210
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 2, 1979
0.4615[(f3/13) f4+
-
11 + 1 ] / F
qp, = feed quality for equivalent binary system R = reflux ratio = L I D R , = minimum reflux ratio Rs = defined by eq 3 S =-separation factor = xD(l - x w ) / ( I - xD)x, V, V = vapor rate in rectifying and stripping sections, respectively XD = mole fraction of light component in distillate XF = mole fraction of light component in feed x, = composition at bottom of rectifying section or top of stripping section x, = mole fraction of light component in bottoms Greek Letters a = relative volatility t l , t q = deviations defined by eq 22 d1, = constants defined by eq 7 Subscripts i = component i k = key component Literature Cited
(B-10)
Nomenclature a1 = K1(xF - xw)
= K I ~ (-~x,)D K i ( x -~ XF) + K~(XF- x,) = K 3 q ( X D - xw) + K 4 ( X D - xF) D = distillate rate d3 = distillate flow of propane F = feed rate f c , = feed rate of methane fco, = feed rate of COz f 2 = feed rate of ethane fi- = f c , + fco, + fi f3 = feed rate of propane f 4 f = f I c 4 + f N C 4 + f I C + f N C 6 + fN6+ flc4 = feed rate of isobutane f N C , = feed rate of normal butane fIc, = feed rate of isopentane f ~ = cfeed ~ rate of normal pentane fc,, = feed rate of heavier components a2 a3
K1
= ( a - 1)'[XD(1 - x,)
-
xw(1
Bauer. R. L., Orr, C. P., Chem. Eng. Prog.,50(6), 312 (1954). Buckiey, P. S.,Cox. R. K., Luyben, W. L., Chem. Eng. Prog., 74(6), 49 (1978). Ellingsen, W. R., AIChESyrnp. Ser., 72, No. 159, 150 (1976). Fauth, G. F., Shinskey, F. G., Chern. Eng. Prog.. 71(6), 49 (1975). Hengstebeck, R. J.. Chem. Eng., 115 (June 13, 1969). King. C. J., "Separation Processes", McGraw-Hill, New York, N.Y.. 1971. Lee, W., Weekman, V. W., Jr., AIChE J., 22, 27 (1976). Luyben, W. L., Ind. Eng. Chem. Fundarn., i 4 , 321 (1975). Nisenfeld, A. E., Fisher Contrds Co., Marshalltown, Iowa, personal communication, 1976. Nisenfeld, A . E., Harbison, J., Chem. Eng. Prog.,74(7), 88 (1978). Shinskey, F. C., "Process Control Systems", Chapter 11, M&aw-Hill, New York, N.Y., 1967. Shinskey, F. G., "Distillation Control", p 43, McGraw-Hill, New York, N.Y., 1977. Smith, D. E., Stewart, W. S., Griffin, D. E., Hydrocarbon Process., 57(2), 99 (1978).
- xD)+lNR+ N s ]
K2 = ( a - l)[xw(l - xD)$1NR$2Ns + xD(xw$)' - I)] K3 = ( a - l)[x (1- xD)$lNR@ANs - (1 - x w ) ( l - (1 - xD)$lNR]] K4 = -a[X,$qG + (1 - X D ) $ ~ - 11 K 5 = see eq 26 L = liquid rate in rectifying section l3 = liquid flow rate of propane N = total theoretical plates NR,N s = number of plates in the rectifying and stripping sections, respectively PT = column pressure q = fraction of feed that is liquid
Received for review August 30, 1976 Accepted November 17, 1978
Removal of Vinyl Chloride from Gaseous Streams by Adsorption on Activated Carbon John F. Scamehorn" Continental Oil Company, Ponca City, Oklahoma 7460 1
A process to reduce vinyl chloride (VCM) concentrations in gaseous streams is discussed. Three steps are involved: adsorption, steam regeneration, and water drying. VCM adsorption data for dry and humid feed streams on dry carbon are presented as well as VCM adsorption data on wet carbon. The carbon bed outlet VCM concentration was shown to increase with decreasing flow rate or increasing feed concentration or beginning the adsorption step with wet carbon. Adiabatic temperatures attained during adsorption were shown to be potentially very high (>200 OC). Some aspects of the steam regeneration step are discussed. The rate of water desorption during drying was shown to be proportional to the amount of water adsorbed on the carbon with the mass transfer coefficient following an Arrhenius relationship. The outlet VCM concentration during drying is also discussed.
Introduction Vinyl chloride (VCM) was identified as a carcinogenic agent several years ago as discussed by Iammartino (1975). This finding resulted in federal government regulations
* Address correspondence to the author at the Department of Chemical Engineering,University of Texas, Austin, Texas 78712. 0019-7882/79/1118-0210$01.00/0
on VCM levels in production facilities (Federal Register, 1974) and in streams emitted to the environment (Federal Register, 1976). The VCM level in gaseous exhaust streams can be reduced by passing the vapor over activated carbon which selectively adsorbs VCM (Pate1 et al., 1976: Raduly, 1974). This paper presents work on the study of a three-step process utilizing activated carbon to reduce
t 2 1979 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 2, 1979 211
. *
IZSTIRRER
NITROGEN
i : C MC Y L I N D E R
DRAIN AIR BATH
AIR REG
I
C O L D WATER CONDENSER
U
VENT
WET-TEST METER
LEGEND THERMOCOUPLE
GAS CHROMATOGRAPH
w
MICRO V A L V E
Figure 1. System flow sheet.
gaseous emission VCM concentrations to EPA approved levels. The three steps of the process consist of (1)adsorption of the VCM on the carbon, (2) regeneration or desorption of the VCM from the carbon by passing steam through the bed, and (3) drying the carbon bed using a vacuum or a purging gas. Step 3 is then followed by step 1and the cycle recommences. During the regeneration step, the VCM would normally be compressed into a storage tank for reuse after passing through a condenser to remove most of the water vapor. A carbon adsorption process scheme in a plant would normally involve two beds; one bed would be on the adsorption step while the other would be regenerating and drying. The functions of the beds would then alternate. The number of independent and dependent variables in this three-step process is very large. Therefore, some selected variables felt to be of great importance were studied in depth in this paper, while others were given only cursory evaluation.
Experimental Equipment and Procedures A flow sheet for the experimental system is shown in Figure 1. The carbon bed consists of a 24 in. long, 2-in. N.P.S., Schedule 40, 316 S.S. pipe with a 3-in. N.P.S. jacket. A small mesh screen is welded to the bottom of the bed to hold up the carbon. A 'Iz in. 316 S.S. thermowell is placed down the center of the bed. Nine thermocouples are evenly spaced in the thermowell. All flows were downflows. Steam, hot water, and cold water or any combination thereof can be placed on the jacket. During VCM adsorption, nitrogen or air goes through the rotameter, through the preheater, and goes through or bypasses the saturator. VCM is then mixed with this stream, which then travels through the bed and then to the gas chromatograph (GC). The rate and VCM concentration of the stream are set by a dry test meter and the GC. Water vapor levels were determined by con-
densation in an ice trap. The stream was then diverted through the bed with the outlet stream from the bed being monitored for VCM concentration. A material bdance on the system resulted in the equilibrium VCM loading. All adsorption studies were done a t atmospheric pressure. To set the steam rate for steam regeneration, the steam was condensed in a graduated cylinder over a measured interval of time. During the timed run, the vapor exiting the bed is passed through the condenser and the water is collected in the knockout flask. The rate of noncondensable gas desorption can then be followed by wet test meter changes. During drying, nitrogen or air goes through the rotameter, the preheater, and the bed and is vented through either the ice bath-collection flask or the wet-dry bulb apparatus. The wet-dry bulb apparatus is used to determine humidity in the low humidity range while the ice bath-collection flask sequence is used for humidities above this range. The outlet from the bed can also be diverted to the GC to measure VCM concentrations. The carbon used in these experiments was Pittsburgh type PCB 12 X 30 activated carbon manufactured by Calgon Corporation. This is a coconut shell based carbon which has the characteristics shown in Table I (data from Calgon product specifications). Isothermal Adsorption of VCM on Dry Carbon Adsorption isotherms describing the loading of VCM on dry carbon are shown in Figure 2. The following equation, which is an empirical, modified Langmuir relationship, has been found to describe the adsorption of hydrocarbons and ethyl chloride on charcoal (Young and Crowell, 1962). bP'in L= (1) 1 + bP'1" Fitting the above equation to the isotherms in Figure 2 predicts the curves shown, which accurately fit the observed data. The values of the constants b and n as a
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 2, 1979
212
Table I. Pittsburgh PCB 12 X 30 Activated Carbon Characteristics 1150-1250
total surface area (N2, BET method), m'/g apparent density (bulk density, dense packing), g/cm2 particle density (Hg displacement), g/cm3 real density (He displacement), g/cm3 pore volume (within particle), cmZ/g voids in dense packed column, % specific heat a t 100 "C iodine number, mg/g minimum carbon tetrachloride adsorption, weight, % minimum ash, maximum, % moisture, maximum, % as packed hardness number, minimum apparent density (bulk density, dense packing), g/cm3 minimum
0.44 0.850 2.2 0.72 50.0 0.25 1200 60 6.0 3.0 92 0.44
(G
VCM
/G
CARBON
I
0 I8
Screen Size Specifications
0
x
0 16
sieve no.
% retained
+ 12 12X 16 1 6 X 20 20 X 30
0-5 20-40 40-70 10-30 0-5
-30
VCM LOADING
Figure 4. Isosteric heat of adsorption. 26'C 47.C
A 68.C
I
' 0
I
005
I
010
FEED HUMIDITY
015
IG
020
025
I Ox)
W A T E R / G DRY A I R )
Figure 5. VCM adsorption isotherms at 2.20 mmHg VCM partial pressure for a humid stream.
26.C
x 47'C
0 22
000, OI
'
'
""" io
' YCH
' " ' 1 " l 10 0
PARTIAL P R E S S U R E
'
' MH
(
"
"
"
io0
'
"",'
,030
"(I
Figure 2. VCM adsorption isotherms for dry gas on dry carbon.
0
005
010
015
020
F E E D H U M I D I T Y ( G WATER / G DRY AIR
025
030
1
Figure 6. VCM adsorption isotherms at 7.32 mmHg VCM partial pressure for a humid feed.
-1 0
20
30
40
50 60 70 80 TEMPERATURE I ' C I
90
I00
Figure 3. Value of the constants in the modified Langmuir equation.
function of temperature are shown in Figure 3. The following equation (Adamson, 1976) provides a means of calculating the isosteric heat of adsorption. The form of the equation used is
(%)/
R
The isosteric heat of adsorption ( 4 ) is a diffbrential heat of adsorption at a given loading. Equation 2 was applied to the data in Figure 2 to find the isosteric heat of adsorption shown in Figure 4. Isosteric heats of adsorption a t various loadings have been tabulated by Mantel1 (1951) for a number of organic compounds. These values vary from 9 to 16 kcal/g-mol. Thus the values obtained here are reasonable. As the loading increases, the outer adsorbed layers begin to take on the properties of the liquid adsorbate. The heat of liquefaction of VCM is 5.5 kcal/ g-mol (Matheson Co., 1961). The extrapolation to this value in Figure 4 represents the tendency toward liquid-like behavior. The resultant parameter of these plots which is of interest for design purposes is the isothermal integral heat of adsorption (41) a t a loading ( L ) . This is the total heat given off when adsorption occurs to a certain loading a t the specified temperature. This value is obtained by integrating Figure 4 as follows
Ind. Eng. Chern. Process Des. Dev., Vol. 18, No. 2, 1979
r"dL
213
281
0 26
L
JO
The effect of feed gas humidity on VCM adsorption isotherms is shown in Figures 5-7. The effect of water competing with VCM for adsorption sites is to decrease VCM loadings. The effect of humidity on VCM loadings is reduced a t higher temperatures and the effect of temperature on VCM loadings is reduced a t higher humidities. I t should be noted that the feed stream is supersaturated over some of the region covered for the 26 "C and 47 "C isotherms. This situation could easily occur in a plant and so is of practical importance. Whether these supersaturated runs are truly equilibrium isotherms might be questioned. However, outlet concentrations remained equal to inlet concentrations after the bed was saturated, so at least a steady state is reached. The crossover of the 47 "C isotherm in Figures 6 and 7 at high humidity is probably an artifact of the experimental procedure. The effect of beginning the adsorption step with some water retained on the carbon (incomplete drying) is shown in Figures 8 and 9. The retained water is uniformly concentrated on the carbon. These values of adsorption are not equilibrium values since the initially retained water would have to be dried until it would be in equilibrium with the feed for this to be the case. However, this is a slow process compared to the adsorption step. Figure 8 shows the adsorption as a function of initial retained water for B dry, high VCM partial pressure feed stream. The water retained on the bed has a strong affinity for the most active adsorption sites available on the carbon. However, as the more active sites become filled, the VCM seems able to better compete with the retained water for the less active adsorption sites. Therefore, the marginal effect of the water on VCM loadings decreases with increasing retained water level. Feed humidity affects VCM loadings in the same way as retained water as seen in Figures 5-7 with low feed humidities resulting in a larger marginal effect than higher water vapor concentrations. Figure 9 shows the adsorption as a function of initial retained water for ti humid (0.277 g of water/g of dry air), low VCM partial pressure stream. The reason this data shows the retained water level having only a small marginal effect on VCM loadings at low water concentrations is due to the high humidity level in the feed gas. The VCM loading is sharply decreased from a dry stream loading even with no initiallly retained water on the bed due to the feed humidity. When a small amount of water is retained on the bed, it is occupying active adsorption sites for which the VCM could not compete very successfully with the water vapor anyway. Therefore, little effect due to retained water is seen until a level is reached where there is a sharp decrease in VCM loading due to initially retained water. It may be that a t this point, the retained water and feed water vapor are approaching occupation of all primary adsorption sites.
0
010
005
FEED HUMIDITY
015
IG
WATER
020
/G
Figure 7. VCM adsorption isotherms a t 13.2 mmHg VCM partial pressure for a humid feed.
0
01 0 2 0 3 0 4 0 5 0 6 0 7 0 8 WATER I N I T I A L L Y O N CARBON ( G WATER / G C A R B O N !
Figure 8. VCM adsorption at 242 mmHg VCM partit.. pressure for initially wet carbon. 07;
0
0 03
5
.
002 0 01
-
0 01
0
02
03
04
05
WATER I N I T I A L L Y O N CARBON IO W A T E R / 0 CAR0ON !
Figure 9. VCM adsorption at 13.2 mmHg VCM partial pressure for a humid feed on initially wet carbon. 24,000-I
22,000-
---
- 2---
INLET V C M CONCENTRATION
>
k 20,000 0. ;18,000 -0 2 16,000L 5 14,000w
z z'
l2,OOO-
0
c
10,000-
8,000-
6,000-
Bed Outlet VCM Concentrations during Isothermal Adsorption The concentration of VCM in the gas exiting the carbon bed during adsorption is of critical importance since the government regulations define the maximum allowable concentration which can be emitted t o the atmosphere. The VCM loading on the carbon when this permissible VCM concentration is reached is an effective loading. The conditions for the adsorption step should be adjusted so that this effective loading is as close to the equilibrium or
030
325
DRY A I R )
3
0
4,000-
, ,_ , _
2,000-
0
-
A
-I
-I
-
-'-
-
-1i
Lll
- 1
I
214
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 2, 1979 30 301
I I
I I
I I
I I
I
V 20
-
30
V
28
y2
a
-
A
R?FXL G 1 G CARBON
T%%%?.E *C 57 66
I 2
F:FE"E%RE ADSORPTION NO NO
0.241 0.111
-
V
I
Ig
1 - 1
A
0 0
0
50
IW
2.28
150
0.60
200
250
xx)
TIME (PAIN)
Figure 11. Outlet VCM concentrations prior to the arrival of the adsorption zone at the bed outlet.
tration breakthrough is very sharp and the effective loading (considering a 10 ppmv VCM level permissible) is about 92% of the equilibrium loading. As seen in this plot, a narrow adsorption zone moves through the bed. Ahead of this zone, VCM concentration levels are low. The effect of feed superficial linear velocity and VCM concentration on bed outlet VCM concentrations is shown in Figure 11. This data is plotted up to the point when the high concentration zone reaches the bed exit. The loading in the bed at the point when this adsorption zone reaches the outlet depends little on flow rate (it is close to the equilibrium loading). However, this high concentration zone reaches the bed outlet sooner a t higher flow rates. Therefore, it is the outlet concentration immediately prior to the arrival of the adsorption zone which is of interest, not this concentration at any particular time. The VCM concentration increases as the adsorption zone approaches the bed exit because there is less carbon contact time for the vapor leaving the adsorption zone, and the carbon the gas contacts is partially saturated with VCM and therefore has a reduced capacity. The increase in the outlet VCM concentration as the feed concentration is increased a t constant flow rate as seen in Figure 11 is predictable from these considerations. However, the sharp decrease in these VCM concentration levels observed as the superficial velocity was increased is the opposite effect expected from carbon contact times considerations alone. The observed effect is probably due to channeling a t low flow rates where a large portion of the gas travels through the bed through paths of small resistance so uniform contact of the carbon across the bed diameter is not obtained. As the flow rate is increased, these channels will accommodate a smaller fraction of the gas flow, resulting in more efficient adsorption. Decreased resistance to mass transfer a t the higher flow rates due to increased turbulence may also explain this data. This data shows that it is important to avoid low linear flow rates during the adsorption step. The effect of leaving water retained on the carbon a t the beginning of the adsorption step on the bed outlet VCM concentration is shown in Figure 12. All runs were a t a superficial velocity of 2.3 ft./min based on nitrogen. Runs 1and 2 were made by loading dry carbon with a dry feed stream with a VCM partial pressure of 439 mmHg and regenerating in a normal manner (which will be described
I
I
i
20
A
x
I
I
I
5
&I
. & I -
10 I5 TIME ( M I N I
RUNS 3,4,5 WERE ON BEDS THAT WERE FREED OF V C Y 8Y AN E X T R A REGENERATION
I20
1
I
25
Figure 12. Outlet VCM concentrations for partially dry carbon prior to the arrival of the adsorption zone at the bed outlet.
later). This was followed by a drying step not carried to completion. The adsorption step then performed resulted in the data shown in Figure 12. Runs 3,4, and 5 were made by loading and regenerating as in runs 1and 2; however, the carbon was then completely dried. The carbon was then loaded with water by performing a standard regeneration run and a partial drying step was performed. The adsorption resulting in the reported data was then performed. The purpose of completely drying the bed in the latter runs was to remove all the VCM from the carbon. The bed outlet VCM concentrations for the runs where the carbon was VCM free before adsorption were extremely low, even with very high residual water levels, while those concentrations for normal runs were much higher. This indicates that almost all the VCM seen in the bed outlet stream prior to the arrival of the high concentration adsorption zone for wet carbon is due to VCM trapped by the residual water on the bed, not to leakage of feed VCM through the carbon. The VCM is probably trapped in pores in the carbon and as the feed stream moves through the bed, it desorbs some of this water from the carbon, allowing trapped VCM to also escape into the gas. This mechanism is supported by the reduction in outlet VCM concentration with time; the opposite effect as seen on dry carbon. This is probably because less carbon is contacted downstream of the adsorption zone as the run progresses, resulting in fewer pores being opened due to water desorption. Therefore, if a high enough degree of steam superheat is used in the steam regeneration step, few pores may be covered, resulting in the outlet VCM concentration during adsorption being below the EPA standard prior to the arrival of the adsorption zone a t the bed exit. During the course of these adsorption experiments, standard adsorption runs were interspersed to measure carbon degradation levels. No significant decrease in adsorption capacity was observed over the 33-cycle period studied. Adiabatic Adsorption of VCM The adsorption step in a commercial unit could take place under essentially adiabatic conditions if no provision for external cooling is made. An energy balance to compute the adiabatic temperature reached at a point on the carbon for a dry feed and initially dry carbon is (4) The simultaneous solution of eq 1, 3, and 4 will yield an
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 2, 1979
A
0
c 0
(56 i5B I5 6 933
318
215
2483
37 8 ,489
,30 2483 2483
37 8
i
i
i Oowl
1
0 01
I
01
1
2
IO
I
i
FEED YCM VOLUME FRACTION
Figure 13. Adiabatic temperatures during adsorption.
i
0
--•
0
adiabatic temperature and VCM loading for a given set of conditions. The heat capacity of VCM was assumed to be that of VCM in the vapor phase, an assumption which has little effect on the results. The adiabatic temperature is the most important variable resulting from these equations since at high temperatures deleterious reactions may occur (e.g., dehydrochlorination of VCM, acetylene formation, and VCM polymerization). The adiabatic temperature is shown in Figure 13 as a function of VCM volume fraction in the feed for several conditions. It can be seen that very high temperatures (well over 200 "C in some cases) can be attained a t a high VCM concentration in the feed. Therefore, adiabatic adsorption on a dry carbon bed with a dry feed is not recommended. There are several ways of bypassing the problems presented by the high heat of adsorption of VCM. The use of external cooling during carbon adsorption of VCM has been proposed by Raduly (1974). In this case, the isothermal adsorption isotherms can be used to predict VCM loadings a t the coolant temperature. However, the provisions for external cooling greatly increase the complexity and cost of the carbon bed. Another scheme to maintain low temperatures is to leave the carbon partially wet prior to adsorption. When the VCM adsorbs, desorption of some of the water keeps the temperature low. Figures 8 and 9 show that a t low residual water levels, little reduction in loading is due to the water. Therefore, by optimizing the initial water content of the carbon, substantially greater VCM loadings may be attained than would be observed in an initially dry adiabatic adsorber in addition to the benefits from the temperature reduction. This optimization would need to be done experimentally in an adiabatic unit. The disadvantage of this processing scheme is the higher bed outlet VCM concentrations as seen in Figure 12. This may necessitate a small, initially dry clean-up bed to reach regulation VCM concentrations.
Steam Regeneration After the adsorption step, the VCM is desorbed from the carbon bed by displacement with steam. Because of the difficulties of maintaining constant flow rates and temperatures of saturated steam in a small pilot unit, only some general considerations were established for this step. A VCM desorption curve was established using saturated steam a t atmospheric pressure a t a standard steam rate (0.0163 g of steam/g of carbon min) for a VCM saturated bed initially at 21 "C. This same steam rate was then applied to a preheated bed (100 OC) a t the same initial condition previous to preheating. The resulting VCM desorption curves are shown in Figure 14 with a slight correction to the preheated run to the total amount of VCM desorbed for easier comparison of the runs. It may
'
IO
1
I
I
I
I
20
30
40
50
60
TIME ( M I N )
Figure 14. Desorbed gas volume during steam regeneration.
be concluded that the heat put into the bed by the steam contributes to the total steam requirements for regeneration because of the difference between the preheated and nonpreheated runs. However, the preheated regeneration still took approximately half as long to desorb the VCM as the normal regeneration, indicating that the purging effect of the steam vapor is also important. Water Drying from Carbon If the carbon bed maintains a uniform water content and temperature during drying, using a drying gas, the entire bed can be viewed as an element about which balances can be written. The following equations represent material balances F(CGoUT- CG") = Kw Wc (5)
F(CGoUTIn all the runs made, CGIN was zero, so CGoUT will be referred to as CG. The above equations can be solved for water concentration in the vapor and adsorbed on the carbon as a function of time, if the rate of water desorption is known. If the rate of desorption is proportional to the amount of water adsorbed, the following equations result Kw = KoCL (7)
Equation 10 predicts that (In CG)vs. t will yield a straight line with slope -KO. The water vapor content of the outlet vapor from the bed and corresponding average temperatures a t the middle of the bed are shown in Figure 15 for a typical run. Little axial temperature gradient was observed in this work. The temperature can be seen to remain fairly constant from 20 to 80 min. During this nearly isothermal period, In CG vs. time is linear. This indicates that eq 7 describes the behavior of the system. If the heat of desorption is produced uniformly across the bed cross section, a parabolic temperature profile would be predicted. However, the higher temperatures a t the wall result in a greater rate of desorption there than in the middle of the bed. These two effects predict an average bed temperature to be closer
216
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 2, 1979 70,
I
I
I
I
I
"
'
,
01
TEMPERATURE JACUET
60'C
--
50'C
40'C
30'C
I
I
I
A OTHERS
..
*.
.' .
t I
001 0
I
'
100 DRYING TIME ( M I N U T E S )
AIR
Np
--
7
1
-0. 0 .
I
MEDIUM
_ _- - -l
t
ZO'C DRYING
1 I
I
I
200
Figure 15. Bed temperature and water concentration in vapor during drying.
to the temperature a t the middle of the bed than to the wall temperature. Convective eddies inside the bed help to level out the temperature profile even more. Also the inner surface of the bed is a t a lower temperature than the jacket temperature due to conductive temperature gradients necessary to allow heat transfer through the wall. All of these effects should produce a radial temperature profile flat enough such that the bed temperature at the center can be used as an average bed temperature. The value of the overall mass transfer coefficient ( K O ) was determined as a function of temperature from the slopes of plots like Figure 15 during their near isothermal periods. The resulting values are presented in an Arrhenius plot in Figure 16. The runs made with air a t the same flow rate can be seen to result in about the same values of KOas the nitrogen runs. Figure 16 shows the value of KOfor several different flow rates with a nitrogen feed. The data indicates that KOis independent of flow rate except a t very low flow rates. This implies that mass transfer resistance in the vapor phase is small except when equilibrium between adsorbed and vapor phase water is closely approached. However, the temperature sensitivity observed is much higher than normally expected for mass transfer operations. Therefore, it seems likely that no simple mechanism can describe this drying process, and eq 7 should be viewed as an empirical relationship. In commercial units, the drying would probably be in an adiabatic bed using a hot feed gas or vacuum drying. The additional use of external heating coils is also possible. The mass transfer rate as a function of temperature is necessary to design this step. The important conclusion from the isothermal data obtained here is that the rate of mass transfer drops so sharply with temperature that high temperatures must be maintained by some means to prevent the drying step from taking excessive time. However, it is difficult a t reasonable drying gas flow rates and temperatures or external heat transfer areas to put the required heat into the system. A more realistic solution is the use of superheated steam in the regeneration step. This has the dual advantage that less steam remains adsorbed, and the final bed temperature is higher a t the
TEMPERATURE ~ O K I - I ~ I O ~
Figure 16. Arrhenius plot of the overall mass transfer coefficient.
T I M E (MIN)
Figure 17. Outlet VCM concentrations during drying for a typical run.
end of regeneration. When the bed is exposed to vacuum or drying gas, the latent heat would provide energy for steam desorption. Careful determination of process conditions could result in a desired water loading and bed temperature after a short drying period. Outlet VCM Concentrations during Gas Drying The outlet VCM concentration during gas drying is important since this drying stream will need to be further processed if the level is high. Figure 17 shows this VCM concentration as a function of time for a typical drying run. The absolute value of these concentrations would not be extrapolatable to an adiabatic drying step. However, the shape of the concentration curve can be seen to be similar to that of water vapor concentration during drying (Figure 15). This implies that the VCM desorption rate is approximately proportional to the water desorption rate. This is consistent with the mechanism discussed earlier in relation to the VCM adsorption step where it was proposed that as water is stripped from the carbon, pores with trapped VCM are opened, allowing the VCM to desorb to the vapor phase. As with outlet VCM concentrations during ad-
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 2, 1979
sorption, this VCM level during drying may become much lower as the degree of steam superheat during regeneration increases. Conclusions Based on this work, the following processing scheme is recommended. The carbon should have some residual water on it a t the beginning of adsorption. After the adiabatic adsorption, the steam regeneration step should be done with superheated steam. The drying step may be done with either a vacuum or a drying gas. The amount of residual water on the bed at the beginning of adsorption should be optimized to maximize VCM loadings while maintaining low temperatures in the bed. This amount of water can be attained by the superheat of the regeneration steam and the drying conditions. The outlet gas from the adsorption step may need to be diverted to a small, dry bed before release to the atmosphere. The outlet vapor from the drying step (when a drying gas is used) may need to be diverted to the operating adsorption bed because of high VCM concentrations. However, these extra steps may be avoidable depending on the specific conditions used. I t is not desirable to set up exact optimum conditions because the capabilities of each production facility will differ. For instance, the degree of vacuum or the superheat of the available steam may vary considerably. Also, the bed heat loss and, therefore, proximity to ideal adiabatic behavior will be an important factor. The data presented should predict the general range of optimum operating conditions for a commercial unit. Acknowledgment The following people are acknowledged for aiding the author in this study: Kang Yang, D. V. Porchey, L. M. Henton, J. D. Reedy, R. C. Lindberg, and J. A. Wingrave. Continental Oil Company is thanked for allowing publication of this work.
217
Nomenclature b = constant, g of VCM/(g of carbon (mmHg)'/") CG = water content in the vapor, g of water/ft3 CG" = water content in the inlet vapor, g of water/ft3 C G = water ~ ~ content ~ in the outlet vapor, g of water/ft3 CL = amount of water adsorbed, g of water/g of carbon CL' = CL at zero time, g of water/g of carbon C,, = gas heat capacity, kcal/g K C,c = carbon heat capacity, kcal/g K C p V c M = VCM heat capacity, kcal/g K D = mass diluant/mass VCM, g / g F = vapor flow rate, ft3/min KO = overall mass transfer coefficient, min-' Kw = rate of water desorption, g of water/g of carbon min L = VCM loading on carbon, g of VCM/g of carbon MVCM = molecular weight of VCM, g/g-mol n = constant P = partial pressure of VCM, mmHg q = isosteric heat of adsorption, kcal/g-mol of VCM 41 = integral heat of adsorption, kcal/g-mol of VCM R = gas constant, kcal/g-mol K t = time, min T = absolute temperature, K Tf = feed gas temperature, K To = initial bed temperature, K W , = amount of carbon in bed, g of carbon L i t e r a t u r e Cited Adamson, A. W., "Physical Chemistry of Surfaces", 3rd ed, p 594, WileyInterscience, New York, N.Y., 1976. Fed. Regist,, 39,35890 (1974). Fed. Regist., 41, 46560 (1976). Iammartino, N. R., Chem. Eng., 82, 25 (Nov 24, 1975). Mantell, C. L., "Adsorption", pp 601-603, McGraw-Hill, New York and London, 1951. Matheson, Co., "Matheson Gas Data Bock", p 413, East Rutherford, N.J., 1961. Patel, P. J., Thompson, C. G., Hourihan, E. J., Stutts, C. S., U S . Patent 3984218 (Oct 5, 1976). Raduly, L., U.S. Patent 3 796 023 (March 12, 1974). Young, D. M., Crowell, A. D., "physical Adswption of Gases", p 1IO, ButterswMths, Washington, D.C., 1962.
Received f o r reuieul April 14, 1977 Accepted October 23, 1978
Optimum Behavior of a Third-Order Process under Feedback Control Thomas W. Weber* Department o f Chemical Engineering, State University o f New York a t Buffalo, Buffalo, New York 14214
Mohan Bhalodia Exxon Co. U.S.A., Linden, New Jersey
The behavior of a third-order overdamped process under proportional-integral control was studied using the integral of the square of the error (ISE) as the performance criterion. The process is characterized by its maximum gain and ultimate period, as found by the Continuous Cycling Method (CCM) of controller tuning by Ziegler and Nichols (1942) rather than by its time constants as used by Jackson (1958). The CCM performance was compared with the optimum for four different disturbance locations. For some processes, the CCM leads to unstable behavior, but for many processes, the CCM gives quite satisfactory results when disturbances occur near the end of the process elements. The CCM controller gain recommendation is conservative and an excellent compromise, but the reset time recommendation is about half as large as that dictated by the ISE. The optimum ISE varies with about the inverse square of the critical frequency, but is nearly independent of the maximum gain.
Introduction A number of different models have been used to characterize the behavior of processes for the purpose of estimating suitable controller settings. The simplest model 0019-7882/79/1118-0217$01.00/0
consists of a first-order element plus a pure time delay, and has been used in a number of studies (Cohen and Coon, 1953; Murrill and Smith, 1966; Lopez et al., 1967; Miller et al., 1967; Smith and Murrill, 1966). These studies 0 1979 American Chemical Society
