Pressure Swing Adsorption for Air Purification. 1. Temperature

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Ind. Eng. Chem. Res. 1996, 35, 2342-2354

Pressure Swing Adsorption for Air Purification. 1. Temperature Cycling and Role of Weakly Adsorbed Carrier Gas John J. Mahle* U.S. Army Edgewood Research, Development and Engineering Center, Aberdeen Proving Ground, Maryland 21010-5423

David K. Friday Guild Associates, Inc., 5022 Campbell Boulevard, Baltimore, Maryland 21236

M. Douglas LeVan Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22903-2442

Nonisothermal effects are known to be generally important in gas-phase adsorption processes. This paper considers the role of a weakly adsorbed carrier gas in pressure swing adsorption for purification. A combination of experimental and mathematical modeling results is presented in order to understand and describe the influence of the carrier gas on the behavior of the bed. Dry air is fed to beds of BPL activated carbon. Variations consider a feed of pure helium and a packing of glass beads or an empty column. The role of the heat capacity of the end regions of the bed is emphasized. For air with activated carbon, which adsorbs weakly with insignificant separation of nitrogen and oxygen, periodic state behavior leads to subcooling of the feed-inlet end of the bed and, for cycles of moderately short duration, to temperature rectification, or the establishment of a permanent oscillating temperature wave in the bed. The effect of the volumetric purge-to-feed ratio on the extent of this region and degree of subcooling is examined. Introduction Pressure swing adsorption (PSA) is based on cycling adsorption beds between high-pressure feed and lowpressure purge to achieve separation or purification of a feed stream. PSA-based purification processes include solvent recovery and air drying. Laboratory-based studies of PSA are often used to investigate new types of cycles and map performance over ranges of operating parameters. In order to scale up these results accurately, nonisothermal effects must often be considered. In general, the influence of nonisothermal behavior in PSA is to reduce the separation versus that obtainable from isothermal conditions because the nonisothermal case leads to adsorption at higher temperature and desorption at lower temperature, both of which reduce efficiency. Large scale PSA systems exhibit close to true adiabatic behavior, with temperature swings being more pronounced than in laboratory studies. Yang (1987) cites industrial examples of temperature swings of 40 °C or more. He also reviews several of the patents that have been proposed to mitigate deleterious thermal effects. A number of experimental studies have examined the nonisothermal effects of PSA. Chihara and Suzuki (1983a,b) provide experimental evidence of the presence of temperature swings and examine their importance in PSA performance. Matz and Knaebel (1987) recorded in-bed temperatures for an air separation PSA cycle. These studies were performed using a single column with negligible void spaces at feed and product ends. The magnitudes of the observed temperature swings relative to the ambient feed temperature were approximately +10 °C for adsorption and -8 °C for desorption. At the periodic state, small variations between the maximum and minimum temperatures were recorded at various positions in the bed. Experiments with two bed diameters (2.36 and 9.50 cm) indicated that there was no increased effect for the S0888-5885(95)00475-1 CCC: $12.00

larger diameter. In-bed temperature measurements of PSA were also reported by Yang and Doong (1985) and Doong and Yang (1986) for the bulk separation of H2 and CH4. Large temperature swings of 20-40 °C were recorded in the bed for a four-step process with heat losses. Ellis et al. (1993) reported a greater separation factor in PSA experiments separating R-12 from air using beds wrapped with insulation. No temperature data were reported. They also report temperature swings of several degrees between the feed and purge steps for laboratory scale air purification. They modeled their results, including an energy balance and the assumption of frozen solid-phase concentrations. Modeling of PSA cycles has evolved to include many effects. However, although the presence of nonisothermal effects in PSA processes has been long recognized, few studies have been presented for models of complete PSA cycles that include nonlinear equilibria, nonisothermal behavior, a rate model, and analysis of pressurization and blowdown. The basis for nonisothermal behavior has been attributed to both heats of adsorption and compression effects. Clearly, an overall energy balance must be satisfied, but local heating and cooling effects may occur. Among the many modeling studies of PSA steps and cycles, the following are most closely related to the present study. Cheng and Hill (1985) simulated heliummethane separation using a mixing-cell model with local equilibrium in the cells and void volumes added at the column ends. They also reported experimental data that included the effects of end caps; no temperature measurements were made, however. Yang and Doong (1985) and Doong and Yang (1986) modeled the nonisothermal effects of a bulk separation process using a finite difference scheme; simulation results agreed well with measured in-bed temperature histograms. Yang and Cen (1986) studied a PSA system that resembled a heat exchanger. Temperature profiles resulting from © 1996 American Chemical Society

Ind. Eng. Chem. Res., Vol. 35, No. 7, 1996 2343

heat transfer between the beds were determined using a mathematical model. Farooq et al. (1988) modeled air drying using activated alumina; air was considered inert, and nonisothermal effects resulted from water adsorption. Kumar (1989) used valve equations in a study on the dynamics of pressurization and blowdown, finding that for blowdown the isothermal model was inadequate especially for high pressures. Ritter and Yang (1991) developed a model for air purification that included the effects of a linear driving force and assumed frozen solid-phase concentrations during pressurization and blowdown. Mutasim and Bowen (1992) developed a nonisothermal multicomponent model with frozen solid-phase concentrations for carbon dioxide separation from air. Lu et al. (1992) present mathematical modeling results for column pressurization and blowdown dynamics including compression effects, and Lu et al. (1993) used a collocation-based mathematical model to describe adiabatic behavior for the data of Cheng and Hill (1985). Void volumes were included at the column ends, but the temperature effects associated with these end regions were not examined explicitly. This paper presents experimental and mathematical modeling results to describe nonisothermal behavior for a laboratory scale PSA system. We consider a particularly simple system to establish the role that a carrier gas can often play in PSA applied for purification. We feed only the carrier gas, in our case pure dry air or helium, to a bed of activated carbon. For air, as we will show, isotherms suggest no separation of oxygen and nitrogen; therefore, our feed is essentially a pure, weakly adsorbed gas. For helium, we consider the feed to be unadsorbed. The temperature transients are measured by in-bed thermocouples. The cycle considered in this paper is a two-step cycle: high-pressure feed and counter current low-pressure purge. Both in the experiments and in the model, pressurization occurs during the initial part of the high-pressure feed step, and blowdown occurs early in the low-pressure purge step. The work is divided into two parts. First, a series of experiments using the different carrier gases with activated carbon and glass bead packings or an empty column is used to identify the basis for observed temperature swings. Then, predictions of a nonisothermal mathematical model for air adsorption in PSA that includes effects of adsorption and desorption, pressurization and blowdown, and heat losses are compared with experimental results. Mathematical Model The mathematical model is developed to describe some important PSA properties. Included in this model are factors to describe the finite rate of pressurization and blowdown, nonlinear adsorption equilibria, and major contributions to nonisothermal effects. Conservation Equations. The material and energy balances are written for a single-adsorbable component. These are

∂c ∂(νc) ∂q )0 Fb + ′ + ∂t ∂t ∂z

(1)

∂us ∂(cuf) ∂(νchf) 2U + ′ + ) - (Tf - Tw) Fb ∂t ∂t ∂z Rc

(2)

In eq 2, the last term accounts for heat transfer to the column wall. Energy effects associated with gas com-

pression and decompression during pressurization and blowdown have been included in the energy balance by writing this equation in terms of internal energies and enthalpy. The internal energy of the stationary phase, the internal energy of the fluid phase, and the enthalpy of the fluid phase are respectively

us ) (cps + cpfq)(Ts - Tref) - λq

(3)

uf ) hf - P/c

(4)

hf ) cpf(Tf - Tref)

(5)

In writing eqs 1-5 we have assumed a constant total bed voidage ′, constant molar and specific heat capacities, and a constant heat of adsorption. In order to model accurately the nonisothermal behavior, a mixing cell is included at each end of the bed for mass and heat transfer. The material and energy balances apply to the these end caps as well, except the terms for accumulation in the stationary phase are neglected and the total bed voidage, ′, is unity. Rate Equations. The internal energy of the wall is described by

∂uw ∂2T mw - k 2w ) -U(Tw - Tf) ∂t ∂z

(6)

uw ) cpw(Tw - Tref)

(7)

where

which allows heat conduction along the length of the column. This equation is solved using the same axial increments as the material and energy balances. No energy loss from the wall to the ambient surroundings is considered in the model. As will be shown in the experiments, this loss is small compared to the energy transferred back and forth between the wall and the bed. As a rate model on fluid to particle mass transfer, we recognize that because this process involves the adsorption of a pure gas feed, mass transfer will be driven by convection (pressure gradients) in the bulk fluid phase and within the macropore structure of the carbon. This is a fast process compared to diffusion in microporous domains. Furthermore, we will adopt the commonly used assumption that heat transfer is rapid between fluid and particles, giving a single local temperature for them (i.e., T ≡ Tf ) Ts). We describe mass transfer in micropores using the linear driving force approximation (Glueckauf, 1955)

∂q ) kq(q* - q) ∂t

(8)

kq ) 15ψDs/Rp2

(9)

with ψ ) 19/15 (Nakao and Suzuki, 1983) where q* is given by the isotherm (equilibrium value at the system pressure). The effective diffusion coefficient of nitrogen on activated carbon was estimated using the correlation of Sladek et al. (1974). Experimental results on carbon molecular sieves are often several orders of magnitude less than this (Ruthven et al., 1994). We assumed the same diffusion coefficient for oxygen. Valve equations are used to control the rate of pressurization and depressurization. Thus, we adopt

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Ind. Eng. Chem. Res., Vol. 35, No. 7, 1996

Table 1. System Parameters Column Properties radius and packed length volume 1.90 Vin (cm3) 57 Rc (cm) L (cm) 24 Vout (cm3) 109 Ro (cm) 2.15 Vbed (cm3) 273 mass thermal conductivity (steel) wall (center sect) (kg) 0.96 k(J/m s K) 16 feed end cap (kg) 0.48 heat transfer coefficients (u) product end cap (kg) 0.96 wall, packed (J/m2 s K) 93 glass wool/beads (kg) 0.03 wall, empty (J/m2 s K) 9 2 3.8 in. tubing (J/m s K) 99 BPL Carbon physical properties nitrogen isotherm Rp (m) 5.0 × 10-4 k0 22.75 Fb (kg/m3) 460 k1 -5101 ′ 0.7 b1 922 R 0.6 rate property τ′ 6 Ds (m2/s) 1.0 × 10-8 cpf (air) (J/mol K) cpg (glass) (J/K)

Heat Capacities 29.1 cps (carbon) (J/kg K) 800 cpw (wall) (J/kg K)

1050 460

other column was at the purge pressure. The first simulation step involved pressure changes. Solution Method. We assumed ideal gas behavior and negligible axial pressure gradients. Also, following Farooq et al. (1988), we assume that the temperature dependence of fluid-phase properties can be neglected relative to the much larger dependence of fluid-phase properties on pressure in PSA. In other words, we assume that an approximately 400% variation in pressure during a PSA cycle affects the gas-phase density much more than an approximately 10% variation in absolute temperature. Using these assumptions eq 1 becomes

′ dP P ∂v ∂q Fb + + )0 ∂t RT dt RT ∂z

and other equations are written similarly. Equation 15 can be integrated from the column inlet to the column outlet to give an overall material balance on the bed in the form

Table 2. Boundary Conditions Feed Bed

Fb

c ) cfeed at z ) 0 T ) Tfeed at z ) 0 Tw (at z ) feed end of adsorbent) ) Tw (feed end cap) Tw (at z ) product end of adsorbent) ) Tw (product end cap) Purge Bed c ) cproduct at z ) L T ) Tamb at z ) L Tw (at z ) feed end of adsorbent) ) Tw (feed end cap) Tw (at z ) product end of adsorbent) ) Tw (product end cap)

the dimensional equation used by Kumar (1989)

Q ) 8.19 × 10-7Cv

x

P21 - P22 (SG)T

(10)

P1 and P2 represent high and low pressures across the valve, respectively, and SG is the specific gravity of air relative to 1 atm and 294.1 K. The minimum value of P2 is 0.53P1, corresponding to sonic velocity. (On the basis of given feed, purge, and ambient pressures and the feed and product flow rates, the valve coefficients for a given set of conditions can be calculated directly from this equation.) Adsorption Equilibria. The adsorption equilibria as a funciton of temperature was represented by a virial isotherm

ln P ) ln q + k0 +

k1 + b1q T

(11)

Boundary and Initial Conditions. Boundary conditions are given in Table 2. As discussed later, in coupling the beds, two cases were examined to establish the feed temperature to the bed being purged: purge inlet temperature equal to product exit temperature and purge inlet temperature equal to ambient temperature. The boundary conditions for eq 6 are also presented in Table 2, where conduction effects are calculated only along the length of adsorbent. This is required because most of the heat transfer occurs in the adsorbent region; the end cap geometry is complex and exhibits lumped parameter behavior. Initially both columns were at 25 °C with air adsorbed. One column was at the feed pressure, and the

(12)

dz + ∫0L∂q ∂t

Vin + ′Vbed + Vout 1 dP + Vbed RT dt c(ν1 - ν0) ) 0 (13)

where Vin, Vbed, and Vout are the volumes of the inlet region, the bed, and the outlet region, and ν0 and ν1 are the velocities at the column inlet and outlet, respectively. The equation set was solved numerically by making the assumptions described above and then writing the spatial derivatives appearing in all of the conservation equations in backward difference form to give a stage model. This gives a set of coupled first-order ordinary differential equations. At any given time, with values known for all dependent variables, it is necessary to calculate values of the first derivatives. This is done as follows. First, the derivatives dq/dt are evaluated using eq 8, and velocities into and out of the column are determined from eq 10. Then, the single value of dP/dt is evaluated using eq 13. Local velocities can then be evaluated from the backward difference form of eq 12. The final time derivatives, dT/dt, can then be evaluated from the backward difference form of eq 2. The Gear’s method solver LSODES (Hindmarsh, 1983) was used to integrate the model equations, which form a sparse, stiff system. Both beds of the two-bed system were integrated simultaneously to give the proper time dependence for approach to periodic state behavior. The latter approach is required when modeling conditions of a time-varying feed condition such as a pulse. The number of stages in each bed was chosen to be 30 as no further increase sharpened wave fronts significantly. Experiments Apparatus. The two-bed PSA system shown Figure 1 was operated to obtain measured temperature behavior over a range of operating conditions. The system was fully automated for unattended operation through use of a Macintosh microcomputer and LabVIEW software. The alternate cycling of the beds was performed using four, three-way, air-actuated ball valves. A highflow solenoid valve was placed on the purge exit line so that a repressurization with product step could be included in the cycle. The feed and product flow rates were controlled using mass flow controllers. Bed pres-


Figure 1. Schematic representation of laboratory scale PSA system.

Figure 2. Column cross-section.

sure was controlled using a globe valve on the product line after the purge split. All tubing was 3/8 in. o.d. stainless steel tubing. Solenoid valves used to control the air actuators were switched using relays controlled by a microcomputer. A schematic drawing of an adsorption column is shown in Figure 2. The columns were made of stainless steel with a wall thickness of 0.25 cm. End caps were attached using flanges. These gave a small volume at the feed end (top) and a large volume at the product end (bottom). The adsorbent was contained near the top of the column and was held in place between a fixed screen located at the top flange and a floating screen that was held in place by a helical spring. A glass wool plug was inserted between the adsorbent bed and the floating screen to filter adsorbent fines, thus, protecting the product mass flow controller. Glass beads, packed to 5 cm in depth, in the product end were used to act as a spacer between the end of the carbon bed and the floating end cap. Table 1 lists the mass and size of the various bed sections. All experiments were performed using a fixed packing depth of 24 cm. The beds were

not insulated except for one experiment, in which they were wrapped with a 1/2 in. layer of foam insulation. Temperature measurements in the bed were obtained by recording the response of 1/32 in. diameter, type T, sheathed, grouned thermocouples (Omega Engineering Inc.) that were installed in one of the beds. Sheathed thermocouples were chosen because the beds were to be packed serveral times which could damaged an exposed juction probe. Time constants of 1.8 s in flowing air and 0.2 s in water were reported by the manufacturer. In a packed bed, conduction from the particle to the probe probably results in a value intermediate between these two limits or a time constant of approximately 1 s. The thermocouples were inserted prior to packing the bed. The ratio of length of the thermocouple in the flow stream to the thermocouple sheath diameter was 32. This is larger than required for minimizing conduction effects along the length of the thermocouple (the manufacturer suggests a minimum of 10 for this ratio). In addition, the thermocouple is secured in the fitting using graphite ferrules which provide thermal insulation between the column wall and thermocouple end. Inlet and outlet temperatures were measured with thermocouples installed in the unpacked end caps, as shown in Figure 2. Ten measured samples were recorded for each temperature providing an average value over a 0.25 s interval. Pressure measurements were recorded using electronic 0-100 psia pressure transducers at the top, within, and at the bottom of one bed. The analog response of these sensors was sampled at 100 Hz. Materials. The adsorbent was BPL activated carbon, 12 × 30 mesh from Calgon Carbon Corp. When glass beads were the packing, 6 mm diameter pellets were used. In all cases the beds were packed using a drop tube. The feed air was taken from a compressor and passed through a refrigerated dryer and then a desiccant dryer to achieve a dewpoint of -70 °C. UH grade helium, >99.99%, was used when helium was the carrier. Parameters. The heat transfer parameters for the packed, adsorption column were determined experimentally by the method of Friday and LeVan (1985). The

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Figure 3. Adsorption equilibria data for nitrogen adsorption on BPL activated carbon at 0, 25, and 37 °C, oxygen adsorption on BPL at 25 °C, and a virial fit to the nitrogen data. Fit parameters are given in Table 1.

heat transfer coefficient U was determined to be 93 J/(s m2 K) at 50 std L/min. This agrees well with the correlation of Yagi and Wakao (1959) for a packed bed, which yields a heat transfer coefficient of 99 J/(s m2 K) at 50 std L/m. On the basis of correlations and experimental evidence, the heat transfer coefficient for an empty column is approximately 1 order of magnitude less than that for a packed column for our flow conditions. For an open column, we used a heat transfer coefficient of 9 J/(s m2 K) at 50 std L/min. The correlation of Seider and Tate (Holman, 1981) was used to calculate the heat transfer coefficient for 3/8 in. i.d. tubing between the product exit and purge inlet for a flow rate of 50 std L/m. The heat transfer coefficients were incorporated into the model using a Re0.8 dependence. The measured heat capacity of the empty bed, cpw, was also determined experimentally by the method of Friday and LeVan (1985) and agrees well with values reported for steel. Literature values for the heat capacities of BPL and glass were used. All parameters are given in Table 1. Results and Discussion Adsorption Equilibria. Adsorption equilibria were measured in our laboratory for nitrogen and oxygen on BPL activated carbon at several temperatures and for pressures up to 0.8 MPa using a volumetric technique. Measured isotherm data on BPL carbon is shown in Figure 3. Pure component isotherms for oxygen and nitrogen are nearly identical, in the low paritial pressure region corresponding to an oxygen mole fraction of 0.21. Thus the assumption was made that air adsorption on BPL carbon could be modeled as nitrogen. Virial fit parameters for the nitrogen data are presented in Table 1. Experiments. Conditions for experiments were chosen to elucidate the nature of the nonisothermal behavior and characterize the temperature effects that occur at periodic state conditions. Seven experiments were performed using weakly adsorbing air or essentially nonadsorbing helium. The in-bed thermocouples were used to measure the temperature behavior transients. Below, experimental results are compared to simulations in order to predict observed behavior. Additional simulation work is used to quantify the controlling mechanisms for heat transfer.

Table 3. Experimentsa run

bed

feed

feed flow (std L/m)

product flow (std L/m)

A B C D E F G

BPL BPL glass beads empty BPL/insulated BPL BPL

dry air helium dry air dry air dry air dry air dry air

98 98 80 80 98 98 98

49 49 40 40 49 88 10

a P feed ) 0.405 MPa, Pfeed/Ppurge ) 4.0, Tfeed ) 25 °C, cycle time ) 30 s.

Table 3 lists the conditions for each of the seven experiments. The base case conditions are a 30 s cycle, a feed superficial velocity of 0.35 m/s, a volumetric purge-to-feed ratio of 2.0, feed pressure of 0.406 MPa, and pressure ratio (feed to purge) of 4.0. All other runs yield a parametric study in which the effect on temperature profiles is evaluated. Pressure profiles measured under all conditions indicate that pressurization and blowdown are fast, requiring a time of less than 1 s for a 95% response at all points in the bed. The rapid pressurization is enhanced by the presence of a large feed ballast tank. The flow rates result in large superficial velocities of approximately 30 cm/s during this part of the feed step. The transient temperature behavior for the approach to periodic state is not considered here. The periodic state is considered to be approached rapidly relative to the time the PSA system would be on stream for air purification. Experimental results indicate that a periodic state is achieved after approximately 50 cycles. Results shown below were measured after more than 200 complete cycles. The base case (run A) was conducted with a feed of dry air to a bed of BPL activated carbon. The recorded temperature profiles at the periodic state are shown in Figure 4. Temperature is plotted versus time for four half cycles with time zero corresponding to the beginning of cycle number 240. Several features of these measured profiles should be noted. The feed thermocouple records the temperature upstream of the bed on the feed step and downstream on the purge step. Similarly, the product thermocouple records the end cap temperature for the column outlet on the feed step and the column inlet on the purge step. The temperatures of the in-bed thermocouples at 5, 10, 15, and 20 cm


Figure 4. Run A: base case. Temperatures at several points in the column are shown as functions of time for two complete cycles (feed followed by counter current purge) at the periodic state. Labels correspond to the feed step. For the purge step, the points labeled feed give the purge product, and points labled product give the purge feed.

Figure 5. Measured in-bed periodic state temperature profile run B. Helium feed to a bed packed with BPL.

appear to respond at the same time on both feed and purge steps and reach steady plateau values. This suggests that heating and cooling are occurring at the periodic state in a batchlike mode, i.e., with little wavelike character. No distinct temperature front can be observed for this cycle. There is only a slight gradient in plateau temperatures, approximately 3 °C, for the in-bed thermocouples. The temperature at 20 cm is highest and at 5 cm lowest at the periodic state for both the feed and purge steps. Important to our study is that the measured temperatures for all of the in-bed thermocouples at the periodic state swing below ambient temperature on both purge and feed steps. The same is true of the feed end cap. The product end cap temperature never falls below ambient temperature indicating that, at some point between the 20 cm thermocouple and the product end, heat is released. The maximum temperature difference between the feed and

purge steps for each in-bed position is approximately 10 °C. In run B, helium was used as the feed gas with packed beds of BPL activated carbon to determine the importance of energy effects associated with adsorption and desorption during pressurization and blowdown. This is the first of several PSA runs conducted to determine the basis for the temperature swings that were observed in run A. As indicated previously, the adsorption capacity of helium on BPL is assumed to be negligible. As shown in Figure 5, the temperature measured in the feed and product end caps for run B exhibit short swings of 1 and 5 °C from ambient on the feed and purge steps, respectively. The in-bed thermocouples provide plateau temperatures 1 °C above ambient on the feed and 0.5 °C above ambient on the purge step. These smaller temperature swings result despite the fact that the molar heat capacity of helium is one-third that of air.

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Figure 6. Measured in-bed periodic state temperature profile run C. Air feed to a bed packed with glass beads.

Figure 7. Measured in-bed periodic state temperature profile run D. Air feed to an empty bed.

Runs C and D were performed to investigate the importance of pressurization and depressurization effects for the bulk gas (Joule-Thomson effect). In run C, dry air was fed to a bed packed with nonporous, nonadsorbing glass beads. The profiles, shown in Figure 6, are similar to those for run B. Small temperature swings were recorded in the feed and product end caps. No temperature swings were recorded with the in-bed thermocouples. The overall heat capacity of the glass beads is more than twice that of activated carbon, suggesting that the presence of any packing would reduce the magnitude of the temperature swings. To investigate the influence of the heat capacity associated with any packing, run D was performed under the same conditions as run A, except that it used empty beds. Figure 7 indicates that under these conditions large temperature swings of 30 °C are observed which quickly dissipate back to ambient temperature. The in-bed thermocouples again seem to respond in a batchlike manner. However, no plateau temperatures are ob-

tained and no net subcooling is observed. This suggests that indeed there are energy effects associated with pressurization and blowdown but the impact on packings with moderate heat capacity is small. Runs A-D indicate that adsorption and desorption of air on activated carbon must provide the most important energy contribution to the observed temperature swings observed in run A. The energy of the steps is being stored either in the heat capacity of the column or the adsorbent, if not in both. Three additional experiments were performed to further identify the cause of the observed subcooling. In run E, the bed was wrapped with insulation to mitigate the effects of any heat losses from the system. The results, shown in Figure 8, indicate that the magnitude of the temperature cycling is the same as for run A. Heat losses from the column are not an important factor contributing to the observed subcooling. Runs F and G investigated the effect of the volumetric purge-to-feed ratio. In run F, a smaller fraction of the


Figure 8. Measured in-bed periodic state temperature profile run E. Air feed to an insulated bed packed with BPL.

Figure 9. Measured in-bed periodic state temperature profile run F. Air feed to a bed packed with BPL, low-purge case.

product was used as purge compared to that of run A. The temperature profiles, given in Figure 9, show that the plateau temperature on the feed step rises slightly above ambient temperature. The temperature in the bed on the purge step is still depressed for the purge step at this low purge rate. Similarly, run G was conducted with a high-purge flow rate. The results, shown in Figure 10, indicate a temperature gradient in the bed that is larger than that for run A. The plateau temperatures in the bed rise significantly above ambient temperature on the feed step. The cooling effect appears for only the thermocouples at the feed end of the bed, i.e., for the feed end cap and at 5 cm. Clearly, the amount of purge is critical to the cooling effect. Further description of the dynamics of runs A, F, and G is possible by use of numerical simulation. Simulation Results. A numerical simulation was conducted for run A using eqs 1-13 and parameters from Table 1. Temperature profiles are presented in Figure 11. Again, the plot presents temperatures at

fixed locations in the same bed during two complete cycles. Most important is that the temperature of the air leaving the bed is above the feed temperature during the feed step and below the feed temperature during the purge step, thus satisfying an overall energy balance for a complete cycle. The average rise of the product temperature above ambient temperature is roughly half of the temperature drop at the purge exit, in inverse proportion to the molar flow rates for the two steps. The temperature profiles for the simulation match the measured data reasonably well, predicting all trends qualitatively and the extent of subcooling quantitatively. The temperature boundary condition for inlet to the purge bed was examined for two cases. A reasonable simulation could only be achieved using the ambient temperature as feed to the purge column. Using the product temperature resulted in larger temperature swings than observed for the high-purge case. It was less significant for the low and moderate purge cases. This boundary condtion is consistent with the observed

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Figure 10. Measured in-bed periodic state temperature profile (symbols alone) and simulation results (lines through symbols) for run G. Air feed to a bed packed with BPL, high-purge case.

Figure 11. Simulation of in-bed periodic state temperature profiles for run A. Air feed to a bed packed with BPL, moderate purge case.

temperature swings in the product end cap and with the presence of a long length (0.2 m) of uninsulated tubing connecting the beds. The loading profiles at the end of the half-cycles, which are not shown, are predicted by the model to be essentially flat, with the loadings corresponding to the bed pressure and temperature. The rapid pressure change associated with flow switching results in a loading and temperature change at all points in the bed. The net movement of the temperature front is small during the duration of each half-cycle. If only pressure changes occurred with no feed or purge flow, then all points in the bed would exhibit above ambient temperature on the pressurization step and below ambient temperature on the purge step; no distinct front would exist. The major influence on the front movement results from the convection of energy into the bed by the feed or purge flow. The location of the temperature

front at the end of the half-cycle is apparent in the model. It is centered between 20 and 24 cm for both feed and purge steps. This location is not obvious for the data because of the absence of a thermocouple in the last few centimeters of the bed. Simulations were conducted for three cases: adiabatic conditions, purge inlet temperature equal to product exit temperature, and purge inlet temperature equal to ambient temperature. For each case, the results are nearly identical and in good agreement with the data. Note that the magnitude of the temperature drop on the purge step for the model and the data is approximately 8 °C. The high molar flow rate on the feed step carries the heat generated by adsorption down the column and returns the bed temperature to the feed temperature. Only a fraction of the product is used for purge, however, and this has the effect of not pushing the temperature wave completely back to the feed end


of the bed. The temperature front is in the region of the bed where the temperature swings above ambient temperature on the feed step and below ambient temperature on the purge step. This temperature cycling or rectifying effect is apparent from these results. This effect is also characteristic of movement of the mass transfer front in PSA separation. If the bed length is long enough to contain the front, then after a large number of cycles the temperature front is contained within a fixed region. As the cycle time is decreased, the movement of this front is reduced. For longer cycles, the temperature front can be pushed out of the bed on each half-cycle. It is possible to estimate the magnitude of the temperature depression observed on the purge step. Given that the high molar flow rate of the feed step restores the bed to roughly the feed temperature, the temperature depression should result from desorption as the bed changes from high to low pressure. This can be expressed by the simplistic energy balance, obtained approximately from eq 3 with ∆us ) 0,

cps∆Ts ) λ∆q

(14)

The magnitude of the change is approximately 8 °C for a pressure ratio of 4 (corresponding to qfeed ) 0.41 mol/ kg, qpurge ) 0.20 mol/kg, and λ ) 39 kJ/mol) and adsorbent heat capacity in Table 1. This is close to that observed experimentally. Two cases for simultaneous contaminant filtration can also be considered. A weakly adsorbed vapor with a nearly linear isotherm that is more strongly adsorbed than nitrogen could lead to similar temperature swings than described here for the carrier gas. For example one can use the isotherm data for refrigerant 22 on BPL reported by Mahle et al. (1994) with a feed of 1000 ppm and inlet and purge pressures of 0.4 and 0.1 MPa to calculate a temperature depression which for this condition is 12 °C. However as the loading goes up it is less likely that the isotherm will remain linear, and at this low concentration it would not be possible to deliver the mass required to achieve these loadings each half-cycle. If the feed is a strongly adsorbed low-concentration contaminant it would behave differently than the cases presented in this work. The loading on the adsorbent would not change with a change in the pressure ratio. Desorption would be unfavorable so that the temperature swing would be less than that for the carrier gas, and subcooling would be less pronounced. The major effect of a strongly adsorbed vapor would be to reduce the capacity for adsorption of the carrier. However in regions ahead of the contaminant wave the subcooling would still occur, and contaminant desorption would still occur at subambient temperatures. This indicates that the importance of the carrier adsorption can apply to both weakly and strongly adsorbed contaminants. The location of the temperature front can also be predicted using some simple rules. If it is assumed that the carrrier adsorbs and desorbs in a batch manner, then the location of the transition should correspond to the ratio of mass flow rates for the feed and purge steps provided the cycle time and bed depth combination is large enough to contain the inlet transition. The velocity of the temperature transition on any individual half-cycle can be calculated as follows:

m ˘ Cf ) WπRc2FbCs

(15)

The speed of the temperture wave associated with convection into the bed, W, can be calculated for the feed

step of the cases discussed in the study, because each case has the same feed flowrate, 98 slpm. The feed transition speed is 0.4 cm/s, or for a 24 cm bed depth the wave would take approximately 60 s to saturate the bed. Because this is longer than the half-cycle time of 15 s, the temperature transition is not pushed out of the bed. On the purge step we can examine the effect of the three cases of low, moderate, and high-purge flow. In the high-purge case 90% of the product flow is used as purge. However because of losses the feed temperature to the purge column is the ambient temperature. In this limit the net energy into the bed by convection for the purge step and feed step are nearly equal. This suggests a placement of the temperature transition in the center of the bed and this is just what is observed in run G. The effective bed depth for these calculations should be 29 cm, i.e. 24 cm of carbon and 5 cm of glass beads. That is to say, the 15 cm probe cycles above and below ambient temperature. Similar reasoning for the moderate purge case would place the temperature transition at 21.5 cm or beyond the 20 cm probe. This is consistent with run A. If the glass beads were not present, the transition would occur closer to 18 cm. This difference is apparent in the model as the 20 cm port shows a slightly higher average temperature than the 15 cm probe. The transition point for run F is beyond the 20 cm port as well. A simulation of run F is presented in Figure 12. Again good agreement is obtained between the data and the model. The slow approach to the final purge temperature for the in-bed thermocouples is not described correctly by the model. This might result from reduced thermocouple response time at this low-purge flow. The behavior of run G, the case with a high-purge rate, could not be described as easily as runs A and F. Simulation assuming negligible energy loss always resulted in larger temperature swings at the product end of the bed than measured. Also, assuming energy losses to ambient temperature in tubing between the product and purge beds gave insufficient temperature swings. Heat transfer to the packed column and empty end caps was implemented using the parameters in Table 1. In both cases, it was not possible to match the temperature at the 20 cm thermocouple if the purge feed was at ambient temperature. The data for run G, shown in Figure 10, indicate that the 20 cm thermocouple temperature is higher than the end cap temperature on the purge step. We note also in Figure 9 that the purge inlet temperature at the end cap is less than the product exit temperature at the end cap. Thus, energy losses associated with the tubing between product exit and purge inlet of the beds must be incorporated in the analysis. This suggested the appropriate boundry condition for purge inlet tempeture. The simulation was performed with the model adding end cap heat capacities and tubing heat loss. The profiles are shown together with the data on Figure 10. Excellent agreement is found between experiment and model for all in-bed ports. At this high-purge rate, the temperature front is located close to the front of the bed. For both the 10 and 15 cm ports, the temperature cycles above the feed temperature on the feed step and below the feed temperature on the purge step. The magnitude of the temperature swing at the 5 cm thermocouple is less than 10 °C for both the data and the model. This is consistent with the predicted location of the temperature front.

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Figure 12. Simulation of in-bed periodic state temperature profiles for run F. Air feed to a bed packed with BPL, low-purge case.

Figure 13. Simulation of in-bed periodic state axial temperature profiles for run A at several times during the cycle.

Figure 14. Simulation of in-bed periodic state of axial temperature profiles for run G at several times during the cycle.

The location and movement of the temperature front can also be visualized by plotting the in-bed temperature versus axial position. Figure 13 and 14 present such plots using the periodic state profile simulations for runs

A and G. The batch type character of the temperature response leads to axial temperature profiles of similar shape throughout the cycle. At the front of the bed the profiles are nearly identical, while movement of the


temperature front beyond 20 cm for run A (Figure 13) and beyond 10 cm for run G (Figure 14) leads to slight differences in the shape of the axial profiles over the course of the cycle. This movement is evident by comparing the profiles from 7.5 to 15 s on the feed step and from 22.5 to 30 s on the purge step. The change in shape of the profiles during the feed and purge steps is related by the requirement that the net change in enthalpy of the bed is zero. The region where this change in shape occurs corresponds to the temperature transition regime. The transition is clearly centered more to the middle of the bed for run G (Figure 14). The temperature profiles beyond 20 cm are again of similar shape; however, the profiles cross and change shape between 10 and 20 cm. This paper has considered only the bed response to a feed consisting of weakly adsorbed (or nonadsorbed) carrier gas. If a more strongly adsorbed component is present in the feed, then in the region where that component is adsorbed appreciably, less carrier gas can be expected to adsorb and the temperature cycling produced in that region would be expected to be less pronounced. In addition, the observed behavior should provide larger temperature swings for larger diameter beds because the ratio of column wall thermal capacity to adsorbent thermal capacity is likely to be less. This adiabatic condition was simulated using the feed and purge flowrate conditions of runs A, G, and F. In each case the temperature profiles were slightly greater in magnitude than the case with wall losses, because once steady state is established the wall in the simulation is not considered to have any losses to the environment. The absence of the heat sink, end caps at the ends of the bed reduces the magnitude of the swing but the placement of the transition is only slightly changed, or the same region of the bed is subcooled. If the adiabatic condition is applied to the product temperature so that the product temperature is used as feed to the purge bed, large temperature swings of the magnitude mentioned earlier by Yang (1987) are predicted. Such adiabatic conditions are reasonable in larger system. Clearly larger pressure ratios can also contribute to increased temperature cycling. The simple expressions presented here can be used to estimate the magnitude of these effects for other system. The importance of these carrier-gas-induced temperature effects for contaminat removal can be significant. As shown in the analysis above there are many practical PSA applications which would lead to temperature depressions for a large fraction of the bed, i.e. low to moderate purge rate, near ambient feed temperatures, and a bed depth greater than the temperature front velocity-half-cycle time product. In such cases the low temperatures of the purge step reduce the desorption of the contaminat and reduce the separation relative to an isothermal operation. Further discussion and examples of this behavior are examined the second part of this study. Conclusions We have measured in-bed temperature profiles to describe nonisothermal effects of PSA accurately. We have focused on a weakly adsorbed carried gas to determine whether or not it can play a significant role in nonisothermal behavior, especially for short cycles. We varied the operating characteristics of a two-bed system and compared experimental results with predictions of a mathematical model.

The adsorption and desorption of air on activated carbon in a PSA system create significant temperature profiles in the bed. These exceed temperature changes caused by compression and expansion (Joule-Thomson effect). The product side of the temperature front exhibits temperature swings to above the feed temperature while the feed side of the front exhibits significant swings to below the feed temperature. The magnitude of the subcooling depends greatly on the volumetric purge-to-feed ratio and on the presence of end caps to store energy over half-cycles. The subcooled temperature profile is caused by two factors. First, adsorption or desorption of the carrier gas occurs over the bed as a whole as the bed is pressurized or depressurized. This leads to uniform temperature cycling but, in itself, gives no net subcooling or wave character in the bed. Second, the imbalance of molar flow rates, with higher rates for the feed step than for the purge step, drives the bed temperature toward the feed temperature. Energy stored in the packing, the bed walls, and particularly the end regions facilitates this process. This gives wave character to the bed profiles, with the temperature being close to the feed temperature over most of the bed during the feed step and subcooling in this region during the purge step. The extent of temperature cycling caused by a weakly adsorbed carrier gas can be significant. In our experiments, we found subcooling of about 10 °C below the feed temperature. For a PSA-based purification process involving removal of a trace contaminant, this magnitude of temperature variation can easily exceed that caused by adsorption of the contaminant. Nomenclature b1 ) parameter in eq 11 c ) fluid phase concentration, mol/m3 cpf ) heat capacity of fluid phase, J/(mol K) cpg, cps, cpw ) heat capacity of glass, stationary phase, and wall, J/(kg K) Cv ) valve flow coefficient, eq 10 Deff ) effective diffusion coefficient, m2/s hf ) enthalpy of fluid phase, J/mol k0, k1 ) parameters in eq 11 kq ) rate coefficient in eq 8, s-1 L ) bed length, m m ˘ ) molar flowrate, mol/s mw ) local column wall mass per unit heat transfer area, kg/m2 P ) pressure, Pa q ) adsorbed phase concentration, mol/kg Q ) volumetric flow rate at STP, m3/s R ) gas constant, 8.314 Pa m3/(mol K) Rc ) inside column radius, m Rp ) particle radius, m t ) time, s T ) temperature, K uf ) internal energy of fluid phase, J/mol us, uw ) internal energy of stationary phase and wall, J/kg U ) heat transfer coefficient, J/(s m2 K) v ) superficial velocity, m/s V ) volume appearing in eq 13, m3 W ) speed of temperature transition in eq 15, m/s z ) axial coordinate, m Greek Letters R ) particle void fraction ′ ) total bed voidage (intraparticle and interparticle) λ ) isosteric heat of desorption, J/mol Fb ) bulk density of packing, kg/m3

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τ ) dimensionless time, eq 12 τ′ ) particle tortuosity ψ ) parameter in eq 9 ζ ) dimensionless axial coordinate, eq 13 Subscripts f ) fluid phase ref ) reference s ) stationary phase w ) wall

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Lu, Z. P.; Loureiro, J. M.; Rodrigues, A. E.; LeVan, M. D. Simulation of a Three-Step One-Column Pressure Swing Adsorption Process. AIChE J. 1993, 39, 1483-1496. Mahle, J. J.; Buettner, L. C.; Friday, D. K. Measurement and Correlation of the Adsorption Equilibria of Refrigerant Vapors on Activated Carbon. Ind. Eng. Chem. Res. 1994, 33, 346-354. Matz, M. J.; Knaebel, K. S. Temperature Front Sensing for Feed Step Control in Pressure Swing Adsorption. Ind. Eng. Chem. Res. 1987, 26, 1638-1645. Mutasim, Z. Z.; Bowen, J. H. Multicomponent Pressure Swing Adsorption for Non-Isothermal, Non Equilibrium Conditions. Chem. Eng. Res. Des. 1992, 70, 346-353. Nakao, S.; Suzuki, M. Mass Transfer Coefficient in Cyclic Adsorption and Desorption. J. Chem. Eng. Jpn. 1983, 16, 114-119. Ritter, J. A.; Yang, R. T. Pressure Swing Adsorption: Experimental and Theoretical Study on Air Purification and Vapor Recovery. Ind. Eng. Chem. Res. 1991, 30, 1023-1032. Sladek, K. J.; Gilliland, E. R.; Baddour, R. F. Diffusion on Surfaces. II. Correlation of Diffusivities of Physically and Chemically Adsorbed Species. Ind. Eng. Chem. Fundam. 1974, 13, 100105. Yagi, S.; Wakao, N. Heat and Mass Transfer from Wall to Fluid in Packed Beds. AIChE J. 1959, 5, 79-85. Yang, R. T. Gas Separation by Adsorption Processes; Butterworths: Boston, 1987. Yang, R. T.; Doong, S. J. Gas Separation by Pressure Swing Adsorption: A Pore-Diffusion Model for Bulk Separation. AIChE J. 1985, 31, 1829-1842. Yang, R. T.; Cen, P. L. Improved Pressure Swing Adsorption Processes for Gas Separation: By Heat Exchange between Adsorbers and by High-Heat-Capacity Inert Additives. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 54-59.

Received for review July 28, 1995 Revised manuscript received April 10, 1996 Accepted April 11, 1996X IE950475C

X Abstract published in Advance ACS Abstracts, June 1, 1996.

Pressure Swing Adsorption for Air Purification. 1. Temperature

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