Repressurization of adsorption purifiers for cryogenic air separation

Chemical Engimxring Science. Vol. 48, No. 4, pp. 753-760.1993. Pristed in Great Britain

@JO!-2509/93 95.00 + CL00 0 1992 Pqamon Press Ltd

REPRESSURIZATION OF ADSORPTION PURIFIERS FOR CRYOGENIC AIR SEPARATION

GREGORY R. SCHOOFS+ Department of Chemical Engineering and Applied Chemistry, Columbia University, New York, NY 10027,

U.S.A.

and

P. PETIT L’Air Liquide, 57, Avenue Carnot, Boite Postale No. 13, 94503 Champigny-Sur-Marne Cedex, France

(First received 6 June 1991; accepted in revised form 2 June 1992)

Abstract-The repressurization and adsorption steps of a molecular sieve adsorption purifier upstream of a cryogenic air separation unit was analyzed with a one-dimensional equilibrium-stage model. Numerical solution of the differential mass and energy balances predicts that the ef3uent gas composition is briefly depleted in nitrogen and the effluent gas temperature undergoes a brief excursion due to preferential nitrogen adsorption on the freshly regenerated 13X molecular sieve. Temperature breakthrough data from an industrial adsorber confirm the theoretical predictions. The results of this analysis demonstrate that the temperature excursion can be used to monitor the performance of the adsorber. The magnitude of the temperature rise can be used to ascertain the amount of presorbed water on, or the extent of degradation of, the 13X molecular sieve and, hence, the subsequent capacity for carbon dioxide adsorption. Disparities in the temnerature excursion nrofile at various locations at the outlet of the 13X molecular sieve bed can be . used to detect flow maldi&ibution problems.

INTRODUCTION

The separation of nitrogen and oxygen from air com- prises one of the most important chemical processes. In 1990, approximately 57 billion pounds of nitrogen and 39 billion pounds of oxygen were produced in U.S.A. (Reisch, 1991). Nitrogen and oxygen rank second and third highest, respectively, in domestic chemical production on a weight basis. Cryogenic distillation, combustion of natural gas or propane with air, pressure swing adsorption (PSA), and per- meable membrane processes have been implemented

accomplish this separation commercially &hroeder, 1981; Taylor, 1981; Kan, 1988). Cryogenic distillation is the economic choice for the large-scale production of high-purity products, and it is the most extensively used of the four methods.

The feed to a cryogenic air separation plant must be free of carbon dioxide and water, and a variety of front end purification strategies have been devised for this task. L’Air Liquide has developed a particularly efficient front end purification system where the im- purities are removed in radial-flow adsorbers consist- ing of concentric, annular beds of activated alumina and 13X molecular sieve (Grenier et al., 1984). These adsorbers operate in a cycle which consists of the following steps: adsorb, depressurize, thermally regen- erate, cool, and repressurize. Two adsorbers are used. While one adsorber is onstream adsorbing water and carbon dioxide from the feed air to the cryogenic unit,

‘Present address: Schoofs Incorporated, 1675 School Street, PO Box 67, Moraga, CA 94556, U.S.A.

the other adsorber is being reactivated by sequencing through the other four steps. A transient temperature excursion in which the &uent temperature typically rises 10-15 K above the feed temperature is observed at the beginning of each adsorption step. Heretofore, this transient temperature excursion has been at-

tributed to an inadequate cooling step or to residual water and carbon dioxide adsorption.

In this paper we analyze the repressurization and adsorption steps of adsorbers used for front end purification of cryogenic air separation processes. Nitro- gen adsorption on the 13X molecular sieve during the repressurization and adsorption steps produces the l&l5 K effluent temperature excursion observed at the start of each adsorption step. Rather than indicat- ing an inadequate cooling step, the temperature excursion results from the exothermic heat of adsorption of nitrogen. The magnitude of the temperature excursion can lx used to evaluate the condition of the 13X molecular sieve and its capacity for carbon dioxide adsorption. Additionally, variations in the rate of the temperature rise and recovery among several thermocouples could be used to identify flow maldistribution problems.

Preferential nitrogen adsorption in 5A molecular sieve has been recognized previously and exploited in pressure swing adsorption processes designed to separate oxygen from air (Ruthven, 1984; Yang, 1987). This paper shows that preferential nitrogen adsorption in 13X molecular sieve also occurs in thermally regenerated adsorbers designed to purify, not separate, air. While preferential nitrogen adsorption leads to the desired separation of oxygen and nitrogen from

753

754 GREGORY R. SCHOOFS and P. PETIT

air in PSA processes, nitrogen sorption is an un- intended and previously unrecognized effect in thermally regenerated, molecular-sieve-based purification processes.

THEORY

Mathematical model A one-dimensional equilibrium model was em-

ployed to quantify the behavior of adsorbers used to purify the feed to cryogenic air separation processes. The assumptions include the following:

(1) The adsorbers are designed for radial flow, and the model can be written in one-dimensional cylin- drical coordinates (r only).

(2) The adsorbent bed is thin and located far from the vessel centerline [i.e. (rl - r2)/r2 Q 11, so that the curvature terms in the mass and energy balances can be neglected.

(3) The adsorbers operate adiabatically. Large industrial adsorber vessels are usually well-insulated, and adiabatic operation is closely approached.

(4) The feed gas is considered to be a binary mix- ture of nitrogen (79 mol%) and oxygen (21 mol%). Other trace components are neglected.

(5) The gas phase behaves ideally. At the highest pressure and lowest temperature considered herein, the compressibility factor of air is approximately 0.994. This value was calculated using the correlation of Lee and Kesler (1975), and is very close to 1.0 which describes an ideal gas.

(6) The gas phase moves via plug flow during the repressurization and adsorption steps. Axial dispersion is formally neglected in the sense that the mathematical model contains no second-order derivatives.

(7) Equilibrium exists between the gas and adsorbed phases at all points within the adsorber. Nitro- gen diffuses very rapidly through the pores of 13X molecular sieve (Ruthvan, 1984), which eliminates the need to include intraparticle mass transfer in the model. The time constant for thermal diffusion through the adsorbent particle is roughly 5 s, which is much less than the time needed to repressurize the adsorber. Interparticle transport resistances are ap- proximated by treating the mass and energy balance equations as an equilibrium-stage model, as discussed below.

(8) The pressure drop in the direction of flow is negligible. The results which follow pertain to adsorbers which have been designed specifically to min- imize pressure drop. The criteria developed by Sundaram and Wankat (1988) indicate that the pressure drop can be neglected during the repressurization step. The pressure drop during the adsorption step can also be neglected because it is much smaller than the inlet pressure.

The mass balance for each component may be written as

(1)

where

and

ci = yiPIRT (2)

aqr aqi 8T aqi ayi -=gg+,,+_-. at ayi at (3)

Neglecting the curvature terms, the component mass balances may be summed to yield the total mass balance

& ap & aT P a&J RTat-RTZat+RTF

The energy balance may be written as

aha a(Chf) ~ ia(:ruoChf) Pbdt+s dt r dr =

0 (5)

where

ha z C, + 5 c..jqj (T- K;cf)- i “i,de (6) ( j=1 > S’ j=1 0

h, = CAT- T,,f) (7)

and

C = P/RT. (8)

Additionally, the energy balance should include Joule heating during the repressurization step, a ther- modynamic phenomenon ignored in previous ana- lyses of adsorption processes. The case of repressuriz- ing an empty vessel by increasing the moles of gas in the vessel while keeping the vessel volume constant has been described elsewhere (Dodge, 1944). We have extended this analysis by assuming that the vessel contains adsorbent and allowing for heat exchange between the gas and the adsorbent. If the feed gas and the adsorbent are at the same temperature initially (T,), the increase in temperature with pressure throughout the adsorber due to Joule heating is given

by

aT bP-22ac-Pdm -= ap 2aP JF=&G

(9)

where

a = PbG(k - l)! K (10)

b = P + P,(k - 1) - aT, (11)

c= - PkT,. (12)

Table 1 lists the boundary and initial conditions which accompany the heat and mass balances for the repressurization and adsorption steps. The adsorber was set to a uniform temperature and composition at the start of the repressurization step. Virtually dry air enters the 13X molecular sieve bed during both the repressurization and adsorption steps.

Repressurization of adsorption purifiers 755

Table 1. Boundary and initial ccmditionst .

Process variable Boundary condition for

repressurization step Boundary condition for adsorption step

0.0 s- 1 Space velocity, a constant

YN*(t = 0, r) Nearly 1 Composition at the end of the repressurization step

YN*(t.r = r1) 0.79 0.79 W, r) P(t) given by the repressurization rate Pressure at the end of the repressurization

and initial pressure step, a constant ?-(t = 0, r) 280-295 K (specified) Temperature at the end of the repressurization

step T(t,r=Q) 28&295 K (specified) 280-295 K (specified)

‘Some process conditions are proprietary and cannot be divulged. It should be apparent, however, that specifying the process variables listed in the left column will permit the differential mass and energy balances to be solved numerically.

Nitrogen and oxygen adsorption in 13X molecular sieve The physical properties of 13X molecular sieve were

obtained from data sheets furnished by the Davison Chemical Division of W. R. Grace & Co. (1986). Nitrogen and oxygen adsorption equilibria in 13X molecular sieve have been measured previously in the appropriate temperature and pressure ranges (Miller, 1987). The multicomponent Langmuir isotherm

aiyi P 4i =

a + 2 b,YjP

(13)

j= 1

with parameters obtained from the pure-component data provides good predictions of the mixed-gas adsorption data. Isosteric enthalpies of adsorption of nitrogen and oxygen in 13X molecular sieve were obtained by applying the Clausius-Claperyon equa- tion to the pure-component data.

In a series of careful experiments, Peterson (1981) showed that l-5 wt% of presorbed water greatly reduces the extent of nitrogen adsorption in 13X molecular sieve. This is a small amount of adsorbed water; 13X molecular sieve holds 29.5 wt% water at saturation (Davison Chemical Division of W. R. Grace dz Co., 1986). Apparently, water adsorbs preferentially on sites near the entrances to the molecular sieve cavities, which hinders or prohibits nitrogen molecules from reaching adsorption sites within the molecular sieve cavities (Barrer, 1978; Peterson, 1981). The data of Miller (1987) were obtained using fresh 13X molecular sieve with no presorbed water, based on a comparison between these data and their corresponding adsorption isotherms with the data of Peterson (1981).

The heat capacities of nitrogen and oxygen adsorbed in 13X (Na-X) molecular sieve have not yet been measured. The heat capacities of linear diatomic molecules adsorbed in type X molecular sieve should each be approximately SR, corresponding to an adsorbed state with five vibrational modes (Barrer, 1978). The data of Barrer and Stuart (1959) indicate that the heat capacity of nitrogen adsorbed in K-X

molecular sieve approaches 5R as the temperature increases to 219 K and the amount of adsorbed nitrogen increases to 1.38 mol Nz per kg K-X molecular sieve. Pending more germane data we used 5R as the heat capacity of both adsorbed nitrogen and adsorbed oxygen in type 13X molecular sieve.

Algorithm The numerical integration of eqs (1))(13) employed

backward finite differences in space and a fourth- order Runge+Kutta algorithm over time (Camahan et al., 1969). All terms in these equations except for the curvature terms were retained. Fifty equilibrium stages were used in the simulation. This first-order backward difference discretization is equivalent to considering the bed as a series of well-mixed, stirred tanks, and the approximate numerical solution obtained in this fashion is mathematically similar to incorporating the expected external mass transfer resistances and dispersion into the model (Wen and Fan, 1975).

The equilibrium model described here should provide an upper bound to the nitrogen and oxygen adsorption phenomena. The model does not explicitly include a variety of factors which may diminish the predicted extent of nitrogen and oxygen adsorption, including mass and heat transfer resistances, deviations from plug flow such as fluid channeling, and sorption of species other than nitrogen and oxygen in the 13X molecular sieve.

EXPERIMENTAL

Data were collected from a commercial adsorber used to purify the feed to a modem, low-pressure, cryogenic air separation plant. Figure 1 shows a schematic diagram of the radial-flow, double-bed adsorber. Wet air flows radially inward through two concentric annular beds during the repressurization and adsorption steps. The outer bed contains activated alumina to remove nearly all of the water vapor; the inner bed contains 13X molecular sieve to remove carbon dioxide. Grids confine the two ad-

756 GREGORY R. SCHOOFS and P. PETIT

sorbents in separate, adjacent beds. Thermocouples are attached to all three grids, thereby permitting direct measurement of the inlet and outlet temperatures of each bed. The 13X molecular sieve bed is thin and located far from the vessel centerline [i.e. (*1 - r2)/r2 - 0.11, so the curvature terms in the mass and energy balances can be neglected. Hence, the model described in the previous section applies to the 13X molecular sieve bed in this radial-flow adsorber.

This adsorber is uniquely well-suited to unambigu- ously identify the effects of nitrogen and oxygen adsorption in 13X molecular sieve. First, negligible

DRY COaFREE AIR

WET AIR

Fig. 1. Schematic diagram of the double-bed, radial-flow adsorber from which the data were acquired. Wet air flows radially inward through two concentric annular beds during the adsorption step. The outer bed contains activated alumina to remove essentially all of the water vapor; the inner bed contains 13X molecular sieve to remove carbon dioxide. Grids confine the two adsorbents in separate,

adjacent beds.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 DIMENSIONLESS POSlTlON

amounts of oxygen and nitrogen adsorb on activated alumina at the process conditions (Maslan et al., 1953). Second, effects resulting from the competitive adsorption of water vapor and carbon dioxide in the 13X molecular sieve are minimized. Only trace amounts of water vapor reach the 13X molecular sieve because the activated alumina bed drys the air to moisture contents below 1 ppm (Newsome et al., 1960; Yang, 1987). The strong influences of water sorption on nitrogen adsorption in 13X molecular sieve (Peterson, 1981) will be minimized because of the very low water concentration. Third, the temperature rise measured across the 13X molecular sieve bed should result nearly entirely from nitrogen and oxygen adsorption, with a minimum of accompanying uncer- tainties. Heat losses to vessel walls, support balls, filters, and entrance and exit pipes are avoided because the thermocouples are attached to the grids which bound the 13X molecular sieve bed. Further, the temperature rise due to water adsorption in the 13X molecular sieve should be less than 0.003 K, based on an energy balance across the mass transfer zone (White, 1988). Carbon dioxide from ambient air will also adsorb in the 13X molecular sieve, but the resulting temperature rise does not exceed 0.5 K.

One would also like to measure the effluent composition during the adsorption step. Unfortunately, neither ports nor instruments were available to make such measurements.

RESULTS AND DISCUSSION

The adsorber contains nearly pure nitrogen at approximately atmospheric pressure prior to the start of the repressurization step. It is repressurized with air. Figure 2 shows the predicted gas-phase composition profile through the 13X molecular sieve bed after the adsorber is repressurized. The dimensionless position of 0.0 corresponds to the grid at the activated alumina-13X boundary, which is the inlet to the 13X

Fig. 2. Predicted composition profile through the 13X molecular sieve bed at the end of the repressurization step. The dimensionless position of 0.0 corresponds to the grid at the activated alumina-13X boundary which is the inlet to the 13X molecular sieve bed. The dimensionless position of 1.0 corresponds

to the grid at the effluent end of the 13X molecular sieve bed.


molecular sieve bed. The dimensionless position of 1.0 corresponds to the grid at the effluent end of the 13X molecular sieve bed. The gas-phase composition of 79 mol% nitrogen at the dimensionless position of 0.0 indicates that dry air entered the 13X molecular sieve bed at the end of the repressurizatian step. The effluent composition equals 87 mol% nitrogen at the end of the repressurization step. This composition roughly equals that of the nitrogen gas which initially filled the adsorber, but was displaced and compressed toward the effluent end of the bed during the repressurization step. The minimum observed at a dimensionless position of about 0.8, corresponding to a position 80% of the way through the 13X molecular sieve bed, results from two competing effects. As one moves from the activated alumina-13X boundary toward the middle of the 13X bed, the gas phase becomes depleted in nitrogen because nitrogen adsorbs preferentially relative to oxygen in 13X molecular sieve. However, the nitrogen content of the gas phase must rise from its low value near the middle of the 13X bed to the higher value of the nearly pure nitrogen gas now compressed at the effluent end of the bed.

Figure 3 shows the predicted temperature profile through the 13X molecular sieve bed after the adsorber is repressurized. Again, the dimensionless position of 0.0 corresponds to the grid at the activated alumina-13X boundary which is the inlet to the 13X molecular sieve bed. The dimensionless position of 1.0 corresponds to the grid at the effluent end of the 13X molecular sieve bed. The combination of heat released by adsorption and Joule heating produces a nearly uniform temperature rise of about 12 K through the 13X molecular sieve bed. Joule heating contributes nearly 2 K to the total temperature rise. The temperature at the activated alumina-13X boundary rises from the air feed temperature because of Joule heating. The slight temperature dip in Fig. 3 near a dimensionless position of0.8 is aligned with the composition dip depicted in Fig. 2. As one moves from the ac-

tivated alumina-13X boundary toward the middle of the 13X bed, the temperature decreases slightly as the nitrogen concentration in the gas phase decreases and, hence, less nitrogen adsorbs in the 13X molecular sieve. The temperature rises toward the effluent end of the bed because more heat is released as additional nitrogen adsorbs in the 13X molecular sieve at the effluent end of the bed.

Figure 4 shows the predicted composition of the gas which emerges from the adsorber at the start of the adsorption step. The dimensionless time equals the number of bed volumes which have passed through the 13X molecular sieve bed, based on an empty bed volume. The nitrogen concentration dips because of preferential nitrogen adsorption in the 13X molecular sieve, but recovers after about two bed volumes of air have passed through the adsorber. This composition front traverses through the adsorber quickly because nitrogen and oxygen are present in high concentra- tions and have small enthalpies of adsorption. The amount of nitrogen lost due to adsorption in the 13X molecular sieve is less than 3 x 10e5 of the total amount of nitrogen which passes through the adsorber. The fraction of nitrogen lost may actually be much less than this because water vapor and carbon dioxide bind more strongly to 13X molecular sieve than nitrogen does, and these species will displace much of the adsorbed nitrogen during the course of the adsorption step.

Figure 5 compares the predicted and observed temperature of the gas which emerges from the adsorber during the adsorption step. The dimensionless time equals the number of bed volumes which have passed through the 13X molecular sieve bed, based on an empty bed volume. The two curves agree closely except at early times, where the empirically observed exotherm rises more slowly than the theoretical prediction. This mismatch probably arises from transport limitations; heat transfer to the innermost grid which holds the thermocouple provides one likely

0.0 0.1 0.2 0.3 0.4 0.5 0.8 0.7 0.8 0.9 1.0 DIMENSIONLESS POSITION

Fig. 3. Predicted temperature profile through the 13X molecular sieve bed at the end of the repressurization step. The dimensionless position of 0.0 corresponds to the grid at the activated alumina-13X boundary which is the inlet to the 13X molecular sieve bed. The dimensionless position of 1.0 corresponds to the grid

at the effluent end of the 13X molecular sieve bed.

GREGORY R. SCHOOFS and P. PETIT

1.0 DIMENSNk”ESS TIME

3.0

Fig. 4. Predicted composition of the et%ent gas during the subsequent adsorption step. The dimensionless time equals the number of bed volumes which have passed through the 13X molecular sieve bed, based on

an empty bed volume.

Y ___--- OAT*

g 305.0 - - THEORY -

_____d_.________

$

C ,/

,-’

.J 300.0 - ,’

L

,I,’

2

,a*’

I‘- 295.0 - :

z

_ a: - ,,*’

E 290.0 I’:

285.0 Ld ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ 0.0 25.0 50.0 75.0 100.0 125.0 t50.0 175.0 200.0

DIMENSIONLESS TIME

Fig. 5. Predicted and empirically observed temperatures of the efIIuent gas during the subsequent adsorption step. The dimensionless time equals the number of bed volumes which have passed through the 13X

molecular sieve bed. based on an empty bed volume.

explanation. The time for the empirically observed exotherm to return to the air feed temperature closely approximates the theoretical prediction. Heat transfer to the innermost grid probably also accounts for the time lag between the theoretical prediction and the empirically observed exotherm at dimensionless times between 100 and 150. The temperature breakthrough curve takes approximately 180 dimensionless time units to pass through the 13X molecular sieve bed, far longer than the nitrogen concentration breakthrough curve requires. (Note the different time scales in Figs 4 and 5.) The slow rate of heat transfer occurs because the heat capacity of 13X molecular sieve greatly ex- ceeds the heat capacity of air, and a lot of air is required to remove the heat held by the adsorbent.

The results displayed in Fig. 5 clearly demonstrate that the temperature rise during the start of the adsorption step results from nitrogen and oxygen ad-

sorption in the 13X molecular sieve. This temperature rise can be used to monitor the success of previous regenerations and the capacity of the 13X molecular sieve for carbon dioxide adsorption. Small amounts of residual water greatly curtail both the amount and the enthalpy of nitrogen adsorption in 13X molecular sieve (Peterson, 1981). Thus, any residual water on the 13X molecular sieve from a process upset or an incomplete regeneration will diminish the temperature rise due to nitrogen adsorption.

Presorbed polar molecules generally diminish the adsorption capacity of molecular sieves for less polar molecules (Barrer, 1978); hence, presorbed water would also curtail the capacity of 13X molecular sieve for carbon dioxide adsorption. However, the loss of adsorption capacity due to an incomplete thermal regeneration is a short-term (one-cycle) problem, and the full adsorption capacity can be restored by a sub-


sequent and complete thermal regeneration. In this the rate of the temperature rise and recovery at vari- case, the temperature rise observed at the start of the ous locations at the effluent end of molecular sieve adsorption step should return to a normal level fol- adsorbers can be employed to detect flow maldistrlbu- lowing a complete thermal regeneration. tion problems.

Degradation of the molecular sieve crystalline structure due to hydrothermal aging or fouling also reduces the adsorption capacity for nitrogen and carbon dioxide. Because such degradation is essentially irreversible, the temperature rise at the start of the adsorption step would be persistently smaller than that for fresh 13X molecular sieve. Hence, the magnitude of the temperature rise at the start of an adsorption step immediately following repressurization can be used to assess the amount of presorbed water on, or the extent of degradation of, the 13X molecular sieve and, hence, the subsequent capacity for carbon dioxide adsorption.

Patents have been applied for based on the technology described herein.

NOTATION

a

ai

b

bi

Installing thermocouples on the grids at various heights and radial positions may provide an iaex- pensive method to identify transport problems through both the activated alumina and 13X molecular sieve beds. Differences in the temperature profile among thermocouples located at different positions in the radial-flow adsorbers would likely be due to flow maldistribution. For example, thermocouples located at various heights of the radial-flow adsorber might provide evidence of lower flow rates at the bottom of the vessel due to adsorbent settling, breakage, or fines accumulation over time. Although nonuniform flow patterns are more likely to present problems in the thin, radial-flow beds described here, a comparison of temperature profiles at various radial positions can be used in a similar manner to ascertain flow maldistribution in large-diameter, axial-flow adsorbers, particularly adsorbers with low length-to-diameter ratios. Thus, spatial variations in the rate of the temperature rise and recovery could be used to identify flow maldistribution problems.

C

G,i

quantity defined by eq. (lo), N mW2 K-r Langmuir adsorption isotherm parameter, mol i/kg adsorbent/(N rnq2) quantity defined by eq. (1 l), N m- ’ Langmuir adsorption isotherm parameter, mz NW1 quantity defined by eq. (12), N ICmm2 heat capacity of adsorbate i, J mol-t K-i

Cf

ci

G

heat capacity at constant pressure of the gas phase., J mallt K-’ gas-phase concentration of species i, mol m-s heat capacity of the adsorbent, J kg- 1 K-i

c

hf

h.

k

‘I,

4i

CONCLUSIONS

The results presented here have clarified the inter- dependence between the steps of thermally regenerated adsorbers used to purify air. The differential heat and mass balances which describe adsorber operation were solved to illustrate the magnitude of preferential nitrogen adsorption in the freshly regenerated 13X molecular sieve during the repressurization and adsorption steps. Temperature breakthrough data from an appropriately configured industrial adsorber confirm the theoretical predictions.

total gas-phase concentration ( = P/ RT), mol mS3 enthalpy of the gas phase, J mol-’ enthalpy of the adsorbent and adsorbed phase, J kg-’ gas-phase heat capacity ratio [ = c/j

(e, -WI number of species total pressure, N me2 concentration of adsorbate i on the adsorbent, mol kg-’ radial location in the adsorbent bed, m gas constant (= 8.314 Jmoll’ K-l) time, s absolute temperature, K reference temperature, K interstitial velocity, m s- ’ superficial velocity (= EU), m s-t ratio of adsorber vessel volume to adsorbent volume

Yi mole fraction of species i in the gas phase

Greek letters &

Ai

This analysis identified several novel aspects re- garding the operation of molecular sieve adsorbers for purifying air to cryogenic air separation processes. The magnitude of the temperature rise due to preferential nitrogen adsorption can be used to monitor the amount of presorbed water on, or the extent of degradation of, the 13X molecular sieve. This, in turn, provides a method for monitoring the subsequent capacity for carbon dioxide adsorption. Variations in

interparticle void fraction isosteric heat of desorption of species i, J mol-’ bulk density of the adsorbent, kg mW3

Subscripts i

j 1

species label

2

species label for summation initial state, or at the inlet end of the 13X molecular sieve bed final state, or at the outlet end of the 13X molecular sieve bed

760 GREGORY R. SCHOOF~ and P. PETIT

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Carnahan, B., Luther; H. A. and Wilkes, J. O., 1969, Applied Numerical Methods. Wiley, New York, NY.

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Miller, G. W., 1987, Adsorption of nitrogen, oxygen, argon, and ternary mixtures of these gases in 13X molecular sieve. A.1.Ch.E. Symp. Ser. No. 259, 83, 28-39.

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Repressurization of adsorption purifiers for cryogenic air separation