Computer Simulation of Plant-Scale Multicolumn Adsorption Processes Under Periodic Countercurrent Operation Juh Wah Chen,l Fay 1. Cunningham,2 and John A. Buege The Upjohn Co., Kalamazoo, M I 49001
A simplified practical method is presented for calculating performance of multicolumn adsorption operations where the columns move periodically countercurrent to a continuous liquid flow. The model derived assumes homogeneous sections or “tanks” in series in the fixed bed column. The number of “tanks” assumed i s a measure of the degree of backmixing. The solutions of the differential equations involved were carried out on a digital computer. By equilibrium and mass transfer relationships determined in the laboratory, the approximate number of “tanks” assumed to accurately simulate the process was selected by comparison of computer calculations with experimental pilot plant data. Proposed plant operating schedules were then calculated to determine the approximate optimum. The concentration in the effluent from each plant column at start-up was compared with the computer prediction and, after an adjustment of the number of “tanks” assumed, agreed well.
T h e scale-up of a column adsorption process from benchscale experimental data to plant-size equipment by simulation techniques was reported previously (Chen et al., 1968). A mathematical model for fixed-bed operation which assumes a n ideal plug-flow condition was developed. B y use of this model in conjunction with laboratory information on mass transfer coefficients and the equilibrium relationship, it was possible to predict the performance of a column adsorption process accurately enough for single-pass operation. However, higher efficiency would be obtained in a multicolumn adsorption process operated under periodic countercurrent conditions in which fluid phase flows continuously from one direction, and the adsorption columns move periodically in the opposite direction, Figure 1 shows how a multicolumn adsorption process would be operated in this manner. Suppose that four columns, A, B, C, and D, are operated in series under a constant flow rate for a certain period of time. The lead column (column A) then would be removed for elution and the remaining three columns advanced one position so that B now becomes the lead column, C moves to the second position, etc., and a freshly eluted column is placed in the trail position. This would complete one cycle of operation. When the operation proceeds under this scheme long enough, a periodic condition would be reached under a given set of operating conditions. To study and optimize the operating scheme described above under different operating conditions and to predict the overall performance of a process, a computer simulation is desirable. Such a simulation would achieve great savings in time and labor, would enable study in detail and with assurance of constancy of key variables. The plug-flow model referred to above is inadequate since, although the single-pass error is small, the cumulative error under periodic countercurrent operation would be intolerable. Use of the plug-flow
model would also unnecessarily complicate the computation procedures for a periodic countercurrent operation. Mathematical Model (“Tanks-in-Series”)
A packed column without backmixing can be considered as a plug-flow reactor. A plug-flow reactor can then be visualized as an infinite number of equal-size, small, completely agitated “tanks” operated in series (Levenspiel, 1962). However, in any industrial-scale column a certain degree of backmixing will be encountered, the degree of mixing varying with the size of column, the linear velocity, the size and shape of the solid adsorbent used, and the efficiency of liquid distribution. Ordinarily, the intensity of backmixing in a packed column can be described using dispersion coefficients determined by a tracer stimulation technique (Levenspiel and Smith, 1957). This technique cannot be applied easily with adsorption columns, however, because it is difficult to find a tracer that does not show some interaction with the solid adsorbent and that does not require data with a degree of precision frequently difficult to obtain, particularly a t large scale. An alternate method which can be used to measure the intensity of backmixing in a fixed-bed adsorption column is to assume a certain number of equal-volume agitated “tanks” operated in series. The effluent-concentration history from each “tank” can then be evaluated on a computer. The calculated values from the last “tank” (the point at which the response is being measured) can then be compared with the experimental data for a given number of “tanks.” If the values match well with each other, the number of “tanks” assumed can be used as a measure of the intensity of the backmixing. If they do not match, the computation can be repeated a t another selected “tank” number until a suitable match is obtained. The larger the number of “tanks” required for a n accurate simulation, the less backmixinn there must be. The advantages of this “tanks-in-series” model are threefold: First, only one computer program is needed to simulate the column adsorption process for different sizes of columns; I
’
Present address, Of Engineering &? Southern Illinois University, Carbondale, IL 62901. * T o whom correspondence should be addressed. 430
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 3, 1972
second, it readily applies to countercurrent periodic operating cycles; and third, i t will keep a chronological record of the liquid-phase concentration and average adsorbent loading of each column. Figure 2 shows schematic diagrams of the previously derived differential bed segment model and the “tanksin-series” model described here. Suppose there are m number of columns on stream for a n adsorption process and each column is packed with It’ amount of solid adsorbent. If each column is subdivided into g number of equal-volume agitated “tanks,” then the total number of agitated “tanks” operated in series is ( m X 9 ) ; and each “tank” contains W / g or w amount of solid adsorbent. The following equations can then be used to express the adsorption process around the n t h “tank.” The continuity equation is (Chen e t al., 1964)
F
= volumetric flow rate, l./day =
K,
ELUATE
E L U A N U FEEDo
CYCLE 2
liquid volume per “tank,” liters = weight of adsorbent per “tank,” kg = liquid concentration of solute, units/l. = liquid concentration of solute in equilibrium with solute on adsorbent, units/l. = overall mass transfer coefficient, units solute adsorbed/(kg of adsorbent) (time in days) (concentration driving force, units/l.)
r
ELUATE
3
Ti
ELUANT
1. CYCLE
where
w C, C,*
FEED
STREAM SPENT
Figure 1 . Multicolumn adsorption process
The rate equation is
where q , = concentration of solute on adsorbent, unitsjkg The empirical equations for the equilibrium relationship of solute X and adsorbent Y previously determined (Chen e t al., 1968) a t p H 8 and 45OC are:
C,*
=
6.0 X 10-5 y, for y n
5 20
(34
and
C,*
= 2.74 X 10-8
qn3.57
for qn
> 20
=
1640 - 3700 q n / q m for q,/qm 5 0.4
(44
and Ka
=
264 - 260 q,/q“ for 1.0 2 qn/q”
> 0.4
TANKS.IU~IERIES MODEL
(3b)
The empirical equations for K,, also previously determined, are :
K,
TO N E X T COLUMN DIFFERENTIAL BED SEGMENT MODEL
(4b)
Rhere q” is the adsorbent’ loading in equilibrium with the feed concentration. Equations 1-4 are the relationships which constitute the mathematical model; their use permits the prediction of the performance of multiple-column adsorption processes a t a n y cycle of operation. Computation. A digital computer program was written in FORTRAN language for the multicolumn adsorption process under periodic countercurrent’ operation. The computation cycle starts with n = 1, and t = 0 and calculates C, and y, through to n = m X g a t the final time. The computer prints out the calculated values for effluent concentration and average loading of each “tank” of each column at selected time intervals. Reliable and stable result’s were
Figure 2. Schematic diagram of differential b e d segment model and “tanks-in-series’’ model
obtained a t a time mesh of 0.0025 day. It required about 2 hr of machine time on a n IB1\1-1410 computer to complete a one-day operating cycle consibting of four adsorption columns operated in series. each column being subdivided into fiveequal-size agitated “tanks.” Only 20 m m of machine time was needed to do the same calculation on a n IBM-7040. Xn IBSI360/30 required about 15 min. Simulation Results
To be sure that the “tanks-in-series” model would simulate the adsorption process, the model was computed for the adsorption of solute X on adsorbent Y under the same conditions as the pilot plant run reported previously, and the results were compared. The concentration-tlme curves calculated by subdividing a 24-in. diameter by 14-ft long adsorption column into 4, 8, 16, and infinite number equalsize agitated “tanks” are shown in Figure 3. To obtain the curve for a n infinite number of “tanks,” the model deInd. Eng. Chern. Process Des. Develop., Vol. l l , No. 3, 1972
431
1.1 1.4[
j
0.8
$
0.7’.
.
0
0.5
. .
0.4
.
u= 0.6
f
(how.)
Figure 3. Effect of number of “tanks” (backmixing) on breakthrough curves
0.3
.
0.2
0
N = no. of equal volume “tanks”
0.1
0.2
0.3
0.4 f
Cz = concentration of solute in liquid phose at height z ( 1 4 ft) 0 = experimental points on 2 4 in. X 1 4 ft pilot column
0.5
ACOLUMN C (TANK 1 5 ) 0.7 COLUMN D I T A N K P O I
0.6
(dvl
Figure 5. Effluent concentrations from each column during the eighth cycle (essentially periodic conditions)
-
Temp, 45”C, pH 8 Cycle time, 0.7 d a y
Feed concn, 1.5 units/l. Flow rate, 1 0 0 I./min Height of each column, 10 f t
140
.120
-
1w
-80
f -
bo
40
I
1
COL. 4 3
5
7
9
“TANK”
11
13
IS
17
19
NUMBER
Figure 4. Computed concentration and loading profile across columns after reaching periodic conditions Feed concn, 1.5 units/l. Flow rate, 100 I./min Height of each column, 10 ft Temp, 45”C, pH 8
Schedule no. 1 Length of cycle, h r 16 Feed concentrations (units/l.) 1 0 Flow rate, l./min 100 Height of column bed, ft 10 KO.of columns in series 4 Total no. of “tanks” 20 S o . of cycles computed 4 Av loading in lead column, units/kg 86 Spent stream loss at end of computation, yo E O
2 16
3 20
4 16
5 16
1.5 100 10 4 20 8
1.5 166.7 12.5 4 20 4
1.5 150 12.5 4 20 5
2.0 100 12.5 4 20 5
125
130
122
121
-0
6.0
IVO
-0
Cycle time, 0.7 day No. of columns, 4 Column diam, 4 0 in.
scribed previously was used. This model assumes a differential bed segment. It can be seen that the best simulation was attained a t something over 16 “tanks” operating in series, perhaps of the order of 20 “tanks.” Since the calculations for 20 “tanks” in series approached the capacity of the largest computer available to us a t that time (JB1\1-1410), 20 “tanks” were chosen to study further the proposed production-scale operations. Initially four plant columns, 40 in. in diameter and with about a 12-ft bed depth, would be on stream in series a t one time, so each column was broken down into five “tanks” to make the total of 20 for calculation purposes. Figure 4 shows typical computergenerated curves of solution concentration and adsorbent loading profiles across a series of four of these columns after operation became periodic, where the difference between cycles is negligible. Typical effluent concentration and adsorbent-loading curves with the same operating conditions as a function of time (within a cycle) are shown in Figures 5 and 6, again a t essentially periodic operation (eight cycles). A number of proposed alternate operating schedules were then computed and the most suitable chosen for plant start-up. Typical results of these calculations are shown in Table I. 432
Table 1. Computation Results for Adsorption Process at Different Schedules Using Five Tanks per Column
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 3, 1 9 7 2
Upon start-up, actual plant data was compared with the calculated data under the same operating conditions, again with five “tanks” per column. This comparison is shown in Figure 7 . As can be seen, the calculated effluent concentration from column A matches the actual performance fairly well considering plant assay and sampling variability but drifts off increasingly with subsequent columns. If four ‘‘tanks” per column are used in the calculations, however, the data match quite well (Figure 7). This is attributed to a slightly larger degree of backmising in the production columns compared with the pilot scale columns. Four ‘Yanks” per column were used for all subsequent calculations. An adjustment such as this limits the usefulness of this method somewhat, particularly with regard to scale-up. Once the simulation has been established, however, the method can be readily used to study process variables. Discussion
This semiempirical method of simulating a multicolumn adsorption process operated periodically, while not highly theoretical, has afforded a simple and practical method of designing and determining the best way to operate a large production facility. The start-up problems associated with a complex production plant for a highly valuable pharmaceutical product were considerably reduced as a result of its use.
I4O
r COLUMN
COLUMN
0
C (TANK IS)
D (TANKM)
Figure 6. Average loading on each column during eighth cycle (essentially periodic conditions) Feed concn, 1.5 unitr/l. Flow rate, 100 I./min Height of each column, 10 f t
Temp, 45OC, p H 8 Cycle time, 0.7 d a y
results are actually more meaningful in some respects as well as more rapid and less costly. Another important advantage is the ready availability of a method for continued adjustment of the process ovcr the years as changes in variables are proposed or imposed. The method has been in continued extensive use to optimize process variables such as flow rate, temperature, cycle time, and amount of adsorbent. It has also been used to evaluate effects on the process of changes in operating schedules and concentration of product in the feed stream. The effect of alternate adsorbents on plant operations has been calculated after the equilibrium and mass transfer rate data were gathered in the laboratory. Backmixing is a serious problem in many fixed-bed operations. The usual approaches with dispersion coefficients are time-consuming and sometimes very difficult to quantitate meaningfully, particularly a t plant scale. This semiempirical method bypasses many of these problems and allows a simplified study of degree of backmixing. The economic importance of approaching plug flow can be determined readily and the need for, versus the cost of, special column internals such as distributors or redistributors can be evaluated.
Conclusions
Figure 7. Effluent concentrations at production column start-up 0 Column A X Column B A Column C V Column D -Computer ---Computer
Rate, 100 I./min Ph, a Temp, 45OC
prediction based on 5 “tanks”/column prediction based on 4 “tanks”/column
I n fact, the only real problems encountered were purely mechanical and were resolved within three months. I n contrast, a similarly complex plant for another product encountered serious process problems for over one year. Great savings in time and money were achieved through the use of this simulation by the elimination of a n extensive laboratory or pilot program which would require eight or more cycles for each change in operating conditions studied. Experimental work in this particular area is very timeconsuming and difficult t o evaluate. Since composition constancy of this particular feed stream could not be assured over a long enough period of time to study experimentally small differences in operating conditions, the simulation
A mathematical model was derived for multicolumn adsorption processes where the columns move periodically countercurrent to a continuous liquid-phase flow. The model assumes a number of homogeneous sections or “tanks” in series in each column. By use of previously determined equilibrium and mass transfer relationships, computer calculations were made with different numbers of Litanks” per column and compared with pilot plant data. An approximate number of “tanks” per column was selected (five) and predictions of liquid-phase concentration and solid-phase loading mere made for several potential sets of operating conditions for the full-scale plant. The selected conditions when applied in the plant at start-up gave results matching the simulation well, after an adjustment of the number of per column from five to four. The method has been in continual use since plant start-up to optimize process variables and evaluate alternate adsorbents. The method has potential as a simplified means of simulating backmixing in many fixed-bed operations. Nomenclature
C = concentration of solute in fluid phase a t t and Z, units/l. Co = initial concentration of feed, units/l. C* = concentration of solute in fluid phase in equilibrium with q, units/l. C, = concentration a t position 2 in column, units/l. D = diameter of column, ft F = volumetric flow rate, l./day g = number of “tanks” assumed for each column H = height of column, ft K , = overall mass transfer coefficient, (units of solute adsorbed)/ (kg of adsorbent) (time, days) (concentration driving force, units/l.) m = number of columns on stream Q = concentration of solute on adsorbent, units/kg t = time, h r V = volume of liquid per “tank,” liters W = weight of solid adsorbent per column, kg w = weight of adsorbent per “tank,” kg X = solute, measured in units Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 3, 1972
433
Y = adsorbent 2 = position in column, ft q” = concentration of solute on adsorbent which is in equilib-
rium with Ca References
Chen, J. W., Belter, P. A., French, G. H., “Simulations of Resin Ion Exchange Processes in Agitated Beds,” reprint, AIChE annual meeting, Boston, MA December 1964.
Chen, J. W., Buege, J. A., Cunningham, F. L., Northam, J. I., Ind. Eng. Chem. Process Des. Develop., 7, 26 (1968). Levenspiel, O., “Chemical Reaction Engineering,” Wiley, New York, IVY, 1962. Levenspiel, O., Smith, W. K., Chem. Eng. Sci., 6 , 227 (1957). RECEIVED for review September 9, 1971 ACCEPTEDApril 17, 1972 Presented at the Division of Industrial and Engineering Chemistry, 154th Meeting, American Chemical Society, Chicago, IL, September 1967.
Removal and Recovery of NO, from Nitric Acid Plant Tail Gas by Adsorption on Molecular Sieves Winfried Joithe,’ Alexis T. Bell,’ and Scott Lynn Department of Chemical Engineering, University of California, Berkeley, C A 94720
Adsorption of NO, on molecular sieves offers a convenient method for removing and recovering NO, from the tail gas of a nitric acid plant. This work examined the adsorption of NO, NOz, and NO/N02 mixtures from a dry carrier gas. The results show that molecular sieves have a high capacity for NO*. Mixtures of NO and NO2 can also b e adsorbed provided that oxygen is present in the carrier gas to oxidize the NO. After exposure of the sieves to NO, in a carrier gas saturated with waier they can b e reactivated wiihout a loss of loading capacity for adsorbing NO, from a dry carrier gas provided the reactivation process has desorbed all of the water vapor.The introduction of an adsorption unit into the flow sheet of a nitric acid plant has been considered and the design of such a unit for a 12O-ton/day plant is discussed. Rough economic esiimates suggest that the costs for the unit can b e recovered in two to four years through increased production.
D u r i n g the production of nitric acid (Chilton, 1968), nitrogen dioxide is absorbed in water by the process 3x02
+ H20
+
2HK03
+ NO
(1)
The nitric oxide formed is reoxidized to nitrogen dioxide by air introduced into the system for this purpose. Absorption and oxidation continue up the absorption tower until the gas stream contains only a few tenths of 1% of the oxides of nitrogen (NO,) a t which point further recovery becomes uneconomical. The tail gas, having a composition similar to that given in Table I, must be treated to recover or destroy the SO, before the gas is released to the atmosphere. The economics of tail gas treatment suggests t h a t recovery of the nitrogen oxides in a form which could be recycled to the absorber would represent the most favorable process. Absorption and adsorption are the only feasible means for achieving a recovery of SO,, and absorption does not appear to be practical a t the concentration levels in question. -4 number of solid materials have been reported in the literature as adsorbents for oxides of nitrogen (Bartok et al., 1969). Those materials on which a reversible adsorption has been obtained include silica gel, alumina, char, and molecular sieves. Of these materials only char and molecular sieves have Present address, Deutsche Shell A.G., Hamburg, West Germany. To whom correspondence should be addressed. 434
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 3, 1972
Table 1. Characteristic of Nitric Acid Plant Tail Gas Physical conditions: Pressure = 7.26 atm; temp = 30°C; mass flow rate = 41,200 lb/hr Species
NO NO2 HzO 0 2 h’2
HiiOo
Concn, vol
yo
0.1 0.15 0.6 3.0 96.15 =o. 00
a sufficiently high adsorption capacity to warrant serious consideration. The use of char as a n adsorbent for nitrogen oxides has not been considered extensively because of potential fire or explosion hazards (Ganz, 1958). Molecular sieves have shown a high adsorption capacity for nitrogen dioxide but essentially no capacity for adsorbing nitric oxide by itself. I n the presence of oxygen, though, molecular sieves can catalyze the oxidation of nitric oxide to nitrogen dioxide which will subsequently adsorb. A recent report of Sundaresan et al. (1967) has discussed the use of molecular sieves for the treatment of nitric acid tail gas. I n these studies the tail gas was simulated by a nitrogen stream containing 3.5y0oxygen to which was added 1800-2600 ppm of nitric oxide. h synthetic zeolite was used
