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Absorption of formaldehyde in waterWinkelman, Jozef

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Chapter 4: Kinetics and chemical equilibrium of the hydration of formaldehyde

33

Chapter 4

Kinetics and chemical equilibrium of the hydration of formaldehyde

Abstract

The reaction rate of the hydration of formaldehyde is obtained from the measured,chemically enhanced absorption rate of formaldehyde gas into water in a stirred cell with a planegas liquid interface, and mathematically modelling of the transfer processes. Experiments wereperformed at the conditions prevailing in industrial formaldehyde absorbers, i.e. at temperaturesof 293-333 K and at pH values between 5 and 7. The observed rate constants could be correlatedas kh = 2.04×105×e-2936/T s-1. Using the results, and the dehydration reaction rate constant,obtained previously at similar conditions, the chemical equilibrium constant for the hydration isobtained as Kh = e3769/T-5.494.

Introduction

Formaldehyde is an important industrial intermediate in the manufacturing of resins,plastics, adhesives and many other products. Because formaldehyde is unstable in its pure,gaseous state it is usually produced as an aqueous solution. In such a solution, formaldehyde isalmost completely hydrated to methylene glycol,

2222 )(OHCHk

kOHOCH

d

h+ . (1)

Methylene glycol, in turn, depending on the strength of the solution, may polymerize to form aseries of polyoxymethylene glycols,

OHHOCHHOHOCHHOOHCH nn 221222 )()()( ++ − . (2)

In the design of formaldehyde absorption and distillation processes, as well as indownstream processing, the kinetics and chemical equilibria of both reactions are important. Theresearch group of Maurer recently studied the kinetics and chemical equilibria of thepolyoxymethylene glycol formation (Hasse & Maurer, 1991; Hahnenstein, Hasse, Kreiter &Maurer, 1994; Hahnenstein, Albert, Hasse, Kreiter & Maurer, 1995)

In the open literature, only two entries with experimental data on the reaction rate constantof the hydration of aqueous formaldehyde, kh, were encountered. Schecker and Schulz (1969)obtained formaldehyde hydration rates from temperature jump experiments and measurement ofthe approach of the formaldehyde concentration to the new equilibrium value with UV-absorption. From experiments at 298-333 K they obtained kh = 7800×e-1913/T s-1 at pH = 4-7.Sutton and Downes (1972) obtained kh = 9.8 s-1 at 295 K from radiolysis of aqueous solutions ofmethanol containing oxygen and semicarbazide hydrochloride in a flow system.


34

Most of the literature data on the chemical equilibrium constant of the hydration offormaldehyde, Kh, were obtained from the carbonyl specific UV-absorption at approximately290 nm (Bieber & Trümpler, 1947; Iliceto, 1954; Landqvist, 1955; Gruen & McTigue, 1963;Siling & Akselrod, 1968; Schecker & Schulz, 1969; Zavitsas, Coffiner, Wiseman & Zavitsas,1970). At this wavelength an electron from a non-bonding oxygen n-orbital is promoted to ananti-bonding π*-orbital of the carbonyl double bond (e.g. Calvert & Pitts, 1966). From theirmeasurements mentioned above, Sutton and Downes (1972) could calculate also Kh at 295 K.Valenta (1960) used oscillographic polarography with pulses of short duration. Then, unhydratedformaldehyde is the only reducible species and its concentration could be obtained. Finally,Bryant and Thompson (1971) derived an expression for Kh from a consistent set of, partlyexperimental, thermochemical data. The values of Kh obtained by the various authors show aconsiderable spreading; differences of more than a factor 3 are found. The reaction enthalpy forthe hydration obtained from the sources mentioned varies from -21.4 to -39.4 kJ mol-1.

In previous work, hK was usually determined from the concentrations of free formaldehydeand methylene glycol in aqueous solutions, i.e. from the equilibrium value of FMG CC / . Wethink that much of the spreading of the reported hK data in the literature can be explained fromthe, occasionally unrecognized, complications in establishing these concentrations. In aqueoussolutions, the concentration of unhydrated formaldehyde is very low because the equilibrium (1)is far to the right. In addition, the molar extinction coefficient of formaldehyde in UV-absorptionis small and its value for aqueous solutions is not known. In more concentrated solutions (sayabove 1 M) the amount of unhydrated formaldehyde is higher, but the then the polymerizationreactions (2) become significant and the methylene glycol concentration is not known anymore.Also, with more concentrated solutions, UV-absorption measurements are hampered bysubstantial nonspecific absorbance. Finally, commercial formaldehyde solutions often containconsiderable amounts of methanol for stabilization; a fact that was not always recognized in olderliterature.

In this contribution, we report on the reaction rate of the hydration of formaldehyde,characterized by the rate constant kh, at conditions prevailing in industrial formaldehydeabsorbers, i.e. at temperatures of 293-333 K and at pH values between 5 and 7. Using theseresults, and the dehydration reaction rate constant, kd, obtained previously at similar conditions(Winkelman, Ottens and Beenackers, 2000), the chemical equilibrium constant for the hydrationis obtained as dhh kkK /= . The hK data obtained this way, as the ratio of measured reactionrates rather than as the ratio of concentrations, are believed to be more reliable for the reasonsmentioned in the section above.

The experimental technique for obtaining the hydration rate is based on the measurement ofthe chemically enhanced absorption rate of formaldehyde gas into water. In general, chemicalenhancement occurs if the absorption of a gaseous component into a liquid is accompanied by achemical reaction of that component in the liquid. If the reaction is fast enough, then theconcentration of the component is reduced in the liquid already near the gas-liquid interface. Thisresults in a larger gradient, and thus a larger flux, of the component, when compared to thegradient and flux without any reaction. The phenomenon is characterized by the so-calledenhancement factor, iE , which is defined as


35

reaction without )(reaction with )(

0

0

=

=≡xi

xii J

JE , (3)

where both fluxes at the gas-liquid interface, 0)( =xiJ , are based on the same concentrationdifference over the liquid film )( ,,, ll iIFi CC − (see e.g. chapter VII in Westerterp, Van Swaaij &Beenackers, 1984).

Formaldehyde absorption experiments are carried out in a stirred cell reactor. The water inthe reactor is stirred with a constant, but limited intensity, in such a way that the liquid surfacealways remains flat, and the value of the gas-liquid interfacial area remains accurately known.This way, the formaldehyde gas to liquid molar flux can be obtained from observed mass transferrate, which, in turn, allows the calculation of the liquid phase chemical enhancement factor forformaldehyde mass transfer and the reaction rate of formaldehyde hydration, respectively, frommathematical modeling of the transfer processes.

The calculation of the desired hydration reaction rate from the observed mass transfer raterequires accurate knowledge of both the gas and liquid phase mass transfer coefficients.Therefore, prior to the kinetic measurements, the mass transfer coefficients prevailing in thestirred cell reactor were accurately measured.

Experimental

The experimental set-up for the kinetic measurements was build around a stirred cellreactor, see Fig. 1. The double walled glass reactor, 0.08 m diameter, 0.1 m height, was equippedwith 4 baffles. Stirring was provided by a 0.046 m 8-bladed turbine stirrer in the gas phase, and a0.050 m flat blade stirrer in the liquid phase on the same shaft, driven via a magnetic coupling.The liquid surface remained perfectly flat for stirring rates of up to 22 Hz. Beyond this limit,some rippling and heightening of water against the baffles was observed. Nitrogen was passedthrough a saturation column, approximately 1 m in height, filled with a 32 wt.% aqueousformaldehyde solution, and flowed either via the head space of the reactor, or directly via a by-pass, to the analysis unit. The signals of the temperature control units, pressure measurement,flow measurement and stirring rate were stored into a computer. The composition of the solutionin the saturation column was accurately determined using the sodium sulphite method (Walker,1964).

The formaldehyde concentration of the gas stream entering and leaving the reactor weremeasured with UV-spectrophotometry using the carbonyl specific absorption around 295 nm. Forthis purpose, a special measuring unit was constructed by Macam Photometrics Ltd.. UV-lightwas obtained from a low pressure deuterium discharge lamp with a stabilised power supply andreference intensity measurement for stable radiation output. Further, the unit was provided withcollimating and alignment optics, a 2 nm band width monochromator, a special long-pathmeasuring cuvet with temperature control, and a photomultiplier tube. The measuring cuvet, witha volume of only 40×10-6 m3, was equipped with two flat mirrors and a concave mirror, in such away that a total optical path length of 1 m was achieved by 12 passes of the light through thecuvet, see Fig. 2. This way, the low extinction coefficient of the absorption band of gaseousformaldehyde was compensated for, and accurate measurements could be made.


36

1

2

3

4

Fig. 1. Experimental set-up, 1: gas supply, 2: saturation column, 3: stirred cell, 4: to analysis unit.

In a typical kinetic experiment, the reactor was filled with the desired amount of distilledwater, and the system, including the saturation column, the UV absorption measuring cuvet, andall connections, was allowed to equilibrate to the desired temperature. Next, the nitrogen flow tothe saturation column was set to the desired rate, and passed directly to the analysis unit, via theby-pass, to measure the reactor inlet formaldehyde concentration. The stirrer was switched to thedesired rate, and the flow was led through the reactor until the achievement of a pseudo steadystate, as indicated by a constant UV-absorption reading from the spectrophotometer, marked theend of the experiment after a few minutes. This way, with an experiment, the hydration wasmeasured at a single pseudo steady state point.

to photo-mutiplier

from mono-chromator

Fig. 2. Measuring cuvet for UV-absorption and optical path of the light.

For the liquid phase mass transfer measurements, the gas supply was switched to CO2, and avacuum pump was connected to the gas phase reactor outlet. Before an experiment, the water wasdegassed for 15 minutes by lowering the pressure to just above the water vapour pressure at thetemperature employed. Next the pressure was lowered even further, and the water allowed to boil


37

for a short time, to drive out any gasses remaining. An experiment was started by pressurising thereactor with CO2 within a few seconds to approximately 0.12 MPa, closing the inlet valve, andrecording the pressure decrease at a rate of exactly 1 Hz until the pressure decrease haddiminished.

Gas phase mass transfer coefficients were obtained by measuring the evaporation rates ofpure liquids into an inert gas stream. For this purpose, a continuous N2, CO2 or He gas supplywas used, while the gas phase reactor outlet was now connected to 3 cold traps in series, cooledwith liquid nitrogen, or, when CO2 gas was used, a mixture of water, ice and CaCl2 atapproximately 258 K. A fourth trap, filled with CaCl2, prevented any moisture from theenvironment to enter. The amount of evaporated liquid was obtained from the weight increase ofthe cold traps. The following combinations of gases and pure liquids were used: N2 with water,octane and ethanol; CO2 with water; He with butyl ether, acetone, anhydrous proprionic acid andbutanol.

Results

Liquid phase mass transfer coefficients

The liquid phase mass transfer coefficients were determined by monitoring the pressuredrop during the absorption of CO2 in water, whilst operating both gas and liquid phases in batchmode. The variation of the CO2 partial pressure with time, obtained from molar balances for CO2over both phases, is given by

l

ll

ll Vt

V

VmSk

VmV

P

P

VmV

g

CO

CO

g

CO

CO

CO

g )1()1(ln 2

22

2

20

+−=

−+ . (4)

where the distribution coefficient, 2COm , was taken from Versteeg and Van Swaaij (1988).

Pressure readings were taken every second, for a total monitoring time varying from about halfan hour to one hour. The individual experiments could be described by equation (4) very well:the mean absolute relative residual (MARR) of the calculated and observed pressures neverexceeded 0.1%.

The experimental lk -values were correlated using dimensionless groups, resulting in

%.ScRe.Sh .. 541780 360580 ±= lll , (5)

where a 4-fold variation of Sc and a 22-fold variation of Re were achieved by measuring atdifferent temperatures and stirring rates, see Fig. 3.


38

10 4 105ReL

10

100Sh

L/Sc L0.

36

Fig. 3. Liquid phase mass transfer coefficients. Symbols: experimental data. Line: Eq. (5).

Gas phase mass transfer coefficients

The gas phase mass transfer coefficients were obtained from the rate of evaporation of pureliquids into carrier gases. This way, any liquid side resistance against mass transfer waseliminated. The gk values were calculated by solving simultaneously the balance equations forthe vapour content of the carrier gas stream,

toti

iin

gvi

satiig PP

PppSk

/1)( ,

, −=−

φ (6)

and the weight of condensed vapour accumulated in the cold traps,

RTPP

P

tMW

toti

iin

gv

i )/1(,

−=

φ (7)

for igk , and iP . No influence of the gas flow rate on gk was observed for any of the

components. The gk data were also correlated via dimensionless groups:

%ScRe.Sh .g

.gg 111630 500700 ±= . (8)

By using eight combinations of carrier gases and liquids, and various stirring rates, a 23-foldvariation of Sc and a 50-fold variation of Re were achieved, see Fig. 4.


39

102 103 104

100

10

1

Sh/S

cg

g0.50

Reg

NNNCOHeHeHeHe

222

2

- water- octane- ethanol- water- butyl ether- acetone- prop. anhydr.- butanol

Fig. 4. Gas phase mass transfer coefficients. Symbols: experimental data. Line: Eq. (8).

UV-analysis of formaldehyde

The formaldehyde concentration in the gas stream was obtained spectrophotometricallyfrom the intensity of the characteristic absorption band of the carbonyl group at a wavelength of295 nm. Simple aldehydes, p.e. acetaldehyde, propionaldehyde and butyraldehydes, show nearlycontinuous absorption spectra in this wavelength region, and obey Beer's law (Calvert & Pitts,1966; Müller & Schurath, 1983)

CII lε=)/ln( 0 . (9)

However, because of its simple structure, the absorption band of formaldehyde showsconsiderably more vibrational and rotational structure, and has a discrete line structure. Becausethe spectral line widths are narrower than the resolution of 2 nm used in the measurements, theabsorbance varies nonlinear with the formaldehyde concentration. This has been reportedpreviously by Moortgat, Seiler and Warneck (1983), Müller and Schurath (1983) and Rogers(1990).

Müller and Schurath (1983) measured the absorption of gaseous formaldehyde in a 2.48 mcell in the concentration range of 0-0.12 mol m-3. They correlated their results according to

)702.2186.2()/ln( 0 CCII −= l . This correlation is illustrated in Fig. 5, together with ourmeasured data, showing a good agreement. The gas phase formaldehyde concentrations of Fig. 5are the ones in the gas stream entering the reactor, and are calculated from the composition of thesolution in the saturation column, using the vapour-liquid equilibrium model of developed by theresearch group of Maurer (Maurer, 1986; Albert, García, Kuhnert, Peschla, & Maurer, 2000), andassuming that the gas leaving the saturation column has reached physical equilibrium with theliquid.


40

0.0 0.05 0.10 0.15 0.20

0.4

0.3

0.2

0.1

0.0

CF,g [mol/m ]3

ln(I

/I) 0

Fig. 5. Absorbance vs. gaseous formaldehyde concentration. Symbols: this work, horizontal bars: standard deviation. Line: Measured by Müller and Schurath

(1983) at 12.00, −=gFC mol/m3 and extrapolated to 0.2 mol/m3.

The absorbances vs. the formaldehyde gas concentrations for the entire concentration rangeemployed here are shown in Fig. 6. They could be correlated with an expression similar to theone obtained by Müller and Schurath, and which is also shown in Fig. 6:

)488.0652.1()/ln( 0 CCII −= l (10)

0.0 0.2 0.4 0.6 0.8

CF,g [mol/m ]3

ln(I

/I) 0

1.2

0.8

0.4

0.0

Fig. 6. Absorbance vs. gaseous formaldehyde concentration. Symbols: this work,horizontal bars: standard deviation. Line: Eq. (10).


41

Kinetic measurements

The gaseous phase above an aqueous formaldehyde solution contains formaldehyde gas,water vapour, and also methylene glycol vapour (Maurer, 1986). Therefore, the gas streamentering the stirred cell from the saturation column will contain these three components, and theabsorption of formaldehyde in the reactor is accompanied by absorption of methylene glycol.Since the vapour pressure of water above an aqueous formaldehyde solution is lower than abovepure water at the same temperature, some evaporation of water will also occur

)(2)(2 lOCHOCH g → , (11)

)(22)(22 )()( lOHCHOHCH g → , (12)

)(2)(2 gOHOH →l . (13)

Once absorbed, formaldehyde will be hydrated according to the reversible reaction (1). Sincewater is present in large excess, the hydration reaction can be characterised by a first-order rateconstant, kh (Bell, 1966):

)( ,,

h

MGFhF K

CCkR l

l −= (14)

The reaction rates of the polyoxymethylene glycol formation reactions, Eq. (2), are very low.Furthermore, if the overall concentration of formaldehyde is low (say below 1 wt.%), theequilibrium constants of these reactions do not favour the formation of polyoxymethylene glycolsand the solution will contain formaldehyde and methylene glycol. Therefore, anypolyoxymethylene glycol formation is neglected in this work.

The experiments are evaluated using the two-film model. This model for mass transfer isbased on the assumption that near the interface in the liquid phase a stagnant film exists, ofthickness lll kD /=δ , where any transport of the components is by diffusion only. Similarly, inthe gas phase a film is present at the interface of a thickness ggg kD /=δ . Using the film modelfor mass transfer, the following equations describe the processes in the stirred cell

),,,()( 2,,,,0 NWMGFiCCSJ gigvin

giin

gvxi =−== φφ , (15)

),,()/()( ,,,,0 WMGFimCCkJ iIFigiigxi =−== l , (16)

),()()( ,,,,0 MGFiCCEkJ iIFiiixi =−== lll . (17)

For the general case of absorption and/or desorption of two gases accompanied by a first-orderreversible reaction in the liquid, Winkelman and Beenackers (1993) derived analytical solutionsfor the enhancement factors of the components involved. Translated to the notation used here,their equation for the enhancement factor of methylene glycol reads


42

ll

ll

,,,

,,,)1(1MGIFMG

FIFFFMG CC

CCEvE

−

−−+= . (18)

With the measured gFC , , and with 02=NJ and ll ,,, WIFW CC = , the set of Eqs (15)-(18)

can be solved for the other gasphase concentrations, gas flow rate leaving the cell, interfaceconcentrations, and mass transfer enhancement factors. In the calculations, it was assumed thatthe formaldehyde and methylene glycol concentrations in the bulk of the liquid are negligiblecompared to the interface concentrations, see the addendum at the end of this chapter. The filmthickness was obtained from Eq (5) using lll kD /=δ , and varied in the experiments fromapproximately 50 to 130 µm. The observed reactor outlet gas phase formaldehyde concentrationsof the individual experiments increased with increasing gas flow rates, and decreased withincreasing stirring rates and temperatures. In Fig. 7 the ratio of the reactor outlet and inletformaldehyde concentrations is plotted versus the quantity )/()( 3

, TNingvφ , which was chosen

intuitively for illustrative reasons only, to reduce the scattering of the data in the plot.

0.8

0.6

0.4

0.2

0.0

( ) /(NT)φv,gin 3

10 10 10-19 -18 -17

C/C

F,g

F,g

in

Fig. 7. Ratio of reactor outlet and inlet gas phase formaldehyde concentrations obtained experimentally.


43

The enhancement factor of formaldehyde calculated from the experimental data, asdescribed in the previous paragraph, can be equated to the one obtained from the differentialequations for diffusion with parallel reaction in the liquid according to the film model

)0()(2

2

, ll δ≤≤−= xK

CCk

dx

CdD

h

MGFh

FF , (19)

)0()(2

2

, ll δ≤≤−−= xK

CCk

dx

CdD

h

MGFh

MGMG . (20)

An analytical solution of (19)-(20) for the EF , with the assumption of negligible liquid bulkphase concentrations, reads (Winkelman & Beenackers, 1993)

vKC

CK

Eh

IFF

IFMGh

R

R

F +

−−

+=

))(1]tanh[

(1 ,,

,,

l

l

φφ

, (21)

where the reaction factor, Rφ , is defined by

hF

hhR KD

vKk )( += lδφ . (22)

With the values of EF obtained from Eqs (15)-(18), the reaction rate constants, kh, were calculatednumerically from (21)-(22), where the equilibrium constant Kh was written as Kh = kh/kd, and kd

was taken from Winkelman, Ottens and Beenackers (2000). The values of Rφ obtainednumerically ranged from 3.7 to 11.4.

Finally, regression of the reaction rate constants with the reciprocal temperature gave

15 )2936exp(1004.2 −−××= s

Tkh . (23)

The mean absolute relative deviation between the data from the individual experiments and fromEq. (23) is 9.6%, see Fig. 8. From the temperature coefficient the activation energy was found asEa = (24.4 ± 2.7) kJ mol-1. Regression of the results according to the transition-state theoryresulted in ∆H≠=(21.8 ± 2.7) kJ mol-1 and ∆S≠=(-152.0 ± 9.5) J mol-1 K-1. The enhancementfactors obtained from Eqs (21)-(23) are plotted against the ones obtained from the experimentaldata and Eqs (15)-(18) in Fig. 9.


44

2.8 3.0 3.2 3.4 3.6

10

30

50

5

3

1000/T

k h [1/s

]

Fig. 8. Arrhenius plot of the formaldehyde hydration rate constant kh. Symbols: ●: this work, mean of 8 to 12 experiments, horizontal bars:

standard deviation; □: Sutton & Downes (1972). Solid Line: this work, Eq. (23). Dashed line: Schecker & Schulz (1969).

0 5 10 15(E )F observed

(E) Fca

lcul

ated

15

10

5

0

Fig. 9. Parity plot of the formaldehyde enhancement factors.


45

With the hydration rate according to Eq. (23), and the dehydration rate obtained previously(Winkelman, Ottens and Beenackers 2000) the equilibrium constant for the hydration offormaldehyde can be obtained as

)494.53769exp( −==Tk

kK

d

hh . (24)

Equation (24) is illustrated in Fig. 10. From the temperature coefficient in Eq. (24) the reactionenthalpy of the hydration was obtained as ∆H = -31.4 kJ mol-1.

The experimental data obtained here can also be used to actually establish the reaction orderof formaldehyde in the hydration reaction, see Appendix C. It turns out that the reaction is indeedfirst order in formaldehyde under the experimental conditions applied.

2.9 3.0 3.1 3.2 3.3 3.4 3.5

1000/T

Kh1000

500

100

300

3000

12

34

5

Fig. 10. Van 't Hoff plot of the formaldehyde hydration chemical equilibrium constant. Solid line: this work, Eq. (24). Symbols: ∇: Landqvist (1955); ∆: Bieber & Trümpler

(1947); □: Valenta (1960); Ο: Iliceto (1954); ◊: Sutton & Downes (1972). Dashed lines: 1: Schecker & Schulz (1969); 2: Zavitsas et al. (1970); 3: Gruen &McTigue (1963); 4:

Bryant & Thompson (1971); 5: Siling & Akselrod (1968).

Discussion

The relation for the liquid phase mass transfer coefficients, Eq. (5) is of a form oftenencountered in the literature. Usually, the exponent of lSc is taken as 1/3 based on theoreticalreasons (Westerterp, Van Swaaij & Beenackers, 1984). The exponent of 0.36, obtained fromfitting the data, is in good agreement with this theoretical value. The value of the exponent of

lRe obtained here, 0.58, is at the lower end of the wide range encountered in the literature for


46

this type of reactor: from 0.5 to 1.0. This may be attributed to the specific design of our liquidphase stirrer.

Data on gas-side mass transfer coefficients in stirred cell reactors are more scarce. Tamir,Merchuk and Virkar (1979) and Yadav and Sharma (1979) investigated the influence of thediffusivity on gk in stirred cell reactors. For n

gig Dk ,∝ they obtained exponents n = 0.632 and n

= 0.487-0.518, respectively. Our exponent of 0.5 of gSc is in good agreement with these data. The reaction rate constants of this work are in reasonable agreement with the results of

Schecker and Schulz (1969), see Fig. 8. However, the activation energy of the hydration,obtained here as 24.4 kJ mol-1, is substantially higher compared to the value of 15.9 kJ mol-1

obtained by Schecker and Schultz. The agreement of Eq. (22) with the value established bySutton and Downes (1972) is excellent.

The chemical equilibrium constant for the hydration of formaldehyde, obtained here as Eq.(24), appears to be within the range of data and relations found in the literature, see Fig. 10. Athorough comparison however is not possible due to considerable spreading of the literature dataas mentioned before. Also, the heat of reaction, ∆H = -31.4 kJ mol-1, appears to be in the widerange data, from -21.4 to -39.4 kJ mol-1, encountered in the literature.

Physical properties

Pure component properties were taken from Daubert and Danner (1985), or predicted usingthe methods given by Reid, Prausnitz and Poling (1988). The distribution coefficient anddiffusivity of CO2 in water were taken from Versteeg and Van Swaaij (1988). Mixture propertieswere calculated using the mixing rules given by Reid et al. (1988). The density and viscosity ofaqueous formaldehyde solutions were taken from Winkelman and Beenackers (2000). Diffusioncoefficients in water were calculated with the Wilke-Chang method (Reid et al., 1988), where thevolume of formaldehyde at its normal boiling point was taken form Daubert and Danner (1985)and that of methylene glycol was obtained with the Le Bas method (Reid, et al., 1988). Thedistribution coefficients mF, mMG and mW were calculated with the model of Maurer for vapour-liquid equilibria of aqueous formaldehyde solutions (Maurer, 1986; Albert, García, Kuhnert,Peschla, and Maurer, 2000).

Conclusions

The reaction rate of the hydration of formaldehyde is obtained from measuring thechemically enhanced absorption of formaldehyde gas into water in a stirred cell with a plane gasliquid interface, and mathematically modelling of the transfer processes. At the conditionsprevailing in industrial formaldehyde absorbers, i.e. at temperatures of 293-333 K and at pHvalues between 5 and 7, the rate is found as kh = 2.04×105×e-2936/T s-1. Using these results, and the dehydration reaction rate constant, kd, obtained previously at similarconditions, the chemical equilibrium constant for the hydration is obtained as Kh = e3769/T-5.494.


47

Addendum

In the calculation of the hydration rate constants, the bulk liquid concentrations offormaldehyde and methylene glycol were neglected. In this addendum, we take a closer look atthe influence of this assumption by modelling the system without neglecting the bulk liquidconcentrations, and comparing the results to the ones previously obtained.

Model equations

During a kinetic experiment, gas flow continuously through the headspace of the stirredcell, while the liquid is in batch mode. The transient component balances over the headspace andthe liquid bulk read

),,()( 0,,,,, WMGFiJSCC

dtCd

V xigigvin

giin

gvgi

g =−−= =φφ (A-1)

),()(, MGFiJSRVndtCd

V xiFii =+= =δll

l (A-2)

with the initial conditions

.,,,,,, ;0:0 satgWgWMGFgMGgF CCCCCCt ====== ll . (A-3)

In Eqs (A-1) and (A-2), x denotes the distance into the liquid, thus 0)( =xJ denotes the flux of acomponent at the gas-liquid interface and δ=xJ )( denotes the flux into the liquid bulk at theinterface of the liquid film and bulk, FR is the rate of the hydration reaction in the liquid bulk,see Eq (14), and the stoichiometric coefficients, in , are given by 1−=Fn and 1=MGn .

The rate constant hk was determined for each experiment by adjusting it until gFC , ,obtained by integration of Eqs (A-1)-(A3) over the experimental run time, was equal to itsmeasured value.

The Fourier times for diffusion in the gas and liquid film (typically of the order of 0.1 s) aremuch smaller than the time scale at which variation of the bulk concentrations take place (the gasphase residence time was of the order of 10 to 20 s). Therefore, during the integration, the fluxesof formaldehyde and methylene glycol at the interface are calculated by solving simultaneouslyEqs (16)-(18) and the expression for the enhancement factor of formaldehyde, which reads in thiscase (Winkelman and Beenackers, 1993):

R

Rh

RFIFF

MGFh

FIFF

MGIFMGh

R

R

FvK

CCCCK

CCCC

K

E

φφ

φφφ

]tanh[)(

]cosh[11]tanh[1

1 ,,,

,,

,,,

,,,

+

−

−

−+

−

−−

−

+= ll

ll

ll

ll

(A-4)


48

where Rφ is given by Eq (22). The fluxes from the liquid film into the liquid bulk are obtained from the analytical

expressions for the concentrations in the film (Winkelman and Beenackers, 1993) bydifferentiation according to ==δxiJ )( δ=− xii dxdCD )/(,l , giving

)]cosh[

11(]tanh[)(

)()()()( ,,,,,,

,0R

R

Rh

MGIFMGFIFFhFxFxF

vK

CCCCKkJJ

φφφδ −

+

+−+−= ==

lllll (A-5)

and

][)()( ,,,,,,, v

CCCCkJJ MGIFMG

FIFFFxFxMGll

lll

−+−+−= == δδ (A-6)

Results

The transient model described above was solved numerically for hk for each experiment.When compared to the hk data obtained Eqs (15)-(18) and (21), the differences were small. Onaverage, the rates obtained here were 0.48 % larger, with a maximum of 1.02 %. Since this iswell within the estimated experimental uncertainty, we conclude that the influence of the bulkconcentration of formaldehyde and methylene glycol can safely be neglected in the evaluation ofthe experiments.

university of groningen absorption of formaldehyde in … 4: kinetics and chemical equilibrium of...

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