Rate-constant measurements in chromatographic columns

The Chemical Engineering Journal, 22 (1981) 85 - 87 @ Elsevier Sequoia S.A., Lausanne -Printed in the Netherlands

85

Short Communication

Rate-constant measurements in chromatographic columns

JULIEN ANDRIEU* University

and J. M. SMITH

of California,

(Received 25 September November 1980)

Davis, CA 95616 1980;

(U.S.A.)

in final form 26

Recently [l] the theory of moments has been developed for a pulse of gaseous reactant which is absorbed and reacts in a stationary liquid phase in a chromatographic column. The theory, applicable to linear processes, accounts for axial dispersion in the gas phase flowing through the packed bed, gas-to-liquid mass transfer, and diffusion and reaction in the liquid coating the inert solid particles. Comparison of moment values obtained from measured response curves with the theoretical expressions provides the possibility of evaluating equilibrium and rate parameters, such as the solubility of the gaseous reactant in the liquid, the reaction equilibrium constant, and the first-order reaction rate constant. In this communication we evaluate the suitability of the chromatographic theory for determination of the rate constants for an irreversible reaction, the absorption and reaction of carbon dioxide in an aqueous NazCOsNaHCOs solution. The rate constant for this homogeneous, first-order irreversible reaction has been measured by classical means by Roberts and Danckwerts [2] . For optimum accuracy in evaluating reaction rate constants from chromatographic measurements, the contributions to the moments of axial dispersion, gas-to-liquid mass transfer, and liquid-phase diffusion should be negligible. Accordingly, our experiments were carried out with high gas flowrates, relatively long columns, and thin liquid films on the inert particles. Under the conditions of the experiments, the Peclet and Sherwood numbers and *On leave from the National Institute of Applied Science, Lyons, France.

the Thiele modulus were estimated to be 250, 3000 and 0.2, respectively. With these large values of Pe and Sh (see Nomenclature for definitions), axial dispersion and gas-liquid mass transfer effects were unimportant. Also, the Thiele modulus 4 is sufficiently low for the concentration gradient of dissolved carbon dioxide to be negligible. With these restrictions, the zeroth moment of the response peak is related to the rate constant kr and the solubility constant H (Henry’s law constant) by the expression [l] IJO

11 =exp kleL L -H% u

Response curves were measured at various gas flowrates when pulses of a gas mixture, containing 1.5% carbon dioxide and 98.5% helium, were introduced to the packed column. The experimental values of cc0 were determined from the response curve by the equation Cuo)exp= & ICr,(t)dt Omo

(2)

The experimental conditions are given in Table 1. For the coating process, glass beads (1 mm nominal diameter) were first washed with demineralized water, dried, and weighed. The beads were added to the carbonatebicarbonate solution and thoroughly stirred. Excess solution was removed by filtration and the particles again weighed to determine the liquid hold-up eL and film thickness S . The coating ratio (mass of liquid coating/mass of dry particles) was about 10% for all experiments. The packed column was prepared by adding particles slowly while vibrating the tube of soft copper. The tube was then coiled for insertion in the chromatograph oven, and the ends stuffed with glass wool. The thermal conductivity detector was operated at 150 “C with 170 mA. The major experimental problem was preparation of columns which gave reproducible data. It is believed that the variations are due primarily to non-uniform liquid coating of the particles, breakdown of the liquid

86

this value of H and the hold-up information in Table 1, the slopes of the lines in Fig. 1 give for the rate constant

TABLE 1 Experimental

conditions

Column Temperature Pressure Diameter (I.D.) Length, column I, L1 column II, Lz

25 “C 1 atm 0.92 cm 0.27 m 0.56 m

Packing, glass beads, diameter

0.092 cm

Bed porosity

(liquid plus gas)

(12i)l = 0.44 s-l (121)s= 0.41 s-l Under the same conditions Danckwerts and Roberts [ 21 reported a value of 1 .O s-l. Their method was a steady-state one using a wettedwall column. In view of the difficulty in measuring reaction rate constants accurately, and the wide range of possible values, the agreement between the two results is satisfactory. We think that improvements in the chromatographic method of measuring reaction rate constants will depend upon improved methods of coating the particle with the liquid and in packing the liquid-laden particles. Also, care must be taken to avoid excessive bleeding (evaporation of the liquid film into the gas stream). In our experiments bleeding was kept to less than 10% by minimizing the running time.

0.40

Liquid Hold-up eL Film thickness 8

-0.06 12-14pm

Gllf3 Hold-up es Flowrate (25 “C, 1 atm) Pulse composition Pulse injection volume

-0.34 41.7 to 117 cm3/min 1.5% Cog in He 1.0 cm3

Coating solution NagCOg cont. NaHCOa cont.

0.625 molal 0.530 molal

Carrier gas

Pure helium

film, and non-uniform bed porosity. After considerable experience, reasonably reproducible moments were obtained from eqn. (2). The final results for the two columns studied are plotted as ln(lOlra) us. L/u in Fig. 1. The data show a linear behavior, as indicated by eqn. (1). The slope of these lines is equal to kleL/HE,. The solubility of carbon dioxide is lower with respect to the solubility in pure water because of the ions (Na+, C032-, and HCO,) and dissolved CO2 present. The true value of H can be calculated by the method of Van Krevelen and Hoftijzer [3] ; at 25 “C, H = 2.2 (mol/cm3 gas)/(mol/cm3 of liquid). With

2.5

I

I

I

I

I

I

Nomenclature

co CL(t)

D Ed H

I

/

I

kf kl L Pe Sh t tin U v

1.9 0.01

006

0.06

0.10

0.12

Fig. 1. Zeroth moment us. residence time.

0.11

0.16

concentration of carbon dioxide in input pulse, g mol/cm3 concentration of carbon dioxide in response peak at bed exit (at bed length L), g mol/cm3 diffusivity of carbon dioxide in liquid, cm2/s axial dispersion coefficient, cm2/s Henry’s law constant for CO2 in liquid, (g mol/cm3 gas)/(g mol/cm3 liquid) gas-side mass transfer coefficient, cm/s first-order reaction rate constant, s-l packed-bed length, cm = Lu/E,, axial Peclet number in gas = kfGH/D, Sherwood number time, s injection time, s superficial gas velocity, cm/s = U/Q, interstitial gas velocity

Greek symbols thickness of liquid layer on particles, cm gas hold-up in bed, cm3/cm3 of’empty Es * column 6

87

liquid hold-up in bed, cm3/cm3 of empty column zeroth moment PO (~O)exp experimental value of p. calculated from response curve by eqn. (2) G = 6 @l/D) ‘12, Thiele modulus EL

References 1 J. Andrieu and J. M. Smith, Chem. Eng. J., 20 (1980) 211. 2 D. Roberts and P. V. Danckwerts, Chem. Eng. Sci., 17 (1962) 961. 3 D. W. Van Krevelen and P. J. Hoftijzer, Chimie et Zndustrie, Transactions of the Congress de Chimie Industrielle, Bruxelles, September 1968, p. 168.