tanks 4, 5, 6), where the last tank yields the simulated signal. In the model, Q is the carrier gas flow rate (measured at laboratory conditions), VD is the portion of void volume with plug flow, and VT is the volume of each tank where perfect mixing is considered. It is also assumed that the gas velocity is constant along the bed, the bed is isothermal, there are no radial concentration gradients, the adsorbent has a bidisperse pore structure (micro- and macropores), and the adsorption isotherm is linear in the studied conditions. This condition is searched by injecting very small amounts of adsorptive, resulting in very low concentrations in the carrier gas. In the case of carbon dioxide in 13X zeolite (the system with the most curved isotherm and highest amount of injected adsorbate), the average concentration of adsorptive in the pulse response is only 0.02% v/v. Even in the case that the isotherm was not linear for such dilute concentration because the isotherm is still curved at very low concentrations, the ability of the model of reproducing the experimental pulses indicates that the assumption of a linear isotherm with an average slope for the studied concentration range is valid, yielding also an average reciprocal diffusion time constant for the studied conditions. The mass balance in the adsorbent bed is

Figure 2. SEM images of crushed 13X zeolite pellets.

loop volume (μL)

v0 ε(μgas − μHe ) L (1 − ε)(1 − εp)

v ∂c D ∂ 2c ∂c 3 1−ε = 2L − 0 − k macro(c − cmacro) ∂t L ∂x Rp ε L ∂x 2 (2)

where c is the adsorptive concentration in the gas phase, t is time, DL is the axial dispersion coefficient, L is the bed length, x is the dimensionless axial coordinate, ε is the bed porosity between particles (pellets or activated carbon granules), Rp is the particle radius, kmacro is the mass transfer coefficient describing the total resistance outside micropores, and cmacro is the average concentration in the macropores. The value of kmacro is given by

RESULTS AND DISCUSSION Measurement of Adsorption Henry’s Law Constants and Reciprocal Diffusion Time Constants from Pulse Experiments. Two important fundamental parameters required to quantify the adsorption affinity and the diffusion rate of the different gases in the studied adsorbents are the adsorption Henry’s law constants and the reciprocal diffusion time constants. They have been measured for hydrogen, carbon monoxide, carbon dioxide, and methane in both adsorbents from pulse experiments. The experimental conditions are given in Tables S1 and S2 (in the Supporting Information). Pulses of helium (considered as a nonadsorbing gas, with nitrogen as

k macro

C

⎛ ⎞−1 ⎜ 1 1⎟ = ⎜ 5D ε + ⎟ m p k ⎜ f⎟ ⎝ τR p ⎠

(3)



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where Dm is the molecular diffusivity of the studied gas in the carrier, τ is the tortuosity of the macropores (taken as 3), and kf is the external mass transfer coefficient, calculated from a literature correlation:30 kf =

0.365 ⎞ u ⎛ 0.765 ⎜ 0.82 + 0.386 ⎟ 2/3 ⎝ ⎠ Re Re εSc

The mass balance in the micropores (in zeolite crystals or microporous region for the activated carbon) is ∂q D ⎛ 1 ∂ ⎛ 2 ∂q ⎞⎞ = c2 ⎜⎜ 2 ⎜xr ⎟⎟⎟ ∂t ∂xr ⎠⎠ rc ⎝ xr ∂xr ⎝

The boundary conditions for this equation are

(4)

where u is the superficial velocity, Re is the particle Reynolds number, and Sc is the Schmidt number. In eq 3, the effect of Knudsen diffusivity was not included, because its effect is usually small in macropores, and it depends on the average pore size used in its calculation. The effect of Knudsen diffusion is included in the value of the measured reciprocal diffusion time constant for micropores. The axial dispersion coefficient was also calculated with a literature correlation:31 DL = 0.73Dm +

xr = 0

9.49εDm 2uR p

NS = v0S bedεc T6

(5)

2

r =1− (6)

⎡ ⎛ t − 0.05 ⎞2 ⎤ 1 ⎟ ⎥ ⎢−⎜ exp ⎢⎣ ⎝ 5 × 10−3 ⎠ ⎥⎦ 5 × 10−3 π

(7)

⎞ ⎟ − 0.05s⎟ ⎟ ⎠

(8)

(9)

where i is the tank number. The boundary conditions for the mass balance in the bed are DL ∂c = v0c T3 L ∂x

x=0

v0c −

x=1

∂c =0 ∂x

(10)

(11)

The mass balance for Tank 4 is dc T4 v S ε(c − c T4) = 0 bed x = 1 dt VT

(16)

(17)

where μHe is the first moment of the fitted helium pulse. The residence time in VD is added to the time scale of the simulated pulse response to take into account the delay time caused by this volume. By doing so, the first moments of the experimental and the simulated pulse responses are equal. Once the values of VT are obtained for different carrier gas flow rates and temperatures, they are used for calculating the reciprocal diffusion time constants of adsorbing gases. The values of this parameter ranged between 0.6 and 0.8 mL in all the studied conditions. For fitting each pulse response, the values of VT and μHe corresponding to its carrier gas flow rate and temperature are introduced in eq 17 and K is calculated with eq 1. With this method, the first moments of the experimental and simulated pulses of adsorbing gases are equal, and the only fitted parameter is the reciprocal diffusion time constant. The model was fitted to each group of pulse responses obtained for the same gas-adsorbent system with the same temperature and different carrier flow rates, imposing a constant value of Dc/rc2. It is important to note that chromatographic methods for diffusion measurements used in the literature usually neglect the effect of dispersion outside the adsorbent bed. A long bed is necessary for that purpose, which can result in a very long pulse

The mass balances for Tanks 2, 3, 5, and 6 are dc Ti v S ε(c − c Ti) = 0 bed Ti − 1 dt VT

∑ (yexp − yexp )2

⎛ (1 − ε)εp ⎞ Tbed ⎜ 6V L⎛ ⎜ ⎟⎟ − TT − + μ 1 VD = Q ⎜ He ⎜ ⎜ ε Tlab v0 ⎝ ⎠ Q Tbed ⎝ lab

where f pulse represents the molar gas flow rate introduced by the pulse in a short time, starting a t = 0 and being maximum at 0.05 s. The function parameters have been chosen arbitrarily because they have negligible effect on the simulated pulse response once the pulse has crossed all the elements in the flow pattern. The mass balance in Tank 1 is fpulse (t ) − v0S bedεc T1 dc T1 = dt VT

∑ (yexp − ycalc )2

where y is the normalized signal. The model was fitted first to the helium pulses, to determine the values of VT for different carrier flow rates and temperatures. The values of VD are calculated as

where Dc/rc2 is the reciprocal diffusion time constant in micropores, xr is the dimensionless radial coordinate in micropores, and q is the adsorbed concentration (mol msolid−3). The pulse is modeled with the following equation: fpulse (t ) =

(15)

The model is solved numerically using the PDECOL package,32 which uses orthogonal collocation on finite elements (OCFE) technique for the discretization of the axial coordinate. Cubic Hermite polynomials were used for the discretization of the radial coordinate in the particle.33 The model is fitted to the experimental pulse responses by minimizing the sum of squared residuals. The fitting quality is evaluated with the coefficient of determination:

3(1 − εp) ∂cmacro 3 = k macro(c − cmacro) − ∂t εp R pεp

xr = 1

(14)

The initial condition is that the dependent variables are zero. The predicted normalized signal is calculated as follows:

The mass balance in macropores is

Dc ∂q rc 2 ∂xr

∂q =0 ∂xr

xr = 1 q = Kcmacro

uR p/ε 1+

(13)

(12) D



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Figure 3. Pulse responses from an bed packed with BPL activated carbon. Gray lines are the experimental signal and black lines are the theoretical signal from the model. The carrier gas flow rates increase from the right to the left, and the corresponding values are given in Supporting Information Table S1. (a) CH4 at 288 K. (b) CO at 289 K. (c) CO2 at 308 K.

Figure 4. Pulse responses from an bed packed with 13X zeolite pellets. Gray lines are the experimental signal and black lines are the theoretical signal from the model. The carrier gas flow rates increase from the right to the left, and the corresponding values are given in Supporting Information Table S2. (a) CH4 at 289 K. (b) CO at 287 K. (c) CO2 at 323 K.

E



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Molecular size seems to have little effect on the mobility of the studied gases in both adsorbents, as the slowest diffusing molecule (carbon dioxide) has the smallest kinetic diameter (except for hydrogen) and the largest molecule (methane) does not have the slowest mobility. In 13X zeolite, this result is expected, as the micropore size (about 8 Å) is significantly larger than any of the kinetic diameters of the studied molecules (Table 3). In BPL activated carbon, which has a broader pore size distribution, this result indicates that the range of micropore sizes where adsorption occurs are also significantly larger than the molecular size of the studied gases. It has been observed that for all the studied adsorbate− adsorbent systems the reciprocal diffusion time constants are inversely proportional (approximately) to the adsorption Henry’s law constant measured in the same conditions, as it is shown in Figure 5. The plots of Dc/rc2 vs K for 13X zeolite and BPL activated carbon were fitted to eqs 18 and 19, respectively:

(with a low maximal height) which is difficult to analyze. In our work, we have observed that dispersion outside the bed is quite important, and it cannot be neglected. For this reason, we have incorporated the external dispersion into the model and have matched directly the experimental pulse responses in the time domain with the ones predicted by the model to measure the diffusion time constants.31 This method is applicable when the experimental pulse responses have not Gaussian shape.29 Tables S1 and S2 show the fitting results (both available as Supporting Information). A comparison between theoretical and experimental pulse responses of carbon monoxide, carbon dioxide, and methane with different flow rates is given in Figure 3 (BPL activated carbon) and Figure 4 (13X zeolite pellets), for the lowest temperature in Supporting Information Tables S1 and S2. The flow rate in the plotted pulses increases in these figures from the right to the left. The fitting quality for hydrogen, and other temperatures, is very similar. It is observed that the model fitted the experimental pulses quite well in most experiments. For carbon dioxide in 13X zeolite the fitting quality is worse, but the model describes the maximum height of the pulses and the pulse width well, which are very sensitive to the value of Dc/rc2. Analysis of the Adsorption and Diffusion Data. The measured values of the adsorption Henry law constants (K) and reciprocal micropore diffusion time constants (Dc/rc2) of hydrogen, carbon monoxide, methane, and carbon dioxide are presented in Supporting Information Tables S1 (in BPL activated carbon) and S2 (in 13X zeolite pellets). The activation energy of diffusion in micropores (Ediff) has been calculated by correlating the diffusion time constants with the Arrhenius equation. For hydrogen, it was not possible to measure the diffusion parameters in both adsorbents because the effect of diffusion resistance on the simulated pulse response was not noticeable. For the rest of gases, it was checked that the micropore diffusion resistance is more important than the one in macropores in the studied conditions, since the values of Dc/rc2 decreased less than 30% (as deduced from values of (Dc/rc2)′ in Supporting Information Tables S1 and S2) when they are calculated assuming that the mass transfer parameter in macropores (kmacro) is infinite. The values of the Henry’s law constant of each adsorbate−adsorbent pair are indicative of the adsorption affinity. The observed differences in adsorption affinities can be explained in terms of the different molecular properties of the adsorbates and the adsorbents, presented in Table 3. The affinities in BPL

Dc rc

Dc rc 2

a

polarizability, Å3 a

dipole moment, Da

quadrupole moment, D Åa

kinetic diameter, Åb

H2 CH4 CO CO2

0.79 2.45 1.95 2.51

0 0 0.11 0

0.52 0 2.84 4.28

2.9 3.8 3.6 3.3

, s −1 = , s −1 =

6.035 K

0.9882 + 0.000025K

5.516 K

(18)

(19)

Figure 5. Plot of Dc/rc2 versus K taking the values from Supporting Information Tables S1 and S2.

It must be noted that the exponent introduced in eq 18 has no theoretical basis. It was introduced to reproduce the deviation from linearity at high values of K observed in Figure 5. This correlation suggests that it is possible to estimate roughly the reciprocal diffusion time constant of a given gas in both adsorbents by estimating the K value only. Although this method is very simplistic, it has the advantage that a kinetic model is not required. The theoretical reason for such correlation is that the diffusion mechanism of the studied systems is similar to the one of surface diffusion, where the diffusivity depends only on the distance between neighboring adsorption sites and the residence time in the adsorption site.36 This similarity derives from the small adsorbate molecular size with respect to the pore opening of the adsorbents. According to surface diffusion theory, diffusion in the adsorbed phase is governed by the residence time in the adsorption site, which is proportional to K and inversely proportional to Dc/rc2. There have been found similarities between the results obtained in this work and adsorption and diffusion data reported in the literature. Sircar and Kumar37 measured the overall LDF mass transfer coefficient of methane in BPL

Table 3. Molecular Properties of Studied Gases gas

2

Reference 34. bReference 35.

activated carbon are ordered according to their polarizabilities. The different ordering for carbon monoxide and methane in 13X zeolite is due to the electrostatic interactions of carbon monoxide with Na cations in zeolite cavities. Carbon dioxide has the highest affinity in both adsorbents due to its strong quadrupole moment. F



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Figure 6. Experimental adsorption isotherms in BPL activated carbon at different temperatures. Lines are obtained with the Langmuir−Freundlich model. (a) Hydrogen. (b) Methane. (c) Carbon monoxide. (d) Carbon dioxide.

Figure 7. Experimental adsorption isotherms in 13X zeolite pellets at different temperatures. Lines are obtained with the Langmuir−Freundlich model. (a) Hydrogen. (b) Methane. (c) Carbon monoxide. (d) Carbon dioxide. The black thick line depicts a carbon dioxide isotherm on 5A zeolite at 298 K reported in the literature.28

activated carbon, resulting in 1.3 s−1 The value obtained in this work, calculated as 15 Dc/rc2 at 298 K (setting kmacro to infinite), is 1 s−1. The reported value of K for methane (20 m3

gas/m3 particle at 300 K)38 in other activated carbon (Maxsorb) is similar to the one found in this work (31 m3 gas/m3 particle at 300 K). Seikh et al.38 also measured the G



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Table 4. Langmuir−Freundlich Parameters and Average Isosteric Heat of the Studied Gas−Adsorbent Systems ads

gas

BPL BPL BPL BPL 13X 13X 13X 13X

H2 CH4 CO CO2 H2 CH4 CO CO2

a, mol kg−1 7.3775 3.2220 3.3201 −2.4532 6.8776 7.5284 2.2088 2.5093

b, mol K kg−1

k0, Pa−1

0 0 0 3095.0 0 0 0 691.69

1.6068 1.9903 1.6169 3.2373 6.0504 7.2149 4.0290 1.0778

overall LDF mass transfer coefficient of methane, obtaining a value of the same order of magnitude (2.95 s−1). The value of Dc/rc2 for CO2 at 298 K in other activated carbon (modified Norit R2030)39 is 0.029 s−1, very similar to the one obtained here for BPL activated carbon (0.031 s−1). The values of Dc/rc2 for CO2 in 13X zeolite pellets are of the order reported by Kamiuto et al.40 in the same system (between 0.0002 and 0.002 s−1 for temperatures between 303 and 343 K). To simulate the multicomponent adsorption isotherm in both adsorbents, the basic information required is adsorption equilibrium isotherms of the pure components. These isotherms were measured in a volumetric apparatus, and the experimental results are presented in Figures 6 and 7. They have been fitted with the Langmuir−Freundlich equation because it gives a good reproduction of the experimental data, and it is possible to obtain an explicit multicomponent isotherm (LRC correlation) from the pure adsorption isotherms easily, which has been used widely for simulating PSA cycles in the literature.4 The resulting isotherm parameters are given in Table 4. The isosteric heat of each gas introduced in the PSA model (Qst in Table 4) was calculated as the average value applying the van’t Hoff expression to the corresponding Langmuir−Freundlich equation: Q st =

1 nF

∫0

nF

⎛ ∂ln p ⎜−R ⎜ ∂(1/T ) ⎝

⎞ ⎟ dn ⎟ n⎠

10 10−9 10−9 10−9 10−10 10−10 10−10 10−9

Q, K

m

Qst, kJ mol−1

919.96 2216.2 1965.9 1964.0 1142.1 2018.2 2804.5 3354.4

1 1 1 0.8666 1 1 1 0.8608

7.6 18.4 16.3 20.9 9.5 16.8 23.3 31.6

This comparison is shown in Table 5 for the gas-adsorbent pairs with m = 1 in the studied pressure range (H2, CO, and Table 5. Comparison between the Values of the Adsorption Henry’s Law Constant Calculated from Pulse Experiments and Volumetric Data adsorbent

gas

T, K

Kpulse

Kvolumetric

BPL BPL BPL 13X 13X 13X

H2 CH4 CO H2 CH4 CO

298 308 288 308 289 287

1.3 40 20 1.5 37 92

0.9 31 17 1.1 36 95

CH4). It is observed that the values are rather similar. The values obtained from pulse experiments are slightly higher than the ones obtained from volumetric data in most cases because it is difficult to measure the initial slope of the adsorption isotherm with the volumetric method accurately, particularly when the curvature of the isotherm is significant. Evaluation of Performance of BPL Activated Carbon and 13X Zeolite in Hydrogen Purification by PSA. The performance of BPL activated carbon and 13X zeolite in hydrogen purification by PSA has been evaluated by simulation. A PSA process based on these adsorbents has been designed, using operating conditions typical of industrial PSA processes for hydrogen purification. A four-column PSA cycle for this purpose has been considered, including the following sequence of steps:28 (1) Adsorption (ADS): feed gas is introduced in the column at the high cycle pressure. (2) Depressurizing equalization 1 (DEQ1): the column is depressurized through the light end and the released gas is used to pressurize other column at a lower pressure. (3) Provide purge (PP): the column is depressurized again through the light end and the released gas is used to purge other column. (4) Depressurizing equalization 2 (DEQ2): like DEQ1 starting from the final pressure of the PP step. (5) Blowdown (BD): the column is depressurized down to the low cycle pressure through the feed end, and waste gas is obtained. (6) Receive purge (RP): the column is purged through the light end with the feed end open at low cycle pressure, using the gas released from other column undergoing PP step. Waste gas is obtained from the feed end. (7) Pressurizing equalization 2 (PEQ2): the column is pressurized through the light end with gas coming from other column undergoing DEQ2 step.

(20)

where nF is the adsorption capacity calculated at feed conditions. An average isosteric heat is used because, although this parameter usually depends on adsorbent loading, a constant value is introduced in PSA models for simplicity. The average values of isosteric heat presented in Table 4 for BPL activated carbon are quite similar to the ones calculated for other activated carbon (C30−53) introducing their Langmuir parameters28 in eq 20, resulting in Qst H2 = 7.1 kJ mol−1; Qst CO = 16 kJ mol−1; Qst CO2 = 21 kJ mol−1; and Qst CH4 = 15.5 kJ mol−1. For 5A zeolite, using also literature parameters,28 the isosteric heats are slightly higher than in 13X zeolite, resulting in Qst H2 = 10.8 kJ mol−1; Qst CO = 24.9 kJ mol−1; Qst CO2 = 38 kJ mol−1; Qst CH4 = 18.1 kJ mol−1. This result is expected taking into account the stronger electric potential of calcium cations in 5A zeolite. A way of checking the consistency of the adsorption equilibrium data determined from pulse experiments and volumetric data is to compare the values of the dimensionless Henry’s law constants calculated from both methods. This parameter can be calculated from volumetric data as follows if m is equal to 1 in the Langmuir−Freundlich equation: K = nmax kρp RT/(1 − εp)

× × × × × × × ×

−9

(21) H



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Figure 8. Simulated PSA cycle for hydrogen purification. (a) Connectivity between steps. F = feed gas, L = light product (rich in hydrogen), W = waste gas (rich in impurities). (b) Cycle time schedule.

the four columns follow the same sequence of steps at different times, the process is simulated solving the equations for one column only, following the step sequence in Figure 6a. Danckwert’s boundary conditions have been used to impose the component mole flow rates and heat flow when gas is introduced in the column, and linear pressure variations have been assumed in the steps where final pressure is fixed beforehand (DEQ1, DEQ2, BD, and BF). In each cycle, component molar flow rate histories of discharged gas in DEQ1, DEQ2, and PP steps are stored in the computer memory and used as boundary conditions (interpolated in time with Hermite cubic polynomials) in PEQ1, PEQ2, and RP steps, respectively. In PEQ1 and PEQ2 steps, the final pressure is not known beforehand, as it depends on the amount of gas discharged from DEQ1 and DEQ2 steps. A trial and error method was used to set the final pressures of DEQ1 and PP steps (the final pressure of DEQ2 step was fixed to 2.8 bar, as commented previously), until the final pressures of PEQ1 and PEQ2 steps were practically the same as the ones of DEQ1 and DEQ2 steps, respectively. The model has been solved with the orthogonal collocation on finite elements method, using cubic Hermite polynomials and solving the resulting implicit ODE system with DLSODIS subroutine in ODEPACK package, a public domain FORTRAN code developed by Alan Hindmarsh, freely available on the Web.43 Although the model has not been validated with experimental PSA results obtained for the studied system, it is reasonable to expect that their predictions are reliable because it is based on conservation equations and the equilibrium and kinetic model parameters have been measured experimentally. The application of PSA simulation using models based on conservation equations and fundamental adsorption and diffusion parameters for studying and comparing the potential performance of different adsorbents in separations by PSA is accepted in the literature.22,44−46 To design the process, different combinations of feed superficial velocity and proportion of activated carbon in the column were tested, simulating the PSA cycle until the cyclic steady state was reached. The performance parameters taken

(8) Pressurizing equalization 1 (PEQ1): like PEQ2 using the gas released from a column undergoing DEQ1 step. (9) Backfill (BF): the column is pressurized through the light end with light product up to the high cycle pressure, and it is ready for another cycle. A scheme of the cycle indicating the connectivity between different steps is shown in Figure 8a. The cycle time schedule for the four columns is shown in Figure 8b. The composition and temperature of the feed gas is assumed to be 76% H2, 4% CO, 17% CO2, 3% CH4, and 298 K, which can be an example of feed gas to a PSA process for hydrogen production by SMR.41 The design specification is that the purity of hydrogen product must be higher than 99.99%. The column length has been set to 8 m, and the column radius to 0.8 m. Each column contains one layer of BPL activated carbon particles (starting from the feed end), followed by a second layer of 13X zeolite pellets. The high and low cycle pressures have been set to 16 and 1 bar, respectively. The duration of adsorption step has been set to 4 min,4 and the duration of equalization and blowdown steps has been set to 30 s, as indicated in Figure 8b. The initial pressure of the blowdown step has been set to 2.8 bar, which is a realistic value in industrial PSA processes for hydrogen purification.42 The model for simulating the process is based on the mass, energy and momentum balances, and model equations are presented in Table 6. Transport and gas properties (molecular diffusivity of each component in the gas mixture, gas conductivity, gas viscosity, heat capacities) were calculated at feed conditions with AspenPlus. Heat and mass axial dispersion Peclet numbers were set to a very high value (500) to assume plug flow. The adsorbent properties (particle density and porosity) have been taken from Table 1, and the reciprocal diffusion time constants of all components at 298 K have been taken from Supporting Information Tables S1 and S2. A very high value (30 s−1) was assumed for the reciprocal diffusion time constant of hydrogen, which had little effect on the simulation results. The same bed porosity (0.4) and particle radius (0.7 cm) has been assumed in both adsorbent layers. As I



Article

industrial PSA hydrogen purification process from SMR off-gas described in a patent,42 which yields 99.999% hydrogen with 86% recovery and a productivity of 4.9 mol H2 kg−1 h−1. This simulation is called case 1 from now on. The pressure history in case 1 is presented in Figure 9, and Figure 10a and b shows the

Table 6. Model for a PSA Process total mass balance in gas phase

ε

∂C ∂ 3 = − (uC) − (1 − ε) ∂t ∂z Rp

i=n

∑ kmacro,i(Cyi − cmacro,i) i=1

mass balance of ith component in the gas phase ∂(Cyi ) ∂ ∂ ⎛ ∂yi ⎞ 3 ε = − (uCyi ) + DL ε ⎜C ⎟ − (1 − ε) k macro, i ∂t ∂z ∂z ⎝ ∂z ⎠ Rp

(Cyi − cmacro, i) mass balance in macropores

εp

∂cmacro, i ∂t

=

⎛D ⎞ 3 k macro, i(Cyi − cmacro, i) − ρp 15⎜ c2 ⎟ (ni* − ni) Rp ⎝ rc ⎠ i

adsorption rate in micropores ⎛D ⎞ ∂ni = 15⎜ c2 ⎟ (ni* − ni) ∂t ⎝ rc ⎠i equation of state P C= RTg

Figure 9. Pressure history for case 1.

momentum balance

−

spatial profiles of component mole fraction and adsorbed concentrations at the end of the adsorption step, when the production of hydrogen finishes in one column. According to the gas mole fraction spatial profiles, apparently only carbon monoxide penetrates into the 13X zeolite layer, being captured in this layer before it contaminates the hydrogen product. Methane is completely removed by the activated carbon layer. However, the adsorbed concentration profiles show that a significant amount of carbon dioxide accumulates in the zeolite layer (because it is not easy to desorb carbon dioxide at 1 bar due to the high curvature of its isotherm), although not high enough so as to degrade completely its capacity for removing carbon monoxide. In other simulations, it was observed that the performance gets worse if the proportion of activated carbon in the column is increased or decreased around 55%. For example, using the operating conditions of case 1, a 60% activated carbon layer leads to 99.991% hydrogen product (case 2), and a 50% activated carbon layer leads to 99.951% hydrogen (case 3). This indicates that it is not necessary to remove completely carbon dioxide in the activated carbon layer. This result was already pointed out by Park et al.,28 who simulated a similar PSA process with 5A zeolite. In order to compare the performance of 13X and 5A zeolite in the same PSA process, a simulation was carried out using the operating conditions of case 1, replacing the 13X zeolite layer by a 5A zeolite layer (case 4). The required model parameters in 5A zeolite layer (particle density, mass transfer coefficients, isotherm parameters, and average isosteric heats of the four components) have been taken from the work by Park et al.28 Particle porosity was set to a very low value (0.0001), and kmacro was set to a very high one (0.1 m s−1), because neither particle porosity nor macropore resistance were considered in their model, using an overall LDF parameter. The resulting performance parameters were: hydrogen purity = 99.81%, hydrogen recovery = 92.6%, productivity = 7.4 mol H2 kg−1 h−1. Although recovery and productivity increases with 5A zeolite, the performance is worse because the required purity is not achieved. Figure 10c and d show the spatial profiles of gas mole fractions and adsorbed concentrations for case 4. It is observed that, although the amount of carbon dioxide which has accumulated in the zeolite layer is slightly higher for 13X zeolite (Figure 10b), carbon

1.75(1 − ε)ρg 150μ(1 − ε)2 ∂P = u+ u2 3 2 ∂z ε 4R p ε 32R p

energy balance in the gas phase (adiabatic column)

∂ ∂ 2T ∂ 3 (εc vgCTg) = λ 2 − (uCc pgTg) + (1 − ε) hsg (Ts − Tg) ∂z Rp ∂t ∂z energy balance in the adsorbent i=n i=n ⎛ ∂n ⎞ ∂ 3 (ρp c psTs + εpc vgTs ∑ cmacro, i) = ρp ∑ ⎜Q st i i ⎟ − hsg (Ts − Tg) ⎝ ∂t ∂t ⎠ Rp i=1 i=1

multicomponent adsorption isotherm (extended Langmuir−Freundlich)

ni* =

nmax , i(kipi )m 1+

j=n ∑j = 1 (kjpj )m

nmax , i = ai +

bi T

⎛Q ⎞ ki = k 0, i exp⎜ i ⎟ ⎝T ⎠

heat transfer correlation kg hsg = (2 + 1.1Re 0.6Pr1/3) 2R p

into account were hydrogen purity, hydrogen recovery, and productivity, defined as follows: hydrogen purity =

(moles H 2 out)ADS − (moles H 2 in)BF (moles out)ADS − (moles in)BF × 100

(22)

hydrogen recovery =

(moles H 2 out)ADS − (moles H 2 in)BF × 100 (moles H 2 in)ADS

(23)

hydrogen productivity =

(moles H 2 out)ADS − (moles H 2 in)BF (cycle time)(mass of adsorbents in one column) (24)

It was found that 0.097 m s−1 and 55% of activated carbon gave the highest recovery with the required purity, resulting in a hydrogen purity of 99.993% (calculated CO concentration = 63 ppm) with 90.3% recovery, and a productivity of 7.2 mol H2 kg−1 h−1. This performance is comparable to that of an J



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Figure 10. Simulated spatial profiles of gas mole fraction and adsorbed concentration at the end of the adsorption step. (a) Gas mole fractions in case 1. (b) Adsorbed concentrations in case 1. (c) Gas mole fractions in case 4. (d) Adsorbed concentrations in case 4.

mechanism in micropores similar to surface diffusion, where the mobility in the adsorbed phase is determined by the residence time of the adsorbate in the adsorption site. The observed correlation is useful for estimating the order of magnitude of the reciprocal diffusion time constant for other gases by measuring the adsorption Henry’s law constant only, if the same mechanism applies to the micropore diffusion process. The performance of BPL activated carbon and 13X zeolite in a PSA process for hydrogen recovery from SMR off-gas has been evaluated using a simulation tool. This process can produce hydrogen with purity higher than 99.99%, 90% recovery, and a productivity of 7.2 mol H2 kg−1 h−1. 13X zeolite performs better than 5A zeolite for the operating conditions considered in the simulated process. The reason is the higher competition of carbon dioxide with carbon monoxide in the 5A zeolite layer, which leads to a lower carbon monoxide adsorption capacity, and hence a higher carbon monoxide concentration in the hydrogen product. Although the PSA results obtained in this work are theoretical, they show the potential advantages of using 13X zeolite in hydrogen purification from SMR off-gas by PSA. Thus, it is recommended to study this PSA process experimentally in the future.

monoxide concentration profile propagates in 5A zeolite layer to a greater extent than in the 13X zeolite layer (Figure 10d), resulting in a lower hydrogen purity. This behavior is caused by the higher affinity of carbon dioxide toward 5A zeolite than for 13X zeolite, as it is deduced from the carbon dioxide isotherm on 5A zeolite presented in Figure 7d. If the adsorption capacity of carbon monoxide in 13X and 5A zeolite is compared at feed conditions, using the extended Langmuir−Freundlich equation, it significantly higher for 13X zeolite (0.043 vs 0.018 mol kg−1). Since carbon dioxides accumulates in the zeolite layer in both cases, the higher affinity toward carbon dioxide of 5A zeolite results in a higher competitive effect which makes the effective working capacity of carbon monoxide lower than in the 13X zeolite.

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CONCLUSIONS

The adsorption Henry’s law constants and the reciprocal diffusion time constants of hydrogen, carbon monoxide, methane, and carbon dioxide on BPL activated carbon and 13X zeolite pellets have been measured. The affinities in BPL activated carbon are ordered as follows: hydrogen < carbon monoxide < methane < carbon dioxide, which coincides with the ordering of their polarizabilities. The affinities in 13X zeolite are ordered as follows: hydrogen < methane < carbon monoxide < carbon dioxide. The different ordering for carbon monoxide and methane in 13X zeolite is due to the electrostatic interactions of carbon monoxide with Na cations in zeolite cavities. Carbon dioxide exhibits a much stronger affinity than the other components in both adsorbents due to the electrostatic interactions generated by its quadrupole moment. Reciprocal diffusion time constants are inversely proportional to the adsorption Henry’s law constants for the studied gases in both adsorbents. This behavior is indicative of a diffusion

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ASSOCIATED CONTENT

S Supporting Information *

Tables S1 and S2 as mentioned in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +34 91 3944119. Fax: +34 91 3944114. E-mail address: [email protected]. K



Article

Notes

y = mole fraction in the gas phase z = axial coordinate, m

The authors declare no competing financial interest.

■

Greek Symbols

ACKNOWLEDGMENTS Financial support from the Ministry of Economy and Competitiveness of Spain through project CTQ2012-34626 and of the Research Council of Norway through the RENERGI program by the project Novel Materials for Utilization of Natural Gas and Hydrogen (grant 190980/S60) are gratefully acknowledged. V.I.A. thanks the Ministry of Education, Culture and Sport of Spain, for financial support received through the “José Castillejo” Program.

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NOTATION a = parameter in Langmuir−Freundlich equation, mol kg−1 b = parameter in Langmuir−Freundlich equation, mol K kg−1 c = adsorptive concentration in the gas phase, mol m−3 C = total gas concentration, mol m−3 cp,g = gas heat capacity at constant pressure, J mol−1 K−1 cp,s = adsorbent heat capacity, J mol−1 K−1 cv,g = gas heat capacity at constant volume, J mol−1 K−1 Dc = micropore diffusivity, m2 s−1 DL = axial dispersion coefficient, m2 s−1 Dm = molecular diffusivity, m2 s−1 Ediff = activation energy of diffusion, J mol−1 f pulse = function defined in eq 8 hsg = solid to gas heat transfer coefficient, W m−2 K−1 k = parameter in Langmuir−Freundlich equation, Pa−1 k0 = preexponential constant in Langmuir−Freundlich equation, Pa−1 kf = external mass transfer coefficient, m s−1 kg = gas conductivity, W m−1 K−1 kmacro = combined mass transfer coefficient in the external film and the macropores, m s−1 L = bed length, m m = exponent in Langmuir−Freundlich equation n = adsorbed concentration, mol kg−1 ; number of components NS = normalized signal nmax = maximal adsorbed concentration, mol kg−1 p = adsorptive pressure, Pa P = pressure, Pa Pr = Prandtl number q = adsorbed concentration, mol m−3 Q = volumetric flow rate, m3 s−1; parameter in Langmuir− Freundlich equation, K Qst = average isosteric heat, J mol−1 R = gas constant, J mol−1 K−1 r2 = coefficient of determination rc = half diffusion length in micropores, m Re = particle Reynolds number Rp = radius of adsorbent particle, m Sbed = bed cross-section, m2 Sc = Schmidt number T = temperature, K t = time, s u = superficial velocity, m s−1 v0 = interstitial velocity, m s−1 VD = plug-flow volume, m3 VT = tank volume, m3 x = dimensionless axial coordinate xr = dimensionless radial coordinate

ε = bed voidage fraction between adsorbent particles εp = particle porosity λ = axial heat dispersion coefficient, W m−1 K−1 μ = first moment of the pulse response, s; gas viscosity, Pa s ρg = gas density, kg m−3 ρp = particle density, kg m−3 τ = tortuosity

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Adsorption and Diffusion of H2, CO, CH4, and CO2 in BPL Activated

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