Optimal design of tubular and packed-bed homogeneous flow

The packed-bed and the tubular reactor types are compared with respect to peak-broadening and pressure drop. It is demon- strated that in optimized fo...
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Anal. Chem. 1980, 52, 2-9

Optimal Design of Tubular and Packed-Bed Homogeneous Flow Chemical Reactors for Column Liquid Chromatography J. F. K. H u b e r , ” ‘ K. M. Jonker, and H. Poppe Laboratory for Analytical Chemistry, University of Amsterdam, Amsterdam, The Netherlands

The performance of homogeneous flow chemical reactors is discussed theoretically and investigated experimentally. The packed-bed and the tubular reactor types are compared with respect to peak-broadening and pressure drop. It is demonstrated that in optimized form both reactor types can be used in combination with usual HPLC columns for reaction times up to 2 min without significant loss in chromatographic resolution even of nonretarded compounds. For strongly retarded compounds, much larger reaction times are allowed, e.g., 10 mln for a capacity factor of 3. The packed-bed reactor is found to be superior with regard to peak-broadening and pressure drop and is to be preferred in critical cases.

In chromatography, chemical reactions can be used to improve the separation or the detection. The detection can be improved by: (a) Lowering the detection limit as the result of a conversion of the sample components to products for which the detector has a higher sensitivity and/or (b) Raising the selectivity of detection to avoid interferences with substances which cannot be sufficiently resolved by the chromatographic separation. Chemical reactions can be carried out in pre-column or post-column, on-line or off-line mode. Pre-column reactions change the chromatographic as well as the detection properties of the compounds which may require a compromise. Furthermore artifact forming is more likely in pre-column reactions since the reaction is carried out with the sample mixture. Therefore post-column reaction will be preferable in general. For post-column operation, the column effluent can be collected in fractions, a suitable reagent is added, and the reaction products are measured by means of a spectrophotometer or a spectrofluorometer. Such a procedure can be automated in principle. A more straightforward approach, however, is the use of a flow reactor. Moreover in modern high efficiency column liquid chromatography with columns of 10000 theoretical plates or more, such a batch-wise monitoring of the column effluent would necessitate the processing of hundreds of fractions which must be smaller than half of the volume standard deviation of the corresponding chromatographic peaks (1). Reactions suitable for use in flow reactors in combination with chromatographic columns have to meet the following requirements: (a) The reagents and solvents should give no interfering signals in the detector. If this is not the case, the interfering compounds must be destroyed in a second reactor before they reach the detector (2). (b) The reaction kinetics must be fairly fast to avoid large reactor volumes which cause a significant peak-broadening and therefore a loss in resolution. (c) The reaction yield should be high to achieve a high precision and a low detection limit. (d) For the same reason the products formed should be stable, especially when the components have different reaction rates. Present address, Institut fur Analytische Chemie. Universitat Wien, Vienna, Austria. 0003-2700/80/0352-0002$01.OO/O

On-line flow reactors are used in gas chromatography (3, 4 ) as well as in column liquid chromatography. In the latter

case they are mainly applied in the analysis of biochemical mixtures. A well-known example of a post-column flow reactor is the ninhydrin reactor, which is routinely used for the colorimetric detection of amino acids separated by ion-exchange chromatography (5,6). Fluorogenic reactors for amino acids have been described also (7-9). Post-column flow reactors were also described for carbonyl-containing compounds ( I O ) , organic acids ( 1 2 , 12),thioridazine and its metabolites (Z), and hydroperoxides (3). Most flow reactors described so far consist of a narrow tube through which the effluent-reagent mixture flows in the required reaction time. For a given flow rate, the volume has to be chosen according to the reaction time needed. Very few packed-bed reactors, consisting of a tube filled with a granular inert material, have been described so far (13,14). The peak variance produced by the reactor should be small compared to the variance of the chromatographic column since otherwise a decrease in resolution and peak height results. T o reduce the peak-broadening effect of the reactor, gas-segmented liquid flow has been used (5,10,15). Such a segmented-flow reactor, however, requires a debubbling device between reactor and detector or the use of a microprocessor (16). In this work the optimum design of packed-bed and tubular homogeneous flow reactors is discussed with regard to its application in column liquid chromatography.

THEORY Effect of the Reactor on the Resolution. The chromatographic resolution R,, of two peaks is defined as

where VR, and VR,are the retention volumes of two components i and j and uv, is the volume standard deviation of the first of both components. Assuming a Gaussian concentration peak, its maximum is given by

where Q, is the amount of the component injected. The total peak variance is described by the following equation:

(3) where oLrk2 are the volume variances created by the different elements of the chromatographic system. These elements are the injection device, the separation column, the flow reactor including the mixing device, and the detector. The necessary connectors are considered to be part of these elements. A t ideal mixing of the column effluent stream with a reagent stream, the resolution is not affected, as V R and oL, are multiplied by the same factor ( u + u 2 ) / ~ 1 ,in which tol and u’?are the flow rates of the eluent and the reagent, respectively. Because of the dilution, c, is divided, however, by this factor. ,c 1979

American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980

In reality, convective mixing phenomena will cause additional peak dispersion resulting in a reduction of the resolution and an additional dilution. A further peak dispersion and therefore decrease of resolution and increase of dilution is caused by the reaction chamber itself. The effect of the reactor on the peak width will depend on the dispersion characteristics of the separation column. Neglecting the contribution of the sampling device, the volume standard deviation of a component i leaving the chromatographic column is described by

where VRi is the retention volume and Ncithe theoretical plate number of the column for component i. After the column effluent is mixed with the reagent in a suitable mixing device and the reaction mixture has passed the reactor, the standard deviation will have increased according to Equation 3 leading to the following expression:

in which uZri is the variance produced by the reactor. Defining the theoretical plate number of the reactor as q / u t , , = PIri, substitution of Equation 5 in Equation 1 and considering that VR,- VRi has been multiplied also by the factor (wl + wJ/wl results in

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as used in column liquid chromatography lead to low transversal (radial) mixing. The same effect will be observed for packed bed reactors. On the other hand, small particles are necessary to reduce longitudinal dispersion. Analogous contradictory requirements concerning longitudinal and transversal mixing occur in tubular and segmented flow reactors. For optimum reactor design, it is therefore important to review briefly the theory of radial mixing. Radial mixing of a component in a fluid stream can be described by a formula entirely analogous to that for longitudinal mixing as long as the radial distribution curve of the components does practically not reach the walls of the flow bed

in which u,i = standard deviation of the radial concentration profile of component i, generated by a point source in the center of the fluid stream; H,;= theoretical plate height for radial dispersion of component i; and z = distance downstream from the point source. If the radial distribution curve reaches the boundary of the fluid stream, Equation 9 is no longer valid, which is immediately clear if one realizes that the standard deviation cannot exceed that of a rectangular function, describing the uniform distribution of the test compound over the cross section of the fluid stream. This is in fact the situation to be aimed at in a chemical flow reactor. It is reasonable to expect that this latter situation is practically reached a t a given distance r?

where R?” = (VRj - VRi)/uvCi is the maximum value of the resolution determined by the column only and V, is the reactor volume. Equation 6 describes the influence of the reactor on the resolution in terms of volumes and theoretical plate numbers of chromatographic column and reactor. With V , = (wl+ w 2 ) t rand VRi = wltRi,Equation 6 can be transformed to an expression which describes the influence of the reaction time t,, which is the average residence time in the reactor, on the resolution:

in which Lmin= critical length below which the radial mixing is not complete and which in a flow reactor defines a region in which the conversion rate is at least partly transport-limited; a = numerical factor depending on the criteria for total radial mixing and the initial distribution of the mixing compound; and rf = radius of the flow stream. The theoretical plate height Hrifor radial dispersion depends strongly on the geometry of the flow system. For laminar flow in an open tubing (tubular reactor), in the absence of secondary flow caused by coiling, the expression for Hriis simply

H . = -2Dim U

where tni is the average residence time of the component i in the chromatographic column. For a given reactor both t, and Nridepend on the flow velocity in the reactor. From Equation 7 the basic relationship for flow reactor design can be derived ti;

- >>

Nci

t;

-

Nri

It can be seen that the maximum allowable reaction time depends on the corresponding theoretical plate number of the reactor. Radial Mixing of Two Liquid Streams. The required residence time in a chemical reactor is determined by the degree of conversion aspired and the conversion rate. The overall conversion rate depends also on transport phenomena. T o achieve a high reaction rate necessary to decrease the reaction time, the reagent concentration must be high and the mixing of sample and reagent solution must be fast. From experimental results obtained with packed columns, it is known (17) that low particle to column diameter ratios

where Dim= diffusion coefficient of component i in the moving phase and u = flow velocity averaged over the flow cross section. Combination with Equation 10 results in the expression:

L min. = - f- f

w

2 i ~Dim

in which w = rrf2u is the flow rate. For w = 30 & i s , with Dim = cm2/s and a = 1,e.g., this results in I,- = 477 cm. It must be concluded therefore that a straight short tubing will not allow one to achieve complete radial mixing. A narrow coiled tubing should give better radial mixing, however, because of secondary flow effects. For packed-bed reactors, an expression for the theoretical plate height can be given

in which A, = numerical factor, characterizing convective radial dispersion; d, = particle diameter; and T, = radial tortuosity factor. Values between 0.15 and 0.06 have been found (17,

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ANALYTICAL CHEMISTRY, VOL. 52, NO. 1 , JANUARY 1980

18)for 2h, For most practical cases the first term in Equation 13 can be neglected because of the flow velocity used. Taking this into account and combining Equations 13 and 10 results in

L min. = -

cy

rf

2 W p

(14)

For rf = 3 mm, d , = 0.023 mm, a = 1 and 2X, = 0.15 a value of &in = 261 cm results, which indicates that lack of radial dispersion may also present a problem in the use of packedbed reactors. For both tubular and packed bed flow reactors, care should be taken therefore that the liquid streams are perfectly mixed before entering the reactor. Later in this paper experimental evidence will be presented to prove that the theoretical predictions made above are valid indeed. From Equation 14 it can be inferred that a packed column of low column to particle diameter ratio is necessary to bring about perfect radial mixing within a short length. In such a column, pressure drop is negligible and longitudinal mixing can be kept insignificant by using small column diameters giving short residence times. Longitudinal Mixing and Pressure Drop in Tubular Flow Reactors. The theoretical plate number of a tubular flow reactor is described by the expression (19) derived for mixing by flow in a tubing which reads a t sufficiently high flow rate

where rf = inner radius of the reactor tubing and D,, = diffusion coefficient of component i in the reaction mixture. T o avoid a reduction of the chromatographic resolution Equation 8 must be fulfilled. With regard to Equation 15, it reads (16) The pressure drop &J, over a straight tubular reactor for laminar flow is described by

where 7, = dynamic viscosity of the reaction mixture a t the temperature of the reactor and w,= w 1+ w q = flow rate in the reactor. For optimum reactor design, the flow rate w,,the diffusion coefficient Di,and the dynamic viscosity qr cannot be adjusted independently. They are determined by the conditions required for the chromatographic process and the chemical reaction. The only parameters which can be freely chosen are the reactor length (determining the reaction time) and the reactor radius. From Equations 16 and 17 it can be seen that the maximum allowable reaction time decreases with the second power of the radius of the reactor tubing and the pressure drop for a given reaction time decreases with the sixth power of the radius. By eliminating rf from Equation 16 by means of Equation 17 we find:

This expression shows that for higher flow rates obtained with larger diameter separation columns, the performance of tubular reactors becomes worse. Further it can be seen, that the maximum allowable reaction time increases with the power one fourth of the pressure.

Coiling of tubular reactors diminishes the longitudinal mixing due to secondary flow effects; in the region of analytical chromatographic interest, the decrease can be about a factor of five, as shown in the Experimental part of this paper. A theoretical treatment of this phenomenon can be found in literature (20, 21). Longitudinal Mixing and Pressure Drop in PackedBed Flow Reactors. The mixing in a packed-bed flow reactor can be described by the corresponding theoretical plate number. At sufficiently high flow rate, the equation (22) of the theoretical plate number for flow in a packed-bed reads:

with A , = cross section area of the reactor; tf = fraction of the cross section which is flowed through, i.e., the interparticle porosity: d , = particle diameter of the packing; XI = factor depending on the packing geometry describing the convective mixing in longitudinal direction. From Equations 8 and 19, the following relationship obtains

The pressure over a packed-bed can be expressed by the equation:

The flow rate w,and the viscosity 7, are fixed by the conditions for the chromatographic separation and the chemical conversion. The interparticle porosity ti and the geometrical factor XI for convective mixing can only be varied within a narrow range so that the cross section area A, and the particle diameter d , remain as optimization parameters for a given reaction time. From Equations 20 and 21 we recognize that the maximum allowable reaction time decreases with the first power of the product A,d, and the pressure drop decreases for a given reaction time with the second power. By eliminating A,d, from Equation 20 by means of Equation 21, we find:

From this expression it can be seen, that the maximum allowable reaction time increases with the power one third of the pressure drop. Noteworthy, and in contrast to what is the case for tubular reactors, the flow rate has no influence. With the aid of Equation 22 a nomogram (Figure l?)was constructed. I t should be noted that the same result can be reached with different values of d,, provided that the product A,d, remains constant. There are, however, two limitations. The first is the obvious fact that the diameter ( - A l l 2 ) of the reactor tubing should be at least equal to several times the particle diameter. The second is the condition that the plate height contribution due to longitudinal diffusion is negligible; otherwise the approximation H = 2hld, would not be valid. This second limitation is visualized in the nomogram on the d,(min) axis, giving the smallest value of d, at which longitudinal diffusion is still negligible. The results of this optimization study are different from those obtained by Deelder et al. (14). They used a plate height expression with assumed parameters which yield a minimum in the H - ( u ) curve, which minimum is then recommended as the final operating point. Most experimental results, however, do not show such a minimum; the treatment given here leaves one more degree of freedom ( A , or d p ) which is

ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980

5

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1

MIXIhG

COLUMN

J

1

141

r

- - - 7

4

L - _

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Figure 1. Block diagram of apparatus used for flow reactor testing. (1)Eluent reservoir and pump, (2)Sampling valve, (3)Reagent reservoir, (4) Proportioning pump, (5) Pulse damper, (6) Manometer, (7) Mixing device, (8) Thermostated reactor, (9) Cooled capillary, (10) Photometer, (11)Flow restrictor, (12)Flow meter, (13)Integrator, (14)Recorder

--.cadFigure 2. Swagelok Tee, modified to obtain better mixing of eluant and ninhydrin solution stream

a considerable advantage in practice. EXPERIMENTAL Apparatus. In this study the ninhydrin reaction was used to test different reactors. The apparatus used (see Figure 1) was a home-made amino acid analyzer according to the principle of Stein and Moore ( 5 ) mostly assembled from commercially available parts. A constant flow pump (Varian 4100) was used as eluent delivery system. A high pressure sampling valve (Valco CV-6-UHP a-C20) provided with a custom made sample loop of 200 X 0.15 mm resulting in an injection volume of 8.64 pL was used. The mixing manifold was a modified 1/16-in.Tee (Swagelok, see Figure 2). The upper and the lower connection were drilled through at 1.6 mm and two flat and smooth capillaries (1.6-mm o.d., 0.25-mm i.d.) were connected so that the distance between them was about 0.1 mm. Eluent was fed from the upper connection and ninhydrin reagent from the side branch in a 2 to 1 ratio. For the proportioning of the ninhydrin solution, a reciprocating pump was used (Milton Roy Type 196-39). The mixing manifold was connected to the flow reactor by means of a mixing column of 200-mm length with an internal diameter of 1.1 mm filled with glass beads of 150-km diameter to assure adequate mixing of the eluent and reagent. The packed bed reactors were made from titanium tubings 150 X 6.0 mm, 316 stainless steel tubings 50 X 6.0 mm, 250 X 2.8 mm, and 500 X 2.8 mm and filled with glass beads of different particle diameter. Tubular reactors were made from 316 stainless steel capillary tubings of 18000 X 0.25 mm and 3000 x 0.8 mm and Teflon tubings of 15 000 X 0.5 mm and 10 000 X 0.35 mm. The capillary tubings were coiled in different diameters. To minimize the necessary reactor volume, the required reaction time was decreased by raising the temperature as described (23);140 "C proved to be the optimal temperature giving a fast reaction and low noise of detection. The reactors were thermostated by means of a silicone oil bath (Haake FT) or an air thermostat (from a Perkin-Elmer 1220 liquid chromatograph). Temperatures could be kept constant within 0.1 "C. At the outlet of the reactor a 250 X 0.15 mm capillary cooled with tap water was attached to cool the reaction mixture to about ambient temperature. Leaving out this device increases the detector noise considerably. The detector used was a spectrophotometer (Perkin-Elmer LC 55). A needle valve behind the spectrophotometer was used to maintain a

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I"r?

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J

SPLITTING

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TEE

Flgure 3. Experimental setup to study radial mixing. Aqueous phenol solution 0.1 glL mixed in 1:l volume ratio with water. Splitting at the outlet Tee in 1:l volume ratio. Flow rates varied between 1 and 40 mL/h (for each stream). Experiments reported were carried out with Swagelok '/,& Tee connections. The splitting Tee could be rotated with respect to the remainder of the setup

backpressure of about 10 bar to pretent boiling of the reaction mixture at temperatures above its boiling point. This can be done without danger for the detector cell as it withstands pressures up to 175 bar. An automatic flowmeter as described (24)was used. The flow rate of the liquid mixture measured at the outlet of the reaction detector was constant with an estimated standard deviation of 0.2%. Reagents. Ninhydrin solution was prepared according to literature (25)and kept under nitrogen. Amino acids used were chromatographically pure, obtained from Ajinomoto. Procedure. For control, the standard deviation arising from the combined sampling valve, connecting tubes, and photometric detector was first determined experimentally. Then the reaction chamber (packed column or open tubing) was added between the sampling valve and the detector and the standard deviation of the residence time distribution in the reaction cell of a test component was determined at different eluent flow rates. Connecting tubes were kept as short as possible. Potassium biphthalate 0.005 M was used as inert sample and the UV detector was set at 275 nm. Standard deviations were calculated from measurements on the stripchart recorder. Next the mixing manifold was installed between the sample valve and the reaction chamber and the measurement of the standard deviation was repeated. After that, the reagent delivery system was connected to the mixing manifold and using 0.001 M glycine as sample, standard deviations of the whole reaction detection systems were measured. The detector was set at 570 nm. RESULTS AND D I S C U S S I O N Radial M i x i n g of Reagent Solution and C o l u m n Eff l u e n t . The purpose of a mixing chamber for the column effluent and the reagent solution in front of a flow reactor is to achieve complete radial mixing with negligible longitudinal mixing. The extent of mixing obtained with a number of mixing devices was estimated by mixing a phenol solution with pure water in the volume ratio 1:1and splitting at the downstream side of the device. Half of the liquid stream was fed to a n UV detector, the other half was discarded (see Figure 3). The splitting of the flow into exactly equal parts was adjusted by means of control valves in the split lines. When complete mixing occurs, the absorbance in the UV detector will be half the absorbance of the original phenol solution. If the mixing is not complete, the absorbance observed will depend on how the splitting a t the outlet matches the transverse concentration distribution. If there is no mixing at all, the absorbance can vary between zero and the value of the original solution depending on the splitting. The splitting of one half of the effluent, which is experimentally accessible without too much effort, is too crude to determine the exact extent of mixing. The deviation of the observed

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ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980

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,b

Id,

2;O

SAG

IiGG

2,bO

-

50cO

lGC'O0 *;bo0

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lsec/crnil-+

Figure 5. Correlation of the observed inhomogeneity IpI with the value of L / w for open tubings. Conditions as in Figure 3. Length of the tubings, between 5 and 40 cm. (x) 0.1 mm i.d.; (+) 0.25 mm i.d.; (0)0.50 mm i.d.

Figure 4. Dependence of the observed inhomogeneity on the relative angular position of mixing and splitting Tee. Conditions as in Figure 3; Flow rates 20 mL/h phenol solution and 20 mL/h water. (A) Open tubing, 10 cm X 0.5 mm i.d.; (B) Open tubing 10 cm X 0.1 mm i.d.; (C) packed tubing 5 cm X 1.0 mm i.d., with 25-pm glass beads; (D) packed tubing 10 cm X 1.0 mm i.d., with 110-pm glass beads; (E) packed tubing 5 cm X 1.0 mm i.d., with 110-pm glass beads

absorbance from the value predicted for complete mixing, however, has a maximum corresponding to the mixing actually occurring, i.e. the real degree of nonmixing is equal to or worse than the result observed. The observed deviation or inhomogeneity can be expressed as

'P

Aobsd - Amled

-1

Lmd, From experimental results with other mixing systems it can be concluded that such devices do not perform significantly better than Swagelok Tees. This holds especially for such devices that are popular in "stopped flow" reaction kinetics systems. When scaled down to dimensions compatible with HPLC-demands for small contribution to peak broadening (small longitudinal dispersion), their favorable mixing characteristics are lost. Extra Dispersion Outside the Reactor. Leaving out the mixing device and the reactor cell, the volume standard deviation is generated by the injection valve, the connecting tubings, and the flow-through cell of the detector. It was measured using potassium biphthalate as sample and the eluent as mobile phase. Connecting the mixing device and adding eluent solution instead of ninhydrin in a 1:2 volume ratio and holding constant the total flow rate gave the same result, showing that the contribution of the mixing device and the mixing process to the volume standard deviation is negligible. Results are shown in Figure 6 in terms of the volume standard deviation nu as function of the flow rate w,. It can be seen that the peak broadening of this system corresponds to about 15 pL. Dispersion in the Reactor without Chemical Reaction. A reactor was added to the former system and the volume standard deviation of the total system was measured at 22 and 95 "C at different flow rates using potassium biphthalate. Theory predicts for open tubings and packed columns a proportionality between the volume variance n'v, and the re-

ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980

I-

uI

0

1 10

20

30

-

40

7

/

50

w

crys,

Flgure 6. Plot of the volume standard deviation as function of the flow I

rate for the effects, arising from outside the reactor

010

d

LIP , 2

5

10

20

50

w (uvsec)

0

/ 0

5

10

20

15

+w

lpl/seci

Flgure 7. Relationship between the volume standard deviation normalized for the volume and the flow rate for tubular reactors of the same tubing diameter but different lengths. i.d. 0.5 mm, lengths: (A) 15250 m m , ( 0 ) 1 0 2 5 0 m m , ( V ) 5 2 5 0 rnm and ( 0 ) 3 0 0 0 mm

Figure 8. Volume variance of different reactors at 22 O C normalized for the volume. (V-V-V) Packed-bed reactor 2.8 mm filled with bar.s/pL2. 20-25 p m glass beads, normalized pressure drop (A-A-A) Packed-bed reactor 2.8 mm filled with 50-63 p m glass beads, normalized pressure drop 2. bar.s/pL2. (0-0-0) Packed-bed reactor 6.0 mm filled with 20-25 pm glass beads, normalized pressure drop < 10-4 bar.s/pL2. (V- -V-- -V)Tubular reactor 0.25-mm i.d., 23-mm coil diameter, normalized pressure drop 2.5 X bar.s/pL*. (0---0---0) Tubular reactor 0.35-rnm id., 100-mm coil diameter, normalized pressure drop 3 X bar-s/pL2. ( 0 - - 0---0)Tubular reactor 0.80-mm i.d., 180-mm coil diameter, normalized pressure drop