Absorption of Formaldehyde in Water

RIJKSUNIVERSITEIT GRONINGEN

Absorption of formaldehyde in water

Proefschrift

ter verkrijging van het doctoraat in deWiskunde en Natuurwetenschappenaan de Rijksuniversiteit Groningen

op gezag van de Rector Magnificus, dr. F. Zwarts,in het openbaar te verdedigen op

vrijdag 6 juni 2003 om 14.15 uur

door

Jozef Gerhardus Maria Winkelmangeboren op 2 juli 1961

te Warnsveld

Promotores: Prof. dr. ir. L.P.B.M. JanssenProf. dr. ir. H.J. HeeresProf. dr. ir. A.A.C.M. Beenackers†

Beoordelingscommissie: Prof. dr. A.A. BroekhuisProf. dr. P.D. IedemaProf. dr. ir. G.F. Versteeg

Aan mijn ouders

Acknowledgements

The research reported on in this thesis was supported financially by Dynea B.V., Delfzijl, TheNetherlands, a formaldehyde producer, and by the Technology Foundation (STW) in theNetherlands.

Contents

Contents

1. Introduction 1

2. The kinetics of the dehydration of methylene glycol. Abstract 5Introduction 5Experimental 7Results 8Discussion 14Physical properties 16Conclusions 17

3. Simultaneous absorption and/or desorption with reversible first-order chemicalreaction.

Abstract 19Introduction 19Absorption with first-order reversible reaction and desorption 20Special and limiting cases 23Applications 26Conclusions 31

4. Kinetics and chemical equilibrium of the hydration of formaldehydeAbstract 33Introduction 33Experimental 35Results 37Discussion 45Physical properties 46Conclusions 46Addendum 47

5. Modeling and simulation of industrial formaldehyde absorbers. Abstract 49Introduction 49Reactions in aqueous formaldehyde solutions 50Development of absorber model 52Mass transfer rates 53Energy transfer rates 55Physical and chemical parameters 56Vapour liquid equilibria 56

Contents

Computational method 59Results 61Conclusions 66

6. Simulation of industrial formaldehyde absorbers: the behaviour of methanol and non-equilibrium stage modelling.

Abstract 69Introduction 69Reactions in aqueous methanolic formaldehyde solutions 70Vapour liquid equilibria in formaldehyde-water-methanol mixtures 73Model development 74Mass transfer rates 76Energy transfer rates 78Method of solution 79Results 83Conclusions 92

7. Epilogue 93

Symbols 95

References 99

Appendix A: Correlations for the density and viscosity of aqueous formaldehydesolutions. 103

Appendix B: The equilibrium composition of aqueous methanolic formaldehydesolutions. 117

Appendix C: The reaction order of formaldehyde in its hydration reaction. 123

List of publications 129

Samenvatting in het nederlands (Summary in Dutch) 131

Dankwoord 137

Chapter 1: Introduction

1

Chapter 1

Introduction

This thesis describes theoretical and experimental work on the absorption of formaldehydein water and the development of chemical engineering models for the description andoptimization of industrial formaldehyde absorbers. This introduction gives a short description ofthe industrial formaldehyde production process, and of the formaldehyde absorption step therein.The introduction ends with an outline of the other chapters and appendices.

Formaldehyde is an important base chemical in the process industry with a worldproduction rate of approximately 10 million metric tons annually (Weirauch, 1999). Historically,one of the first important applications was in the production of artificial indigo. Nowadays, itsmain applications are in the production of engineering plastics and resins, especially urea, phenoland melamine resins, of which large quantities are used in the plywood and particle boardmanufacturing industry, and also in the manufacturing of rubber, paper, fertilisers, explosives,preservatives, etc. (Walker, 1964; Cancho et al., 1989).

Formaldehyde is industrially produced from methanol. The production is perfomed atapproximately atmospheric pressure. Three major steps can be identified, see Fig 1. In a firststep, the liquid methanol is vaporized into an air stream, and steam is added to the resultinggaseous mixture. In a second step, the gaseous mixture is lead over a catalyst bed, where themethanol is converted to formaldehyde via partial dehydrogenation and partial oxidation. Thetemperature of the gaseous product increases to approximately 870 K because of the highlyexothermic character of the conversion of methanol to formaldehyde.

steam

air

methanol

tail gas

water

55 wt% formalin

VAPORIZER REACTOR ABSORBER

Fig. 1. Simple scheme of the formaldehyde production process.


2

To prevent thermal decomposition of formaldehyde, the gas stream is cooled directly afterpassing over the catalyst. In a third step, the formaldehyde is absorbed in water in an absorptioncolumn, because formaldehyde in its pure, gaseous form is highly unstable, and also because thereactor product stream contains the formaldehyde diluted in other gases, mainly nitrogen. Fromthe absorber, the commercial product is obtained: an approximately 55% by weight solution offormaldehyde in water, or formalin.

The design, operation and optimization of formaldehyde absorbers is complicated by anumber of factors, of which two important ones are the reactions in the liquid phase and theexothermicity of the processes in the absorber. Formaldehyde absorbers operate less efficientthan could have been expected based on the good apparent solubility of formaldehyde in water.The reason is that, in aqueous solutions, formaldehyde reacts with water to methylene glycol andhigher poly(oxymethylene) glycols via a series of reversible reactions

2222 )OH(CHOHOCH + (1)

OHHO)HO(CHHO)HO(CH(OH)CH 2n21n222 ++ − . (2)

The good apparent solubility of formaldehyde in water is actually the good solubility ofmethylene glycol, and the capacity of the solution to accommodate poly(oxymethylene) glycols.Formaldehyde itself, like most gases, is only sparingly soluble in water.

The rate of the hydration reaction (1) is relatively fast, causing chemical enhancement of thegas-to-liquid transfer of formaldehyde. The formation rate of the higher poly(oxymethylene)glycols is low, with reaction times in the order of tens of minutes to hours, depending on thetemperature.

The absorption of formaldehyde, and its consequent hydration, as well as the condensationof steam are exothermic processes. Therefore, the temperature of the liquid increases as it flowsdown the absorber.

Because of factors such as the ones mentioned above, formaldehyde absorbers generally aredivided into different absorption sections. Each of the absorption sections, or beds, is providedwith a relatively large, externally cooled liquid recirculation stream. A typical example of aformaldehyde absorber is shown in Fig. 2.

This thesis

The major aim of this work is the development of reliable models that are capable, first, ofaccurately describing the performance of current formaldehyde absorbers, second, of predictingthe influence of changing various operating parameters, and third, of optimising the performanceof the absorber columns towards formaldehyde absorption efficiency and capacity. To achievethis goal, knowledge of the kinetics of the principal reaction (1) and the consecutivepolymerisation reactions (2) is of major importance. The kinetics of the latter, the formation ofthe poly(oxymethylene) glycols, have been investigated extensively by other research groups(p.e. Dankelman et al., 1988; Hasse & Maurer, 1991; Hahnenstein et al., 1994, 1995).


3

feed

product

tail gaswater

Fig. 2. Scheme of a typical formaldehyde absorber.

The investigations into the kinetics of the principal reaction are treated in the next threechapters. Following these are two chapters on the development of chemical reaction engineeringmodels for formaldehyde absorbers, a concluding chapter, and some additional material.

Chapter 2 describes the experimental work on the determination of the dehydration rate ofmethylene glycol, the reverse of reaction (1). Using a traditional wet chemistry methodology, thedehydration rates where obtained from the measured formation rates of hydroxymethanesulphonate from the reaction of formaldehyde with -2

3SO , at various temperatures. The resultscould be correlated to an Arrhenius type expression.


4

In Chapter 3, a theoretical treatment is presented of the problem of simultaneousabsorption and/or desorption of two components, accompanied by a first-order reversible liquidphase reaction among the two. The analytical solutions developed here for the concentrationprofiles in the mass transfer film and for the enhancement factors are used in the next chapter.

Chapter 4 describes the experimental determination of the kinetics of the hydration offormaldehyde in water. The measurements are based on the chemically enhanced absorption offormaldehyde gas into water in a stirred cell and mathematical modelling of the transfer process.The temperature dependency of the hydration rate constant correlates well to an Arrhenius typeexpression. From the results of this chapter, combined with those of chapter 2, the equilibriumconstant of the hydration of formaldehyde is obtained.

In Chapter 5 a model is developed for formaldehyde absorbers, based on differentialequations for the mass and energy balances in each phase. The resulting set of coupled boundaryvalue problems is solved by a semi-transient method.

In Chapter 6 the absorber model is extended with a description of the behaviour ofunconverted methanol that enters the absorber. Also modelled now are vaporisation andreabsorption of methylene gylcol and hemiformal, the principal reaction products offormaldehyde with water and methanol. The modelling is based here on a non-equilibrium stagemodel.

Concluding remarks can be found in Chapter 7. In the appendices, some additional material can be found: Appendix A presents the results

of experimental work on the determination of the viscosity of aqueous formaldehyde solutionsand correlations for the density and viscosity of aqueous formaldehyde solutions as a function ofthe temperature and the strength of the solution; Appendix B elucidates some calculationmethods to obtain the equilibrium composition of solutions containing formaldehyde. Someadditional material to chapter 4, on the determination of the reaction order of formaldehyde in thehydration reaction, is included in Appendix C.

Chapter 2: The kinetics of the dehydration of methylene glycol.

5

Chapter 2

The kinetics of the dehydration of methylene glycol.

Abstract

The kinetics of the dehydration of methylene glycol were measured under conditionsrelevant in industrial formaldehyde absorbers (293 K ≤ T ≤ 333 K; 6.0 ≤ pH ≤ 7.8). The rapidreaction between formaldehyde and SO3

2− to hydroxymethane sulphonate (HMS−) was used as aformaldehyde scavenger:

OHOCH(OH)CH 2222 +→ dk ,−−− →+ 32

fast232 )SO(OCHSOOCH ,

−+−− →+ 32fast

32 (OH)SOCHH)SO(OCH . At the experimental conditions, the rate determining step in the formation of HMS− appeared tobe the dehydration of methylene glycol. The observed reaction rate constant for the dehydrationof methylene glycol could be correlated as 1/67057 s1096.4 −−⋅= T

d ek . The dehydration rate isshown to be independent of the concentrations of both sulphite and hydroxide ions at theconditions applied here.

Introduction

For a detailed model of the absorption process of formaldehyde, as well as in the furtherapplications of formaldehyde, the kinetics of the dehydration of methylene glycol (see eq. (1)),are important.

The literature data on the dehydration rate of methylene glycol are limited to ambienttemperatures. Using various chemical scavengers, LeHénaff (1963) and Bell et al. (1966)obtained kd = 4.5×10-3 s-1 at 293 K and 5.1×10-3 s-1 at 298 K, respectively. From theformaldehyde production and subsequent reaction in the radiolysis of methanol in a flowmeasurement system, Sutton and Downes (1972) calculated kd = 4.4×10-3 s-1 at 295 K. Los et al.(1977) found kd = 5.7×10-3 s-1 at 298 K with pulse polarography. Funderburk et al. (1978)obtained kd = 4.2×10-3 s-1 at 298 K using carbazides and hydrazine as trapping agents.

In this contribution we report on the reaction rate of the dehydration of methylene glycol,characterized by the reaction rate constant kd, at the conditions prevailing in industrialformaldehyde absorbers; at the wider temperature range of 293-333 K and at a pH between 6 and7.

The experimental method applied uses the reaction of sodium sulphite with formaldehyde.In aqueous solution sulphite ions react specifically with the carbonyl group of aldehydes orketones to form α-hydroxy sulphonates (Blackadder and Hinshelwood, 1958). The sulphite ionsdo not react with methylene glycol. The reaction of sulphite with formaldehyde is fast


6

(LeHénaff, 1963; Boyce & Hoffmann, 1984), and under suitable conditions the formation rate ofthe product, hydroxymethane sulphonate, CH2(OH)SO3

− (HMS−), is completely determined bythe dehydration rate of methylene glycol. Sulphite then is a trapping agent, or chemicalscavenger, of any formaldehyde produced by the dehydration of methylene glycol.

In the mechanism of the HMS− formation, the following reactions are relevant here

OHOCH)OH(CH 2222 +

h

d

k

k, (1)

+−− + HSOHSO 23

2

3

aK, (2)

−−

−

−+ 32

2

2232 SO)O(CHSOOCH

k

k, (3)

−−

−

−− ++ OHSO)OH(CHOHSO)O(CH 32

1)HMS(2

232

awKK. (4)

Sørensen and Andersen (1970) studied the kinetics of the HMS− formation from sodiumsulphite and formaldehyde at 298 K in strongly alkaline aqueous solutions (pH 9-12). At thesehigh pH values they found the rate determining step of the overall reaction to be the dehydrationof methylene glycol catalysed by hydroxide ions, and obtained kd = 1.7×103[OH−] s-1 at 298 K.The initial concentrations of formaldehyde, 20-38 mol m-3 , and sulphite, 29-37 mol m-3 , were ofcomparable magnitudes.

Boyce and Hoffmann (1984) studied the rate of formation of HMS− from formaldehyde inacidic solutions (pH = 0-3.5) at temperatures from 288 K to 313 K. They concluded that the ratedetermining step in the HMS− formation involves the nucleophilic addition of bisulphite and/orsulphite ions to the carbonyl group of formaldehyde. They also found bisulphite to be theprincipal reactant at pH < 2, whereas at pH > 4 the reaction is carried by sulphite. The initialconcentrations of formaldehyde, 10-100 mol m-3, were considerably higher than the initialsulphite + bisulphite concentrations, 0.25-1.25 mol m-3.

From the overall reaction equation, which results from adding eqs (1), (3) and (4), it is seenthat the formation of HMS− is accompanied by the release of hydroxide ions

−−− +→+ OH(OH)SOCHSO(OH)CH 322322 . (5)

By using sodium bisulphite in combination with sodium sulphite, a buffering capacity isintroduced and the conditions can be chosen in such a way that the pH rises only modestly for aconsiderable length of time as compared to the time needed to get close to the maximumconversion of sulphite.


7

Experimental

A stock solution containing approximately 1% by weight of formaldehyde was prepared bydissolving paraformaldehyde (Janssen Chimica) in water and allowing to equilibrate severaldays. The overall formaldehyde concentration in the stock was determined accurately with thesulphite method (Walker, 1964). The low overall formaldehyde content in the stock solutionensures that any polymeric forms of formaldehyde can be neglected (see Appendix B). Reagentgrade sodium bisulphite and sodium sulphite (Janssen Chimica) were used to prepare 100 mlaliquots of buffer solutions of these components just prior to the experiments. Because carbondioxide can interfere with the pH measurements, and oxygen can induce oxidation of bisulphiteor sulphite, the water used in the experiments and in the preparation of the solutions was doubledistilled, and boiled out and stored with nitrogen purging.

A Metrohm type E561/1 pH meter was used. The output signal from the pH meter was sendto a computer with a frequency of exactly 1 Hz for later analysis. The experiments were carriedout in a closed, double walled vessel, kept at the desired temperature by circulating water. Thevessel was equipped with a nitrogen inlet, for purging prior to the experiment, a pH electrodeand a septum sealed inlet for adding reagent solutions via syringes.

Before an experiment was started, the desired amount of buffer solution was added to 100ml water in the stirred reaction vessel, and allowed to attain thermal equilibrium. Meanwhile, asample of the formaldehyde stock solution was brought to the same temperature in a separatevessel also under nitrogen. The injection of a desired amount of this formaldehyde stock solutioninto the reaction vessel marked the start of the experiment.

Experiments were performed at 5 temperatures ranging from 293 to 333 K. At eachtemperature 8-10 experiments were performed with various sulphite/bisulphite ratios of thebuffer solution, and with various amounts of buffer solution and formaldehyde stock solutionadded to the reaction vessel. This way, the following ranges of variation in initial concentrationswere realised: pH0 = 6-7, [NaHSO3]0 = 1.5-8.0 mol m-3, [Na2SO3]0= 0.3-5.2 mol m-3, and[CH2(OH)2]0 = 4-25 mol m-3. The concentrations were chosen in such a way that[CH2(OH)2]0 > Stot in all experiments, where Stot denotes the total concentration of sulphur:

03203 ]SONa[]NaHSO[ +=totS . (6)

It should be noted here that [NaHSO3]0 and [Na2SO3]0 are the initial molar concentrations ofreagentia used to make up the solution. They are not a priori identical with the true initialconcentrations of bisulphite and sulphite ions, [HSO3

−]0 and [SO32−]0, since these are determined

by the dissociation constants governing the system. The build-up of pyrosulphate according to

OHOSHSO2 22523 +−−

is proportional to the square of the HSO3− concentration (Hayon et al., 1972). However, the

equilibrium constant of the reaction is very small, and the S2O52− concentration becomes


8

negligible in solutions containing less than 50 mol m-3 of sulphur (Golding, 1960; Deister et al.,1986). Since the total sulphur concentrations employed here were always less than 15 mol m-3,we can safely neglect any pyrosulphate formation.

Results

An example of the pH readings recorded during an experiment is shown in Fig. 1. Theprofile is typical for all experimental results: after a gradual increase there is a sharp upturn ofthe pH corresponding to a decrease of the concentration of hydrogen ions.

In this section we will first explain qualitatively the origin of the typical profiles of themeasured pH curves, and secondly show how quantitative kinetic information was extractedfrom the experimental data.

12

10

8

6

0 20 40 60 80 100

t (s)

pH

Fig. 1. pH as a function of time for a typical experiment (no. 20.1): T = 293 K, [NaHSO3]0 = 4.311 mol m-3, [Na2SO3]0 = 1.146 mol m-3, and [CH2(OH)2]0 = 22.84 mol m-3.

For each of the data points of an experiment, [H+] was used to calculate the concentrationsof the other relevant species, [H2SO3], [HSO3

−], [SO32−], [HMS−], [OH−], [Na+] and [CH2(OH)2],

from the sulphur balance

]HMS[]SO[]HSO[]SOH[ 23332

−−− +++=totS , (7)

the sodium balance

]Na[]SONa[2]NaHSO[ 03203+=+ , (8)


9

the carbon balance

][HMS](OH)[CH](OH)[CH 22022 −+= , (9)

the charge balance

][OH][HMS]2[SO][HSO][Na][H 233

−−−−++ +++=+ , (10)

the water ionisation equilibrium

WK=−+ ]OH][H[ , (11)

and the two sulphite dissociation equilibria

132

3]SOH[

]H][HSO[aK=

+−, (12)

23

23

]HSO[

]H][SO[aK=

−

+−. (13)

In writing the carbon balance, the contribution of CH2O was neglected because theequilibrium of eq. (1) is far to the left and the concentration of free formaldehyde is very low(Zavitsas et al., 1970). The calculations showed that [H2SO3] was always negligible. Thereforethis species was neglected in the further considerations. For the remaining sulphur containingcomponents the concentrations vs. pH are shown in Fig. 2 for experiment no 20.1. It may benoted that before the large pH jump, [SO3

2−] remains constant. This was found to be the case forall experiments, and can be explained by subtracting the sulphur balance, eq. (7), from the chargebalance, eq. (10), substituting eqs (6) and (8) for Stot and [Na+], and rearranging, giving

]H[]H[]SONa[]SO[ 032

23 +

+− −+= WK. (14)


10

6 7 8 9

pH

5

4

3

2

1

0

HSO3-

SO -32

HMS-

10 11

conc

entra

tion

(mol

/m)3

Fig. 2. Concentrations of sulphurous components vs. pH of experiment no 20.1, see Fig. 1. Symbols: calculated points. Lines: for illustrative purposes only.

It can easily be shown that, for the range of [Na2SO3]0 and pH0 values employed here, in order toobserve a decrease of the sulphite concentration from [SO3

2−]0 with say 1%, an increase of thepH is needed varying from pH > 9 at 293 K to pH > 8 at 333 K. The highest pH measured beforethe large pH jump occurred was 7.8. It can therefore safely be assumed that [SO3

2−] is constantfor pH < 7.8.

Now, the typical pH profile of Fig. 1 can be explained qualitatively. The SO32− ions that

react with formaldehyde to HMS− are replenished with new ones obtained from the dissociationof HSO3

− . The gradual decrease of [HSO3−] results in a decrease of the buffering capacity of the

mixture and a gradual increase of the pH. At the point where all HSO3− initially present is

consumed, the buffering capacity breaks down completely, resulting in the large pH jump. Anydata points beyond the pH jump, i.e. those with pH>8, are not used in the current analysis.

In writing the mechanism of the HMS− formation, eqs (1)-(4), it is assumed that the ionequilibria, eqs (2) and (4), are established rapidly. The equilibrium of eq (4) is far to the right atpH < 8, and the concentration of HMS2− is negligible. Because SO3

2− is the better nucleophile bya factor of 105 compared to HSO3

− (Burnett, 1982), and based on the results of Boyce andHoffmann (1984), see introduction, the direct addition of bisulphite ions to formaldehyde wasneglected in the scheme of the reaction mechanism.

Since the equilibrium of the overall HMS− formation reaction, eq (5), is far to the right(Dasgupta et al., 1980; Deister et al., 1986) the decomposition of HMS−, via the reverse ofreactions (4) and (3), can be neglected for the first part of the measured pH profiles, i.e. beforethe pH jump occurs. The rate of HMS− formation then is


11

]SO][OCH[d

]HMSd[ 2322−

−= k

t. (15)

Applying the steady state principle to [CH2O] in reactions (1) and (3) gives

]SO[

])OH(CH[]OCH[

232

222 −+

=kk

k

h

d , (16)

where kh is the pseudo-first-order rate constant for the hydration of formaldehyde, see eq (1).Substitution of eq (16) into eq (15) gives

]SO[

])OH(CH][SO[d

])OH(CHd[d

]HMSd[232

2223222

−

−−

+=−=

kk

kktt h

d . (17)

Before the pH jump, i.e. pH < 7.8, the sulphite concentration remains constant. This allows theintegration of eq (17)

tkobs−=− 02222 ])OH(CHln[])OH(CHln[ , (18)

where

]SO[

]SO[232

232

−

−

+=

kk

kkk

h

dobs . (19)

The experimental data appear to be very well described by eq (18). An example is shown in Fig.3 for the data also used in Figs 1 and 2.

Rewriting eq (19) as

dd

h

obs kkkk

k1

]SO[1/1

23

2 +=−

(20)

shows that the values of (kh/k2) and kd at each temperature should follow from the kobs dataobtained whilst varying [SO3

2−]. However, at each temperature applied, a regression analysis ofthe data according to eq (20) showed that the variation of 1/kobs with 1/[SO3

2−]was not significant (95% confidence level). A plot of the data obtained at 323 and 333 Kaccording to eq (20), shown in Fig. 4, illustrates this nicely. Apparently we have k2[SO3

2−] >> kh, and eq (19) reduces to kobs = kd .


12

3.2

3.1

3.0

2.9

2.80 10 20 30 40 50

t (s)

ln(

)

mol

/m3

[CH

(OH

)]

22

Fig. 3. Data of experiment no 20.1, see Fig. 1, plotted according to eq (18).

1/[SO ] (m /mol)32- 3

0 1 2 3 4 5

1/k

(s)

obs

102

101

1

333K

323K

Fig. 4. Data plotted according to eq (20). Symbols: 1/kobs obtained from eq (18) for a single experiment.Lines: mean value of 1/kobs at a given temperature.

The reaction rate, eq (17), then reduces to

](OH)CH[d

](OH)CHd[d

]HMSd[22

22dk

tt=−=

−. (21)

This way, it is demonstrated that, under the experimental conditions applied, the rate offormation of HMS− is completely controlled by the dehydration rate of methylene glycol.


13

Regression of the reaction rate constants with the reciprocal temperature gave

−×=

Tkd

6705exp1096.4 7 s-1. (22)

Equation (22) describes the data obtained from the individual experiments with a mean absoluterelative deviation of 13%, see Fig. 5. From the temperature coefficient the activation energy wasfound as Ea = (55.8 ± 2.7) kJ mol-1. Regression of the reaction rate constants according to thetransition-state theory resulted in ∆H≠ = (53.2 ± 2.7) kJ mol-1 and ∆S≠ = (-106.3 ± 8.7) J mol-1 K-1

for the dehydration reaction.

2.7 2.9 3.1 3.3 3.5 3.7

10

10

10

-1

-2

-3

1

1/ T x 10 (K )3 1-

k (s

)d

- 1

Fig. 5. Arrhenius plot of the methylene glycol dehydration rate constant kd. Symbols: mean value of at least 8 experiments. Horizontal bars: standard deviation. Line: eq (22).


14

Discussion

The reaction rate constant for the dehydration of methylene glycol obtained from eq (22) at293 K, kd = 5.7×10-3 s-1 compares well with the literature data mentioned in the introduction.However, the mechanism obtained here for the reaction of sulphite with formaldehyde inaqueous solution, i.e. the rate limiting dehydration of methylene glycol, differs from both themechanism obtained by Sørensen and Andersen (1970) and by Boyce and Hoffmann (1984), seethe introduction of this chapter.

Since the variation of kd with [SO32−] appeared not to be significant, see Fig. 4, the addition

of SO32− to formaldehyde can not be rate controlling. Probably, Boyce and Hoffmann (1984)

found otherwise because of the large excess of methylene glycol and the high acidities in theirexperiments. Hydrogen ions are known to catalyse the dehydration of methylene glycol underacidic conditions (Funderburk et al., 1978).

In order to check for the possible catalysis of the dehydration of methylene glycol byhydroxide ions, which Sørensen and Andersen (1970) found rate determining at their conditions,eq (21) can be extended to

( ) ](OH)CH[]OH[d

](OH)CHd[22OH,

22 −+=− dd kkt

. (23)

Because this equation cannot be integrated analytically, the method of Himmelblau et al. (1967)was used to fit the experimental data. Integration of eq (23) gives

∫ −−−=−it

didi tktk0

OH,02222 d]OH[](OH)CHln[](OH)CHln[ , (24)

where the subscript i denotes the ith data point from an experiment. The integral on the righthand side of eq (24) was evaluated numerically for each data point. The trapezoidal rule sufficesfor this purpose because the values of [OH−] vary smoothly, and data points were obtained everysecond. The constants kd and kd,OH were calculated using multiple regression according to eq (24)applied to all the data points from all the experiments at a specific temperature simultaneously.The kd,OH values thus obtained appeared to decrease with increasing temperature, andkd,OH[OH−]<<kd for all experiments. From this it follows that catalysis of the dehydration ofmethylene glycol by hydroxide ions is not significant at the conditions used here. Thisconclusion is consistent with the measurements of Funderburk et al. (1978) who showed that theinfluence of OH− is significant only for pH > 8 at 298 K.

The same conclusion can be drawn from inspecting the relative residuals of the kd values,by comparing the values obtained from eq (22) with those obtained from the individualexperiments, as a function of the measured initial pH, see Fig. 6. The residuals were calculated as


15

%100)(

)()(residual

experiment

experimenteq(22) ×−

=d

dd

k

kk. (25)

If the dehydration rate would be susceptible to catalysis by hydroxide ions at the conditionsemployed here, a systematic deviation would be expected in Fig. 6 from more positive residualsat lower pH, i.e. low [OH−], to more negative ones at higher pH, with higher [OH−]. The absenceof such a trend indicates the absence of catalysis by hydroxide ions in this pH region.

Similarly, any catalysis of the dehydration of methylene glycol by hydrogen ions, asobserved under acidic conditions (Funderburk et al. ,1978), can be excluded in the p|H regionconsidered her, based on Fig. 6.

The observation of Sørensen and Andersen (1970) that the HMS− formation rate iscompletely determined by kd,OH[OH−] can be attributed to the much higher alkalinity of theirsolutions, where the pH ranged from 9 to 12.

6 7

pH6.5

100

50

0

-50

-100

resi

dual

of k

(%)

d

+13%

-13%

Fig. 6. Relative residuals of the kd values from individual experiments compared to the value obtained from eq (22).

Physical properties

All the calculations mentioned in this chapter were corrected for non-ideal behaviour. Thissection explains how and why these corrections were performed.

Because of the electrical interactions between ionic species, even quite dilute electrolytesolutions exhibit non-ideal behaviour. Thermodynamic treatments then require the use ofactivities in stead of concentrations for the charged species. Here, activity coefficients were used


16

to correct for the deviations from ideal behaviour, allowing the thermodynamic dissociationequilibrium constants to be expressed as a function of the temperature only.

The temperature dependence of the thermodynamic equilibrium constant for thedissociation of H2SO3, Ka1

th , was obtained by regression of the data measured by Devèze andRumpf (1964)

−== +−

+−08.42009exp

]SOH[]H][HSO[

)H()3HSO(32

31 T

K tha γγ . (26)

Similarly, Ka2th , for the dissociation of HSO3

− , was obtained from the data measured by Hayonet al. (1972)

−==

−

+−

−

+−39.141400exp

]HSO[

]H][SO[

)3HSO(

)H()23SO(

3

23

2 TK th

a γ

γγ. (27)

The thermodynamic dissociation constant of water was taken from Stumm and Morgan (1970,p.76)

TT

K thw ×−−== −+

−+ 01706.099.44700875.12)]OH][Hlog([log)OH()H(

1010 γγ . (28)

The concentration based equilibrium constants Ka1, Ka2 and Kw of eqs (11)-(13) were obtained bycorrecting the corresponding thermodynamic equilibrium constants for the influence of the ionicstrength according to the Güntelberg modification of the Debye-Hückel limiting law (Stumm &Morgan, 1970, p.83)

5.0

5.0

5.1

26

1)(1020.4ln

µ

µ

εγ

+×−=

T

zii , (29)

where ε is the dielectric constant of water, varying from ε = 80.14 at 293 K down to ε = 66.78 at333 K (Handbook of Chemistry and Physics), zi denotes the charge number of ion i, and the ionicstrength, µ, is given by

∑ −=i

ii zC )10(21 23µ , (30)

where the summation runs over all ionic species. Because of the non-linearity of the equations, the concentrations of the components and the

concentration based equilibrium constants had to be calculated using an iterative method. A


17

successive approximation method, initialised by taking all activity coefficients equal to 1.0,proved to be efficient for this purpose.

Conclusions

For the nearly neutral conditions employed here, pH-range 6.0-7.8, the rate determining step inthe reaction of sulphite with formaldehyde in aqueous sulphite bisulphite buffer solutions is thedehydration of methylene glycol. The dehydration rate appeared to be independent ofconcentrations of both sulphite, [SO3

2−], and hydroxide, [OH−], ions as opposed to the resultsobtained by Boyce and Hoffmann (1984) at very acidic conditions, pH-range 0-3.5, and bySørensen and Andersen (1970) at more alkaline conditions, pH-range 9-12.

The methylene glycol dehydration rate constant obtained in this work at 293 K agrees wellwith the values obtained by other authors at 293-298 K. The experimental kd values attemperatures ranging from 293 to 333 K could be described with an Arrhenius-type equation,from which an activation energy of Ea = (55.8 ± 2.7) kJ mol-1 was obtained.

Chapter 3: Simultaneous absorption and/or desorption with reversible first-order chemical reaction.

19

Chapter 3

Simultaneous absorption and/or desorption with reversible first-order chemical reaction.

Abstract

The problem of gas absorption accompanied by a first order reversible reaction, producing avolatile reaction product, is considered. A general analytical solution is developed for the filmmodel, resulting in explicit relations for the concentration profiles in the film and for the masstransfer enhancement factors. The solution is not restricted to equal diffusivities, and is alsoapplicable to the simultaneous absorption and reversible reaction of two gases. Several limitingcases are derived. It is shown that enhancement factors are possible with values larger than one,but also smaller than one, and even negative. The latter occurs in the industrially importantabsorption of formaldehyde in aqueous solution.

Introduction

In the description of interphase mass transfer accompanied by chemical reactions, it iscommon practice to incorporate the effects of reactions on the mass transfer rates in enhancementfactors. In the extensive literature on mass transfer enhancement by chemical reaction, manycontributions can be found on analytical and approximate analytical expressions for theenhancement factors for a number of reaction stoichiometries, with single or multiple reactionsand with irreversible or reversible reactions [e.g. Westerterp et al. (1984, Chap. 7 and 8) and thereferences therein]. The greater part of this literature is devoted to the absorption of a reactingspecies from a gaseous phase to a liquid phase, where it reacts to non-volatile products. For thistype of operation, the enhancement factor for the transferred component, defined as Eq (12) has alower limit of one.

Recently, Landau (1992) published analytical solutions for the case of first order reactions,irreversible and reversible, involving a non-volatile reactant present in the liquid phase only, anddesorption of the volatile reaction product. Here also, the enhancement factor for the transferringspecies has a minimum of one. In fact, by linking the description of the processes in theinterfacial region to those in the bulk, Landau showed that the enhancement of productdesorption is negligible if the reactant originates completely from the liquid.

A different situation arises if two gases absorb in a liquid, accompanied by reversiblereactions. Cornelisse et al. (1980) numerically simulated the absorption of H2S and CO2 in anamine solution accompanied by complex reversible reactions, and showed that, under certainconditions, negative enhancement factors are possible for such systems. As far as we know,Cornelisse et al. were the first to point out the possibility of negative enhancement factors.


20

In our work on the simulation of the absorption of formaldehyde in water we came across avery simple system displaying negative enhancement factors: the absorption of a gas,accompanied by a first order reversible reaction and partial desorption of the reaction product.The purpose of this contribution is to analyse this type of absorption kinetics.

Absorption with first-order reversible reaction and desorption

Gas absorption accompanied by a first order reversible reaction and partial desorption of thereaction product

)()( AA l→g (1))()( PA ll ↔ (2))()( PP g→l (3)

with the reaction rate equation

)(1 KCCkR P

AA −= (4)

can be described according to the film model by the following equations for diffusion withreaction:

AA

A RxCD =2

2

,d

dl (5)

AP

P RxCD −=2

2

,d

dl (6)

and boundary conditions

IPP

IAA CCCCx === ,:0 (7)

PPAA CCCCx === ,:δ . (8)

The concentrations in the bulk liquid are not necessarily at equilibrium. Equations (5) and (6) canbe solved analytically for the concentrations of A and P in the film:


22

Substitution of eq (13) into (15) gives

R

R

RPIP

PA

PIP

AIA

R

R

PvK

CC

CCK

CC

CCK

vE

φφ

φφφ

]tanh[)(

]cosh[111

)(]tanh[1

1+

−

−

−+

−

−

−

−

−= . (16)

From eqs (12) and (14) it is seen that the sign of E depends on the direction of masstransfer, i.e. the sign of 0)/d(d =xxC , and on the sign of the concentration difference over the

film, )( CC I − . If the combined effects of mass transfer and reaction cause the concentration ofa component at the interface to be equal to the concentration in the liquid bulk, an asymptote isfound for the enhancement factor of that component. Small deviations from this situation resultin either positive or negative enhancement factors. We will return to this remarkable behaviourbelow.

For ll ,, PA DD = (i.e. v = 1) a solution of eqs (5)-(8) was presented earlier by Shah andSharma (1976). Their eq (269) gives a relation for the desorption rate of the product P throughthe gas-liquid interface, )(,

IPPPP CCEk −l , which contains EP implicitly. However, their

equation seems to contain some misprints because calculations using it gave erroneous results. In engineering calculations, the bulk phase concentrations are usually available from

macroscopic balances. A combination of eqs (13) and (15) with the rate balances

)()/( ,,, AIAAAA

IAgAAg CCEkmCCk −=− l (17)

)()/( ,,, PIPPPP

IPgPPg CCEkmCCk −=− l (18)

allows the calculation of the unknown interface concentrations and enhancement factors from theknown bulk phase concentrations. If the gas phase resistance to mass transfer is negligible so thatmass transfer is completely liquid-film-controlled, eqs (17) and (18) can be replaced by

gAAIA CmC ,= and gPP

IP CmC ,= .

From the general scheme outlined above, several interesting special cases can be derived.Here we will look at some of these in detail.


21

vKCCvx

vKCvCx

vKCCK

x

vKCKC

x

C

PAIP

IA

PA

R

RIP

IA

R

R

A

++

+++

−+

+−

++−

−

=

)()1(

]sinh[

]sinh[

]sinh[

)1(sinh

δδ

φδ

φ

φδ

φ

(9)

and

)]()([)( PIPA

IAA

IA

IPP CCCCvxCCvCC −+−−−+=

δ. (10)

The parameters φR and v are defined as

l

l

l ,

,

,

1 and)(

P

A

AR D

Dv

KDvKk

=+

= δφ . (11)

The enhancement factor for component A for a non-instantaneous reaction defined as

)(

dd

,

0,

AIAA

x

AA

ACCk

xC

DE

−

−

≡ =

l

l

(12)

is found from Eq (9) as

R

R

RAIA

PA

AIA

PIP

R

R

AvK

CC

CCK

CC

CCK

E

φφ

φφφ

]tanh[)(

]cosh[11

]tanh[1

1+

−

−

−+

−

−−

−

+= . (13)

Similarly, the enhancement factor of component P for a non-instantaneous reaction, defined as

)(

dd

,

0,

PIPP

x

PP

PCCk

xC

DE

−

−

≡ =

l

l

(14)

is found from eqs (10), (12) and (14) as

PIP

AIA

APCC

CCEvE

−

−−+= )1(1 (15)


23

Special and limiting cases

Instantaneous reversible reaction, volatile reactant and product If the reaction is instantaneous, the rates of the forward and backward reactions of eq (2)

have infinite values, and chemical equilibrium will prevail everywhere in the liquid. For thissituation, the right-hand sides of eqs (5) and (6) become undefined. Elimination of the reactionterm AR from (5) and (6) the gives

02

2

2

2=+

dxCdD

dxCdD P

PA

A .

With the equilibrium condition AP KCC = and the boundary condition (7), this equation caneasily be solved for AC in the liquid film:

)( AIA

IAA CCxCC −−=

δ. (19)

A balance at the interface states that the amounts of A and P arriving at the interface from the gasphase equal the amounts of A and P that diffuse from the interface into the liquid film:

00,,,, )()()/()/( == −−=−+− xP

PxA

APIPgPPgA

IAgAAg dx

dCDdx

dCDmCCkmCCk .(20)

Substitution of eqs (17)-(19) and the equilibrium condition AP KCC = into eq. (20) gives therelation between the enhancement factors AE and PE :

KEvE AP

1)1(1 −+= . (21)

Now, with a known set of bulk phase concentrations, the interface concentrations andenhancement factors can be calculated from eqs (17), (18) and (21) together with the equilibriumcondition I

AIP KCC = .

Volatile reactant, nonvolatile reaction product For the case where the reaction product P is nonvolatile, the mass transfer enhancement

factor for P is not defined anymore. For this case, from eqs (10) and (12) and the condition0)/d(d 0 ==xP xC , an expression is found for I

PC

))(1( AIAAP

IP CCEvCC −−+= . (22)


24

Substitution of eq (22) into (13) results in an equation for EA which is only valid if0)/d(d 0 ==xP xC :

R

R

RAIA

PA

A

vK

CCv

CCKvK

E

φφ

φ

]tanh[1

]cosh[11

)(1

+

−

−

−++

= . (23)

This expression is similar to the one obtained by Onda et al. (1970). If also the reaction isinstantaneous, taking the limit for ∞→Rφ of eq (23) gives

vKEA +=1 (24)

which is contained in the solution given for this case by Astarita and Savage (1980).

Nonvolatile reactant, volatile reaction product Another special case is the situation where the product P is volatile, but where the reactant

A originates completely from the liquid phase and is nonvolatile, 0)/d(d 0 ==xA xC . Then wehave from eq (10)

)]()([1d

d

0P

IPA

IA

x

P CCCCvx

C−+−

−=

= δ(25)

Substitution of eq (25) into (14) gives

PIP

AIA

PCC

CCvE

−

−+=1 (26)

Furthermore, from eq (9) together with 0)/d(d 0 ==xA xC an expression for IAC is found, which

is substituted into eq (26) to find

R

R

RPIP

PA

P

vK

CCCCK

vK

E

φφ

φ]tanh[

]cosh[111

+

−

−

−−+

= . (27)


25

If the reaction is instantaneous, there is chemical equilibrium in the liquid: IA

IP KCC = and

AP CKC = . For this case eq (27) reduces to:

KvEP +=1 . (28)

This equation was derived by Westerterp et al. (1984, p.423). It is also implicitly present in theexpression obtained by Shah and Sharma (1976) for the desorption flux of P, but their eq (61)unfortunately contains a misprint.

Irreversible reaction The first order irreversible reaction can be regarded as a limiting case of the reversible

reaction, with K going to infinity. While eq (15) is still valid, EA can be found for this case bytaking the limit of eq (13). In this way we indeed get the classical result:

AIA

RAIA

R

RA

KA

CC

CCEE

−

−== ∞

∞

∞

∞→∞

]cosh[/]tanh[

)(lim ,

,

,,

φφ

φ(29)

with

l,

1, )(lim

AR

KR D

kδφφ ==∞→

∞ . (30)

Simultaneous absorption and reaction of two gases Recently, van Swaaij and Versteeg (1992) presented a review on gas-liquid mass transfer

with reversible reactions. For the simultaneous absorption and reaction of two gases they notedthat reversible reactions have not been studied so far. For this case, if the reaction between thetwo absorbed gases is first-order-reversible according to the scheme

)()( AA l→g (31))()( PP l→g (32))()( PA ll ↔ (33)

it may be noted that the problem is also stated by eqs (5)-(8), and that these equations areindependent of the direction of mass transfer. Also the solution in terms of the concentrationprofiles (9) and (10) and the enhancement factors (13) and (16) are independent of the directionof mass transfer. Thus, for the case of absorption of two gases, A and P, accompanied by a firstorder reversible reaction in the liquid, the mass transfer rates and enhancement factors can beobtained from eqs (13) and (16) combined with eqs (17) and (18).


27

φR=0.12

4.47

10

50

∞

x/δ0 0.2 0.4 0.6 0.8 1

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

C CA A-

m CA A,g

Fig. 2. Dimensionless concentration of A in the liquid film. Parameter values as mention in example 1.

φR=∞

2

4.47

10

50

x/δ0 0.2 0.4 0.6 0.8 1

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

v m CA A,g

C CP P-

0.1

Fig. 3. Dimensionless concentration of P in the liquid film. Parameter values as mention in example 1.

These are shown in Figs 2 and 3 as dimensionless concentration differences vs. the depth inthe liquid film, for various Rφ values. At the critical value of 47.4=Rφ , the value of I

PC equalsthat of PC . This results in the asymptotic behaviour of PE because )( , PiP CC − is in the

denominator of eq. (14). However, note that although IPC equals PC , there is still desorption of

P as indicated by the positive gradient PC at the interface. At larger values of Rφ the reaction is

fast enough to make IPC larger than PC , and EP becomes negative. At smaller values of Rφ , the


28

production of P by reaction cannot keep up with the vaporisation of P: IPC becomes smaller than

PC and PE is positive. In Figs 2 and 3, the lines indicated with ∞=Rφ denote the limitinginstantaneous case where the concentration profiles are given by eq. (19) and the equilibriumcondition AP KCC = .

The influence of the volatility of the reaction product P on AE is shown in Fig. 4, using thesame set of parameters except for the value of )/( ,, PlPPg kmk . The line marked with

)/( ,, PlPPg kmk = 0 denotes the limiting case of volatile reactant with a nonvolatile reactionproduct. The dimensionless the concentration profiles of P vs. the depth in the liquid film areshown in Fig. 5 for a relatively fast reaction ( 10=Rφ ). It may be noted that the positive gradientof P at the interface, and therefore the desorption rate of P, decreases with a decreasing volatilityof P. Also, in the limiting case of a nonvolatile reaction product P, we indeed have

0)/( =xP dxdC = 0.

1 10 10 10 102 3 4

φR

EA

102

10

1

2

kg,Pm kP l,P

=0

10

20

Fig. 4. The influence of the volatility of P on EA. Parameter values as mention in example 1.


26

Applications

In this section we will illustrate the remarkable behaviour of gas absorption accompanied by areversible first order reaction, producing a volatile reaction product. The first two examples showthe asymptotic behaviour of the enhancement factor for product desorption and for reactantabsorption with selected sets of parameters. The third example describes an industriallyimportant case of negative enhancement.

Example 1The following values are chosen for the parameters: 0, =gPC mol m-3, )/( ,, AlAAg kmk =

)/( ,, PlPPg kmk = 10 , )/( , gAAA CmC = 04.0 , )/( ,gAAP CvmC = 2.0 , and 0.5/ =vK . Figure 1

show the variation of AE and PE with Rφ calculated from eqs (13), (15), (17) and (18). AEincreases monotonously with increasing Rφ until the limiting instantaneous value of ∞→RAE φ)(

= 37.73 is reached for very large Rφ . PE displays an asymptote at 47.4=Rφ . If 47.4<Rφthen we have 1≥PE , but surprisingly, if 47.4>Rφ then PE is always negative, with a limitingvalue of ∞→RpE φ)( = 47.13− for very large Rφ . This remarkable behaviour can be understoodby inspection of the concentration profiles in the liquid film.

100

50

0

-50

-1000.1 1 10 10 10 10

2 3 4

φR

E , EA P

PA

P

Fig. 1. Variation of EA and EP with φR. Parameter values as mention in example 1.


29

x/δ0 0.2 0.4 0.6 0.8 1

2.5

2.0

1.5

1.0

0.5

0.0

v m CA A,g

C CP P-

2

kg,Pm kP l,P

=0

10

20

Fig. 5. The influence of the volatility of P on CP in the liquid film. Parameter values as mention in example1.

0.1 1 10 10 10 102 3 4

φR

EA

10

10

10

4

3

2

10

1

1

10

102

103

∞K/ =v

Fig. 6. The influence of the reversibility of the reaction on EA. Parameter values as mention in example 1.

The influence of the reversibility of the reaction, as indicated by the value of vK / , on AEis shown in Fig. 6. Again, 0, =gPC mol m-3, )/( ,, AlAAg kmk = )/( ,, PlPPg kmk = 10 and

)/( ,gAAP CvmC = 2.0 were used. The liquid bulk phase concentration of A was taken in

chemical equilibrium with that of P. AE increases with vK / until the limiting case of a firstorder irreversible reaction is reached for vK / ∞→ , where AE is given by eq. (29).


30

Example 2The same set of parameters as in example 1 is used here, i.e. 0, =gPC mol m-3, )/( ,, AlAAg kmk

= )/( ,, PlPPg kmk = 10 and 0.5/ =vK . The only difference being that now the concentration of

A in the gas phase is lowered in such a way that we now have )/( , gAAA CmC = 5.0 and

)/( , gAAP CvmC = 5.2 . This change in the conditions drastically alters the variation of AE and

PE with Rφ , as illustrated in Fig. 7. Now it is the enhancement factor of the absorbing gas, AE ,that displays an asymptote. This occurs at 5.17=Rφ . The dimensionless concentration profiles

in the liquid film associated with 5.17=Rφ are shown in Fig. 8. The value of IAC equals that of

AC , but there is clearly absorption of A at the interface as is revealed by the initially largenegative gradient of AC in the film. At large values of Rφ , the absorption of A cannot keep upwith the disappearance of A due to reaction in the film; the reaction product acts as a sink forcomponent A, and I

AC becomes smaller than AC which causes negative enhancement factors forA. On the other hand, if 5.17<Rφ , then the mass transfer of A is relatively faster, and AE is

positive because AIA CC < . The limiting instantaneous reaction enhancement factors for this

situation are 5.26)( −=∞→RAE φ and 5.6)( =∞→RPE φ . The linear profiles of AC and PC in

the liquid film for ∞→Rφ , obtained from eq. (19) and the equilibrium condition AP KCC = ,are also shown in Fig. 8.

50

25

0

-25

-500.1 1 10 10 10 10

2 3 4

φR

E , EA P

A

P

A

Fig. 7. Variation of EA and EP with φR. Parametervalues as mention in example 2.


31

φR=17.5

∞

x/δ0 0.2 0.4 0.6 0.8 1

C CA A-

m CA A,g

0.0

-0.1

-0.2

-0.3

-0.4

0.0

-0.5

-1.0

-1.5

-2.0

φR=17.5

∞

v m CA A,g

C CP P-

Fig. 8. Dimensionless concentration of A and P in theliquid film. Parameter values as mention in example 2.

Practical example Formaldehyde is commercially produced by gas phase oxidation of methanol with air. The

gaseous reactor product stream contains formaldehyde and is fed to an absorber to dissolve theformaldehyde in water. In water, formaldehyde (A) reacts reversible to methylene glycol (P).Because of the large excess of water, this reaction can be considered here as pseudo first order.At the bottom part of the absorber, the entering gas does not yet contain any methylene glycol( 0, =gPC mol m-3). For this region of the absorber, the following parameter values are typical

for an industrial formaldehyde absorber:, )/( ,, AlAAg kmk 95.0= , )/( ,, PlPPg kmk 31038.3 −×= ,

vK / 2.21= , 4.1=φ , )/( ,gAAA CmC 24.0= , )/( , gAAP CvmC 14.5= . From eqs (13), (15),

(17) and (18) the enhancement factors are calculated as 55.1=AE and 13.0−=PE , indicatingthat negative enhancement factors may occur in the absorption of formaldehyde.

Conclusion

A new analytical solution is presented for the concentration profiles and mass transferenhancement in the general case of gas absorption accompanied by a first order reversiblereaction, producing a partly volatile product. The solution is not restricted to equal diffusivities.From this general solution, several known limiting cases are readily derived. The solution is alsoapplicable for the case of the simultaneous absorption and first order reversible reaction of twogases. It is shown that enhancement factors are possible with values not only larger than one butalso smaller than one, and even negative enhancement factors are possible. The latter occurs inthe industrially important absorption of formaldehyde in aqueous solution.

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.

Chapter 5: Modeling and simulation of industrial formaldehyde absorbers

49

Chapter 5

Modelling and simulation of industrial formaldehyde absorbers

Abstract

The industrially important process of formaldehyde absorption in water constitutes a case ofmulticomponent mass transfer with multiple reactions and considerable heat effects. A stablesolution algorithm is developed to simulate the performance of industrial absorbers for thisprocess using a differential model. Good agreement with practice was achieved. Using the model,the conditions of one of the absorbers of Dynea B.V. were optimized, leading to considerablemethanol savings.

Introduction

Formaldehyde, CH2O, is produced on a large scale as a raw material for a great variety ofend products. Its industrial production starts from methanol. Air and vaporized methanol,combined with steam and recycled gas, are passed over hot silver grains, at ambient pressure.Here the methanol is converted to formaldehyde by partial oxidation and by reduction at about870 K. To prevent thermal decomposition of formaldehyde, the gases are cooled immediatelyafter the catalyst bed.

The reactor product gas stream has a temperature of 420 K and consists typically of N2(50%), H2 (15%), water vapor (20%) and formaldehyde (15%). Minor amounts of by-productsand unreacted methanol are neglected in this study. This stream is passed through a partialcondenser, where the temperature is reduced to 328 K and part of the water vapor andformaldehyde are condensed. The resulting mixed gas-liquid stream is subsequently fed to theabsorber.

Because it is impossible to handle in its pure, gaseous form, formaldehyde is almostexclusively produced and processed as an aqueous solution: formalin. The latter is obtainedcommercially by absorbing the gases leaving the reactor in water.

The goals in optimizing the absorber performance seem conflicting. On the one hand theformaldehyde content of the tail gas should be minimized. On the other hand however, theformaldehyde concentration in the product liquid leaving the absorber should be as high aspossible, thereby reducing the absorbing ability of the liquid in the column.

A scheme of the absorber studied is shown in Fig. 1. The gaseous part of the two-phasestream entering at the bottom of the column passes upwards through two beds, randomly filledwith modern high performance Pall-ring like packing. The tail gas is partly recirculated to thereactor. Make up water enters at the top of the column and flows downward, meanwhile takingup heat and absorbing formaldehyde and water from the gas stream. Each of the absorption bedshas an external liquid recirculation with heat exchangers. Just below the top bed, the absorber isequipped with a partial draw off tray to provide a buffer for the upper liquid recirculation pump.At the bottom of the column a liquid layer is kept as a buffer for the lower liquid reciculationpump.


50

feed

product

tail gaswater

Fig. 1. Scheme of a formaldehyde absorber.

Reactions in aqueous formaldehyde solutions

Besides direct heat transfer between gas and liquid, and the mass transfer of water andformaldehyde, a number of reactions have to be considered in modeling the performance offormaldehyde absorbers. In formalin the dissolved formaldehyde is present principally in theform of methylene glycol, CH2(OH)2, and a series of low molecular weight polyoxymethyleneglycols, HO(CH2O)nH (e.g. Walker, 1964). As an example the equilibrium composition of anaqueous 50 wt.% formaldehyde solution is shown in Fig. 2.

Although the concentration of the unhydrated monomeric formaldehyde is well under 0.1%even in concentrated solutions, all dissolved aldehyde remains available for chemical reaction indownstream processing because of the reversibility of the reactions.

The following reactions take place in the absorber: hydration

2222 )OH(CHOHOCH + (1)

with kinetics


51

)/(1WFWF1 hh KCCCkr −= (2)

were

eqWF

WFh CC

CK

= 1 (3)

polymerization reactions

OHHO)HO(CHHO)HO(CH(OH)CH 2n21n222 ++ − )2( maxnn ≤≤ (4)

with kinetics

)/(11 nWWFWFWFnn KCCCCkr

nn−=

−(5)

were

eqWFWF

WWFn

n

n

CC

CCK

=

−11

. (6)

Here, nmax denotes the largest polymer considered. The concentration of the polyoxymethyleneglycols decreases rapidly with increasing molecular weight, even for concentrated solutions (Fig.2). Therefore, the largest polymer considered here is WF10 (nmax = 10). This way, there are tenreactions in the liquid between twelve components. The reaction rate of a species can be represented as

∑=

=max

1,

n

jjjii rR ν . (7)

From eq (7) and the stoichiometry of reactions (1) and (4) it follows

1rRF −= (8)

max...321 nW rrrrR ++++−= (9)

max1...2 4321 nWF rrrrrR −−−−−= (10)

)2( max1 nnrrR nnWFn<≤−= + (11)

)( maxnnrR nWFn== . (12)


52

1

10

10

10

10

-1

-2

-3

-4

F W 1 2 3 4 5 6 7 8 9 10WFn

x

Fig. 2. Equilibrium molar fractions of F, W, and WFn (n=1..10) in 50 wt% formalin at 343 K.

Development of absorber model

The methods found in the literature for the modeling of packed columns generally belong toeither of two types. In the first type the packed height is divided into a number of segments.Within each segment the conditions are supposed to be uniform in both phases. This type ofmodels can be subdivided into equilibrium stage models (p.e. King, 1980), where the streamsleaving each stage are assumed to be in equilibrium with each other and departures from thisassumption are accounted for by one of several types of stage efficiencies, and nonequilibriumstage models (p.e. Krishnamurty & Taylor, 1985), where material and energy balance relationsfor each phase are solved simultaneously with mass and energy transfer rate equations.

In the second type of models, differential mass and energy balances for each phase arewritten for a small section of packing, and the differential equations are numerically integratedover the total packed height (p.e. Hitch et al., 1986).

Our model for the formaldehyde absorber belongs to the second type. In a subsequent papera stage model will be introduced for this type of column.

Since our first goal is the simulation of existing industrial formaldehyde absorbers, theheight of the packing in the absorption beds is fixed. Major assumptions of the model are: (1) theabsorption beds operate adiabatic; (2) the packing is fully wetted, therefore the interfacial area isthe same for heat and mass transfer; (3) heat and mass transfer relations are based on theresistances in series model; (4) the counter current gas and liquid streams in the absorption bedsare in plug flow; (5) gas to liquid mass transfer of N2 and H2 is negligible because of their lowsolubility in formalin; (6) the liquid in the partial draw off tray and at the bottom of the column(the buffers for the recirculation pumps) is ideally mixed and heat and mass transfer to this liquidis negligible.

With these assumptions, the component balances for the gas and liquid phases read


53

),(, WFiaSJdzdv

gii =−= (13)

)..1;,,( max, nnWFWFiSRaSJdzdl

niii ==−−= ll ε . (14)

The energy balances for the gas and liquid phases are

aSqdz

dTCpv g

g

igii −=∑ )( , (15)

∑∑ ∆−−−=j

jRji

ii HrSaSqdzdTCpl )()( , ll

ll ε . (16)

The component and energy balances for the liquid on the partial draw off tray and at the bottomof the column read

iBini

outi RVll += (17)

∑∑ ∆−=−j

jRjBi

iini

inout HrVCplTT )()( ,l . (18)

Mass transfer rates

The gas phase mass fluxes are calculated from

),()( ,,,, WFiCCkJ Igigiiggi =−= (19)

were the interfacial concentrations are coupled by

),(,, WFiCmC Igii

Ii ==l . (20)

The fluxes on both sides of the interface are equal:

Iigi JJ l,, = . (21)

In the liquid, the diffusional transport is accompanied by chemical reactions, which causes masstransfer enhancement. Therefore the enhancement factor, Ei, is incorporated in the fluxes at theliquid side of the interface

)( ,,,, llll iIiii

Ii CCEkJ −= . (22)


54

Also, the fluxes into the liquid bulk, l,iJ , become different from the fluxes at the interface, IiJ l, .

In a preliminary study this situation was assessed by solving the differential equations for masstransfer with reactions in the film

)..1;,,( max2

2

, nnWFWFiRdx

CdD nii

i ==−=l . (23)

Assuming the polyoxymethylene glycols are nonvolatile, the boundary conditions of eq (23) are

0,,:0,

,

,

, =−=−==dx

dCDJ

dxdC

DJ

dxdCx nWF

W

IWW

F

IFF

l

l

l

l (24)

ll ,: ii CCx == δ . (25)

The eqs (19)-(25) were solved numerically for a variety of conditions expected to prevail informaldehyde absorbers, using a fourth order Runge-Kutta method in combination with ashooting method. The results showed that the polymerization reactions (4) are by far too slow tohave any influence on the diffusion fluxes, and the gradients of the concentrations of the higherpolyoxymethylene glycols in the film are negligible,

)..2( max,)0( nnCCnn WFxWF ==≤≤ llδ . (26)

On the other hand, the hydration reaction (1) causes significant mass transfer enhancement. In column simulations it is not convenient to calculate the fluxes from the numerical

integration procedure described above. Therefore, an approximate method was developed, similarto the method of Onda et al. (1970). The differential equations (23) for the formaldehyde andmethylene glycol concentrations in the film are linearized by taking the water concentration inthe film equal to that in the bulk. The resulting set of equations can be solved analytically to giveexpressions for EF and l,FJ

R

RWh

F

WF

RFIF

WFFWh

F

WFW

F

WF

FCK

DD

CC

CCCKD

DCK

DD

E

φφ

φ

]tanh[1

)]cosh[

11(1

,,

,

,,

,,,

,

,,1

,

,

1

111

ll

l

ll

lll

l

ll

l

l

+

−−

−++

= (27)

[

]IFF

IFFWF

IFWhWF

WFFWhWF

R

RWh

F

WF

RIFF

JCCkCCCKk

CCCKkCK

D

DJJ

llllllll

llll

ll

lll

,,,,,,,,

,,,,

,,

,,,

)()(

)(]tanh[

]cosh[11

11

111

−−+−+

−−

−=

φφ

φ

(28)


55

with

)(,

,,

, 1 hWF

FW

F

hR KD

DC

Dk

l

ll

ll += δφ . (29)

Given the bulk concentrations in both phases, all the fluxes can now be calculated iterativelyfrom eqs (19)-(22), (27)-(29) and the balances

)( ,,,, llll FIF

IWW JJJJ −−= (30)

)( ,,,1 lll FIFWF JJJ −= . (31)

The mass transfer rates calculated this way proved almost identical to the ones obtained bynumerically solving eqs (19)-(25).

Energy transfer rates

The energy transfer rates contain a conductive and a convective part

)()(,, lorgjHJqEi

jTjijijj =+= ∑ . (32)

The film model of simultaneous mass and energy transfer leads to (p.e. Krishna and Taylor,1986)

)()( lorgjTTAhq Ijfjj =−= (33)

where Af is the Ackermann heat transfer correction factor for non-zero mass transfer fluxes inphase j

1−=

fCf

fe

CA (34)

)(,,

lorgjh

CpJC

j

ijiji

f ==∑

. (35)

The interfacial temperature, IT , follows from a balance around the interfacial region, lEEg = :

∑∑ +=+i

Tiii

gTgigig HJqHJq )(,,)(,, llll . (36)


56

This balance can be rewritten as

hRFIF

i

Iii

iivap

Iggigig

HJJ

TTCpJHTTCpJqq

))((

)(])([

,,

,,,,,

∆−−+

−+∆+−+= ∑∑

ll

llll. (37)

Physical and chemical parameters

The mass transfer coefficients, gik , and l,ik , and the specific area, a, were calculated from Onda

et al. (1968). The partial liquid hold up, lε , was taken from Otake and Kunigita (1958). The heattransfer coefficients, gh and lh , were evaluated from the mass transfer coefficients using theChilton-Colburn analogy.

To predict the heat and mass transfer coefficients, pure component and mixture physicalproperties are needed. The pure component properties were taken from Daubert and Danner(1985), or if not available, calculated using the predictive methods recommended by Reid et al.(1988). Densities and viscosities of the liquid were taken from Appendix A. Other mixtureproperties were calculated from the mixing rules recommended by Reid et al. (1988).

The reaction rate and equilibrium constant of the hydration reaction, hk and hK , weretaken from the results reported in Chapters 2 and 4 of this thesis. The reaction rate and theequilibrium constants of the polymerization reactions, kj and Kj (j=2..nmax), were measured byDankelman et al. (1988) over the temperature range of 293-353 K.

Vapor liquid equilibria

Generally, at low pressure, vapor phase non-ideality can be neglected, and vapor-liquid equilibriacan be described with

siiii PxPy γ= (38)

where the liquid phase non-ideality is accounted for by the activity coefficient, iγ , which usuallyis temperature and composition dependent.

The interpretation of published vapor-liquid equilibrium data for the formaldehyde-watersystem is complicated by the fact that the analytical methods, used by various authors, do notdistinguish between different forms of formaldehyde present in the system, and the experimentalresults are presented in terms of overall compositions. To find vapor liquid equilibrium relationships for formaldehyde and water, experimental datawere used of Kogan et al. (1977), Maurer (1986) and Hasse (1990). First the true molar fractionswere calculated from the reported overall composition and the equilibrium relations (3) and (6).After this, for each experimental point, the quantity s

ii Pγ was calculated.


57

25

20

15

10

8

6

4

2

00 20 40 60 80

W [wt%]F

γF FPS

[MPa]

293 K

313 K

323 K

343 K

353 K

363 K

Fig. 3. Values of γFPFS. Lines: calculated from eq (49). Symbols: experimental data,

( , ): Kogan (1977), ( , ): Maurer (1986), ( , ): Hasse (1990).

Finally, sFF Pγ and s

WW Pγ were smoothed as a function of T and liquid phase composition

]109198.7

100723.3103681.786.31464822.25exp[

25

25

F

FFsFF

W

WTWT

P

−

−−

×−

×+×−−=γ(39)

]65.74

75.31400428.22exp[−

−=T

P sWWγ . (40)


58

100

5

0 0 20 40 60 80

W [wt%]F

γW WP S

[kPa]

293 K

313 K

323 K

343 K

353 K

363 K

10

80

60

40

Fig. 5. Values of γWPWS. Lines: calculated from eq (49). Symbols: experimental data,

( , ): Kogan (1977), ( , ): Maurer (1986), ( , ): Hasse (1990).

Equations (39) and (40) are illustrated in Figs 3 and 4. The deviation of the calculated lines fromthe experimental points is generally within the experimental accuracy limits, the mean deviationsare 3.4% for formaldehyde and 1.5% for water. The equilibrium ratio mi (eq 20) can now easilybe calculated from

sii

toti

P

RTCm

γl,= . (41)


59

Computational method

The eqs (13)-(16) form a set of 16 coupled non-linear differential equations which describe anabsorption bed. If the entering gas and liquid streams are specified, a two point boundary valueproblem results. Several strategies for solving this type of problems for absorbers have been putforward.

Treybal (1969) used a shooting method to model single solute systems. This method startsby assigning trial values to the outlet gas stream conditions, and calculating the outlet liquidconditions from overall balances. The numerical integration from bottom to top has to berepeated until convergency is achieved on the trial values. Feintuch and Treybal (1978) extendedthis model to multicomponent systems, but reported convergence problems due to equationsbecoming mathematical indeterminate in one of several nested iteration loops. Kelly et al. (1984)used the shooting method to model the physical absorption of acid gases in methanol.

Another way to solve the set of equations is by dynamic simulation. Von Stockar and Wilke(1977), using a relaxation technique developed by Stilchmair (1972) and Bourne at al. (1974) forplate columns, could avoid convergence problems by simulating the packed column start-up andintegrating the model equations with respect to time up to steady state. Hitch et al. (1987) alsodeveloped an unsteady-state solution algorithm. Besides the advantage of providing informationon transient behaviour, they state that the relaxation method can handle complex systems withoutthe convergence problems encountered with other methods. This type of method is highly stablebecause it follows the actual behaviour of start-up procedures.

Srivastava and Joseph (1984) solved the two-point boundary value problem associated withpacked separation columns by using orthogonal collocation for the spatial discretisation. Thoughthe method worked well for the steady state calculation of a binary system, with multicomponentsystems no steady state solution could be obtained directly. A dynamic simulation had to becarried out to find the steady state as the asymptote of the transient response.

All methods mentioned above have been applied for single absorption beds, with specifiedentering gas and liquid streams. The formaldehyde absorber considered here, however, consistsof two packed beds (Fig. 1). A further complicating factor, from the problem solving point ofview, is the presence of the liquid recirculations around each packed bed. Figure 5 shows thestreams that have to be considered in modeling the formaldehyde absorber. Specified are theinput streams 1A, 7 and 10, and the temperature and total mass flow of the liquid recycle streams5A and 5B. The actual entering streams of the packed beds are a priori unknown.

Because of its superior convergency and stability characteristics, a transient approach wasused to solve the equations that describe the absorber. Initially, the composition of the liquid inboth packed beds, and of the liquid streams shown in Fig. 5, are all set equal to that of the make-up stream 1A (pure water). The liquid temperatures in and around each bed are initially set equalto the corresponding liquid recycle stream temperatures, which are input parameters.


60

tail gas9make up

topbed

1A2A 5A

3A 4A

8

7

10

2B1B

3B 4B

5B

6

bottombed

gas feedliquid feed

formalingas streamliquid stream

Fig. 5. Flow diagram of the absorber of Fig. 1.

After initialization, a two-step cycle procedure is started. The first step starts with thespecified conditions of the gas feed stream 7, to integrate the eqs (13) and (15) up the bottombed. The resulting molar flows and temperature of stream 8 are used as the startingvalues to integrate eqs (13) and (15) up the top bed. During the integrations, the interphase fluxesare calculated using the stored liquid phase conditions. The calculated values of gT , vF and vW inthe absorption beds are stored. In the second step, new liquid phase conditions are calculated.Starting with the specified conditions of stream 1A and the old values of stream 5A, the molarflows and temperature of stream 2A are calculated, and used as starting values for the integrationof eqs (14) and (16) down the top bed. During this integration, the calculated liquid phaseconditions are used in conjunction with the stored gas phase conditions to obtain the mass andheat fluxes. Next, eqs (17) and (18) are used to calculate stream 4A. The molar flows of stream5A follow from the molar fractions, and the specified total mass flow rate of stream 5A. Thetemperature of 1B is set equal to that of 4A, and the molar flow rates follow from the differencesbetween 4A and 5A. Now, the same sequence is repeated for the lower section of theformaldehyde absorber, to arrive at stream 6.

The sequential update of gas and liquid phase conditions is repeated until the differencesbetween successively calculated molar flow rates and temperatures have fallen below presetcriteria, and steady state is reached, see Fig. 6. In practice 40 to 60 iterations were required,depending somewhat on the operating conditions.

In contrast to the unsteady-state algorithms found in the literature, this algorithm does notneed a separate routine for the calculation of time derivatives and advancement in the timedirection. Furthermore, our algorithm contains only one level of nested iteration (which is thecalculation of the interfacial conditions necessary to obtain the fluxes in the packed beds, and thecalculation of the streams 4A and 4B from the non-linear algebraic eqs (17) and (18)).


61

start

input: feed streams, mass flow rates

initialize liquid phase conditions

store gas phase conditions

integrate gas phase equations up the packedbeds using Runge-Kutta

and temperature of liquid recycles

integrate liquid phase equations down thepacked beds and calculate liquid streams

store liquid phase conditions

convergence achieved?

stop

Fig. 6. Logic flow diagram for computing the absorber.

Results

A typical set of calculated temperature and vapor phase molar flow profiles is shown in Fig.7. The presence of two packed absorption beds is clearly revealed in this figure. The occurence oftemperature maxima, found here in the bottom bed, is often encountered in exothermicabsorption with solvent evaporation (e.g. experimental observations of Raal and Khurana (1973)and Bourne et al. (1974), and calculations of Stockar and Wilke (1977) and Krishnamurty andTaylor (1986)). The liquid flowing down from the upper part of the bottom bed increases intemperature due to the heats of absorption and reaction. But lower in the bottom bed, the liquidmeets an unsaturated gas flow, and the heat effect of solvent evaporation causes a drop in lT .

Because lTT ing < the gas temperature rises while flowing upwards, until a maximum is reached.

Above the maximum gT exceeds lT , with the former decreasing because the energy transfer isnow directed towards the liquid.

The features of the temperature profiles are reflected in the profile of the molar flow rate ofwater in the gas phase, see Fig. 7. The mass transfer of formaldehyde , on the other hand, isalways directed towards the liquid and is not influenced much by the changes in temperature.Therefore, the gas phase molar flow rate of formaldehyde is monotonously decreasing. Theprofiles of the liquid phase molar flows are not very exciting due to the large liquid recycle ratio'sused in formaldehyde absorbers.

The influence of several operating parameters on the performance of the absorber wasinvestigated. Important output parameters are the temperature rise of the liquid in each of thepacked beds, lT∆ , the relative amount of formaldehyde that leaves the absorber with


62

vaporliquid

waterformaldehyde

vvin

T

[C]

70

60

50

40

2

1

00.0 0.5 1.0(bottom) (top)

relative height

Fig. 7. Typical calculated profiles.

the tail gas, inF

outF vv / , and the composition of the liquid streams leaving each of the packed beds,

calculated here as the overall weight percentage formaldehyde, WF. The influence of the recycle ratio's is shown in Figs 8 and 9. R is defined here as the ratio of

the liquid mass flow rates of 5A and 1B for the top bed, and 5B and 6 for the bottom bed (seeFig. 5). Increasing the recycle ratio increases the absorber efficiency, i.e. reduces in

FoutF vv / . This

is caused by a combination of more favourable hydrodynamics and lower mean temperatures. Forexample, increasing Rb has virtually no influence on bT ,l∆ , but decreases the internal maximumof the temperature profile.

Figures 10 and 11 show that increasing the temperature of a liquid recycle has a negativeeffect on the absorber efficiency. Increase of Tt

Rec causes a decrease of the amount offormaldehyde absorbed in the top bed, but an even larger decrease of the amount of waterabsorbed in this bed. This results in a reduction of the temperature rise of the liquid in the topbed, and a larger weight percentage formaldehyde in the liquid leaving both beds, see Fig. 10.The overall temperature rise of the liquid in the bottom bed with increasing Tb

Rec becomes evennegative, see Fig. 11, due to the increasing water evaporation. This is of course a hypotheticalsituation, because it would mean that the heat exchanger in the recycle would have to heat upinstead of cooling the liquid stream.


63

top-bed

top-bed

bottom-bed

bottom-bed

∆TL

WF

[Wt%]

vFout

vFin

WF

[Wt%]

57

56

55

54

Rt

40 60 80 100

43

41

39

37

16

12

8

4

0

0.08

0.06

0.04

0.02

0

Fig. 8. Influence of tR on lT∆ , inF

outF vv / and FW .

top-bed

top-bed

bottom-bed

bottom-bed

∆TL

WF

[Wt%]

vFout

vFin

WF

[Wt%]

57

56

55

54

Rb

4020 30

43

41

39

37

16

12

8

4

0

0.08

0.06

0.04

0.02

0

Fig. 9. Influence of bR on lT∆ , inF

outF vv / and FW .


64

top-bed

top-bed

bottom-bed

bottom-bed

∆TL

WF

[Wt%]

vFout

vFin

WF

[Wt%]

57

56

55

54

TtRec

4025 30

43

41

39

37

10

8

6

4

2

0

0.08

0.06

0.04

0.02

0

35 45

Fig. 10. Influence of ctT Re on lT∆ , in

FoutF vv / and FW .

top-bed

top-bed

bottom-bed

bottom-bed

∆TL

WF

[Wt%]

vFout

vFin

WF

[Wt%]

57

56

55

54

TbRec

7055 65

43

41

39

37

15

10

5

0

0.08

0.06

0.04

0.02

0

60

-5

Fig. 11. Influence of cbT Re on lT∆ , in

FoutF vv / and FW .


65

top-bed

top-bed

bottom-bed

bottom-bed

∆TL

WF

[Wt%]

vFout

vFin

60

50

40

30

20

1030 2

10

8

6

4

2

0

0.08

0.06

0.04

0.02

0

1make-up [m /hr]3

Fig. 12. Influence of the amount of make-up water on lT∆ , inF

outF vv / and FW .

Increasing the amount of make-up water has a positive influence on the absorber efficiency,see Fig. 12. This is caused by a reduction of the formaldehyde content of the liquid, whichreduces the backpressure from the liquid phase. However, this reduction in WF is oftenundesirable because of extra storage and transport costs.

A higher pressure increases the driving forces for absorption, thus reducing inF

outF vv / , see

Fig. 13. However, the extra water absorption is even higher, so that WF still will be reduced. Inpractice, this can be compensated for by reducing the amount of make-up water.

Finally, the influence of varying the total feed rate (streams 7 and 10 in Fig. 5) is illustratedin Fig. 14 for both a constant and a proportionally increased make-up water supply. Withincreasing column loads, ∆Tt

L increases while the absorption efficiency )/1( inF

outF vv− goes

down. With a constant make-up, not only a decrease but surprisingly also an increase in therelative feed rates results in a diluted liquid product. The latter effect is caused by a strongerreduction of formaldehyde absorption efficiency relative to water: a maximum of WF results.

The model was tested by simulating industrial absorbers of two plants of Dynea B.V., TheNetherlands: one absorber with a configuration as shown in Fig. 1, and another absorber withthree packed beds and a slightly different configuration. In both cases, using the actual operatingparameters, the model could very well predict the performance of the columns.


66

top-bed

top-bed

bottom-bed

bottom-bed∆T

L

WF

[Wt%]

vFout

vFin

WF

[Wt%]

57

56

55

541.0 1.8

43

41

39

37

10

8

6

4

2

0

0.08

0.06

0.04

0.02

0

1.4P [bar]

Fig. 13. Influence of the total pressure on lT∆ , inF

outF vv / and FW .

Next, the model was used to optimize the performance of the first absorber, by simultaneouslyvarying the parameters shown in Figs 8-12 and 14. This resulted in a savings of 1% in the costsof methanol (the basic material for making formaldehyde) for this particular formaldehyde plant.

Conclusions

The absorption of formaldehyde is an important step in the industrial formalin production. In theabsorber column, the process of formaldehyde and water absorption is accompanied by a numberof reactions in the liquid phase and considerable heat effects, necessitating separate liquidrecycles with external heat exchangers. For the simulation of this type of column we developed amodel based on the appropriate differential equations, without using HETP or HTU concepts.The model is completely predictive. The convergence problems often encountered with this typeof complex modeling could be avoided by using a stable, semi-transient solution-algorithm.


67

3

2

1

0

0.08

0.04

056

55

54

530.5 1.0 1.5

15

10

5

0

45

35

25

bottom bed

bottom bed

top bed

top bed

constant make-upmake-up pro rata

∆TL

∆TL

vFout

vFin

WF

(wt%)

WF

(wt%)

Fig. 14. Influence of the relative feed rate on lT∆ , inF

outF vv / and FW .

Our results from simulations with varying process parameters suggest favourable absorberperformance with high liquid recycle ratio's (Figs 8 and 9), low temperatures of the recirculatedliquid (Figs 10 and 11) and a large amount of make-up water (Fig. 12), although the latter may belimited by a minimum desired formaldehyde content of the product stream.

The suggestions mentioned above have been tested in practice and have led to a moreefficient absorption column.

Chapter 6: Simulation of … absorbers: the behaviour of methanol and non-equilibrium stage modeling.

69

Chapter 6

Simulation of industrial formaldehyde absorbers: the behaviour of methanol and non-equilibrium stage modelling.

Abstract

A model is presented for the commercially important formaldehyde absorption in thepresence of methanol. Incorporated in the model are a large number of liquid phase reactions, gasliquid heat transfer, and mass transfer with reaction of water, formaldehyde, methylene glycol,methanol and hemiformal. The evaporation of water, methylene glycol and hemiformal in thelower part of the column creates an internal circulation of these components. In this part of thecolumn negative enhancement factors are obtained for mass transfer with reaction of methyleneglycol and hemiformal. This indicates that approximate methods for calculating mass transferenhancement factors due to reaction might fail for absorption with chemical reaction andsimultaneous product desorption. The performance of an industrially applied packed column withliquid recirculations is simulated using a non-equilibrium stage model. A solution algorithm isdeveloped and carefully described. The influence of a number of process parameters on thebehaviour of methanolic species in the absorber is investigated.

Introduction

Formaldehyde is industrially produced by partial oxidation and dehydrogenation ofvaporised methanol in air over a solid catalyst at approximately atmospheric pressure. Thereactor product gas stream consists of water vapour, formaldehyde and some unreacted methanolin an inert matrix of nitrogen, hydrogen and carbon dioxide (minor amounts of by-products areneglected in this study). This gas mixture is passed through a partial condenser, where thetemperature is reduced to 328 K and part of the water vapour and formaldehyde are condensed.The resulting stream is subsequently fed to the absorber to extract the formaldehyde from the gas,and to obtain the commercial product: a concentrated aqueous formaldehyde solution containingsome not-converted methanol.

A scheme of the absorber studied is shown in Fig. 1. The gas stream entering at the bottomof the column passes upwards trough two packed beds, randomly filled with a modern highperformance Pall-ring like packing. Make-up water enters the top of the column and flowsdownward, meanwhile exchanging heat and mass with the gas stream. Each of the absorptionbeds is equipped with an external liquid recirculation with heat exchangers. Just below each bedan amount of liquid is kept to provide buffers for the liquid recirculation pumps.In a previous paper (Winkelman et al., 1992) a model for the formaldehyde absorber wasdeveloped, based on differential equations for the mass and energy balances in each phase. Theresulting set of coupled boundary value problems was solved by a semi-transient method. Thepresence of methanol in the absorber was neglected, and only formaldehyde and water wereassumed to be absorbed or desorbed. In this contribution the behaviour of methanol in theabsorption process is fully incorporated in the model. Also included in the model are vaporisationand re-absorption of methylene glycol and hemiformal, which are the primary reaction products


70

feed

product

tail gaswater

Fig. 1. Scheme of the formaldehyde absorber.

of formaldehyde with water and methanol, and which are formed in the liquid. The absorber ismodelled using a non-equilibrium stage model.

Reactions in aqueous methanolic formaldehyde solutions

Besides heat and mass transfer between gas and liquid, a number of reactions have to beconsidered in modelling the performance of formaldehyde absorbers because formaldehydereacts with both water and methanol. In aqueous solutions the dissolved formaldehyde (F) reactsfast with water (W) to form methylene glycol, CH1(OH)1, denoted by WF1

2222 (OH)CHOHOCH + . (1)

The reaction rate is given by )/(

11 hWFWFh KCCCkr −= , (2)

where Kh is the chemical equilibrium constant for this hydration, defined as


71

eqWF

WFh CC

CK

= 1 . (3)

The equilibrium of reaction (1) is far to the right, which means that in an aqueous solution theconcentration of free formaldehyde is very low.

Methylene glycol, formed by reaction (1), slowly polymerises to form a series of lowmolecular weight poly(oxymethylene) glycols, HO(CHO)nH, denoted here by WFn

OHHO)HO(CH(OH)CHHO)HO(CH 2n2221n2 ++− )..2( maxnn = , (4)

with reaction rates

)/(11 nWWFWFWFnn KCCCCkr

nn−=

− )..2( maxnn = , (5)

and the equilibrium constants

eqWFWF

WWFn CC

CCK

N

n

=

− 11

)..2( maxnn = . (6)

If methanol (M) is present in the solution, formaldehyde reacts with it in a similar manner as withwater, producing hemiformal, CH3OCH2OH (MF1)

OHOCHCHOHCHOCH 2332 + , (7)

with the reaction rate

( )111 /1

KMCCCkmrm MFMF −= , (8)

where the equilibrium constant is defined as

eqMF

MF

CCC

KM

= 1

1 . (9)

The formed hemiformal also polymerises slowly to a series of polymers, higher hemiformals inthis case, CH3O(CH2O)nH, denoted by MFn

OHCHHO)O(CHCHOHOCHCHHO)O(CHCH 3n23231-n23 ++ )..2( maxnn = (10)

with reaction rates


72

( )nMFMMFMFnn KMCCCCkmrmnn

/11−=

− )..2( maxnn = , (11)

and equilibrium constants

eqMFMF

MMFn CC

CCKM

n

n

=

− 11

)..2( maxnn = . (12)

Here, nmax denotes the largest polymer. In Fig. 2 the equilibrium molar fractions are shown of anaqueous solution containing 55 wt % formaldehyde and 1 wt % methanol. The concentrations ofthe higher poly(oxymethylene) glycols and hemiformals decrease rapidly with increasingmolecular weight. Therefore the largest polymers considered here are WF10 and MF10, with nmax= 10 for both types of polymers. This way, there are 20 chemical reactions in the liquid phase,and the total number of liquid phase components amounts to 23. The production rates of theindividual species are found from

∑=

+=max

1,, )(

n

kkkikkii rmmrR νν , (13)

where ki,ν denotes the stoichiometric coefficient of component i in the reaction forming the k-thpoly(oxymethylene) glycol (negative for reactants and positive for reaction products). Likewise,

kim ,ν denotes the stoichiometric coefficient in the formation of the k-th hemiformal. From eq(13) and the stoichiometry of the reactions (1), (4), (7) and (10) it follows

1

10

10

10

-1

-2

-3

xi

F

W

M

i=1

i=1

23

45

6

23

4

5

6

7

MFi

WFi

Fig. 2. Equilibrium molar fractions in an aqueous solution containing 50% by weight formaldehyde and 1% by weight methanol, at 333 K.


73

11 rmrRF −−= , (14)

max21 nW rrrR +++−= K , (15)

max1 321 2 nWF rrrrR −−−−= K , (16)

)2( max1 nnrrR nnWFn<≤−= + , (17)

)( maxnnrR nWFn== , (18)

max21 nM rmrmrmR +++−= K , (19)

max1 321 2 nMF rmrmrmrmR −−−−= K , (20)

)2( max1 nnrmrmR nnMFn<≤−= + , (21)

)( maxnnrmR nMFn== . (22)

The concentration of the unhydrated monomeric formaldehyde is very low due to thereactions mentioned above: well under 1%, even in concentrated solutions. However, the totalamount of dissolved aldehyde remains available for chemical reactions in downstream processingbecause of the reversibility of the reactions.

Vapour-liquid equilibria in formaldehyde-water-methanol mixtures

Several models have been put forward to describe the vapour-liquid equilibria in pseudobinary formaldehyde-water systems (e.g.: Kogan et al., 1977; Brandani et al., 1980). A method tomodel the vapour-liquid equilibria in pseudo ternary formaldehyde-water-methanol mixtures hasbeen presented by the group of Maurer (Maurer 1986; Albert et al., 2000). This method is usedhere to calculate the vapour liquid equilibria at the gas-liquid interface in the absorber.

Several substances in a formaldehyde-water-methanol mixture can vaporise. These are notonly the monomeric formaldehyde, water and methanol, but also the first reaction products offormaldehyde with water and methanol which are methylene glycol and hemiformal,respectively. The higher polymers always remain in the liquid phase because of their high boilingpoints and negligible vapour pressure (Maurer, 1986). With the method of Maurer, thethermodynamic equilibrium of the vapour-liquid system is calculated from the overallcomposition of the liquid (e.g. weight percentages formaldehyde and methanol) using chemicalequilibrium conditions and overall composition balances in the liquid phase, combined with thephysical equilibria for the components that can vaporise,

),,,,( 11 MFMWFWFiPxPy siiitoti == γ , (23)

where the activity coefficients, γi, are calculated with the UNIFAC method (Gmehling et al.,1982). In the column simulations, however, the liquid phase in a stage is not at chemicalequilibrium. To calculate the gas phase concentrations at the interface, in equilibrium with theliquid phase concentrations at the interface, we proceed in the following way. The equilibriummolar fractions are calculated from the overall composition of the liquid according to the methodof Maurer. Once the equilibrium molar fractions are known, the activity coefficients and partialpressures can be calculated. These partial pressures are then corrected for the deviations of the


74

actual liquid phase molar fractions at the interface from those calculated from the chemicalequilibrium conditions. Here it is assumed that the activity coefficients do not vary substantiallywith the change in composition from chemical equilibrium to the actual composition at theinterface.

Model development

Simulation of continuous absorption processes is often based on stage models. The columnis assumed to consist of a sequence of stages, each representing a section of the packing. Withineach stage the temperature and composition of the gas and liquid phases are assumed to beconstant. In this context, equilibrium stage models are widely used: the streams leaving a stageare assumed to be in equilibrium with each other and departures from this assumption areaccounted for by a stage efficiency.

Krishnamurthy and Taylor (1985a,b) pointed out several drawbacks of the equilibrium stageapproach for separation processes. They developed a non-equilibrium stage model, wherematerial and energy balances for each phase are solved simultaneously with the mass and energytransfer rate equations. In modelling the formaldehyde absorber, we followed the same approach.

A schematic representation of a non-equilibrium stage is shown in Fig. 3. The packed bedsshown in Fig. 1 consist each of a number of such stages, see Fig. 4. Vapour and liquid streamsfrom adjacent stages are brought into contact on the stage and are allowed to exchange mass andenergy across their common interface. The model of a stage consists of material and energybalances for each phase and rate equations for inter-phase mass and energy transfer.

∆Zj

H

v

T

g

i

g

j

j

j

H

v

T

g

i

g

j+1

j+1

j+1

H

T

l

l

j-1

j-1

j-1li

H

T

l

l

j

j

jli

H Tl lj,F j,F j,Fli

H Tl lj,D j,D j,DliJi,l

j

qljqg

j

Ji,gj

Aj Rij

gas liquid


75

Fig. 3. Representation of a non-equilibrium stage.

viN+1

vi1

li1,F

li1,F

liN,D

liN,D

liN,F

liN

li0

T

T

1

2

T

T

N-1

N

....

B

B

1

2

B

B

N-1

N

....

Fig. 4. Absorber layout for non-equilibrium stage model.

The balance equations are denoted by Ψ. The component balance for component i on stage jreads for the gas phase

0,1

, =+−≡Ψ + jjgi

ji

ji

jgi Ajvv , (24)

and for the liquid phase

0,,,

1, =+−∆−−−≡Ψ − jD

ijF

ijj

ijjj

ij

ij

ij

i llZSRAJll lll ε . (25)

The energy balance on stage j for the gas phase is given by

0,,1

,1

,, =++−≡Ψ ∑∑∑ ++

i

jgi

jgi

jjg

j

i

jgi

ji

i

jgi

ji

jgE HJAqAHvHv , (26)

and for the liquid phase


76

0,,

,,,

,

,,1

,1

,,

=+−

−−−≡Ψ

∑∑

∑∑∑ −−

i

jDi

jDi

i

jFi

jFi

i

ji

ji

jjj

i

ji

ji

i

ji

ji

jE

HlHl

HJAAqHlHl

ll

llllll

. (27)

With the assumption of constant heat capacities of the components over the temperature range ofadjacent stages, the energy balance eqs (26) and (27) are rewritten in terms of temperatures andmolar flows. For the gas phase this gives

0)( ,11

, =+−≡Ψ ∑ ++ jg

j

igi

ji

jg

jg

jgE qACpvTT . (28)

Similarly, for the liquid phase it follows

( ) 0)()(

)()( ,,,

,11

,

=∆−+∆−∆−

−+−−≡Ψ

∑

∑∑ −−

kkRkkRk

jji

ijF

ijFjjj

ii

ji

jjjE

HmrmHrZS

CplTTAqCplTT

ε

llllllll

. (29)

The lowest stage in each of the packed sections represents the buffer for the liquid recirculationpumps (see Figs 1 and 4). The interfacial area is very small here, and in the model it is assumedto be zero.

Mass transfer rates

For clarity, the subscript j, indicating the stage number, has been dropped from all symbolsthroughout this section. The calculation of the fluxes is based on the two film concept, with thepositive direction defined from the gas to the liquid phase. The gas phase mass transfer rates aregiven by

),,,,()( 11,,,, MFMWFWFiCCkJ Igigiiggi =−= , (30)

where the gas phase concentrations at the interface, IgiC , , are coupled to those in the liquid phase

by

),,,,( 11,, MFMWFWFiCmC Igii

Ii ==l . (31)

For the calculation of the equilibrium ratios, mi, see the section on vapour-liquid equilibria. Thefluxes on either side of the interface are equal:

),,,,( 11,, MFMWFWFiJJ Iigi == l . (32)


77

At the liquid side of the interface, the diffusional transport of the transferred components isaccompanied by chemical reactions. This causes enhancement of the mass transfer rates. Also,the fluxes into the liquid bulk, l,iJ , differ from those at the interface, I

iJ l, . In a previous paper,we showed the polymerisation reactions to be too slow to have any influence on the diffusionfluxes in the film, and the gradients of the concentrations of the higher polymers in the liquidfilm to be negligible (Winkelman et al., 1992). So, the hydration of formaldehyde, eq. (1), andthe hemiformal formation, eq. (7), are the only reactions affecting the fluxes of the transferredcomponents.

To account for these parallel reactions in the liquid phase, the film model is applied

),,,,,0( 1111,11,2

2MFMWFWFixrmmr

dxCdD ii

ii =≤≤−−= δνν , (33)

with the boundary conditions

Ii

ii J

dxdCDx l,:0 =−= , (34)

l,: ii CCx == δ . (35)

The set of eqs (30)-(35) can not be solved analytically because of the non-linearity of thereaction rates in eqs (33). Therefore, an iterative shooting method was used to calculate theinterfacial concentrations and the mass fluxes, given the bulk phase concentrations. From aninitial guess of the interfacial concentrations, the gradients at the interface were calculated witheqs (30)-(32) and (34), and the differential eqs (33) were numerically integrated from 0=x to

δ=x using a fourth order Runge-Kutta method. The interfacial concentrations were repeatedlyupdated, using a multi-dimensional Newton-Raphson method, until the obtained concentrationsat δ=x match the liquid phase bulk concentrations. From the numerically calculated gradientsat δ=x , the flux into the liquid bulk is obtained

δ=

−=x

iii dx

dCDJ l, . (36)

The numerical effort of the above procedure is greatly reduced by noting the mutualdependency of several interfacial concentrations and fluxes. This can be understood fromconsidering methanol and hemiformal as an example. Addition of eqs (33) for these twocomponents results in

02

2

2

21

1=+

dx

CdD

dxCdD MF

MFM

M . (37)

Integrating twice while applying boundary conditions (34) and (35) gives an explicit relation forthe interfacial concentration of methanol as a function of the interfacial concentration ofhemiformal:


78

]//[)](

)/([

,,,,,

,,,,,,,,

111

1111

MMgMMFIMFMF

MFIMFgMFMFgMMgMMg

IM

mkkCCk

mCCkCkCkC

+−−

−++=

llll

llll. (38)

Similar equations are obtained for IWC l, as a function of I

WFCl,1

, and for IFC l, as a function of

IMFC

l,1 and I

WFCl,1

. Thus, if the values for IWFC

l,1 and I

MFCl,1

are chosen or updated, the

values of IFC l, , I

WC l, and IMC l, can be calculated from eq (38) and its analogs. This way, the

problem of mass transfer of five components, with two parallel reactions can be solved byiteration on two interfacial concentrations only.

Energy transfer rates

The film model gives the following expressions for the conductive heat fluxes from the gasphase, gq , and into the liquid phase, lq , (Krishna and Taylor, 1986)

)(,I

ggfgg TTAhq −= , (39)

)( lll TThq I −= . (40)

The Ackermann factor, Af, corrects the conductive energy transfer rate in the gas phase for non-zero mass transfer rates.

∑=−

=i

gigigCff CpJ

hCf

eCfA ,,

1 where,1

. (41)

For the liquid phase, this correction is negligible. If heat and mass transfer occur simultaneously, the total energy transfer rate contains a

conductive and a convective contribution on either side of the interface. From a balance aroundthe interface it follows that the total energy fluxes out of the gas phase and into the liquid phasemust be equal

∑∑ +=+i

iii

gigig HJqHJq lll ,,,, , (42)

where the summations are over all transferred species. Expressing the enthalpies in terms of heatcapacities and temperature differences, and introducing heats of vaporisation and reaction gives

))(())((

)()(

1,,,1,,,

,,,,,,

1111 RgMFMFRgWFWF

iii

I

iivapgi

igigi

Igg

HmJJHJJ

CpJTTHJCpJTTqq

∆−−+∆−−+

−+∆+−+= ∑∑∑

ll

llll. (43)


79

In deriving eq (43), it is assumed that the variation of the heat capacities is negligible if thetemperature changes from Tg to TI and from TI to lT and that the heats of reaction of both thehydration of formaldehyde and the hemiformal formation in the film are liberated at the interface.Further, the reaction products of these two reactions are taken as key components, thus allowingthe reaction rates in the film to be expressed as flux differences of these key components. Fromeqs (39)-(43), both the interfacial temperature and the values of the heat transfer rates, gq and

lq , were calculated.

Method of solution.

Newton's method for simultaneous correction was used to solve the model because it ismore effective than tearing algorithms (Krishnamurthy and Taylor, 1985a). The total number ofunknown bulk phase variables on a stage j is 30: 5 gas phase molar flow rates, the gas phasetemperature, 23 liquid phase molar flow rates and the liquid phase temperature. These are storedin a vector ( jX )

jMFMFMWFWFWFgMFMWFWFT

j TlllllllTvvvvvX ),,,,,,,,,()(10110111 ,, lKK= . (44)

Other quantities, such as the mass and energy transfer rates and the temperature andconcentrations at the gas-liquid interface, are functions of the bulk phase variables, and aretherefore not considered as independent variables in the solution process. The unknown variablesin ( jX ) must be found by solving the component balance eqs (24) and (25), and the energy

balance eqs (28) and (29). These equations are ordered in a vector ( jΨ )

jEMFMFMWFWFWF

gEgMFgMgWFgWgFT

j

),,,,,

,,,,,,()(

,,,,,,,,

,,,,,,

101101

11

llllllll KK ΨΨΨΨΨΨΨΨ

ΨΨΨΨΨΨ=Ψ. (45)

Specified quantities are the molar flow rates and the temperature of the feed to the last stage, themake-up water molar flow rate and its temperature, the mass flow rates of the two liquidrecirculation streams and the temperatures of the recirculation streams entering the first stage ofeach of the two packed beds. From initial estimates, the variables are repeatedly updated with Newton's method, using theequation

currentcurrentnext )(])()][([ Ψ−=− XXJ , (46)

where (X)current and (X)next denote the current and next estimate for the vector (X) which containsall bulk phase variables

Tn

T XXX ))(),..,(()( 1= , (47)


80

(Ψ) denotes the vector of current discrepancies of the set of equations to be solved and whosesolution is given by 0)( =Ψ

))()(()( 1T

nTT ΨΨ=Ψ K , (48)

and [J] denotes the Jacobian matrix with elements

j

iji X

J∂Ψ∂

=, . (49)

The variables and equations are grouped in such a way that the Jacobian matrix has the wellknown block tridiagonal structure, shown in Fig. 5. The top bed of the absorber contributes to theJacobian the submatrices [S]j, [T]j and [U]j, which contain the partial derivatives of the functionspertaining to stage j with respect to the variables of the stages j-1, j, and j+1, respectively. In asimilar way, the submatrices [A]j, [B]j and [C]j originate from the bottom bed in the absorber.Formally, the submatrices have dimensions (30×30), but [S]j and [A]j are very sparse. Thesolution algorithm is adapted to use this sparseness, in order to save on computer storagerequirements and calculation time. Because of the presence of the liquid recirculations, thecomposition of the liquid on the first stage of each absorption bed depends partly on thecomposition of the last stage. This is reflected in the presence of the two off-diagonalsubmatrices RT and RB in Fig. 5.

Most of the partial derivatives in the submatrices [T]j and [B]j of the Jacobian are toocomplicated to calculate analytically, and are therefore obtained from finite differenceapproximations. The entries of all the other submatrices are obtained from analytical expressions.

T1

S2

U1

T2 U2

RT

SN-1 TN-1 UN-1

SN TN UN

RB

A2 B2 C2

A1 B1 C1

AN-1 BN-1 CN-1

AN BN

Fig. 5. Structure of the Jacobian matrix for the formaldehyde absorber.


81

Despite the presence of the two off-diagonal submatrices, the matrix generalisation of theThomas algorithm can be used to solve eq. (46) for (X)next. With this algorithm, the Jacobianmatrix is first converted to the so-called upper diagonal form by a recursive elimination. Most ofthe sparsety of the Jacobian is preserved during the elimination process. Additional entries appearonly in the columns between the submatrices [RT] and [TN], and between [RB] and [BN]. From theupper triangular form, the solution for (X)next is found by repeated back substitution.

Unfortunately, the solution method described above showed a poor convergence (e.g. largecomputation time) or did not result in a solution at all. The latter particularly if the initialestimates of the variables were not very close to the final solution. The reason for thisunsatisfactory behaviour is not completely clear, but possibly part of the problem is caused by thegreat difference in the orders of magnitude of the terms in the energy balances as compared tothose in the mass balances. Therefore, the solution method was changed in such a way that theenergy balance equations and the temperatures where skipped from eq. (46). The remainingmodified eq. (46) now contains only the component balance equations and the molar flow rates,and is solved in an inner loop

jMFMFMWFWFWFMFMWFWFT

j lllllllvvvvvX ),,,,,,,()(10110111 ,,

loopinner KK= (50)

jMFMFMWFWFWF

gMFgMgWFgWgFT

j

),,,,

,,,,,()(

,,,,,,,

,,,,,loopinner

101101

11

lllllll KK ΨΨΨΨΨΨΨ

ΨΨΨΨΨ=Ψ. (51)

The inner loop iterations continued until the sum of square residuals of the mass balances, SSRM,satisfied the condition

( ) 262,,

2,, ]/[10)()( smolSSR

j igjigjiM

−<Ψ+Ψ= ∑∑ . (52)

Subsequently, the temperatures were found by solving the energy balances in an outer loop usingeq. (46) with (Xj) and (Ψj) now defined as

jgT

j TTX ),()(loopouter l= , (53)

jEgET

j ),()( ,,loopouter lΨΨ=Ψ . (54)

Convergency of the energy balances was supposed to be obtained once the sum of squareresiduals of the energy balance equations, SSRE, satisfied the condition

( ) 232,

2, ]/[10)()( sJSSR

jgEgEE <Ψ+Ψ= ∑ . (55)


82

The solution algorithm is summarised in Fig. 6. The calculations are initialised by assigningguessed values to the molar flow rates and to the temperatures at the first stage, and by simplytaking the conditions at the other stages identical to the first stage. Although the initialisation isnot very sophisticated, the algorithm converges readily to a solution defined by eqs (52) and (55).

Once calculated solutions were available for some situations, these were used as startingvalues, to initialise the calculations for other sets of operating parameters. This leads to aconsiderable reduction of the calculation time.

The transfer coefficients and other physical and most of the chemical properties needed inthe calculations were obtained as described by Winkelman et al. (1992). The chemicalequilibrium constants for reactions involving formaldehyde and methanol where taken fromMaurer (1986). Because no open literature is available on the rates of reactions involvingmethanol these rates were taken equal to the rates of the corresponding reactions involving water,i.e.: kmi = ki (i = 1..nmax).

START

input parameters

initialize variables

calculate ( ) and [ ]Ψ Jfor inner loop

update flowrates

SSR <10M-6

calculate ( ) and [J]Ψfor outer loop

update temperatures

SSR <1E 03

END

No

oute

r loo

pin

ner l

oop

No

Fig. 6. Algorithm for computing absorber performance.


83

Results

Fig. 7 shows a typical example of the convergence behaviour of the double-loop solutionalgorithm. In this figure, the values of SSRM calculated with inner loop iterations are plottedagainst the values of SSRE from the outer loop. The calculations were initialised by using thesame guessed molar flow rates and temperatures for all the stages. To cut calculation time, thevalue of SSRE was not calculated during the inner loop calculations. In constructing Fig. 7, thevalue of SSRE during the inner loop iterations was therefore assumed to equal the one calculatedfrom the next outer loop iteration. It is seen that the number of inner loop iterations per outerloop iteration reduces steadily from four to just one as the conditions approach the final solution.Fig. 7 also illustrates that the improvement per individual iteration is greater the closer we are tothe final solution (up to several decades in terms of SSR-values). This is typical for Newton'smethod. The concentrations necessary for the calculations of the mass transfer fluxes from eqs (30)-(38)can be calculated from the molar flow rates in several ways (Krishnamurthy and Taylor,1985a,b). The simplest option is to assume constant bulk compositions, and to calculate theconcentrations from the molar flow rates leaving the stage. If the bulk compositions are assumedto vary linearly, then the concentrations have to be calculated from the average of the molar flowrates entering and leaving the stage. For the simulation of packed columns, Krishnamurthy andTaylor (1985c) obtained the best results using the average composition for the bulk vapour

jgtot

i

ji

ji

i

ji

jij

gi Cv

v

v

vC ,1

1

, 5.0

+=∑∑ +

+, (56)

110.4

0.02

4x10-4

2x10-5

END

START

102

106

1010

1014

10

10

10

10

10

10

10

5

0

-5

-10

-15

SSR /(W)E2

SSRE

(mol/s)2

Fig. 7. Typical convergence path. Numbers indicate the largest temperature correction


84

in either phase with an outer loop iteration step. Dashed lines: inner loop iterations. Solid lines: outer loop iterations.

20 40 60 80 1000

0.24

0.23

0.22

0.21

0.20

total number of stages

vMout

vMin

Fig. 8. Relative amount of vapour phase methanol leaving the bottom-bed vs. the total number of stages applied; ( ): fluxes based on average vapour

composition; ( ): fluxes based on exit vapour composition.

and using the exit composition for the bulk liquid

jtot

i

ji

jij

i Cl

lC ll ,,

∑= . (57)

We, therefore, applied the same method. The influence of the method of calculating the vapourbulk composition is illustrated in Fig. 8, where, as an example, the relative methanol vapourphase molar flow rate leaving the bottom-bed is shown as function of the total number of stagesapplied. The bulk liquid phase composition was always calculated from the exit liquid molarflows. Using the stage exit molar flows to calculate the fluxes leads to lower driving forces formass transfer, and therefore less absorption of methanol. The effect of the total number of stageson the solution was studied by varying this number while always allocating 50% to the top- andthe bottom-bed, respectively. The many calculated output variables (molar flow rates andtemperatures) all asymptotically approached a constant value with increasing the number ofstages. Again, Fig. 8 may serve as a typical example.

Generally, the variation in the results appeared to become negligible above 60 stages.Therefore all remaining calculations were performed with 60 stages (30 in each absorption bed).

A typical set of calculated bulk vapour and liquid temperature profiles is shown in Fig. 9.The cooler gas stream entering the bottom-bed is quickly heated up to the liquid temperaturebecause of a large heat transfer capability and a much lower heat capacity of the gas streamrelative to the liquid stream. Similarly, the warm gas stream entering the top-bed from the


85

bottom-bed is rapidly cooled down to the liquid temperature level. As the liquid flows

0 10.25 0.5 0.75

relative height

65

64

63

62

61

60

44

42

40

38

36

34

T[C]

T[C]

Fig. 9. Typical temperature profiles in the absorber; ( ):liquid; ( ):gas.

downwards, its temperature rises, predominantly due to the heat effects connected withcondensation and reaction. In the lower part of the bottom-bed, solvent evaporation results in atemperature maximum. Interestingly, the temperature profiles obtained here using a non-equilibrium stage model are quantitatively similar to those obtained previously with a differentialmodel (Winkelman et al., 1992).

After inspection of the results, it turned out that the Ackermann correction factor for thevapour phase, Af,g, deviates very little from unity. This can be easily understood. For masstransfer to have a significant influence on the vapour phase conductive energy flux, say morethan 5% (Af,g ≤ 0.95), it follows from eq. (41) that Cf > 0.1. With typical values for the vapourphase heat capacity Cpi,g ≈ 40 J/(mol K) and the heat transfer coefficient hg ≈ 40 J/(m2 K s) thisresults in a condition for the fluxes: 1.0, ≥∑ viJ mol/(m2 s), which is larger than can beexpected in absorption columns for the solubilities typical in formaldehyde absorption. Further,the temperature differences in the liquid film, jjI TT l−, , are generally well below 0.1 K becauseof the low resistance against heat transfer in the liquid phase. According to these observations,the following assumptions are justified: 1=fA and jjI TT l=, . This allows for considerablesimplifications in the calculation of the energy transfer rates because apparently there is no needto calculate the interfacial temperature. This way, eqs (39)-(43) reduce to

)( lTThq ggg −= , (58)

))(())((

)(

1,,,1,,,

,,,,

1111 RgWFWFRgWFWF

iivapgi

igigigg

HJJHJJ

HJCpJTTqq

∆−−+∆−−+

∆+−+= ∑∑

ll

ll. (59)

Fig. 10 shows typical profiles of relative vapour phase molar flow rates in the formaldehydeabsorption column. Because of the large liquid/gas ratio, the liquid phase composition does not


86

change much with the stage number of the packed section and is therefore not shown in Fig. 10.

vi

viin

0 10.25 0.5 0.75

relative height

2

1

0

i=W

i=F

i=M

Fig. 10. Typical profiles of relative vapour phase molar flow rates.

Similar to the temperature profiles, also these profiles clearly reveal the division of de packedheight in two absorption beds. The gas feed to the absorber is undersaturated with water. In thelower part of the bottom bed this leads to desorption of water. In the upper part of the bottom-bed, but even more in the top-bed, the water vapour condenses. This way an internal circulationof water is created. The mass transfer of both formaldehyde and methanol is always directedtowards the liquid. Again, the profiles obtained here for formaldehyde and water using a non-equilibrium stage model are very similar to those obtained previously using a differential model.

The relative vapour molar flow rates of the reaction products methylene glycol andhemiformal are sown in Fig. 11. These components are not present in the gas feed, and similar towater, they are desorbed in the lower part of the bottom-bed and re-absorbed higher in thecolumn.

vivF

0 10.25 0.5 0.75relative height

0.03

0.02

0.01

0.00

i=WF1

i=MF1


87

Fig. 11. Typical profiles of relative molar flow rates of the vaporised reaction products.

v vWF MF1 1+vF

0 10.25 0.5 0.75relative height

0.10

0.05

0.00

vMF1

vM

1.5

1.0

0.5

0.0

Fig. 12. Fraction of converted formaldehyde and methanol in the gas phase relative to the uncombined, free components.

Fig. 12 shows that the amount of formaldehyde that is transported in the gas phase in associatedform is relatively low compared to the amount of free formaldehyde: it always accounts for lessthan 10% of the total amount of formaldehyde in the gas phase. On the other hand, the amount ofhemiformal is substantial compared to the amount of free methanol in the gas phase (in thebottom-bed it becomes even the larger one of the two). But both the amounts of methanol andhemiformal are small relative to formaldehyde and water.

The numerical evaluation of the fluxes, as described in the section on mass transfer rates,allows for the calculation of the mass transfer enhancement factors, Ei

)( ,,,

0

lll iIii

x

ii

iCCk

dxdCD

E−

−

= = . (60)

Remarkable results are obtained for the reaction products methylene glycol and hemiformal,see Fig. 13. The enhancement factor of hemiformal is smaller than one in many of the stages.Methylene glycol has even negative enhancement factors in some of the stages. Thisphenomenon is not some numerical peculiarity, but results from the combined action of masstransfer and reaction. This becomes clear by taking a closer look at the concentration profiles ofmethylene glycol in the stagnant liquid film adjacent to the gas-liquid interface. These profilesare shown in Fig. 14 for the stages 50 to 54 (the stage numbers are also indicated in Fig. 13). Theprofiles were obtained from the numerical method described in the section on mass transfer rates.In these stages, the positive gradient of the concentration near x = 0 indicates that the flux ofmethylene glycol at the interface is directed towards the gas phase. Therefore the numerator of eq(60) is always negative here. However, the concentration difference of methylene glycol over the


88

film in the denominator of eq (60), ll ,, 11 WFIWF CC − , changes sign in going from stage 52 to 53.

EWF1

0 10.25 0.5 0.75

relative height

EMF1

5

0

-5

-10

-15

-20

2.0

1.5

1.0

0.5

0.0

5450

Fig. 13. Mass transfer enhancement factors of the reaction products;( ): methylene glycol; ( ): hemiformal.

C CWF1, WF1,l l−

mol/m3

1

0

-10 10.25 0.5 0.75

x/δ

stage 5051

52

53

54

Fig. 14. Concentration profiles of methylene glycol in the film at the interface for the stages 50-54.

For the stage numbers 53 and 54 the denominator is negative, resulting in positive enhancementfactors, whereas for the stage numbers 50-52 the denominator is positive, resulting in negativeenhancement factors. Recently, the possible occurrence of negative enhancement factors wasshown also by analytically solving the case of mass transfer with a single first-order reversiblereaction (Winkelman and Beenackers, 1993).

In a previous contribution, we already discussed the influence of several operatingparameters on the temperature rise of the liquid in the packed beds, on the formaldehydeabsorption efficiency and on the overall weight percentage of formaldehyde in the liquid leaving


89

the packed beds (Winkelman et al., 1992). New aspects here are the role of methanol andhemiformal. Below, we focus on these aspects only.

Fig. 15 illustrates the influence of the temperature of the liquid recycle stream of the top-bed, Rec

tT . Increasing RectT results in higher partial pressures of methanol and hemiformal, and

therefore in increasing relative molar flows of these components in the gas stream leaving thetop-bed and thus in less absorbed methanol in the liquid leaving the bottom-bed. With increasing

RecbT the vapour pressures of methanol and hemiformal in the bottom-bed increase. This causes

increased levels of these components in the top-bed, and higher amounts leaving the absorberwith the gas stream, see Fig. 16. Although the higher amounts of absorbed methanoliccompounds enter the bottom-bed with the liquid flowing down from the top-bed, this cannotcompletely compensate for the decreased absorption of methanol and hemiformal in the bottom-bed and the overall amount of methanol leaving the bottom-bed with the liquid stream decreases.

0.14

0.12

0.10

0.08

0.06

0.04

viout

vMin

25 30 35 40 45

T [C]tRec

WM[wt%]

2.0

1.9

1.8

1.7

i=M

i=MF1

bottom

Fig. 15. Influence of RectT on the relative amounts of methanolic compounds in

the exit gas and in the exit liquid stream.

0.12

0.10

0.08

0.06

viout

vMin

55 60 65 70 75

T [C]bRec

WM[wt%]

2.0

1.9

1.8

1.7

i=M

i=MF1

bottom


90

Fig. 16. Influence of RecbT on the relative amounts of methanolic compounds in

the exit gas and in the exit liquid stream.0.12

0.10

0.08

0.06

viout

vMin

30 40 50 60 70 80 90

Rt

WM[wt%]

1.95

1.90

1.85

1.80

i=M

i=MF1

bottom

Fig. 17. Influence of Rt on the relative amounts of methanolic compounds in the exit gas and in the exit liquid stream.

viout

vMin

20 25 30 35 40

Rb

WM[wt%]

1.95

1.90

1.85

1.80

i=M

i=MF1

bottom

0.11

0.10

0.09

0.08

0.07

0.06

Fig. 18. Influence of Rb on the relative amounts of methanolic compounds in the exit gas and in the exit liquid stream.

The influence of tR , the amount of liquid recycled around the top-bed, is illustrated in Fig.17. The amounts of methanol and hemiformal leaving the absorber with the gas stream decreasewith increasing tR , while at the same time the weight percentage of methanol in the liquidleaving the absorber at the bottom is almost constant. This might seem conflicting, but is causedmainly by a decrease of the temperature rise of the liquid in the top-bed with increasing tR . The


91

result is even more formaldehyde and water absorption, and therefore an increase of the totalamount of liquid entering the bottom-bed from the top-bed which tends to dilute the methanolicspecies. Similarly, the temperature rise of the liquid in the bottom-bed decreases with increasing

bR , leading to more formaldehyde and water absorption in the bottom-bed, dilution of themethanol and lower weight percentages of methanol in the liquid leaving the absorber, see Fig.18. On the other hand, the increased absorption of formaldehyde and methanol in the bottom-bedresults in lower amounts of these components absorbed in the top-bed. This reduces the liquidflow in the top-bed, resulting in a higher temperature rise, increased vapour pressures ofmethanol and hemiformal, and higher amounts of these components leaving the top-bed with thegas stream.

Interesting phenomena were observed if the amount of make-up water is varied. In bothabsorption beds, the amount of methanol in the gas stream increases with increasing amounts ofmake-up water, whereas the amount of hemiformal decreases. This is caused by a shift in therelative amounts of reaction products in the liquid phase. Due to the lower overall amounts offormaldehyde present in the liquid, less methanol combines with formaldehyde to formhemiformal, and more methanol is present in the uncombined form. This results in a higherpartial pressure of methanol and a lower partial pressure of hemiformal. The amounts of thesecomponents leaving the absorber with the gas stream react correspondingly to increasingamounts of make-up water, see Fig. 19.

viout

vMin

0 2 4 6

WM[wt%]

2.5

2.0

1.5

1.0

i=M

i=MF1

bottom

0.12

0.10

0.08

0.06

0.04

relative amount of make up water

Fig. 19. Influence of the relative amount of make-up water on the relative amounts of methanolic compounds in the exit gas and in the exit liquid stream.


92

Conclusions.

The industrially important process of formaldehyde absorption in the presence of methanol issimulated using a non-equilibrium stage model. The model takes into account the mass transferof formaldehyde, water and methanol, and their primary reaction products methylene glycol andhemiformal. In the liquid a large number of reactions take place, giving rise to numerous liquidphase components.

The double loop solution algorithm, solving the component balances in an inner loop andthe energy balances in an outer loop, proved to be stable and converged readily despite a simpleinitialisation and a large number of equations. The non-zero mass flux correction of theconductive energy fluxes proved to be negligible. Similarly, it was found that the resistanceagainst energy transfer in the liquid phase is negligible under practical conditions. In this type ofmodelling it is useful to check whether these simplifications are possible, because they reduce thecalculation effort significantly.

The evaporation of water, methylene glycol and hemiformal in the lower part of the columncreates an internal circulation of these components. In this part of the column negativeenhancement factors are obtained for mass transfer with reaction of methylene glycol andhemiformal. This indicates that approximate methods for calculating mass transfer enhancementfactors due to reaction might fail for absorption with chemical reaction and simultaneous productdesorption.

Chapter 7: Epilogue.

93

Chapter 7

Epilogue

The research reported in this thesis was instigated upon a request from Dynea B.V.concerning the absorbers in their formaldehyde plants. Since formaldehyde is a bulk chemical, itscost price is critical, and the production facilities need constant adjustments to increase theefficiency and to reduce the costs. But despite the need for a remunerative production process,the absorption columns didn't operate optimally for many years. They were bottleneckingproduction levels, hampering efficiency increases, and preventing reduction of the consumptionof methanol, which is the raw material in the production of formaldehyde. Internally, tests wereconducted with the absorbers aimed at getting insight into the influence of various processparameters on the performance, without much success though. With the lapse of time, some testswere even repeated, without the results getting any better. It turned out that the number ofpossible variations and process parameters was too large, and their influence on the absorberperformance too complicated to be able to achieve an understanding, let alone optimisation, thisway.

The strategy opted for to tackle the absorber problems was the development of reactionengineering models from first principles, to describe the performance of the columns and theeffects of variations in the operating parameters on the efficiencies.

From an initial survey of the literature, concerning the availability of physical en chemicaldata on the reactions in, and properties of aqueous formaldehyde solutions, it was concluded thatexperimental work was needed on the kinetics of the main reaction, the hydration offormaldehyde, and the density and viscosity of the solutions. Consequently, the kinetics of thedehydration of methylene glycol were measured, the influence, in general, of a reversiblereaction on gas liquid mass transfer was studied theoretically, the kinetics and equilibrium of thehydration were measured, and the density and viscosity of aqueous formaldehyde solutions weredetermined, see Chapters 2, 3 and 4 and Appendix A of this thesis, respectively. Data on the rateand equilibrium of the relatively slow formation of the series of poly oxymethylene glycols, andon the vapour liquid equilibria pertaining to formaldehyde containing systems, are readilyavailable from the literature, especially from the publications by the research group of Maurer(e.g. Maurer, 1986; Hasse, 1990; Hahnenstein et.al, 1994, 1995; Albert et.al, 2000).

Various reaction engineering models were developed, see Chapters 5 and 6 of this thesis,and translated to computer code. They were adapted to, p.e., the different absorption columnconfigurations that were operational. In a first instance, the models were successfully tested fortheir ability to describe the current performance of the absorbers. Next, the effect of variations ofthe operational parameters on the column performances was investigated. This resulted in a newoptimised set of operational conditions and an increased efficiency of the absorber performance.

Chapter 7: Epilogue.

94

The advantages of the absorber models are threefold. The model predicts exactly theconsequences of any alterations in the tuning, and the process-engineers now have completecontrol over the column performance. Because of the higher efficiency of the absorbers, the sameformaldehyde production level can now be achieved with less methanol consumption andconsiderable savings. An advantage of a more psychological nature is the ending of internaldiscussions for years on absorber operation among the engineers, and the clarity and univocalnature of the instructions that can now be given to the operators in the plant.

The results obtained here are not just confined to usage in the modelling and optimisation offormaldehyde absorbers. They were also, for example, successfully applied in the modelling ofindustrial formaldehyde-methanol-water distillation, where methanol is separated fromformaldehyde water mixtures. In general, with the availability now of a complete description ofaqueous formaldehyde systems, the results are of use in the design of many separation processesinvolving formaldehyde.

Symbols

95

Symbols

a interfacial area, m-1 fA Ackermann heat transfer correction factor jA interfacial area in stage j, m2

C concentration, mol m-3 Cpi molar heat capacity of i, J mol-1 K-1 D diffusivity, m2 s-1 d stirrer diameter, m E energy flux, W m-2 E chemical enhancement factor for mass transfer, - Hi molar enthalpy of i, J mol-1

jRH )(∆ reaction enthalpy of reaction j, J mol-1

ivapH ,∆ molar heat of vaporization of i, J mol-1 h heat transfer coefficient, W m-2 K-1 HMS− hydroxymethane sulphonate, CH2(OH)SO3

− J molar flux, mol m-2 s-1 K chemical equilibrium constant, - Ka1, Ka2 acid dissociation constants of H2SO3 and HSO3

−, respectively, in terms ofconcentrations, mol m-3

Kh chemical equilibrium constant of the formaldehyde hydration, - Kw dissociation constant of water in terms of concentrations, (mol m-3)2 k reaction rate constant, m3 mol-1 s-1

1k first order reaction rate constant, s-1

k2 rate constant for the reaction of formaldehyde with −23SO , m3 mol-1 s-1

hd kk , rate constants for the dehydration of methylene glycol, and the pseudo-first-orderhydration of formaldehyde, respectively, s-1

gk gas phase mass transfer coefficient, m s-1

lk liquid phase mass transfer coefficient, m s-1 l optical path length, m li liquid phase component molar flow rate, mol s-1 M molar weight, kg mol-1 m distribution coefficient ( gCC /l , at equilibrium), - N stirrer rate, s-1

maxn number of CHO segments in the largest polymers considered P pressure, Pa

siP saturated vapor pressure of i, Pa

q conductive heat flux, W m-2 R ideal gas constant, J mol-1 K-1 Ri production rate by reaction of i, mol m-3 s-1

Symbols

96

Rt, Rb liquid recycle ratio for the top and bottom bed, - Re Reynolds number, ηρ /2Nd , -

jr rate of reaction j, mol m-3 s-1 S Chapter 4: gas liquid interfacial area, m2 S cross sectional area of the column, m2 Stot total concentration of sulphur, mol m-3 Sc Schmidt number, Dρη / , - Sh Sherwood number, ggg Ddk / or lll Ddk / , -.

ESSR sum of square residuals of the energy balances, W

MSSR sum of square residuals of the mass balances, mol s-1 T temperature, K ∆Tl temperature rise of the liquid, K t time, s V volume, m3 VB volume of liquid on the partial draw off tray at the bottom of the column, m3 v diffusivity ratio (= ll ,, / PA DD in Chapter 3; = ll ,, / MGF DD in Chapter 4), - vi gas phase molar flow rate of i, mol s-1 W weight WF overall weight percentage of formaldehyde in the liquid, wt.% WM overall weight percentage of methanol in the liquid, wt.% x liquid phase molar fraction, -; distance in the film, m x~ overall liquid phase molar fraction, - y gas phase molar fraction, - Z height of packing, m z charge number of ionic species, -

jZ∆ height of stage j, mGreek letters γ activity coefficient δ film thickness, m ε extinction coefficient, m2 mol-1; dielectric constant of water lε partial liquid holdup, -

η viscosity, Pa s µ ionic strength νi,j stoichiometric coefficient of component i in reaction j, - ρ density, kg m3

Rφ reaction factor, -

g,vφ gas phase volumetric flow rate, m3 s-1 Ψ vector of discrepancies of the set of balance equationsSubscripts 0 initial 2,3,.. polymerization reactions

Symbols

97

A reactant b bottom bed F formaldehyde g gas phase h hydration reactioni component i j reaction j l liquid phaseM methanol

nMF hemiformal, CH2O(CH2O)nH, max1 nn ≤≤ MG methylene glycol max maximum n number of CH2O segments in a polyoxymethylene glycol P reaction product t top bed tot total W water WFn polyoxymethylene glycol with n CH2O segments ∞ irreversible reaction, limit for ∞→K Superscripts — (overbar) bulk conditions D liquid draw offF liquid feedI interface in incoming or feed conditions j stage j out outgoing stream Rec liquid recirculation stream sat saturated th thermodynamic equilibrium constant based on activities

References

99

References

Albert, M., García, B.C., Kuhnert, C., Peschla, R., & Maurer, G. (2000). Vapor-liquid equilibrium ofaqueous solutions of formaldehyde and methanol. A.I.Ch.E. J., 46, 1676-1687.

Allan, J.M. & Teja, A.S. (1991). Correlation and prediction of the viscosity of defined and undefinedhydrocarbon liquids. Can. J. Chem. Eng., 69, 986-991.

Astarita, G., & Savage, D.W. (1980). Gas absorption and desorption with reversible instantaneous chemicalreaction. Chem. Engng Sci., 35, 1755-1764.

Bell, R.P. (1966). The reversible hydration of carbonyl compounds. In Adv. Phys. Org. Chem., Gold, V. Ed.,Vol.4, 1-29, London: Academic Press.

Bell, R.P., Evans, F.R.S., & Evans, P.G. (1966). Kinetics of the dehydration of methylene glycol in aqueoussolution. Proc. Roy. Soc. (London) Ser.A, 291, 297-323.

Bieber, R. & Trümpler, G. (1947). An`genäherte spektrographische Bestimmung der Hydratations-gleichgewichtskonstanten wässriger Formaldehydlösungen. Helv. Chim. Acta, 30, 1860-1865.

Blackadder, D.A., & Hinshelwood, C. (1958). The kinetics of the decomposition of the addition compoundsformed by sodium bisulphite and a series of aldehydes and ketones. Part I & II. J. Chem. Soc. 1958,2720-2727; 2728-2734.

Bohne, D., Fischer, S. & Obermeier, E. (1984). Thermal conductivity, density, viscosity and Prandtl-numbers of ethylene glycol-water mixtures. Ber. Bunsen-Ges. Phys. Chem., 88, 739-742.

Bourne, J.R., Von Stockar, U., & Coggan, G.C. (1974). Gas absorption with heat effects. I. A newcomputational method. Ind. Eng. Chem. Process Des. Dev., 13, 115-123.

Boyce, S.D., & Hoffmann, M.R. (1984). Kinetics and mechanism of the formation ofhydroxymethanesulfonic acid at low pH. J. Phys. Chem. 88, 4740-4746.

Brandani, V., Di Giacomo, G. & Foscolo, P.U. (1980). Isothermal vapor-liquid equilibria for the water-formaldehyde system. A predictive thermodynamic model. Ind. Eng. Chem. Process Des. Dev., 19, 179.

Bryant, W.M.D., & Thompson, J.B. (1971). Chemical thermodynamics of polymerization of formaldehydein an aqueous environment. J. Polym. Sci. A-1, 9, 2523-2540.

Burnett, M.G. (1982). The mechanism of the formaldehyde clock reaction. J. Chem. Ed. 59, 160-162. Calvert, J.G., & Pitts, J.N., (1966). Photochemistry. New York: John Wiley & Sons, Inc. Cancho, J.C., Sanchez, A.M.E., Tena, A.A., & Moreno, M.C. (1989). Evolution and current methods for

obtaining formaldehyde. Chem. Biochem. Eng. Q., 3, 51-55. Chase, J.D. (1984). The qualification of pure component physical property data. Chem. Eng. Prog., 4, 63-

67. Cornelisse, R., Beenackers, A.A.C.M., Van Beckum, F.P.H., & van Swaaij, W.P.M. (1980). Numerical

calculation of simultaneous mass transfer of two gases accompanied by complex reversible reactions.Chem. Engng Sci., 35, 1245-1260.

Dankelman, W., Muizenbelt, W.J., & Leentjes, H. (1988). AKZO Engineering, internal report. Dasgupta, P.K., DeCesare, K., & Ullrey, J.C. (1980). Determination of atmospheric sulfur dioxide without

tetrachloromercurate(II) and the mechanism of the Schiff reaction. Anal. Chem., 52, 1912-1922. Daubert, T.E., & Danner, R.D. (1985). Data Compilation Tables of Properties of Pure Compounds. New

York: American Institute of Chemical Engineers. Deister, U., Neeb, R., Helas, G., & Warneck, P. (1986). Temperature dependence of the equilibrium

CH2(OH)2 + H2SO3− = CH2(OH)SO3

− + H2O in aqueous solution. J. Phys. Chem., 90, 3213-3217. Devèze, D., & Rumpf, P. (1964). Étude spectrophotométrique des solutions aqueuses de gaz sulfureux dans

divers tampons acides. Compt. Rend., 258, 6135-6138. Feintuch, H.M., & Treybal, R.E. (1978). The design of adiabatic packed towers for gas absorption and

stripping. Ind. Eng. Chem. Process Des. Dev., 17, 505. Funderburk, L.H., Aldwin, L., & Jencks, W.P. (1978). Mechanisms of general acid and base catalysis of the

reaction of water and alcohols with formaldehyde. J. Am. Chem. Soc., 100, 5444-5459. Gmehling, J., Rasmussen, P. & Fredenslund, A. (1982). Vapor-liquid equilibria by UNIFAC group

contribution. Revision and extension 2. Ind. Eng. Chem. Proc. Des. Dev., 21, 118.

References

100

Golding, R.M. (1960). Ultraviolet absorption studies of the bisulphite-pyrosulphite equilibrium. J. Chem.Soc., 3711-3716.

Gruen, L.C., & McTigue, P.T. (1963). Hydration equilibria of aliphatic aldehydes in H2O and D2O. J.Chem. Soc., 5217-5223.

Hahnenstein, I., Hasse, H., Kreitler, C.G. & Maurer, G. (1994). 1H- and 13C-NMR spectroscopic study ofchemical equilibria in solutions of formaldehyde in water, deuterium oxide, and methanol. Ind. Eng.Chem. Res., 33, 1022-1029.

Hahnenstein, I., Albert, M., Hasse, H., Kreitler, C.G., & Maurer, G. (1995). NMR spectroscopic study ofreaction kinetics of formaldehyde polymer formation in water, deuterium oxide, and methanol. Ind. Eng.Chem. Res., 34, 440-450.

Hasse, H. (1990). Dampf-Flussigkeits-Gleichgewichte, Enthalpien und Reaktionskinetik informaldehydhaltigen Mischungen. PhD Thesis, Universität Kaiserslautern, Germany.

Hasse, H., & Maurer, G. (1991). Kinetics of the poly(oxymethylene) glycol formation in aqueousformaldehyde solutions. Ind. Eng. Chem. Res., 30, 2195-2200.

Hasse, H. & Maurer, G. (1991). Vapor-liquid equilibrium of formaldehyde-containing mixtures attemperatures below 320 K. Fluid Phase Equilibria, 64, 185.

Hayon, E., Treinin, A., & Wilf, J. (1972). Electronic spectra, photochemistry, and autoxidation mechnism ofthe sulfite-bisulfite-pyrosulfite systems. The SO2

−, SO3−, SO4

− and SO5− radicals. J. Amer. Chem. Soc.,

94, 47-57. Himmelblau, D.M., Jones, C.R., & Bischoff, K.B. (1967). Determination of rate constants for complex

kinetic models. Ind. Eng. Chem. Fundam., 6, 539-543. Hitch, D.M., Rousseau, R.W., & Ferell, J.K. (1986). Simulation of continuous separation processes:

multicomponent, adiabatic absorption. Ind. Eng. Chem. Process Des. Dev., 25, 699. Hitch, D.M., Rousseau, R.W., & Ferell, J.K. (1987). Simulation of continuous separation processes:

unsteady state multicomponent, adiabatic absorption. Ind. Eng. Chem. Process Des. Dev., 26, 1092. Iliceto, A. (1954). Sul sistema acque-formaldeide. Nota VI. Equilibri della fasi liquida e gassosa. Gazz.

Chim. Ital., 84, 536-552. Kelly, R.M., Rousseau, R.W., & Ferrell, J.K. (1984). Design of packed, adiabatic absorbers: physical

absorptuion of acid gases in methanol. Ind. Eng. Chem. Process Des. Dev., 23, 102. King, C.J. (1980). Separation Processes, 2nd ed., New York: McGraw-Hill. Kirk-Othmer Encyclopedia of Chemical Technology (1994). 4th ed. Kroschwitz, J.I., Exec. Ed., Howe-

Grant, M., Ed., John Wiley & Sons, New York. Kogan, L.V., Blazhin, Y.M., Ogorodnikov, S.K., & Kafarov, V.V. (1977). Liquid-vapor equilibrium in the

system formaldehyde-water. Zhur. Prikl. Khim., 50, 2682-2687. Krishna, R., & Taylor, R. (1986). Multicomponent mass transfer: theory and applications. In: Handbook of

Heat and Mass Transfer, Vol. 2, Chap. 7, pp. 259-432, Houston: Gulf Publ. Company. Krishnamurthy, R. & Taylor, R. (1985a). A non-equilibrium stage model of multicomponent separation

processes. Part I: Model description and method of solution. A.I.Ch.E. J., 31, 449. Krishnamurthy, R. & Taylor, R. (1985b). A non-equilibrium stage model of multicomponent separation

processes. Part II: Comparison with experiment. A.I.Ch.E. J., 31, 456. Krishnamurthy, R. & Taylor, R. (1985c). Simulation of packed distillation and absorption columns. Ind.

Eng. Chem. Process Des. Dev., 24, 513. Krishnamurty, R., & Taylor, R. (1986). Absorber simulation and design using a nonequilibrium stage

model. Can. J. Chem. Eng., 64, 96. Landau, J. (1992). Desorption with chemical reaction. Chem. Engng Sci., 47, 1601-1606. Landqvist, N. (1955). On the polarography of formaldehyde. Acta Chem. Scand., 9, 867-892. Lee, R.J. & Teja, A.S. (1990). Viscosities of poly(ethylene glycols). J. Chem. Eng. Data, 35, 385-387. LeHénaff, P. (1963). Sur la vitesse de déshydratation du méthylène-glycol en formaldéhyde. Compt. Rend.,

250, 1752-1754.

References

101

Lileev, A.A., Poblinkov, D.B., Lyashchenko, A.K. & Shepotko, M.L. (1982). Study of the effects of somepolar additives on water according to data of various structure-sensitive methods. Deposited Doc.VINITI 3101-82 (Russian Institute of Scientific and Technological Information).

Los, J.M., Roeleveld, L.F., & Wetsema, B.J.C. (1977). Pulse polarography. Part X. Formaldehyde hydrationin aqueous acetate and phophate buffer solutions. J. Electroanal. Chem. Interfacial Electrochem., 75,819-837.

Maurer, G. (1986). Vapor-liquid equilibrium of formaldehyde- and water-containing multicomponentmixtures. A.I.Ch.E. J., 32, 932-948.

Moortgat, G.K., Seiler, W., & Warneck, P.J. (1983). Photodissociation of HCHO in air: CO and H2 quantumyields at 220 and 300 K. J. Chem. Phys., 78, 1185-1190.

Müller, R.E., & Schurath, U. (1983). Generation of formaldehyde in test atmospheres with lowconcentrations of hydrogen and carbon monoxide. Anal. Chem., 55, 1440-1442.

Nhaesi, A.H. & Asfour, A.A. (1998). Prediction of the McAllister model parameters from pure componentproperties of regular binary mixtures. Ind. Eng. Chem. Res., 37, 4893-4897.

Onda, K., Takeuchi, H., & Okumoto, Y. (1968). Mass transfer coefficients between gas and liquid phases inpacked columns. J. Chem. Eng. Japan, 1, 56-62.

Onda, K., Sada, E., Kobayashi, T., & Fujine, M. (1970). Gas absorption accompanied by complex chemicalreactions - I Reversible chemical reaction. Chem. Engng Sci., 25, 753-760.

Otake, T., & Kunigita, E. (1958). Mixing characteristics of irrigated packed towers. Kagaku Kogaku, 22,144.

Perry, R.H., Green, D.W. & Maloney, J.O. (1984). Perry’s Chemical Engineers Handbook, McGraw-Hill,New York.

Raal, J.D., & Khurana, M.K. (1973). Gas absorption with large heat effects in packed columns. Can. J.Chem. Eng., 51, 162.

Reid, C.R., Prausnitz, J.M., & Sherwood, T.K. (1977). The Properties of Gases and Liuids. 3rd ed., NewYork: McGraw-Hill.

Reid, R.C., Prausnitz, J.M., & Poling, B.E. (1988). The properties of Gases and Liquids. 4th ed., New York:McGraw-Hill.

Rogers, J.D. (1990). Ultraviolet absorption cross sections and atmospheric photodissociation rate constantsof formaldehyde. J. Phys. Chem., 94, 4011-4015.

Schecker, H.G., & Schulz, G. (1969). Untersuchungen zur Hydratationskinetik von Formaldehyd inwäßriger Lösungen. Z. Phys. Chem. NF, 65, 221-224.

Secor, R.M., & Beutler, J.A. (1967). Penetration theory for diffusion accompanied by a reversible chemicalreaction with generalized kinetics. A.I.Ch.E. J., 13, 365-373.

Shah, Y.T., & Sharma, M.M. (1976). Desorption with or without chemical reaction. Trans. Instn Chem.Engrs, 54, 1-41.

Siling, M.I., & Akselrod, B.Ya. (1968). Spectrophotometric determination of equilibrium constants of thehydration and protonation of formaldehyde. Russ. J. Phys. Chem., 42, 1479-1482.

Skelding, A.A. & Ashbolt, R.F. (1959). New data for the densiometric determination of methanol informalin. Chem. Ind., 1959, 213-218.

Soliman, K. & Marschall, E. (1990). Viscosity of selected binary, ternary and quartenary liquid mixtures. J.Chem. Eng. Data, 35, 375-381.

Sørensen, P.E., & Andersen, V.S. (1970). The formaldehyde-hydrogen sulphite system in alkaline aqueoussolution. Kinetics, mechanisms, and equilibria. Acta Chem. Scand., 24, 1301-1306.

Srivastava, R.K., & Joseph, B. (1984). Simulation of packed-bed separation processes using orthogonalcollocation. Comp. Chem. Eng., 8, 43.

Stilchmair, J. (1972). Untersuchungen zum dynamischen Verhalten einer Absorptions-Bodenkolonne.Chem. Ing. Techn., 44, 411.

Stockar, U. v., & Wilke, C.R. (1977). Rigorous and short-cut design calculations for gas absorptioninvolving large heat effects. 1. A new computational method for packed gas absorbers. Ind. Eng. Chem.Fundam., 16, 88-93.

References

102

Stumm, W., & Morgan, J.J. (1970). Aquatic Chemistry, Wiley, New York. Sutton, H.C., & Downes, T.M. (1972). Rate of hydration of formaldehyde in aqueous solution. J. Chem.

Soc., Chem. Comm., 1-2. Tamir , A., Merchuck, J.C., & Virkar, P.D. (1979). Effect of diffusivity on gas-side mass transfer

coefficient. Chem. Engng Sci., 34, 1077. Treybal, R.E. (1969). Gas absorption and stripping in packed towers. Ind. Eng. Chem., 61, 36. Valenta, P. (1960). Oszillographische Strom-Spannungs-Kurven III. Untersugung des Formaldehyds in

gepuffertem Milieu. Collect. Czech.. Chem. Commun., 25, 853-861. Van Swaaij, W.P.M., & Versteeg, G.F. (1992). Mass transfer accompanied with complex reversible

chemical reactions in gas-liquid systems: an overview. Chem. Engng Sci., 47, 3181-3195. Versteeg, G.F., Blauhoff, P.M.M. & Van Swaaij, W.P.M. (1987). The effect of diffusivity on gas-liquid

mass transfer in stirred vessels. Experiments at atmospheric and elevated pressures. Chem. Engng Sci. ,42, 1103-1119.

Versteeg, G.F., & Van Swaaij, W.P.M. (1988). Solubility and diffusivity of acid gases (CO2 and N2O) inaqueous alkanolamine solutions. J. Chem. Eng. Data, 33, 29-34.

Walker, J.F. (1964). Formaldehyde. 3rd ed., ACS Monograph Series, Reinhold, New York. Weirauch, W. (1999). 2000 to be tough for methanol producers. Hydrocarbon Processing, 78(11), 21.Westerterp, K.R., Van Swaaij, W.P.M., & Beenackers, A.A.C.M. (1984). Chemical Reactor Design and

Operation. 2nd ed., John Wiley & Sons Ltd, New York. Winkelman, J.G.M., Sijbring, H., Beenackers, A.A.C.M. & De Vries, E.T. (1992). Modeling and simulation

of industrial formaldehyde absorbers. Chem. Engng Sci., 47, 3785. Winkelman, J.G.M., & Beenackers, A.A.C.M. (1993). Simultaneous absorption and desorption with

reversible first-order chemical reaction: analytical solution and negative enhancement factors. Chem.Engng Sci., 48, 2951-2955.

Winkelman, J.G.M., Ottens, M., & Beenackers, A.A.C.M. (2000). The kinetics of the dehydration ofmethylene glycol. Chem. Engng Sci., 55, 2065-2071.

Winkelman, J.G.M., & Beenackers, A.A.C.M. (2000). Correlations for the density and viscosity of aqueousformaldehyde solutions. Ind. Eng. Chem. Res., 39, 557-562.

Winkelman, J.G.M., Voorwinde, O., Ottens, M., Beenackers, A.A.C.M. & Janssen, L.P.B.M. (2002). Thekinetics of the hydration of formaldehyde. Chem. Engng Sci., 57, 4067-4076.

Yadav, G.D. & Sharma, M.M. (1979). Effect of diffusivity on true gas-side mass transfer coefficients in amodel stirred contactor with a plane liquid interface. Chem. Engng Sci., 34, 1423-1424.

Zavitsas, A.A., Coffiner, M., Wiseman, T., & Zavitsas, L.R. (1970). The reversible hydration offormaldehyde. Thermodynamic parameters. J. Phys. Chem., 74, 2746-2750.

Appendix A: Correlations for the density and viscosity of aqueous formaldehyde solutions.

103

Appendix A

Correlations for the density and viscosity of aqueous formaldehyde solutions

Abstract

Empirical correlations are presented for the density and viscosity of aqueous formaldehydesolutions as a function of temperature (T) and overall weight percentage of formaldehyde (WF).Experimental density data from the literature, at T = 288-338 K and with WF = 1.6-50 wt %, aredescribed with an average absolute residual (AAR) of 0.14%. Experimental viscosity data, bothnew and from the literature, at T = 288-333 K and with WF = 1.6-50 wt %, are described with anAAR of 1.8%. The residuals of the correlations are free of trending effects as a function of T andWF. It is shown that both properties can be described using liquid mixture correlation methodsfrom the literature with almost the same accuracy relative to the empirical correlations.

Introduction

Formaldehyde is an important industrial base chemical. One of the key steps in itsproduction is the absorption of gaseous formaldehyde in water, usually in a packed absorber. Theperformance of the absorbers depends on the process operation variables, such as thetemperature, the pressure, and the flow rates, and on the hydrodynamic properties of the packing,such as the mass-transfer coefficients, the specific interfacial area, and the liquid phase hold-upin the packing. Therefore, in modelling, design, and optimisation calculations of theformaldehyde absorbers, the hydrodynamic properties have to be evaluated. In the literature theseparameters are usually correlated to, among other things, the liquid-phase physical properties,especially the density and viscosity. Also, in the specification sheets of packing manufacturers,the performance of the packing types is often given as a function of these liquid-phase properties,along with various flow-rate parameters.

Two literature sources were found giving correlations for the density of aqueousformaldehyde solutions, ρm. Walker (1964) gives a correlation for ρm as a function of the strengthof the solution, WF, which is valid at 291 K only,

)291(31000.1)( 3291 KTWFKm =+×=ρ , (1)

and the temperature coefficients in the range of T = 288-303 K for WF = 15 and 45 wt %, fromwhich, using eq (1), the following correlations can be obtained:

)303288%,15()291(2.01045)( %15 KTwtWT Fwtm −==−+=ρ , (2))303288%,45()291(4.01135)( %45 KTwtWT Fwtm −==−+=ρ . (3)

The Kirk-Othmer Encyclopedia of Chemical Technology (1994) presents a correlation forρm, which reads (slightly modified to yield consistent units)


104

)]328(1055.00.1)][45(31119[ 3 TWFm −×+−+= −ρ . (4)

No information is given on the accuracy of eq (4), nor on the temperature and concentrationrange for which it is valid. The same source also presents a correlation of the viscosity ofaqueous formaldehyde solutions, ηm, which slightly modified reads

)]15.273(024.0039.028.1[10 3 −−+= − TWFmη . (5)

Equation (5) is valid for rather concentrated solutions, WF = 30-50 wt %, and for T = 298-313 K.No information is given on the accuracy of eq (5).

In this contribution the results of a study to correlate the available literature data on ρm andηm as a function of T and WF are reported. Also, the results of a series of viscosity measurementsof aqueous formaldehyde solutions are reported.

Density

Three literature sources were found reporting data on ρm; see Table 1. Lileev et al. (1982)specified the strength of the solutions in terms of the overall formaldehyde molar fraction, Fx~ ,from which we calculated WF, because these units were used by the other authors mentioned inTable 1:

%100)~1(~

~×

−+=

WFFF

FFF MxMx

MxW . (6)

The experimental results show that ρm varies with T and WF and that always Wm ρρ > (for0>FW ). Fig. 1 shows the density difference )( Wm ρρ − as a function of WF, with ρW from

Perry et al. (1984) It shows that a considerable fraction of the observed variation of ρm can beaccounted for by introducing a linear dependency of )( Wm ρρ − on WF. Least-squaresregression of the data accordingly, followed by an analysis of the residuals, ∆i, defined as

%100)(

)()(

exp

exp ×

−=∆

im

mcalcmi ρ

ρρ, (7)

showed that the residuals have a clear trend as a function of T, indicating an inadequacy in therelation which makes extrapolation unreliable outside the applied experimental conditions. Theresiduals tend to increase monotonically with increasing T, justifying the introduction of anadditional temperature-dependent parameter. Using multiple regression the following equationwas thus obtained:

FWm WT )108166.60950.5( 3−×−+= ρρ . (8)


105

Table 1. Literature data on the density of aqueous formaldehyde solutions. Ref. T (K) WF (wt %) ρm (kg m-3) data points1 291-338 2-50 1005.4-1570.0 273 288, 298 6-43 1018.4-1135.4 164 288, 298, 308 1.6-17 997.4-1045.4 15

alldata

288-338 1.6-50 997.4-1570.0 58

0 20 40 60

160

120

80

40

0

ρρ

mW

−

(k

g/m

)3

W (wt%)F

WalkerSkelding & AshboltLileev et al.

Fig. 1. Density difference between aqueous formaldehyde solutions and water, both at the same temperature. ρm: from the literature sources indicated.

ρW: Perry et al. (1984).

When eq (8) was applied to a 15 wt % solution, at 288 ≤ T ≤ 303 K, the difference with eq (2)(Walker, 1964) was always less than 0.1%. Similarly, with a 45 wt % solution, at the sametemperatures, the difference between eqs (8) and (3) (Walker, 1964) was no more than 0.3%.

For eq (8) an average absolute residual (AAR) of 0.14% was found, with a maximumabsolute residual (MAX) of 0.69%. The AAR is calculated from

∑=∆=

n

iin 1

1AAR . (9)

More importantly, however, the residuals obtained with eq (8) do not show any systematicvariation with T or WF; see Figs 2 and 3. Therefore, eq (8) is a reliable empirical equation for ρm.With eq (4) (Kirk-Othmer Encyclopedia of Chemical Technology, 1994) an AAR of 0.42%(MAX of 1.8%) was observed, which is 3 times as high as the value of eq (8).


106

280 300 320 340T (K)

rela

tive

resi

dual

s (%

)

4

2

0

-2

-4

Fig. 2. Relative residuals of the empirical density correlation (8) as a function of T. Symbols: see Fig. 1.

0 20 40 60W (wt%)F

rela

tive

resi

dual

s (%

)

4

2

0

-2

-4

Fig. 3. Relative residuals of the empirical density correlation (8) as a function of WF. Symbols: see Fig. 1.

Many literature methods for the calculation of liquid mixture densities use the criticalproperties and acentric factors, i.e., vapour pressure vs. temperature correlations, of theindividual components (p.e. Reid et al., 1988) and are therefore not suitable here because therequired properties of the higher poly(oxymethylene) glycols (POMs) are unknown. AlthoughAmagat’s law originally holds strictly only for mixtures of ideal gases, it is also recommendedfor the calculation of liquid densities of mixtures of similar components (Perry et al., 1984),

∑=i

iim VxV . (10)


107

To apply eq (10), the composition of the liquid has to be considered. In aqueous solutions,formaldehyde is hydrated to methylene glycol and a series of POMs:

2222 (OH)CHOHOCH + , (11))..1(OHO)HO(CH(OH)CHO)HHO(CH 21i2222 ∞=++ + i . (12)

Methylene glycol and the POMs only exist in formaldehyde solutions. They cannot be isolated ina pure form, and their pure-component properties cannot be measured directly.

The equilibrium of eq (11) is far to the right and the concentration of free formaldehyde inaqueous solutions is negligible compared to those of methylene glycol and the higher POMs.Then, for the formaldehyde-water system, Amagat’s law can be written as

∑∞

=++=

1)(

iWFiFWWWm xiVVxVV , (13)

where it is assumed that the molar volumes of the POMs can be written as the sum of thevolumes of the constituent groups. The subscript WFi denotes HO(CH2O)iH, i.e., the componentconsisting stoichiometrically of water and i formaldehyde units.

With the molar balance

11

=+ ∑∞

=iWFiw xx , (14)

the overall formaldehyde balance

∑

∑∞

=

∞

=

++=

1

1

)1(

~

iWFiW

iWFi

Fxix

ixx , (15)

and the substitution ρ/MV = , eq (13) can be rewritten as

FF

F

W

W

m

m Vx

xMM~1

~

−+=

ρρ. (16)

Because every molecule in the solution is either a free water molecule or a water moleculechemically bonded to one or more formaldehyde units, the true total concentration in the solutionis equal to the overall water concentration. Therefore, the true mean molar weight of the solution,Mm, can be obtained as

)100/(1 F

Wm W

MM

−= , (17)


108

and the model equation for the density of aqueous formaldehyde solutions, from inserting eqs (6)and (17) in eq (16) and rewriting, becomes

FFWFF

FWm VWMW

Mρ

ρρ

+−=

)100(100

. (18)

The only parameter in eq (18) to be determined from the experimental data is the molar volumeof the CH2O groups in the POM molecules, VF. By taking VF constant, an AAR of 0.45% wasobtained (MAX of 1.7%). Not surprisingly, however, taking VF constant resulted in a clear trendof the residuals of eq (18) as a function of T, varying in the expected direction, i.e., from negativevalues at the lower temperatures to positive values at the higher temperatures.

Because of the clear trend of the residuals, a second parameter to account for the influenceof T on VF seems justified. Least-squares analysis of the experimental data according to eq (18)resulted in the following optimum parameters for VF:

TVF63 1059.3010709.12 −− ×+×= . (19)

Figs 4 and 5 illustrate the relative residuals of ρm calculated with eqs (18) and (19) as a functionof WF and T. No trend in the residuals was found. Here, an AAR of 0.22% was found (MAX of0.69%).

At first glance, eqs (8) and (18) might seem paradoxical: eq (8) correlates ρm linearly withWF, while eq (18) correlates 1/ρm similarly. This is not a true inconsistency because thecoefficient of WF is positive in eq (8), resulting in an increase of ρm with an increase of WF,whereas the overall coefficient of WF in the denominator of eq (18) is negative, giving the samedirection of variation of ρm with WF.

280 300 320 340T (K)

rela

tive

resi

dual

s (%

)

4

2

0

-2

-4

Fig. 4. Relative residuals of the density correlation obtained from Anmagat’s law (eq 18) as a function of the temperature. Symbols: see Fig. 1.


109

0 20 40 60W (wt%)F

rela

tive

resi

dual

s (%

)

4

2

0

-2

-4

Fig. 5. Relative residuals of the density correlation obtained from Anmagat’s law (eq 18) as a function of WF. Symbols: see Fig. 1.

Viscosity

Table 2 summarizes literature data on the viscosity of aqueous formaldehyde solutions.Because this data set is rather limited, we performed additional viscosity measurements with aSchott automated viscosity meter (described in more detail by Soliman & Marschall, 1990) Thesolutions were prepared by dissolving a desired amount of paraformaldehyde (Janssen Chimica)in distilled water. By keeping high efflux times (120-360 s), the error due to kinetic energy wasassumed negligible. Although the vapour pressure of pure formaldehyde at the highesttemperature of the measurements, 325 K, is more than 1.1 MPa (Reid et al., 1988), itsconcentration is so low because of the reactions (11) and (12) that the formaldehyde vapourpressure over a 33 wt % solution is only approximately 1 kPa (Maurer, 1986). Thus, theinfluence of possible evaporation of formaldehyde on the measurements is neglected. Theviscometer was calibrated at each temperature using pure water. The absolute viscosity wasdetermined from the measured kinematic viscosity using the density obtained from eq (8). Theresults are shown in Table 3, where each data point is the mean of three measurements whoseflow times were within 0.15 s. The total uncertainty of the viscosity data was estimated to be±1.5%.

Table 2. Literature data on the viscosity of aqueous formaldehyde solutions. T (K) WF (wt %) 310×mη (Pa s) data points

1 298, 333 5-50 0.54-1.87 164 288, 298, 308 1.6-17 0.7487-1.6086 15

alldata

288-333 1.6-50 0.54-1.87 31


110

Table 3. New experimental data on the viscosity of aqueous formaldehyde solutions. 310×mη (Pa s)

WF (wt %) T = 297.85 K T = 307.15 K T = 318.05 K T = 325.25 K5 1.0295 0.8417 0.6830 0.6011

15 1.2853 1.0537 0.8470 0.746525 1.6377 1.3365 1.0619 0.927933 2.0456 1.6483 1.3129 1.1277

Over a wide temperature range, the logarithm of the kinematic viscosity, η/ρ, uses tocorrelate linearly with 1/T for pure liquids (Reid et al., 1988). This appears also to hold forformaldehyde solutions for a constant WF. The influence of the composition could be accountedfor by correlating )/ln( mmm Mρη linearly both to 1/T and WF. Finally, from an analysis of theresiduals it was found that an additional term, linearly with T, was needed to obtain a correlationfree of trending effects of the residuals. The empirical correlation developed this way is

TWTM F

mm

m 0404.01036.9564490.47ln 3 +×++−=

−

ρη

, (20)

with an AAR of 1.8% (MAX of 7.5%) for 288 ≤ T ≤ 333 K. ρm and Mm are obtained from eqs (8)and (17), respectively. Equation (20) is illustrated in Fig. 6. The residuals of eq (20) did not showany clear trend as a function of WF or T; see Figs 7 and 8.

0 20 40 60W (wt%)F

100

80

60

40

20

WalkerLileev c.s.Perry c.s.this work

η ρ Mm

mm

x109

kmol

.mkg

.s

2

()

Fig. 6. ηm/ρmMm as a function of WF for various T. Symbols: ηm from the sources indicated, ρm and Mm from eqs (8) and 17, respectively. Lines: ηm/ρmMm calculated with the

empirical viscosity correlation (20).


111

0 20 40 60W (wt%)F

20

10

0

-10

-20

resi

dual

(%)

Fig. 7. Relative residuals of the empirical viscosity correlation (20) as a function of WF. Symbols: see Fig. 6.

20

10

0

-10

-20

rela

tive

resi

dual

(%)

280 300 320 340

T (K)

Fig. 8. Relative residuals of the empirical viscosity correlation (20) as a function of T. Symbols: see Fig. 6.

In addition to eq (20), we also tested an Antoine-type of temperature dependency,augmented with a linear term in WF, i.e., ln(ηm/ρmMm) = p1+p2/(T+p3)+p4WF. After optimizationof the parameters using nonlinear regression, the same AAR (1.8%) was observed; however,MAX was somewhat larger (8.6%) as compared to eq (20).


112

The methods found in the literature for obtaining the viscosity of liquid mixtures are oftenbased on the mole fraction average of the logarithms of the pure-component viscosities, extendedwith various types of correction factors (Perry et al., 1984; Reid et al., 1988). Applying molefraction averaging to the formaldehyde-water system gives

∑∞

=+=

1lnln

iWFiWFiWwm xx ηηη . (21)

In the literature it is shown that for various homologous series the logarithm of the pure-component viscosities varies linearly with the molecular size (p.e. Chase, 1984; Allan & Teja,1991; Nhaesi & Asfour, 1998). This concept cannot be tested directly for methylene glycol andthe POMs, because they cannot be obtained in pure form.

However, experimental viscosity data are available for the closely related series of ethyleneglycol and the poly(ethylene glycols) HO(CH2CH2O)iH or PEGi. Here, we will use these data justto illustrate the concept before returning attention to the aqueous formaldehyde solutions. Wefound that for 294 ≤ T ≤ 333 K the viscosities of PEGi can be described by

ibaiPEG +=ηln , (22)

with Ta /340660.15 +−= and Tb /8.1321925.0 +−= . Fig. 9 shows experimental data of theviscosities of PEGi (i=1..6) and the straight lines calculated with eq 22. Although the viscosity ofthe monomer, ethylene glycol, deviates somewhat, the overall agreement is satisfactoryconsidering the simplicity of the correlation.

10

10

10

-1

-2

-3

1 2 3 4 5 6

molecular size i

η (P

a.s)

Lee & TejaBohne c.s.

Fig. 9. Viscosity of poly(ethylene glycols) as a function of the molecular size i at various T. Symbols: experimental data from the sources indicated.

Lines: calculated with eq (22).


113

Assuming this concept also applies to the series of methylene glycol and the higher POMs gives

iBAWFi +=ηln . (23)

With eqs (14), (15) and (23), eq (21) can be rewritten as

Bx

xAxxF

FWWWm ~1

~)1(lnln

−+−+= ηη . (24)

Least-squares regression of the experimental data to eq (24) resulted in the following parametervalues:

TA /717497.17 −= , TB /504872.14 +−= . (25)

The true molar fraction of water, xW, in the solutions was calculated by solving the equilibriumequations for the reactions (12)

221

2 Kx

xx

WF

WWF = , (26)

)3(311

≥=−

iKxxxx

WFWFi

WWFi , (27)

simultaneously with the balances (14) and (15), where Fx~ was obtained from eq 6. Theequilibrium constants K2 and K3 for the formaldehyde-water system were taken fromHahnenstein et al. (1994)

0 20 40 60W (wt%)F

η mx1

0(P

a.s)

3

2

1

0.5

Fig. 10. Viscosity of aqueous formaldehyde solutions. Symbols: experimental data, see Fig. 6. Lines: calculated with eq (24).


114

The accuracy of eq (24) is comparable to that of eq (20) (AAR of 2.0% and MAX of 7.6%).The correlation is illustrated in Fig. 10. The residuals do not show any trend as a function of T orWF as shown in Figs (11) and (12).

When applied to all of the data, the errors of eq (5) (Walker, 1964) for the viscosity ofaqueous formaldehyde solutions were large (AAR of 15.6% and MAX of 93%). When only thedata within the ranges of WF = 30-50 wt % and T = 298-313 K were considered, an AAR of 3.5%(MAX of 6.2%) was obtained, thereby demonstrating the more limited applicability of eq (5).

0 20 40 60W (wt%)F

20

10

0

-10

-20

resi

dual

(%)

Fig. 11. Relative residuals of the viscosity correlation (24) as a function of WF. Symbols: see Fig. 6.

20

10

0

-10

-20

rela

tive

resi

dual

(%)

280 300 320 340

T (K)

Fig. 12. Relative residuals of the viscosity correlation (24) as a function of T. Symbols: see Fig. 6.


115

Conclusions

The density and viscosity of aqueous formaldehyde solutions can be accurately and reliablyobtained as a function of the temperature and the strength of the solution with the simpleempirical correlations obtained here. The empirical density correlation (eq 8) employs twoadjustable parameters that were optimised using three literature sources of density data. Theempirical viscosity correlation (eq 20) has four coefficients that were optimised using twoliterature data sources together with a series of new additional measurements.

The residuals of the correlations presented are free of trending effects as a function of boththe temperature and the weight percentage of formaldehyde. Therefore, we conclude that thecorrelations can be used reliably in engineering calculations with a small extrapolation to coverthe entire range of conditions prevailing in formaldehyde absorbers, i.e., 280 ≤ T ≤ 340 K and 0 ≤WF ≤ 60 wt %.

A mixture density correlation method from the literature, where the molar volume of themixture is obtained as the molar fraction average of the pure-component molar volumes,appeared to represent the data with almost the same accuracy. In this case two coefficients werefitted to the data, to correlate the molar volume of the CH2O groups linearly to the temperature.

Similarly, a literature method for liquid mixture viscosities, where the logarithm of thepure-component viscosities are molar fraction averaged, resulted in almost the same accuracyrelative to the empirical correlation. In this case, it was assumed that the logarithm of theviscosities of the homologous series of methylene glycol and the higher POMs varies linearlywith the molecular size of the components. This way, the molar fraction average method containstwo temperature-dependent parameters, i.e., four adjustable coefficients.

At first glance it seems surprising that the empirical relations for the density (eq 8) andviscosity (eq 20) both result in somewhat lower AAR values as compared to the relations thatwere arrived at starting from methods found in the literature (eqs 18, 19 and 24, respectively),even though in both cases the same number of coefficients were adjusted to the experimentaldata. This may reflect, however, the difficulties still encountered at present in the development oftheory applicable to estimating liquid mixture properties.

Appendix B: Equilibrium molar fractions in aqueous methanolic formaldehyde solutions

117

Appendix B

Equilibrium molar fractions in aqueous methanolic formaldehydesolutions

In aqueous mixtures of formaldehyde and methanol, the equilibrium composition is determinedby a series of reactions:

2222 (OH)CHOHOCH + , (1)OHHO)HO(CH(OH)2CH 22222 + , (2)

)3(iOHHO)HO(CH(OH)CHHO)HO(CH 2i2221-i2 ∞=++ L , (3)

OHOCHCHOHCHOCH 2332 + , (4)

)2(iOHCHHO)O(CHCHOHOCHCHHO)O(CHCH 3i23231-i23

∞=++

L. (5)

The equilibrium conditions, in terms of molar fractions, for the reactions read

WF

WF

xxx

K 11 = , (6)

221

2

WF

WWF

x

xxK = , (7)

)3(11

3 ∞==−

Lixxxx

KWFWF

WWF

i

i , (8)

MF

MF

xxx

KM 11 = , (9)

)2(11

2 ∞==−

Lixxxx

KMMFMF

MMF

i

i . (10)

In addition, three overall balances combine the overall molar fractions, Fx~ , Wx~ and Mx~ , withthe true molar fractions in the mixture:

∑∑

∑∑∞

=

∞

=

∞

=

∞

=

++

++

=

11

11

1

~

iMF

iWF

iMF

iWFF

F

ii

ii

ixix

ixixxx , (11)


118

∑∑

∑∞

=

∞

=

∞

=

++

+

=

11

1

1

~

iMF

iWF

iWFW

W

ii

i

ixix

xxx , (12)

∑∑

∑∞

=

∞

=

∞

=

++

+

=

11

1

1

~

iMF

iWF

iMFM

M

ii

i

ixix

xxx . (13)

The set of eqs (6)-(13), in principle, provides enough information to calculate all molarfractions. However, we have an infinite number of eqs (8) and (10), and the summations in (11)-(13) have no upper limit. These problems can be overcome by using some simple properties fromthe theory of power series. Thus, by substitution of the molar fractions of the reaction productsobtained from (7)-(10), the summations in (11)-(13) can be written as

111

WFi

WF xSxi=∑

∞

=

,vK

vKS3

21 1

1−

+= , (14)

121

WFi

WF xSixi=∑

∞

=

, 23

2

3

22 )1(1

1vK

vKvK

vKS−

+−

+= , (15)

Mi

MF xSmxi 1

1

=∑∞

=

,vKMKMK

vKMSm211

11 −= , (16)

Mi

MF xSmixi 2

1

=∑∞

=

, 2211

112 )( vKMKMK

vKKMSm−

= . (17)

where the quantities S1, S2, Sm1 and Sm2 are introduced for ease of notation. With (14)-(17) theoverall balances, eqs (11)-(13) can be rewritten as

)1()~1()(~)1)(~(

121

12111 SmSxK

KvSmxSmvxKxF

MFWF +−

−++−= , (18)

21

2~1

)1(~1

SmxSmxSx

xM

WFMM −+

+= , (19)

MWWFWWW xSmxxSSxxx 212~)~(~

1+−+= , (20)

where v is defined as

W

WF

xx

v 1= . (21)


119

The set of eqs (18)-(21) can easily be solved for 1WFx , Mx and Wx by iteration on v, where

v is limited to 10 <≤ v . The other molar fractions, Fx , )2( ≥ixiWF and )1( ≥ix

iMF , can beobtained from (6)-(10) straight forward. Figure 1 illustrates the smooth variation of the ratio vwith the overall formaldehyde molar fraction. Here, 1K was taken from Winkelman et. al (2002),

2K , 3K and 2KM were taken from Hahnenstein et. al (1995), and 1KM was obtained bymultiplying WMK (Hahnenstein et. al, 1995) and 1K , where WMK the equilibrium constant is ofthe reaction OHOHOCHCHOHCH(OH)CH 223322 +=+ .

0.0 0.1 0.2 0.3 0.4 0.5

0.20

0.16

0.12

0.08

0.04

0.00

x~F

vT

Fig. 1. Variation of the ratio v with Fx~ at temperatures of 300, 320 and 340 K. Solid lines: 0~ =Mx ; dotted lines: 05.0~ =Mx .

Simplifications

1. Free formaldehyde is not important

If the very small molar fraction of free formaldehyde is not important, then eq (18) reduces to

)1)(~1(

~)1(~

12

211 SmxS

xSmSmxxF

MFWF +−

−+= . (22)

The system now consists of eqs (19)-(22), and can be solved in the same way as before, byiteration on v.


120

2. No methanol present If the mixture does not contain any methanol then of course Mx~ , Mx and )1( ≥ix

iMF all are

zero, and eqs (18) and (20) for obtaining 1WFx and Wx reduce to

21

1

)~1()~(

1 SxKvxKx

F

FWF −

−= , (23)

1)~(~

12 WFWWW xSSxxx −+= . (24)

For this case, Fig. 2 illustrates the relative amount of methylene glycol with increasing overallformaldehyde content in aqueous solutions. The figure shows that at low concentrations, saybelow 1 mmol/l, virtually all the formaldehyde is present as methylene glycol, and the amount ofpoly oxymethylene glycols is negligible.

0.0 0.1 0.2 0.3 0.4 0.5

1.0

0.8

0.6

0.4

0.2

0.0

x~F

T

x~F

xWF1

Fig. 2. The relative amount of methylene glycol at temperatures of 300, 320 and 340 K.

If also the very small molar fraction of free formaldehyde is not important, p.e. in the calculationof the viscosity (see Appendix A), then the ratio v can be obtained from the cubic equation

0432

23

1 =+++ avavava , (25)

with the coefficients

)~21)(( 2331 FxKKKa −−= , (26)))(2~3()1(~

23332 KKxKxKa FF −−+−= , (27))1(~21 33 Kxa F −−= , (28)

Fxa ~4 −= . (29)


121

The physically significant root of eq (24) can easily be identified: either the cubic has only onereal root, or the cubic has only one root in the correct region, i.e., 10 <≤ v . The true molarfractions of water and methylene glycol are now obtained from

)2()1()1()1(

~1

~1

322

3

322

3

vKvKvKvKvKvK

xxx

F

FW

−+−

−+−−

−= , (30)

vxx WWF =1

. (31)

A further remark: if the overall molar fractions of formaldehyde and water are exactly equal, i.e.5.0~~ == WF xx , then the cubic equation (25) degenerates to a quadratic one in v, and true molar

fractions of water and methylene glycol can be obtained directly from

32211

1 KKxWF

++= , (32)

)1(1 21Kxx WFW +−= . (33)

Appendix C: The reaction order of formaldehyde in the hydration.

123

Appendix C

The reaction order of formaldehyde in its hydration reaction.

Method

The measurements described in Chapter 4 can be used to obtain the reaction order offormaldehyde in the hydration, as well as the reaction rate constant. Note that the experimentalconditions and measured data allowed for the calculation of the interface concentrations and theenhancement factors, i.e. the gradients at the interface, of formaldehyde and methylene glycolwithout any information on the kinetics of the hydration reaction. These quantities are indexedhere as observed.

To establish the reaction order of formaldehyde in the hydration, the equations for diffusionwith parallel reaction in the liquid film are used

FF

F RdxCdD =2

2 )0( δ≤≤ x , (1)

FMG

MG RdxCdD −=2

2 )0( δ≤≤ x , (2)

with the boundary conditions

observedIFMGxMGobservedIFFxF CCCC )()(;)()( ,0,0 == == , (3)

MGxMGFxF CCCC == == δδ )(;)( . (4)

Here, the rate of the reaction is written as

MGdn

FhF CkCkR F −= )( , (5)

where Fn denotes the reaction order of formaldehyde. The additional condition

observedxF

xF

dxdC

dxdC

,00 )()( == = , (6)

allows the determination of the reaction rate constant, hk . The gradient of methylene glycol atthe interface is not independent, but is determined by the one of formaldehyde and the interfaceconcentrations. This can easily be seen by adding eqs (1) and (2), integrating twice, and applyingboundary conditions (3) and (4), giving


124

])([)( ,,,, MGIFMGFIFFFIFFIFMGMG CCCCvxCCvCC −+−−−+=δ

, (7)

and

])([1)()( ,,00 MGIFMGFIFFxF

xMG CCCCv

dxdCv

dxdC

−+−−−= == δ. (8)

Thus, for individual experiments we have no further information available to determine Fn .Therefore, the following strategy was adopted. For a given value of Fn , the reaction rateconstants, )( Fnhk , were calculated for all experiments by solving eqs (1)-(7) (see below). Next,the individual rate constants were fitted to an Arrhenius type expression

RTEFnh

aekk /)(ˆ −

∞= , (9)

and the mean absolute relative residual, marr, of the reaction rates was calculated

i

alleriments

i Fnh

FnhFnh

kkkmarr ∑

=

−=

exp

1 )(

)()(ˆ. (10)

This procedure was repeated for Fn values ranging from 0.0 to 2.0.

Analytical and approximate analytical solutions

In general, the equations (1)-(7) can be solved numerically only. However, an approximatedanalytical solution for the enhancement factor can be obtained by linearization of Fn

FC )(

according to )1/()(2 1, +−

FFn

IFF nCC F . Argument for this linearization is found in the solutionfor irreversible nth order kinetics, which, to a good approximation, equals the solution for firstorder kinetics, provided that the reaction rate constant, k, is replaced by )1/(2 1 +− nkCnIF(Westerterp, Van Swaaij & Beenackers, 1984). This way, the enhancement factor is very similarto the analytical solution obtained by Winkelman & Beenackers (1993) for first order reversiblereactions,

']'tanh[)'(

)]'cosh[

11(')')('

]'tanh[1(1 ,,

,

φφ

φφφ

vK

CCCCK

CCCC

KE FIFF

MGF

FIFF

MGIFMG

F+

−−−

+−

−−−

+= , (11)


125

however, here with

')'(''

KDvKk

F

+= δφ , (12)

1, )(

12' −

+= Fn

IFFF

h Cnkk , (13)

1, )(

)1(2'' −

+== Fn

IFFdF

h

dC

knk

kkK . (14)

For a given value of Fn , the reaction rate constants were obtained from eqs (11)-(14)iteratively, using the experimental data and the observed values of the formaldehyde enhance-ment factors. The simple secant iteration method proved adequate for this purpose.

Note that for a first order reaction in formaldehyde, i.e. 1=Fn , eqs (11)-(14) represent theexact analytical solution. The only other case that allows for an exact solution is the zero orderreaction, 0=Fn , where the enhancement factor is given by

0

0

,

,

0

0

,00 ]tanh[

)]tanh[

1(/)]cosh[

11(1)(

=

=

=

=

==

−

−−−

−−

−

+=

F

F

F

F

FF

n

n

FIFF

MGIFMG

n

n

FIFF

MGdh

nnF

v

CCCC

CCCkk

E

φφ

φφ

φ(15)

where

MG

dn D

kF

δφ ≡=0 . (16)

Numerical solution

Equation (1), with FR given by (5), MGC by (7), and the boundary conditions by (3), (4)and (6), was solved for the formaldehyde concentration profile and the reaction rate constantsimultaneously by replacing the differential equation by finite difference equations on a grid ofmesh points on the interval )0( δ≤≤ x . Here, jFC )( denotes FC at mesh point j, i.e. at

)( xjx ∆= , where Nj L1= and Nx /)( δ=∆ . A finite difference approximation of eq (1) with second order accuracy reads

jFjFjFjF

F Rx

CCCD )(

)(

)()(2)(2

11 =∆

+− +− )11( −= Nj L . (17)


126

The boundary conditions (3) and (4) give two more equations

IFFF CC ,0)( = , (18)

FNF CC =)( . (19)

An additional equation is obtained from a second order Taylor series approximation of 1)( FC :

02

22

001 )(2

)())(()()(dxCdx

dxdCxCC FF

FF∆

+∆+= . (20)

The second derivative in (20) is equal to FF DR /)( 0 , see eq (1), while the first derivative is setequal to the observed gradient at the interface.

The 2+N equations (17)-(20) can be solved for the unknowns hk and )0()( NjC jF L= .Because of the nonlinearity in the reaction rates jFR )( Newton-Raphson iteration was used. Forthis purpose, the equations, labeled by jF , are written as

0)(2

)())(()()( 02

,0011 =∆

−∆−−= =−F

Fobservedx

FFF D

RxdxdCxCCF , (21)

0)( ,00 =−= IFFF CCF , (22)

0)()()()(2)(2

11 =∆

−+−= +− jFF

jFjFjFj RDxCCCF )11( −= Nj L , (23)

0)( =−= FNFN CCF . (24)

The vector of unknowns TNFFh CCk ])(,,)(,[ 0 L=y is updated with a correction y∆ , i.e.

yyy ∆+= currentnew , until convergence is achieved, where the vector of corrections y∆ isobtained from the matrix equation

∑−=

−=−=∆∂

∂N

kjk

k

j NjFyyF

1

)1( L . (25)

Results

The calculated marr data from eq (10), obtained with the approximate analytical solutionand with the numerical method, are shown in Fig. 1 below as a function of the reaction order offormaldehyde, Fn . The data show a clear minimum around 1=Fn , allowing the conclusion thatthe hydration is indeed of the first order in formaldehyde.


127

A second conclusion is that the results obtained with the approximate analytical solutionmethod are virtually identical to those obtained from the numerical method. Therefore, at least atthe circumstances considered here, the approximate analytical method is suitable for calculatingmass transfer enhancement factors.

Fig. 1. Marr of the reaction rate constants, see eq (10), vs. the order of formaldehyde in the hydration.Line: numerical solution; symbols: approximate analytical solution.

0.0 0.4 0.8 1.2 1.6 2.0

40

30

20

10

0

reaction order of formaldehyde

mar

r [%

]

List of publications

129

List of publications

The following publications originated from this work:

J.G.M. Winkelman, H. Sijbring, A.A.C.M. Beenackers & E.T. De Vries (1992). Modeling and simulation of industrial formaldehyde absorbers. Chemical Engineering Science, 47, 3785. (included as Chapter 5)

J.G.M. Winkelman, S.J. Brodsky, & A.A.C.M. Beenackers (1992). Effects of unequal diffusivities on enhancement factors for reversible reactions: numericalsolutions and comparison with DeCoursey’s method. Chemical Engineering Science, 48, 2951-2955.

J.G.M. Winkelman & A.A.C.M. Beenackers (1993). Simultaneous absorption and desorption with reversible first-order chemical reaction:analytical solution and negative enhancement factors. Chemical Engineering Science, 48, 2951-2955. (included as Chapter 3)

J.G.M. Winkelman, M. Ottens & A.A.C.M. Beenackers (2000). The kinetics of the dehydration of methylene glycol. Chemical Engineering Science, 55, 2065-2071. (included as Chapter 2)

J.G.M. Winkelman & A.A.C.M. Beenackers (2000). Correlations for the density and viscosity of aqueous formaldehyde solutions. Industrial & Engineering Chememistry Research, 39, 557-562. (included as Appendix A)

J.G.M. Winkelman, O. Voorwinde, M. Ottens, A.A.C.M. Beenackers & L.P.B.M. Janssen(2002). The kinetics and chemical equilibrium of the hydration of formaldehyde. Chemical Engineering Science, 57, 4067-4076. (included as Chapter 4)

Samenvatting in het Nederlands

131


Deze dissertatie beschrijft theoretisch en experimenteel werk aan de absorptie van formaldehydein water. Met resultaten hiervan zijn chemisch-technische modellen ontwikkeld voor debeschrijving en optimalisatie van industriële formaldehydeabsorbeurs. Deze samenvatting geefteerst algemene informatie over formaldehyde, en de commerciële productie ervan. Daarna wordtingegaan op het doel van dit werk, en vervolgens het uitgevoerde onderzoek en de resultaten.

Formaldehyde

Formaldehyde is een belangrijke grondstof in de chemische industrie. Het is met name eenhoofdbestanddeel van veel soorten kunststoffen en -harsen. Daarnaast worden kleinerehoeveelheden formaldehyde gebruikt als ontsmettings- en conserveringsmiddel (‘sterk water’),en bij de productie van rubbers, speciale betonsoorten, explosieven, meststoffen, genees-middelen, papier, etc. In 2000 werd wereldwijd ongeveer 10 miljoen ton formaldehydegeproduceerd.

In zuivere vorm is formaldehyde een gas. Het kan echter niet in zuivere vorm worden opgeslagenof vervoerd omdat formaldehydegas niet stabiel is. Het zuivere gas reageert snel, bijvoorbeeldmet de wand van een container waarin het is opgeslagen, tot een onbruikbare vaste stof. Daaromwordt formaldehyde vrijwel uitsluitend geproduceerd, verhandeld en vervoerd als een oplossingvan het gas in water.

Industriële productie van formaldehyde

Bij de industriële productie van formaldehyde is methanol, ofwel methylalcohol, de grondstof.De methanol wordt verdampt en gemengd met lucht. Dit gasmengsel gaat naar een reactor.Methanoldamp reageert in de reactor met zuurstof uit de lucht tot formaldehyde. Het gas dat uitde reactor komt, bestaat voornamelijk uit stikstof en formaldehyde. Soms bevat het gas ook nogeen hoeveelheid niet-omgezette methanol. Dit gasmengsel wordt naar een absorbeur geleidwaarin het formaldehydegas oplost in water. Hierbij onstaat het commerciële product: een gecon-centreerde oplossing van formaldehyde in water, ofwel formaline. In de praktijk wordt formalinevaak verhandeld met een sterkte van 37 of 55 gewichtsprocent formaldehyde.

methanol-verdamper reactor absorbeur formaline

afgasluchtmethanol

water

Fig. 1. Belangrijke stappen in de industriële productie van formaline.


132

Absorbeur

Een absorbeur wordt gebruikt om een gasvormige stof op te lossen in een vloeistof. Het gaswordt onderaan het kolomvormige apparaat naar binnen geleid, en stroomt naar boven. Devloeistof wordt bovenaan geïntroduceerd, en stroomt neerwaarts. Om zoveel mogelijk gas op telossen is het voordelig om de neerstromende vloeistof en het omhoog stromende gas intensiefmet elkaar in contact te brengen. Dit kan onder meer worden bereikt door de absorbeur te vullenmet een pakking. In de praktijk wordt vaak een gestorte pakking gebruikt: de kolom wordtgevuld met een willekeurige stapeling van bijvoorbeeld bolletjes, ringen, of één van de veleandere vormen die commercieel beschikbaar zijn. Door de vloeistof over de pakking te versprei-den ontstaat een groot contactoppervlak tussen de vloeistof en het gas.

In het onderste deel van een absorbeur wordt de oplossing verzameld, zodat deze kan wordenafgevoerd voor verdere verwerking of opslag. Bij formaldehydeabsorbeurs wordt een deel van deoplossing die beneden aankomt weer teruggevoerd naar de bovenzijde van de absorbeur. Devloeistof loopt dan nogmaals door de kolom, en absorbeert meer gas. Dit leidt tot een meergeconcentreerde oplossing. In figuur 2 is een voorbeeld te zien van een absorbeur met eenvloeistofterugvoer. De pakking is in de figuur schematisch aangeduid met bolletjes.

afgas

water

gas

oplossing

koel-water

Fig. 2. Een absorbeur met één absorptiebed, en extern gekoelde vloeistofterugvoer.


133

Over het algemeen werken absorbeurs efficiënter als het gas goed oplost in de vloeistof, enminder efficiënt als de oplosbaarheid van het gas klein is. Formaldehyde is schijnbaar goedoplosbaar in water, gezien het feit dat oplossingen met wel 55 gewichtsprocent formaldehydegangbaar zijn. Maar de formaldehydeabsorbeurs opereren minder efficiënt dan op grond van dezegoede schijnbare oplosbaarheid verwacht mag worden. De belangrijkste reden hiervoor is dat inde oplossing het formaldehyde met water reageert tot methyleenglycol. Deze hydratatiereactie iseen evenwichtsreactie: methyleenglycol kan ook weer terugreageren tot formaldehyde en water.Op zijn beurt kan methyleenglycol weer verder reageren tot een serie polymere vormen vanformaldehyde, de zogenaamde poly-oxy-methyleenglycolen. Deze polymerisatiereacties zijnlangzaam, en het zijn ook weer evenwichtsreacties, zie figuur 3.

methyleen-formaldehydehydratatie

dehydratatiewater glycol methyleen-glycol

polymerisatie

depolymerisatie

poly-oxy-

Fig. 3. Reacties van formaldehyde opgelost in water.

De goede schijnbare oplosbaarheid van formaldehyde in water is dus eigenlijk de goedeoplosbaarheid van methyleenglycol en de capaciteit van de oplossing om poly-oxy-methyleen-glycolen op te nemen. Formaldehyde zelf is, zoals de meeste gassen, slecht oplosbaar in water.

De hydratatiereactie is relatief snel, en bij evenwicht is de hoeveelheid vrij formaldehyde veelkleiner dan de hoeveelheid methyleenglycol: het hydratatie-evenwicht ligt sterk aan de zijde vanmethyleenglycol. Dit zorgt ervoor dat de overdracht van formaldehyde vanuit het gas naar devloeistof chemisch versneld is. Formaldehydeabsorbeurs werken dus minder efficiënt dan opbasis van de goede ‘schijnbare’ oplosbaarheid verwacht mag worden, maar meer efficiënt danwanneer het formaldehyde niet zou reageren in de oplossing. Een verdere complicerende factor is dat bij de absorptie van formaldehyde en de daaropvolgendehydratatiereactie veel warmte vrij komt. Ook bevat het gas dat de absorbeur binnenkomt eenhoeveelheid stoom die, vooral bij condensatie, veel warmte afgeeft . De temperatuur van de neer-stromende vloeistof neemt hierdoor toe. De warmte die vrijkomt wordt afgevoerd door devloeistofterugvoer te koelen met koelwater (zie fig. 2).

Onder meer vanwege dit type complicaties zijn formaldehydeabsorbeurs vaak onderverdeeld inmeerdere secties of absorptiebedden. Elke sectie heeft dan een vloeistofverdeler, -opvang en -terugvoer met externe koeling. De vloeistof uit de bodem van de ene sectie wordt voor een deelteruggevoerd naar de top van dezelfde sectie. De rest wordt naar de top van de volgende sectiegeleid. Iets dergelijks geldt voor de gasstroom: het gas dat uit de top van een sectie treedt, wordt


134

aan de onderzijde van een vorige sectie ingevoerd. Er ontstaat een patroon zoals geïllustreerd isvoor een tweetal secties in figuur. 4. In de praktijk zijn de secties boven elkaar geplaatst, in éénenkele kolom, zodat de installatie compact blijft.

afgas

water

gas

koel-water

oplossing

koel-water

Fig. 4. Een schakeling van twee absorptiebedden, elk met een extern gekoelde vloeistofterugvoer.

Dit proefschrift

Het belangrijkste streven van het onderzoek is de ontwikkeling van betrouwbare chemisch-technische modellen voor industriële formaldehydeabsorbeurs. Het doel hiervan is drieledig. Teneerste het nauwkeurig beschrijven van het gedrag van bestaande formaldehydeabsorbeurs.Vervolgens het voorspellen van de invloed die veranderingen in de manier van bedrijven hebbenop de prestatie van de absorbeurs. En ten slotte het optimaliseren van de absorptie-efficiëntie en -capaciteit van formaldehyde in de absorbeurs. Om deze doelstellingen te bereiken is het vanbelang om de snelheid te kennen van de reacties in de oplossing (zie fig. 3) bij verschillendeconcentraties en temperaturen. Anders gezegd: de kinetiek van de reacties moet bekend zijn.

De kinetiek van de polymerisatie- en depolymerisatiereacties is uitgebreid onderzocht en in deliteratuur beschreven door andere researchgroepen. Over de reactiesnelheid van de hydratatie vanformaldehyde en de dehydratatie van methyleenglycol is slechts fragmentarisch gepubliceerd. Erzijn een handjevol data bekend, over het algemeen slechts bij kamertemperatuur. De gegevensdie in de literatuur zijn te vinden over de chemische evenwichtsconstante van de hydratatie


135

vertonen een grote spreiding: als we verschillende publicaties met elkaar vergelijken dan zit daarsoms meer dan een factor 3 verschil tussen. Daarom zijn de kinetiek en het chemisch evenwichtvan de hydratatie/ dehydratatiereactie nader onderzocht. Dit onderzoek en de resultaten ervanworden, na een inleidend hoofdstuk, beschreven in de hoofdstukken 2, 3 en 4 van dit proefschrift.In de hoofdstukken 5 en 6 worden modellen ontwikkeld voor de simulatie en optimalisatie vanindustriële formaldehydeabsorbeurs. In een drietal appendices wordt onderzoek naar de fysischeeigenschappen van formaline en enig aanvullend materiaal op de eerdere hoofdstukkengepresenteerd.

In hoofdstuk 2 is het onderzoek aan de orde naar de reactiesnelheid van de dehydratatie vanmethyleenglycol. Hierbij is gebruik gemaakt van de snelle reactie van sulfiet met formaldehydewaarbij hydroxide-ionen vrijkomen. De concentratie van de hydroxide-ionen kan eenvoudigworden gemeten. In een oplossing van methyleenglycol en sulfiet wordt formaldehyde gevormdvia de dehydratatiereactie. Dit formaldehyde reageert zeer snel met sulfiet. De toename van deconcentratie van hydroxide-ionen is dan een maat voor de snelheid van de dehydratatie vanmethyleenglycol. De reactiesnelheid van de dehydratatie is op deze wijze gemeten bijtemperaturen die relevant zijn voor formaldehydeabsorbeurs (circa van 20 tot 60 oC).

Hoofdstuk 3 geeft een theoretische verhandeling over de absorptie en/of desorptie van tweecomponenten samen met een evenwichtsreactie in de vloeistof tussen die twee. De analytischeoplossingen die hier worden afgeleid geven de absorptie- en/of desorptiesnelheid als functie vanchemische en hydrodynamische eigenschappen van het systeem en de concentraties van decomponenten. De theoretische resultaten die hier zijn bereikt worden toegepast in het volgendehoofdstuk.

De bepaling van de kinetiek van de hydratatie van formaldehyde wordt beschreven in hoofdstuk4. De metingen zijn gebaseerd op de chemisch versnelde absorptie van formaldehyde in water enhet mathematische model van hoofdstuk 3 voor dit proces. Als een gasstroom met daarin form-aldehydegas over water wordt geleid, dan zal het formaldehyde in het water gaan oplossen. Alshet opgeloste formaldehyde niet zou reageren, dan zou een bepaalde mate van verzadigingoptreden aan het oppervlak van de vloeistof. Deze mate van verzadiging is mede bepalend voorde oplossnelheid. Nu echter het opgeloste formaldehyde wegreageert via de hydratatiereactie, zalde mate van verzadiging aan het vloeistofoppervlak veel kleiner zijn. Dit resulteert in een hogereoplossnelheid dan wanneer de reactie niet zou optreden: de absorptie is chemisch versneld. Demate waarin de absorptie chemisch versneld wordt, is afhankelijk van de reactiesnelheid. Door deabsorptiesnelheid te meten kan via een wiskundig model de reactiesnelheid worden berekend. Opdeze manier is de hydratatiesnelheid van formaldehyde gemeten over het traject van 20 tot 60oC.Met deze resultaten, en die van hoofdstuk 2, is ook de chemische evenwichtsconstante bepaaldover hetzelfde temperatuurtraject.

De industriële absorptie van formaldehyde in water wordt gekenschetst door simultane stof-overdracht van meerdere componenten, gepaard met meerdere simultane reacties in de vloeistofen aanzienlijke warmte-effecten. In hoofdstuk 5 wordt een model gepresenteerd waarmee ditproces wordt gesimuleerd. Het model is gebaseerd op differentiaalvergelijkingen voor de stof- enenergiebalansen in de gasfase en in de vloeistoffase. Voor de resulterende set van gekoppeldegrenswaardeproblemen is een stabiele oplosmethode ontwikkeld via een semi-tijdsafhankelijke


136

benadering. Het model bleek zeer goed in staat om het gedrag van bestaande formaldehyde-absorbeurs te simuleren. Met het model zijn vervolgens de procescondities van een absorbeur bijDynea B.V. geoptimaliseerd waardoor een hogere capaciteit en een aanzienlijke besparing van degrondstof methanol zijn bereikt.

In hoofdstuk 6 wordt het absorbeurmodel uitgebreid met de beschrijving van het gedrag van niet-omgezet methanol dat via de gasstroom de absorbeur binnenkomt. In het model zijn een grootaantal reacties in de vloeistoffase opgenomen, alsmede warmte-uitwisseling tussen de gas- envloeistofstroom, en chemisch versnelde stofoverdracht van formaldehyde, water, methyleen-glycol, methanol en hemiformal. Het gedrag van industriële formaldehydeabsorbeurs met externgekoelde vloeistofrecirculatie wordt gesimuleerd met het model van niet-evenwichts-trappen. Ditmodel is toegepast om de invloed te onderzoeken die de verschillende procesomstandighedenhebben op het gedrag van methanol in de absorbeurs.

De appendices geven enig aanvullend materiaal. Zo worden in appendix A de resultatengepresenteerd van de experimentele bepaling van de viscositeit van formaline bij verschillendetemperaturen en verschillende formaldehydegehaltes. Ook worden hier correlaties gegeven om deviscositeit en dichtheid van formaline nauwkeurig te berekenen als functie van de temperatuur ende concentratie. In appendix B worden enkele methoden toegelicht voor de berekening van deevenwichtsamenstelling (zie fig. 3) van oplossingen van formaldehyde in water, en vanformaldehyde en methanol in water. Appendix C ten slotte bevat additioneel materiaal bijhoofdstuk 4. Hier wordt aangetoond dat de hydratatiereactie eerste orde in formaldehyde is,ofwel dat de reactiesnelheid van de hydratatie recht evenredig met de concentratie van form-aldehyde is.

137

Dankwoord

Iedereen die aan dit proefschrift heeft meegewerkt wil ik van harte bedanken. Enkele mensen wilik hier speciaal noemen. Allereerst Prof. dr. ir. A.A.C.M. (Ton) Beenackers, die mijn leermeesteris geweest. Zijn enthousiasme en vakkennis waren van onschatbare waarde, niet alleen voor hetpromotieonderzoek, maar ook tijdens de vele projecten waar we nadien samen bij betrokkenwaren. Zijn plotselinge heengaan blijft ontstellend. Prof. dr. ir. L.P.B.M. Janssen en Prof. dr. ir.H.J. Heeres dank ik voor hun bereidheid de promotie af te ronden en voor hun suggesties tenaanzien van de uiteindelijke tekst. De leden van de leescommissie, Prof. dr. A.A. Broekhuis,Prof. dr. P.D. Iedema en Prof. dr. ir. G.F. Versteeg, dank ik voor hun aandacht en snellebeoordeling. Dynea B.V. heeft dit werk niet alleen financieel ondersteund; zeer nuttig waren ookde uren die ik doorbracht met dhr S. Doorn en dhr E.T. de Vries. Veel werk is gedaan door de afstudeerders Hermen Steven Giesbert, Henk Sijbring, MarcelOttens en Olaf Voorwinde. Hun bijdragen waren onmisbaar voor de totstandkoming van ditproefschrift. Evenals die van Luuk Balt voor zijn prachtige ontwerpen van de meetopstellingen;Oetse Staal voor zijn inbreng in de automatisering; Karel van der West en Jaap Struik voor hetbetere sleutel- en schroefwerk; Rob Cornelissen voor de ware kunstwerken in glas; en Jan HenkMarsman voor wie elk analyseprobleem weer een uitdaging bleek. Ten slotte dank ik mijnfamilie en vrienden voor hun directe en indirecte bijdragen bij de totstandkoming van ditproefschrift, in het bijzonder Piety Groeneveld, Wiveca Jongeneel en Anthony Runia.

Absorption of Formaldehyde in Water

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