University of Groningen

Collected tales on mass transfer in liquidsBollen, Arnoud Maurits

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RIJKSUNIVERSITEIT GRONINGEN

Collected tales on mass transfer in liquids

Proefschrift

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

op gezag van deRector Magnificus, dr. D.F.J. Bosscher,

in het openbaar te verdedigen opvrijdag 26 november 1999

om 14.15 uur

door

Arnoud Maurits Bollengeboren op 22 juli 1966

te Groningen

Promotor: prof. ir. J.A. Wesselingh

ISBN: 90-367-1157-6

‘Zo jong nog, en nu reeds niets gepresteerd.’ (W. Pauli)

Beoordelingscommissie:prof. dr. H.W. Hoogstratenprof. dr. R. Krishnaprof. E.L. Cussler

ACKNOWLEDGEMENTS

i

ACKNOWLEDGEMENTS

Now that the work is done, I am somewhat disappointed to discover that this thesis has becomea collection of rather loosely connected chapters instead of a sound, solid scientific epos with adistinct beginning and a distinct end. Well, it’s too late now, and I just hope that those whohave the courage to plough their way through it will feel, afterwards, that it was worth theeffort.

I would like to thank everybody who has directly contributed to the realisation of this thesis,especially those who did more than they were obliged to on account of their function. If theshoe fits, wear it. First of all, I should mention my promotor, Prof. Hans Wesselingh forcreating the most pleasant atmosphere in his group in which there was always room for a joke,a difference of opinions or an exchange of views on all sorts of subjects. Also, he managed topick the most agreeable persons as my collegues, even without consulting me first. I will alsokeep good memories of Trudi, who has never hesitated to forward her view on things, or to dowhat she felt was necessary, even if I sometimes felt that it was not. I greatly appreciated thework lunches and dinners over at their place.

Working in a pleasant atmosphere adds to the zest for work. Some persons who were notscientifically involved, have, by way of just being there, made important but invisiblecontributions to this thesis. First and foremost, I would like to say special thanks to allmembers of the ‘9-uur koffie’ (= nine o’clock coffee) bunch. The students whom I had thehonour to supervise were another source of pleasure: Bart Venneker, Jan Wegenaar, TeunDuijnstee, Martin de Boer and Lamberto Eldering. Many were the moments I enjoyed workingwith them. Many also were the moments I did not. They would then be asking either for myattention or for things of a more concrete nature, while I was trying to concentrate on somevery interesting and at that time probably very important matter. I may not always have beenvery accesible, for which I apologise. I am also sorry that I have not been able to include any ofthe work of Martin de Boer and Teun Duijnstee in this thesis. Finally, the students whopopulated room 5118.0210 (‘de waterzaal’), and most of whom were pleasant company, cannotbe left unmentioned, but they are too numerous to list here.

My brother Guido also made a very important contribution to this book by way of lending me acomputer on which many of the calculations were done, and also some of the text processing.Other people I should mention are my room mates Atze-Jan van der Goot and Cor Visser, thetechnicians Jan ‘Is-het-voor-thuis?’ Bolhuis and Marcel de Vries, and the librarians, whosomehow manage to stay friendly and helpful under circumstances that definitely would driveme crazy.

This research has been financially supported by the Council for Chemical Sciences of theNetherlands Organization for Scientific Research (CW-NWO). DSM-Research initiated andcontributed to the investigations on liquid-liquid extraction. In this respect, I would especiallylike to thank Ton Simons of DSM Research for his stimulating and enthousiastic co-operation.

SUMMARY

iii

SUMMARY

Diffusion in liquids determines the rate of mass transfer in many processes, both natural andindustrial. In liquid-liquid extraction for example. This thesis culminates in a mass transfermodel using the Maxwell-Stefan equations to describe liquid-liquid batch extraction. Thisprocess necessarily involves strongly non-ideal liquid mixtures, and diffusion in such mixturesis the thread of this thesis. After the first two introductory chapters (a general and a technicalone), a few matters concerning the Taylor dispersion method for the determination of diffusioncoefficients are discussed in chapters 3 and 4. Then, in chapter 5, the behaviour of diffusivitiesin demixing mixtures is investigated. In chapter 6 the model for liquid-liquid batch extractionis developed, which is subsequently applied in chapter 7 to systems in which emulsification isknown to occur during extraction.

A problem in multicomponent diffusion is obtaining the diffusion coefficients. One of theinstruments that allow routine measurements in liquids is the Taylor capillary. This capillaryusually is some 20 m long, and therefore it is usually coiled. In chapter 3 the effects of coilingon the accuracy of the measurements is investigated theoretically. In a few extreme cases, itturns out that small coil diameters can introduce large errors. In those cases it is necessary toreduce the flow drastically.

The Taylor dispersion method requires very sensitive and accurate composition measurementof the eluent flow. For a ternary mixture, it is commonly thought that two components have tobe monitored simultaneously, which makes the method more difficult to use. Yet, in chapter 3it is theoretically proven that it is possible to obtain multicomponent diffusivities bymonitoring only one composition. The price that must be paid is that at least two experimentsare needed for one set of ternary diffusivities.

The theory of the Taylor method assumes that the diffusivities and the total concentration ofthe mixture do not depend on composition. In reality such mixtures are rare. In chapter 4numerical simulations show that effects of composition variations are usually small, and thatquite large concentration differences between the tracer pulse and the eluent liquid can beapplied.

Liquid-liquid extraction usually involves diffusion in mixtures with compositions near ademixing boundary. There are indications that the diffusivities might behave differently in suchmixtures. These are based on diffusion measurements near consolute points in binary mixtures.Such consolute points are, in a way, analogues for the spinodal curve. To see whetherdiffusivities really misbehave, the data are re-examined in chapter 5. It turns out to be difficultto obtain accurate thermodynamic data of the mixtures near the consolute point. Nevertheless,no evidence is found of serious anomalies in the behaviour of the diffusion coefficients nearthe consolute point, but unambiguous proof that they behave normally cannot be given either.This means that there is no reason not to use the usual mass transfer equations for describingliquid-liquid (batch) extraction.

SUMMARY

iv

In chapter 6 a model is developed for a stirred ternary batch extractor with a flat liquid-liquidinterface. Important parts of the model are the thermodynamic equilibria used and the two masstransfer ‘films’ on either side of the interface. This type of model turns out to be very sensitiveto thermodynamic and mass transfer parameters. Numerical stability and accuracy are also aproblem. A good description of experiments from literature could only be obtained afteroptimising the model parameters.

During the extraction in certain mixtures, such as water-caprolactam-benzene, an emulsion canform in one of the phases. A possible explanation is that the multicomponent mass transferdrives the system into the liquid-liquid demixing zone. The extraction model of chapter 6 isused in chapter 7 to see whether this might be the case. The model can yield composition pathspassing through the demixing zone, but only for rather improbable values of the modelparameters. This strongly indicates that other processes must play a role in the formation of theemulsion.

A good model of liquid-liquid extraction will undoubtedly need a proper multicomponentmodel of the mass transfer in the extractor. This thesis shows how such models can be set upand used. It also shows many problems related to obtaining model parameters and doing modelcalculations. Finally, it contains indications that also other parts of liquid-liquid extractiontheory such as thermodynamics, the behaviour of interfaces and the two-phase flow inequipment need to be improved.

CONTENTS

v

ACKNOWLEDGEMENTS i

SUMMARY iii

1. INTRODUCTION 1

1.1 Liquid-liquid extraction fundamentals 11.1.1 The ternary composition diagram 11.1.2 The binodal curve 21.1.3 The spinodal curve 31.1.4 Final equilibrium 31.1.5 Composition paths 5

1.2 A microscopic view on extraction 51.2.1 Mass transfer across the interface 51.2.2 The role of diffusion in extraction 6

1.3 Practical extraction methods 71.3.1 Purity and efficiency 71.3.2 Mixer-settlers 71.3.3 Extraction columns 9

1.4 Structure of this thesis 9

2. A THEORETICAL FRAMEWORK FOR MASS TRANSFER 11

2.1 Notational matters 112.2 Defining systems 12

2.2.1 Components 122.2.2 Thermodynamic conditions 132.2.3 Composition 132.2.4 Frames of reference 14

2.3 Two mass transfer models 172.3.1 Fick’s transfer model 182.3.2 The Maxwell-Stefan transfer model 202.3.3 Choose your weapon 21Notation 22References 23

3. TAYLOR DISPERSION THEORY 25

3.1 The Taylor dispersion experiment 253.1.1 Theory of the dispersive process 253.1.2 The capillary: coiled or straight? 27

3.2 Retrieval of diffusivities from experimental data 333.3 Conclusions 38

Notation 39References 40

CONTENTS

vi

4. NUMERICAL SIMULATION OF TAYLOR DISPERSION 43

4.1 Derivation of the equations 444.2 Composition-independent parameters 46

4.2.1 Discretisation of the differential equation 474.2.2 Solving the discretised equation 49

4.3 Composition-dependent parameters 514.3.1 Discretisation and solution of the equations 524.3.2 Example: methanol / tetrachloromethane 52

4.4 Results 534.5 Conclusions 57

Appendix A. The convection-diffusion equation at the capillary axis 57Appendix B. Expressions for the coefficients for composition-independent

parameters 58Appendix C. Cubic spline interpolation 59Appendix D. The amount of tracer in the tube section 61Appendix E. Expressions for the coefficients for composition-dependent

parameters 62Notation 64References 65

5. DIFFUSION NEAR CONSOLUTE POINTS 67

5.1 The world according to Cussler 675.2 Determination of Γ from VLE data 70

5.2.1 The ideal gas GE method 705.2.2 The non-ideal gas GE method 725.2.3 The numerical integration method 73

5.3 The system triethylamine-water 755.4 The system nitrobenzene-n-hexane 805.5 Conclusions 82

Notation 82References 83

6. MODELLING LIQUID-LIQUID BATCH EXTRACTION 85

6.1 The physical system 856.2 Solving the flux equations 86

6.2.1 Difference approximation 87Linear mean composition 90Cubic mean composition 90Logarithmic mean composition 91

6.2.2 Numerical integration 916.3 Solving the dynamic equations 92

CONTENTS

vii

6.4 Composition dependence of relevant physical properties 926.4.1 Total concentration 936.4.2 Activities 936.4.3 Diffusivities 946.4.4 Film thicknesses 95

6.5 Results 966.5.1 Initial flux solutions 976.5.2 Dynamic model solutions 99

6.6 Comparison with the model of Krishna et al. 1036.7 Conclusions 104

Appendix A. Combined fit of the LLE and VLE data 105Appendix B. Multiple subfilm difference approximation with barrier layer 108Notation 109References 110

7. EMULSIFICATION IN LIQUID-LIQUID BATCH EXTRACTION 113

7.1 The physical system 1147.2 Solving the flux equations 1157.3 Solving the dynamic equations 1157.4 Composition-dependence of relevant physical properties 116

7.4.1 Total concentration 1167.4.2 Activities 1167.4.3 Diffusivities 1177.4.4 Film thicknesses 117

7.5 Batch extraction measurements 1177.6 Results 119

7.6.1 Initial flux solutions 1207.6.2 Dynamic model solutions 120

7.7 Conclusions 123Appendix A. Liquid-liquid equilibria of the systems used 124Appendix B. The binodal curve, the distribution coefficients and the plait point 126Notation 126References 127

SAMENVATTING (Dutch summary for laymen) 129