Article pubs.acs.org/IECR
Experimental Study of a Pulsed-Pressure-Swing-Adsorption Process with Very Small 5A Zeolite Particles for Oxygen Enrichment Vemula Rama Rao and Shamsuzzaman Farooq* Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive, Singapore 117585, Singapore S Supporting Information *
ABSTRACT: The pressure drop characteristics, dynamic column breakthrough, and pulsed-pressure-swing-adsorption (PPSA) experiments in an adsorption column packed with very fine 5A zeolite particles of mixed size in the range 63−75 μm are presented. A multipurpose experimental setup was designed and constructed to perform these experiments. The pressure drop and axial dispersion were very high in the adsorption column. Darcy’s equation and the correlation by Langer et al. were recalibrated to account for the increased pressure drop and enhanced axial dispersion, respectively. With these recalibrated constituent models, the numerical process model, solved using COMSOL Multiphysics software, was able to correctly capture the measured experimental breakthrough and PPSA performance results. The principal conclusion from this study is that the high axial dispersion and pressure drop in a column packed with very fine 5A zeolite particles are due to the surface roughness and clustering of the particles and channeling in the column, which are detrimental to the performance of the PPSA process. Therefore, the maximum oxygen product purity obtained in a simple two-step PPSA process was limited to 90% O2 in the product stream) and significant size reduction, the PPSA process has to be cycled at a fast rate, and in most of the cases, the cycle times are in fractions of a second, which are very small compared to a conventional PSA process. The adsorption step durations, which are in milliseconds (ms), dictate the necessary response time while selecting various instruments used for analysis, detection, and control of the experimental process. The optimum adsorbent particle size is in the micron range, which is much smaller compared to the commercial-grade materials available in the market. For a fixed bed length and pressure drop, the individual step duration is inversely related to the square of the adsorbent particle size, which means the process has to be cycled 4 times faster for every doubling of the adsorbent size. Thus, the response times of available sensors and control devices guide the choice of the adsorbent particle size. On the other hand, although the cycling frequency is directly proportional to the square of the bed length, the portability issue limits how much the bed length can be increased. Similarly, the cycling frequency is directly proportional to the pressure drop along the bed length, but the maximum pressure of the device is limited by the safety issue for personal use. The required adsorber diameter is much bigger than the adsorber length to deliver 5 SLPM of high purity oxygen. If the adsorber diameter is bigger than the adsorber length, the flow distribution within the bed would not be uniform. The practical solution to this problem is to use several smaller-diameter columns in parallel. Because all of the parallel columns would be uncoupled (i.e., the flow from one column will not be fed to another column) and identical, it was concluded that using one small-diameter column was sufficient for experimental validation. In the experimental design of a PPSA process with a small column, minimizing the dead volumes at the entrance and exit of the column were very critical. Otherwise, feed and product contamination from mixing with residual gas in the dead space could severely compromise the process performance. In order to have a good estimate of the expected gas volume and flow rate in and out of the column during the two steps of a PPSA process, detailed calculations, using the process simulator developed in our previous study,7 were carried out for a set of preliminary operating parameters chosen on the basis of the design considerations discussed above. The results, presented in Table S1 in the Supporting Information, were very useful to specify the flow rate range of the flow controllers and meters and appropriately size the fittings, valves, and piping to keep the dead volumes at the minimum level while also keeping the pressure drop in the feed line as low as possible. Selection of the adsorbent, adsorber dimensions, selection of the instruments, and construction of the experimental setups used and
Figure 1. SEM images of ground binderless 5A zeolite adsorbents separated between 63 and 75 μm sieves.
The column was constructed from standard, stainless steel, seamless tubing having 1.27 cm outside diameter and 1.08 cm inside diameter. The column was 10.08 cm in length. Thus, the length-to-diameter ratio was sufficiently high to neglect the entrance effect. The smallest adsorption step duration was 381 ms in the range of feed pressure and particle size investigated. All of the devices used in the experimental study were selected in such a way that their response times were much faster than 381 ms. The response times of these devices specified by their manufacturers are summarized in Table S2 in the Supporting Information. 2.2. Single-Component Equilibrium Measurement. The single-component adsorption isotherms of nitrogen and oxygen were measured at two different temperatures using a constant-volume apparatus on a binderless 5A zeolite adsorbent sample with a particle size of around 1.6 mm. The constantvolume apparatus used in this study is schematically shown in Figure S2 in the Supporting Information, and it required 1 g of adsorbent. The sample preparation and experimental procedure are also detailed in the Supporting Information. Singlecomponent adsorption isotherms of nitrogen and oxygen on a binderless 5A zeolite measured at two different temperatures in this study are shown in Figure S2 along with Langmuir isotherm model fits, and the Langmuir isotherm model parameters are given in Table S3, all in the Supporting Information. 2.3. Multipurpose Experimental Rig. A multipurpose experimental setup was designed to perform the pressure-drop, 13158
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earlier was used, which is detailed together with the experimental procedure and conditions in the Supporting Information. 2.6. Experimental Study of the PPSA Process. After the pressure-drop and dispersion characteristics of the adsorption column packed with 63−75 μm size particles were verified by conducting independent equilibrium, pressure-drop, and breakthrough experiments, a set of experiments were conducted to demonstrate the performance of the PPSA process using the same multipurpose experimental setup mentioned earlier. A detailed description of the experimental setup and procedure is presented in the Supporting Information. The effects of the adsorption time (ta), desorption time (td), and inlet column pressure (PH) on the PPSA process performance were experimentally studied by variation of one variable at a time while the bed length (L), adsorbent particle size (dp), and the other two operating variables remained unchanged. The experimental results along with the isothermal and nonisothermal simulation results are discussed in section 4.
breakthrough, and PPSA experiments. Critical aspects such as the minimum dead volume and pressure drop at the entrance and exit of the column, available control and sensing instrumentation, and particle size were taken into consideration. The schematic of the experimental setup (Figure S3) and its operation are detailed in the Supporting Information. 2.4. Pressure-Drop Characteristics. The literature data available on pressure-drop effects in an adsorption column are very limited. Some important studies on the effect of pressure drop in an adsorption column on the process performance of rapid cycling processes are discussed next. Pressure-drop characteristics in the blowdown and pressurization steps were first studied by Sundaram and Wankat.8 They concluded that accounting for the pressure drop is very important in a rapid cycling adsorption process due to the shock moment of adsorption and desorption fronts within the column in short durations. Later, Buzanowski et al.9 observed that the pressure drop led to the spreading of concentration fronts in an adsorption column packed with small-size adsorbent particles because of increase of the gas velocity toward the exit. Sereno and Rodrigues10 studied and validated the steady-state Darcy and Ergun equations to predict the pressure drop in an adsorption column during pressurization and depressurization steps by comparing them with results from simulations using full momentum balance. Kikkinides and Yang11 performed experimental and theoretical studies on the pressure drop in a column packed with 13X zeolite adsorbent under isothermal conditions and concluded that the pressure drop caused early breakthrough. Yang et al.12 observed the same behavior in a nonisothermal system from the simulation study. They also showed that the pressure drop effect was negligible on the process performance in a multibed PSA process at cyclic steady state. Webley and Todd13 used the Ergun equation to represent the experimental pressure-drop characteristics of columns packed with 1.7 mm uniform LiLSX adsorbent particles under adsorbing and nonadsorbing conditions. Using Ergun parameters obtained by fitting nonadsorbing experiments, they were able to predict the depressurization and breakthrough profiles very well. However, we could not find any study in which the effect of very finely ground (irregular shape and size) particles on the pressure-drop characteristics in an adsorption column was investigated. Therefore, experiments were conducted to study the pressure-drop characteristics of the adsorption column and examine the validity of the Darcy equation for flow through a bed packed with particle sizes of interest in this PPSA study. The experiments were conducted in the multipurpose experimental setup described in the Supporting Information, where the experimental procedure is also detailed. The experimental and modeling results are presented in section 4. 2.5. Dynamic Column Breakthrough (DCB) Study. DCB experiments are useful for verifying equilibrium data from volumetric/gravimetric experiments, usually conducted with a small amount of adsorbent. They are also useful for investigating the transport mechanism. The similarity of the DCB experiments with the real cyclic adsorption process experiments further provides preliminary data for testing the basic assumptions of the process model. In this study, the single-component and binary breakthrough runs were conducted at different inlet pressures by introducing a step change in the mole fraction of the adsorbable component (or one of the two adsorbable components for binary mixtures) in the feed to the column inlet. The same multipurpose rig mentioned
3. MODEL DEVELOPMENT 3.1. Pressure-Drop modeling. Because the pressure drop along the column affects the gas flow through the column, an appropriate model to predict the pressure-drop characteristics is important for an accurate estimation of the PPSA process performance. The experiments described in section 2.4 were used to examine the validity of Darcy’s law for modeling the pressure-drop characteristic of the adsorption column packed with 63−75 μm crushed 5A zeolite particles. The underlying assumptions behind Darcy’s law are as follows: (i) The bed porosity is uniform along the bed length and cross-sectional area. (ii) The bed permeability is constant throughout the bed. (iii) The bed is packed with uniform-sized spherical particles. (iv) No channeling or bypass of the flowing fluid through the packed bed. (v) The pressure drop along the bed is linear. The general form of Darcy’s law, presented in terms of the interstitial gas velocity (uz), is as follows: μ ΔP = uz ; L kp
kp =
d p 2 ⎛ ε ⎞2 ⎜ ⎟ ; k1 ⎝ 1 − ε ⎠
k1 = 150
(1)
where ΔP is the pressure drop along the adsorption column of length L, uz (=u/ε) is the interstitial gas velocity, u is the superficial velocity, μ is the gas viscosity, and kp is the bed permeability, which is a function of the adsorbent particle size (dp), bed voidage (ε), and Darcy’s constant (k1). Darcy’s law relates the pressure drop along the column with the flow rate and bed permeability. Because many of the above assumptions may not be valid for flow through porous media under all experimental conditions, it has been suggested (by Raichura14 and Macdonald et al.15) that the empirical Darcy’s constant (k1 = 150), which depends on the column diameter to particle diameter ratio (Rd = Dc/dp), must be calibrated with pressuredrop experiments conducted under actual conditions. In the present study, the irregular shape and size of ground 5A particles was a clear deviation from assumption iii, which has also affected the other assumptions. By a comparison with the results from the Ergun equation, Darcy’s law was found to be adequate for breakthrough and PPSA process simulations. 13159
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k1 in Darcy’s law was obtained by minimizing the error between the experimentally measured pressure drop along the column and estimated pressure drop from Darcy’s equation (eq 1) in two different ways. The root-mean-square deviation (RMSD) was defined by the following equation: ⎛ ⎜ 1 ∑⎜ n − 1 i=1 ⎜ ⎝ n
RMSD =
( ΔLP )expi − ( ΔLP )modeli ⎞⎟ ⎟ ( ΔLP )modeli ⎟⎠
the Supporting Information. On the basis of published studies on oxygen and nitrogen transport in 5A zeolite (Ruthven and Xu16), it was assumed that molecular diffusion in the macropores controlled the rate of mass transfer, which was approximated using the linear driving force (LDF) model. The breakthrough experiments had three clear stages: initialization, adsorption, and desorption. The column inlet pressure was maintained at the desired level by saturating the column with one of the feed gases (initialization) used in the breakthrough experiments before introducing a step change in the feed gas composition at the entrance of the column. The boundary conditions discussed by Rao et al.7 were adjusted, as appropriate, to closely capture what could be achieved experimentally. For example, in the breakthrough measurements, the experimentally measured concentration profiles at the inlet of the column after subtraction of the sensor response still showed some spread arising from mixing of the residual gas with fresh gas in the remaining unavoidable dead volume at the entrance of the column. In order to predict the experimental breakthrough response at the column exit, it was important to consider the dispersion in the extra-column dead volume at the inlet in the simulation. The corrected inlet blank response was used as an input boundary condition to model experimental breakthrough results. 3.3. Axial Dispersion in a Column Packed with Very Fine Zeolite Particles. Using small particles in a macropore molecular diffusion-controlled system significantly reduces the mass-transfer resistance, thus increasing the significance of axial dispersion and its accurate estimation. Several publications in the literature have revealed high axial dispersion in columns packed with small particles. A detailed review on axial dispersion was presented by Delgado. 17 Edwards and Richards18 studied the axial dispersion in a column packed with 64−124 μm particles and concluded that the axial dispersion was very high with finer particles, which was attributed to the formation of channels in the column. Bischoff19 modified the correlation of Edwards and Richardson18 for axial dispersion to a more general form. Moulijn and Vanswaaij20 concluded that the axial dispersion was high in a column packed with small particles because of the clustering of small size particles, which led to channeling in the column. Langer et al.21 proposed the following modified equation for estimating the effective axial dispersion coefficient for a wide range of flow rates and particle sizes:
2
(2)
In the above equation, (ΔP/L)exp is the experimentally measured pressure drop along the column, (ΔP/L)model is the estimated pressure drop along the column using Darcy’s law, and n is number of data points. Darcy’s constant was estimated using methods 1 and 2 detailed below. Method 1. In this method, the empirical Darcy’s constant, k1, was obtained by minimizing the RMSD between the experimental pressure drop measured as a function of the interstitial inlet velocity and model estimate according to eq 1. In this approach, the change in the interstitial velocity along the column length was not taken into account in the pressure-drop calculations. The interstitial inlet velocity was used for uz. The main assumption in this approach that the pressure drop along the column is linear from the entrance to the exit of the column may not be valid in a very long column or a column packed with small-size packing material and having high pressure drop. Method 2. To better estimate the Darcy’s constant for flow through a column packed with very small-size zeolite adsorbent particles, the following total mass balance equation at steady state was solved to allow for the velocity variation along the bed length: ∂u ∂(cuz) ∂c = c z + uz =0 ∂z ∂z ∂z
(3)
where c is the molar density of gas entering and leaving the column, uz (=u/ε) is the interstitial gas velocity, and z is the distance in the direction of flow. The above equation is reduced to the following form upon substitution of the ideal gas law.
P
∂uz ∂P =0 + uz ∂z ∂z
(4)
The differential form of Darcy’s law is applied to account for the pressure drop: μ ∂P = uz ; ∂z kp
d p2 ⎡ ε2 ⎤ kp = ⎢ ⎥ k1 ⎣ (1 − ε)2 ⎦
DL = γ1DM + (5)
In order to solve eqs 4 and 5, two boundary conditions necessarily followed from the experimental conditions. uz = u 0
at z = L
⎛ Pe∞⎜1 + ⎝
βγ1DM ⎞ d puz̅
⎟
⎠
(7)
where Pe∞ is the limiting value of the Peclet number, which is a function of the adsorbent particle size according to eq 9, and β is the radial dispersion factor. A better estimate of the axial tortuosity factor, γ1, can be obtained from the following correlation, which is a function of the bed voidage (Ruthven5).
at z = 0
P = ambient
d puz̅
(6)
The equations were solved in COMSOL Multiphysics to find the Darcy’s constant (k1) that minimized the RMSD between the experimentally measured and calculated pressure drops. 3.2. Isothermal and Nonisothermal Modeling of the DCB and PPSA Experiments. The model equations and boundary conditions describing the DCB and PPSA experiments under isothermal assumption are similar to those discussed in a previous publication from this laboratory (Rao et al.7). The nonisothermal model equations are presented in
γ1 = 0.45 + 0.55ε
(8)
The term βγ1DM accounts for the effect of the radial concentration and velocity gradients on the axial dispersion. At low flow rates, βγ1DM ≫ dpu̅z, the molecular diffusion term (first term) in eq 7 dominates the axial dispersion and, therefore, it is independent of the gas velocity. At high flow rates, βγ1DM ≪ dpu̅z, the turbulent contribution (second term) dominates the axial dispersion and, therefore, the axial 13160
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dispersion increases and the increase is directly proportional to the gas velocity. Both mechanisms are important in the transition regime where βγ1DM ≈ dpu̅z. The theoretical value of β is estimated as 8 from a highly turbulent random walk model. Many authors proposed a range of values for β between 0.7 and 45. For small size particles, Hsu and Haynes22 proposed a value of 0.7 for β in a column packed with 340 μm NaY zeolite catalyst particles. In another study, Langer et al.21 proposed a value of 1 for β in a column packed with 560 μm spherical glass beads. The value of the limiting Peclet number (Pe∞) depends on the particle size (Ruthven5), as follows: Pe∞ = 2,
d p ≥ 0.3 cm
⎛ dp ⎞ Pe∞ = 3.35⎜ ⎟ , ⎝2⎠
d p ≤ 0.3 cm
Figure 2. Plot of the pressure drop along the column as a function the superficial gas velocity. The column was packed with binderless 5A zeolite adsorbent particles. RMSD(method 1) = 0.0119 and RMSD(method 2) = 0.00073. k1 = 150 results in 2 orders of magnitude lower pressure drop.
(9)
The limiting Peclet number increases with increasing particle size for small particles and approaches a constant value of 2 for dp ≥ 0.3 cm. In the case of small particles, Pe∞ is low and the axial dispersion is high because of the tendency of small particles to stick together to form clusters, where each cluster gives the hydrodynamic/aerodynamic effect of a single larger particle in the flow field. The clustering of small particles is a likely consequence of large interaction forces between the particles compared to the gravity force. It causes a nonuniform distribution of fine particles and leads to channeling in the column. In conclusion, the parameter β characterizes the effect of the local radial concentration and velocity gradients on the axial dispersion and the parameter Pe∞ characterizes the effect of channeling on the axial dispersion in a column packed with fine particles. Hence, eq 7 for the axial dispersion coefficient, with a fitting parameter β and the limiting Peclet number (Pe∞) estimated from eq 9, was used to characterize the dispersion in the present study.
4. EXPERIMENTAL AND SIMULATION RESULTS 4.1. Pressure-Drop Analysis. 4.1.1. Column Packed with 63−75 μm 5A Zeolite Adsorbent Particles. The best fit of the two methods (methods 1 and 2 detailed in section 3.1) to the experimental results obtained from a 10 cm long column packed with 63−75 μm binderless 5A zeolite adsorbent particles are shown in Figure 2, together with the corresponding optimum k1 values. The two k1 values were somewhat different, and method 2 gave a lower RMSD. Therefore, method 2 was adopted for the estimation of Darcy’s constant in the rest of the study. It should be noted that the optimum k1 value from either method was much greater than 150. In order to further understand these results, experiments were performed by varying the column-to-particle diameter ratio (Rd). 4.1.2. Effect of the Column-to-Particle Diameter Ratio (Rd) on Darcy’s Constant. The optimum Darcy’s constant (k1) values obtained from the pressure-drop experiments for different column to particle diameter ratios (Rd), along with the data available in the literature, are plotted as a function of Rd in Figure 3a. The bed voidages in each of these runs are shown in Figure 3b. It should be noted that the literature data are for nonadsorbing particles. The Darcy’s constant is approximately 150 at Rd ≈ 24, and a further increase or decrease of Rd resulted in an increase of the Darcy’s constant in the case of adsorbent particles. The wall effect becomes
Figure 3. Effect of column-to-particle diameter ratio (Rd = Dc/dp) on (a) the Darcy’s law constant and (b) the bed voidage in a 0.5-in.diameter column and packed with zeolite adsorbent particles ranging from ∼69 μm to 3.6 mm diameter. The inside diameter of the column used in these experiments was 1.08 cm. The literature values are from Raichura.14
significant as the column-to-particle diameter decreases below 24, and it results in an increase of the bed voidage near the column wall. Note the overall increase of the bed voidage in these runs shown in Figure 3b. As a consequence, it causes channeling toward the column wall, which leads to an increase in the pressure drop due to a longer flow path from the entry to the exit, thus increasing Darcy’s constant above 150. The 13161
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very small size adsorbent particles can significantly increase axial dispersion because of clustering and consequent channeling in the column. As discussed in section 3.3, the radial dispersion factor (β) captures the effect of the radial concentration and velocity gradients on axial dispersion and the limiting value of the Peclet number (Pe∞) captures the clustering effect. In the literature, discussed in the previous section, the limiting value of the Peclet number (Pe∞) has been very well correlated with the adsorbent particle size for dp < 0.3 cm and is equal to 2 for dp > 0.3 cm. However, there is no available correlation for the radial dispersion factor (β) with any of the process parameters in the literature. The estimation of β from tracer experiments in a short column is prone to high error because of the very short residence time. Instead, the effect of the variation of β on the spread of the breakthrough profile was studied. The results are compared in Figure 5 with a
Darcy’s constants obtained from experiments in this study in the region Rd < 24 were close to the data available in the literature, as shown in Figure 3a. The data for Rd > 24, for crushed zeolite particles 24 was most likely due to the clustering of very small charged zeolite adsorbent particles, which led to the formation of zones with different bed voidages and permeabilities within the column. This resulted in variation of the bed resistance to gas flow across the column, thus increasing the length of the flow path from the inlet to the exit. Furthermore, the nonuniform size/shape and surface roughness of the ground zeolite particles (see Figure 1) also contributed to increased pressure drop. In Figure 3b, it is shown that a minimum in bed voidage (ε) was observed with the particle size. The bed voidage increased significantly for very small particles, which indirectly supports the possibility of clustering. 4.1.3. Column Packed with 75−90 μm Glass Beads. To further verify if the surface roughness of the crushed zeolite particles and their charge-induced clustering might have caused the significant increase in the pressure drop along the column for Rd > 24, pressure-drop experiments were performed with a column of the same diameter and length but packed with inert spherical glass beads in the size range 75−90 μm, which was close to the smallest size of crushed 5A zeolite particles (63−75 μm). The bed voidage for glass beads was 0.346 compared to 0.556 for the smallest zeolite particles shown in Figure 3b. The best-fit Darcy’s constant, as may be seen from Figure 4, was
Figure 5. Experimental breakthrough results compared with simulation for different values of the radial dispersion factor, β. For experimental details, see run 2 in Table S5 in the Supporting Information. Symbols represent experimental data, and lines represent simulation results.
representative experimental run. It is important to note that Darcy’s constant was fixed from an independent experimental study (k1 = 4136.2). The LDF rate constant for macropore molecular diffusion-controlled transport was independently estimated from the following well-known expression (Ruthven et al.16): ki = Ω
εpDp ⎛ c0 ⎞ ⎜⎜ ⎟⎟ rp2 ⎝ q0 ⎠ i
where i = A or B (11)
where Dp is the macropore diffusivity and Ω (=15) is an empirical parameter that depends on the cycle time for faster cycling processes. The macropore diffusivity (Dp = DM/τ) is related to the molecular diffusion coefficient (DM) and tortuosity factor (τ = 3). εp (=0.33) is the particle porosity, and q0 is the adsorbent loading estimated from the Langmuir isotherm at c0. The LDF rate constant was very large for 69 μm (average of 63−75 μm range) particles and did not practically contribute any spread to the breakthrough response. Thus, for the results in Figure 5, β was the only fitting parameter. β equal to 0.2 gave the best fit, and this value was used to analyze the remaining experimental breakthrough results. 4.2.2. Effect of the Darcy and Ergun Parameters on the Breakthrough Curve. To analyze the effect of Darcy’s constant on breakthrough simulations, the isothermal model equations were solved using COMSOL Multiphysics with MATLAB. On
Figure 4. Plot of the pressure drop in a 10 cm column packed with 75−90 μm size spherical glass beads. The bed voidage was 0.35.
124.77, which is close to 150. Therefore, indirect evidence seems to suggest that the nonuniform size/shape, surface roughness, and clustering of small zeolite adsorbent particles obtained by crushing bigger binderless particles led to the increase of Darcy’s constant beyond 150 for size 24 observed for a crushed 5A zeolite adsorbent. In order to confirm that the Darcy’s constant corresponding to the best fit of the oxygen breakthrough at the column exit also satisfied the overall mass balance, the experimental and predicted velocity profiles at the inlet and the exit of the column are also compared in Figure 6b,c for the same representative run (run 2 given in Table S5 in the Supporting Information). Although the source (cylinder) pressure was held constant, the column inlet pressure still dropped for a very short time in the early part of the adsorption step because of adsorption of oxygen. Similarly, a rise in the inlet pressure was observed in the desorption step because of oxygen desorption. For k1 = 4136.2, the simulated exit velocity in the adsorption step matched very well with the experimental results but deviated somewhat from the experimental results in the desorption step. However, at the inlet, the model prediction was closer to the experimental data during desorption than during adsorption. The overall predictions for the adsorption/ desorption runs capture the correct qualitative trends. Given that k1 was estimated from pressure drop experiments with an inert gas, the extent of quantitative agreement is satisfactory. 4.2.3. Effect of the Heat-Transfer Parameter on Nonisothermal Modeling of Breakthrough Experiments. The nonisothermal model equations for DCB simulations have been detailed in the Supporting Information. A systematic parametric study was performed in order to analyze the effect of the inside heat-transfer coefficient (hin) on breakthrough simulations. The Darcy’s constant (k1 = 4136.2) and radial dispersion factor (β = 0.2) established from isothermal simulations were kept fixed in the nonisothermal simulations while estimating the effect of the inside heat-transfer coefficient (hin). The specific heat of
Figure 6. Effect of Darcy’s constant (k1) on (a) the adsorption and desorption breakthrough time, (b) the inlet interstitial velocity, and (c) the exit interstitial velocity compared with experimental results for a representative single-component breakthrough of 50% O2 in He. For experimental details, see run 2 in Table S5 in the Supporting Information. Symbols represent experimental data, and lines represent simulation results.
adsorbate in the adsorbed phase (Cpa) was assumed to be the same as the gas-phase specific heat (C̅ pg). The adsorbent specific heat (Cps) was taken from the literature (Farooq and Ruthven23). The effective thermal conductivity (Kz) was taken as 5 times the thermal conductivity of the gas mixture (Kg; McCabe et al.24). The same representative experimental run was used for calibrating the inside heat-transfer coefficient (hin). It was observed that the concentration breakthrough obtained from simulation was not sensitive to the inside heat-transfer coefficient in the range over which it was varied. The effect of the inside heat-transfer coefficient (hin) on temperature 13163
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temperature, as may be seen from Figure 7. The best-fit value (hin = 64.5 W/m2·K) obtained was kept fixed in the remaining simulations discussed next. 4.3. DCB Experiments and Simulation: Results and Analysis. In order to establish the gas-transport mechanism in 5A zeolite powder (63−75 μm), a series of single-component (50% O2 in He) and mixture (oxygen and nitrogen) breakthrough experiments were conducted. The operating conditions specific to each experiment are compiled in Table S5 in the Supporting Information, the common parameters are given in Table S6 in the Supporting Information, and the coefficients and physical property parameters are summarized in Table S7 in the Supporting Information. In the case of the nonisothermal model, the column wall was assumed to be at the same temperature as the circulating water in the jacket of the column. Furthermore, the effect of axial dispersion on the spread of breakthrough curves was analyzed by setting a very large value for the LDF mass-transfer rate constant, ki, in the nonisothermal model. All of the simulation results presented henceforth are predictions using parameters obtained from correlations and independent single-component experiments. 4.3.1. Single-Component Breakthrough Experiments. Experimental results from single-component breakthrough measurements conducted at two different inlet pressures have been compared with the model predictions in Figure 8. These runs are different from run 2 used earlier for the calibration of heat-transfer and axial dispersion parameters. Both isothermal and nonisothermal simulation results have been reported, and also the effect of the axial dispersion on breakthrough curves in the nonisothermal model is presented.
breakthrough profiles were investigated and compared with the measured temperature profile. The results are shown in Figure 7. Because the concentration breakthrough profiles were not
Figure 7. Effect of the inside heat-transfer coefficient (hin) on the adsorption and desorption temperature profiles at the middle of the column length compared with the experimental temperature measured at the center of the column for a representative single-component breakthrough of 50% O2 in He. For experimental details, see run 2 in Table S5 in the Supporting Information. Symbols represent experimental data, and lines represent simulation results.
affected by this parameter, they are not included in the figure. It is clear that the inside heat-transfer coefficient (hin) had an effect on the temperature breakthrough profile. hin affected the spread of the profile but had little effect on the peak
Figure 8. Experimental concentration profiles at the column exit and temperature profiles at the middle of the column compared with simulation results for two single-component breakthrough runs of 50% O2 in He. For experimental details, see runs 1 and 4 in Table S5 in the Supporting Information. Symbols represent experimental data, and lines represent simulation results. Nonisothermal model results including mass-transfer resistance and axial dispersion are practically indistinguishable from the results when the mass-transfer resistance is neglected, which is denoted as “Dispersion (Nonisothermal)”. 13164
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Figure 9. Binary experimental concentration profiles at the exit and temperature profiles at the middle of the column length compared with simulation results for two experimental runs of nitrogen−air breakthrough. For experimental details, see runs 6 and 8 in Table S5 in the Supporting Information. Nonisothermal model results including mass-transfer resistance and axial dispersion are practically indistinguishable from the results when the mass-transfer resistance is neglected, which is denoted as “Dispersion (Nonisothermal)”.
equilibrium data, shown in Table S3 in the Supporting Information, was used in the binary simulations. Similar to single-component breakthrough modeling, the same Darcy’s constant (k1) obtained from independent pressure-drop experiments using helium gas, as well as the radial dispersion factor (β) and inside heat-transfer coefficient (hin) obtained from fitting the single-component concentration breakthrough at the column exit and temperature profile at the middle of the column, respectively, measured in a representative experiment (run 2 in Table S4 in the Supporting Information), was used in all of the binary breakthrough simulations. The parameters are reported in Table S6 in the Supporting Information. The experimental concentration breakthrough profiles measured at the exit of the column and the temperature profiles measured at the middle of the column length for two runs are shown in Figure 9 for switching the feed gas to air from nitrogen, with which the bed was previously saturated, and vice versa. The predictions from the isothermal and nonisothermal simulation models are also included in the figure. It is important to note that nitrogen was desorbed when oxygen was adsorbed, which resulted in a net drop in the temperature. The reverse resulted in a net temperature rise. The simulated concentration breakthrough profiles matched well with the experimental results. The isothermal and nonisothermal model predictions were practically overlapping with each other. This is not surprising because the measured temperature changes were very small. The maximum measured temperature rises/drops were
