An experimental study of the countercurrent moving-bed chromatographic reactor

Chemical Engmeering Science, Vol 44, No. 9, pp Primed in Great Britain.

AN

1771-1781, 19119

EXPERIMENTAL MOVING-BED

0

nlw-25w/x9 63M+oM 1989 Pergamon Press

plc

STUDY OF THE COUNTERCURRENT CHROMATOGRAPHIC REACTOR

BARRY B. FISH and ROBERT W. CARR’ Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455,

(Received 20 October

U.S.A.

1988, accepted 1 February 1989)

Abstract-The results of an experimental investigation of the performance of a countercurrent moving-bed chromatographic reactor are presented. The test reaction is the hydrogenation of 1,3,5-trimethylbcnzene vapor at 190°C by F’t supported on 3(t50 mesh Al,Os. Simultaneousreaction and separation of the reactant and product, 1,3,5-trimethylcyclohexane, occur during the continuous contacting, giving good product purity. Coqversions can, in some cases, significantly exceed the equilibrium conversion expected in a tubular reactor operating at the same temperature and feed conditions. The dependence of product purity and conversion upon experimental conditions is investigated. A dispersionless, adsorption equilibrium model is presented for the two cases of a linear isotherm and a Langmuir isotherm. The trends of observed reactor behavior with changes in feed rate and feed position are satisfactorily accounted for by the models.

INTRODUCTION

Much of the research on countercurrent moving-bed chromatographic reactors (CMCRs) has been concerned with the development of mathematical models. The work has resulted in interesting predictions of reactor behavior and performance. Model development has generally assumed plug flow of both the solids and counterpropagating carrier gas in an isothermal reactor, with various assumptions about adsorption rates and isotherms, reaction kinetics and dispersion. An interesting feature of dispersionless, adsorption equilibrium models is the predicted existence of internal and boundary concentration discontinuities. In the first theoretical treatment, the reactant was fed at the bottom of the reactor, in which an irreversible first-order solid-catalyzed reaction occurred (Viswanathan and Aris, 1974). In the ideal case of no dispersion and instantaneous adsorption equilibrium, described by a Langmuir isotherm, the model predicted situations where the reaction can be driven to completion in a finite length of bed, with the recovery of a pure product. Similar conclusions were reached when a linear adsorption isotherm was applied to a similar reactor using a simplified model (Takeuchi and Uraguchi, 1976a, b). These authors later suggested that an exhausting section should be used to circumvent loss of reactant adsorbed on the catalyst in the bottom feed configuration (Takeuchi and Uraguchi, 1977a). Their linear models showed that the CMCR can be used to improve the selectivity of intermediate products in first-order consecutive reactions compared with fixed-bed reactors, and to exceed the equilibrium conversion in reversible reactions (Takeuchi et al., 1978). The theory for reversible firstorder catalytic reactions in a bottom feed configur-

‘Author to whom correspondence should be addressed.

ation, and with a Langmuir isotherm, has also been developed (Cho et al., 1982). The nonlinear dispcrsionless, adsorption equilibrium model predicted that pure product can be formed from pure reactant without the use of an additional separation unit. Inclusion of dispersion in the model was found to predict enhanced overall conversion, while nonequilibrium adsorption enhances it when adsorption rates are very small. Cho’s analysis has been developed further with a detailed look at shock formation and behavior (Petroulas et al., 1985a), and calculations of CMCR performance (Petroulas et al., 1985b). The predictions that reaction and separation occur simultaneously, and that high product purity can be obtained, were reconfirmed. In the bottom feed configuration, calculated conversions are lower than the maximum attainable with a fixed-bed reactor due to loss of adsorbed reactant, on solid exiting at the bottom. With the addition of a length of reactor below the feed, however, conversions exceeding that in a fixed bed are predicted, while maintaining high product purity. Other work has considered multiple steady states in a nonisothermal CMCR (Thoma and Vortmeyer, 1978), the performance of a CMCR for acid-catalyzed cellulose hydrolysis (Song and Lee, 19821, the development of design equations for arbitrary kinetics and adsorption isotherm (Altshuller, 1983), and analytical solutions for a linear, ideal model (Eroshenkova et cl., 1985). Very little experimental work on the CMCR has been reported. In a study of the oxidation of CO over Al,O, it was demonstrated experimentally that reaction and separation occur simultaneously, as predicted by the models (Takeuchi and Uraguchi, 1977b). Comparison of observed axial concentration profiles of CO and CO1 with theoretical curves from their linear model agreed at low gas to solid flow ratios, but at higher values of this ratio deviation of observation from linear model predictions was attributed to nonlinearity of adsorption isotherms.

1773

1774

BARRY

B. FISH

and

Preliminary results for the catalytic hydrogenation of 1,3,5-trimethylbenzene, which has the trivial nomenclature mesitylene (MES), in a CMCR has appeared (Petroulas et al., 1985b), as have details of apparatus design and construction (Fish et al., 1986), and computer-aided experimentation with the CMCR (Fish et al., 1988). In this paper we present the results of an experimental investigation of the hydrogenation of MES in this laboratory’s CMCR. Both the overall performance and the axial concentration profiles verify the predictions of the mathematical models. Experimental conditions are found for the production of high-purity product at conversions substantially larger than the maximum (equilibrium) from a fixed bed. The existence of an upper limit to the production rate, above which a pure product cannot be obtained, is predicted and experimentally verified.

ROBERT

W.

CARR

adsorbed, can be carried downward, adsorbed on the solid. Any unreacted B is desorbed in the stripping section, which has a higher temperature and carrier flow rate than the remainder of the column, and is removed at the stripping section take-off. A steady-state mass balance, neglecting dispersion, on any cross-section of the reactors gives

MODELS

The predictions of two steady-state ideal reactor models are presented in this section, for later comparison with experimental results. Both models assume adsorption/desorption equilibrium, no dispersion in the gas or solid phase, and a first-order reversible reaction occurring on the solid surface in the isothermal CMCR. The first model uses a linear adsorption isotherm, while the second adopts a Langmuir isotherm. The linear model provides analytical solutions from which the effects of variations in operating conditions on the concentration profile are easily seen. While there have been previous treatments of nonlinear models for reversible reactions (Cho et al., 1982; Petroutas et al., 1985a, b), they have been primarity concerned with the bottom feed configuration, with only briefconsideration of the side feed. Further analysis of the side feed configuration is presented here, building on previous results. Figure 1 is a schematic diagram of th’e CMCR. It corresponds both to the laboratory apparatus used in this study, and to the situation modeled in this section. The reaction product, A, moves up the column and is removed at the top, while B, being more strongly

(1)

=o.

(2)

and

inte-

dn,

dca

-&U~dx+(l-&)Usdx+(l-c)n,k,

-_(I -&)H& Summing to eliminate grating gives

the reaction

terms

+E~,(C,+Cd-(1--)~,(n,+n~)=

REACTOR

=o

-E)n,k;

+(I

IV is the total net flux through independent of reactor position. Linrur

(3)

w’.

the reactor,

and is

model

If a linear

isotherm

n, and n,

is used to eliminate

ni = NKiCi

(i = A, B)

(4)

the flux becomes

U,NK, x

Let

+ EU,C, 1-E 1 -cu

i

U,NK,

l--Eus

for

TVNKi=~i 9

= W’.

(5)

>

9 i=A

or 5.

(6)

We can now obtain one differential equation in terms of C,, which can be easily solved. Substitute eq. (4) into eq. (2), then solve eq. (5) for C,, and substitute C, into eq. (2). The result is

2+x,+

T=O

where Solids

(8) 1

. Product Take-of1 Solids

Rl?CyCle

I

T=--

us ug I-E

Fig.

t

__

Reactant

Feed

P

1. Schematic of the countercurrent chromatographic reactor.

k,NKA

l--E

EUB (1 -UA)(UB-

This can be integrated

to

(9)

give

QedsX=SC,+

moving-bed

W’ _. 1) EU!,

T

(10)

where Q is a constant of integration. In this analysis, B is the reactant, an adsorbs more strongly than A. The operating conditions of the CMCR will be adjusted so that erg> 1, and oA < 1. In this way, B will always move downward in the reactor, and A will always move upward (Fish et al., 1986). Under these conditions the obvious feed position is near the top of the reactor, in order to utilize the entire reactor length, and allow

Countercurrent

moving-bed

only the product, A, to leave the top. It will be shown that a reactor of sufficient length can convert nearly all of the reactant, even when the reaction is equilibriumlimited. Since the A produced travels upward, a natural boundary condition is C, = nA =0 at the bottom. Also, &=C:i, where b+ designates a position just inside the bottom of the reactor. This fixes W’ for the entire reactor: W’ = &UBC;+(l-uS).

[

emSX+

(fig- lKK(e-“X(1 - UA)+ K,K( 1 -a,)

1)

1

(12)

If the feed rate of B, R,, is specified this gives the concentration of B just inside the top. A mass balance on B at the top gives 1).

R,=C’,&,(a,-

(13)

Equation (12) can now be used to calculate Ci’ from CB=CL. at x=H-. This model gives rise to concentration discdntinuities at the boundaries due to infinite mass transfer rates. A mass balance on A at the top gives cl,=(l-a,)c;-.

(14)

Cl, = 0, because no feed can move upward and hence out of the top. The carrier gas entering the bottom contains no B. This causes a concentration discontinuity of B at the bottom:

nb,-Cb,+(u8- 1):.

UE

u,(l -s)

( 5)

By knowing the amount of B leaving the reactor, the conversion, ‘la, can be calculated:

CL, which is the vapor phase concentration at the top feed location, can be calculated from eq. (12) at x = H, . from which e-SH-__1

vs= e-SH

-

KKe(u,-

1775

Table i. Predicted conversions for the linear model with top feed Conversion 1.1 1.3 I.4 1.5 1.7 1.79

l/(ae-

0.9998

0.611 0.722 0.778 0.833 0.944 0.994

1)

10

0.868 0.708 0.521 0.143 0. i27

3.33 2.5 2 1.43 1.27

(11)

Q can now be solved for in terms of C”,’, and the axial concentration profile is C,=Cg

reactor

chromatographic

1)’

(17)

l--a,

For this linear model, the conversion is independent of the feed rate, and depends only on the reactor height and the operating conditions. There is a range of allowable operating conditions specified by the ratio of the linear adsorption parameters, since u,/u~ = K. We require bA < 1 and us > 1, therefore K < uA< 1, and 1~ uB < l/K. Table 1 gives the results for varying solids flow, keeping all other kNKBk_ conditions the same. For this example, H--& v, =4.616, K-2, and K,=l.

,

Table 1 shows that unit conversion can be closely approached, even though the reaction is equilibrium-

limited. As the solids flow rate decreases, the conversion increases. The best conversion is achieved when us approaches 1 and 0” approaches K. This is easily understood, since, as ITS varies from l/K to 1, the downward velocity of B decreases, and its residence time increases. Also, as 0” approaches K, the upward velocity of A increases, decreasing its residence time. However, slow movement of B may allow time for diffusion out of the top of a practical reactor, although this could probably be overcome by lowering the feed point. Another drawback may bc more critical. Table 1 also lists l/(0,- l), which is proportional to the concentration of B just inside the top of the reactor [see eq. (13)]. Thus, as us is decreased, Cg increases, and if the linear isotherm is adequate at some arbitrary erg, it may fail as the solids flow rate 1s decreased, unless the feed rate is decreased. Nonlinear model While the linear model provides a convenient approach to design, it will most probably be inadequate for practical reactors, where productivity requirements will require operation at high concentrations. To describe saturation of the solid, a Langmuir isotherm can be employed in the ideal adsorption equilibrium model. The finite carrying capacity so introduced implies that at high concentrations all of the B cannot be transported down on the solids. Some must therefore move up the reactor, suggesting that the feed location should not be at the top, but at an intermediate position. Reaction can then occur in the section above the feed, causing the concentration of B to decrease, and in turn also its upward velocity. With sufficient length, the velocity of the B front can decrease to zero, giving a product stream of pure A. This qualitative description emerges from a material balance for the nonlinear model. Although the theory has been previously treated (Cho et al., 1982; Petroulas et al., 1985a), a short review, with the results presented in physical terms, for comparison with experiment, is given below. The steady state balance is as before [eqs (lH3)]. In dimensionless form, eq. (3) becomes yA+,‘B_“A_ys= u.4

W’ (1 -&)U,N

0s

= w.

The dimensionless Langmuir isotherm vi=.

Yi

l+Y‘4+Y,

(i=A

or B)

(181

BARRY B. FISH and ROBERT W. CARR

1776

when substituted into eq. (IS), is then used to give the nonhnear adsorption equilibrium model: YA -0.A

YA

+yB_ OB

l+Y,+Y,

W =?A_\,

A

WA and

A and

VA

YB

=w

t+lJ,+y,

W.9=2-v

B’

(1%

(20)

ag-1

OB

Maximum

are proportional to the net flux of component i through any cross section of the reactor. The flux of each component must be constant at the boundaries of the reactor. At the top W,

Fig, 2. Invariants and equilibrium line in the (yA, ye) phase plane for 0” il and a,>l.

and at the bottom Yf_,b_YP’ ui

YP’

t

(21)

1+ybAI+y;+;’

ui

We then have 1 -eNK, dy, -=---dT E U, k,y, - KY, 1 +YA+YB

x

= F(YA>

Ys)

(22)

where

Several cases are of interest for the CMCR. The solution will be presented in the (yl, yB) phase plane. The top feed case, already considered for the linear problem, will be considered first. If oA< 1, any A produced in the reactor moves upward and just inside the bottom of the reactor C,=nA -0. Therefore, for the entire reactor, W = yg/o, - yr/(l + yi’). Equation (19) can be plotted in the (yA, ys) phase plane, as in Fig. 2, for a given value of rg. In the Iinear case, the invariant was a straight line, but in this case it is curved. First, let the feed rate of B just inside the top be low enough so that the solid is not saturated, and all 8 fed moves downward in the reactor. To solve this prdblem, we guess yg, and calculate W. Equation (22) can be integrated numerically from 5 = 0 to the top of the reactor. The downward flux of B can then be calculate&just inside the top of the reactor. If this is the B feed rate, it is a solution. If not, guess another y$‘, and repeat the procedure. The maximum downward flux of B can be obtained by taking the derivative of W, with respect to yB, considering yAm a constant, and setting it equal to zero: dW,

downward

1

dy, =G-

l+YA

(1 +YA+YgY =O

YB=JGY”)qd~ +YA).

(23)

At yB given by eq. (23). W, has its largest negative value (see Fig. 2). This line can be plotted in the (yA,ys) phase plane. The intersection of eq. (19) and eq. (23) gives the largest allowable value for yB just under the feed, and the corresponding highest downward flux of B. We can fmd $’ such that integration of eq. (22) along W=constant from <=O to t= 1 gives values of (yA,yB) at <= 1 which satisfy eq. (23). We can calculate the B flux at 5 = 1. As long as the B feed rate/area is less than this maximum downward B flux, all B fed will move downward, and the product gas stream will contain no B. If B feed rate/area is greater than this maximum, all B fed cannot move downward in the reactor, and some of the B fed will move out of the reactor in the product stream. Higher B feed rates will not affect the concentration profile of the reactor. Next, consider a B feed rate high enough that B travels upward above the feed point. Then the feed point should be lowered to some location’along the side of the reactor. If adsorption is fast enough, both components are in adsorption equilibrium just above and just below the feed point. The concentration profile beLow the feed is obtained by finding vg such that integration of eq. (22) from <=O to c= Hi, the reactor position just under the feed, gives (yA. ya) which satisfy eq. (23). The concentrations of A and B just above the feed point are found from a mass balance at the feed point. F, is known from solving the problem for the lower section of the reactor. A mass balance on component B gives bSY2+

F,=F-F,=lJ,$ B

1 + yy+

Requiring the flux of A to be constant below the feed point gives

#

>.

(24)

above and

(25) Equations (24) and (25) can be solved for yA and ye above the feed. Because F, is positive, ygi must lie to the right of W,=O.

Countercurrent

moving-bed

chromatographic

reactor

1171

We can now look at the various situations which can occur in the section of the reactor above the feed. yA and ys are known just above the feed. We can immediately calculate W for the upper section of the reactor, and plot eq. (19) in the (yA, ye) phase plane. (r”,‘, y”,‘) (7”. ys) just above the feed will be designated for the rest of the analysis. Case I. Assume W=constant crosses the equilibrium line before W, =0 as in Fig. 3. To the right of the W,=O line in the (yA, ye) plane, the flux of both A and B are always upward in the reactor. Equation (22) can be integrated from x= H; to 1 to find & for any reactor length. As the reactor becomes longer, & gets smaller, and approaches its equilibrium value for an infinitely long reactor. Equation (21) can he used to find y>, yfs. In this case component B is always found in the product stream for any reactor height, and the reactor behavior is similar to a fixed-bed reactor. In most practical situations, v> = vi = 0. In this case, any values of vf and vk have no bearing on the concentration profile inside the reactor. Because the fluxes of A and B are upward everywhere inside the upper section of the reactor, anything being fed into the top adsorbed on the solids immediately desorbs, and only affects the existing stream concentrations. Case

2. Consider

the

phase

plane

in Fig. 4. The

W=constant line crosses W,=O before the equilibrium line. If the reactor is short enough, integration of eq. (22) gives y: >& In this case the flux of A and B are both upward in the reactor, and the behavior is similar to case 1. Case 3. The phase plane is the same as in case 2, but the reactor is long enough so that integration of eq. (22) gives yg = yz. Applying the top boundary condition gives W, = 0. Therefore if ufs= 0, $, = 0. The flux of B just inside the top of the reactor is zero, therefore no B leaves the reactor in the product stream. This reactor

height

will be designated

Fig. 4. Invariants in the (yA, ys) phase plane for oA < 1 and lsgz 1 when Wcrosscs W,-0 before the equilibrium line. See case 2. decreases. In case 3, the flux of B just inside the top of is zero. If we increase the reactor height the reactor above H*, we should still expect yL=O. B cannot move upward above H* due to the bottom feed. Any B found above H* is a result of the back reaction A-B. B formed from this process will travel downward. B cannot be produced above H+ at a high enough concentration so that it can have an upward flux. If it could be, the phase plane would be like case 1, where the fluxes of A and B are always upward in the reactor, and cases 2 and 3 would not exist. Because any B produced above H* moves downward, the boundary condition just inside the top is rL-=O

for

vt,=O.

This must also be on the W=constant line, so 75 is also defined. In this case, we must have a concentration discontinuity inside the reactor. For a particular reactor height greater than H*, we can find a solution by integrating

H*.

Case 4. Assume the phase plane is the same as in cases 2 and 3, but H> H*. In case 2, as the reactor gets longer, the concentration of B just inside the top

B- can be found for any fi- by We need to find y:-. y’ using W,=constant and W, =constant across a jump. $i- will be less than )$, and greater than the equilibrium value. The important point is that the existing stream concentration will be unchanged for H> H*. The jump always crosses the line where

.

F(y,, ye) = m, so there is no problem

in the integration of eq. (22). For the case in Fig. 5, & approached the equilibrium line as the reactor height is increased. viis on the left of F(y,, ys)= to. For the case in Fig. 6, yiis between F(y,, ys) = co and W,=O line. As H gets large, 7:. gets close to the left side of the equilibrium line. Calculations Sample calculations presented Fig. 3. Invariants in the (yA, yB) phase plane for dA i 1 and clBB 1when Wcrosnes the equilibrium line before W, = 0. See case 1.

next.

For

of this

reactor problem,

performance

are

1-s NKBkE u, )-

H----

=4.616, K =& and K, = 1. The feed rate in Tablk 2 is dimensionless, but it is directly proportional to the

BARRY B. FISH and ROBERT W. CARR

feed rate into the reactor for constant carrier

actual

flow: B feed rate/column area Fd=~-------=Iw;JI ENU,

Fig. 5. (yA,yB) phase plane for case 4. with & approaching the equilibrium line as reactor height increases.

UB

-.

N&

Table 2 shows the results of a feed position just under the top of the reactor with feed rates insufficient to flood the column. It is interesting to note that the effects of the nonlinearity actually increase the conversion. Assume now that the reactor length has been doubled, and the feed position is in the middle. The feed rate can now be increased to the point of flooding. Table 3 summarizes some of the results of this configuration. For this I-ENK, k; =9.232, K=$, and K,= 1. problem, H---E Fu is proportional

UC7

to the upward flux of B above the feed point, and defined by F,=

B flux just above the feed point EN U,

= @$22& N&l

F, is simply a convenient dimensionless feed rate used to specify the problem. It contains the same information as eq. (24):

W=constant Y,b’r,b’ s-1

>

y

Q-1

B Fig. 6. (yAPys)phase plane for case 4, with &- between F(y,,, y,) = co and W’,= 0.

Once the feed rate is high enough to flood the column, the concentration profile below the feed point remains unchanged for higher feed rates. The fluxes of A and B are both upward above the feed, and the flux of B below the feed is at its maximum downward value. Figure 7 shows the progression of the steady-state

Table 2. Predicted conversions for the nonlinear model with top feed Fd (feed rate)

=.!+

0.429 x 10-s 0.117x 10-5

I.5 1.5

0.97 X 10-5 1.52 X 10-s 2.41 x 1O-5 3.72 x lo- 5 7.83 X lo- 5

Conversion

Linear conversion

0.552

0.521

0.530 0.217 0.262 0.328 0.417 0.605

1.7 1.7 1.7 1.7 1.7

0.143

Table 3. Predicted performance of the nonlinear model with side feed configuration’

9.9 x 12.4x 14.9 x 19.8 x 24.7 x 24.7 x 29.7 x 7.4 x

to-5 lO-5 10-s 10m5 IO- 5 1O-5 1O-5 10-S

Conversion

F,

F,+F.,

6.37 x 10-S 7.96 x 10-l 9.55 x 10-Z 0.11145 0.139 0.131 0.157 0.0557

‘F, = @(c&‘X,)=flux

1.4

1.9

1.4 1.6 1.6 1.7 1.7 1.2

0.953 0.96 1 0.968 0.901 0.922 0.876 0.896 0.998

of B/&NU,,F,= 1~~(~~NK,).

F, F,+F, 0.693 0.755 0.795 0.6946 0.756 0.684

0.737 0.879

Shock position 0.91 0.96 0.94 0.98 0.96

0.98

Countercurrent moving-bed

0

t Feed Point

1

chromatographic

Feedboint

’

1779

reactor

t

Feed Point

1

5-

Fig. 7. Progression of steady-stateconcentration profiles with increasingfeedrate from left to right for the parameters of the sample calculation, and crs = 1.7. concentration profiles as the feed rate is increased for ds= 1.7. The steady-state concentration shock in the top part of the reactor is moving up as the feed rate increases. The maximum feed rate for this reactor length, beyond which a pure product cannot be expected, occurs when the internal shock coincides with the top of the reactor. Table 3 also contains F,/(F, + Fd). This showed that for uB = 1.4 as much as 80% of the feed travels upward above the feed without decreasing product purity, even though the reactor lengths above and below the feed are the same. The important points here are that the flux of B upward is much higher than the flux of B downward. All the B that travels upward above the feed is converted to A, so the overall conversion is improved, as well as improving the production rate. Again, we need to optimize the operating parameters. The feed rate cannot be increased indefinitely if a pure product is required. If the reaction goes to equilibrium above the feed, and the concentration of B is still high enough that B has an upward flux, no further increases in reactor height will increase product purity. The maximum upward flux of B which allows for only component A in the product stream for a long enough reactor, corresponding to the largest positive value of W occurs when W=constant crosses W,= 0 and the equilibrium line at the same time. This gives a maximum value of Y,, at the top given by

EXPERIMENTAL

Since the construction details of the CMCR have already been published (Fish et a!., 1986), as has the computer control (Fish et al., 1988), only a brief outline will be given here. A schematic representation is given in Fig. 1. The reactor and associated solids handling units are all of stainless steel construction. The reactor is a 2.24 x 1.3 x 1O-2 m ID vertical tube fitted with 23 evenly spaced 3.2 x 10F3 m swagelok ports that can be interchangeably used for sampling, thermocouple stations or the feed location. The bottom 0.56 m of the column is used as a stripping section for regeneration of solids, having a higher temperature and carrier gas flow rate than the reactor. Swagelok ports (6.4 x IO-’ m) at the top and between the reactor and stripping section are used for top and bottom product take-off. Solids are initially placed in a top reservoir, and pass through an inverted conical preheating section from which they enter the column. The rate of gravity driven solids flow is regulated by a variable aperture at the bottom, from which the solids emerge ino a bottom reservoir. Solids are periodically recycled to the top reservoir by pneumatic lift. During recycle the reactor is isolated by valving off, and is able to continue to operate undisturbed by the recycle operation. The reactor and preheating vessel are resistively heated, the reactor having three separately controlled heating sections. Sampling is accomplished by withdrawing a gaseous stream which is only a very a,-1 small fraction of the total gas flow from the desired -_(I -K). (27) port for analysis by a gas chromatograph (GC). A l+K, Varian 3700 FID CC was used for all analytical work. A laboratory microcomputer was used for data A limiting case If we would like to maximize production while acquisition and control of the experiment. Twelve keeping conversion near unity, we should fix u,,=uJB* temperatures from points along the reactor and in the preheating vessel are recorded and displayed by the as in the linear case. In this way vg can be made to approach zero as closely as desired by increasing the computer. Three reactor temperatures and one prereactor length below the feed. (dYA/dYB)lnanlinear ca(ie heater temperature are used for feedback control using PLD controller software. The reactor temperaapproaches (dyd/dyB)llinear Fpss as ys+O. The feed rate ture, typically 19O”C, could be controlled to within could be adjusted so that W=constant in the upper reactor section crosses the equilibrium line and W,= 0 1°C. Gas phase sample streams are selected along the reactor, at the top and bottom take-offs, and in the at the same time. In this way, an infinitely long reactor solenoid length above and below the feed would allow for the stripping section by computer-operated maximum production rate of A while requiring nearly valves. A sample is automatically injected into the GC every 5 min. The computer provides a real time display complete conversion of B.

yf4=

1780

BARRY

B. FISH and ROBERT W. CARR

of sample position, reactor temperatures and gas phase composition for each sample taken during an experiment. The hydrogenation of MES to 1,3,5-trimethylcyclohexane (TMC), catalyzed by 0.74% (w/w) Pt AlaO,, is the test reaction. This is a particularly clean reaction; no side products were detected by FID/GC. It is equilibrium-limited, the conversion being about 0.4 in a 25% (v/v) mixture of H2 in N2 at 190°K (Egan and Buss, 1959). The HZ-N, mixture served as the carrier gas. Furthermore, the AlaO, is a suitable chromatographic adsorbent for the MES-TMC separation. The catalyst, obtained as pellets, was crushed and graded to 3@50 mesh. Since the catalyst is very active, it was necessary to obtain suitable reaction rates by using a mixture of 15% catalyst with 85% pure AI,O, of the same particle size range. The AI,O, was treated with a solution of KOH in CH,OH to deactivate highenergy adsorption sites. Without this treatment it was not possible to completely remove,MES from the solid in the stripping section. Catalyst activation was accomplished by heating at 380°C in 300 cm”(STP)/min of flowing H, for 9 h. GC analysis of sample streams, withdrawn from the reactor were done with a packed A1,03 column. Measurements of U,, U, and NK, are required to

rate. The kinetics are apparently more complex simple first-order, and a completely satisfactory expression has not yet been found.

than rate

determine the ui. The solid flow rate, U,, was measured on line by the rate at which the catalyst particles filled the calibrated control valve volume, and the gas flow rate, U,, was measured by a calibrated rotameter. The adsorption parameters, NK,, were obtained from pulsed chromatography retention times in a 6.4 x 1o-3 m column packed with Pt-Al,O,. Figure 8 shows the 190°C isotherm for MES on

concentration gradient occurs near the top, reminiscent of ideal model predictions of a top shock. At the higher feed rate the effect of the nonlinear isotherm is evident. There is a large increase in MES concentration around the feed point, and the column is clearly in a flooded condition with MES being transported not only downward, but also up and out of the top take-off. The product purity has now decreased

A1,OX. This curve was obtained by the method of breakthrough curves on a 6.4 x 10 3 m column packed with the Al,O,-Pt solids, and with pure Nz carrier to prevent this reaction. The data, fitted with the Langmuir isotherm, gave K,,, = 2.4 x IO’ for the adsorption constant on A1,0,. The reaction kinetics were investigated in a mtcrocatalytic reactor packed with a portion of the solids mixture from the CMCR. For fixed conditions a fit to integral reactor data could be obtained with a reversible first-order pseudo-homogeneous rate expression. However, the rate coefficients were found to depend upon the inlet concentration of reactant, and the flow

dramatically, although the concentration profile below the feed is virtually unchanged. Operation at a feed rate of 2.71 x 1O-4 dm”/h over a period of several hours showed that the reactor drifts back and forth from the flooded condition to.one with low MES above the feed, and high product purity. The amount of product, TMC, changes very little during these excursions. This feed rate is apparently at the

RESULTS

Experimentally determined axial concentration profiles in the CMCR are presented in Figs 9-13. The first series of experiments was done with the feed port located approximately 0.2 m below the top product take-off, and with relatively low feed rates. Figure 9 shows the MES and TMC profiles for feed rates of 1.54 x 10-4 and 2.7 x 1Oe4 dm3/h at fixed solid and carrier flows. The MES was fed as a liquid. It vaporized rapidly upon entering the reactor. In these experiments cMES= 1.83 and crTMc 0.47, so that MES is expected to move down the column and TMC is expected to move up. At the lower feed rate in Fig. 9 the product is nearly pure TMC, and very little MES is present at either the top or bottom take-off, indicating nearly complete conversion. Both TMC and MES show dispersion about the feed point. TMC is not present at the bottom take-off, and is seen to be transported upward as expected. MES, on the other hand, is transported downward, also as expected, and it also exists above the feed point. A steep MES

0 004

r

str,ppmg

&on

Take

on

Position From Top in Inches

0

0.002

0.004

Mole Fraction

Fig. 8. Adsorption

0.008

0.006

MES

isotherm

of MES.

0010

Fja. 9. Axial CMCR concentration arofiles for ton feed cokguration. Circles, 0.154 ml MES,&; triangles, 0.371 ml MES/h. Filled symbols, MES; onen symbols. TMC. dUEr =1.83, 0 ,,=0.47. T= 19O”C, T=22+C in stripping &I tion. Carrier flow, I I/min; solids velocity, 0.042 m/min.

Countercurrent

moving-bed chromatographic

threshold between well-behaved and flooded conditions, and gives a very sensitive operating region. The sensitivity can be attributed to small variations in solid and carrier flow rates, or possibly also the feed flow rate, although the syringe pump delivers a very steady flow. Figure 10 shows the effect of increased solids flow rate. In these experiments solids flow was increased, giving oMEs = 2.83 and ~~~~ = 0.74, all other conditions remaining unchanged. Now at the feed rate of 2.71 x 10m4dm3/h MES is transported downward, and the previously noted fluctuations are absent. Even at the higher flow rate of 3.84 x 10e4 dm3/h the reactor is not flooded. Both TMC and MES are distributed along the entire reactor length, except at the top takeoff, where MES has decreased to a low value, giving good product purity. However, the higher solids flow shortens the MES residence time sufficiently that the conversion decreases, and there is MES present in the stripping section. The appearance of TMC below the feed point is not because it is being carried downward, but iather because it is being formed by reaction in significant quantities compared to lower feed rates, and then swept to the top. Figure 11 shows the effect of a further increase of solids flow, with dklEs= 3.67 and a,,,=0.97, which causes both TMC and MES to move down, and very littte of either is found at the top take-off. Most likely, dTMC is actually greater than 1. There is some error in the calculated gi due primarily to uncertainty in the measured solids flow rate and the estimation of E. This experiment clearly shows the operational limits of the CMCR. That is, if one attempts to increase productivity by increasing the feed rate, it is necessary to increase the solids flow rate also (at some loss of conversion). But there is a clear upper limit to the solids Row rate, and hence to the productivity. If the feed position is moved down to an intermediate position along the reactor, an improvement in productivity can be made. This is shown in Fig. 12,

0.004

r II

o

46

32

Position From

*

60

,

Top in Inches

Fig. 10. Axial CMCR concentration profiles for top feed configuration. Circles, 0.154 ml MES/h; triangles, 0.271 ml MES/h; squares, 0.384 ml MES/h. Filled symbols, MES; open symbols, TMC. n,,,=2.84, n,,,=O.74. T= 190°C; T =225”C in strlpping section. Carrier flow, I I/min; solids velocity,

0.065 mjmin.

1781

reactor

r

owl

.

Q 0

0

“““Lot” 16

,

32

46

64

60

Fig. Il. Axial CMCR concentration profiles for top feed configuration. Filled symbols, MES; open symbols, TMC. Feed rate. 0.154 ml MES/h; dhlEs= 3.67; oTMC=0.97. T = 190°C; T-225°C in stripping section. Carrier flow, 1 I/min; solids velocity. 0.085 m/min.

Fig. 12. Axial CMCR concentration profiles for side feed configuration. Circles, 0.384 ml/b; triangles, 1.16 ml/h. Filled symbols, MES; open symbols, TMC. dhlEs= 1.83, (disc = 0.47. T= IYO”C, T=225”C in stripping section. Carrier flow, 1 l/min; solids velocity, 0.042 m/min. where the feed is located 0.81 m from the top of the reactor. In these experiments, the solids flow has been decreased to the condition of Fig. 10, but the feed rate of 3.84 x 10e4 dm3/h, which would have permitted MES to exit in the top feed position, gives excellent performance, both from the standpoint of product purity and conversion. The lower feed position permits operation in a flooded condition, since as MES moves upward it reacts and its concentration may decrease sufficiently to approach the linear region of the adsorption isotherm, where MES must move downward. This is the physical explanation of the internal shock predicted by ideal models. In the laboratory, of course, the shock will not be observed. What is seen in Fig. 12 is a concentration gradient decreasing from the feed point to the top take-off. Increasing the feed rate to 1.16 x lo- 3 dm3/h floods the column to the point where reaction cannot decrease MES concentration enough (unless the reactor is lengthened or the temperature is increased) and product purity deteriorates. Finally, Fig. 13 shows that in the side feed configuration productivity can, as before, be increased by increasing the solids flow rate, but at the cost of decreased conversion.

BARRY

1782 3.OE-2

r

.

B.

FISH

and

.

Fig. 13. Axial CMCR concentration proliles for side feed configuration. Circles, 0.384 ml ME.?@; squares, 0.575 ml MES/h; triangles, 1.16 ml MES/h. Filled symbols, MES, open symbols, TMC. dhlas=2.83; cTMc=0.74. T= 190°C; T =225X in stripping section. Carrier flow, 1 I/n&; solids velocity, 0.065 m/min.

Table 4 summarizes the experimental data, giving product purities and reactant conversions, calculated by substituting experimentally determined top and bottom MES concentrations into eq. (16). The product purity does not take into account the large excess of carrier gas, since it is noncondensible and may be easily removed from the TMC. DISCUSSION

The ideal model provides useful insight into CMCR behavior, and the trends predicted by the model are in qualitative agreement with experimental observations. At low feed rates, MES is transported downward, and TMC upward, as predicted for species with g> 1 and c < 1, respectively. At higher feed rates, MES also is seen to move upward, as predicted when the adsorbent becomes saturated. Gas phase concentration gradients occur near the feedpoint, and at the top, in the vicinity of shocks predicted by the ideal model. Better definition of the shape of the gradients is unfortunately not possible due to the spacing of the sample ports. Furthermore, conversions significantly exceeding equilibrium are attained at some conditions, confirming the theoretical predictions in Tables 1 and 3. Quantitative agreement cannot be expected since the internal and boundary concentration shocks are artifacts of model assumptions. Furthermore, the current model assumes only one type of site for adsorption and reaction, but the reaction is

ROBERT W. CARR

initiated by adsorption on Pt, while the separation is effected by adsorption on the support, Al,O,. KM,, on Pt is estimated, from the reactor data, to be around 1.4 x 1Oa ml/mol, and K,,, on Al,O, is 2.4 x LO’ml/mol, from breakthrough curves. This difference should be taken into account before attempting to test the model quantitatively. Making the modification is premature, however, since a satisfactory kinetic rate expression is not yet available. To simulate actual behavior at positions where shocks are predicted, a Fickian dispersion term could be added to eqs (1) and (2), or the requirement of adsorption/desorption equilibrium could be relaxed. The latter can be done in two ways. One is to assume adsorption and desorption occur at finite rates, and the other is to assume some mass transfer resistance between the gas phase and the solid phase. The gas phase concentration next to the solid surface can be taken to be in adsorption equilibrium. There could be both a bulk phase mass transfer resistance and finite adsorption/desorption rates. More complex models would describe diffusion into and out of a porous catalyst and heat affects due to reaction. While dispersion must surely occur in the fluid phase, it is probably not significant in the solid phase because the solids visually seem to experience plug flow. Inclusion ofgaseous dispersion would replace an internal concentration shock with a smooth gradient (Petroulas et al., 1985b). In the ideal model the boundary shock at the top is caused by the clean solid stream abruptly contacting a gas stream containing at least one adsorbable species upon entering the reactor. This situation creates a very large driving force for adsorption just inside the reactor. Although adsorption rates may be very fast they are not infinitely so, and they give a gradient rather than a shock near the top. Dispersion may or may not cause a gradient, depending on its effect relative to the effect of finite mass transfer. This question should be investigated when attempting to accurately model a practical reactor. The addition of a dispersion term can have similar effect to finite mass transfer or finite adsorption rate models (Petroulas et al., 1985b). Various models and model solutions for fixed-bed adsorbers have been

compared (Ruthven, 1984). The conclusion is that a linear driving force model can give solutions which can accurately describe real systems in many cases. The appropriate

coefficient

may be due to mechanisms

Table 4. Experimental performance of the CMCR Run

Feed location

Purity

Conversion

2.83 1.83

TOP TOP

1.83

Side

2.83

Side

0.94 0.9 0.88 0.95 0.49 0.89 0.88 0.92

0.86 0.5 0.31 0.88 0.34 0.52 0.56 0.46

Production rate (moJ/h) 9.4 5.6 8.5 2.43

x x x x

10-d 1o-4 1O-4 lo-’

2.sa X 10-3

1.44x10-3

2.32 x JO-3 3.84 x 1O-3

Countercurrent

moving-bed chromatographic

different from the original formulation. An extension to the Glueckauf approximation suggests that the k is a linear reciprocal of the effective coefficient function of various other resistances if the isotherm is linear.

Acknowledgements-This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under contract number DEAC02-76-ER02945. The authors thank Rutherford Aris for encouragement and helpful comments.

NOTATION

cross-sectional area of reactor gas phase concentration of component i, mol/ volume dispersion coefficient flux of B moving downward below the feed point in Fig. 7 flux of B moving upward above the feed point in Fig. 7 reactor reactor reactor

length position position

K,IK, adsorption tration)-’

just below the feed point just above the feed point

equilibrium (i=A or B)

constant,

(concen-

k&rsurface reaction rate constant for (time)) ’ surface reaction rate constant for (time)- 1 solid phase saturation concentration solid phase concentration, mol/volume feed rate, mol time- 1 carrier gas velocity solid phase velocity dimensionless flux of ith species axial distance

Greek

letters

Yi

KG

E

interparticle

vi

nJN

A+B, B-A,

r

void fraction

[ 1’

[ I’-

---INK_ E

u,

'

x/H denotes tor denotes reactor

conditions conditions

outside just

the top of the reac-

inside

the top

denotes reactor [ I*’ denotes reactor

conditions conditions

outside

the bottom

just inside the bottom

of the of the

REFERENCES

Altshuller, D., 1983, Design equations and transient behavior of the countercurrent moving bed chromatographic reactor. Chem. Engng Commun. 19, 363-375. Cho. B. K., Aris, R. and Carr, R. W., Jr., 1982, The mathematical theory of a countercurrent catalytic reactor. Proc. R. Sot. A-353, 147-189. Egan, C. J. and Buss, W. C., 1959, Determination of the equilibrium constants for the hydrogenation of mesitylene. The thermodynamic properties ofthe 1,3,5-trimethylcyclohexanes. J. phys. C/tern. 63, 1887-1890. Eroshenkova, G. V., Volkov, S. A., Slin’ko, M. G. and Sakodynskii. K. I., 1985, Chromatographic reactor with a moving catalyst bed. 77teo. 0s. khim. Tekhnol. 19,475481. Fish, B., Carr, R. W. and Aris, R., 1986, The continuous countercurrent chromatographic reactor. Chem. Engng Sci. 41,661~660. Fish, B. B., Carr, R. W. and Aris, R., 1988, Computer aided experimentation in countercurrent reaction chromatography and simulated countercurrent chromatography. tihem. Engng Sci. 43, 1867-1873. R., 1980, A Hinduja, M. J., Sundaresan, S. and Jackson, crossflow model of dispersion in packed bed reactors. A.1.Ch.E. J. 26, 274-281. Petroulas, T., Aris, R. and Carr, R. W., 1985a, Analysis of a countercurrent moving-bed chromatographic reactor. Comput. Math. Applic. 11, 5-34. Petroulas, T., Aris, R. and Carr, R. W., 1985b, Analysis and performance of a countercurrent moving bed chromatographic reactor. Chem. Engng Sci. 40, 2233-2240. Ruthven, D. M., 19X4, Principles of Adsorption nnd Adsorption Processes. John Wiley, New York. Song, S. K. and Lee, Y. Y., 1982, Countercurrent reactor in acid catalyzed cellulose hydrolysis. Chem. Engng Commun. 17, 23-30. Takeuchi, K. and Uraguchi, Y., 1976a, Separation conditions of the reactant and the product with a chromatographic moving bed reactor. J. them. Engng Japan 9, 164-166. Takeuchi, K. and Uraguchi, Y., 1976b, Basic design of chromatographic moving bed reactors for product refining. J. them. Engng Japan 9, 24&248. Takeuchl, K. and Uraguchi, Y., 1977a, The effect of the exhausting section on the performance of a chromatographic moving bed reactor. J. them. Engng Japan 10, 12-74.

l-&U

ui

[ ]*

1783

reactor

of the

Takeuchi, K. and Uraguchi, Y., 1977b, Experimental studies of a chromatographic moving bed reactor. J. them. Engng Japan 10, 455460. Takeuchi, K., Miyauchi, T. and Uraguchi, Y., 1978. Computational studies of a chromatographic moving bed reactor for consecutive and reversible reactions. J. them. Engng Japan 11, 216220. Thoma, K. and Vortmeyer, D., 1978, Multiple steady states of a moving bed reactor-theory and experiment. ACS Symp. Ser. 65, 539-549. Viswanathan, S. and Aris, R., 1974a, Countercurrent moving bed chromatographic reactors. Proc. 3rd ISCRE, Ado. Chem. Ser. 133, 191-204. Viswanathan, S. and Aris, R., 1974b, An analysis of the countercurrent moving bed reactor. SIAM-AMS Proc. 8. 99-124.