Ind. Eng. Chem. Res. 1987,26, 1638-1645
1638
Kissin, Y. V.; Feulmer, G . P. J. Chromatogr. Sci. 1986,24, 53. Kissin, Y. V.; Feulmer, G. P.; Payne, W. B. J. Chromatogr. Sci. 1986,
3,11,15-Me3-6-CI6=,108560-60-7; 3,11,15-Me3-7-C16=,108560-61-8; 7,11,15-Me3-l-C18=,104256-41-9;7,11,15-Me3-2-C,,=, 104256-42-0; 7,11,15-Me3-3-CI6=,108560-62-9;2,6,10,14-Me4-1-C15=,2140-82-1; 2,7,11,15-Me,-l-C1,=, 104256-43-1; 3,8,12,13-Me4-1-C17=, 104256-44-2; 4,9,13,17-Me4-1-C18=, 104256-45-3; 6,11,15,19Me4-1-C,o=, 108560-63-0; 6,11,15,19-Me4-2-C20=, 108560-64-1; 2,6,11,15,19-Me,-2-Czo=,108560-65-2; pristane, 1921-70-6;phytane, 638-36-8; squalane, 111-01-3.
24, 164.
Kochi, J. K., Ed. Free Radicals Wiley: New York, 1973; Vols. I and 11.
Kossiakoff, A.; Rice, F. 0. J . Am. Chem. SOC.1943, 65, 590. Kovats, E. 2.Anal. Chem. 1961, 181, 351. Ranzi, E.; Dente, M.; Pierucci, S.; Biardi, G. Ind. Eng. Chem. Fundam. 1983,22, 132. Spivakovskii, G . I.; Tishchenko, A. I.; Zaslavskii, I. I.; Wulfson, N. S . J. Chromotogr. 1977, 144, 1.
Literature Cited Benson, S. W. The Foundations of Chemical Kinetics; McGraw-Hill: New York, 1960. Kissin, Y. V. J . Chromatogr. Sci. 1986, 24, 278.
Received for review June 30, 1986 Accepted April 27, 1987
Temperature Front Sensing for Feed Step Control in Pressure Swing Adsorption Michael J. M a t z and K e n t
S. Knaebel*
Department of Chemical Engineering, The Ohio State University, Columbus, Ohio 43210
Analysis of the progression of adsorbent bed temperatures provides a means for controlling the duration of steps in a pressure swing adsorption (PSA) cycle. This technique was tested for separation of oxygen from air with zeolite 5A. I t was found that the concentration and temperature fronts coincided during breakthrough experiments at fixed pressures from ambient to 4 atm for temperatures of 5 , 25, and 45 "C. Furthermore, when all steps of the PSA cycle were combined, it was possible to control the duration of the feed step, regardless of whether the pressure was constant or varied linearly during that step. It was also possible to predict, a priori, the trajectories of the concentration fronts by a simple equilibrium theory.
I. Introduction Pressure swing adsorption (PSA) systems consist of columns which contain solid adsorbents that are synchronously pressurized, fed, depressurized, and purged. The process exploits the tendency for the uptake of components to increase in different proportions as pressure rises, which gives rise to selective adsorption of certain components over a pressure range. When the selectivity and/or pressure range are sufficiently large, a PSA system is able to produce high-purity products. Common separations are hydrogen from hydrocarbons and oxygen from air (Cassidy and Holmes, 1984). Pressure swing adsorption systems are relatively simple to operate, i.e., in timed cycles, when flow rates, compositions, and the pressure range are fixed and when the adsorbent is maintained at maximum adsorbent capacity. Performance may suffer, however, when the adsorbent capacity is diminished or when operating or ambient conditions vary significantly. In such cases, one would employ sophisticated composition-monitoringinstruments to synchronize steps in the cycle to maintain product purity. The purpose of this paper, however, is to suggest that it may be possible to use relatively simple instruments, e.g., thermocouples, to compensate for adsorbent capacity loss and variable operating conditions without inordinate effects on performance. A partial explanation, in the context of oxygen separation from air, follows. Heat evolves in a packed bed of zeolite 5A as air displaces oxygen due to the uptake of nitrogen and release of oxygen by the molecular sieve. This is caused by the higher adsorption capacity and higher heat of adsorption of nitrogen relative to oxygen. Simultaneous axial bulk flow, adsorption, and heat release lead to composition and thermal waves that propagate toward the product end of the column. Assuming that these fronts coincide, the penetration of nitrogen into the bed can be determined 0888-5885/87/2626-1638$01.50/0
by measuring the temperature profile within the bed. In operating a PSA system, it is of signal importance for such waves to approach but not breach the end of the column. Recovery and/or purity of the product is reduced by either insufficient or excessive axial displacement of the composition wave. Accordingly, those aspects of PSA performance can be enhanced by terminating the feed step when breakthrough is imminent. In previous related work, Pan and Basmadjian (1970) derived approximate criteria for combined, constant pattern thermal and composition wave fronts. Kowler and Kadlec (1972) considered experimental and theoretical aspects of PSA control but restricted their attention to direct composition control, with a cell model as the basis of their theory. Chihara and Suzuki (1983), in a numerical simulation of air drying with activated alumina, predicted that thermal waves were attenuated from the feed end toward the product end. For air drying with a variety of adsorbenta, Carter and Barrett (1973) experimentally observed varying degrees of sharpness but uniform coincidence of the composition and thermal waves. Similarly, Yoshida and Ruthven (1983) obtained a solution to a model of adiabatic adsorption for a rectangular isotherm. They presented data for air drying with three adsorbents in which, while their shapes are not sharp, the composition and thermal waves coincided. Sircar et al. (1983) considered the effect of heat loss through the column wall, as well as other effects in both experimental and theoretical studies with ethane in helium on zeolite 5A. They found a minor effect of heat loss on the velocities of both the composition and thermal waves but found that the waves coincided regardless of the extent of heat loss. Finally, Kaguei et al. (1985) employed a detailed mathematical model and experimental temperature and concentration profiles in order to estimate parameters of adsorption. Specifically, they determined the 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1639
&;ye A
Vent to Low P
,
@ tZ
z=L
+
rPezi;aoitn with Product
2.0
Figure 1. Column orientation and flow directions during the four actual steps of a typical PSA cycle.
isotherm slope, the heat of adsorption, and the heattransfer coefficient through the column wall, all for adsorption of carbon dioxide from nitrogen with activated carbon. Isosteric heats of adsorption for oxygen and nitrogen on molecular sieve 5A have been determined as -3.37 and about-5.0 kcal/mol, respectively (Miller et al., 1986). In that work it was found that the heat of adsorption for nitrogen, however, increases at low loading and approaches a limiting value of about -8.0 kcal/mol at zero coverage. As shown in the Experimental Section of this paper, temperature shifts during feed and purge do not significantly affect the adsorption capacity for the air-oxygen zeolite 5A system. Temperature excursions as high as 50 OC have been noted in a molecular sieve drying system for a 2-propanol-methanol-water feed stream (Garg and Yon, 1986). Also, temperature rises of 60 OC have been observed in H2/CH4and H2/C0 activated carbon systems (Yang and Cen, 1986). In that study it was found that addition of inert particles with high heat capacity may attenuate the thermal wave (which, unabated, would reduce the adsorbent capacity of the column) and sharpen the concentration shock front. That approach, however, may impair temperature front sensing for PSA separation of oxygen from air on molecular sieve. 11. Theoretical Aspects It was hypothesized earlier that the position and movement of the composition wave may be inferred from that of the thermal wave. Before that hypothesis is examined, however, some elementary concepts of composition wave analysis are explored. Following that, the approach used to predict breakthrough is described. A. Equilibrium Theory. A simple theory that applies to pressure swing adsorption for a binary mixture in which linear isotherms exist has been proposed (Knaebel and Hill, 1985). That theory applies to the four-step cycle shown in Figure 1. The high-pressure feed step commences with the bed filled with the weakly adsorbed (light) species at the highest pressure. This step allows uptake of the more strongly adsorbed (heavy) component in the feed onto the adsorbent. The next step, termed blowdown, allows depressurization of the packed column, which fills the interstices with enriched heavy component as it desorbs. Subsequently, the light component purges the bed and displaces the heavy component. Finally, the column is repressurized by product, though in some alternative cycles feed is used. That theory is based on local equilibrium between an adsorbent and a binary mixture of adsorbates with linear isotherms. The governing partial
differential equations are solved by the method of characteristics, and the solution has been experimentally validated for the case of pressurization with product (Kayser and Knaebel, 1986). A basic assumption of this theory is that each column operates isothermally. Although this assumption contradicts the underlying concept of the present research, it is practically valid since temperature variations associated with adsorption and desorption for air do not significantly affect the capacity of the zeolite 5A adsorbent over the range of conditions studied. Other assumptions include ideal behavior of the binary gas mixture and absence of dissipative effects such as axial dispersion and pressure drop across the bed. A concentration shock wave is formed in a bed when the gas fed to it contains more of the heavy component than that in the gas phase of the fixed bed. For example, when air is passed into a bed of zeolite 5A that has been pressurized with oxygen, there is an abrupt shift from pure oxygen to air that propagates through the bed. The following development shows that a priori prediction of the path of that wave is possible, based on easily measured values. As stated previously, prediction of the trajectory nand subsequent termination) of that wave leads to favorable performance. For a PSA system with a constant-pressure feed step and a packed bed initially saturated with the pure light component, the theory predicts that the duration of the high-pressure feed step is no greater than the time for the composition shock wave to traverse the bed, i.e.
where
= + (1 - c)KA (2) If pressure is allowed to vary during the adsorption step of PSA, a somewhat more involved solution is required. The special case of constant molar feed and product flows and constant feed and product compositions yields a linear pressure change with time, which is the situation of interest here. That case has been considered fully elsewhere (Kayser and Knaebel, 1987), and only the results pertinent to temperature front sensing are summarized here. Continuity yields the criterion for this situation to occur. The result is YA
dP
[40 - &]/L = P'
(3)
4j = (uP)j[l+ (P - l ) ~ j l c / ~ ~
(4)
-=
dt
where and the subscript j refers to a specific condition, e.g., at the feed or product end. When pressure varies, the movement of the composition shock wave is governed by the characteristic equations that are given by Knaebel and Hill (1985) and by eq 3. The solution to these, expressed as the time and position of the shock, can be used to determine the duration of the feed step. After some algebraic manipulations, the following result is obtained
where
n = P(t)/P,
1640 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987
This equation reduces to the theory of Knaebel and Hill (1985) for pressurization with feed, i.e., when = 0. Thus, the trajectory can be determined from volumetric flow rates, column length, and feed and product compositions, all of which should be constant during the feed step. Kayser and Knaebel (1987) have considered several detailed and general effects, such as whether the composition shock wave may disintegrate due to desorption. During the purge step, oxygen displaces enriched nitrogen in the interstices and induces desorption of nitrogen from the adsorbent. The concentration of the effluent gas slowly changes to pure oxygen, at which point the step is terminated. The shock phenomenon is not seen in this step. Rather, a gradual change in composition, sometimes called a simple wave, occurs as dilute material is fed into a bed containing enriched gas. Since fewer moles are involved during desorption of nitrogen and adsorption of oxygen during the purge step, and since the composition wave is not sharp, the enthalpy change is small and the associated thermal wave is diffuse. Hence, following the progression of the purge step by temperature sensing is difficult. For this reason, temperature front sensing was only implemented during the feed step of pressure swing adsorption cycles. B. Feed Step Control Algorithm. As explained previously, a constant shock velocity is predicted by theory if pressure remains constant during the feed step. Conversely, the theory suggests that a nonlinear trajectory occurs with linearly changing pressure. Rather than rely on that theory (which requires information concerning flow rates, pressure, composition, and adsorbent-adsorbate properties), the approach taken here was to assume that the composition and thermal waves were coincident and that the path could be extrapolated along a parabolic curve to anticipate breakthrough. Some details are presented here to show that the method is simple enough to be carried out by a microcomputer in real time. Since for the case of four (or more) thermocouples, it would be serendipitous for the actual path to be parabolic, the solution for the system of equations involves a nonzero residual, r , the Euclidean norm of which is to be minimized
W=AB+r where the vectors and matrix are given by W = Wj A = ajk B = bk
(7)
and wj = times at which the thermal shift occurred at position xj, a,k = (lz - l)-order polynomial terms of positions x i , e.g., a23 = and bk = coefficients of the polynomial with j = 1 to 4 and k = 1 to 3. The least-squares criterion is AT(W- AB*)= 0. Thus, a simple approach to finding the best fit values of the coefficients B* = bk* is to solve
ATAB* = ATW (8) e.g., by Gaussian elimination. A t the expense of not smoothing the process data, the order of the polynomial could be increased to permit a direct solution to eq 7, i.e. with r = 0 . Finally, the length of the packed bed is used to determine the ultimate time for the feed step as t H = bl* + bz*L + b3*L2 (9) 111. Experimental Section The experimental systems for breakthrough and pressure swing simulation studies were similar but not identical. Despite that, the thermocouple placement in the
,Three -Way Solenoid
Inlet
Oxygen Inlet
Isothermal Bath-._
To Mass Spectrometer TO Gent
or Vacuum
Figure 2. Breakthrough apparatus and instruments. Valves were manipulated by and all temperatures and gas compositions were recorded by a microcomputer-based data acquisition system.
adsorption columns remained the same in both studies. The following two sections describe the apparatus used for cyclic flow experiments. Further details are presented elsewhere (Matz, 1986). A. Breakthrough Studies. Breakthrough experiments were conducted by passing air into an adsorption column until breakthrough was complete. Then the bed was cocurrently purged with oxygen at the same flow rate and total pressure. High-purity oxygen (99.99%) and zero air (21.0% oxygen and 79.0% nitrogen) were used in the experiments. Molecular sieve 5A (Linde, 16 X 40 mesh, medical grade) was employed as the adsorbent. The column had five thermocouples (Omega Engineering, 0.0625-in. diameter, exposed junction) inserted laterally along the axis, with the thermocouple junctions at the center line. The product gas composition was continuously monitored by a mass spectrometer (Perkin-Elmer, MGA 1200). Figure 2 is a diagram of the breakthrough apparatus and instruments. These experiments were performed over a pressure range up to 4 atm and temperatures of 5, 25, and 45 "C. For conciseness, the last condition has been omitted from further discussion because it merely reinforced the observations drawn at the other temperatures. During breakthrough experiments, the ambient (column wall) temperatures were maintained by placing the column horizontally in a constant-temperature bath containing an ethylene glycol-water mixture that was circulated. The bed was spring-loaded to prevent settling, which would lead to a spurious breakthrough pattern. Pressure was kept constant during both the shock wave and simple wave steps of the breakthrough study. The influent or effluent flow rate was set by a mass flow meter/controller. During high-pressure experiments, the flow controller was placed downstream from the bed; otherwise, it was upstream. In order to ascertain the maximum capacity of the column to avoid inadvertent contamination of the product, the instrument lags and flow dead time were measured. For example, the dead time for the gas to pass through the piping and the switching time of the solenoid valve were negligible, but the response times for the mass flow controller and the sampling lag in the mass spectrometer were significant. Therefore, these two contributions were combined in a lumped dead time for the apparatus. In addition, the time for the signals to be read and converted by the computer was included in this sum. Experimental conditions are listed in Table I.
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1641 Table 111. PSA Conditions
Table I. Breakthrough Conditions experiment condition pressure, atm feed flow rate, L(STP)/min bath temp, "C interstitial velocity, cm/s Re (PFU~D~/PL) feed time, s purge time, s thermal wave velocity, cm/s
experiment
1
2
3
2.72 6 25 20.4 14.2 60 140 2.16
4.08
4.08 7 5 14.8 17.5 75 198 1.37
8 25
18.1 19.0 60 140 2.08
Table 11. PSA Valve Sequence" valve label
SbP pressurization
sv1 sv2 sv3 sv4
feed 1
0 0
1
0 0
0
1
blowdown
Durge
0 1 0 0
0
1 1 0
0 represents the normal state (unenergized) and 1 signifies solenoid activation. Figure 3 indicates the normal and activated states of each valve.
Air
Inlet
7
C O M , & ~ C , N C ~ ~ ~
,kSs Spectrometer
Oxygen
Mass
Spectrometer Figure 3. PSA simulation apparatus and instruments. Valves were manipulated by and all temperatures and gas compositions were recorded by a microcomputer-based data acquisition system. The valve sequence is shown in Table 11. NC = normally closed; NO = normally open; COM = common. sv3
1
2
3
39
11
49 71 95 117 139 149 161 205 5.0 0 4.9
12 35 57 19 29 71 41 83 52 90 96 70 81 99 127 148 2.2 3.2 0.051 -0.029 9.0 2.2 2.9 3.4 6.7 6.2
6.6
25
4" 260 295 575 915 1215 1505 1530 1630 2260 3.2 0 5.4 9.9
"This experiment was performed with the larger bed listed in Table IV; others were performed in the smaller bed. Table IV. Column Specifications" material L,cm i.d., cm o.d., cm stainless steel 81.3 2.36 2.54 aluminum 76.8 9.50 10.20
MAn,g
e
268.0 4065.0
0.48 0.48
"Thermocouples were placed at 5.1, 22.9,40.6, 58.4, and 76.2 cm from the entrance of the bed for both columns.
Experimental conditions are listed in Table 111, and column dimensions are given in Table IV. Two columns were used to determine whether column diameter affected the viability of temperature front sensing. I t was presumed that the larger column would be more nearly adiabatic even though the velocity was decreased in nearly the same proportion as the cross section was increased, i.e., 9.4 vs. 16.2. Both columns were uninsulated and exposed to ambient room air.
L U
Inlet
condition pressurization step end, s TC step response, s no. 1 no. 2 no. 3 no. 4 no. 5 feed step end, s blowdown step end, s purge step end, s feed pressure, atm P', atm/s feed flow rate, L(STP)/min product flow rate, L(STP)/min O2 purge flow rate, L(STP)/min
sv4
B. PSA Simulation. The four steps in a typical PSA cycle were examined in a series of four experiments in a single column. These only simulated PSA operation because all of the product was exhausted rather than recycled; instead a reservoir of the pure light component was used for pressurization and purge. This avoided the transient period in which the product would become increasingly purer, during which temperature front sensing may not have been easily applied. Despite that, a sufficient number of cycles preceded collection of the data reported here in order to ensure attainment of cyclic steady state. The purpose of this study was to implement breakthrough results and to verify the feasibility of control of PSA cycles by temperature front sensing. Figure 3 is a diagram of the apparatus used in PSA experiments. The oxygen, air, and adsorbent used for these experiments had the same specifications as described earlier. The valve sequencing for the PSA system is listed in Table 11. Similar allowances for dead time were made here as for the breakthrough apparatus. Also, an additional flow meter was placed at the feed end as the controller was moved to the product end during experiments in which there was a linear change in column pressure during feed.
IV. Results A. Breakthrough Studies. The purpose of this section is to examine thermal wave behavior under idealized conditions, i.e., with constant pressure and no flow reversal. In general, the shock and simple waves that are generated in breakthrough studies reveal the sharpness of the thermal front and the extent of coincidence with the composition front. In addition, adsorbent capacity changes may be inferred from trends in temperature data. These aspects are critical for implementation of feed step control. Figure 4A shows concentration vs. time for the effluent gas during experiment 1: both the shock and simple waves are identified. At approximately 45 s the shock wave emerged from the bed as the effluent gas concentration suddenly shifted. The gradual change in effluent composition from air back to oxygen was characteristic of the simple wave of desorption, which began at about 80 s. Figure 4B is a plot of temperature vs. time for each thermocouple in the adsorption column for experiment 1. The temperature rise at each thermocouple occurred after approximately the same interval of time elapsed during the feed step. Since the thermocouple positions were equidistant, the thermal wave had a constant velocity, as expected for constant-pressure adsorption steps. Furthermore, it was observed that breakthrough of the composition wave occurred immediately following the temperature rise nearest the end of the bed. Therefore, it was concluded that the waves were coincident and that the times at which thermal step responses occurred could be used to predict the duration of the feed step. The temperature drop in Figure 4B is associated with desorption that occurs during the purge step. Since the
1642 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1 7 --7
100
35 80 30 W
60
U
3
I4 U
25
W
SIMPLE
40
a
I
WAVE
W
c
W
20
1
I
20
15 SHOCK WAVE
10
0 0
50
100
TIME
35
I-
I
150
0
200
50
100
TIME
(Si
1
I
150
200
(51
Figure 5. Temperature profiles from breakthrough experiment 2, at 4.08 atm and 25 O C .
I -
1
15
10
4
U
5
W
a r W I-
I I
10
0
50
- 5
I
100
0
150
200
TIME (SI
Figure 4. (A, top) Effluent oxygen and nitrogen concentrations tor 02-air. Breakthrough experiment 1, at 2.72 atm and 25 O C . (B, bottom) Temperature profiies during breakthrough experiment 1, at 2.72 atm and 25 "C. Thermocouples are numbered sequentially from the entrance of the bed.
flow direction for both the feed and purge gases was the same, thermocouples placed nearest the feed end of the column recorded a decrease in temperature first. Simple wave propagation was traced by the minimum temperatures at each position. Despite that, recognizing the time when the minimum temperature occurred at each thermocouple is difficult because only a fraction of a Celsius degree drop corresponds to purge completion. Therefore, unless all noise in the temperature data is eliminated, control of the regeneration step appears impractical. Figures 5 and 6 show temperature data taken from experiments 2 and 3, respectively. The purpose of these two graphs is to illustrate the change of adsorbent capacity with pressure and temperature. The temperature shifts shown in Figure 5 at a higher pressure are larger than those in Figure 4B. In addition, temperature shifts at a lower base temperature in Figure 6 are larger than those of Figure 5 at the same pressure. As the adsorbent capacity increased at lower temperatures and higher pressures, more nitrogen adsorbed onto the molecular sieve and a greater heat release was observed. Breakthrough experiments established the framework for controlling the feed step of PSA cycles. Unfortunately, the data also demonstrated the difficulty of purge step control under low-pressure conditions. B. PSA Results. The primary differences between breakthrough experiments and PSA simulations were that
I I
-10 0
50
100
150
200
TIME ( s )
Figure 6. Temperature profiles for breakthrough experiment 3, at 4.08 atm and 5 "C.
the feed and purge flow directions were cocurrent in the former and countercurrent in the latter and that feed step control was implemented in the latter. Other differences between the two studies included the addition of the pressurization and blowdown steps in the PSA simulations. During these steps, temperature inside the bed increased and decreased, respectively, due to gas compression or expansion, as well as adsorption or desorption. The temperature profiles during the feed step of experiment 1 are shown in Figure 7A. The thermal wave associated with adsorption can be envisaged moving through the column as temperature rises at successive positions. The PSA data acquisition system identified the sequence of step responses to have occurred at 49,71,95, and 117 s, and breakthrough was predicted at 149 s by eq 8 and 9. Approximately, a 10 "C step response was recorded by each thermocouple during the feed step. Figure 7B shows the percent oxygen in the effluent gas during the feed step. A t 149 s, breakthrough was imminent, as indicated by the slight drop of the oxygen purity. Therefore, that time was predicted reliably from the temperature data, as described above. The steep concentration rise at the start of the feed step was an artifact of the sample switching sequence of the mass spectrometer; it did not reflect unusual behavior of the adsorption process. Additional PSA experiments were conducted in which the pressure varied during the feed step. In the first of these, pressure increased linearly, and it amounted to si-
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1643 I
I
I
35
--
-
U
L
30
W
W
U
(I
3 I4
(I
I4
U W
a 5
+
20
10
0
25
50
75
r1
loo
80
I
a
I
+
20
125
150
175 200
m > X 0
60
W U
a: W Q
15
20
10
30
TIME
-1
1
+ ' I
1 ;
-1 '
50
40
(SI
z
W
25
W
100
TIME
+ z
30
3
25
W
w
35
U
60
70
(s)
Figure 8. Temperature data from the feed step of PSA experiment 2; pressure increases linearly from 2.0 to 5.2 atm. Data from other steps are omitted.
I
I
20 0
t
0
20
40
60
80
TIME
100
1 120
140
160
(si
Figure 7. (A, top) Temperature profiles in PSA experiment 1with a constant feed pressure of 5.0 atm and a purge pressure of 1 atm. Flow reversal occurs at 149 s. (B, bottom) Effluent gas composition during the feed step of PSA experiment 1 (cf. Figure 7A). Note that data from other steps are omitted.
multaneous feed and pressurization. The results are shown in Figure 8. As the bed pressure rose, the adsorbent capacity also increased. This trend can be inferred from Figure 8 because the time intervals between temperature shifts increased, indicating deceleration of the thermal wave. The PSA data acquisition system recorded the first four temperature rises at 12, 19, 29, and 41 s, and breakthrough was predicted to occur at 70 s, again by eq 8 and 9. The increased capacity is also shown by the increasing temperature rise as the thermal wave moves through the column. The concomitant rise of the base temperature in the column is due to partial pressurization during this step. In the next PSA experiment, pressure decreased linearly, as in simultaneous feed and blowdown. The results are shown in Figure 9. The trends are opposite of those observed during simultaneous pressurization and feed. For example, the time for the thermal wave to pass between equidistant thermocouples decreased as the pressure decreased (i.e., 35,57, 71, and 83 s, respectively), indicating acceleration of the thermal wave. Furthermore, the temperature rise due to adsorption slowly diminished, i.e., as the wave propagated through the bed. Breakthrough was predicted to occur at 96 s by eq 8 and 9. As in the experiments at constant pressure, the effluent gas composition was flat (though not shown graphically) during the feed step of experiments in which the pressure varied. Again, this was a result of precise prediction of
22.0
I '
20
I
I
I
I
I
I
I
30
40
50
60
70
80
90
TIME
I
I
100
(SI
Figure 9. Temperature data during the feed step of PSA experiment 3; pressure decreases linearly from 3.2 to 1.1atm. Data from other steps are omitted.
breakthrough and synchronized valve switching, which prevented contamination of the oxygen product. Finally, due to the impact of heat loss through the column wall as noted in previous research (e.g., Chihara and Suzuki, 1983; Sircar et al., 1983; Kaguei et al., 1985; and Yang and Cen, 1986), an experiment was conducted in a 9.5-cm i.d. column for comparison with the previous experiments, Le., in a 2.3-cm-i.d. column. With approximately the same column length, pressure, ambient temperature, and flow rate but with a longer cycle time for the PSA simulation, there was no significant effect of the larger column diameter. Specifically, the temperature profile at each point was essentially unaffected, and the range of temperatures was only slightly greater in the larger column (i.e., about 2 "C).
V. Comparison of Results and Theory This section is intended to unify the foregoing sections by showing that the experimentally measured trajectories of the shock waves are in close agreement with the predictions of a simple equilibrium theory. Specifically, predictions of the theory that applies at constant pressure (Knaebel and Hill, 1985) and of the extension that applies when pressure varies at a uniform rate (Kayser and Knaebel, 1987) are compared with experimentallyobserved results.
1644 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987
performance should also be affected. For example, combination of both the feed and pressurization steps and the blowdown and purge steps tends to decrease recovery of the light product, but those combinations lead to a simple sequence of operation and a simple flow sheet. When a two-column system is operated with those combined steps, the purge gas requirement of one column can be supplied by the other column through a throttling valve. For all that, there may be performance and/or economic aspects of certain combinations of steps that lead to advantages over the standard PSA cycle, and temperature front sensing should be suitable for controlling the feed steps for all of those alternatives.
100
80
Lo
I
60 W H
+
40
20
Acknowledgment n
v
0.0
0.2
0.4
0.6
0.8
:.0
DIMENSIONLESS COLUMN LENGTH
Figure 10. Actual thermal wave paths (denoted by symbols) and theoretical shock wave trajectories for PSA experiments 1-3.
Figure 10 shows the path of the thermal wave during the feed step of three different PSA cycles. The first occurs a t constant pressure, a second is for increasing pressure, and a third applies when pressure decreases. In all cases, the thermal wave data are shown as individual symbols, and the predicted trajectories are shown as solid lines, based on the values of PL,P', and flow rates listed in Table 111, the parameters listed in Table IV, and the experimentally determined value of p = 0.6 (Kayser and Knaebel, 1986). As can be seen, in each of the three cases the deviations of the theoretical predictions from the data are small.
VI. Discussion and Conclusions The thermal effects involved in the pressure swing adsorption cycle have been exploited to control the highpressure feed step under constant molar flow conditions. As such, the pressure either remained constant, increased linearly, or decreased linearly with time. Conversely, control of the purge step appears difficult to implement unless virtually all noise is eliminated from the temperature data. The feasibility of temperature front sensing for control of the adsorption step of a PSA cycle is assured by coincidence of the thermal and concentration waves. Although the experiments performed were oriented toward separation of oxygen from air with molecular sieve SA, the approach should be applicable for other systems with constant and varying feed step pressure. Conversely, the approach may not be as useful for temperature swing adsorption processes, because in such applications the thermal wave may lead the composition wave(s). Temperature front sensing alone would therefore lead to incomplete utilization of the adsorbent. The significance of this approach may be enhanced by its tolerance of disturbances or upsets that were not explicitly evaluated here. For example, deactivation of adsorbent may be caused by impurities in the feed. Typically, the column would deactivate from the feed end toward the product end and the effective bed length would decrease. Consequently, some thermocouples may record a diminished or even negligible temperature rise. Accordingly, details of the feed control algorithm could be modified to adapt to such foreseeable conditions without altering the basic concept of the approach. The justification for studying the PSA feed step under varying pressure conditions is that such a combination of steps may lead to process simplification, although overall
The assitance of Dr. Kenneth G. Ikels of the School of Aerospace Medicine, Brooks AFB, TX, is gratefully acknowledged. The 5A molecular sieve was kindly furnished by the Union Carbide Corporation. This research was sponsored by the Air Force Office of Scientific Research/AFSC, United States Air Force, under Contracts F33615-83-D-0601 and F49620-85-C-0013.
Nomenclature A = matrix of polynomial terms of axial positions of thermocouples AT = transpose of the matrix A a k = individual polynominal terms of axial positions d = vector of polynominal coefficients bk = individual polynominal coefficients D = diameter K , = slope of the equilibrium isotherm for component i L = column length MAD = mass of adsorbent P = pressure P'= rate of pressure change during feed step, defined by eq 3
PL = initial feed step pressure Q F = volumetric flow rate of feed r = residual vector Re = Reynolds number (pFutDp/p) t = time u = interstitial velocity Vb = volume of empty bed
W = shock time vector w, = individual times at which the thermal shock passes the respective thermocouple positions x , = positions of the thermocouples y = mole fraction of more strongly adsorbed component z = axial position
Greek Symbols
p = separation factor (PA/&) = t/Y, y 1= € (1 - t ) K l t = void fraction of bed = fluid viscosity Pl
+
9, = constant defined by eq 4 n = feed step pressure ratio defined by eq 6 p = fluid density Subscripts A = more strongly adsorbed component
B = less strongly adsorbed component b = bed F = feed gas H = feed step i = component index I = inlet j = position index L = purge step 0 = outlet gas p = particle SH = shock wave
Znd. Eng. Chem. Res. 1987,26, 1645-1653 Superscript * = denotes best-fit criterion
Literature Cited Carter, J. W.; Barrett, D. J. Trans. Znst. Chem. Eng. 1973,51,75-81. Cassidy, R. T.; Holmes, E. S. AZChE Symp. Ser. 1984, 80(233), 68-75. Chihara, K.; Suzuki, M. J . Chem. Eng. Jpn. 1983, 16, 53-60. Garg, D. R.; Yon, C. M. Chem. Eng. Prog. 1986, 82(2), 54-60. Kaguei, S.; Yu, Q.; Wakao, N. Chem. Eng. Sci. 1985, 1069-1076. Kayser, J. C.; Knaebel, K. S. Chem. Eng. Sci. 1986,41, 2931-2938. Kayser, J. C.; Knaebel, K. S. Chem. Eng. Sci. 1987, in press. Knaebel, K. S.; Hill, F. B. Chem. Eng, Sci. 1985, 40, 2351-2360.
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Kowler, D. E.; Kadlec, R. H. AZChE J . 1972, 18, 1207-1218. Matz, M. J. M.S. Thesis, The Ohio State University, Columbus, 1986. Miller, G. W.; Knaebel, K. S.; Ikels, K. G. AZChE J . 1986, in press. Pan, C. Y.; Basmadjian, D. Chem. Eng. Sci. 1970, 25, 1653-1664. Sircar, S.; Kumar, R.; Anselmo, K. J. Znd. Eng. Chem. Process Des. Deu. 1983, 22, 10-15. Yang, R. T.; Cen, P. L. Ind. Eng. Chem. Process Des. Deu. 1986,25, 54-59. Yoshida, H.; Ruthven, D. M. Chem. Eng. Sci. 1983, 38, 877-884.
Received for review July 29, 1986 Revised manuscript received March 23, 1987 Accepted April 25, 1987
Dominant Mechanisms for Color Differences in the Mechanical and the Electrostatic Spraying of Metallic Paints Stuart L. Inkpen and James R. Melcher* Laboratory for Electromagnetic and Electronic Systems, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Color differences in metallic paints sprayed by traditional mechanical sprayers and newer electrostatic sprayers have motivated the detailed investigation of these devices. The dominant mechanism for this color difference has been identified. The amount and size distribution of the metallic flake deposited by the electrostatic sprayer is significantly different than that deposited by the mechanical process. For the devices investigated, the mass percent of flake and average flake size deposited by the mechanical sprayer are respectively twice and more than twice what they are for the electrostatic sprayer. This is a consequence of the low efficiency of the mechanical sprayer. These results imply that for color control with low-efficiency sprayers (mechanical), cognizance is required of the disparity between input and workpiece flake content and size distribution and that for highly efficient processes (electrostatic), a new approach to color control is required.
Background The painting industry is responding to environmental concerns by using electrostatic sprayers to increase the deposition efficiency. In the automotive industry, the efficiency is between 10% and 40% for a mechanically applied paint coat but between 60% and 90% when applied electrostatically. By use of these two different processes, most paints can be matched by varying standard painting parameters. However, electrostatic deposition of metallic paints tends to result in a darker appearance. This is often ascribed to alignment of the conducting flake by the electric field. Although this mechanism is not eliminated as a contributing factor, it is shown here that this is not the dominant mechanism, at least for the specific equipment studied here. Rather, it is found that the selective deposition of drops by the mechanical sprayer (that is, minimized in the electrostatic sprayer) is the dominant mechanism. Possible Mechanisms for Electrically Induced Color Variation The basic configuration of a high-speed turbobell electrostatic painter is shown in Figure 1, where four process stages are distinguished (a) formation of drops, (b) flight to the workpiece, (c) impact with the workpiece, and (d) postimpact. Whether the atomization and delivery are purely mechanical or purely electrostatic, or any combination, these stages are potential contributers to the coloration of the final product. The spray devices chosen for this project were a Binks hand-held sprayer and a RansOSSS-5S85/S7/2626-1645$01.50/0
burg Turbobell. The Binks spray gun uses mechanical atomization and delivery, while the Ransburg Turbobell uses both electrostatic and mechanical atomization and delivery. There are four mechanisms proposed that may contribute to the electrically induced color variation: (1)flake orientation (formation, flight, impact, and postimpact), (2) electrophoresis of the flake or other pigments (postimpact), (3) differential evaporation of solvents (flight), and (4) variation in the amount and size distribution of deposited flake (flight). The final angle of the flake has a large effect on the color (Wojtkowiak, 1983). I t is possible that this orientation could be modified in any of the paintingstages by electrical forces, although the earlier the stage, the less likely the persistence of the effect. Electrically induced flake orientation is briefly considered in the next section, where it is found unlikely that it is the dominant mechanism for electrically induced color variations. Electrophoresis of the flake as well as the other pigments would cause their spatial variation and a resultant change in color. This requires an electric field in the paint and a substantial double layer surrounding the particles. Experiments show that for the paints used, electrophoresis requires field strengths on the order of lo4 V/m for noticeable motion of the flake or pigments in times of interest. Fields in the paint are typically estimated to be 2 orders of magnitude less. If there were a mechanism for imposing a high electric field in the paint, such as a substantial corona current in the air, electrophoresis would 0 1987 American Chemical Society
