1 Introduction

Recently, the reduction of greenhouse gas (GHG) emissions has been emphasized in various industrial fields in order to prevent global warming. Therefore, many adsorptive technologies have been reported to recover clean fuel sources (H2, CH4, CO, etc.) and to capture CO2 from various effluent gases.

Since H2, CH4 and CO are used as chemical raw materials or as clean fuel sources, great needs from various industrial fields lead to strong economic motivation for the development of adsorption processes to recover these gases from reforming gas, syngas, coke oven gas, bio-gas and more traditional sources (Lee et al. 2008; Grande and Rodrigues 2007; Ahn et al. 2001; Yang and Lee 1998). For example, efficient H2 recovery from the off-gas of the integrated gasification combined cycle (IGCC) is an important issue for green power generation (Lee et al. 2014b). After carbon capture in the IGCC, recovered H2 can be used to power hydrogen turbines and as a renewable energy source.

Pressure or vacuum swing adsorption (PSA or VSA) process using porous adsorbents is a promising process for such purpose which can meet the requirement for high separation efficiencies with respect to energy and environmental targets. To select proper adsorbents and to design efficient adsorption processes, adsorption equilibrium and kinetic data for each component on a porous adsorbent are the most important factors. The effluent gases from traditional and non-traditional processes consist of 3–6 major components after various pretreatment processes including particle removal, drying and/or large molecule removal. For example, the coal gasifier in the IGCC generates a mixture gas containing CO2, CO, N2, CH4, Ar and H2 (Lee et al. 2014a). Bio-gas and natural gas are mainly composed of CH4, CO2 and N2 (Cavenati et al. 2006; Grande and Rodrigues 2007). Coke oven gas and other effluent gases from iron and steel industries contain H 2 , CH4, CO 2 , N2, and CO, and reforming gas in petrochemical industries consists of H2, CO2, CH4 and CO as a main component (Yang and Lee 1998; Ahn et al. 2001). In many studies of adsorption processes, two different adsorbents such as activated carbons and zeolites are simultaneously applied to one adsorptive unit for optimal process design (You et al. 2012; Ahn et al. 2001, 2012; Cavenati et al. 2006; Siriwardane et al. 2001). Naturally, to meet the proper selection criteria for designing the processes, the kinetic behaviors and thermodynamic characteristics of various gases in adsorbents should be understood.

In adsorptive processes, pelletized adsorbents are generally packed into an adsorption bed to minimize pressure drop in the bed. Zeolite pellets consist of micropores in zeolite crystal, macropores among zeolite crystals and binder. Therefore, studies have analyzed the contributions of macropores and micropores in the rate-determining step of N2, CH4 and CO2 in zeolite 4A, 5A, CaX and 13X pellets (Ahn et al. 2002, 2004; Silva et al. 2012; Hu et al. 2014). In a carbon molecular sieve, controlled micropores significantly affect the adsorption kinetics, and the kinetic difference among adsorbates strongly depends on molecular size and adsorption affinity (Bae and Lee 2005; Giesy and LeVan 2013; Yang et al. 2014). There are few studies of adsorption kinetics of activated carbon granules with wide pore size distribution from micropores to macropores (Gray and Do 1991; Himeno et al. 2005).

In this study, the adsorption kinetics of four pure components (CO2, CO, N2 and CH4) on commercial activated carbon granules and zeolite LiX pellets is described because these components are generally found in H2 off-gases and various effluent gases. The adsorption of H2 and Ar was too fast to evaluate their adsorption rates on the adsorbents. The adsorption uptake curves were measured using a volumetric method at three different temperatures of 293, 308 and 323 K and pressures up to 100 kPa. The effective diffusion time constants (D/R2) of each component on each adsorbent at various pressure and temperature conditions were obtained by correlating a non-isothermal kinetic model with experimental uptake curves. The effect of adsorption heat on adsorption kinetics was evaluated by comparing the results of isothermal and non-isothermal kinetic models. The controlling mechanism of diffusion in zeolite LiX was determined by comparison of the effective diffusion time constants of different sizes of zeolite pellets. The results allow optimized design of various adsorptive processes for H2 recovery and CO2 capture.

2 Theory

In a volumetric system, a certain amount of adsorbate gas is injected into the cell, and the pressure is monitored until it reaches an equilibrium state. The pressure change was calculated based on the amount adsorbed using the virial coefficients and known volume of the adsorption cell.

The adsorbents, activated carbon and/or zeolite, packed in the adsorption bed have a certain range of granule or pellet size. In the study, a certain number of adsorbents were used in the adsorption cell as received from manufacturers. Since both micropore and macropore diffusions are described by the same form of Fick’s diffusion law, the effective diffusion time constant could be interpreted as a micropore diffusivity (Dc/r 2c ) or effective macropore diffusivity (Dp/R 2p ), depending on the controlling diffusion mechanism of each system. In the study, the effective diffusion time constant (D/R2) obtained from the experimental uptake curve was assumed to reflect the overall diffusion mechanism of an adsorbate in various pores of the adsorbent pellet.

The adsorption kinetic model for experimental uptake is derived from Fick’s diffusion law in the cell assuming constant diffusivity (D). To analyze the adsorption kinetics, the simplest analytical solution for a constant volume system, which assumes isothermal condition and a linear equilibrium relationship, was derived as follows: (Crank 1956)

$$\frac{{M_{\infty } - M_{t} }}{{M_{\infty } - M_{0} }} = \sum\limits_{n = 1}^{\infty } {\frac{{6\alpha^{\prime } (\alpha^{\prime } + 1)}}{{9\alpha^{\prime } + 9 + \alpha^{\prime 2} \beta_{n}^{2} }}} \exp \left( { - \beta_{n}^{2} \frac{D}{{R^{2} }}t} \right)$$
(1)

where

$$\tan \beta_{n} = \frac{{3\beta_{n} }}{{3 + \alpha^{\prime} \beta_{n}^{2} }}$$
(2)
$$\alpha^{\prime} = \frac{3V}{{4\pi R^{3} K}}$$
(3)

In Eqs. (1)–(3), Mt, M0 and M∞ represent the amount adsorbed at ambient time t, initial time 0 and equilibrium, respectively, V is the volume of the system, R is the radius of the adsorbent sample and K is the effective Henry’s law constant at a corresponding pressure interval in a stepwise change.

When the isothermal model is applied to experimental data, a key factor that generates significant error is the heat effect generated by the heat of adsorption. The heat generated leads to increased temperature in the system, and heat is dissipated into the surroundings. Therefore, the adsorbate molecules diffuse faster at higher temperatures while adsorption of molecules on the adsorbent surface is retarded due to thermal resistance and equilibrium shift (Ahn et al. 2002, 2004; Do 1998). Due to the heat of adsorption, the former isothermal model was modified to reflect the non-isothermal condition induced by heat release (Kočiřík et al. 1984). The following equations are the analytical solution for a non-isothermal condition in a volumetric system:

$$\frac{{M_{\infty } - M_{t} }}{{M_{\infty } - M_{0} }} = \mathop \sum \limits_{n = 1}^{\infty } \frac{{9\left( {1 + K\frac{{V_{s} }}{{V_{g} }}} \right)\left[ {\frac{{Y_{n} }}{{\beta_{n}^{2} }}} \right]^{2} \exp \left( { - \beta_{n}^{2} \frac{D}{{R^{2} }}t} \right)}}{{\frac{1}{{\varphi_{n} }} + \frac{3}{2}\frac{{\beta^{\prime}}}{{\varphi_{n} }}\left[ {\beta_{n} \cot \beta_{n} \left( {\frac{{Y_{n} }}{{\beta_{n}^{2} }}} \right) + 1} \right] + \frac{3}{2}K\frac{{V_{s} }}{{V_{g} }}\frac{1}{{\beta_{n}^{4} }}\frac{{A_{n} }}{{\varphi_{n} }}}}$$
(4)

in which βn are the roots of:

$$\left( { - \beta_{n} + \alpha } \right) + 3 \beta Y_{n} - 3K\frac{{V_{s} }}{{V_{g} }}\frac{1}{{\beta_{n}^{2} }}\left( { - \beta_{n} + \alpha } \right)Y_{n} = 0$$
(5)

and where

$$A_{n} = Y_{n} \left[ {\left( {\beta_{n}^{2} - \alpha } \right)\beta_{n} \cot \beta_{n} - 2\alpha } \right] + \beta_{n}^{2} (\beta_{n}^{2} - \alpha )$$
(6)
$$Y_{n} = \beta_{n} \cot \beta_{n} - 1$$
(7)
$$\frac{1}{{\varphi_{n} }} = \frac{1}{\beta }\left( {1 - 3K\frac{{V_{s} }}{{V_{g} }}\frac{{Y_{n} }}{{\beta_{n}^{2} }}} \right)$$
(8)

In Eqs. (4)–(8), Vs and Vg are the volume occupied by the solid and the gas, respectively.

In this model, two parameters (α, β) regarding the rate of heat transfer and heat of adsorption are defined as follows:

$$\alpha = \left( {\frac{ha}{{\rho_{s} C_{s} }}} \right)/\left( {\frac{D}{{R^{2} }}} \right)$$
(9)
$$\beta = \frac{\Delta H}{{\rho_{s} C_{s} }}\left( {\frac{{\partial q^{*} }}{\partial T}} \right)_{{c_{0} ,T_{0} }}$$
(10)

where α is the external surface area divided by the volume of the adsorbent; ρs and Cs represent the density and heat capacity of the sample, respectively; h is the overall heat transfer coefficient; and ΔH is the heat of adsorption.

Parameter α describes the relative ratio of heat transfer (ha/ρsCs) to effective diffusion time constant (D/R2). Therefore, a large value of α implies that the heat generated during adsorption transferred into the surroundings rather than increasing the temperature of the adsorbent. A small value of α, on the other hand, implies that heat generation is concentrated at the initial part of the uptake because of the rapid uptake of molecules. Therefore, temperature increases during the adsorption, which reduces the equilibrium capacity. The slope of the uptake curve changes with time until heat is fully dissipated into the atmosphere.

Parameter β represents the heat of adsorption (ΔH/ρsCs) and the temperature dependence of the equilibrium capacity on the adsorbent (∂q*/∂T). When the equilibrium shift with temperature increase is minor, the kinetic result is close to that predicted by the isothermal model. On the contrary, if an adsorbate has strong temperature dependence with a large value of β, the uptake curve deviates from the isothermal model, resulting in a heat transfer-controlled system.

The reliability of simultaneous non-linear regression for three parameters (α, β and D/R2) in Eq. (4) is not guaranteed in general. Therefore, to obtain (ha/ρsCs) and β as a first step, the kinetic model of an entirely heat-controlled system was presented in the asymptotic form of kinetic models as follows: (Hu et al. 2014; Lee and Ruthven 1979; Ruthven et al. 1980)

$$\frac{{M_{\infty } - M_{t} }}{{M_{\infty } - M_{0} }} = \frac{\beta }{1 + \beta } \exp \left[ {\frac{ - hat}{{\rho_{s} C_{s} (1 + \beta )}}} \right]$$
(11)

In the corresponding system, the uptake curve is linear on a semi-log scale for time t.

As a result, α and β were obtained first from the latter part of the experimental uptake curve by using Eq. (11), and then the effective diffusion time constant was obtained by fitting the entire uptake curve using the non-isothermal kinetic model, Eq. (4). In this approach, the secant method, incremental search method (ISM) and least-squares method were used for non-linear regression using MATLAB (Mathworks, Inc.). In addition, a few sets of uptake data were fitted using the isothermal model in order to evaluate the thermal effects on adsorption.

In this study, experimental deviation from the model was estimated by the following coefficient of determination (R2):

$${\text{R}}^{2} = 1 - \frac{{\mathop \sum \nolimits ({\text{q}}_{\exp } - {\text{q}}_{\text{ni}} )^{2} }}{{\mathop \sum \nolimits ({\text{q}}_{\exp } - \bar{\text{q}})^{2} }}$$
(12)

where qexp was the experimental point; qni was the value from the non-isothermal kinetic model; and \(\bar{\text{q}}\) was the mean value of the experimental data. When the model agreed well with the data, the value of R2 approached 1.

3 Experimental section

3.1 Material

Spherical zeolite LiX pellets and cylindrical activated carbon granules were supplied by ZEOCHEM Co. (Z10-05-03) and KURARAY CHEMICAL Co. (coal-derived activated carbon; 2GA-H2J), respectively. The zeolite LiX and activated carbon were analyzed using an automatic volumetric sorption analyzer (BELSORP-Max) with CO2 at 298 K. Table 1 presents the measured and supplied physical properties of the adsorbents. Gases used as adsorbates (CO2, CO, N2 and CH4) were of high purity (>99.99 %).

Table 1 Physical properties of adsorbents
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3.2 Experimental procedure

A high-pressure volumetric system in Fig. 1 (BELSORP-HP) was used to measure adsorption equilibrium and uptake. Prior to the experimental run, zeolite LiX was regenerated at 623 K in an oven and activated carbon at 393 K in a vacuum oven for longer than 8 h. The mass of adsorbent was measured by a microbalance with an accuracy of ±10 µg.

Fig. 1
figure 1

Schematic diagram of volumetric apparatus

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Before deciding on the sample mass in the volumetric system, two sample masses (0.3922 and 0.8779 g) were tested for the N2/zeolite LiX system at 293 K in a pressure range of 0–100 kPa. The difference between the uptake curves obtained from two different sample masses was very small and the effective diffusion time constants were almost the same within the experimental error range. However, a smaller amount of sample showed slightly more fluctuation in the isotherm measurement. In the study, 0.8779 g of zeolite LiX with the average pellet size of 1.5 mm and 1.3811 g of activated carbon were used for the experiments.

The adsorbent was placed into the adsorption cell with a ceramic cap (Swagelok SS-8-VCR-2-GR-.5M) with 0.5 μm pores after two He purge. Then, it was assumed that the flow resistance into the adsorption cell is negligible. To minimize error caused by moisture and any trace of pollutants adsorbed during the installation of the adsorption cell, the zeolite LiX and activated carbon in the cell were reactivated at 623 and 393 K, respectively, under vacuum for longer than 12 h.

The system, composed of gas storage tanks, lines, valves and gauges, was set in an air bath, while the temperature of the adsorption cell was controlled by a water bath circulator. Two temperature controllers for each air bath and water bath were used in order to keep the temperature of the internal system and adsorption cell constant. The internal volume of the system and the dead volume in the adsorption system were measured by using helium gas at an experimental temperature.

The internal system was purged with helium gas before experiments, followed by an evacuation process with vacuum pumps. After repeating the purge/vacuum step three times, a specified amount of adsorptive gas was released into the internal system. The experiment was carried out by injecting a small amount of adsorbate into the adsorption cell at a constant temperature, and the pressure variation was monitored with an electrical pressure sensor (Full scale: 0.133 MPa (abs) × 1 unit, Accuracy: ±0.08 % of full scale). Once equilibrium was reached, a certain amount of adsorbate was again injected into the adsorption cell, and this procedure was repeated with a stepwise pressure change. For each experiment, all thermodynamic and uptake data were recorded automatically on an interfaced computer. The amount of gas adsorbed was calculated from the measured data on temperature, volume and pressure based on the compressibility factors from NIST thermodynamic isotherm properties (Linstrom and Mallard 2001). The recorded pressure change was converted into fractional uptake data at the equilibrium pressure.

4 Results and discussion

4.1 Comparison of isothermal and non-isothermal kinetic models

Five to six sets of uptake data for CO2, CO, N2 and CH4 on zeolite LiX and activated carbon at 298, 308 and 323 K were compiled at similar pressure conditions for each adsorbate over a pressure range of 15–90 kPa. Since the kinetic models assume a linear equilibrium relationship, it was assumed for the linear relationship between pressures of a stepwise change in the range of 3–9 kPa, depending on the adsorbate and the pressure condition. The effective diffusion time constant was obtained by fitting each experimental uptake curve using a non-isothermal kinetic model.

Figures 2 and 3 represent the experimental uptake curves for CO2, CO, N2 and CH4 at 293 K in zeolite LiX and activated carbon, respectively. The non-isothermal kinetic model predicted reasonably well the experimental uptake curve for each adsorbate with R2 values higher than 0.98 for all gases. As a representative case, the isothermal model results for CH4 on zeolite LiX and CO on activated carbon are shown in Figs. 2 and 3. The same effective diffusion time constant obtained from the non-isothermal model was applied to the isothermal model.

Fig. 2
figure 2

Experimental and theoretical uptake curves of various gases on zeolite LiX at 293 K: short dashed line non-isothermal diffusion model; solid line isothermal diffusion model

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Fig. 3
figure 3

Experimental and theoretical uptake curves of various gases on activated carbon at 293 K: short dashed line non-isothermal diffusion model; solid line isothermal diffusion model

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Over the range of measurement time, the isothermal model predicted the uptake curves during the initial period time, but the deviation from the experimental results increased with time even though their heats of adsorption were smaller than that of CO2, as shown in Fig. 4. The adsorption of the adsorbates on zeolite LiX and activated carbon was disturbed by a thermal effect and was completely controlled by the heat when approaching equilibrium. The result implied that isothermal diffusion at the initial period time was changed to the non-isothermal diffusion by the heat release from the heat of adsorption with time. Although the non-isothermal model accurately predicted the experimental uptake curves, the deviation from the CO2 uptake curve was relatively higher than that of the other curves. The assumptions of constant diffusivity and instantaneous equilibration of adsorbate in the experimental range might lead to greater deviation in the CO2 uptake curve than in those of the other components.

Fig. 4
figure 4

Adsorption isotherms at 293 K and isosteric heats of adsorption on adsorbents with respect to the adsorbed amount on a, b zeolite LiX and c, d activated carbon: (circle CO2; up-pointing triangle CO; square N2; down-pointing triangle CH4) (Data from Park et al. 2014)

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4.2 Adsorptive kinetic behaviors

The isosteric heat of adsorption and the adsorption isotherm are key factors that affect adsorption rate. Because the high isosteric heat of adsorption arises from a strong affinity, it increases the molecular diffusion rate but prevents adsorption on the adsorbent surface. In general, a slower adsorption rate is expected at a higher isosteric heat of adsorption. To explain the adsorptive kinetic behaviors, the adsorption isotherms and the isosteric heats of adsorption for all gases on zeolite LiX and activated carbon are presented in the same experimental pressure range in Figs. 4a and b, respectively.

As shown in Fig. 4, the adsorption isotherm and heat of adsorption of N2 on activated carbon were the lowest in all the adsorbate/adsorbent systems. In Figs. 2 and 3, the uptake curve of N2 on activated carbon was curved around 5–7 s more steeply than the other curves. This uptake curve indicates that the adsorption of N2 occurred mainly in the initial time period, but the adsorption rate of N2 with relatively weak adsorption affinity was affected by a thermal effect even though the heat of adsorption was relatively low. However, the result could be expected for fast thermal equilibrium in the N2/activated carbon system.

The effective diffusion time constants obtained from the uptake curves are listed in Tables 2 and 3, and presented in Fig. 5. The order of adsorption rate on zeolite LiX was CO2 ≪ CO < N2 < CH4 at 293 K over the whole pressure range, as shown in Fig. 5a. In Fig. 4b, the isosteric heats of adsorption of CO2, CO, N2 and CH4 on zeolite LiX were CH4 < N2 < CO ≪ CO2, which is opposite the adsorption rate order. For adsorption on activated carbon, the order of adsorption rate was CO2 ≪ CH4 ≤ N2 < CO. According to Fig. 4b, the sequence of adsorption rates of gases was not perfectly matched with the order of the isosteric heat of adsorption: N2 ≤ CO < CH4 < CO2.

Table 2 Effective diffusion time constants and non-isothermal model parameters (ha/ρsCs and β) of CO2, CO, N2 and CH4 on zeolite LiX obtained from the experimental uptake curves and the non-isothermal model
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Table 3 Effective diffusion time constants and non-isothermal model parameters (ha/ρsCs and β) of CO2, CO, N2 and CH4 on activated carbon obtained from the experimental uptake curves and the non-isothermal model
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Fig. 5
figure 5

Effective diffusion time constants (D/R2) at 293 K obtained by non-isothermal diffusion model: a zeolite LiX and b activated carbon (circle CO2; up-pointing triangle CO; square N2; down-pointing triangle CH4)

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Because the heat generation is concentrated at the early stage, the influence of heat of adsorption on adsorption rate is quite strong at this stage. On the other hand, when the system approaches equilibrium, the adsorption rate is more affected by heat transfer rather than heat generation. The contributions of these two effects to the adsorption rate differ among adsorbate/adsorbent systems.

As mentioned in the non-isothermal kinetic model in Eq. (4), the effective diffusion time constant was affected by the two parameters of heat of adsorption (β) and rate of heat transfer (α). The values used for the non-isothermal kinetic model are listed in Tables 2 and 3. The relative heat transfer rates of gases, α, represents the influence of the heat transfer rate (ha/ρsCs) compared to the diffusion rate. Therefore, if the system has a large α value, it is controlled by adsorption affinity due to immediate heat release. In the opposite case, the contribution of slow heat transfer to adsorption rate is increased because the generated heat precludes additional adsorption on the surface.

The adsorption rate of CO2 with the largest isosteric heat of adsorption on activated carbon was slower than that of the other gases. However, the adsorption rate of N2, which was expected to be the fastest, was similar to that of CH4. When comparing approximate heat transfer rates in terms of α, CO2 and CH4 were greater than 1, whereas N2 and CO were 0.24 and 0.50 respectively. Therefore, due to relatively slow heat transfer, the adsorption of N2 on the activated carbon surface is disturbed by the generated heat. Consequently, the adsorption uptake curve for activated carbon is drastically changed, as shown in Fig. 3. In addition, Fig. 4a implies that N2 and CO had low adsorption affinity on activated carbon, resulting in low isosteric heats of adsorption. As a result, a slower than expected adsorption rate for N2 and CO was observed on activated carbon.

In the case of zeolite LiX, CO2 had an α of 1.8, while the others (CO, N2 and CH4) had values of 0.81, 0.58 and 0.56, respectively. Although the relative heat transfer rate for CO2 was faster than those of the others, the approximately 2–3 times higher isosteric heat of adsorption shown in Fig. 4 generated high thermal resistance during CO2 adsorption and slow CO2 adsorption. The other gases showed significant differences between the isosteric heats of adsorption but not between relative heat transfer rates. As a result, since the heat transfer rates were not sufficiently high to quickly release the produced heat, the order of adsorption rates on zeolite LiX followed the decreasing order of isosteric heat of adsorption.

4.3 Dependence of pressure and temperature on adsorption kinetics

Figure 5 represents the effective diffusion time constants of gases on zeolite LiX and activated carbon at 293 K as a function of pressure. The effective diffusion time constants for the gases were on the same order of magnitude except for that of the CO2/zeolite LiX system. The effective diffusion time constants of some gases, especially N2 on zeolite LiX and CO on activated carbon, increased slightly with pressure, while CO2 and CO on zeolite LiX and CO2 and CH4 on activated carbon remained nearly constant. The pressure dependences may have arisen from changes in the slope of the adsorption isotherm and the isosteric heat of adsorption.

The diffusion in pelletized zeolites is affected by both micropore and macropore diffusions, but it is hard to determine the controlling diffusion mechanism of the zeolite system by the effective diffusion time constant. Thus, a controlling mechanism in zeolite pellet was indirectly examined by measuring the adsorption rate by changing the macropore diffusion length (Lee and Ruthven 1979). Figure 6 is the comparison between the effective diffusion time constants in different size pellets of zeolite LiX (1.5 and 0.8 mm). The effective diffusion time constant of CO2 in Fig. 6a, that has the highest adsorption affinity to zeolite LiX, was not affected by the pellet size, whereas CO and CH4 showed a little difference at a relatively low pressure range. It implied that the contribution of micropore diffusion to the effective diffusion time constants in CO2, CO and CH4/zeolite LiX systems is much higher than that of macropore diffusion.

Fig. 6
figure 6

Comparison of diffusion time constants for adsorption of a CO2, CO, CH4 and b N2 in two different size of zeolite LiX pellet at 293 K: (solid symbol for 0.8 mm; blank symbol for 1.5 mm; circle CO2; up-pointing triangle CO; square N2; down-pointing triangle CH4)

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The effective diffusion time constants of N2 in zeolite LiX showed a certain difference between two different size pellets in Fig. 6b. The uptake at the smaller size pellet was faster in the whole pressure range. Therefore, the macropore diffusion worked as a controlling step in the effective diffusion time constant. However, the difference at a low pressure was relatively small when compared with the difference in N2/zeolite 10X system (Ahn et al. 2002). It may stem from the relatively strong adsorption affinity of N2 with zeolite LiX. Then, the difference between two different size pellets decreased with an increase in pressure, which could be interpreted as the transition of the controlling step from macropore diffusion to micropore diffusion. It was also confirmed that the effective diffusion time constants increased as the slope of isotherm decreased, which implied the decrease in macropore diffusion contribution with pressure (Hu et al. 2014; Ahn et al. 2002).

The diffusion rate in macropore controlled system is easily affected by pressure because the slope of isotherm decreases with pressure. If the slope of the isotherm is steep, adsorption potential is high near the adsorbent crystal surface when adsorbate molecules are trapped near the micropores, which resist diffusion in macropores (Ahn et al. 2004). As shown in Fig. 4a, the slopes of adsorption isotherms decreased with increasing pressure. In zeolite LiX, the slope changes of adsorption isotherms from pressures greater than 20 kPa became very small in CO2 and CO, and those in N2 and CH4 were not significant over the entire pressure range. In activated carbon, the slope changes of adsorption isotherms were relatively smaller than those in zeolite LiX over the entire pressure range. The isosteric heats of adsorption in Fig. 4b decreased with increasing loading amount, resulting from decreasing adsorption affinities of CO2 and CO with zeolite LiX and CO2 and CH4 with activated carbon. The other systems showed relatively constant heats of adsorption.

In Fig. 5, the adsorption rate increased because the influence of adsorption potential decreased with pressure. However, such phenomena were observed only in the low-pressure range, and the CO2/adsorbent systems did not show any significant changes over the entire pressure range. Considering the slope change of the isotherms and the isosteric heat variation with pressure, the two phenomena had offsetting effects on adsorption rate. The CO/activated carbon system, which had relatively fast adsorption compared to the other systems, increased the effective diffusion time constant at high pressures. Because of the stepwise increment in pressure for the volumetric device, sufficiently high pressure guaranteed higher surface coverage on the adsorbent, which interrupted diffusion and adsorption of molecules on the adsorbent surface. The pressure effect on the adsorption rate is significant at low pressures and becomes weaker with increasing pressure.

The comparison of uptake curves between the two pressures is shown in Fig. 7. As mentioned before, adsorption was rapid in the early stages of all the systems and then approached equilibrium as the system became heat-controlled. At higher pressures, the uptake curve was smooth during the initial period of time, and the adsorption rate also was faster.

Fig. 7
figure 7

Effect of pressure on uptake curves of a CO2/zeolite LiX, b N2/zeolite LiX, c CO2/activated carbon, and d CO/activated carbon at 293 K. (short dashed line non-isothermal kinetic model; solid line heat transfer control limit)

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The uptake curves of the CO2/zeolite system in Fig. 7a almost overlapped in the initial period time, and their difference gradually increased with time. The uptake curves of CO showed a similar trend. On the other hand, since the N2/zeolite LiX system with slow heat transfer rates resulted in a heat-controlled system at higher pressures earlier than at lower pressures, the uptake curves showed a parallel decrease along the predicted lines by the heat controlled limit cases after passing certain period of time shown in Fig. 7b. CH4 showed an uptake curve similar to that of N2. As shown in Fig. 4b, the heats of adsorption of CO2 and CO in zeolite LiX were relatively high and decreased with increasing loading amount, while those of N2 and CH4 were almost constant.

In the activated carbon systems, the uptake curves of CO2 and CH4 had the same trend as those of CO2 and CO on zeolite LiX, while CO and N2 showed similar behavior to N2 and CH4 on zeolite LiX during the initial period. As shown in Fig. 4b, the heats of adsorption of CO2 and CH4 were relatively high and decreased with an increasing loading amount, while those of CO and N2 were almost constant. This implies that the initial uptake was strongly affected by the heat generated from adsorption.

Figure 8 represents the effect of temperature on the uptake curves of CO2 as a representative case. The results at other pressure conditions are shown in Tables 2 and 3. The adsorption rate increased with temperature due to faster molecular diffusion with higher kinetic energy. The temperature dependence of the amount adsorbed was highest for N2 on zeolite LiX and CH4 on activated carbon (Park et al. 2014). The isotherm results according to temperature were in agreement with the dependence of the adsorption rates because lower surface coverage at higher temperature could result in an increased adsorption rate.

Fig. 8
figure 8

Effect of temperature on uptake curves of CO2: a zeolite LiX and b activated carbon (circle T = 293 K; up-pointing triangle T = 308 K; square T = 323 K; solid symbol for about 20 kPa; blank symbol for about 80 kPa; short dashed line non-isothermal diffusion model)

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The level of temperature dependence depended on adsorbate/adsorbent system as well as applied pressure. Generally, the temperature effect on adsorption rate is stronger in a system with higher temperature dependence on equilibrium capacity. As shown in Fig. 8, the shapes of uptake curves of CO2 at similar pressure were similar regardless of temperature and adsorbent. However, the effects of temperature on effective diffusion constant on zeolite LiX were similar regardless of pressure, while those on activated carbon were higher at higher pressure than at lower pressure.

5 Conclusion

The adsorption uptakes for CO2, CO, N2 and CH4 on zeolite LiX and activated carbon were measured at 293, 308 and 323 K up to 100 kPa. The effective diffusion time constants (D/R2) of each component on each adsorbent were obtained by fitting a non-isothermal kinetic model with experimental uptake curves.

At the same pressure and temperature, the order of adsorption rates on zeolite LiX was CO2 ≪ CO < N2 < CH4, but the isosteric heats of adsorption showed the opposite order (CH4 < N2 < CO ≪ CO2). The order of adsorption rates on activated carbon was arranged as CO2 ≪ CH4 ≤ N2 < CO, but the sequence of adsorption rates was not perfectly matched with the order of isosteric heats of adsorption (N2 ≤ CO < CH4 < CO2).

The adsorption rates of the gases on zeolite LiX and activated carbon were affected by the isosteric heats of adsorption, heat transfer rate and adsorption affinity. Even though the heat of adsorption was small, it significantly affected the adsorption rate if the heat transfer rates were not sufficiently high to quickly release the generated heat. In addition, the initial uptake was strongly affected by the heat generated from adsorption.

The slope change in the isotherm and the isosteric heat variation with pressure produced an off-set effect on adsorption rate. The contribution of micropore diffusion on the zeolite LiX system seemed to be stronger than that of macropore diffusion. The effect of pressure on adsorption rate was significant at low pressure and became weaker with increasing pressure because of the decreased slope of the adsorption isotherm, decreased isosteric heat of adsorption and high surface coverage with pressure. The dependence of adsorption rate on temperature was in agreement with the isotherm results, showing that the adsorption rate increased with temperature.

Activated carbon granules and zeolite LiX pellets are widely used in adsorptive cyclic processes with respect to equilibrium separation for simple gas mixture. Even though adsorption equilibrium and selectivity work as a key factor in the separator design, the order of magnitude in the value of adsorption rate also contributes to improving the design accuracy in adsorptive separation processes. Therefore, the adsorption kinetic results obtained from the volumetric method in the study contribute to improving the design accuracy of various adsorptive processes using zeolite LiX and activated carbon for various effluent gases with CO2, CO, N2 and CH4.