In Situ Electrochemical Regeneration of Activated Carbon

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In situ electrochemical regeneration of activated carbonFischer, Vincent Marco

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IN SITU ELECTROCHEMICAL

REGENERATION OF ACTIVATED

CARBON

Vincent M. Fischer

Copyright (c) 2001 by V. M. Fischer

Printed by Koninklijke Wöhrmann, Zutphen.

ISBN 90-367-1476-1

All rights reserved. Neither this publication nor any part of it may be reproduced orutilised in any form or by any means, electronic or mechanical, includingphotocopying, microfilming, and recording, or by any information storage andretrieval system, without the prior written permission from the copyright owner.

Printed in the Netherlands.

RIJKSUNIVERSITEIT GRONINGEN

IN SITU ELECTROCHEMICAL

REGENERATION OF ACTIVATED CARBON

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 oktober 2001

om 14.15 uur

door

Vincent Marco Fischer

geboren op 12 januari 1972te Offenbach am Main

promotor: Prof. ir. J.A. Wesselingh

ISBN 90-367-1476-1

Aan Ilse

I

S U M M A R Y

In densely populated or industrial areas the quality of water can become aproblem, therefore wastewater treatment facilities are required. Adsorptiontechnology can be used to clean aqueous streams containing relatively lowconcentrations of impurities. The most common used adsorbent is activatedcarbon, due to its very large internal surface area. On this surface large amountsof impurities can bind. After time, the carbon will become saturated andinactive. There is a large economical drive for regeneration of inactivatedcarbon. Regeneration can be achieved by altering process conditions so that theadsorbed species will desorb. The methods that are applied today are either notefficient enough or too expensive. This is the reason to study a possible newmethod called electrosorption. Electrosorption basically deals with the effectsof an applied electrical potential on the sorption behaviour of (in this case)uncharged molecules.

The influence of electrical potential on adsorption

A solid electrode in contact with an electrolyte solution leads to excess ofcharge in the solution. This induces a similar charge inside the electrode, knownas the electrical double layer. A double layer is required for electrosorption tooccur. The simplest model to describe it is the Helmholtz model, which isequivalent to an ideal parallel-plate capacitor. The Helmholtz model is unable toexplain experimental found influences of potential and ion concentration onthe differential capacity. A more advanced model, the Gouy-Chapman modelpredicts the capacity to be a strong function of potential and temperature and aweak function of concentration. This prediction is in error with actualbehaviour at higher applied potentials. Both models are combined in the Sternmodel. Generally differences between Stern and Helmholtz models are smallunless ion concentrations and applied potentials are very low. Accuratelydescribing a double layer is no simple task.

The material between the two charged layers can be compared to the dielectricof a capacitor. Its electrical behaviour is expressed by the dielectric constant,which is not constant but depends on (strong) electrical fields. A potential

II

dependent dielectric constant can be derived if the complete Langevin equationis used instead of its Taylor approximation as is done in literature. This doesresult in more smoothed capacity curves.

To help explain the mechanism of electrosorption, the adsorbed molecules aretreated as a different thermodynamic phase with respect to the bulk liquid. Theequilibrium adsorption constant gives the amount of molecules adsorbing forcertain bulk conditions. Because no Faraday reactions take place, the electricalfield can only have influence by changing its value. In our capacitor model,adsorption and desorption can be visualised by slabs of dielectric (water andpollutant) that move in between the charged plates. It can be calculated that ifthe applied potential is increased, the force pulling water inside (and pushingout the pollutant) increases. Using the law of mass action, the change in thesystems Gibbs energy can be related to a change in the desorption rateconstant.

Electrosorption isotherm data

Theoretically the Langmuir type isotherms are the ideal choice for describingelectrosorption data, as they contain the adsorption equilibrium constant. Theirbiggest disadvantage, a poor fit with experimental data, is solved by adding anfit parameter to the equation.

Our electrosorption theory predicts a bell shape dependence of the surfaceloading with applied potential. The maximum of the bell can shift to positive ornegative potentials due to specific orientation adsorption or charges of theadsorbing pollutant molecule. Plotting the scarce available data from literaturein a single graph reveals only a slight bell shape. However, most of the data is ofpoor quality and usually only one potential ‘branch’ is measured. However itwas found that charged molecules indeed show strong shifts of their maxima.Fitting various data series with the model gives reasonable results only if theeffectiveness of the electrosorption is decreased. This is done by introducing abed efficiency and taking into account ohmic losses in the system.

Comparing predicted electrosorption data with isotherms taken for aphenol/water system to which varying amounts of methanol are added

III

provides a first benchmark. It is concluded that electrosorption in theory canachieve similar shifts in the isotherm with relative ease.

It was extensively attempted to reproduce the electrosorption experimentsconducted in literature but with little success. Early erroneous effects suggestedlarge influences of the potential but it was discovered that this was due tounaccounted for chemical reactions. Later results did show only slight or noinfluence of the applied potential.

Transient electrical behaviour of packed beds

A typical packed bed electrode consisting of AC granules has properties unlikeany normal electrode. It has a very large surface and therefore a very largeelectrical capacity. As resistances in the carbon matrix and in the pores cannotbe neglected, the characteristic time for charging the double layer is even larger,resulting in a sluggish system.

The external response of a packed bed electrode can be modelled by a Laplacemethod if it is considered a black box. More complex electrical circuits can andmust be simplified to keep the calculations practically. The presence of internalresistances leads to a potential distribution in the electrode, instead of theexternal applied potential. The Laplace method cannot be used to determinethe local potentials inside the bed, instead the concept of infinite resistors inseries is used to derive a differential equation. The resulting problem iscompletely analogous to heat transfer in a slab of material. By variation ofboundary conditions three different solutions were obtained:

• The no losses model: Solid phase resistances can be neglected with respectto pore phase resistances

• The internal losses model: Solid and pore resistances are in the same orderof magnitude.

• The external losses model: Part of the polarising potential is lost in the bulkliquid.

IV

Measuring electrical properties

If the applied potential is suddenly changed a current will run through thesystem until a new equilibrium is reached. Transient current experiments werefound to be a good tool for obtaining electrode properties. Converting the i(t)data by plotting i√t vs. √t gave specific shaped curves. Only the external lossesmodel was able to fit the experimental data accurately.

It was found that the capacity remains constant small step sizes in the order of10 mV. If the bed efficiency is set to unity, porous graphite has an experimentalcapacity of 0.285 F/m2, while Ambersorb 572 has a capacity of 0.158 F/m2.This suggests that half the Ambersorb surface is not accessible for double layerformation. Direct determination of the electrical resistance of the bed andsingle particles gave values 10-100 times higher than those derived fromtransient experiments. Direct measurement did show a strong influence ofmechanical pressure on bed resistance. Higher pressures lead to better electricalconductivity in the bed.

Reducing the electrolyte concentration reduces the capacity and increases thetotal resistance of the system. The bulk liquid resistance is directly related to theconductivity of the electrolyte. The constancy of the capacity over largerpotential differences is uncertain and was therefore examined. It was found tobe true for porous graphite but not for the Ambersorb, where the capacitychanged a factor of two. Furthermore, the theoretical and experimental linesdid not agree much. The resistance was found to be no function of the appliedpotential. Reported literature values for AC differential capacities vary a factorof 5. This is probably due to the heterogeneous nature of this type of material.Furthermore, the actual size of the electrical accessible area is unknown. Thepresence of organic compounds did not have a significant effect on the capacityor resistance.

Designing an electrosorption unit

An electrosorption installation was designed for cleaning a wastewater streamof 20 L/min containing 5 mol/m3 of phenol. The liquid flow is described withthe axial dispersion plug flow model. Mass transfer resistance is assumed to beexternal of the solid phase. No unwanted Faraday reactions occur.

V

To estimate the equipment dimensions a set of characteristic times is used.Some characteristic times need to be larger than others, as some processes needto be finished before others. If all resulting inequalities are satisfied, the designis within its operational window. The following times are defined: The averageresidence time of the liquid, the adsorption time, the desorption time, thedispersion time, the mass transfer time and the double layer charging time. Thedesorption time should be larger than the time required for charging the doublelayer. The adsorption time should be much larger than residence time. Thedispersion time should be larger than the residence time and the residence timeshould exceed the mass transfer time.

The bed length and the liquid speed (determined by the column with) influence5 out of 6 characteristic times and therefore are the most important designparameters. In order for the process to be in its operational window, the bedlength should be in the order of 10 mm and the liquid speed in the order of 10-4

m/s. The complete model is implemented in the numerical simulation packagegPROMS. A large number of adsorption/desorption breakthrough simulationswere conducted while values of variables were varied and their influenceexamined.

Some dynamic aspects

The encountered phenomenon of streaming current is examined here.Streaming current is caused by the movement of the GC excess charge due tothe movement of the liquid. The experimental currents measured are 2.5 timeslarger than those predicted by the theory. This might be due to anunderestimation of the activated carbon outer surface area that contributes tothis effect.

A relation exists between charge and mass transfer as was discovered duringearlier experiments. The adsorption of polluting compounds causes a transportof charge. If the relative amount adsorbing is compared to the relative amountof charge transported, a reasonable linear relation is found. The theoretical(absolute) amount of charge transferred associated with a certain degree ofadsorption can be calculated. This theoretical value is about 2-20 times largerthan the experimentally found values. A probable reason for this is that not all

VI

adsorbing molecules contribute to the current generation. This is the case ifadsorption takes place outside the double layer. The difference becomes morepronounced at higher potentials, as is predicted by our electrosorption model.

The operating costs for four different type of regeneration methods areestimated using some educated guesses and compared. Steam regenerationseems the most cost-effective option, while the no-regeneration case is themost expensive one.

VII

C O N T E N T S

Chapter 1: Introduction

1.1 Background 11.2 Problem statement 41.3 Literature survey 51.4 Approach and thesis outline 10

Chapter 2: Influence of electrical potential on adsorption

2.1 The structure of the polarised solid liquid interface 132.2 The dielectric 212.3 Adsorption of organic compounds 312.4 Looking back 37

Chapter 3: Electrosorption isotherm data

3.1 The potential dependent isotherm 393.2 Fitting literature data 423.3 New electrosorption data 573.4 Looking back 69

Chapter 4: Transient electrical behaviour of packed bed electrodes

4.1 Introduction 714.2 The non-dimensional electrode 744.3 The dimensional electrode 824.4 Looking back 92

Chapter 5: Measuring electrical properties

5.1 Transient experiments 955.2 Results 1005.3 Variation of process conditions 1035.4 Looking back 116

VIII

Chapter 6: Designing an electrosorption unit

6.1 Process description 1196.2 The mathematical model 1276.3 Results 1356.4 Looking back 150

Chapter 7: Some dynamical Aspects

7.1 Streaming current 1537.2 The relation between mass and charge transfer 1597.3 Economics 167

Chapter 8: Conclusions 175

List of symbols 183

References 189

Appendices

A. Contact adsorption of ions 195

B. Listing of gPROMS input files 201

C. Economics 215

Samenvatting 219

Dankwoord 225

1

C H A P T E R 1

INTRODUCTION

1.1. Background

Water is needed for all life on earth. It may seem that we have it in abundancewith two thirds of the planet covered by oceans, but unfortunately, it is notquantity but quality that counts (Figure 1.1). Especially in densely populated orindustrial areas the quality of water can become a problem. These areas have ahigh demand and produce large amounts of wastewater. Beyond a certain pointthe natural occurring purification processes are no longer sufficient and groundwater quality will start to decrease, causing both environmental en economicalproblems. With an ever-increasing world population these problems will getbigger in the future. One solution is the installation of wastewater treatmentfacilities. This is where adsorption comes into play.

Adsorption can be used for the removal of organic pollutants from aqueousstreams. The polluting molecules accumulate on the inner surface of a poroussolid phase therefore depleting the liquid phase. Adsorption is often the laststage of a water treatment section because it is more effective whenconcentrations are low. The material most used as adsorbent is activated carbon(AC). It is made from peat, wood, coconut shells, coal or synthetic highpolymers by heating them under controlled conditions. Traditionally, activatedcarbon has been used for removal of odours, tastes and colours from bothwater and gas. A wide range of carbons with different pore size distributions,surface chemistry and shapes are available commercially. For wastewaterapplications hydrophobic carbon granules possessing a large mesopore


2

structure are most convenient. The AC granules are packed inside a column.The liquid enters the column on one side and flows through the packed bed.The pollutants will adsorb onto the carbon and the purified liquid leaves thecolumn at the outlet.

Water on Earthtotal 100%

salt 97.5%

liquid 30.6%

fresh 2.5%

permafrost 69.4%

ground 98.7% lakes 0.96% soil 0.16%

rivers 0.02%atmosphere 0.12% organisms 0.01%

Figure 1.1: Overview of all water on earth. The amount of fresh liquidwater is less then 1%.

Activated carbons have a very large surface area due to the presence ofmicropores, typically in the order of 1000 m2 per gram of carbon. This is whythe uptake of pollutants can be as high as fifty percent of the carbon mass.However, given enough time, the carbon will become saturated. In order toprevent deactivation of the column, the spent carbon must either be replacedby new carbon or regenerated. Replacement is expensive, but can be thecheapest solution if pollutant concentrations are low, hence ensuring a longoperational life. Regeneration of the carbon allows it to be re-used a number oftimes; this can be done in situ as well as off site.

Off site regeneration consists of a number of steps. First the column isemptied. Then the deactivated carbon is transported to a thermal regenerationfacility. There the carbon is heated to 1000 °C in a hydrogen atmosphere to boiloff or pyrolyse the adsorbed load together with about 10% of the carbonmatrix. Transporting the carbon back to the site and refilling the columncompletes the operation. The disadvantage of the method is the relatively high


3

cost that is in the same order as that for buying new carbon. Reducing costs isdifficult, as the biggest contribution comes from transporting the carbon.Thermal regeneration cannot be used to treat all spent carbons. Norit N.V.does generally not accept carbons with loads higher than 10% (Rexwinkel,1998). Lower loads might not be accepted if they can lead to production ofdioxins in the furnace.

For the in situ regeneration the carbon remains inside the column. The processis divided into two cycles. In the adsorption cycle the column removespollutants from the waste stream. It is followed by the desorption cycle wherethe column is regenerated. Desorption of adsorbed molecules can be achievedby changing process conditions. For instance increasing the temperature, orreducing the pressure, shifts the adsorption equilibrium towards desorption.The desorbing pollutants are collected in a washing stream. The concentrationsin the washing fluid are much higher than in the process stream. As a result thewaste is reduced to a much smaller volume. This is an important outcome aswaste disposal costs depend on volume only, not on the concentration ofpollutant dissolved.

As outlined by Suzuki (1990, chapter 9) there are five processes available for thein situ regeneration of spent carbon:

1) desorption by an inert stream or low pressure stream,

2) desorption at high temperature,

3) desorption due to a changing affinity between adsorbate and adsorbent,

4) desorption by extraction using strong solvents, and

5) removal of adsorbates by decomposition.

Methods 1) and 2) are used for gas phase operation only. The other threemethods are applicable for liquids. Some examples: Adsorbed organic acidscan be removed with an alkaline solution because the dissociated acids adsorbfar worse then the non-dissociated (method 3). An organic solvent can be usedto extract or displace adsorbed hydrophobic molecules (method 4). The fifthmethod can be used if the adsorbed molecules can be converted into smalleror less harmful molecules that tend to desorb better. All methods can restore


4

only part of the adsorption capacity because they are not ‘powerful’ enough tochange the adsorption equilibrium much. The regenerative performance getsworse for multi-component systems. Furthermore elution of the column isslow due to the unfavourable desorption kinetics when compared toadsorption. This means that a lot of effluent is produced. For better resultstwo methods can be combined as is done in steam regeneration where a hightemperature and an oxidising environment are applied.

1.2. Problem statement

The previous section indicates that regenerating spent adsorbents is the mosttroublesome and expensive part of adsorption technology. According to Lengand Pinto (1996) regeneration accounted for about 75% of the total operatingand maintenance costs needed for running a granular packed bed AC plant. Itseems there is no ideal solution that can be applied generally and probably therewill not be one soon. The various regeneration methods in use today havelimited applicability and are bound to their various niches by economicrestraints. This situation creates a large drive for investigating new ways toregenerate spent adsorbents. One of these is called electrosorption and it is thesubject of this thesis.

Electrosorption is short for electrochemically influenced sorption. It basicallydeals with the effects that an applied electrical potential has on the sorptionbehaviour. Two effects can be identified. For low potentials the adsorptionequilibrium of molecules is a function of the solid-liquid potential drop, even ifthey are not charged. This rules out simple coulombic interactions asmechanism. By changing the applied potential one is able to change theadsorption equilibrium similar to a type 3 method of Suzuki.

When the applied potentials are higher, electrochemical Faraday reactions occurin addition to equilibrium changes. By exchanging electrons with the electrode,adsorbed molecules can be oxidised or reduced, converting them to lessabsorbable components or even to carbon dioxide and water (the type 5method of Suzuki).


5

Electrosorption is a hybrid process that combines elements from adsorptionand electrochemistry. Electrochemical principles dictate that the system mustcontain at least two electrodes that are connected via an external electricalcircuit. Both must be in contact with an electrolyte. The electrodes used in thiswork are packed beds of carbon particles with liquid flowing through. Insidethese electrodes both charge- and mass transfer limitations will occur. In orderto avoid limitations an optimal design must be found.

1.3. Literature survey

1.3.1. The discovery of electrosorptionThe phenomenon of electrosorption was discovered in 1875 by theelectrochemist Lippmann (Gouy, 1903). He carried out experiments using acapillary electrometer, an instrument that consists mainly of a capillary tubefilled with mercury serving as electrode. The object was to measure the surfacetension γ of the mercury at various conditions. Applying an electrical potentialcauses the mercury to become polarised. This results in a reduction of itssurface tension, due to coulombic repulsion of charges on the surface.Lippmann added surface active compounds to the electrolyte and he found anexcess reduction of the interfacial tension when these molecules adsorbed onthe mercury interface.

The excess reduction of capillary curves was the first direct proof of theelectrosorption phenomenon. In 1903, Gouy published the first part of hisextensive capillary curve data collection. Electrocapillary curves recorded in thepresence of an organic compound had a very characteristic shape. If no organiccompound was present, a plot of γ versus the polarising potential φ yielded aparabola. Adding surfactants resulted in a lowering of the curve. This effect waslarge for small potentials and diminished when the potential was increased (seealso Figure 1.2). With increasing |φ|, desorption of organic molecules becomesmore pronounced than adsorption. At high potential differences all curvescoincide, suggesting that hardly any organic molecules remain on the surface.Gouy (1916, 1917) concluded that there was a definite relation between appliedpotential and adsorptive behaviour of neutral organic compounds.


6

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

φ [V]

400

380

360

420γ

[10

N]

-5(a)

(b)(c)

(d)(e)

(f)

Figure 1.2: Electrocapillary curves for different concentrations tert-butanol in 1 N NaCl solution: (a) 0, (b) 10, (c) 50, (d) 100, (e) 200and (f) 400 mol/m3. The adsorption of alcohol causes the decrease in γaround φ = 0 (Gouy, 1903).

1.3.2. Theoretical workFrumkin (1925, 1926) attempted to derive the equations needed to describeGouy’s data. He used the resemblance of a polarised interface to an electricalcapacitor in order to calculate and predict changes in adsorption. Butler (1929)followed a similar, but more molecular approach by introducing the molecularpolarisability and the dipole moment into the equations. Butler reasoned thatelectrosorption occurred because these parameters change as molecules movefrom a region with a low field (bulk) to a region with a high field (interface).Parsons (1959) compared the Frumkin and Butler theories and found that theywere essentially the same. He was the first to look at the relation betweenadsorption and differential electrical capacity (Parsons, 1959; Breiter andDelahay, 1959; Parsons, 1963). Further understanding of the mechanismbehind electrosorption came when Bockris et al. (1963) published their modelfor the structure of the electrified interface, now known as the triple layermodel. Bockris et al. explained the potential dependency of the adsorption ofneutral species on polarised electrodes by taking into account the change inenergy of orienting water dipoles with a changing electrical field and due tocompetitive adsorption of organic molecules.


7

Between 1965 and 1975 workers in the field of electrosorption becamepolarised themselves into two quarrelling groups: The ‘Russian school’ followedthe ideas of Frumkin and the ‘British school’ that of Bockris. Both groups triedto prove the superiority of their own concepts at the expense of the other(Bockris et al., 1967; Damaskin, 1969; Gileadi, 1971; Damaskin, 1971; Frumkinet al. 1980). As was to be expected this did not lead to new insights. Only minorimprovements were made on both the original Frumkin and Bockris theories(Schuhmann, 1987).

Before the early 1970’s all research on electrosorption dealt exclusively withmetal electrodes. These can be considered one-dimensional and have smallsurface areas. A packed bed of carbon granules is at least two-dimensional andpossesses a very large surface area. As a result the latter has a huge electricalcapacity. This leads to a very sluggish electrical response. Electrical charging ofa packed bed can take days if the bed length is too large. The electrical potentialinside a packed bed electrode is not constant but a function of time and place.

Posey and Morozumi (1966) studied the ‘Potentiostatic and GalvanostaticCharging of the Double Layer in Porous Electrodes’. They determinedanalytical solutions to describe potential distributions inside semi-infiniteporous electrodes in the absence of Faraday reactions. Their results aremathematically analogous to one-dimensional heat transfer in slabs of material(Carslaw and Jaeger, 1959) as the conducting matrix can be considered to be aninfinite number of resistors in series. Charging a packed bed electrode isequivalent to charging a network of resistors and capacitors. Each capacitorrepresents an infinitesimal part of the surface. Resistors are situated betweencapacitors and represent carbon and liquid electrical resistances. Understandingthe electrical behaviour of large surface materials resulted in attempts to usethem for the desalination of salt water (Johnson and Newman, 1971).

Alkire and Eisinger (1983a) performed the first dynamic simulations of apacked bed electrosorption unit. They used a one-dimensional plug flow modelwith axial dispersion to describe the liquid flow through the bed. Mass transferresistance was assumed to be external. An analytical potential distributionequation was used and the coupling between isotherm (a modified Langmuir)and applied potential was done by means of an empirical expression. Chue et al.


8

(1992) improved the model by taking intra-particle mass transfer into accounttogether with a potential dependent Freundlich isotherm. Card et al. (1990)differentiated between bed porosity and micro-pore porosity. This resulted in atwo-dimensional model with the direction of the overall current penetrating themicro-pores perpendicular to the direction of the liquid flow. This flow-by bedconfiguration is better than a flow-through configuration with current and flowparallel, because for the flow-by configuration it is possible to keep the bedsmall in the direction of the current and long in the direction of the flow (Xu etal., 1992). They used the results from experimental obtained two-dimensionalpotential distributions to design an electrochemical packed bed reactor for theelectrochemical reduction of nitrobenzene to produce p-aminophenol.

1.3.3. Experimental workAll early electrosorption experiments focussed on the dropping mercuryelectrode because of its smooth and well determined surface area. An additionaladvantage is the direct relation between the molecular composition at themercury interface and the surface tension of the metal, resulting in veryaccurate experimental data. From surface tension measurements a relativelylarge potential dependency of the adsorption became obvious, as was shownearlier (Figure 1.2).

Wroblowa and Green (1963) were the first to do similar experiments with solidmetal electrodes. Their radioactive tracer method was sensitive enough todetermine the amount of thiourea adsorbing on their (small surface) goldelectrode. A similar technique was used by Gileadi et al. (1965) to determine theelectrosorption of ethylene gas on platinum electrodes. These results show thesame quadratic relation between adsorption and potential although the dataseems less smooth compared to the mercury measurements. Both Wroblowaand Gileadi found the difference between minimum and maximum adsorptionto be a factor of three to five. It increased for higher concentrations anddecreased with electrode age. For both ethylene and thiourea the maximaladsorption occurred at relatively large and positive potentials.

Strohl and Dunlap (1972) considered the possible use of electrosorption as ameans of separating mixtures. For separation purposes a large surface is


9

essential. The authors found that they could alter the adsorptive capacity of apacked bed of graphite particles by changing the applied potential. They couldalso change the uptake of a specific quinone from a multi-component mixture.Their column breakthrough data reveals a large effect of the applied potential,even exceeding a factor of five.

In 1985 McGuire et al. published potential dependent isotherm data forelectrosorption of phenol on activated carbon under various conditions. In1994 Costarramone et al. studied competitive electrosorption using two ternarysystems containing chloroform/benzoic acid and chloroform/phenol. Threefollow up studies were done by Hazourli et al. (1996) for the same system. In1997 Schäfer and in 1998 Bán et al. measured electrosorption isotherms foraromatic substances with positive, negative and no charge. A displacement ofthe maximum adsorption was found as expected due to coulombic interactionwith the charged activated carbon. Janocha et al. (1999) measuredelectrosorption for the substances OPE (1-o-[4-(1,1,3,3-tetramethylbutyl)-phenyl]-decaoxyethylen) and phenol. For OPE a small dependence on potentialwas found (about a factor of 2) but the adsorption for phenol was foundindependent of the applied potential for well over a 2 V range, which seems tobe in disagreement with earlier work.

Experimental data regarding the electrical behaviour of packed bed electrodesappeared in literature around 1970. Evans (1966), Johnson and Newman (1971)and Oren et al. (1984) measured the differential capacity of various activatedcarbons and graphite electrodes by recording charging currents in response to astep in applied potential. In 1975 Tiedemann and Newman determineddifferential capacities for medium sized surface areas using the Posey-Morozumi analytical solutions for potential distributions. Zabasajja and Savinell(1989) used the Bockris triple layer model together with the Tiedemann andNewman method to determine the effects of surface coverage on electricalcapacity. Actual potential distributions can only be measured directly by smallprobing electrodes on various positions in the bed (Alkire and Eisinger, 1983b;Card et al., 1990).

Strohl and Dunlap (1972) and Chue et al. (1992) looked at the dynamicbehaviour of the packed bed electrosorption unit. Chue et al. monitored the


10

outlet concentration while the bed was forced to a different potential. From theresulting change in concentration in time they could determine the ratiobetween the sorption wave and the potential wave going through the bed.Eisinger and Keller (1990) determined the characteristic times of four processesand used them as their primary design parameters. They also investigatedprocess configurations and power consumption.

Only recently experiments have been conducted in which the applied potentialswere much higher, in order to electrochemically oxidise or reduce the adsorbedcomponents. Slavinskii et al. (1984) examined the regeneration of a packed bedloaded with nitrotoluene using a constant current density of 20-40 A/m2.Narbaitz and Cen (1994) tried to regenerate a carbon loaded with phenol. Theyfound high efficiencies of up to 95% with no apparent carbon losses. Zhang etal. (2000) found improvement in the regeneration of activated carbon adsorbedwith phenol after applying 2-20 A/m2.

1.4. Approach and thesis outline

In this thesis we investigate the electrosorption phenomenon both theoreticallyand experimentally. Our aim is to see whether electrochemical regeneration ofspent activated carbon is technically (and economically) feasible. The first stepis to investigate the mechanism behind the influence of the potential on theadsorption equilibrium. This is done in chapter 2. The potentials that can beapplied are limited to ± 1.5 V because at higher potentials Faraday reactionsoccur. These Faradaic reactions are unwanted for they cause a leakage ofcurrent, as carbon, ions and water molecules get oxidised or reduced. On theother hand the same Faraday reactions could be useful for regenerating theadsorbent because also the adsorbed pollution will be converted. This highvoltage electrodynamic regeneration will not be investigated in this work,however. It is a completely different process and the electrostatic alternative ismore attractive from an economic point of view as current is only needed forinitial charging of the electrode and after this no current runs duringdesorption.


11

The outline of the thesis is discussed in more detail below. The relationsbetween the various chapters are visualised in Figure 1.3.

• In chapter 2 the electrified interface is studied in detail to investigate themechanism of electrosorption. A number of double layer models isexamined. Special attention is paid to the influence of the electrical field onthe dielectric constant of the solute and the solvent. Adsorption on acharged electrode is found equivalent to the moving of a slab of dielectric ina parallel plate capacitor. Using thermodynamics, changes in stored energycan be translated to changes in adsorption equilibrium.

• In chapter 3 the potential dependent equilibrium constant is combinedwith an appropriate isotherm equation. Experimental electrosorption data iscompared with theory. Comparing the electrosorption effects to those of analternative regeneration method provides an initital benchmark. The energyrequirements associated with desorption of one mole phenol are estimated.New experimental electrosorption data is presented and compared withtheory and literature data.

• Chapter 4 discusses the electrical behaviour of the packed bed electrodesubjected to a change in applied potential. First electrodes without physicaldimensions are considered. Laplace transformation is used to obtain thecurrent responses for these systems. To include dimensions in the equations,an electrical circuit that behaves analogous to a packed bed electrode isconstructed. Simplifying assumptions are made and for three different casesthe potential distribution models are presented.

• In chapter 5 transient current experiments are presented. Theseexperiments provide the data for validating the distribution functions. It willbe shown that only the external losses model is capable of adequately fittingthe data. The influence of mechanical pressure, ionic strength, potential andconcentration on the total capacity and the total resistance is alsodetermined.

• Chapter 6 deals with modelling an electrosorption unit. A firstestimation of optimal dimensions of the unit is obtained from sixcharacteristic times and their order of magnitude. A theoretical model ispresented including differential equations to describe mass and charge


12

transfer and the coupling between these. The computer program gPROMSwas used to do dynamic simulations. The results are examined for a numberof different input variables and configurations.

• In chapter 7 three miscellaneous subjects are treated. First thephenomenon of streaming current is examined. Secondly, experimentalresults suggesting a coupling between mass and charge transfer areinvestigated. The adsorption seems related to current peaks found duringexperiments. Thirdly, an approximate economic calculation is donecomparing electrosorption process costs to three alternative processes.

• In chapter 8 the concluding remarks can be found.

Chapter 2 Chapter 3

Chapter 4 Chapter 5

Chapter 6 Chapter 7

Measuring IsothermsModelling the polarisedinterface

The Interface

Mass Transfer

Charge Transfer

Measuring electricalproperties

Modelling of packed bedelectrodes

Modelling an electrosorber Streaming currentAdsorption current

Economicevaluation

Conclusions

Chapter 8

Figure 1.3: Outline of the thesis.

13

C H A P T E R 2

INFLUENCE OF ELECTRICAL

POTENTIAL ON ADSORPTION

2.1. The structure of the polarised solid liquid interface

2.1.1. Excess of chargeIn a quiescent electrolyte solution at thermodynamic equilibrium, all moleculesin the bulk phase experience a zero net force on a time average scale. Thismeans that all water dipoles are completely randomised (no net overall dipolemoment exists) and all positive and negative ions are distributed equallythroughout the liquid. The bulk can be considered an isotropic andhomogeneous phase.

Things differ close to an interface. The presence of a solid phase disturbs theuniformity of the bulk liquid phase. Forces operating here possess a netdirection leading to a structured arrangement of water molecules and ions. Neara phase boundary water dipoles need not have a random orientation andseparation of charge is likely to occur. This means an excess of charge is presentin the solution. The excess charge generates an electrical field that causes aninduced charge inside the electrode. This induced charge will be of equal sizeand opposite sign to the charge in the liquid. In figure 2.1 the ‘inter-phaseregion’ is depicted and the shading indicates the excess charge. Although excesscharge is present in both the liquid and the solid phase, the inter-phase regionas a whole remains electrically neutral. The separation of charge that occurs is


14

called the electrical double layer. Its existence is essential for electrosorption, aswill be shown.

WorkingElectrode

Interphase region

Electrolyte

CounterElectrode

Excess chargedensity

powersupply

Figure 2.1: The system under investigation: two electrodes in anelectrolyte solution. The shading in the blown-up area denotes theexcess-charge density on the electrode and in the liquid.

Although an electrical double layer will form spontaneously most of the time itis more convenient to charge (polarise) the solid phase externally in order toinfluence the properties of the double layer directly. A basic set-up consists ofan electrolyte solution containing two carbon electrodes connected to anelectrical source (Figure 2.1). The electrodes can be polarised by applying apotential difference between them. The electrode connected to the negativepole will gain an excess of free electrons qM, the other a deficit -qM. These freecharges will be located close to the outer surfaces of the electrodes and theresulting electrical field will cause the electrolyte solution to rearranges itself.Both electrodes will end up being surrounded by a region of ionic excess chargeof equal size and opposite sign.

Of interest is the appearance of the double layer on a molecular scale.According to Bockris and Reddy (1970a) and Trasatti (1980) a chargedelectrode can be compared to a huge ion: emerged in water, both will behydrated in a similar way. The electrode surface is never ‘empty’. Simple


15

reasoning shows that at least 70% of the emerged electrode surface is coveredwith water molecules (Bockris and Reddy, 1970b). Taking directing forces intoaccount yields an even higher percentage. The water molecules closest to theelectrode surface represent the primary hydration layer surrounding dissolvedions. They are firmly bound and almost completely oriented due to strongdipole-charge forces. Surrounding the primary water layer is a secondary layerwith a thickness of about two molecules. These are less strongly held and onlypartly oriented as dipole-charge forces diminish quickly with distance. Beyondthe hydration layers of the electrode, the (hydrated) counter ions are found.

The line that can be drawn through the centres of the closest ions is known asthe Outer Helmholtz Plane or OHP. Beyond the OHP is a region where theremaining ionic excess charge gradually decreases towards zero until thehomogeneous bulk phase is reached. A representation of this model for thepolarised inter-phase is shown in Figure 2.2.

Electrode

Double layer

Bulk liquid

Outer Helmholtz Plane

Figure 2.2: Schematic representation of the polarised inter-phase(Bockris and Reddy, 1970b). The negatively charged electrode iscovered by a row of primary water molecules (darkest), secondaryhydration water and solvated positive ions. Beyond the OHP isthe diffuse double layer. Negative ions are assumed to be notsolvated. Free water molecules outside the OHP are not shown.


16

2.1.2. The Helmholtz model for the double layerThe simplest model for the double layer is the Helmholtz model. In this modelit is assumed that all excess charge is located in two perpendicular planes: oneinside the electrode and one in the solution. All counter ions are situated on afixed distance from the surface. The charge on both planes is equal inmagnitude and opposite in sign. This system has a well-known equivalent inelectricity theory: the ideal parallel-plate capacitor. The differential Helmholtzcapacity CH (in F/m2 ) for such a capacitor is given by:

dC r

Hεε= 0 2.1

where d is the distance between the plates of the capacitor, equal to the OHP,ε0 is the permittivity of the vacuum and εr is the dielectric constant of thematerial inside the capacitor. The dielectric will be discussed in section 2.2. Alist of symbols used can be found at the end of this work. In the simplest caseboth εr and d are constant. The Helmholtz model then predicts a constantcapacity that is independent of the potential drop. This constant capacity iscalled the integral Helmholtz capacity KH. From the definition of the differentialcapacity:

φ≡

ddqC M 2.2

it follows that the relation between the charge density qM on the plates and thepotential drop φ is linear if this is the case. Hence:

φεε=φ=d

Cq rM

0 2.3

If the dielectric is isotropic, the potential drop varies linearly with distance,resulting in a homogeneous electrical field E (= φ/d). The position of the OHPwith respect to the solid phase (the value of d) can be estimated using the modelfor the double layer outlined in the previous section. The OHP is minimal if nosecondary hydration molecules are present and the primary water molecules of


17

both electrode and counter ions are stacked as hexagons as depicted in Figure2.3. The arrows represent the orientation of the water dipoles.

Electrode Bulk liquid

30°

2rA

rA 3 rA rA ri

2 + 3 + r r rA A ion

Figure 2.3: Determining the minimal OHP for KCl electrolyte.The water radius rA is taken as 0.14 nm based on experimentaldata of the O-O bond length in water and ice (Bockris andReddy, 1970a, chapter 1). The ionic radius rion of K+ is 0.133nm.

The Helmholtz capacitor thickness d is the distance between the centre of thecounter ion and the boundary of the solid phase, hence: d = 2rA + √3rA + rion. Avalue d = 0.656 nm is obtained if rA = 0.14 nm and rion = 0.133 nm. It is larger ifsecondary hydration layers are present and if the stacking of the watermolecules is more chaotic. If the potential drops one volt between the solid andthe liquid phase, the electrical field E inside the double layer is in the order of109 V/m. Any electrical fields in the bulk phase can be neglected with respectto this inter-phase field.

The predictions of the Helmholtz model can be compared to experimentaldata. In Figure 2.4 the differential mercury capacity is plotted as function of thepotential difference relative to a normal calomel electrode. As can be seen fromthe graph, the capacity is not constant but a weak function of the potential. Theexception to this is the dent at –400 mV, which will increase with decreasingionic strengths.


18

14

18

22

26

30

34

38

0 -0.4 -0.8 -1.2 -1.6 -2

φ vs. NCE [V]

C [

F/cm

2 ]µ

(a)

(b)

Figure 2.4: Experimental differential capacity of mercury incontact with sodium fluoride: (a) 0.1 N NaF and (b) 0.01 NNaF (Reeves 1980).

2.1.3. The Gouy-Chapman model for the double layerThe Helmholtz model is unable to explain the potential and concentrationdependency of the differential capacity. Gouy and Chapman tried to tackle thisproblem by liberating the counter ions from their rigid two-dimensional sheetand spreading them out into the solution. The mathematical derivation of theGouy-Chapman model is rather lengthy and will not be discussed here. Detailscan be found in Bockris and Reddy (1970b), Delahay (1965, chapter 3), Reeves(1980) or Prentice (1991). Starting point is the Poisson equation, whichdescribes the potential distribution in the liquid and the Boltzmann function,which describes the distribution of the counter ions. Combining these twogives the following result for the total charge density in the double layer:

( )

φεε−=RT

zFRTcq MrionGC 2

sinh2 2/10 2.4

where cion is the concentration of the electrolyte, z is the ionic charge numberand F is Faraday’s constant. Combining the expression for the charge in the


19

diffuse layer with the definition of the differential capacity (Eq. 2.2) results inan equation for the diffusive or Gouy-Chapman capacity:

φ

εε=RT

zFRT

czFC MionrGC 2

cosh22/122

0 2.5

The Gouy-Chapman model predicts the capacity to be a strong function of thepotential and the temperature and a weaker function of the electrolyteconcentration.

2.1.4. The Stern model for the double layerComparing the Gouy-Chapman model predictions (both Figure 2.4 and Figure2.5) with experiments (see chapters 4 and 5 for capacity-potential data ofactivated carbon and porous graphite electrodes) reveals a discrepancy.According to the Gouy-Chapman model, the capacity becomes infinite alreadyat moderate potentials due to the large contribution of the cosh term in Eq. 2.5.This behaviour is not found experimentally (Delahay 1965, chapters 1 and 3).Although the capacity can increase rapidly if applied potentials are small, thisincrease diminishes at higher potentials.

Not only the Helmholtz but also the Gouy-Chapman model fails to describethe complete capacity-potential curve. Stern tried to improve it by dropping thepoint-charge approximation (Delahay 1965, chapter 3 and Reeves 1980). As aresult, counter ions can no longer approach the surface indefinitely due tosterical hindrance. Stern predicted that part of the excess counter ions would bestuck in a compact layer near the surface while the rest is smeared out in adiffuse layer further in the solution. From the electroneutrality condition itfollows that the charge on the electrode (M) must equal the sum of the chargein the compact layer and the diffuse layer:

diffusecompactM qqq += 2.6

Charge stored in two different regions suggests the usage of two capacitors inseries. The simplest interpretation of the Stern model is to describe thecompact layer with the Helmholtz model and the diffuse layer with the Gouy-


20

Chapman model. The plane of closest approach is the OHP. From staticelectricity theory it follows that the replacement (Stern) capacity for an electricalcircuit containing two capacitors in series equals the reciprocal summation ofthe two, hence:

GCHST CCC111 += 2.7

The Stern model predicts that large Gouy-Chapman capacities are cancelled bysmall Helmholtz capacities. For large salt concentrations and large appliedpotentials the Stern capacity will be equal to the Helmholtz capacity, as 1/CGC

<< 1/CH. Most of the excess charge is squeezed onto the Helmholtz plane andonly little is scattered in the Gouy-Chapman area. The GC contribution is onlyof importance for very low ionic strengths and small potentials. A plot of thethree double layer models as function of the potential (Figure 2.5) confirmsthis.

φ [V]

C [F

/m]2

simplified Stern model capacity

parallel plate orHelmholtz capacity

diffuse layer orGouy-Chapmancapacity

0.2 N

0.1 N

0.02 N

0 0.35 0.7-0.35-0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Figure 2.5: The differential capacity as a function of potential.For the Helmholtz model (Eq. 2.1): d = 0.6556 nm and εr =11.7. For the Gouy-Chapman model (Eq. 2.5): T = 293 K, εr= 24 and z = 1.

Because the differences between the Stern and the Helmholtz model are smallunless ion concentrations and potentials are very low the Stern model is no real


21

improvement. Describing double layers accurately seems a difficult task. Formany systems the compact double layer capacity varies markedly with potentialand can be asymmetric. It was found that for positive potentials the capacity isusually much higher then for negative values. A solution frequently adopted inliterature is to derive the compact double layer values from experimental results(Dalahay 1965, chapter 3). Grahame (1947) was among the first to furtherimprove the Stern model.

2.1.5. Contact adsorption of ions: The triple layer modelThe Stern model is faulty in assuming that the OHP is the closest approach tothe surface. Ions (some of them) can contact adsorb, e.g. touch the bare surface(Grahame, 1947; Bockris and Reddy, 1970b). To allow this, both ion andsurface must be stripped of their hydration shells. Using thermodynamics it canbe shown that it is energetically favourable for large negative ions to contactadsorb while it is unfavourable for positive ions and small negative ions(Bockris and Reddy, 1970b). The presence of contact adsorbed ions has a largeeffect on the electrical capacity and provides an explanation for the differencesfound between the positive and negative branches of the capacity potentialcurve. Capacities obtained for positive potentials are usually higher (Grahame,1947; Breiter and Delahay, 1959; Bockris et al. 1963; Prentice, 1991). This seemsin accordance with the fact that the contact adsorbing ions are negative.

The mathematical derivation of the triple layer model is rather complex. It canbe found in appendix A. With it, a more detailed, although still not perfect,prediction of capacity vs. potential curves can be made. In the remainder ofthis work no further attention is paid to ions contact adsorbing as it does notgenerate new insights with regard to electrosorption. Instead, the Stern model isimproved by implementing a field dependent dielectric constant.

2.2. The dielectric

2.2.1. Calculating εεεεr from molecular properties

So far the structure of the charged plates of the equivalent capacitor has beenthe main focus. Not much attention has been paid to the material between


22

those charged layers, the dielectric. The dielectric behaviour of a substance isdetermined by its dielectric constant εr (≡ ε/ε0). Despite the name, it is not aconstant. In the bulk phase, under standard conditions, the dielectric constantof water is about 80. When exposed to a strong electrical field it can be as lowas 5 or 6 (Kortüm, 1965). Because strong fields exist inside the double layer aswas shown earlier, bulk values for εr cannot be used but the dependency on thefield strength is required.

A strong electrical field will cause a material to become polarised. The amountof polarisation is expressed by the dielectric polarisation P. If we apply Gauss’law to one half of an empty capacitor and again for a capacitor filled with thesubstance under investigation the relation between P end εr is obtained (VonHippel, 1954; Kortüm, 1965):

( )EP r 10 −εε= 2.8

The polarisation P is equivalent to the dipole moment per unit volume of thematerial (Von Hippel, 1954). It is the additive result of N average elementarydipole moments µ , so µ= NP . The average elementary dipole momentassociated with a molecule is assumed to be proportional with the local fieldstrength E’ acting on it (Von Hippel, 1954; Kortüm, 1965; Atkins, 1990,chapter 22). This local field is usually not equal to the external applied field Eext

due to interference of neighbouring molecules:

ENP tot ′α= 2.9

where αtot is the polarisability of the individual molecules, due to four differentmechanisms. Assuming they act independently means that their effects can beadded. The following mechanisms can be identified:

1) Electronic polarisation αel is the result of slightly displaced electron cloudssurrounding the nuclei.

2) Atomic polarisation αat can occur when more than one type of atom ispresent in a molecule. In essence it is a slight alteration of bond lengths.


23

3) Orientation or dipole polarisation αdi can occur if permanent dipoles arepresent, these tend to align themselves to the direction of the field.

4) Space charge or interfacial polarisation αint is not relevant as both solventand solute molecules do not possess permanent charges.

In order to calculate P from Eq. 2.9, expressions for αtot and E’ are needed. Fora mono-atomic gas, the total polarisation depends only on the radius of theatom. If the dielectric consists of molecules with permanent dipole µ, they aresubject to a torque that tends to align them to the field. The energy of amolecule in a local field depends on the angle ϕ towards this field:

ϕµ−= cos'EU 2.10

The overall mean dipole moment depends on the competition between thealigning influence of the field and the randomising influence of thermal motion.Using Boltzmann statistics to describe this competition and integrating over allspace angles Von Hippel (1954), Kortüm (1965) and Atkins (1990) obtained themean dipole moment:

kTEx

xeeeexx xx

xx ' and 1)( with )( µ=−−+=µ=µ −

−

2.11

where )(x is called the Langevin function. It is plotted in Figure 2.6. Forelectrical fields below 109 V/m it can be approximated by the first term of itsTaylor series: xx 3

1)( ≈ so that the average dipole moment reduces to:

kTE

3'2µ=µ 2.12

For fields above 109 V/m the Taylor approximation is less accurate as can beseen from the graph and Eq. 2.11 must be used instead. The total averagedipole moment for a species without an electrical charge in a strong field isgiven by:


24

''

'

EEkTE

aeltot

µµ+α+α=µ

2.13

For less strong fields the linearised Langevin function can be used:

'3

2

EkTaeltot

µ+α+α=µ 2.14

2 109 4 109 6 109 8 109

x/3

( )x

E [V/m]

µµ /

[-]

0.5

1

0

0 1010

Figure 2.6: The Langevin function as a function of the fieldstrength. For fields above 109 V/m the deviation from thelinearised approximation x/3 becomes significant.

To calculate the local field E’, Mossotti used the following hypothetical modelfor the dielectric: a reference molecule is surrounded by an imaginary sphere tosuch extend that the dielectric beyond it can be considered a continuum (VonHippel, 1954; Kortüm, 1965). If there are no molecules inside the sphere, thefield acting on the reference molecule would be due to the external applied field(Eext = E1) and due to the dipoles that line the sphere walls (E2). In realitymolecules are present inside the cavity and this can be accounted for by anadditional contribution E3 to the local field:


25

32 EEEE ext ++=′ 2.15

E2 was found to be (Von Hippel, 1954; Kortüm, 1965; Atkins, 1991):

( ) extr EE 131

2 −ε= 2.16

If the dielectric material consists of non-associating neutral molecules without adipole moment, E3 can be neglected. Combining Eq. 2.9, 2.15 and 2.16 willresult in the famous Clausius-Mosotti equation. If the molecules have apermanent dipole, ignoring E3 leads to erroneous results. Onsager improvedthe Mosotti dielectric model by adding the ‘reaction field’. This field is due tothe polarisation caused by the dipole moment of the central molecule on thesurrounding medium. Onsager found for the relation between εr and P:

( )( )( )22

22

02

2'3

+ε

+ε−εε=

∞

∞∞

n

nnEPr

rr 2.17

where 2∞n is the square of the refractive index, extrapolated to infinite

wavelengths. For most liquids it is approximately equal to 2 (Kortüm, 1965).The Onsager model is valid for non-associated liquids only. Associating liquidsare able to form intermolecular bonds (e.g. hydrogen bonds in water) and haveunusual high dielectric values. Kirkwood tried to improve the Onsager modelby assuming that each molecule in an associated liquid is connected to itsneighbours. A rotation of one dipole requires rotation of the neighbours aswell. Kirkwood found the following equation accurate up to 10% (Kortüm,1965):

( )( )''

'9121

'3 0 EkkTE

ENPE KW

r

rr

µµ+α==ε

+ε−εε 2.18

The amount of dipoles N is given by N = ρNAV/M. The kKW or Kirkwoodconstant, as it was named by us, is a semi-empirical constant that appeared inKirkwood’s equation in slightly different form. Basically Kirkwood had toincrease the influence of the mean molecular dipole on the polarisation because


26

his formula predicted too low values. The constant includes the effect of theassociated nature of the liquid, as expressed by g = 1 + z cos(β) where z is thenumber of immediate neighbours and β is the mean angle between theirrespective dipoles. Kortüm reported a value of g = 2.5 for water at roomtemperature by assuming that water had 4 immediate neighbours (in the formof a tetraeder) and their mean dipole angle is therefore about 68°.

Component α

·10-40 C2m2/J

µ

·10-30 Cm

ρ

kg/m3

M

kg/mol

kKW

-

water 1.65 6.17 997 0.018 4.438

methanol 3.28 5.7 791 0.032 4.753

ethanol 5.26 5.64 789 0.046 5.249

acetone 6.373 9.61 787 0.058 1.881

1-propanol 6.74 5.17 800 0.060 6.532

phenol 10 4.08 1073 0.094 6.742

benzyl alcohol 11 5.70 1045 0.108 3.919

Table 2.1: physical properties of water and a number of organiccompounds needed for the calculation of the dielectric constant.Data from Weast and Astle (1979).

Furthermore Kirkwood suggested that the mean dipole moment of theassociated complex was approximately 4/3 times higher then that of an isolatedmolecule. Hence his kKW for water became 4.44 (= 2.5·(4/3)2), very close to thevalue 4.438 that is needed to obtain the experimentally determined dielectricconstant of water. Presented in Table 2.1 are Kirkwood constants calculatedfrom the difference between experimentally found dielectric constants, andtheoretical dielectric constants obtained from Eq. 2.18 using the reportedexperimental values for α and µ.

As can be seen from the table, the Kirkwood constant has a value of about 5for water and the various alcohols. For acetone the much lower value of 2 wasfound. In Figure 2.7 the Kirkwood constant is plotted against the moleculardipole moment and an inverse relationship is found. For large dipole moments


27

much lower corrections are needed. If kKW is considered independent of thefield strength, the dielectric constant as a function of increasing field strengthcan be calculated (see Table 2.2).

µ [10 C m /J]-40 2 2

k

KW [-

]

Figure 2.7: The relation between the molecular dipole momentand the Kirkwood correction factor. The solid line represents thebest linear trend line through these points: kKW = -0.882µ +10.09.

Component εr

E=0 V/m

εr

E=109 V/m

εr

E=2·109 V/m

εr

E=1010 V/m

εr

E=1011 V/m

water 80.1 70.1 53.8 15.8 3.10

methanol 33 29.5 23.4 7.72 2.16

ethanol 25.3 22.6 18.1 6.31 2.09

acetone 21.01 16.2 11.2 3.90 1.79

1-propanol 20.8 19.0 15.6 5.74 2.03

phenol 12.4 11.7 10.3 4.66 2.13

benzyl alcohol 11.916 10.8 8.81 3.76 1.96

distance from ion ∞ nm 1.2 nm 0.85 nm 0.38 nm 0.12 nm

Table 2.2: The dielectric constant as a function of the electricalfield for a number of components. Also given is the equivalentdistance from an ion in vacuum because r = √(e0/(ε04πE)).


28

Primary water making up the hydration layer of an ion is assumed to have adielectric value of 5 to 6 (Bockris et al. 1963, Bockris and Reddy 1970b).According to the Kirkwood formula, a dielectric constant of 5.74 is obtainedfor water molecules subjected to a field E = 3.6·1010 V/m. For comparison, thedistance from a monovalent ion is given. Here the field emanating from the ionhas the same size. For phenol εr = 2.68 and for benzyl alcohol εr = 2.34 underthe same conditions. It seems the Kirkwood model can predict the correctdielectric constants. The obtained results are plotted in Figure 2.8.

0

25

50

75

1001.5 2 2.5 3 3.5

2 4 6 8 10 12

E [10 V/m]9

ε r [-]

14 16 18

r [nm]10.5

Figure 2.8: The dielectric constant as a function of the electricalfield (solid line) and the distance from an ion (dotted line).

2.2.2. The use of a constant dielectric constantIt should be observed that when the linearised form of the Langevin equation isused (Eq. 2.14), the electrical field is eliminated from the equation and thedielectric constant is indeed a constant. This approach is generally used inliterature. In order to account for the field at the inter-phase a lower value for εr

is applied. For the primary hydration water immediately surrounding theelectrode a value of about 6 is used. The secondary water, further away, is givena value of about 40.


29

This new insight has consequences for the double layer model. From Figure 2.3it follows that the Helmholtz capacitor is now filled with two different layers ofmaterial. This is mathematically equivalent to two capacitors in series. The firstcapacitor has a thickness 2rA and the second a thickness √3rA + rion. Thereplacement capacity for these two capacitors in series is:

2,01,0

321

r

ionA

r

AH rrr

C

εε++

εε

= 2.19

Using the values of 6 and 40 for the two dielectric constants, the replacementHelmholtz capacity is: CH ≈ 0.16 F/m2. This value corresponds to theexperimentally found constant capacity region for mercury at large negativepotentials.

From Eq. 2.19 it follows that it is mainly the first layer of molecules thatdetermines the electrical capacity of the system, due to the large difference indielectric constants. It is also the layer in which adsorption of organiccompounds is assumed to take place (see section 2.3).

The problem with the constant dielectric approach is the fact that theconditions at the inter-phase are not constant but change. The use of limitingdielectric values based on extreme conditions is less reliable if applied potentialsare small and conditions are mild. To account for this, a potential dependentdielectric constant can be used.

2.2.3. The use of a potential dependent dielectric constantThe dielectric constant remains potential dependent if the complete Langevinequation is applied instead of the Taylor approximation. For electrical fieldsclose to zero, large dielectric constant are obtained that tend to decrease if thefield becomes larger. It was found that the Kirkwood correction constant hadto be lowered to 1.5, or too high theoretical differential capacities are obtained(see chapter 5 for these experimental values). The idea behind a lowerKirkwood constant is that molecules close to the carbon surface behave


30

differently from bulk molecules because they have fewer neighbours and aresubject to strong directional forces.

From Figure 2.9 it can be seen that the Helmholtz capacity curve becomesparabolic instead of flat. The curvature depends on the double layer thickness.Smaller values for d give a more parabolic shape. The maximum lies at φ = 0 Vbut it is overlapped by a dent (the GC capacity contribution).

-500 500

0.2

00

0.4

(a)

(b)

φ [mV]

C [F

/m]2

0.3

0.1

Figure 2.9: The simplified Stern capacity if field dependency of thedielectric constant is taken into account. Curve (a) for a systemwith water only, curve (b) when 50% benzyl alcohol is adsorbedon the surface.

Until now the view on the dielectric has been completely molecular. Secondaryhydration water has a higher dielectric constant than primary water. The overallfield is not homogeneous and therefore position dependent. Despite this, moreunderstanding of electrosorption is achieved by switching to a macroscopicmodel: that of an ideal electrical capacitor. In this model a homogeneous slab ofmaterial represents the dielectric, which is subject to a homogeneous electricalfield. The field strength is no function of the distance to the surface, hence thedielectric value inside the slab remains constant.


31

2.3. Adsorption of organic compounds

2.3.1. The mechanism behind electrosorptionAs was shown, conditions in the inter-phase differ strongly from those in thebulk phase. It is common in adsorption related problems to distinguish theadsorbed molecules as a different thermodynamic phase with respect to thebulk liquid (Tien, 1994). The same approach is followed here. The double layerregion is called phase II, the bulk of the solution is phase I. The followingassumptions are made:

• The system contains water (A), traces of a neutral organic pollutant (B)and inert ions to provide the counter ions. The bulk liquid can beconsidered infinitely diluted with respect to B

• Activities can be replaced by concentrations.

• All adsorption sites are covered with either water or organic moleculesthat compete for the same sites. Ion adsorption is not taken into account.

• Adsorption of B takes place completely inside the double layer byreplacing primary hydration water.

• Adsorption and desorption are completely reversible.

• No Faraday reactions occur (see also section 4.1).

Adsorption of organic molecules is described with an isotherm equation. Theisotherm relates the surface concentration θ (phase II) to the bulk mole fractionx (phase I). If more B is added to the bulk liquid, more B will adsorb on thecarbon surface. In doing so, a molecule of B must replace ν water moleculesalready adsorbed on that site at the interface. For the equilibrium can bewritten:

IIIIII BABA +ν⇔+ν 2.20

The equilibrium constant K is defined as:


32

IBIIA

IIBIA

III

III

des

ads

xxxx

BABA

kkK

,,

,,ν

ν

ν

ν

=== 2.21

Electrode

A

B

phase IBulk phase

phase IIAdsorbed phase

capacitor plates1 2

Figure 2.10: The adsorption equilibrium for the polarised carbonelectrode. Adsorption of organic compounds takes place inside thedouble layer (phase II).

The general isotherm equation can be written as:

)(θ= fKx B 2.22

where f(θ) is a certain expression for the surface coverage. For θ can be written:θ = q / qmax, with q the surface concentration and qmax the maximal monolayercoverage, both in mol/kg carbon. Because no Faraday reactions take place, theelectrical field can only influence the adsorption process itself. This is expressedby writing the equilibrium constant K as function of the electrical field:

)()()( θ=φ= fxKxEK BB 2.23

The surface equals a plate capacitor (Helmholtz model) that is being held at aconstant value φ (potentiostatic operation). It is important to realise thatadsorbing molecules change the average dielectric constant of the capacitor.The movement of two slabs of dielectric illustrates the process of adsorption.One slab represents the solute, the other the solvent. If B is preferentially


33

adsorbing, the solute slab B moves further inside the capacitor, pushing thewater slab out at the same time. The opposite occurs if it is A that ispreferentially adsorbing. See Figure 2.11.

x

d

dielectric slab(water)

organicspecies

F

V

counter ions

polarised carbon

Figure 2.11: Adsorption from an electrical point of view. Thepolarised interface is a parallel plate capacitor. Adsorption anddesorption are symbolised by slabs of water and organic movingbetween the charged plates. Water is pulled inside with force F.

Using electrostatics it is not difficult to determine the total amount of electricalenergy stored in the system. From the second law of thermodynamics it followsthat a system will always try to minimise its internal energy. For our capacitor(at a constant potential) the internal energy depends only on one variable: theoverall dielectric constant. Two situations are compared: 1) the area betweenthe plates is completely filled with the organic material, 2) the area between theplates is completely filled with water.

The electric field E is the same in both situations E1 = E2 = φ /d. The amountof charge q per m2 accumulated onto the Helmholtz capacitor was given in Eq.2.3. The total amount of charge is given by: Q1 = q1SB, with SB the surface areaneeded for one mole B to adsorb on. The electrical energy Uel,1 of the capacitorfilled with organic material is (Shen and Kong, 1983):


34

dS

EdSU BBrBBrel 2

2,02

1,021

1,φεε

=εε= 2.24

If the system goes from situation 1) to situation 2) the amount of charge storedwill increase because the dielectric constant of water is larger. All other variablesremain the same:

1,0

2,02 Qd

SESQ BAr

BAr >φεε

=εε= 2.25

The electrical energy of the capacitor increases as well:

1,

2,02

2,021

2, 2 elBAr

BArel UdS

EdSU >φεε

=εε= 2.26

Before concluding that Uel,2 > Uel,1 so that organic will replace water, it must berealised that the capacitor itself is not thermodynamically isolated as it isconnected to an external power source. The energy changes of this ‘battery’must be taken into account also. If water replaces the solute, the charge on thecapacitor increases from Q1 to Q2. The constant voltage battery spends storedelectrical energy equal to φ(Q2 - Q1) in order to do so. The total electrical energyof the whole system therefore equals the sum Uel,2 + Uel,batt where the latter is:

( ) ( )dSQQU B

BrArbattel0

,,2

12,εε−εφ−=−φ−= 2.27

The change in total electrical energy when the system is taken from 1) to 2) is:

( )

( )d

SU

dS

dS

UU

BBrArel

BBrArBArbattelel

2

22

0,,1,

20,,

2,0

,2,

φεε−ε−=

φεε−ε−

φεε=+

2.28


35

The total electrical energy of the system with water as its dielectric material issmaller than the energy with the organic compound as dielectric. The change inelectrical energy ∆Uel can be written as:

( ) ( ) 221

20,,

2φ−−=

φεε−ε−=∆ BA

BBrArel CC

dS

U 2.29

where Cx is the total molar capacity of x in F/mol. The important conclusion isthat water will always be pulled inside the plates and organic molecules will bepushed out. The net electrostatic force pulling is given by:

xUUF el

el ∂∂−=−∇= 2.30

The force vector points in the direction of the decreasing electrical storedenergy of the system. The tendency to exchange B for A is big if the differencebetween their dielectric constants is large and if the potential difference overthe capacitor is large.

2.3.2. From thermodynamics to kinetics

Because values for εr can be derived from molecular properties, the derivationof Eq. 2.29 is an important result as it allows one to predict the theoreticaleffects of a potential on the adsorptive behaviour. In order to do so the changein stored energy must be translated to a change in the equilibrium constant.

If one assumes the system is at constant temperature and thermodynamicallyreversible, the change in the Gibbs free energy going from 1) to 2) (desorptionof adsorbed component B) is equal to the change in internal energy. It is alsoequal to the total work done. To determine the amount of work we use thesame method as in Appendix A for describing contact adsorption of ions.Because the adsorbing molecules have no charge, the lateral interactioncontribution to the work is neglected. The two other contributions remain:

1) Chemical work arising from forces between electrode and ion.2) Electrical work arising from interactions of the ion with the electrical field.


36

Because the chemical work is considered independent from E or φ one has:

)()()( 000 φ∆+∆=φ∆+∆=φ∆ elchemelchemdes UUGGG 2.31

Using the law of mass action the change in Gibbs energy can be related to achange in the desorption rate constant:

)(ln)(0 φ−=φ∆ desdes kRTG 2.32

By combining Eq. 2.29, Eq. 2.32 and including the potential independent partof the Gibbs energy in the desorption constant k0,des, representing thedesorption rate constant if no field is present, one obtains:

( )

φ−

=

φ∆−=φ

RTCC

kRTUkk BA

desel

desdes

221

,0,0 exp)(exp)( 2.33

Combining Eq. 2.21 with Eq. 2.33 yields the equilibrium constant as functionof the potential:

( )

φ−−

=φRT

CCKK BA

221

0 exp)( 2.34

This equation is valid if the organic compound B has no permanent dipolemoment, such as benzene, or if the molecule does not adsorb in a specificorientation, resulting in no additional net potential drop. The term φN isincluded to account for such an extra potential drop:

( )

φφ+φ−−

=φRT

CCCKK NBBA

221

0 exp)( 2.35

Eq. 2.35 was first derived by Frumkin (1926) and gives the desired relationbetween K and φ. The potential dependent equilibrium constant can beincorporated in an appropriate isotherm equation in order to fit or predictexperimental electrosorption data, which is done in chapter 3.


37

2.4. Looking back

What is achieved in this chapter? The final result is the potential dependentisotherm equation. In general form it is written as in Eq. 2.23. The potentialdependency is included in the adsorption equilibrium constant K. The variationof the equilibrium constant is related to a change in Gibbs free energy of theadsorption reaction by the law of mass action (Eq. 2.35).

The change in the Gibbs energy is equal to the work done while replacing onemole of adsorbed B by A and it is also equal to the change in stored electricalenergy of the system (Eq. 2.29). The energy stored in the double layer dependson the total electrical capacity of the system and the applied potential (actually½Cφ2).

The capacity of the system is described by the Stern model (Eq. 2.7). The Sterncapacity is the reciprocal addition of the diffuse or Gouy-Chapman capacity(Eq. 2.5) and the compact or Helmholtz capacity (Eq. 2.19). The dielectricconstants for A and B appearing in these two models are calculated with theKirkwood formula (Eq. 2.18). The Kirkwood constant is set to a value of 1.5 toaccount for the differing conditions close to the solid surface.

The dielectric constant is related to the molecular polarisability of thecomponent. This is the result of three sources: electronic, atomic andorientation polarisation. The first two are proportional to the electrical field.The last one depends on the permanent dipole moment of the molecule as well.The amount of orientation polarisation can be calculated using the Langevinequation (Eq. 2.11). The variable x appearing in this formula gives the ratiobetween the aligning effect of the field against the randomising effects ofthermal motion. For small fields (below 109 V/m) a Taylor approximation canbe used, resulting in a constant dielectric value.

38

39

C H A P T E R 3

ELECTROSORPTION

ISOTHERM DATA

3.1. The potential dependent isotherm

3.1.1. Langmuir-like isothermsThe isotherm gives the relation between bulk and surface concentration. Thisrelation is usually based on model assumptions. In the simplest model everyadsorption site is equivalent, only monolayer adsorption occurs and nointeractions exist between molecules at adjacent sites. If the equilibrium in Eq.2.21 with ν = 1 is considered, the rate of adsorption of component B is foundto be proportional to the fraction of the surface not occupied by it (1-θ) and tothe bulk fraction xB. The rate of desorption is proportional to θ. At equilibriumboth rates are equal:

( ) θ=θ− desBads kxk 1 3.1

Replacing the kinetic constants kads and kdes with the potential dependentequilibrium constant (Eq. 2.22) gives:

BB xKKxf )(1

)( φ==θ−

θ=θ 3.2


40

The result is the Langmuir isotherm, often only useful as a first approximationor for simple systems. Parsons (1963), Delahay (1965, chapter 5), Gileadi (1967,chapter 1) and Damaskin et al. (1971, chapter 3) gave isotherms for morecomplex systems. A number of them are listed in Table 3.1. They can all bederived from the basic Langmuir isotherm by changing one or moreassumptions.

Name isotherm Equation f(θ)

Henry θ=

Langmuirθ−

θ=1

Langmuir (ν > 1)[ ]

ν

−ν

ν νθ−ν+θ

θ−θ=

1)1()1(

Volmer

θ−θ

θ−θ=

1exp

1

Helfand-Frisch-Lebowitz ( )

θ−θ−

θ−θ= 21

2exp1

Frumkin ( )θ−θ−

θ= a2exp1

Virial )2exp( θ−θ= a with a < 0

Temkin )2exp( θ−= a

Table 3.1: Langmuir like isotherm equations. The constant a isthe Frumkin interaction parameter that can be positive(attraction) or negative (repulsion).

For low surface coverage the Langmuir isotherm is identical to the linear Henryisotherm (1 – θ ≈ 1). If the adsorbed molecule B occupies more then one site(ν >1), the Langmuir isotherm becomes more complex (Gileadi, 1967 chapter1). The Temkin isotherm takes into account interactions between adsorbedmolecules. Each additional molecule will adsorb with less ease as the heat ofadsorption does not remain constant but changes (linearly) with coverage. TheVolmer and the HFL isotherms consider the adsorbed phase as a two


41

dimensional fluid of rigid particles. The Frumkin and Virial isotherms take intoaccount long-range interactions between adsorbed molecules that can beattractive or repulsive. Both the logarithmic Temkin and the Langmuir isothermcan be considered special cases of the Frumkin isotherm. Typical plots of theseisotherms are given in Figure 3.1 for phenol on activated carbon. Excluding theHenry isotherm, the Langmuir isotherm gives the highest surface coverage for acertain bulk concentration.

c [g/m ]3

θ [-

]

HenryLangmuir

Frumkin

Volmer

Virial

HFL

150010005000

0.5

1

Figure 3.1: Various isotherms for phenol on activated carbon.Parameters used: K = 0.00439 and a = -1.

3.1.2. The Freundlich isothermGenerally, the empirical Freundlich isotherm describes adsorption of organiccompounds on activated carbon better than the Langmuir-like isotherms. Anumber of attempts were made to provide the Freundlich isotherm with a moretheoretical background. Halsey (1952) and Rudnitski and Alexeyev (1975) couldobtain it from the Langmuir isotherm using the following assumptions:

1) The adsorbent surface is heterogeneous.

2) The site energies are distributed exponentially.

3) For all sites with the same energy a Langmuir isotherm is applicable.

Summation of all these Langmuir isotherms yields the Freundlich isotherm:


42

FnBF xKq = 3.3

with KF and nF semi-empirical constants and generally 0<nF<1. The Freundlichisotherm does not contain the equilibrium constant and hence is no function ofthe electrical potential. In order to describe electrosorption the isotherm mustbe modified. Because of the empirical nature of the isotherm it is simplyassumed that KF depends on the potential similarly to the equilibrium constant:

)()( φ∝φ KK F and nF is assumed to be independent of the potential. Theseassumptions are supported by the observation of McGuire et al. (1985) that KF

was much more sensitive to φ than nF.

In order to improve the fit of Langmuir type isotherms it is possible to use xn

instead of x. This results in Langmuir-Freundlich, Volmer-Freundlich etc.isotherms that tend to fit data much better, however at the cost of introducingan additional (empirical) fit parameter.

3.2. Fitting literature data

3.2.1. Loading versus potential curves

The electrosorption model (Eq. 2.36) predicts bell shaped curves when K(φ)and q(φ) are plotted versus φ. The position of the maximum depends on thepotential difference at open circuit conditions caused by adsorbed solutedipoles. For a neutral molecule, the open circuit potential will be close to zero.In Figure 3.2, the theoretical equilibrium loading of phenol on activated carbonas a function of φ is plotted for both the Langmuir and the Freundlichisotherm. The steepness of the loading curve depends not only on molecularproperties and characteristics of the double layer, but also on the type ofisotherm used. Increasing the φN value (in Eq. 2.36) will cause both a shiftingand an increase of the maximum surface loading of the carbon.

If the concentration B is high, the Langmuir isotherm becomes a horizontalline, the monolayer coverage qmax. In our electrosorption model the monolayercoverage is no function of the applied potential. This means that switching to ahigher potential no longer causes desorption of B. However the adsorption of


43

organic compounds on activated carbon usually shows a Freundlich type ofbehaviour. The Freundlich and to a lesser extend the Langmuir-Freundlich donot have the ‘problem’ of a constant, potential independent, monolayercoverage at higher concentrations.

Electrosorption enhances desorption but Figure 3.2 suggests it is possible toenhance adsorption as well, be it under certain conditions only. If the solute hasa permanent dipole and adsorbs with a specific orientation (not completelyrandom) this generates a potential difference. Applying an equal and oppositeexternal potential will nullify this and adsorption of the solute will be enhanced.If the solute bears a charge, the open circuit potential will be displaced moresignificantly. Negatively charged particles will be attracted to positive surfacesdue to coulombic interactions. The (contact) adsorption of ions is treated inappendix A.

200

400

-2 -1 0 1 2φ [V]

q [m

g/g]

800

600

0

Figure 3.2: The theoretical change in surface coverage as functionof the potential for two isotherms. Black lines, Freundlich (KF,0 =41.72, nF = 0.377), grey lines, Langmuir (K0 = 0.00439, qmax

= 710.2). Concentration is 500 kg/m3, φN = 0 and 1000 mVfor solid and dotted lines.

The collection of experimental electrosorption data available from literature isvery small. Most of the data is presented in the form of isotherms at variousapplied potentials. These isotherms can be converted to q(φ) curves by keepingthe bulk concentration constant and taking the corresponding surface loads for


44

all applied potentials. The bulk concentrations used were between ½ and ¾ ofthe maximum concentration reported.

0-0.5 0.5 1-1-1.5 1.5

1

0.5

0.75

1.25

0.25

0

φ [V]

θ [-

]

0-0.5 0.5 1-1-1.5 1.5φ [V]

10

5

7.5

12.5

2.5

0

θ [-

]

Figure 3.3a) and b): Overview of available electrosorption data inliterature. Series are scaled, for zero potential the loading is set tounity. In a): squares, phenol, McGuire et al. (1985); rectangles,naphtalenesulfonic acid anion; circles, benzylalcohol; plusses,methylquinolinium, Bán et al. (1998); pentagrams, o-nitrophenol, Chue et al. (1992); black diamonds β-naphtol,Alkire and Eisinger (1983b); white diamonds, 1,8-dichloro-9,10-anthraquinone; triangles, phenanthrene quinone, Strohl andDunlap (1972). In b): diamonds, 9-10-Anthraquinone-1-sulfonic acid; squares, 1.2-naphtaquinone-4-sulfonic acid, Strohland Dunlap (1972); triangles, EDA, Eisinger and Keller(1990).


45

The results are plotted in Figure 3.3a) and b). For better comparison, all seriesare scaled, by setting the surface loading to unity at zero applied potential. InFigure 3.3b) three data series are plotted that have a more strongly displacedmaximum of adsorption. From these, 9-10-Anthraquinone-1-sulfonic acid and1,2-naphtaquinone-4-sulfonic acid have a negatively charged group and theiradsorption is strongly enhanced if the carbon is positively charged. The thirdseries (EDA) does not show the (expected) bell shape. EDA adsorption is lowfor small potentials and increases for larger potentials.

An explanation for the anomalous behaviour of EDA could be the occurrenceof Faradaic reduction/oxidation already at low potentials. Eisinger and Keller(1990) did report that potentials of only +150 mV were sufficient to causeoxidation of EDA. An unaccounted for reaction interferes with determiningadsorption, as it is calculated from the difference in bulk liquid concentrationsbefore and after the experiment. Any reactions will contribute to the apparentadsorption.

The data series in Figure 3.3a) vaguely show a bell shape. Adsorption is highestaround zero potential and decreases with increasing potential. However, mostseries contain only a few data points or cover only one side of the bell. Thisstrongly reduces the reliability of the data. Despite the experimental uncertainty,an attempt was made to fit the data with the electrosorption model (Eq. 2.36).

In Figure 3.4 the results are presented for a selection of the data. Marksrepresent measurements of various authors, lines are calculated using theFreundlich isotherm with a potential dependent KF constant unless statedotherwise. The required KF,0 and nF,0 are taken from the reported open circuitisotherms and are summarised in Table 3.2. The displacement of the maximumφN is kept (close to) zero for neutral molecules. For charged molecules largevalues were needed to obtain a reasonable fit. Values for α, µ, ρ and M neededfor calculating the polarisability P and the dielectric constant are reported inTable 2.1 for water, phenol and benzyl alcohol. For the other components thefirst two properties had to be estimated. The error made by this estimation isrelatively small as the electrosorption Gibbs free energy only weakly dependson α and µ if the molecule is relatively large.


46

All Kirkwood constants are set to a value of 1.5 as was explained in chapter 2.The values for r, c and z regarding the supporting electrolyte are obtained fromthe various articles. Molecular dimensions are needed to estimate the thicknessof the first layer in the Helmholtz capacitor (Eq. 2.20) and to convertdifferential capacities into integral capacities. The following relations are used:

A

mol

NSr 2

1= 3.4

The molecular radius r depends on the molar surface area Smol, which in turn iscalculated from:

31

32

Amol NMS

ρ= 3.5

the molar mass M and the density ρ. The molar surface area depends on theorientation of the adsorbed molecule. Mattson et al. (1969) report a value of 0.4nm2 for planar adsorbed phenol, yielding an area of about 2.40·105 m2/mole.Eq. 3.5 predicts a value of 1.69·105 m2/mole, which is in the same order ofmagnitude.

While fitting the experimental data it was found that the measuredelectrosorption effects were always smaller then the theoretical effects. In orderto account for this, two efficiency factors are introduced. The first is the bedefficiency:

( ) )(1)( 0exp φη+η−=φ KKK 3.6

If the bed efficiency η is smaller than one, part of the packed bed electrode areais electrically inaccessible because the pore size is too small and there is notenough room for an electrical double layer. The adsorption equilibriumconstant in these parts of the bed (no changes in potential) remains K0. Forgraphite and glassy carbons η is probably higher than for activated carbonbecause of the more extensive micropore structure of the latter.


47

Another source of inefficiency is the loss of part of the applied potentialdifference due to ohmic resistances in the system. In order to compensate forthese, higher potentials have to be applied.

0.2

0.4

00 1-1

q [g

/g]

φ [V]

benzyl alcohol

methyl quinolinium

naphtalenesulfonic acid

N

CH3

+

CH OH2

SO3-

0 1-1

250

200

150

100

50

q [m

g/g]

φ [V]

phenol

phenolate

O-

OH

0

OH

β-naphtol

0 1-1φ [V]

1.5

1

0.5

0

K [1

0]6

2-2


48

O

O

phenanthrenequinone

Freundlich

Langmuir-Freundlich

50

100

0

capa

city

of b

ed [

ml]

0 1-1φ [V]

2

Figure 3.4a) to d) experimental data and model fits: a) threecompounds on activated carbon (Bán et al. 1998). b) phenol (andphenolate?) on activated carbon (McGuire et al., 1985). c) β-naphtol on glassy carbon (K values) (Alkire and Eisinger,1983b). d) Breakthrough curves of phenanthrenequinone (Strohland Dunlap, 1972).

In Figure 3.4a) three data series are plotted: The change in carbon loading asfunction of potential for benzyl alcohol (neutral), methyl quinolinium(positively charged) and naphtalenesulfonic acid anion (negatively charged). Thedisplacement of the maximum is perfectly illustrated. An extensive set ofvariables is needed to calculate the model lines: α, µ, ρ, M, kKW, rion, cion, z, KF,0,nF,0, φN and η. Parameters not found in literature (Weast and Astle, 1979) wereestimated. In Table 3.2 an overview is given of some of the values used toobtain a reasonable fit between electrosorption model and measured data. Anattempt was made to keep the two efficiency parameters as constant aspossible.

Figure 3.4b) shows electrosorption data for phenol. These data points cannotbe fitted adequately with our model. This could be the result of a Faradaicstimulated transition from phenol to the phenolic anion due to an increasinglypositive charged carbon. To illustrate this, two model lines are drawn in thefigure: One represents phenol, the other the phenolic anion. The onlydifference between the curves is a different φN value used.


49

Name component qmax

[g/kg]

K0

[varies]

nF,0

[-]η φ/φappl φN

benzyl alcohol - 0.4 0.29 0.75 0.5 -0.1

methylquinolinium 0.3255 2.25 0.127 0.75 0.5 -1.5

naphtalene sulfonic acid 0.375 2.75 0.0927 0.6 0.5 +1.9

phenol (1)

(2)

-

-

50

50

0.275

0.275

0.7

0.7

0.5

0.5

-0.3

+1.0

β-naphtol - 1.35E+6 - 0.77 0.5 +0.2

Phenanthrenequinone 86 500 0.015 1.0 0.5 +1.0

Table 3.2: Adsorption constants (Langmuir-Freundlich orFreundlich) and efficiencies used for fitting the experimental datain Figure 3.4.

In Figure 3.4d) experimental results from Strohl and Dunlap (1972) are plotted.The markers do not represent isotherm data, but column breakthrough curves.For small potentials, the column performance is much better than for higherpotentials, also the big plateau is remarkable. The Freundlich isotherm is unableto describe such a plateau but the Langmuir-Freundlich isotherm is.

A cautious conclusion from the fitting of these experimental results is that theydo not give a cause to doubt the validity of the electrosorption model. A moredistinct conclusion is not justified at this point considering the poor quality ofthe available data. It was found that the bed efficiency strongly influences theshape of the loading curve. At higher potentials K will become constant insteadof decreasing towards to zero. This feature can be used to estimate the bedefficiency from experimental results obtained at higher potentials.

Generally the changes in loading predicted by the model are too large. Theexperimental changes are a factor of two smaller. To explain this it is assumedthat half of the applied potential is lost due to ohmic resistances. A potentialthat is twice as high is needed to obtain the wanted result. Furthermore asubstantial part of the bed is considered electrochemically inactive. It can be


50

concluded that the experiments give about 40% of the effects predicted by ourtheory.

3.2.2. Physical feasibility of electrosorptionIt is important to establish the theoretical maximal effects that can be inducedon the adsorption equilibrium with an applied potential. The maximal potentialthat can be used is the potential where electrochemical conversion of wateroccurs. At standard conditions the thermodynamic potential difference toconvert water into oxygen and hydrogen gas is +1.23 V. The actual potentialdifference is higher due to over-potentials and ohmic losses (Prentice, 1991).Also the reaction can be kinetically hampered, proceeding at a very slow rate.To remain on the safe side however, applied potentials must not be too high toprevent electrolysis.

In order to benchmark the changes in adsorption equilibrium due toelectrosorption, they are compared to experimental chemical regeneration datapublished by Suzuki (1990). Suzuki reports isotherm data for phenol onactivated carbon in presence of methanol1. The methanol causes a decrease inphenol adsorption as can be seen from Figure 3.5. The experimental data isfitted with the potential dependent Freundlich isotherm. The potentials neededto produce the same decrease of the isotherm are calculated and shown in thegraph. The bulk concentration is assumed to remain at the same value. A singleconstant nF value was used and KF = KF(φ). Furthermore: φN is zero, η is set to100% and 0.5 N KCl is the fictive electrolyte.

The Freundlich isotherm with one potential dependent parameter fits theexperiments very well. The deviation at the 0% methanol series is due to theuse of an average nF value instead of the best value. The theoretical potentialsfor this idealised benchmark (100% bed efficiency) are, with exception of the100% MeOH line, below the maximum allowable potential (see also section

1 In a second text o-chlorobenzoic acid is mentioned instead of phenol. It is not clear which of the two texts is in

error so it is assumed that the experimental data represents phenol. Calculated model data for o-chlorobenzoicacid is in the same order of magnitude as for phenol but are far more uncertain because electrical propertiesare unknown and have to be estimated


51

4.1). Reducing the bed efficiency will of course increase the required potentialsor the installed surface area.

600

500

400

300

200

100

01000800600400200

cB [g/m ]3

q [m

g/g]

MeOH 0%

20%

40%

60%

80%

100%

0V

0.43V

0.67V

0.93V

1.15V

1.33V

φ

Figure 3.5: Adsorption isotherms for phenol on activated carbonin the presence of methanol. Dots are data reported by Suzuki(1990, chapter 9). The applied potentials give a similar decreaseof the isotherm due to the electrosorption phenomenon.

Comparison of methanol induced desorption and electro-desorption indicatesthat, at least in theory, the latter can be as effective a tool for regeneration asthe chemical method. Additionally, our model makes it possible to predict theisotherm for various potentials, using only the open circuit isotherm constantsand the molecular properties of the solute and the solvent.

3.2.3. Economical feasibilityElectrical energy requirements

Electrosorption has to be competitive with alternative regeneration techniques.This means that not only technical but also economic considerations determinethe success of the method. The energy requirements for electrosorption, apartfrom those needed for pumping and other secondary process operations can bedivided into two parts. Electrical energy is needed to:

• Polarise the surface of the packed bed electrode.

• Replace the adsorbed component (B) by water (A).


52

A schematic view of the regeneration process is given in Figure 3.6. In situation, the activated carbon is saturated with organic material B. Part of the surfaceremains covered with A, depending on the bulk liquid concentration and theadsorption equilibrium. If the packed bed is polarised situation is obtained.The polarising energy is given by:

221 φ= totcharge CU 3.7

After the desorbing potential has been established throughout the bed, watermolecules will replace part of the adsorbed organic molecules (situation ).

Charging Desorption

2 31

Carbonsurface

water

organiccompound

Formation of double layer Exchange of dielectricSaturated bed

Figure 3.6: Schematic picture of the carbon surface. Part of it iscovered with water and part with an organic compound. Twoenergy-consuming steps occur: formation of the double layer andreplacing the organic by water.

Not all B will desorb, some molecules will remain on the surface. Replacing Bby A alters the overall dielectric constant and hence the system capacity. Thechange in capacity requires an additional amount of energy equal to:

( ) 2,,2

1 φ−= BtotAtotdes CCU 3.8

Desorbing one mole of phenol

The amount of electrical energy needed to desorb one mole of phenol can becalculated using Eq. 3.7 and Eq. 3.8. The values of three variables as functionof concentration and applied potential are examined: Ucharge, Udes and m the


53

amount of carbon in the bed. This is the bed size from which exactly one moleof B will desorb. It is not equal to the molar surface Smol,B because the surfacecoverage is lower than unity and desorption of B is never 100%. Lower surfacecoverage and poor desorption characteristics increase the required bed size.

In order to describe a surface covered by a binary mixture the capacity modelhas to be refined. The surface is represented by two parallel capacitors. One forthe surface area covered with A, the second for the area covered with B. Seealso the left circuit in Figure 3.7. The relative size of both capacitors dependson the surface coverage of B.

B

Ctot,Bθ

Ctot,A(1- )θ

CH,B

CGCCH,A

CGC

A A A

A A

A

B

Figure 3.7: A polarised carbon electrode in contact with awater/phenol mixture is described by 6 capacitors. The topbranch represents the surface area with adsorbed B, the lowerbranch represents the surface area with adsorbed A.

In chapter 2 it was found that in order to describe the double layer moreaccurately, three capacitors in series are needed. Two capacitors for thecompact or Helmholtz double layer and one for the diffuse or GC double layer.This means that a total of six capacitors is required (the right circuit in Figure3.7). Only one of these six capacitors contains the dielectric B, the others are‘filled’ with water. The overall capacity can be calculated from:

+

θ−+

+

θ−

=

GCAH

B

GCBH

BBBETtot

CCCCqq

MSC 111

11

,

0,

,

0,

103.9


54

where q0 is the surface load at open circuit conditions and q1 is the surface loadif a potential is applied. Also:

BBET

BmolB MS

Sq ,00, =θ 3.10

The surface coverage must be determined experimentally before Eq. 3.9 can beused to calculate energy requirements. Suzuki (1990, chapter 9) provides thisdata. See section 3.2.2. The first term in Eq. 3.9 ensures that exactly one mole isdesorbing. SBET is the BET surface area of 1 kg activated carbon (assumed tobe 1.1 106 m2/kg). The CH and CGC represent the modified Helmholtz and theGouy-Chapman capacities. They are calculated using Eq. 2.36 and Eq. 2.5.

Results

The energy needed for charging the bed depends on the surface coverage andthe applied potential, whereas the energy needed to desorb B is a function ofpotential only. The surface coverage in turn depends on the isotherm used andthe bulk liquid concentration. In Figure 3.8 the energy requirements versuspotential and concentration are given. A higher concentration means a highersurface coverage and therefore less waste of charging energy.

0.4 0.6 0.8 1.0 1.2 1.4

5

10

15

20

25

30

35

00.2 200 400 600 800 1000 12000

c B [g/m ]3φ [V]

U

char

ge [k

J/m

ol]

cB is varied :[g/m ]3

1000750

500

250

φ is varied [ ]:V

0.430.67

0.93

1.15

1.33

Udes

Figure 3.8: The change of electrical energy with c and φ. Dottedline denotes the desorption energy, other lines the charging energy.

If the energy requirements are plotted against the potential, a minimum can beobserved around 0.65 V if cB = 250 g/m3. At higher concentrations no


55

minimum is found. If the applied potentials are small, a larger bed needs to beinstalled, increasing charging costs. This effect becomes even more pronouncedfor lower bulk concentrations. From the graphs it can be seen that energy costsgo down with decreasing potential. This is because the stored electrical energydepends quadratically on the potential (Eq. 3.7 and 3.8). A numerical overviewof the required surface area, charging and desorption energies is given in Table3.3.

cB [g/m3] →

φ [V] ↓

1000 750 500 250

Property

4.282 6.5 10.24 19.26 Ucharge [kJ/mol]

2.633 2.633 2.633 2.633 Udesorb [kJ/mol]

0.43

0.667 0.787 0.98 1.433 m [kg]

5.043 7.269 10.81 18.62 Ucharge [kJ/mol]

5.613 5.613 5.613 5.613 Udesorb [kJ/mol]

0.67

0.343 0.39 0.464 0.627 m [kg]

6.195 8.807 13.06 22.61 Ucharge [kJ/mol]

9.242 9.242 9.242 9.242 Udesorb [kJ/mol]

0.93

0.235 0.268 0.322 0.443 m [kg]

7.62 10.67 15.63 26.72 Ucharge [kJ/mol]

12.4 12.4 12.4 12.4 Udesorb [kJ/mol]

1.15

0.2 0.229 0.274 0.376 m [kg]

9.089 12.57 18.21 30.69 Ucharge [kJ/mol]

14.98 14.98 14.98 14.98 Udesorb [kJ/mol]

1.33

0.187 0.213 0.255 0.347 m [kg]

Table 3.3: Energy costs and installed amounts of carbon forelectro-desorption of one mole phenol at various bulkconcentrations and applied potentials.

The required charging energy needed to desorb phenol lies between 4.3 kJ/moland 30.7 kJ/mol. The desorption energy lies between 2.6 kJ/mol and 15kJ/mol, about one third of the total energy demand of 7 to 45 kJ/mol phenoldesorbed.


56

The actual energy needed for charging the bed is higher than this theoreticalamount because in real systems electrical losses will occur due to electricalresistances in the solid and the liquid phase. Higher potentials must be appliedto account for this. These do not change the amount of stored electrical energy,as the potential drop over the solid liquid interface remains unchanged.Furthermore the counter electrode must be charged. The total potential dropwill be distributed over the WE and the CE. If the electrodes are equal, thesame goes for the potential drop.

System configurations

The energy use of the system depends on configuration aspects as well. If theadsorption constant depends symmetrically on the applied potential and themaximum lies close to zero, it is better to use two packed beds instead of one.The first packed bed is our normal working electrode and the second bed is thecounter electrode. For a symmetrical dependence on the potential a positivelyand a negatively charged bed both reduce the adsorption constant to the sameextent. This means no energy is lost on faraday reactions at an inert counterelectrode. If two electrosorption units are used in series, part of the electricalenergy stored inside the double layer can be re-used. This stored energy of thefirst electrosorption unit can be used to polarise the electrodes of the secondunit (at most) halfway.

Conclusions and discussion

Eisinger and Keller (1990) reported energy requirements of 1.5-4.3 kWh per kgEDA depending on process configuration for the recovery of one mole ofEDA from brine solution. This translates to 216 - 620 kJ/mol EDA. Thesevalues are 15-30 times higher then found for the electrosorption of phenol inthis work. It must be stated that EDA loading on activated carbon was a factorof 10 lower then that of phenol at higher bulk concentrations. Also it isuncertain if evaporation costs for the concentrated EDA effluent were includedin their calculation. None the less, their energy costs seem to be rather high.For comparison, heating an amount of water containing 10% phenol from298K to 373 K, requires about 300 kJ/mol phenol.


57

3.3. New electrosorption data

3.3.1. Experimental details: Materials usedThe carbons used in this work are ROW 0.8 SUPRA from Norit N.V. (TheNetherlands) and Ambersorb® Carbonaceous Adsorbent type 572 from Rohmand Haas co. (USA). The ROW 0.8 SUPRA is an extruded type of activatedcarbon with a diameter of 0.7 to 0.8 mm and lengths between 3 and 10 mm.The Ambersorb 572 is a granular synthetic carbon made from a highlysulfonated styrene-divinylbenzene precursor. The beads are between mesh sizes20/50 and possess an excellent mechanical strength. No attrition could beobserved for the Ambersorb 572 where the ROW 0.8 SUPRA did producesome fine carbon dust easily. Additional precautions had to be made in order toprevent the carbon powder to interfere with the analytical UV method.

Surface areas of the carbons were determined using adsorption of nitrogen. TheBET areas found were 780 m2/g for ROW and 1150 m2/g for Ambersorbclose to the reported values of the manufacturer. For Ambersorb a particledensity of 0.49 g/ml and a micro/meso/macro pore porosity (in ml/g) of 0.41,0.19 and 0.24 was reported by the manufacturer. Although the Ambersorb israther hydrophobic compared to activated carbons from a natural precursor,spontaneous wetting of the pores with water did occur.

All chemicals used were obtained from Merck Company. The phenol and thebenzyl alcohol were both P/A grade (>99%). The KCl was extra pure grade(99%). The water used to make the solutions is reverse osmosis water that hasbeen de-ionised prior to use.

3.3.2. Experimental details: The set-upOpen circuit isotherms were measured using a batch method. In a thermostaticbath, held at 298 K, a number of sample vials were rotated slowly head overtail, see also Figure 3.9. The slow speed ensured that the carbon particlesmoved from top to bottom twice during each rotation. The movement of thecarbon enhances the contact with the liquid phase, greatly reducing the time toreach equilibrium, to about half an hour. The residence time in the bath was


58

however at least 12 hours. All vials were filled with the same liquid containingsmall amounts of benzyl alcohol or phenol. The amount of carbon addeddiffered per vial. After equilibrium was reached, the remaining organicmolecules in the solution are determined by measuring the UV adsorption at254 nm using an UV photospectrometer from Pharmacia Biotech, type UV-1.

thermostated bath

Figure 3.9: Side view of the batch set-up for determining opencircuit isotherms. Each vial contains the same solution and adifferent amount of carbon. The movement of the carbon particlesduring rotation ensures good mixing.

In order to measure the influence of the electrical potential on the adsorptionequilibrium a different set-up is required. The cell must allow for good electricalcontact between carbon particles and external circuit. A number of cells weredesigned and tested before the final set-up evolved.

A schematic overview of the set-up used is given in Figure 3.10. The tank isfilled with 0.5 N KCl electrolyte and can be stirred. Nitrogen gas is added to theliquid to remove dissolved oxygen. A peristaltic pump pumps the brine throughthe cell and then back to the tank. The cell itself contains two packed beds: theworking (WE) and counter electrode (CE). Both are connected to an Amelgeneral-purpose potentiostat, type 2051, that is used to set a certain potentialdifference between the WE and the reference electrode (RE). If no referenceelectrode is present, the RE outlet is connected directly to the CE outlet.


59

Otherwise the RE is an Ag/AgCl electrode with an external 3 N KCl solutionreservoir, supplied by Metrohm. The amount of current that flows through theapparatus is monitored by the potentiostat or by an additional ammeter(Keithley multimeter or picoammeter) that can be included in the circuit.

V

A

Cell

data

PC

UV - spectrometer

Mixing tank

potentiostat

Ammeter

N gas2

addition of pollutant

peristaltic pump

WE

CE

RE

Figure 3.10: The experimental set-up used for determiningelectrosorption isotherms. A small amount of solvent is added tothe mixing tank. After equilibrium is obtained, more solvent isadded. This is repeated 5 - 10 times to construct an isotherm.

In the small cell, shown in Figure 3.11, both beds are separated by a glass fritbut are in contact with the same liquid. The bed diameter is 52 mm and the bedthickness is about 5 mm. For the large cell, shown in Figure 3.12, a NAFION®450 membrane separates the working and the counter electrode. The counterelectrode is connected to a separate mixing tank and separate fluid circuitcontaining no organic compound. The bed diameter for the large cell is 90 mmand the thickness between 5 and 10 mm.


60

glass frit

WE

CE

Pt-wire

glass wool

liquid in

liquid out

carbon bed

Figure 3.11: Close up side view of the small electrochemical cellfor determining electrosorption isotherms. Glass wool is used toreduce the bed porosity. Platinum wire is used as current collector.

membrane holderRE connector

filter

CE leadconnector

graphiteplate

Carbon bedmembranebolts

liquid inlets

liquid outlets

RE connector

crosssection

WE CE

Figure 3.12: Close up view of the large cell. A Nafion 450membrane separates both beds. This way any asymmetry of theloading curve can be investigated. The beds can be mechanicallypressed. Current collectors are graphite disks on the outside of thebeds.


61

A pulse of benzyl alcohol or concentrated phenol solution can be added to themixing tank. At the same moment the measurements start and the decrease inconcentration is monitored online with the UV photospectrometer. To this enda second, peristaltic pump is used to continuously pump a small flow from tankto UV, and back again. The measured currents and absorption signals areconverted to voltages, collected and stored by a data acquisition unit connectedto a personal computer.

3.3.3. Experimental details: ProceduresFor each new measurement fresh carbon is used. The compartments in thesmall cell can hold 5.5-7 g of carbon. For the large cell this is 20-25 g. Incombination with the small cell 4 litres of electrolyte are used, for the large cellthis is 20 L. After filling the electrodes, the potentiostat is set to a specific valueup to 1.5 V. Next the apparatus and carbon are rinsed by 4 or 20 L of 0.5 KClfor at least 24 hours. This is done to remove impurities and carbon dust fromthe bed, to allow time for the double layer to form and charging currents to dieout and to make sure that the carbon beds are free of entrapped air.

To obtain the first point of the isotherm, the washing liquid is replaced by freshelectrolyte solution. A certain amount of benzyl alcohol or phenol is then addedto the mixing tank. Part of the added impurity will adsorb on the activatedcarbon and (pseudo) equilibrium is reached within a few hours. The recordedcB(t) and i(t) data are stored in the computer. The final concentration is notedand a small liquid sample is retrieved for later (batch) analysis. Then a new pulseof solute is added in order to determine a second point of the isotherm. Thisprocedure is repeated 5 to 9 times in order to get the isotherm over a broadconcentration range. After the isotherm at the set potential has been derived,the whole measurement is repeated a number of times for different potentials,two different solutes (phenol and benzyl alcohol) and two different carbons.

3.3.4. ResultsBatch experiments

With the batch set-up, up to ten isotherm data points can be produced at thesame time, therefore the measurement is completed within 24 hours. The data


62

obtained with the batch set-up was found to be very sensitive to experimentalinaccuracies. Furthermore it can only be used for determining open-circuitisotherms. Relative errors are in the order of 50% and a significant percentageof the data yielded nonsense. Attempts to improve the reliability of the methoddid not succeed completely. ‘Purified’ results are shown in Figure 3.13.

phenol on Norit ROW 0.8 SUPRA

phenol on Ambersorb 572

benzyl alcohol on Ambersorb 572

phenol (Suzuki, 1990)

phenol (Tien, 1994)

1 10 100 1000 1000010

100

1000

c [g/m ]3

q [m

g/g]

Figure 3.13: Results obtained with the batch method. Points aremeasurements from this work, lines are reported isotherms fromliterature.

Although a log scale is used, the scatter in the data is still significant. Forcomparison two isotherms equations reported in literature (Suzuki, 1994; Tien,1990) are plotted in the same graph. The data seems to be in the same order ofmagnitude.

Continuous experiments

From the packed bed configuration (Figure 3.10) much better data is obtained.The disadvantage of this method is that it also takes far more time to determinethe complete isotherm. All data points must be measured one after the other,determining an isotherm takes one to two weeks. An example of the outputobtained with this set-up is shown in Figure 3.14.


63

10 20 30 400

t [ks]

1

2

3

4

5

6

7

8

UV

sign

al [m

V] current [m

A]

2.0

1.6

1.2

0.8

0.4

0

(a)

(b)

Figure 3.14: Typical result obtained using a flow through cell: (a)current, (b) concentration.

Both the current and the concentration as function of time are recorded forapproximately 10 hours. The concentration curve (b) clearly shows the initialaddition of benzyl alcohol. After 8 hours about 95% of the adsorptionequilibrium is reached and the liquid concentration becomes constant. Thecharging curve is not a horizontal line but shows a peak at the beginning of themeasurement, indicating a change in the electrical properties of the system.

This change seems to be related to the changes in bulk concentration as bothhave the same time dependency. If absolute changes in concentration are large,the current flowing through the system is also high. In chapter 2 it was shownthat the system capacity changes when component B is adsorbing. In chapter 4it will be shown that this results in a charging current. The occurrence of massand charge transfer at the same time will be examined in chapter 7.

The charging current does not decrease to zero but to a constant value of 0.4mA. The reason for this is a phenomenon called streaming-current. Thephysical background of this phenomenon and experimental data are presentedin chapter 7.

Benzyl alcohol on Ambersorb 572

The solid phase concentration q was calculated from the difference in initial andfinal bulk concentration. To get the isotherm the solid concentration was


64

plotted versus the bulk concentration. Isotherms where measured for a numberof different potential drops. The results for benzyl alcohol on Ambersorb 572can be seen in Figure 3.15. The following conclusions were drawn: Changingthe potential changes the position of the isotherm. If the applied potentialbecomes –500 mV or lower, the isotherm starts to decrease after an initialincrease. This decrease is more pronounced if the potential is lower.

For a simple one component system, a decreasing isotherm is in variance withthermodynamics. It means that if more benzyl alcohol is added to the bulkphase, more adsorbed benzyl alcohol will desorb. This result is illogical andsome error must have been made and overlooked.

0

50

100

150

200

250

300

350

0 200 400 600 800 1000 1200

cB [g/m ]3

q [g

/kg]

-100 mV-300 mV

-500 mV-600 mV-800 mV

Figure 3.15: Adsorption isotherms for benzyl alcohol onAmbersorb 572. Decreasing isotherms were found.

GC-FID analysis of the samples revealed traces of benzaldehyde in the mixture.It seems that some of the benzyl alcohol is oxidised to form benzaldehyde. Theoverall reaction is:

OHCH22 OCH2+ O (aq)2 + 2 H O2

A small amount of oxygen is dissolved in the electrolyte. This oxygen allows theconversion of the alcohol- to the aldehyde group by taking the remainingprotons. The concentrations of benzaldehyde found in the samples were


65

relatively low, only a few percent of the benzyl alcohol was converted. Thiscould not explain the large deviations of the isotherms.

Analysis of the UV spectrum of benzaldehyde revealed that at 254 nm theabsorption was 88 times higher than that of benzyl alcohol. As the UV methodcannot discriminate between the various molecules absorbing, all contributionsare added. The resulting too high absorption leads to too high apparent liquidconcentrations. Because the solid concentration is calculated from the changesin liquid concentration it can explain the decreasing isotherms. The increasedproduction of benzaldehyde at higher potentials suggests an electrochemicalcontribution to this process although the potentials applied are relatively lowfor Faraday reactions to occur.

cB [g/m ]3

q [g

/kg]

0

50

100

150

200

250

300

350

0 200 400 600 800 1000

-100 mV

-300 mV

-500 mV

-600 mV-800 mV

Figure 3.16: Adsorption isotherms for benzyl alcohol onAmbersorb 572 for oxygen free conditions.

All isotherm measurements for benzyl alcohol on Ambersorb 572 wererepeated while applying a nitrogen atmosphere to the system. Bubblingnitrogen gas through the solution was found to remove almost all dissolvedoxygen from the system and hence the oxidation of benzyl alcohol is prevented.The obtained results are shown in Figure 3.16.


66

cB [g/m ]3

q [g

/kg]

0

50

100

150

200

250

300

350

0.1 1 10 100 1000

-100 mV-300 mV-500 mV-600 mV

-800 mV

Figure 3.17: As Figure 3.16 but on a semi-log scale.

Removing the oxygen prevents the reaction to benzaldehyde. The decreasingisotherms have disappeared but unfortunately with it most of the potentialdependent effects. A bell shaped decrease of the surface loading, as function ofthe applied potential was not found and no other trend could be abstractedfrom these data. The large effects of the potential on the adsorptive behaviourof benzyl alcohol found by Bán et al. (1998) could not be reproduced.

300

250

200

150

100

50

0

cB [g/m ]3

q [g

/kg]

0.1 1 10 100 1000

500 mV

-500 mV

0 mV

-1000 mV

open circ

1000 mV

-1500 mV

Figure 3.18: Electrosorption isotherms for phenol on Ambersorb


67

Phenol on Ambersorb 572

The experiments described above were repeated with phenol instead of benzylalcohol and applied potentials were taken between –1.5 V and +1.0 V. Theresulting isotherms are plotted in Figure 3.18. A graph almost identical toFigure 3.16 was found. Obtained carbon loads were slightly lower than for thebenzyl alcohol. If the loads at a surface concentration of 500 g/m3 are put indecreasing order it is found that: +500 mV > +1000 mV > -500 mV > -1000mV > 0 V and open circuit > +1000 mV. The large effects reported byMcGuire et al. (1985) could not be reproduced.

300

250

200

150

100

50

0

cB [g/m ]3

q [g

/kg]

1 10 100 1000

open circ+1000 mV

Figure 3.19: Phenol adsorption on Norit ROW 0.8 SUPRA.

Phenol on Norit ROW 0.8 SUPRA

The last system examined was phenol adsorbing on Norit ROW 0.8 SUPRA.Only two lines were measured due to experimental difficulties. The carbon loadfor +1000 mV was found to be somewhat lower than the loading at the opencircuit potential.

Desorption experiments

A number of desorption experiments were done to check the validity of theisotherms measured. The bed was saturated with component B (phenol) priorto the measurement. After equilibrium was reached, the applied potential wassuddenly changed and the effects on the bulk concentration were monitored.


68

t [s]

UV

sign

al [A

BS]

0

0.5

1

1.5

2

2.5

0 4000 8000 12000 16000

Figure 3.20: As a result of suddenly switching off the appliedpotential of –1500 mV, the bulk concentration decreases 23%.The double layer no longer hampers adsorption of phenol.

It was found that some of these experiments produced hardly any change in thebulk concentration, while others gave larger effects than expected from thecorresponding isotherm measurements. The maximal effects found are in theorder of 20-25%. An example is the plot in Figure 3.20 where the bulkconcentration decreases 23% due to the enhanced adsorption of B.

φ [mV]

q [m

g/g]

0

50

100

150

200

250

300

350

-2000 -1000 0 1000

Figure 3.21: The loading of benzyl alcohol and phenol ontoAmbersorb 572 as a function of the applied potential. Nosignificant effects were found.


69

3.3.5. DiscussionIf the various results for q, obtained at identical bulk concentrations are plottedas function of the applied potential, the electrosorption model predicts a bellshaped function. Comparing Figure 3.2 to Figure 3.21 reveals that thesetheoretical effects could not be determined experimentally. Only a slightdecrease of loading with increasing absolute potential is visible.

3.4. Looking back

Theoretically the Langmuir type isotherms are the ideal choice for describingelectrosorption data as these isotherms contain the equilibrium constant. Thebiggest disadvantage of these isotherms, their poor fit with experimental data,can be solved by raising the bulk fraction x to the power of n, where 1 > n > 0.n However has only an empirical meaning.

The electrosorption model predicts a bell shaped dependence of the surfaceloading with applied potential. The position of the maximum is not fixed atzero applied potential but it can shift to more positive or negative potentials.An additional potential drop created by a specifically adsorbing component Bcauses this shift. If the component B has a free charge, the shift of themaximum will be more pronounced.

Plotting all available literature data in the same graph reveals a number ofthings. The data is generally of poor quality and only one potential ‘branch’ isusually examined experimentally. A bell shaped dependence is only visible ifone wishes hard enough to see it. Charged molecules indeed shift theirmaximum loading according to the theory.

Fitting these experimental data with the model gives reasonable results if theeffectiveness of the phenomenon is decreased. This is done by introducing abed efficiency (the fraction of the electrochemically accessible area and the totalarea) and assuming that part of the applied potential is lost due to ohmicresistances in the bed.


70

In order to benchmark the effects of the potential on the loading, they arecompared with the influence of added methanol to the bulk phase. It wasconcluded that the required potentials to achieve similar decreases of theisotherm are feasible. The theoretical energy requirements needed for desorbingone mole of phenol range between 4.3 and 30.7 kJ/mol.

It was attempted extensively to reproduce the electrosorption experimentsconducted in literature but with little success. Early erroneous effects suggesteda large influence of the applied potential on the adsorption of benzyl alcohol onAmbersorb 572. It was however discovered that the higher applied potentialscaused oxidation of the benzyl alcohol to benzaldehyde. These type of errorscan occur for adsorption experiments in a solid-liquid system as the solidconcentration cannot be measured directly (easily). Instead solid concentrationsare usually derived from changes in the bulk concentration so that unaccountedfor mechanisms, such as evaporation or Faraday reactions tend to increase theapparent total adsorption.

After special precautions where taken to prevent this, the influence of thepotential on the adsorptive behaviour diminished as well. Differences betweenisotherms obtained for various potentials are in the order of 10% at best,literature results could not be reproduced.

Two interesting features were encountered though. Desorption experimentssuggest a potential effect that is (somewhat) larger then the measured effectfrom the isotherms experiments. Furthermore, analysis of the current goingthrough the system suggests that the model for describing the electrosorptionphenomena is correct, as there seems to be a strong relation between theamounts of charge and mass transferred.

71

C H A P T E R 4

TRANSIENT ELECTRICAL

BEHAVIOUR OF PACKED BED

ELECTRODES

4.1. Introduction

4.1.1. Faradaic and non-faradaic processesTwo types of processes occur at electrodes: Faradaic and non-faradaic. Afaradaic process is characterised by the transfer of charges (electrons) across thecarbon-solution interface, causing oxidation and reduction reactions to occur.These reactions are governed by Faraday’s law, which means that the amountof chemical reaction caused by the flow of the current is proportional to theamount of electricity passed. For all electrochemical systems there is a range ofpotentials where no reactions occur.

Non-faradaic processes can also generate currents. The composition andstructure of the double layer region can change with changing potential or bulkcomposition, even in the potential range where no reactions are possible.Electrosorption is a ‘no charge transfer’ process and therefore non-faradaic.The only currents in the system under consideration are due the charging of thedouble layer. Modelling this charging current as a result of the gradualpolarisation throughout the packed bed electrode will be the aim of section 4.2.


72

4.1.2. Ideal polarizable and non-polarizable electrodesWhether a certain potential allows for faradaic reactions depends on the natureof the system (especially on the type of electrodes used). An electrode, whereno charge is transferred to the solution, regardless of potential, is called an idealpolarised electrode (IPE). No real electrode can behave like an IPE for allpotentials, but most can for limited ranges. The larger the range, the more idealthe electrode. Carbon is a relatively good IPE. Electrodes that do not or hardlyreact to a change in potential, but simply leak more or less charge, are known asnon-polarizable electrodes.

The simplest description of the electrical behaviour of a polarised surface is acapacitor, as was discussed in chapter 2. The equivalent circuit for a real surfacewith electrical losses is a shunt connection of a resistor and a capacitor, seeFigure 4.1. The difference between ideally polarizable and non-polarizable isnot of kind but of degree.

C

R

liquid phasesolid phase

Figure 4.1: The equivalent electrical circuit for a realsurface contains a resistor and a capacitor. If R goes toinfinity, the surface is ‘ideally polarizable’. If R goes tozero, the surface is ‘non polarizable’ or ‘reversible’. The Cis the overall capacity, including Helmholtz and Gouy-Chapman contributions.

4.1.3. Properties of a carbon packed bed electrodeThe structure of the carbon electrode is not just a flat two-dimensional surface.The packed bed electrode consists of a large number of granules. The macro,meso and micro pores inside these granules contribute to the electrode surface.Some parts of the surface are harder to reach for both ions and electrons (gaps)


73

than others. The physical dimensions of the bed determine its electricalbehaviour. The total surface area contained in one cubic meter of packed bedelectrode is expressed by the following formula:

( ) BETpbed SVA ρε−= 1 4.1

with V the volume of the bed, εbed the bed porosity, ρp the particle density andSBET the BET surface area per gram of carbon. Because the total surface area isvery large, the total capacity is very large, in the order of 100 F/g carbon. Thisresults in some unexpected phenomena as will be shown. The surface area thatis actually used for electrosorption, e.g. the area that is electrochemicallyaccessible, is probably smaller than the BET area. The micropores contributemost to the BET, but some are too small for double layer formation. Anymolecule adsorbed within these pores is not subject to a change in potential.This problem was solved in chapter 3 by introducing the bed efficiency.

Due to electrical resistances, the potential within the electrode is not constantand not equal to the externally applied potential. Instead a distribution ofpotential exists: The local potential is a function of both time and place.Because the local adsorption equilibrium depends on the local potential, thedistribution in the bed must be determined. Mathematical models for variouspotential distributions are derived in section 4.3.

It is difficult to determine potential distributions experimentally. To do this, anumber of probes have to be inserted in the bed, which is not an easy task dueto the small distances generally involved. Another solution is to use theobservation that different potential distributions give rise to different chargingpatterns. Useful information can be obtained from the (external) response ofthe electrode to a sudden change in potential. The actual composition of thepacked bed electrode remains a black box governed by two parameters only, anoverall capacitance C and an overall resistance R. By comparing theexperimental transient behaviour with calculated responses for variousdistributions, the most likely distribution can be determined. Experimentalresults are discussed in chapter 5. The following sections examine the use of


74

simple equivalent circuits to simulate the external response of a non-dimensional electrochemical system containing at least two packed electrodes.

4.2. The non-dimensional electrode

An equivalent circuit containing resistors and capacitors can be used to modelthe electrical behaviour of an electrochemical cell. Three cases are considered.In the first case (section 4.2.1) the cell under consideration contains two packedbed electrodes that are both identical and IPE’s. In the second case (section4.2.2) the charging current for a system with two identical electrodes that areidentical but non-IPE’s is calculated. In the third case (section 4.2.3) a systemwith two non-identical, non-IPE is looked examined.

4.2.1. The response of two identical IPE’sA circuit containing two identical IPE’s can be transformed to a circuit withone overall capacitor and one overall resistor, using the specific addition rulesfor capacitors and resistors. The resulting equivalent circuit is shown in Figure4.2. The total capacity is half of the electrode capacity, the total resistance is twotimes the electrode resistance.

∆φ

C

R

i(t)

Figure 4.2: Simplest RC circuit. C represents the workingand counter electrode. The resistance over the double layer isinfinite (IPE). R is the sum of all other resistances. If thepotential is changed a charging current i(t) will flow.

When the potential ∆φ is changed, a current i will flow until capacitor C haschanged the amount of charge stored. The time needed for the system to


75

respond to this change is governed by the characteristic time τ = RC. As a smallpacked bed electrode, can have a total capacity in the order of 1000 Faradseasily, the characteristic time for a system with total resistance of 10 Ω is 10000seconds. It will take more then 8 hours (3τ) before 95% of the charging currenthas died away. Because of this sluggish behaviour of packed bed electrodes,charging currents can be generated and analysed with ease (see also chapter 5).

A mathematical expression for the transient behaviour of a RC-circuit, can befound with Laplace transformation. In the Laplace or s-domain the variouscomponents of the circuit (capacitors and resistors), can simply be added usingtheir specific addition rules (Von Hippel, 1954; Bard and Faulkner, 1980). Forany circuit the required steps are:

1) Draw the appropriate RC circuit.

2) Get the total replacement resistance in the s-domain by adding allcomponents.

3) Transform Ohm’s law and fill in the expression for the replacementresistance. Rewrite the resulting i(s) function as fraction of two polynomials.

4) For the fraction: Split the denominator and factorise the numerator.

5) Transform this expression back to the time domain to get the function i(t).

This procedure can be applied to our problem. The RC circuit is shown inFigure 4.2. The total replacement resistance Rtot(s) is the sum of the resistanceand the reciprocal capacitance (Von Hippel, 1954; Bard and Faulkner, 1980):

sCRsRtot

1)( += 4.2

Ohm’s law transformed to the s-domain is:

)()( sRsis tot=φ∆ 4.3

The potential difference ∆φ is a so-called Heaviside-function. At t = 0 thisfunction has the value 0 and at t > 0 it has the value ∆φ. Transformation of the


76

Heaviside-function to the s-domain results in the 1/s term in Eq. 4.3. Bycombining Eq. 4.2 and Eq. 4.3 the following result is obtained:

+

φ∆=

RCsR

si 11)( 4.4

Eq. 4.4 is already in the desired form for step 5). Back substitution of Eq. 4.4 tothe time domain yields the desired i(t) relation:

−φ∆=RC

tR

ti exp)( 4.5

This well-known formula predicts an exponential decrease of the current after astep change in potential from 0 to ∆φ (See also Figure 4.5). The initial current att = 0 is determined by the resistor R. If t = 3τ the current is 5% of its initialvalue. If t goes to infinity, the current goes to zero. This is logical because thecircuit in Figure 4.2 is not an electrically closed one.

4.2.2. The response of real electrodesAlthough Laplace transformation is quite unneeded for the previous example, itcan be used for more complex RC circuits with relative ease. If the systemcontains two electrodes that are identical but not IPE, the associated equivalentcircuit is given in Figure 4.3.The procedure outlined in section 4.2.1 is followedagain. The total replacement resistance is:

sCR

RRRsR

dl

electrodetot+

+=+= 11)( 4.6

The electrode surface resistance Relectrode is connected (in series) to the externalresistance R. It consists of the shunt connection of C and the double layerresistance Rdl.


77

∆φ C R

i(t)

Rdl

Figure 4.3: RC circuit for two identical non-IPE’s. Rdl isthe resistance over the double layer. Because the circuit isnow electrically closed, the current will decrease not to zerobut to the constant value ∆φ/(R + Rdl).

Combining this result with Ohm’s law (Eq. 4.3) and rewriting the result in apolynomial form gives the following expression:

( )[ ]( )

++

+φ∆=++

+φ∆=

++

φ∆=

CRRRRss

CRsCRRRRCRRs

CRss

sCR

R

ssi

dl

dl

dl

dldldl

dl

dl

2

)(11/

11

/)( 4.7

Splitting the denominator and substituting b = (R + Rdl)/RRdlC yields:

( )

+φ∆+

+φ∆=

bsRbssCRRsi

dl

11)( 4.8

This factorised expression is in the proper form for back transformation:

( )[ ] ( )btR

btbCRR

tidl

−⋅φ∆+−−⋅φ∆= expexp11)( 4.9

Replacing b and simplifying gives the final result:


78

+−+

φ∆++

φ∆= tCRRRR

RRRR

RRti

dl

dl

dl

dl

dl

)(exp)(

)( 4.10

The result contains two terms, the first is time independent, the second is timedependent. This was expected beforehand. After the capacitor is fully charged,the circuit becomes a plain closed loop with resistances R and Rdl in series. InFigure 4.5 a plot of this function can be found. If Rdl goes to infinity, the timeindependent contribution becomes zero and the time dependent contributionbecomes equal to Eq. 4.4.

4.2.3. The response of two non-ideal, non-equal electrodesA cell contains two electrodes and not just one (the working electrode WE andthe counter electrode CE). If these electrodes have different properties (forexample a different surface area), the equivalent circuit must be alteredaccordingly. In Figure 4.4 the circuit for two non-IPE electrodes is given.

∆φCWE

R

i(t)

RWE

CCE

RCE

Figure 4.4: General applicable RC circuit containing aworking and counter electrode that are non-IPE and notequal.

The total replacement resistance for this circuit is:

CEdlCE

WEdlWE

totCEtotWEtotsC

RsC

R

RRRRsR+

++

+=++=

,,

,, 11

11)( 4.11


79

It is formed by three elements, the two electrodes and the external resistance.Combining Eq. 4.3 with Eq. 4.11 gives:

CECE

CE

WEWE

WE

RsCsR

RsCsRsR

si

++

++

φ∆=

11

)( 4.12

Collecting all terms with s in the numerator and the denominator yields:

CECEWEWE

CECEWEWE

WEWEWEWE

CECEWEWE

CEWE

CECEWEWE

WEWECECECEWECECEWEWE

RCRC

RCRCRCRC

RCRRCRRR

RCRRCRCRRCRRRCRRC

e

d

c

b

cbsssedss

Rsi

1

2

2

:with )(

)(

=

=

=

=

++++φ∆=

+

++

+++

4.13

In order to transform this expression to the time domain, the denominatormust be factorised and the fraction must be split in three parts. The roots s = αand s = β for the equation s2 + bs + c = 0 are given by the ABC formula.Hence:

β+α++

β+α++

β+α+φ∆=

))(())(())(()(

ssse

ssd

sss

Rsi 4.14

The three fractions appearing in Eq. 4.14 can be transformed to the timedomain, resulting in the following three expressions:

(1) [ ])exp()exp(1 tt β−β−α−αβ−α

(2) [ ])exp()exp( ttd β−−α−α−β


80

(3) [ ])exp()exp()()(

tte β−α−α−β+β−αβ−ααβ

Combining these and rearranging gives the desired expression:

β−

β−αβ+β−β−α−

β−αα+α−α+

αβφ∆= )exp(

)()exp(

)()(

22

tedtedeR

ti 4.15

It can be seen that two exponential terms appear in Eq. 4.15, which means thatthere are two characteristic times associated with the circuit in Figure 4.4, onefor each electrode. In order to further investigate Eq. 4.15, simplifications aremade in order to see if Eq. 4.5 and Eq. 4.10 can successfully be derived from it.If it is assumed that the double layer resistances are infinite, they can beremoved from the circuit. The system is now expected to behave according toEq. 4.5. If RWE = RCE = ∞, the constants in Eq. 4.13 become zero except for b= (CWE + CCE)/RCWECCE. The time independent part (no leaking current) andthe exp(-βt) term in Eq. 4.15 become zero as well. The remaining expression is:

+−φ∆= tCRCCC

Rti

CEWE

CEWEexp)( 4.16

Eq. 4.16 is found to be equivalent to Eq. 4.5 because the replacement capacityfor two capacitors in series is equal to C = CWECCE/(CWE + CCE).

A second simplification is made. If it is assumed that both electrodes are equalbut not IPE it means that: RWE = RCE = Rdl and CWE = CCE = C. Applying thisto simplify the constants in Eq. 4.13 and after recalculating α and β thefollowing result is obtained:

+−

+φ∆+

+φ∆= t

CRRRR

RRR

RRRti

dl

dl

dl

dl

dl

2exp2

22

)( 4.17

If 2Rdl is replaced by Rdl and C by ½C, Eq. 4.9 becomes Eq. 4.10. The chargingcurrent as predicted by Eq. 4.5, Eq. 4.10 and Eq. 4.15 are plotted in Figure 4.5.If a semi-logarithmic scale is used, Eq. 4.5 produces a straight line. The other


81

two lines become constant for high t values. The effect of using a circuit withtwo different electrodes instead of a single replacement electrode is relativelysmall, especially if the electrode with the larger capacitance has the lowestdouble layer resistance.

1000

100

10

1

0.1

0.011000 2000 3000 40000

t [s]

i(t)

[mA

]

Eq. 4.5

Eq. 4.10

Eq. 4.15

Figure 4.5: Charging current for all three cases. Theparameters used are: ∆φ = 1 V, R = 2 Ω, C = 250 F.For Eq. 4.10: Rdl = 600 Ω. For Eq. 4.15: RWE = 200Ω, RCE = 400 Ω, CWE = 350 F and CCE = 875 F. Ifthe values for RWE and RCE are interchanged, the outputfrom Eq. 4.15 will coincide with that from Eq. 4.10.

It can be concluded that the Laplace transform is a good tool for acquiring thecurrent response based on a certain equivalent circuit. If the number ofcomponents in the circuit increases, the mathematical derivation becomesrather lengthy however. On the other hand, most circuits can be simplifiedextensively using the specific addition rules for resistors and capacitors in orderto define replacement resistors and capacitors. Most circuits can be reduced tothe one shown in Figure 4.3. The main disadvantage of this method to describea packed bed electrode is the inability to use it for calculating the potentialdistribution inside the electrode. It can only be used to calculate the externalresponse of the system. The potential distribution is however required forcalculating the local adsorption coefficient.


82

4.3. The dimensional electrode

4.3.1. Equivalent circuit of a packed bed electrodeThe real porous electrode is a three-dimensional packed bed. The potentialdistribution inside this bed can be described mathematically with one-dimensional, two-dimensional or three-dimensional formulae, depending on thetype of current collector that is used. The main function of the current collectoris to connect the electrode to the external circuit. If it has no dimensions, like awire point, the potential distribution in the bed is three-dimensional. If thecurrent collector is one-dimensional (a wire) or two-dimensional (a gauze or aplate) the potential distribution in the bed is two- or one-dimensional. The two-dimensional case is considered here.

RL

Rpore

RM

Rdl

x

z

porouselectrode

electrolyte

Rlead

C

Figure 4.6: Two-dimensional representation of a packedbed electrode. For a description of the variables see the text.


83

Figure 4.6 shows an extensive two-dimensional circuit representing the packedbed electrode. The x coordinate gives the position relative to the pores:Increasing means further inside. The z coordinate gives the distance from thecurrent collector. The polarised electrode surface is described by an infiniteamount of series each containing an infinite number of capacitors. Resistorsseparate the series and the capacitors. Each individual capacitor represents asmall part of the chargeable solid-liquid interface. Associated with eachcapacitor m is a characteristic time τm that increases with m because the overallresistance is a (linearly increasing) function of m. As a result, capacitors locatedfurther from the current collector will charge slower than those nearby.

In Figure 4.6 five different resistors can be identified. The Rlead resistorrepresents the resistance of wires, current collectors and other exteriorequipment. Normally these are rather small. The RM resistors represent the solidresistance of the packed bed. Rpore indicates the liquid resistance inside the pores.RL indicates bulk liquid resistance and Rdl the double layer resistance. Thefollowing simplifying assumptions are made:

• The working electrode is identical to the counter electrode.

• The double layer resistance is infinite.

• The solid matrix is much more conductive than the liquid phase and itselectrical resistance can therefore be ignored.

• Lead resistances can be neglected with respect to other resistances.

• All pores are parallel and positioned perpendicularly to the chargingelectrode and they are fully accessible for double layer formation.

Applying these assumptions simplifies the circuit shown in Figure 4.6: and thecircuit shown in Figure 4.7 is obtained. If Laplace transformation, as outlined insection 4.2.1, is applied to these m resistors in series (or m capacitors in shunt)the current response for a step change in potential is found to be:

+−

+φ∆=

m poreLporeL CmRRt

mRRti

)(exp)( 4.18


84

Rliq

∆φ Rpore Rpore Rpore

C C C C

Figure 4.7: Simplified, one-dimensional infinite-resistors-in-series model for the packed bed electrode.

In this formula the currents of m RC circuits are summed. The contribution ofthe circuits with large m values can be neglected for all but very large processtimes. Because Eq. 4.18 does not contain the place coordinate x, it cannot beused to calculate the potential distribution inside the bed. For this a differentapproach is needed.

4.3.2. No Losses modelFigure 4.8 visualises what happens during the charging of an idealised packedbed electrode. The current density lines represent the gradual build-up of thedouble layer. The solution potential is a function of time and position but thesolid phase potential is a constant because the solid resistance is assumed to bezero. Because all pores are identical, the process of charging can be describedby a one-dimensional equation.

The charging current i(t) was derived in Eq. 4.18. Starting point for thederivation of the i(t,x) function is Eq. 2.2. Rewriting the charge on the electrodeqM in terms of the current gives:

ttxCtxi

∂φ∆∂= ),(),( 4.19


85

φM

φM-φL(x,t) =∆φ(x,t)

i(x,t)porePolarizing

Electrode

0

i(x,t)

0 1xξ

L

Porous Electrode

Figure 4.8: Charging of a porous electrode with idealisedpores (one-dimensional and perpendicular to the workingelectrode). The externally set potential will slowly penetratethe pores.

Because of the finite conductivity of the solution phase, the passage of currentintroduces a gradient of ∆φ(x,t) over the length of the pores. The Daniel-Beckequation gives the distribution of potential inside the pore (Posey andMorozumi, 1966). For the one-dimensional case it can be written as:

),(),(2

2

txiA

Lx

tx

pore⋅

κ=

∂φ∆∂ 4.20

where κpore is the conductivity of the liquid inside the pores, A is the averagecross sectional area of the electrolyte in the electrode and L is the length of thepore (electrode). Using a dimensionless bed length ξ = x/L and combining Eq.4.19 and Eq. 4.20 yields the following result:

2

2

2

2 ),(1),(),(ξ∂

ξφ∆∂τ

=ξ∂

ξφ∆∂κ=

∂ξφ∆∂ tt

CAL

tt pore 4.21

This is the fundamental relation for charging the double layer in a one-dimensional porous electrode. In order to solve Eq. 4.21 a set of appropriateboundary conditions are required. The potential on the front side of the bed is


86

equal to the externally applied step (prescribed). For the backside of the bed aNeumann (no flux) boundary condition is applied:

( ) 0, ;),0(1

=

ξ∂ξφ∆∂φ=φ∆

=ξ

tt ext 4.22

If the bed is uncharged in the beginning, the initial condition is ∆φ(ξ,0) = 0.Posey and Morozumi (1966) derived the analytical solution for this system:

( ) ( )∞

=

τπ+−ξ−π+

+−

π−=

φξφ∆

0

2221

21

21

)(exp)1()(cos)(

121),(

m

m

ext

tmmm

t 4.23

With Eq. 4.23 the potential can be calculated as a function of time, place andexternal potential. If it is plotted versus the dimensionless bed length ξ for fourdifferent t values, the graph in Figure 4.9 is obtained. It can be seen that if t ≈ τ,the potential inside the bed has almost reached its set value of one volt. Notethat the additional term –(m + ½)2π2 appearing in the exponent of Eq. 4.23reduces the system response with respect to the characteristic timesencountered before.

∆φ [

V]

ξ [-]

0.01 τ

0.1 τ

0.5 τ

τ

0.5

1

010 0.5

Figure 4.9: The potential distribution in the bed duringcharging. The external potential is switched from 0 to 1 V,the characteristic time is 1000 s.


87

4.3.3. Carbon resistance not zero: internal lossesIn actual applications the carbon matrix resistance can not always be neglected.The electrical properties of the packed bed differ from those of the carbonitself (chapter 5). A lower conductivity is caused by poor inter-particle contacts.Applying pressure to the bed can improve the situation (also chapter 5).

In the previous section it was assumed that RM << Rpore. In this section it isassumed that RM ≈ Rpore. In Figure 4.6 it can be seen that the Rpore and RM

resistors are situated on different branches of the electrical circuit. Transport ofcharge in the carbon matrix is due to movement of electrons and in the poresdue to movement of counter ions. No charge can cross the interface becausethere are no Faraday reactions. This however does not imply that ions in theliquid can move independently from the electrons in the solid phase! Theelectro-neutrality principle dictates that for each excess electron present at thesurface, a compensating positive ion must be in the liquid nearby. This meansthat the electrical resistances in the carbon and the liquid act as if they are inseries: Both retard the formation of the double layer. Tiedemann and Newman(1975) considered these resistances to be parallel, but we do not agree with theirpoint of view. The expression for the overall replacement resistance is:

totLMpore

Mpore

totleadLMporelead A

dALRRRRRR

κ+

ε−εκκε−κ+εκ

+=+++=)1(

)1(4.24

The pore, solid and bulk liquid conductivities are given by κpore, κM and κL

respectively. The boundary conditions change as well:

∂φ∆∂τ=

ξ∂φ∆∂

∂φ∆∂τ−=

ξ∂φ∆∂

=ξ=ξ tt 21

10

; 4.25

Two characteristic times appear in the boundary conditions. They are related tothe pore resistance and the solid resistance respectively. Posey and Morozumi(1966) give the analytical solution for Eq. 4.21 with these boundary conditions:


88

( )

τ−ξ−+ξγ−=

φξφ∆

mm

mm

mm

ext

tYYY

YYt 2exp)sin(

)1(cos)cos(21),( 4.26

Here Ym is the positive root of the equation cos(Ym) = -γ, with γ the ratio of thesolid and pore phase resistances (Erdélyi, 1954; Posey and Morozumi, 1966).When γ is zero, the ‘no losses’ solution from section 4.3.1 is obtained. UsingEq. 4.26, ∆φ versus the dimensionless bed length can be plotted. This is donein Figure 4.10 for two different values of γ.

0.5 10ξ [-]

γ = 0.99

00.5 1

1

0.5

0ξ [-]

∆φ [

V]

0.005 τ0.05 τ

0.25 τ

0.5 τ

γ = 0.1

0.5 τ

0.25 τ

0.05 τ

0.005 τ

Figure 4.10: Influence of the solid phase resistance on thepotential distribution inside the bed. When significant, thebackside of the electrode will charge before the interior.Potential step and characteristic time similar to Figure 4.9

It can be seen from the right graph that the backside of the bed is chargedfaster than the interior of the bed. This is because two resistances prevent thetransport of charge to the interior of the pores and only one the transport tothe backside. This behaviour becomes more pronounced if the γ value is larger.

4.3.4. Liquid ohmic resistance: external lossesIf an ohmic resistance exists between reference/counter electrode and workingelectrode, part of the potential difference will be lost. In the experimental set-updescribed in chapter 3, the liquid ohmic resistance is in the order of 0.1 – 1.0ohm. The potential lost depends on the product iR and generally is 2 - 20 mV.The actual driving force for charging the bed is therefore lower than the appliedpotential difference, which in turn effects the potential distribution. This


89

problem is mathematically analogous to the problem of heat radiation lossesfrom a slab that is being heated. Carslaw and Jaeger (1959) have derived andpublished many analytical solutions for these types of problems. Heat radiationinto the surroundings is incorporated by using an appropriate mixed boundarycondition for the front side of the bed (Posey and Morozumi, 1966):

ttxt

∂φ∆∂τ−φ=φ∆ ),(),0( 0 4.27

The boundary condition for the end of the bed remains the same (see Eq.4.22). The resulting analytical solution is (Posey and Morozumi, 1966;Tiedemann and Newman, 1975):

[ ]( )( )

( )λ

=

λ+λ+

τ−ξ−

−=φξφ∆

1tan of root positive th the with

)cos()sin(1

exp)1(cos21),(

2

0

mmm

m mmmm

mm

XXmX

XXXX

tXXt

4.28

0

1

0.5∆φ [

V]

0.5 10ξ [-]

λ = 0.2

0.005 τ0.05 τ

0.25 τ

0.5 τ

λ = 1.0

0.5 10ξ [-]

0.5 τ

0.25 τ

0.05 τ0.005 τ

Figure 4.11: Influence of the loss parameter λ on thepotential distribution. Other conditions similar to Figure4.9.

The parameter λ is a measure of the amount of potential drop that is lost in thebulk liquid phase. It is defined as the ratio of liquid resistance to total resistance(Erdélyi, 1954; Posey and Morozumi, 1966; Tiedemann and Newman, 1975).The higher λ becomes, the higher the losses. If λ goes to zero, Eq. 4.28 reduces


90

to 4.23. If the liquid resistance is high, λ is large and the electrode charge will bemuch lower due to the lower local potential drop. It can be seen from Figure4.11 that for increasing λ values the potential distribution becomes more flat.

4.3.5. Validating models, charging currentsIn order to validate the three distribution models, it is most convenient tocalculate the resulting charging currents during polarisation of the bed. Thecharging current is related to the change in potential at the front of the bed.According to Ohm’s Law the latter must be differentiated towards ξ anddivided by the total resistance:

0

),(1)(=ξ

ξ∂ξφ∂−= t

Rti 4.29

Applying this for the three models results in the wanted charging currentexpressions. They can be found in Table 4.1. For all cases a function is obtainedthat contains an infinite sum of exponents. A similar result was found by thedirect Laplace transform method (Eq. 4.18). The infinite sum appearing is dueto the infinite amount of resistors in series. Only a few terms in the sumcontribute to the current, except for very small values of t. For long times onlythe first term is important. Because no information on Ym and Xm can beobtained from experiments, they are used as fit parameters.

Due to the utilisation of the prescribed boundary condition, some numericalstability problems where encountered for the no losses-model. The cosine formof the analytical solution (shown in Table 4.1) converges rather poorly for smallt values. For these cases the Taylor form is better. For time periods up to 0.1 s,a summation over 50 terms gives a good enough result, however. In this work avalue n = 200 is used for numerical calculations so no stability problems ornumerical caused deviations are to be expected.


91

Equation No Losses model

Boundary

conditions( ) 0, ;),0(

1

=

ξ∂ξφ∂φ=φ

=ξ

tt ext

Potential

distribution( ) ( )

∞

=

τπ+−ξ−π+

+−

π−=

φξφ∆

0

2221

21

21

)(exp)1()(cos)(

121),(

m

m

ext

tmmm

t

Transient

current

∞

=

τπ+−

φ=

1

2221 )(exp

2)(

m

ext tmR

ti

Internal Losses model

Boundary

conditions

∂φ∂τ=

ξ∂φ∂

∂φ∂τ−=

ξ∂φ∂

=ξ=ξ tt 21

10

;

Potential

distribution

( )

γ−=

τ−

ξ−+ξγ−=

φξφ∆

)cos( of root positive th the is where

exp)sin(

)1(cos)cos(21

),( 2

mm

mm

mm

mm

ext

YmY

tYYY

YYt

Transient

current

τ−

φ=

mm

ext tYR

ti 2exp2

)(

External Losses model

Boundary

conditions( ) 0,;

),(),0(

1

=

ξ∂ξφ∂

∂φ∂

τ−φ=φ=ξ

t t

txt ext

Potential

distribution[ ]

( )( )

( )λ

=

λ+λ+

τ−ξ−

−=φ

ξφ∆

1tan of root positive th the is where

)cos()sin(1

exp)1(cos21

),(2

mmm

m mmmm

mm

ext

XXmX

XXXX

tXXt

Transient

current λ+λ+

τ−

φ=

m mmm

mmext

XXX

tXX

Rti

)cos()sin()1(

exp)sin(2

)(

2

Table 4.1: Mathematical overview of the three distributionmodels and the resulting charging currents.


92

4.4. Looking back

In this chapter electrical resistances were considered for the first time. Togetherwith the capacitors introduced in chapter 2 they account for the electricalbehaviour of the system. The first resistance encountered was that across thedouble layer. A small double layer resistance results in a reversible electrodewhile a high resistance results in a polarizable electrode. The solid-liquidpotential drop of the former can not be altered easily because excess charge willsimply leak into the solution. Besides this so-called faradaic current, also nonfaradaic currents can flow through the system, for instance due to a change insurface charge. It is this current that is of interest.

A typical packed bed electrode made up of activated carbon granules hasproperties unlike any normal electrode. It has a very large surface and thereforea very large electrical capacity. As resistances in the carbon matrix and in theliquid in the pores can not be neglected, characteristic times are even larger,resulting in sluggish behaviour.

The external response of a packed bed electrode can be modelled byconsidering it a black box. The response to a step in potential for relativelysimple RC circuits can be analysed using Laplace transformation. It was foundthat more complex circuits can almost always be simplified to the basic circuitshown in Figure 4.3.

The presence of internal resistances leads to a potential distribution in theelectrode instead of a constant potential, equal to that applied externally. TheLaplace transform method cannot be used because of the lack of a spacialcoordinate. The concept of infinite resistances in series is used extensively inheat transfer problems. Analogous to the heat distribution in a slab of material,equations and boundary conditions for the potential distribution in an idealisedpacked bed electrode can be obtained. Applying different simplifyingassumptions leads to different analytical solutions. Three cases were considered:

No Losses model. Solid resistances are considered to be much smaller thanliquid resistances and are ignored. There are no ohmic losses between thereference and the working electrode. This means that the potential on the front


93

side of the bed is equal to the applied potential. A ‘no flux of potential acrossthe surface’ condition is used for the backside.

Internal Losses model. The resistance of the carbon phase is considered to beof the same order as the liquid resistance. Both retard the electric response andare in series. Again no ohmic losses between reference and working electrodeare taken into account. One boundary condition describes the solid matrixresponse, the other the liquid phase response.

External Losses model. The part of the potential lost due to ohmic resistancein the liquid between reference electrode and working electrode is substantial.This is incorporated using a ‘radiating boundary condition’ for the front of thebed. At the back again the ‘no flux across the surface’ condition is used.

The three potential distribution functions obtained can only be validatedexperimentally from the recorded charging current versus time. Therefore thepotential distribution must be converted to a charging current with the help ofEq. 4.29.


94

95

C H A P T E R 5

MEASURING ELECTRICAL

PROPERTIES

5.1. Transient experiments

5.1.1. Aim of the chapterIn order to obtain the local adsorption equilibrium, the potential distribution inthe packed bed must be calculated. If the bed is considered a homogeneousphase containing ideal (perpendicular) pores, the distribution functions (Eq.4.23, Eq. 4.26 or Eq. 4.28) from chapter 4 can be used to describe the potentialdistribution. Beforehand it is difficult to determine which of these models isbest. The ‘no losses’ model relates the local potential to two electrical propertiesonly: The total resistance R and the total capacity C of the system. In the othertwo models an additional loss parameter is used. For the internal losses model γdefines the ratio RM and R. In the external losses model, λ defines the ratio RL

and R. The total resistance was defined as the sum of lead, pore, solid andliquid resistances (Eq. 4.24).

Values of these electrical properties must be determined if the distributionmodels are to be validated with experiments. Lead and liquid resistances can bemeasured directly with the use of an ohmmeter or conductometer. The first


96

never exceed a few mΩ, but liquid resistances can be a few ohms, depending ongeometry of the cell and the salt concentration used.

local potential

distribution function

T&N plot

transientexperiments

selection of model & electrical properties

i√ t versus √ t

φ φas function of , time and placeext

Figure 5.1: Calculation of the local potential requires values ofelectrical properties. These can be derived from experimentaltransient current data.

The resistance of the electrode material (carbon) can be measured directly, butrequires a special set-up (see section 5.3.1). The electrical capacity and the poreresistance cannot be measured directly but they can be derived from theexternal transient behaviour of the system. In chapter 4 it was found that largesurface electrodes only slowly respond to changes in applied potential. Chargingcurrents take hours to fade out and can therefore be measured with ease. Thecharging current can be fitted directly using the calculated i(t) functions derivedfrom the three distribution models, which are listed in Table 4.1 and Table 5.1.Alternatively the data can be converted to a so-called T&N plot (Tiedemannand Newman, 1975). In a T&N plot i(t)√t is plotted versus √t in order to obtaina parabolic curve that improves the fitting procedure.

5.1.2. Experimental set-upThe system shown in Figure 5.2 is used to determine the response to stepchanges of 10 mV in addition to a certain base potential, following Zabasajjaand Savinell (1989). No linear voltage sweeps are used (Alkire and Eisinger,


97

1983b; Eisinger and Keller, 1990). The computer stores the resulting chargingcurrent between the WE and the CE.

transientdata

PC

WE CERE

V

A

potentiostat

Ammeter

N2

gas for mixingand dearation

porousgraphite tube

activated carbon granules

top viewelectrode

electricalcell

16 mm26 mm

550 mm

10 mm

Figure 5.2: Experimental three electrodes set-up for conductingtransient experiments. The Ag/AgCl RE electrode is filled with3 N KCl. Both WE and CE are porous graphite tubes filledwith 6-7 g AC. A step of 10 mV is superposed on a constantpotential. The electrolyte is 0.5 N KCl

Various electrical cells, similar to the one depicted in Figure 5.2, have beenused. They consist of one or two connected glass or perspex tubes with adiameter of 50 mm and a length of 500-550 mm. The cell can be filled with 0.5N KCl solution. Nitrogen gas can be bubbled through to replace dissolvedoxygen and provide a means of stirring the electrolyte. The working and thecounter electrodes are identical smooth graphite porous tubes (previously usedas support for catalytic membranes) with a 6 mm inner and 10 mm outerdiameter. The inner area can be filled with activated carbon particles. It takes 5to 6 g of activated carbon to fill a tube. The electrical resistance of the drygraphite tube was measured and determined at 1.68 Ω /m tube length.

If used in the experiment, the reference electrode is located close to theworking electrode on the far side of the counter electrode. It is an Ag/AgCl


98

electrode supplied by Metrohm. Surrounding the silver metal is a reservoir filledwith 3.00 N KCl solution. Its potential versus the Standard HydrogenElectrode is 0.222 – 0.059 log cCl- or 0.194 V (Prentice, 1991).

The potentiostat is from Metrohm, type E611 and its potential setting can bechanged in steps of 1, 10 or 100 mV. Base potentials used ranged from –600 to+600 mV. The current generated by the potentiostat in order to maintain its setpotential was measured and recorded using a Keithley, type 2000, multimeter.Charging currents were typically in the order of 10-0.1 mA following a stepchange of 10 mV. These values indicate that the total resistance in the systemmust be in the order of an ohm.

Before starting an experiment, it was ensured that the system was in electrical(pseudo) equilibrium. Residual currents had to be smaller than 5% of the initialcurrent. A large number of experiments was conducted in order to assess theinfluence of various system parameters such as: reproducibility, step size,behaviour of empty tubes, base potential, salt concentration and effects ofadded traces of organic compounds. Only a small portion of the collected datais presented below.

5.1.3. T&N plotsA typical current versus time plot is shown in Figure 5.3. Two graphite tubesfilled with 6.17 g of Ambersorb 572, are subjected to a change in appliedpotential of 10 mV. The initial current generated by the potentiostat is 8.76 mA.After 2500 seconds it has decreased to 0.79 mA. An exponential fit functionwith 3 variables can fit perfectly either the first or the last part of the data.

More information is obtained if a so-called T&N plot is used: i(t)√t is plottedversus √t. This is done in Figure 5.4. The resulting curve has a parabolic shapewith a maximum at 25 s½, or 625 s. The data is fitted with the transient currentfunctions derived from the three potential distribution models (Table 5.1).From Figure 5.4 it follows that only the external losses model can describe theexperimental data. The slight deviations at the beginning of the experiment arecaused by an initial overload of the electrical equipment. Those at the end aredue to residual currents still present from earlier experiments.


99

10

25002000150010005000

fit function:y=a+b*exp(-x/c)

a = 0.2041447b = 4.2083001c = 1241.0489r = 0.9962

i [m

A]

t [s]

graphite tubeAC = 6.17 g

= 10 mV∆φ8

6

4

2

Figure 5.3: Response of graphite tube filled with activated carbonto a potential change of 10 mV. Base potential is +500 mV.

0.06

0.02

0.04

0.08

03020 40100 50

i(t)

i [A

s]

1/2

t [s ]1/2

no losses

internal losses

external losses

Figure 5.4: T&N plot for the data from Figure 5.3. Only theexternal losses model is able to describe all of the experimentaldata.

From this result it was concluded that the assumptions of the no losses and theinternal losses models are in variance with actual bed behaviour. Both modelsare no longer considered in the remainder of this work.


100

From the fit of the external losses model with the experimental data, the valuesof the electrical properties can be extracted. The resistance and thecharacteristic time depend on the λ value that is chosen. If λ = 0.5, R = 2.7 Ωand τ = 1699 s. If λ = 1, R = 1.69 Ω and τ = 1029 s. Higher λ values result inlower values for τ and R but their ratio (the total capacity) remains constant(here 611 F).

Model Expression for transient current1) No losses model

∞

=

τπ+−

φ=

1

2221 )(exp

2)(

m

ext tmR

ti

2) Internal losses model

γ−=

τ−

φ=

∞

=

)cos( where

exp2

)(1

2

m

mm

ext

Y

tYR

ti

3) External losses model

λ=λ+λ+

τ−

φ=

∞

=

/1)tan( where)cos()sin()1(

exp)sin(2

)(1

2

mm

m mmm

mmext

XXXXX

tXX

Rti

Table 5.1: Transient current functions as derived from the threepotential distribution models. For their derivation see section 4.3.

If Eq. 4.5 (which does not contain the loss factor λ) is used to fit the same data,the following values can be derived: R = 2.269 Ω en τ = 1355 s. The externallosses and the black box models yield the same values if λ = 0.7 is chosen. Thecontribution of the liquid resistance to the total resistance is significant.

5.2. Results

5.2.1. ReproducibilityThe reproducibility of transient current experiments is good. Variation betweenduplicate experiments is in the order of 5%, but occasionally errors of 20% orhigher were found. This can be explained by the constant deterioration of theelectrical contacts (clamps). The combination of salt water and electricity causesalmost all metals to corrode very quickly. Corrosion leads to poor electricalcontacts, and to significant increases in R and therefore τ.


101

5.2.2. Effects of step sizeThe effect of the potential step size was examined by comparing T&N plots for1, 5 and 10 mV steps. The only observable effect was the increase of the i(t)curve by a factor of 5 or 10 respectively (see Figure 5.5), which is predicted bythe model. Because the form of the curve hardly changes it was concluded thatfor potential differences below 10 mV, C and R do not depend on φ. Theslightly deviating first seconds of the 10 mV line are due to an initial overloadof the potentiostat.

0

0.01

0.02

0.03

0.04

0 5 10 15 20 25

t [s ] 1/2√

i(t)

t [

A s

] 1/

2√

∆φ: 1 mV

∆φ: 5 mV

∆φ: 10 mV

Figure 5.5: Effect of potential step size on the T&N plot forporous graphite, base potential is +300 mV.

5.2.3. Behaviour of empty tubesThe electrical response of empty graphite tubes was studied and compared withthat of tubes filled with activated carbon to determine the contribution of thegraphite. A typical transient response for porous graphite is shown in Figure5.6. The charging current declines fast due to the small specific surface of thegraphite tubes. After 150 s most of the graphite surface is polarised. Thegraphite BET area was experimentally determined to be 3.5 m2/g. An emptygraphite rod weighs 44 g and has a surface area of 154 m2.

Graphite electrodes behave more ideally than the activated carbon electrodes ascan be seen from their transient data. Fitting it gives much better results. The


102

line in Figure 5.6 is from a three-parameter exponential fit function. Whencompared with Eq. 4.10, it follows that the Rdl = ∆φb/(a(a + b)) = 11.07 Ω, R= ∆φ/(a + b) = 0.843 Ω and the total capacity for this system is C = 31.7 F, orfor one electrode C = 63.4 F. If it is assumed that the BET surface of theporous graphite is completely accessible for the electrical double layer, thedifferential capacity has a value of 0.285 F/m2.

60 120100200

6

10

14

8

12

4

0

i [m

A]

t [s]

fit function:y=a+b*exp(-x/c)

a = 0.8396951b = 11.017695c = 26.72178r = 0.9952

graphite tubeAC = 0 g

= 10 mV∆φ

2

40 80

Figure 5.6: Response of empty graphite tubes to a potential changeof 10 mV. Base potential difference is -300 mV.

The calculated double layer resistance seems rather low. A possible explanationis that residual currents from earlier experiments cannot be distinguished fromfaradaic currents and both contribute to a higher offset of the transient current.This is expressed by a higher fit constant ‘a’ and it results in a lower Rdl.

5.2.4. Effect of surface areaIf the graphite tubes are filled with activated carbon, the total surface areaincreases fifty-fold. The BET surface areas for Norit ROW 0.8 SUPRA andAmbersorb 572 were experimentally determined to be 782 and 1183 m2/gcarbon. In Figure 5.3 the response of a graphite tube filled with Ambersorb wasplotted versus time and due to the much larger characteristic time the chargingprocess requires more time. From fitting the data, the total resistance is foundto be 2.26 Ω and the double layer resistance 46.7 Ω. The total resistance is


103

about twenty times lower than the double layer resistance. This was found formost experiments. However, this constant ratio can be an experimental artefactas a new experiment is started after residual currents are 5% of the initialcurrent.

The total capacity for the system in Figure 5.3 is 576 F, so 1152 F for oneelectrode. The total surface of 6.17 g Ambersorb is 7300 m2. The differentialcapacity is therefore 0.158 F/m2. This value is roughly half of the graphitedifferential capacity, probably due to electrochemically inaccessible microporesin the activated carbon matrix.

Although the differential capacity for the porous graphite is two times highercompared to Ambersorb 572, its effect on the total capacity of the system canbe safely neglected. The total surface area of the graphite is only 155 m2, whilethe Ambersorb surface is more than 7000 m2.

5.3. Variation of process conditions

Both the resistance and the capacity depend on a number of system properties.A number of these, including mechanical pressure, the electrolyteconcentration, base potential, concentration of organic compound, areexamined.

5.3.1. Mechanical pressureThe electrical resistance of a packed bed of carbon particles is not the same asthe resistance of the particles itself. To measure the effective resistance ofparticle, a special clamp was constructed. It was found that these measurementsdid not gave very accurate data. Relative errors were in the order of 200% dueto the small size (< 5 mm) and brittle character of the particles. There was astrong influence of the force applied to the clamp. The electrical resistance of adry ROW 0.8 SUPRA particle was none the less estimated to be between 1 and5 Ω/mm particle length. These values seem extremely large compared toreported values for comparable carbonaceous products by manufacturers.


104

force( )mg

(optional)liquid in

(optional)liquid out

metal probes

stamp

carbon bed

teflon holder

distributionof probes

71 mm

10 mm

Figure 5.7: Experimental set-up used for determining theelectrical resistance of a packed bed. The bed height isapproximately 10 mm.

To estimate the electrical resistance of a packed bed of Norit granules, the set-up shown in Figure 5.7 was constructed. Within a holder made of perspex isroom for a carbon bed of 10 mm in length and 70 mm in diameter. Liquid can(optionally) be flown through the bed. The in- and outlet are separated fromthe bed by glass frit. The carbon can be pressurised with a perspex stamp thatmoves up and down freely. Placing weights on the stamp allows for variation ofthe pressure on the bed. At the bottom of the holder 9 probes of stainless steeland a diameter of 10 mm are present. These are used to determine resistancesat various points in the bed.

Resistances are measured with an RCL meter from Philips, type 6303A. About25 different probe combinations were examined in each experiment. The resultis a surface plot showing the electrical resistance as function of x and y co-ordinates. If more pressure is applied to the bed, resistances decrease as can beobserved from the four graphs in Figure 5.8.

Legend(all values in /mm)

128-160

160-192

192-224

224-256

256-288

288-320

320-352

>352112-128

64-80

80-96

96-11232-48

16-32

48-64

0-16

Figure 5.1: Changes in electrical resistance as function of increasingpressure. Measured per cm packed bed containing Norit ROW 0.8SUPRA. No liquid is present. Top left: 0 Pa. Top right: 900 Pa. Bottomleft: 5000 Pa. Bottom right: 33000 Pa.

105



106

The surface plot in the top left (no pressure) shows an average resistance forthe loosely packed bed between 100 and 200 Ω/mm. Within the bed largedifferences in local conductivity can be identified. The surface plot in thebottom right represents the bed under a pressure of 33 kPa and here the overallconductivity is much better. The high ‘mountains’ have almost completelydisappeared. A small amount of mechanical force can increase bed conductivitysignificantly but poorly conducting ‘cavities’ inside the bed are difficult toremove entirely.

The measured resistances can be compared to transient experiment results. Theelectrodes used are graphite tubes filled with carbon. The effective bed lengthfor charge transfer is half the inner tube diameter of 6 mm. Calculatedresistances are in the order of 3 Ω , hence 1 Ω/mm. From the direct resistancemeasurements, values at least 10 times higher, were obtained. The transientmethod is considered far better than the direct 2-point measurement, so the toohigh results of the direct method are discarded.

5.3.2. Electrolyte concentrationFor all experiments, a 0.5 N KCl solution is used as electrolyte. Without ions,no polarisation, no double layer and hence no electrosorption. If theconcentration of ions decreases, the capacity is expected to go down. TheGouy-Chapman model (section 2.1.3) predicts a gradual decrease (Figure 2.5)but the Helmholtz model is independent of the salt concentration, providedthat enough ions are available to form the double layer. In Figure 5.9 it can beseen that for ionic strengths below 0.1 N, the experimental determined capacitydecreases rapidly.

Both the liquid and the pore resistances depend on the ionic concentration(Figure 5.9). The conductivity (in S/m) of the liquid depends on the ionicstrength. The relation between the conductivity κL and RL is given by:

AdR

LL κ

= 1 5.1


107

where A is the electrode area and d the distance between the WE and CE. Theconductivity of a solution depends on the number of ions. This is expressed bythe molar conductivity Λmol:

ionmolL cΛ=κ 5.2

400

300

200

100

0.60.50.40.30.20.10

60

40

20

0

Capacity

Resistance

cion [mol/l]

R[Ω

] C[F]

Figure 5.9: The capacity and the resistance as function of the ionicconcentration. The characteristic time decreases slightly if the saltconcentration increases.

Kohlrausch’s law relates the limiting molar conductivity for an infinite dilutedsolution to actual molar conductivity:

210ionmm cΚ−Λ=Λ 5.3

with Κ the Kohlrausch constant. For KCl Κ = 71.66 S m2½/mol3½ (Atkins,1990 chapter 25). The limiting molar conductivity is the sum of contributionsfrom all individual ions. For a 1:1 electrolyte:

−+ λ+λ=Λ0m 5.4


108

R [

]Ω

2

4

6

0

cion [mol/m ]35004003002001000

d A/ m= 2.909 -1

WE CE

cion [mol/m ]3

R [

]Ω

5004003002001000

20

40

60

80

0

d A/ m= 48.545 -1

WE CE

Figure 5.10a) and b): Comparing the increase of the totalresistance obtained from transient current experiments to thetheoretical values predicted by Eq. 5.5. A constant (non liquid)resistance of 0.8 Ω is added as well.

For KCl, λ+ = 73.48 S cm2/mol and λ- = 76.31 S cm2/mol. The limiting molarconductivity is 149.79 S cm2/mol. The relation between Rliq and cion becomes:

Ad

ccR

ionionliq 2

366.7179.1491−

= 5.5


109

Eq. 5.5 is used to describe experimental resistances obtained from transientcurrent experiments at various salt concentrations. Two different cellconfigurations were used. For the configuration in Figure 5.10a), the electrodesare located 16 mm apart. The cell in Figure 5.10b contains a Nafion 450membrane between the WE and CE. As a result the factor d/A and the liquidresistance increase about twenty times.

The correlation between theory and experiment is reasonable as can be seenfrom the graphs. Again the (bulk) liquid resistance almost completely makes upfor the total resistance. The increase of the total resistance with decreasing saltconcentration can hence be explained as well. The pores are filled with liquid,so the pore resistance should be directly related to the bulk liquid resistance.Alkire and Eisinger (1990) calculated the pore conductivity from the bulkconductivity by correcting the latter for the tortuosity of the solid phase:

Lpore

porepore κ

ε−ε

=κ32

5.6

with εpore the particle porosity. It remains questionable whether a tortuositycorrection can describe the behaviour inside the smallest pores. The use of Eq.5.6 leads to a reduced pore conductivity (15-70% lower) and larger poreresistances. But there is also an opposite effect. Due to double layer formation,the salt concentration in smaller pores is higher than in larger pores, whichincreases the conductivity.

5.3.3. Base potentialThe capacity remains constant if changes in potential are kept smaller than 10mV (section 5.2.2). The potential swaps applied in an electrosorption processare much larger, in the order of a volt. Constancy of the capacity for these largedifferences is uncertain and needs to be examined. This was done byconducting multiple transient experiments while varying the base potential innine steps from –500 mV to +500 mV. The capacities obtained are plottedversus the potential. Two different electrode set-ups were examined: 1) emptygraphite electrodes and 2) graphite electrodes filled with Ambersorb 572.


110

The result for the porous graphite electrodes is plotted in Figure 5.11 for threeindependent series of measurement. From the graph it follows that the capacityis slightly lower near zero applied potential, but still largely independent of thepotential and averaging about 0.3 F/m2. Only the Helmholtz layer seems tocontribute significantly to the total capacity.

φ [mV]

C [F

/m2 ]

0.15

0.2

0.25

0.3

0.35

0.4

500 300 100 -100 -300 -500

Figure 5.11: Potential dependent capacities for porous graphite.Three measurement series are presented. The grey line is theprediction from the capacity model from chapter 2.

Evans (1966) determined differential capacities for both intermediate and highsurface graphite. He found values of 0.35 F/m2 and 0.19 F/m2 respectively.Alkire and Eisinger (1983b) measured the differential capacity for glassy carbonand found values between 0.067 and 0.093 F/m2. Oren et al. (1984) proposed atheoretical Helmholtz capacity for graphite between 0.15 and 0.20 F/m2, avalue they confirmed experimentally.

Starting with the Helmholtz model, theoretical differential capacities can beestimated. For an ideal parallel plate capacitor: C = ε0εr/d. If d = 0.656 nm andεr = 20, the capacity is 0.270 F/m2. Alternatively, the capacity equals theamount of charge on the plates divided by the voltage drop between them. Ifeach square nanometer of polarised surface contains 2 charges (electrons andcounter ions) and the potential drop is 1 V, there are 2 1018 ions per m2. Thisgives a capacity of 0.322 F/m2. Both estimations seem to indicate that


111

capacities up to 0.3 F/m2 are not unreasonable. The porous graphite used inthis work has mainly a mesopore structure, so size exclusion effects are notexpected for this material.

For the Ambersorb a similar graph was constructed. In Figure 5.12 it can beseen that the capacity of the Ambersorb is more potential dependent. Thedifferential capacity decreases with decreasing applied potential, a minimalcapacity is found at zero applied potential. At +500 mV the differential capacityis about two times higher than for 0 mV.

-500 500

0.2

0.1

00

φ [mV]

C [F

/m]2

pure waterbenzyl alcohol added

Figure 5.12: Potential dependent capacities for Ambersorb 572.The markers are measurements, the grey lines are modelpredictions from chapter 2. Dotted lines give the capacity if 50%of the surface contains adsorbed benzyl alcohol. The theoretical bedefficiency is set to 50% for the model lines.

The experimental capacity models derived in chapter 2 predict a lower capacitynear zero potential caused by the GC contribution. The experimental results inFigure 5.12 can be compared to the theoretical plots in Figure 2.5, Figure 2.7and Figure 2.11. It seems that theory and experiment do not agree much. Thecurves differ in shape, the experimental depression is stronger and broader thanthe theoretical one. Permanent charged surface groups shifting the local pointzero charge to higher absolute potentials might be the cause of this. Thesesurface groups however will reduce at the same time the depth of the dent evenfurther. A deeper dent would be encountered if the salt concentration in the


112

pores for some reason is lower then the bulk value of 0.5 N. This seems ratherunlikely.

Obtaining the differential capacity for activated carbon is a problem. Valuesreported in literature tend to vary a factor of five. Johnson and Newman (1971)report differential capacities up to 0.30 F/m2 while Eisinger and Keller (1990)report a capacity of 0.082 F/m2. Card et al. (1990) determined the differentialcapacities for three types of activated carbon to be 0.17, 0.42 and 0.58 F/m2.Their assumption is that a varying micropore depth is responsible for thesedifferences.

This broad range of values shows once more that there is no such thing as oneactivated carbon. There are many different types due to the nature of theprecursor material and the activation method used. The result is a collection ofmaterials that posses a large variations in structure, in pore distribution and inthe presence of surface groups. These properties can cause large differences inelectrical capacities.

Most authors report a single average capacity. From Figure 5.12 it can be seenthat the applied potential during the determination of the capacity is importantbut usually no information is provided about this. For metal electrodes thecapacity as function of the potential has been determined with high frequencymeasurements (Breiter and Dalahay, 1959; Wroblowa and Green, 1963; Gileadiet al., 1965). These data show large fluctuations in the differential capacity, bothas a function of potential and surface coverage. Breiter and Delahay (1959)found that increasing concentrations of n-amyl alcohol from 0 to 0.1 N causedthe differential capacity to decrease from 0.5 to approximately 0.05 F/m2 at aconstant potential close to zero. The electrosorption model from chapter 2predicts this behaviour, because the adsorbed organic molecules decrease theoverall dielectric constant of the polarised electrode (see also 5.3.4).

A constant potential method gives much more constant values (see Figure 5.12and also Alkire and Eisinger, 1990). Alkire and Eisinger report the differentialcapacity of graphite to vary not more than about 20%, between 0.067 and 0.093F/m2 over a range of 1 V. They also report that the adsorption of β-naptholbarely affected differential capacities.


113

Zabasajja en Savinell (1989) examined both graphite and activated carbonelectrodes and reported that only 5% of their carbon surface waselectrochemically accessible, whereas their graphite surface was totallyaccessible for double layer formation1. Constant differential capacities of 0.50F/m2 for the activated carbon and 0.12 F/m2 for the graphite were assumed.Johnson and Newman (1971) did something similar. They assumed atheoretical differential capacity of 0.30 F/m2 and reached the exact oppositeconclusion: most of their specific surface area was available for double layerformation.

0 -600-4002000

2

3

1

600

R [

]Ω

∆φ [mV]400 -200

3.5

2.5

1.5

0.5

Figure 5.13: The total resistance is independent of the potential.

Unlike the capacity, the resistance was found to be no function of the basepotential. In Figure 5.13 two different data series are plotted. No apparentinfluence is found.

5.3.4. Concentration of organic componentThe model for electrosorption, derived in chapter 2, predicts a decrease in thecapacity if component B (benzyl alcohol or phenol) is added to the electrolyte.Part of the benzyl alcohol will adsorb and as a result the overall dielectricconstant goes down. A lower dielectric constant leads to a lower total capacity 1 The problem is that both the differential capacity and the size of the accessible area are unknown. Only if a

value is assumed for one, can the other be calculated


114

of the system. Decrease of the capacity with increasing concentration would beevidence in favour of the electrosorption mechanisms proposed in chapter 2.

Electrical capacities were measured during electrosorption experiments (seesection 3.3.2 for the experimental details). Before a new pulse of benzyl alcoholwas added to the system, a transient experiment was conducted. The setpotential value (between –500 mV and +100 mV) was suddenly increased by 10mV. The resulting charging data was recorded. Fitting yields the total capacityand the total resistance as function of benzyl alcohol concentration. The resultsare plotted in Figure 5.14 for the relative change in capacity and in Figure 5.15for the relative change in resistance.

70006000500040003000200010000

140

120

100

80

60

40

20

0

c B [g/m ]3

C/C 0 [

%]

Figure 5.14: The total capacity as function of bulk liquidconcentration (after adsorption). The capacity seems to decrease(only) slightly.

A description of the cell that was used can be found in section 5.1.2. Thegraphite tube set-up was found to be perfect for transient experiments, butmass transfer of B from the quiescent electrolyte to the Ambersorb inside thetubes took too much time. Bubbling nitrogen gas through the solution gave toolittle radial convection. As a result the rate of adsorption was very low.


115

In Figure 5.14 the change in the differential capacity with respect to the initialcapacity is plotted against the bulk concentration. The best trend line throughthis cloud of points suggests a slight decrease in capacity with increasingconcentration, in the order of 5% although the fit is poor. The scattering in thedata is in the order of 20%.

c B [g/m ]3

70006000500040003000200010000

160

140

120

100

80

60

40

20

0

R/R 0 [

%]

Figure 5.15: The total resistance as function of bulk liquidconcentration (after adsorption). The scatter is higher than for thecapacities.

The same is done for the resistance in Figure 5.15. Scattering of data is evenhigher, in the order of 30-40%, resulting in an even lower R2. The trend linesuggests an even smaller increase of the resistance with increasingconcentration. The electrical conductivity of the liquid goes down if the fractionB increases. Because the liquid resistance was found to be a major contributorto the total resistance, this will have immediate effects on R. However thebenzyl alcohol only forms a small fraction of the liquid, even at the highestconcentrations.


116

5.4. Looking back

Experimental transient current experiments were found to be a good tool forobtaining electrode properties. Due to the large characteristic times, thesemeasurements are easy to monitor. Converting the data to T&N plots gavespecific shaped curves. By comparing them to the three potential distributionmodel outputs, it was found that only the external losses model was able to fitthe data accurately.

A number of variables were examined. The error in duplicate measurementswas usually 5 to 10% but could be up to 20%. Changing the applied potentialstep size between 1 to 10 did not gave unpredicted effects. By assuming a bedefficiency of one, the differential capacity for the porous graphite was found tobe 0.285 F/m2, and for Ambersorb 572 0.158 F/m2. This value is about twotimes lower and indicates that only half of the Ambersorb pore matrix isaccessible for double layer formation. The effect of the porous graphite on thetotal capacity can be neglected, as the specific BET surface of the graphite is155 m2 while that for the Ambersorb inside is more than 7000 m2.

The electrical resistances of packed beds were measured and compared to theelectrical resistance of the particles and the values calculated from transientexperiments. Transient experiments give values that are ten times lower thanthe particle resistance, and 100 times lower than the bed resistance. Increasingthe pressure on the bed indeed reduced its electrical resistance. The resultsobtained with the direct method must be regarded as being relatively only.

Reducing the electrolyte concentration reduces the capacity and increases theresistance in the system. The resistance of the liquid bulk phase is related to theconductivity of the electrolyte (Figure 5.1). This was shown using transientexperiment results. The fit between theory and experiment is reasonable.

The capacity remains constant if changes in potential are smaller than 10 mV(section 5.2.2). Constancy of the capacity for larger differences is uncertain andwas therefore examined. It was found that the capacity of porous graphite islargely independent of the potential, only slightly lower near zero appliedpotential, the average value is about 0.3 F/m2. The Helmholtz layer gives the


117

biggest contribution to the total capacity. The capacities determined forgraphite in literature are in the same order of magnitude but tend to besomewhat smaller. Theoretical considerations indicate that capacities up to 0.3F/m2 are not unreasonable. The capacity of the Ambersorb (Figure 5.12) ismuch more potential dependent. At +500 mV the differential capacity is abouttwo times higher than at 0 mV. Theory and experimental curves do not agreemuch. The experimentally found depression is stronger and broader for reasonsunknown.

Reported values for the differential capacity of activated carbon vary a factor offive. Probable because different types of carbon have been used, with differentproperties. Furthermore both the differential capacity and the size of theaccessible area are unknown. Only if a value is assumed for one, can the otherbe calculated. It is assumed that the graphite surface is completely accessibleand the AC surface not. This vision is supported by Zabasajja en Savinell (1989)and opposed by Johnson and Newman (1971).

Unlike the capacity, the resistance was found to be no function of the basepotential. No apparent influence has been found.

The benzyl alcohol concentration does not have a large effect on the capacityor the resistance. The capacity decreases slightly with increasing concentration,in the order of 5% although the fit is poor. The scattering in the data is in theorder of 20%. The scattering in the resistance data is even higher, in the orderof 30-40%. The trend line suggests a very small increase with increasingconcentration. Perhaps because the electrical conductivity of the liquid goesdown if the fraction B increases but in all cases the benzyl alcohol onlyrepresents a small fraction of the liquid.


118

119

C H A P T E R 6

DESIGNING AN

ELECTROSORPTION UNIT

6.1. Process description

6.1.1. OverviewAn electrosorption unit resembles a classic packed bed adsorption column, butthere are differences. The carbon packed bed has two main functions: it mustremove the dissolved pollutants from the bulk liquid and it must function as anelectrode. These two tasks can be in conflict as can be seen from the bedporosity. In order to minimise the pressure drop, the bed must have a highporosity. In order to have minimal electrical resistance, the porosity should beas low as possible, ensuring good intra-particle contacts. In this chapter anattempt is made to find the optimal design for a commercial electrosorptionunit. To obtain all the necessary parameters a mathematical model for theprocess was developed that was solved numerically using the gPROMS packagefrom Process Systems Enterprise Ltd.

In the electrosorption unit both charge and mass transport takes place. Agraphical representation of the packed bed can be found in Figure 6.1. At theleft the liquid containing water (A), a polluting substance (B) and inert ionsenters the column. Inside the bed axial and radial dispersion can take place inaddition to the convective fluid flow. Component B moves from the bulk liquidphase to the solid phase during adsorption and vice versa during desorption.


120

Electrons are transported to or from the carbon granules by flat graphitecurrent collectors integrated in the bed. In Figure 6.1 a single current collectorset-up is shown, but it is possible to use more than one collector to improvecharging characteristics. The collectors can be positioned close to the CE(counter electrode) or on the opposite side. If the collector is located at theback, the charging will be counter-current relative to the liquid flow. If thecollector is at the front of the bed, the charging will be co-current. No othercurrents than that for charging the electrode are assumed to flow through theapparatus.

The counter electrode is an essential part of the process. Without it, the packedbed cannot be polarised. However no special attention will be paid to thestructure and appearance of the CE as it is not important from a modellingpoint of view. The CE is in all aspects identical to the WE (working electrode),only its charge is opposite. Completely to the right of Figure 6.1, the depletedliquid leaves the column.

0 Lx

J (Fluxof B)

Φ (flow in)

radialD (dispersion)

CE(not considered)

WE

Current collectorco-current set-up

Current collectorcounter-current set-up

A

u (interstitialvelocity)

axial

charge transfer

masstransfer

Figure 6.1: Schematic view of an electrosorption unit showing anumber of relevant variables. Mass and charge transfer processesoccur simultaneously in the bed. The counter electrode can be asecond packed bed or a metal electrode.


121

The equipment was sized based on a hypothetical wastewater stream of 2 litresper minute (3.33 10-5 m3/s) containing 5 mol/m3 of phenol. The mass transferresistance is assumed to be external, this means that the carbon particles can beconsidered a homogeneous phase. During the adsorption stage, the bed is heldat a potential favouring adsorption equal to the open circuit potential: φads = 0.In order to regenerate the bed and desorb the phenol, the potential is changedto a certain value φdes. As a result two processes are set in motion: charging ofthe electrical double layer and replacement of adsorbed organic molecules bywater molecules. In chapter 4 it was shown that charging of the double layer isslow due to the resistivity of the system. Surface areas close to the currentcollector become polarised much faster than areas further away. Both of theseprocesses are characterised by their own characteristic time constants.

6.1.2. Characteristic timesEisinger and Keller (1990) identified a number of processes taking place in anoperational electrosorption unit. Associated with each of these is acharacteristic time. For optimal performance some processes need to becompleted before others. Using this knowledge, a number of inequalities can beformulated. If all inequalities are satisfied the process design is within the so-called ‘operational window’.

1) The first characteristic time is the average residence time of the liquid in thecolumn (τR). It is defined as the ratio of the volume of the liquid in the packedbed divided by the volume flow:

uLVbedbed

R =Φ

ε==τflow

volume 6.1

where u is the interstitial speed of the liquid. The residence time depends onlyon the bed length and the column diameter as the flow rate was used as anexternal variable.

2) The adsorption time of component B (τads) is the moment that the packedbed has become completely saturated with adsorbed phenol. It is given by:


122

uL

cq

cLAq

inBbed

bedp

inB

bedbedpads

,,

)1()1( ratefeed adsorbate

adsorbedamount maxε

ε−ρ=

Φε−ρ

==τ 6.2

The adsorption time is often close to the breakthrough time because adsorptionfronts tend to be very sharp. The breakthrough time itself must be obtainedfrom simulated column performance data.

3) The desorption time (τdes) is related to the adsorption time, but desorptiontimes are much longer than adsorption times due to the non-linearity of theLangmuir-Freundlich isotherm1. The desorption time is estimated as follows:

adsdes τ=τ 3 6.3

This factor of three is a first assumption. The actual relation betweenadsorption and desorption time depends on the isotherm used.

4) The dispersion time (τID) is the time needed to obtain complete homogeneityin the bed due to dispersion only. It is calculated from the Fourier number setto unity. In this case τ = L2/ID, where ID is the axial dispersion coefficient.(The radial dispersion is of no concern as the diameter of the bed is muchlarger than its length). If only the convective contribution to the dispersion istaken into account the axial dispersion time equals:

uL

d pID

22=τ 6.4

where dp is the diameter of the particle spheres used.

5) The mass transfer time (τMT) is the time needed for a given molecule to reachthe solid-liquid interface when coming from the bulk of the liquid. It is equal to1/kLa, where a is the interfacial area per bed volume (in m2/m3) which dependson the particle size: 1 Because the Langmuir-Freundlich isotherm is used to describe the adsorption equilibrium, the bed can never

be regenerated completely. This is due to its infinite slope for cB = 0 (at least when n < 1).


123

p

bed

da ε= 6 6.5

The mass transfer coefficient kL can be calculated from the Sherwood number(Wesselingh and Krishna, 2000):

31

32

ScRe34.0Shbed

pL

IDdk

ε== 6.6

with Re the Reynolds and Sc the Smith number. Using the definitions for thesedimensionless numbers, the mass transfer coefficient equals:

31

32

34.0

ν

νε=

IDud

dIDk p

pbedL 6.7

where ν is the viscosity of the liquid. After rearranging one obtains:

34

31

32

778.0u

d pMT

ν=τ 6.8

6) The double layer charging time (τdl) was already encountered in previouschapters. The general expression τdl = RC can be rewritten as:

2)1(L

CS

bedpore

bedpBETdl εκ

ε−ρ=τ 6.9

In chapter 4 it was found that if t = τdl, only 63% of the charging wascompleted. In order for the bed to become polarised for 95% a time periodequal to 3 characteristic times is required. The relevant double layer chargingtime is therefore 3τdl.


124

6.1.3. Window of operationThe following rules should be taken into account for an optimal performanceof the unit:

• The desorption time should be bigger than the time needed for charging thedouble layer: τdes > 3τdl or from our definition of the desorption time itfollows that: τads > τdl

• The adsorption time should be much larger (about 100x) than the residencetime of the liquid: τads > τR.

• The axial dispersion time should be larger (about 10x) than the residencetime of the liquid: τID > τR.

• Finally, the residence time should be larger (about 10x) than the masstransfer time: τR > τMT.

In order to calculate the characteristic times the following variable values wereused (see Table 6.1).

Name Value Unit Name Value Unit

qmax 10 mol/kg Dp 0.5 10-3 m

C 0.15 F/m2 ID 4.81 10-8 m2/s

ν 10-3 m2/s L 0.02 m

κ 2.352 S/m εbed 0.45 -

U 1.92 10-4 m/s kL 9.04 10-5 m/s

SBET 1100 m2/g A 9 103 m2/m3

cB,in 5 mol/m3 ρp 1146 kg/m3

Table 6.1: Values used to calculate the characteristic times.

The following results were found:

τR = 104 s

τads = 8.999 104 s


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τdes = 2.70 105 s

τID = 8316 s

τMT = 44.13 s

τdl = 3.93 104 s

Comparing these values to the set of inequalities reveals that almost all of theseare satisfied if the bed length is 20 mm and the liquid speed is 0.2 mm/s. Theadsorption time is about two times bigger than the double layer charging time.The time needed for adsorption is much larger than the residence time. Alsothe dispersion time is larger than the residence time. The residence time islarger than the mass transfer time, although not ten times.

Both the bed length L and the liquid speed u influence five out of sixcharacteristic times, making them the most important design parameters. Table6.2 gives the relation between the six characteristic times, the liquid speed andthe bed length.

Characteristic

Time

Liquid

speed

Bed

Length

τRu1 L1

τadsu1 L1

τdesu1 L1

τIDu0 L2

τMTu-4/3 L0

τdlu1 L2

Table 6.2: The influence of liquid speed and bed length on thecharacteristic times. The bed length can be used to change the ratioof the electrical and the physical process times.

In Figure 6.2 the characteristic times are plotted as function of the bed length.For all L and u, the inequality τads > 100 τR is satisfied so this constraint can be


126

removed. The grey area indicates the allowable range of bed lengths if all othervariables remain unchanged.

L [m]

τ [s

]

0

τR

τads

τID

τdl

τMT

104

105

103

100

10

10.01 0.02 0.03 0.04 0.05

106

lower boundary

upper boundary

Figure 6.2: Characteristic times as function of bed length. Theresidence time is always lower than the breakthrough time. Otherconstraints are satisfied between the upper and lower boundaries.

dp [m]

L [m

]

10-4 10-3 0.01 0.1

10

1

0.1

0.01

τ τads dl=

τ τID R=10

τ τR MT=10

(a)

(b)

(c)

(a)

(b)

(c)

Figure 6.3: Window of operation (grey areas) as function of beddimensions. Drawn: τads = τdl. Dashed: τID = 10 τR. Dottedlines: τR = 10 τMT. For the meaning of a, b, c see the text.


127

For thick beds (> 45 mm), the double layer charging time becomes too large.For very small beds (< 9 mm) the residence time becomes smaller than themass transfer time. Optimal designs have bed lengths between these two values.A thicker bed can be used if multiple current collectors are installed.

In Figure 6.3 the satisfied constraints are plotted as function of L and dp forfour liquid speeds: (a) u = 2 10-6, (b) u = 2 10-5 and (c) u = 2 10-4 m/s. Theoptimal design should be below the drawn lines and above the dotted anddashed lines. The mass transfer is almost never limiting, only for unrealisticallylarge particles (> 1 m). Smaller particles allow for much higher velocities, butthe bed must then be thinner to reduce the double layer charging time.

6.2. The mathematical model

6.2.1. The gPROMS packageThe process was modelled using the software package gPROMS. gPROMS is ageneral purpose modelling, simulation and optimisation tool. It allows for thedirect mathematical description of distributed unit operations by entering theappropriate differential equations together with their boundary conditions. ThegPROMS program will take care of the solving of these. A second feature is thepossibility to combine elementary unit operations (building blocks) to describehigher level and more complex systems.

In gPROMS, the definition of elementary processes is done within MODELentities. Each input file should contain at least one of these. A MODEL entitycontains the knowledge regarding the physical behaviour of the system. Itconsists of a number of declaration sections in which different pieces ofinformation regarding the structure and behaviour of the given system arespecified. The most important are:

• The PARAMETER section. Here the time independent variables aredefined. These variables will not be calculated during the simulation and canbe considered as constants.


128

• The VARIABLE section. Here the time dependent variables are definedthat are calculated during the simulation.

• The EQUATION section. All equations that involve the declaredvariables and parameters. They are used to calculate the value of thevariables.

Besides the physics and the chemistry of the process, the operating proceduresare of equal importance. gPROMS adopts a dual description for processes interms of MODELs and PROCESSes. The latter operate on the MODELs anddescribe the operating procedure that is used to run the process. It is here thatvalues are assigned to constants. It allows for a number of steps to be executedin sequence, parallel or conditionally so a number of adsorption and desorptioncycles can be simulated in a single run. The most important declaration sectionsof the PROCESS section are:

• The UNIT section. Here the connections to the underlying MODELsections are established.

• The SET section is used to assign values to the constants in the variousMODEL sections.

• The ASSIGN section. Usually a number of external variables areneeded to reduce the number of degrees of freedom. They represent theinfluence of the external environment on the system and are given a value inthis section.

• The INITIAL section. In this section the initial values for the systemare determined.

• The SCHEDULE section. Here the operation policy is simulated, thesequence of actions that affect the behaviour of the system. Changes inexternal variables, specification of the running times etc.

More info on gPROMS can be found at http://www.psenterprise.com. Thelistings of the models can be found in appendix B.


129

6.2.2. Theoretical model: The equationsMass transfer: liquid phase

Liquid flowing through a packed bed of granules can be describedmathematically with the axially dispersed plug flow model (Alkire and Eisinger,1983a; Westerterp et al., 1983; Chue et al., 1992; Tien, 1994; Crittenden andThomas 1998). In most cases the deviation from plug flow is small and the flowin the reactor can be considered as piston flow with a superposition of somedispersion. Dispersion is caused by molecular diffusion and turbulent mixing.While the effects of axial dispersion are generally undesirable since they reducethe separation efficiency of the apparatus, ideas on radial dispersion in anadsorption column vary from helpful (Tien, 1994) to undesired (Crittenden andThomas, 1998). The effects of radial dispersion in this system are very smallbecause the bed diameter (0.7 m) is much larger than the bed length (0.02 m).Therefore radial dispersion is not taken into account in this work. From themass balance over a cross sectional area of the bed perpendicular to the fluidflow one obtains the desired expression for the liquid phase:

aJxcID

xcu

tc BBB −

∂∂+

∂∂−=

∂∂

2

2

6.10

Here u is again the interstitial liquid velocity, ID is the axial dispersioncoefficient, J is the flux of component B from the bulk liquid to the solid-liquidand a is the interfacial area per unit volume of solution interface area.

Mass transfer: solid phase

The rate expression used in this work contains only a single mass transferresistance. This resistance lies outside the solid phase in a fluid film surroundingthe carbon particles. This greatly simplifies the model, as the bulk of the solidparticles can now be considered a homogeneous phase. No intra-particleresistances exist so all solid concentrations are equal. The accumulation ofspecies B in the solid phase again follows from a mass balance. If it is assumedthat no B reacts due to unwanted Faraday reactions, one has:


130

aJtq

bedpbed ε=∂∂ρε− )1( 6.11

where ρp is the particle density.

The flux

The flux can be described using a linear rate expression together with an overallmass transfer coefficient kL:

( )intBBL cckJ ,−= 6.12

The driving force for the flux is the (small) difference between the solid-liquidinterface concentration cB,int and the bulk liquid concentration cB.

The isotherm

In chapter 3 isotherm expressions are given that relate the bulk concentrationto the surface coverage q. A potential dependent Langmuir-Freundlichisotherm is used in the model because the Langmuir isotherm is unable toproperly describe the experimental adsorption data:

F

F

nintB

nintB

cKcK

qq,

,max )(1

)(φ+

φ= 6.13

The adsorption equilibrium K is an exponential function of the electricalpotential drop (see Eq. 2.52). Alkire and Eisinger (1983a) used an empiricalquadratic function to describe the dependence of K on the potential:

CBA +φ+φ=φ 2)(K 6.14

where A, B and C are experimentally determined empirical constants. Both Eq.2.34 and Eq. 6.14 give approximately the same influence of the potential. If nopotential is applied, the adsorption equilibrium constant is maximal. If theapplied potential increases, the adsorption constant diminishes. In our model Bis set to zero (no preferential adsorption of the organic compound, leading toan additional potential drop). C is related to the open circuit adsorption


131

constant and A is related to the exponential of the differences in integralcapacity of the system divided by RT. The adsorption equilibrium dependsupon the local potential difference across the double layer and can thereforediffer for various parts of the bed.

Charge transfer

In chapter 4 three analytical solutions for the potential distribution functionwere given. The external losses model gave the best results. In the model thetime and position dependent potential is calculated numerically, so:

2

2

xaCt bed

pore

∂φ∂

εκ

=∂φ∂ 6.15

Again the carbon phase is considered homogeneous, no potential distributionsinside particles are taken into account. The differential capacity is considered tobe constant at first. In reality the differential capacity is a function of potentialand surface coverage. The solution of the model for a non-constant capacity istreated in section 6.3.8.

Additional equations

In the set of equations Eq. 6.10-6.15 a number of variables appear which mustbe calculated using additional equations. The dispersion coefficient ID accountsfor axial dispersion and for molecular diffusion (Alkire and Eisinger, 1983a;Crittenden and Thomas, 1998):

232 p

bed

bed udDID +

ε−ε= 6.16

The diffusivity coefficient D is corrected for the tortuosity of the packed bed.The mixing part of the dispersion coefficient is expressed by the dimensionlessPéclet number. The interstitial liquid velocity is given by:

bedbedbed dAu

επΦ=

εΦ= 2

41

6.17


132

if the packed bed is a cylinder with diameter dbed and length L. The conductivityin the potential distribution equation is the conductivity of the pores. It can becalculated by correcting the bulk liquid conductivity for the tortuosity of thebed:

Lbed

bedpore κ

ε−ε=κ

32 6.18

The liquid electrical resistance inside the bed is therefore larger than outside thebed.

6.2.3. Theoretical model: boundary conditionsThe condition at the two boundaries of the packed bed (x = 0 and x = L) mustbe described with respect to the concentration and the potential. The type ofboundary condition is determined by the assumptions made. For theconcentration:

0 :all ,)2

:all ,0)1

:all ,0)1

0,

0,

=∂∂=

∂∂+==

==

xctLx

xc

uIDcctxb

cctxa

B

BBB

BB

6.19

Boundary 1a) corresponds to a so-called closed boundary condition while 1b) isused for an open boundary (Westerterp et al., 1983). At the end of the bed thereis a no-flux condition. For the electrical potential:

0 ,

,0 0

=

∂φ∂=

∂φ∂λ−φ=φ=

xLx

xLx

6.20

These boundary conditions correspond to a co-current set-up of the potentialdistribution. The current collector is positioned at the front of the bed. If thepotential wave and the liquid flow run counter-currently, the two boundary


133

conditions in Eq. 6.20 are interchanged. The λ appearing in the first boundarycondition in Eq. 6.20 determines the amount of potential that is lost (Carslawand Jaeger, 1959). If the loss factor λ is set to zero, there are no external lossesand the mixed boundary conditions turns into the prescribed boundarycondition of the no-losses model (see chapter 4).

6.2.4. Theoretical model: initial conditionsThe following initial conditions are used for all simulations:

0 :all ,00 :all ,00 :all ,0

=φ=====

xtqxtcxt B

6.21

6.2.5. Theoretical model: discretisation methodsThe differential equations are solved with the use of a spacial discretisationmethod. The packed bed is divided using a grid and on each of the grid pointsthe variables are calculated. No one method can solve all possible problems sothe proper choice of method is very important as an incorrect choice can leadto physically unreal solutions or numerical problems. gPROMS allows thesetting of three parameters.

Numerical method Abbreviation Order

Backward finite difference method BFDM 2, 4, 6

Forward finite difference method FFDM 1, 2

Centered finite difference method CFDM 1, 2

Upwind-biased finite difference method UFDM 2

Orthogonal collocation on finite elements method OCFEM 2, 3, 4

Table 6.3: Spacial discretisation methods for calculatingdistributed systems containing partial derivatives. Taken from thegPROMS user’s guide.


134

These are the discretisation method, the order of the method and the numberof grid lines used. Generally speaking a higher order method and a denser gridleads to more realistic results, but also to much longer calculation times. Themethods implemented within gPROMS are listed in Table 6.3.

With respect to the selection of a proper method it is difficult to come up withgeneral rules. From the gPROMS user guide it was abstracted that BFDM andFFDM should be used for convective processes and CFDM or OCFEM fordiffusive processes:

• The liquid flowing through the packed bed is strongly convective. Thecontribution of the second derivative term arising from dispersionphenomena is not very significant. For this reason a one-sided finitedifference method, taken opposite to the direction of flow, was used. Forthe calculation of the liquid flow through the bed, from left (x = 0) to right(x = L) a second order backward finite differences method (BFDM) wasused.

• On the other hand, the potential distribution inside the bed is a processwith a strong dispersive/diffusive effect (no convective contributions at all).gPROMS advises to use either the centred finite differences (CFDM) or theorthogonal collocation on finite elements (OCFEM) for these kind ofproblems. As the OCFEM led to numerical problems, a second orderCFDM method was used to calculate the potential distribution, although theOCFEM is more efficient than CFDM in terms of the number of discretisedequations/variables needed for attaining the same accuracy.

6.2.6. Theoretical model: the schedule of the simulationEach simulated run covers two consecutive cycles of the process. First there isan adsorption cycle, followed by a desorption cycle. Initially the packed beddoes not contain any B. At t > 0 a polluted inlet stream is fed into the column.The inlet concentrations were varied between 0.5 and 25 mol/m3, 5 mol/m3

being the standard value. No electrical potential is applied during this cycle. Thebed becomes saturated with B and the outlet concentration starts to increase.After 160000 s (about 44 hours) the desorption cycle starts which lasts for


135

640000 s (about 178 hours). The column is washed with electrolyte solutionand a potential difference can be applied during this stage.

6.3. Results

6.3.1. Base case resultsA large number of simulations were performed, most of them variations on thebase case situation. The gPROMS simulations took about one minute ofprocessor time on a Pentium® 166 MHz computer. The parameter values usedfor the base case (and most other simulations) are given in Table 6.4.

Name Value Unit Name Value Unit Name Value unit

qmax 10 mol/kg dp 0.5 10-3 m C 0.15 F/m2

A -0.1 m3/2/(mol½V2) dbed 0.7 m φext 1 V

B 0 m3/2/(mol½V) L 0.02 m λ 0.667 -

C 0.2 m3/2/mol½ εbed 0.45 - tads 160000 s

nLF 0.5 - Φ 3.33 10-5 m3/s tdes 640000 s

SBET 1100 m2/g D 9 10-10 m2/s method BFDM2 -

cB,in 5 mol/m3 ρp 1146 kg/m3 CFDM2 -

Table 6.4: The set of PARAMETERS used for the base casesimulation. Mass transfer related parameters are discretised usingthe BFDM second order method, charge transfer parameters withthe CFDM second order method.

The variables that can be calculated from these input parameters are given inTable 6.5. The bulk concentration is plotted in Figure 6.4 as a function of timefor five different positions inside the bed.


136

Name Value unit Name Value Unit

a 6600 m2/m3 Vbed 7.697 10-3 m3

u 1.924 10-4 m/s kL 9.04 10-5 m/s

ID 4.844 10-7 m2/s κpore 2.352 S/m

Abed 0.384 m2

Table 6.5: The VARIABLE values obtained from the base casePARAMETERS.

The left graph shows the adsorption of B and the right graph shows thedesorption. As can be seen from the left graph, it takes about 96800 s for theoutlet concentration to reach 90% of the inlet concentration of 5 mol/m3 (=τads). The loading curve becomes somewhat steeper towards the end of the beddue to the form of the isotherm. In Figure 6.5 the solid phase concentration isplotted for the same simulation. The changes in the solid concentrationresemble those of the liquid concentration.

20000 40000 60000 80000 1000000

6

5

4

3

2

1

0

t [s]

c B [m

ol/m

]3

x L= x L= 0.76

x L= 0.52

x L= 0.28

x L= 0.04

240000160000800000

t [s]

x L= x L= 0.76x L= 0.52x L= 0.28x L= 0.041)

2)

3)

4)

5)

1)2)

3)4)5)

Figure 6.4: Bulk phase concentration as a function of position inthe bed. At the left the situation during the first 120000 s(adsorption). At the right the situation between the following160000 and 480000 s (desorption). No field is applied.

The right graph in Figure 6.5 shows the desorption of B when no field isapplied to the packed bed. As can be seen from the long concentration ‘tail’,simply washing the pollutant out of the bed takes a long time. The τdes =


137

1005400 s. This is the moment that 90% of the adsorbed B is desorbed. Forthis configuration the desorption cycle will take 10 times more time than theadsorption cycle.

20000 40000 60000 80000 1000000

3.5

3

2.5

2

1.5

1

0.5

0

t [s]

q B [m

ol/k

g]

80000 160000 2400000

t [s]

x L= x L= 0.76

x L= 0.52

x L= 0.28

x L= 0.04

x L= x L= 0.76x L= 0.52x L= 0.28x L= 0.041)

2)

3)

4)

5)

1)

2)3)

4)5)

Figure 6.5: Solid phase concentration as function of position inthe bed. At the left adsorption, at the right desorption.

The characteristic adsorption time calculated in section 6.1.2 predicts that after89990 s the bed will be saturated with phenol. This value lies very close to thevalue obtained from the simulation (96800 s), the bed performs almost at itsoptimum efficiency. The difference can be explained from the fact that theearlier calculation does not take into account that part of the phenol enteringthe bed will leave it before it has become saturated.

Beforehand it was assumed that the desorption time was three times the timeneeded for adsorption. From the simulation results it follows that for theseconditions the desorption time is about 10 times the adsorption time.

6.3.2. Influence of the electrical field

In order to improve the desorption of B (reduce τdes), an electrical field of onevolt is applied that changes the adsorption equilibrium constant from 0.2m3/mol to 0.1 m3/mol. In Figure 6.6 the resulting decrease of the isotherm isplotted.


138

1

2

4

3

5

6

0 5 10 15 20 25

cB [mol/m ]3

q [m

ol/k

g] K = 0.2 m /mol3

K = 0.1 m /mol3

030

Figure 6.6: Applying a potential of one volt shifts the isotherm tothe lower line.

It takes time for the bed to reach the external set potential. In Figure 6.7 thepotential is plotted as a function of the bed length. For a loss factor λ = 0.666the characteristic time for charging of the double layer to 95% is 143000 s (=3τdl). The external losses model is used to describe the potential distribution.This is the reason that the potential at the front of the bed is not equal to theapplied potential of one volt. Comparing the numerical output with theanalytical results (shown in figure 4.11) does not reveal any discrepancies.

Again, the simulated characteristic time can be compared to the one calculatedin section 6.1.3. The 3τdl from the simulation is 143000 s. The analyticallyobtained τdl was 39300 s, and 3τdl is 118000 s. Both are in the same order ofmagnitude. The first is lower because no potential losses were taken intoaccount. The double layer charging time depends on the loss factor applied.The lower the loss factor, the faster the double layer is charged.


139

x L/ [-]

φ [V

]

0.2

0.4

0.6

0.8

1

00.2 0.4 0.6 0.80 1

2 τ

τ

0.5 τ

0.2 τ0.05 τ

Figure 6.7: The potential distribution inside the bed for fivedifferent times. The loss factor λ = 0.666.

The adsorption constant is a function of the applied potential. If at t = 160000s a potential difference of one volt is applied to the bed (and the inletconcentration is set to zero), the desorptive behaviour is improved as can beseen from Figure 6.8 and Figure 6.9. The grey areas represent the differencewith the case when no field was applied.

6

5

4

3

2

1

0

c B [m

ol/m

]3

240000160000800000

t [s]

x L= x L= 0.52

x L= 0.04

Figure 6.8: Influence of the electrical field on the liquidconcentration. The desorption starts at 160000 s.


140

80000 160000 2400000

t [s]

x L=

x L= 0.52

x L= 0.04

3.5

3

2.5

2

1.5

1

0.5

0

q B [m

ol/k

g]

Figure 6.9: Influence of the field on the solid concentration.

The time required for 90% of the adsorbed phenol to desorb is reducedsignificantly. Without the field τdes = 1005400 s (11 ½ days), but with a potentialof 1 V applied, it is reduced to 408100 s (4 ½ days). The actual influence of thepotential on the desorption time depends on the loss factor of the system.

6.3.3. Order of the discretisation methodTo determine the numerical accuracy of the results, the order and type ofdiscretisation method were varied. In Figure 6.10 concentration loading curvesare plotted for a number of situations. As can be seen from the graph thedifferences are not pronounced. Increasing the order of the BFDM methodleads to a steeper concentration curve. Applying an open boundary conditionfor the concentration at the inlet of the packed bed leads to a more flat curve. Itis remarkable that the first order FFDM method yields almost the same resultas the second order BFDM method because the FFDM is considered a poorerchoice for this system than the BFDM as the change in concentration movesfrom left to right. In Figure 6.11 the influence of the order on the potentialdistribution can be found. The situation here is reversed. Second ordermethods lead to a more flat curve as the potential distribution is a diffusive typeof process. This in turn results in larger double layer charging times.


141

BFDM,1BFDM,1, BC2

BFDM,2FFDM,1CFDM,2

0 40000 80000 120000 160000

5

4

3

2

1

0

t [s]

c B [m

ol/m

]3

Figure 6.10: Effect of concentration inlet boundary condition,order and discretisation method on the breakthrough curve.

0 100000 200000 300000

1

0.8

0.6

0.4

0.2

0

1.2

t [s]

φ [V

]

Second order methods(BFDM, CFDM)

First order methods(BFDM, FFDM)

Figure 6.11: Effect of the discretisation method order on thepotential distribution. The type of method used did not result insignificant changes.


142

6.3.4. The concentration of ions and phenolThe salt concentration has a large effect on the double layer charging time. InFigure 6.12 the effects of different salt concentrations can be seen. Lowercharging times give better desorption characteristics, so these processes arerelated.

cion [kmol/m ]3

τ [1

0 s]3

τdes

τdl

0

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1 1.2

Figure 6.12: Effect of the ion concentration on the double layercharging time. A lower charging time results in faster desorptionas can be seen from the graph.

The concentration of phenol in the inlet also influences characteristic times.For most simulations a concentration of 5 mol/m3 was used. In Figure 6.13 itcan be seen that for lower concentrations the various τ values decrease. If theconcentration is reduced by a factor of two, the liquid flow through the columnis increased by a factor of two, in order to keep the mole flow of B constant.The double layer charging time remains constant as it is no function of theconcentration.


143

200

400

600

800

1000

1200

05 10 15 20 25 30

cB [mol/m ]3

τ [1

0 s]3

τdl

τdes (no field)

τads

0

τdes (field)

Figure 6.13: Effect of the phenol concentration on a number ofcharacteristic times. Reducing the inlet concentration (the mole flowremains constant!) leads to reduced characteristic times.

6.3.5. The loss factor

Besides the ionic strength of the electrolyte, the loss factor λ mainly determinesthe charging speed of the bed. A lower value for λ means that a smaller part ofthe applied potential is lost due to ohmic resistances in the liquid phase (seeFigure 6.14).

t [s]

φ [V

]

300000100000 200000

1

0.2

0.4

0.6

0.8

00

λ = 0.05

λ = 1

λ = 0.25λ = 0.5

Figure 6.14: Effect of the loss parameter on the potential at theopposite end of the bed as a function of time.


144

If the bed can be forced to desorbing conditions more quickly, the associatedcharacteristic time will be much faster. The desorption curve as function of thevarious loss parameters can be found in Figure 6.15.

0 40000 80000 120000 160000 2000000

1

2

3

4

5

6

7

8

t [s]

[

mol

/m]

c B3

instantly charged dl

no dl

λ = 0.01

λ = 0.25

λ = 0.05

Figure 6.15: Bulk liquid concentration profile as a function ofloss factor. The ‘instantly charged dl’ curve represents the casewhere the bed is fully charged at t = 0 and the ‘no dl’ curverepresents the case where no potential is applied to the bed.

If the bed is immediately charged, a large amount of B desorbs instantaneouslyresulting in a large peak. This peak will gradually decrease with increasing λvalues. The same is done in Figure 6.15 for the solid concentration.

0 100000 200000 300000 4000000

0.5

1

1.5

2

2.5

3

3.5

t [s]

q [m

ol/k

g]

no dl

instantly charged dl

λ = 1

λ = 0.05

λ = 0.5

Figure 6.16: Solid concentration as a function of the loss factor.Same conditions as Figure 6.15.


145

Again it can be concluded that the differences between an instantly charged bedand an uncharged bed are quite large. The smaller the loss factor, the more theideal situation of an instant charged bed is approached.

λ [-]

τ [1

0 s]3

0

50

100

150

200

250

0.2 0.4 0.6 0.8 1 1.20

τdes

τdl

Figure 6.17: Two τ’s as function of the loss factor. The differencebetween the two increases if the losses are reduced.

6.3.6. Counter current or co current set-upThe actual direction in which the bed is charged might be an important designconsideration. In our one-dimensional model, the bed can be charged from leftto right (co-current set-up) or from right to left (counter-current set-up)depending on the position of the current collector. In the model, this can beachieved by simply interchanging the potential boundary conditions. For smallloss factors, the differences found between the two settings are biggest. InFigure 6.18 the solid and liquid concentration profiles as a function of time areplotted. A semi-log scale was used to obtain a better view on the behaviour atlonger periods.


146

t [s]

q cB

an

d [v

aries

]

0.01

0.1

1

10

6000004000002000000

(a)

(b)

Figure 6.18: Difference between co-current (gray lines) andcounter-current (black lines) charging of the packed bed. (a)Represents the solid phase concentration, (b) the liquidconcentration. For this simulation λ = 0.05. If λ is increased thedifferences tend to become smaller.

It was found that for all values of λ the characteristic desorption time wasroughly the same for both configurations, only for the first 50000-100000 s adifference can be observed. This is within the characteristic double layercharging time, so here the bed is not yet completely polarised. For longerperiods, the lines start to coincide as the bed is now completely polarised. As nomore charging of the double layer takes place, the configuration is no longer ofany influence. It can be concluded that only for t < 3τdl the configuration of thecurrent collector is of any influence. The counter current set-up will work betteras the solid concentration is lower in this case.

6.3.7. Multiple current collectorsA way to reduce the double layer charging time is to use more than one currentcollector. If the packed bed is connected to the external circuit at four pointsinstead of one, it can be considered as four smaller beds in series. Thecharacteristics with respect to mass transfer do not change provided thecollectors do not disrupt the liquid flow through the bed. The bed length forcalculating the charge distribution is now only ¼ of the actual bed length and


147

because the double layer charging time depends quadratically on the length, theτdl is 16 times smaller.

Overall model

Packed bedsubmodel

ParametersVariablesEquations

Boundary conditions

Packed bedsubmodel


Packed bedsubmodel


Packed bedsubmodel


Definition andconnection ofsubmodels

Boundary conditions Boundary conditions Boundary conditions

Inlet Outlet

Process

Value of constantsInitial conditionsSchedule

FIRST LAYER

SECOND LAYER

Figure 6.19: Schematic overview of the multi-layered gPROMSmodel structure.

In the model this is implemented by using a hierarchical structure. The actualbed consists of a number of building blocks, which describe its physicalbehaviour. A higher level block provides the coupling between these units. Alisting for a model consisting of n packed beds in series can be found inappendix B.

6.3.8. A variable electrical capacityAlthough the capacity was experimentally found to be relatively constant, itdoes change with potential and surface coverage. The surface coverage in turnis also a function of the potential. The local potential can be calculated from thedistribution function. But the distribution of potential is largely determined bythe electrical capacity of the system so both depend on each other. For thisreason a constant differential capacity was used as a first approximation. To


148

determine what error is made in doing so a variable capacity is implemented inthe numerical model and results are compared.

If the total surface is partly covered with water (A) and partly with phenol (B)the parallel condenser model gives the total capacity:

BBBABtot CCC θφ+θ−φ=θφ )()1)((),( 6.22

The capacities CA and CB are defined as the reciprocal addition of the capacitiesof the Helmholtz and Gouy-Chapman layers (compare Eq. 3.9):

)()()()(

)(

)()()()(

)(

,

,

,

,

φ+φφφ

=φ

φ+φφφ

=φ

GCBH

GCBHB

GCAH

GCAHA

CCCC

C

CCCC

C

6.23

The Gouy-Chapman capacity CGC can be calculated with Eq. 2.5. Because thedielectric constant changes with potential (section 2.1), the Helmholtz capacityCH is also a function of the potential. All Helmholtz capacities are calculatedusing the following formula:

)(3

)(2

1)(

,0,0

,

φεε++

φεε

=φ

Ar

ion

ir

iiH rr

C 6.24

where i can be A or B depending on the molecules that are adsorbed (comparewith Eq. 2.36). The dielectric constant is calculated from molecular propertiesusing the Kirkwood equation, Eq. 2.34.

When the actual capacities throughout the bed are calculated, the final step is touse them to determine the influence of the potential on the adsorptionequilibrium constant K as derived in chapter 2. No specific orientation ofadsorbed compounds was assumed, therefore Eq. 2.51 could be used:


149

φφ−φ−

=φRT

CCKK BA

221

0))()((

exp)( 6.25

In appendix B the relevant gPROMS listing (listing 3) can be found.

t [s]

K

C[m

/mol

] and

[F/m

]1.

50.

52

0

0.05

0.1

0.15

0.2

0.25

200000 400000 600000 8000000

K

C

switching to desorption

Figure 6.20: The local capacity and the adsorption constant (at x= L/2) during an adsorption and desorption cycle. At 160000 sdesorption starts.

The following results where found while running a simulation using a variablecapacity. In Figure 6.20 the differential capacity C and the adsorption constantK in the middle of the packed bed are plotted as a function of time.

The adsorption of phenol causes the capacity to decrease to a lower value.After the carbon has become saturated with phenol, the capacity becomesconstant. Switching on the potential causes an increase in the capacity as waterreplaces phenol. The final capacity at t = ∞ is somewhat lower than the initialcapacity because the field slightly reduces the dielectric constant of theadsorbed water.

The output of the simulations with a potential and concentration dependentcapacity were found to be almost identical to that of the constant capacitysimulations. In Figure 6.21 the empirical K(φ) function is compared to the


150

more complex equation from chapter 2. Because potential sweeps of 1 V areapplied in all simulations, the influence of the actual potential dependency israther small.

φ [V]

K [m

/mol

]1.

50.

5

-1 0 10

0.1

0.2

potential sweep

φ−−=

RTCCKK BA

2)(exp

2

0

20 01.0 φ−= KK

Figure 6.21: The difference between the (empirical) quadraticdependence of the adsorption constant on the potential and thedependence predicted by our model (chapter 2) is quite small.

6.4. Looking back

In this chapter, an electrosorption installation was designed and modelled,suitable for cleaning a wastewater stream of 20 litres per minute containing 5mol/m3 of phenol. A number of assumptions were made. The liquid flowingthrough the column is described with the axial dispersion plug flow model. Noradial dispersion is taken into account. The mass transfer resistance is assumedto be outside the solid phase. No Faraday reactions occur.

To estimate the equipment dimensions a set of characteristic times was used.As some processes in the adsorber need to be completed before others somecharacteristic times need to be larger than others. If all inequalities are satisfiedthe process design is within its operational window. The characteristic timesused are: (1) the average residence time of the liquid in the column (τR). (2) Theadsorption time of component B (τads). (3) The desorption time of component


151

B, estimated to be: τdes = 3τads. (4) The dispersion time (τID) needed to getcomplete homogeneity in the bed due to dispersion only. (5) The mass transfercoefficient (τMT) is the time needed for a molecule to reach the interface fromthe bulk. (6) The double layer charging time (τdl) or better 3τdl.

The following inequalities were applied: The desorption time should be biggerthan the time needed for charging the double layer. The adsorption time shouldbe much larger (about 100x) than the residence time of the liquid. The axialdispersion time should be larger (about 10x) than the residence time of theliquid and the residence time should be larger (about 10x) than the masstransfer time.

Both the bed length L as the liquid speed u influence five out of sixcharacteristic times, so these two are the most important design parameters. Itfollows that beds length should be in the order of 10 mm and the liquid speedin the order 10-4 m/s.

Numerical modelling of the system was done with the use of gPROMS, ageneral purpose modelling, simulation and optimisation tool. The mathematicalmodel equations and boundary conditions can be written directly into theprogram. Two different discretisation methods had to be applied in order tocalculate the concentration as a function of place and time (convectivebehaviour) and the potential as function of place and time (diffusivebehaviour).

A large number of simulations was conducted. About the same values for anumber of characteristic times were found in comparison to the ones calculatedfrom Eq. 6.1-6.9.

The reduction in τdes due an applied potential of 1 V was almost a factor ofthree. The resulting field was assumed to reduce the adsorption equilibriumfrom 0.2 to 0.1. Charging of the bed was completed for 95% at 143000 s.

Comparing the gPROMS solving methods it was found that the first orderFFDM method yielded almost the same result as the second order BFDMmethod. Theoretically the former is considered a poorer choice for this type of


152

system than the latter. Second order methods give steeper concentrationprofiles, but flatter loading curves, compared to first order methods. The use ofsecond order methods therefore leads to larger double layer charging times.

The salt concentration has a large effect on the double layer charging time. Theτdl starts to increase rapidly for reduced concentrations. Higher concentrationsgive somewhat reduced τdl values. The phenol concentration has an oppositeeffect. Lower concentration gives a decrease of characteristic times.

Higher loss factors give slower charging and therefore poor desorption of theadsorbed phenol.

The effect of system configuration, counter-current or co-current is only visibleif the bed is not yet charged. Counter-current performs slightly better.

Implementing a potential and surface concentration dependent capacity intothe model did not result in large differences.

153

C H A P T E R 7

SOME DYNAMIC ASPECTS

7.1. Streaming current

7.1.1. TheoryThe combination of a moving phase and a polarised interface can result ininteresting phenomena. If a substantial potential difference is applied across acapillary tube filled with an electrolyte, a current will flow according to Ohm’slaw. However, it can also be observed that the solution begins to move.Applying an electrical potential can have the same result as applying a pressuregradient. If both are applied, the resulting liquid velocity is due to the sum ofthese contributions:

Ecpcu 21 +∆= 7.1

or u/E = c2 if no pressure is applied. If an electrical field E has the same resultas a pressure difference, a pressure difference must be able to produce anelectrical current. This current is known as streaming current. It is calculated by:

Ecpcj 43 +∆= 7.2

where j is the current density in A/m2. If no electrical field is present, j/∆p = c3.According to the Onsager reciprocity relation the cross coefficients c2 and c3 areequal (Bockris and Reddy, 1970b). Bockris and Reddy provide a mechanism forthe streaming current phenomenon.

Chapter 7: Some dynamic aspects

154

The electrolyte solution flows past the polarised surface. Near the surface thereis an excess of charge (half of the double layer). This excess charge is located intwo regions: In the compact and in the diffuse double layer region (see alsochapter 2). The thickness of the compact layer does not exceed 1 nm whereasthe diffuse layer is in the order of 10 to 100 nm. For a laminar flowing liquidunder steady state conditions, the viscous force opposes the pressure difference∆p applied to the liquid:

dxdup η=∆ 7.3

The velocity u of the (viscous) fluid element depends on its distance x from thesurface. At x = 0 the velocity is zero. Charges located in the compact doublelayer are therefore fixed. The diffuse region is further away from the surfaceand is subject to the movement of the bulk liquid. (Part of) the excess ions inthe diffuse layer will be dragged along with the flow. The movement of theseexcess charges is defined as current.

The diffuse layer can be described as a plate of charge located a distance χ-1 (theinverse Debye length) from the electrode. If the velocity is u at x = χ-1, a chargedensity qGC in C/m2 is present due to an apparent applied potential φ’ on thecarbon:

r

GCqεεχ=φ

−

0

1

' 7.4

If there is no charge in the diffuse double layer, there will not be a streamingcurrent. In chapter 2 it was found that higher salt concentrations and strongerfields press more of the excess charge into the Helmholtz layer. As a result,more charge is fixed and the charge density at the Debye length will decrease,yielding a lower φ’ value. Removing the Debye length by combining Eq 7.3 andEq 7.4 yields:

uqp GCrεεφ

η=∆0'

7.5


155

If the movement of the charges is considered per meter, qGCu equals a currentdensity j. Substituting and rewriting gives the final result:

dpj r

ηεεφ=

∆0' 7.6

where d is only a proportionality constant (1 m). The streaming currentproduced per bar pressure drop is a constant. To calculate it, the followingvalues are used: The viscosity η of the electrolyte resembles that of seawater:1.01 10-3 kg/(m⋅s). The dielectric constant in the diffuse layer is close to that ofthe bulk value of water, ε0 = 80. The φ’ is a fraction of the total appliedpotential. If it is 500 mV, the streaming current density produced is 34 mA/m2

electrode surface.

7.1.2. ExperimentThe set-up used to measure streaming currents is essentially equal to the onedescribed in chapter 3 for determining isotherms. A manometer is added tomeasure the pressure of the liquid before it enters the cell. The liquid flowthrough the bed was recorded using stopwatch and cylinder. For a schematic ofthe set-up see Figure 7.1.

The mixing tank contains 0.5 N KCl electrolyte solution. Prior to the actualexperiment, the electrolyte is pumped through the cell and recycled to the tank.During measurement of the pressure drop, the liquid flow and the current arerecorded. The cell is filled with Ambersorb 572, 6.5053 g for the WE and6.1149 g for the CE. After the potential is set, the charging current is allowed todecrease for a 24-h period. After a measurement, the pump settings arechanged and a 5-hour stabilisation period is allowed before the nextmeasurement is started.

To convert currents densities to current, the external electrode surface isrequired. As estimation, the sum of all particle outer surfaces is used. TheAmbersorb 572 used has an average diameter of 0.3 mm and the packed bedshave a cylindrical shape. The bed length is 5 mm, the bed diameter is 52 mmand the bed porosity is 0.45. From these three parameters an external electrode


156

area of 0.117 m2 is calculated. The theoretical current produced if this system issubjected to a potential of 1 V and 1 bar pressure difference is 8.192 mA.

V

A

Cell

data

PC

Mixing tank

potentiostat

Amperemeter

peristaltic pump

WE

CE

RE

manometer

determiningflow

Figure 7.1: Experimental set-up for determining streamingcurrent. After a certain potential is established throughout the bed(idl → 0) the pump speed is altered and the change in the currentrecorded.

The following results have been obtained. The liquid flow was determined to beperfectly linear with pump setting. Between pressure drop and pump setting, aconvex relation was found. Streaming current was determined at three differentpotentials: 1.0, 0.75 and 0.5 mV and a number of pump settings. The resultscan be found in Figure 7.2 and the data in Table 7.1 through Table 7.3

From Figure 7.2 it follows that the experimental currents are 2.5 times higherthan predicted by Eq. 7.6. Errors made in estimating the effective electrodesurface could perhaps account for this. The Ambersorb has a distribution ofdiameters and maybe part of the macropores contribute to the currentgenerating surface. Increasing the potential gives higher currents, as is predictedby the theory.


157

∆P [bar]

i [m

A]

0

5

10

15

20

25

30

0 0.2 0.4 0.6 0.8 1 1.2 1.4

φ = 1.0 V

0.75 V

0.5 V

Figure 7.2: Streaming current as function of the pressure drop.Eq. 7.6 predicts a linear relation between i and ∆P.

Increasing the pressure gives an increase in streaming current. This relation isnot the linear one predicted by Eq. 7.6. For larger pressure drops, the increaseis less than expected, especially for the 0.5 V experiment. This effect cannot beexplained by the non-linearity between liquid flow and pressure drop.Correcting for this causes the results to deviate even more.

pump

setting

liquid flow

[ml/s]

pressure drop

[bar]

i recorded

[mA]

0 0 0 0.35

2 1.0258 0.725 18.01851

4 2.0516 0.88 21.80495

6 3.0774 1.125 24.32156

8 4.1032 1.2 26.44412

2 1.0258 0.57 12.72116

4 2.0516 0.925 17.35165

8 4.1032 1.34 21.39451

Table 7.1: Experimental data obtained for an applied potentialof +1000 mV.


158

pump

setting

liquid flow

[ml/s]

pressure drop

[bar]

i recorded

[mA]

0 0 0 0.275754

2 1.0258 0.555 8.473676

4 2.0516 0.81 11.76101

6 3.0774 1.025 11.82766

8 4.1032 1.175 11.95486


pump

setting

liquid flow

[ml/s]

pressure drop

[bar]

i recorded

[mA]

0 0 0 -0.04071

2 1.0258 0.555 2.428166

4 2.0516 0.875 2.5010

6 3.0774 1.075 2.615421

8 4.1032 1.175 2.727831


The fact that the 1.0 V experiment is more linear than the 0.75 V and the 0.5 Vexperiments suggests that the potential is of influence. Intuitively, the systemshould behave more ideally for low potentials but the reverse is true. It ishypothesised that the flow regime close to the particles is of great influence.

Current generation is maximal if the flow is perfectly laminar. If the flowaround the carbon spheres becomes turbulent, the streaming current would bemuch lower due to the complex movement of the liquid (and the ions). Largerpressure drops give rise to more turbulence and a less than linear increase.However, the deviation from linearity is much larger for the 0.5 V experiment,this is explained as follows.


159

If more net excess charge is present it suppresses the laminar-turbulencetransition to a larger extend, as there is more coulombic interaction. This couldincrease the apparent viscosity close to the surface. To check this, the Reynoldsnumber is calculated. Smith et al. (1981) gave the following expression for aliquid flowing through a packed bed:

)1(Re 3

2

bed

pudε−η

ρ= 7.7

For the highest pump setting the superficial liquid speed u is 2 10-3 m/s. Thisresults in a Re number of 0.706. The lowest pump setting gives Re = 0.079,almost ten times lower. According to Smith et al. the flow around a sphere iscompletely laminar if Re < 0.2. For 0.2 < Re < 10 stable eddies will form in thewake of the sphere. This laminar-turbulence transition range indeedcorresponds to the Reynolds numbers found. More research is needed toconfirm that turbulent wakes are the cause for the deviations found.

7.2. The relation between mass and charge transfer

7.2.1. IntroductionDuring the continuous adsorption experiments described in section 3.3 (the set-up used can be found in Figure 3.10), not only the concentration, but also thecurrent was recorded as function of time. A typical output following theaddition of a pulse of fresh solute to the system is shown in Figure 7.3.

It can be seen from the graph that the concentration in the tank increasesimmediately after the solute has been added to the system. After this rapidincrease, the signal starts to decrease as the added benzyl alcohol adsorbs on theAmbersorb surface. After a number of hours, the new equilibrium is reached.


160

10 20 30 400

t [ks]

1

2

3

4

5

6

7

8

conc

entra

tion

[mV

]

current [mA

]

2.0

1.6

1.2

0.8

0.4

0

(a)

(b)

Figure 7.3: The current (a) and concentration (b) after addition of1 ml benzyl alcohol to the mixing tank.

The response of the current to the added benzyl alcohol is very interesting.First because there is a response. Before the pulse was added, the system was inequilibrium so any (remaining) charging currents are low and constant. Thepeak in the current line must be caused by the addition. The top of the peak is1.3 mA above the baseline and it takes in the order of 5000 s (1 hour and 20minutes) to fade out. This is the same timeframe in which most of theadsorption occurs.

To calculate the amount of charge transferred by the excess current, the areaunder the peak is determined. For the peak in Figure 7.3 it is approximately0.65 10-3 A (half height) ⋅ 5000 s (base) = 3.25 C. Using special integrationsoftware gives a more precise value of 3.298 coulomb.

7.2.2. TheoryAs the system is kept at a constant potential by the potentiostat in the set-up(Figure 3.10), a change in the amount of charge is directly proportional to achange of the capacity of the system (Eq. 2.2). In order to explainthermodynamically the electrosorption phenomenon, it was assumed in chapter2 (Figure 2.10) that adsorption takes place inside the double layer. Adsorptionof benzyl alcohol lowers the overall average dielectric constant of the system as


161

it replaces the highly polarizable water. Having a lower capacity, the system cancontain less charge and the external circuit must remove charge from thedouble layer. The result is the current peak.

The change in capacity is the difference between a capacitor filled with waterand a capacitor filled with benzyl alcohol, multiplied by the molar size of theadsorbing compound (Eq. 3.5). This leads to:

GCBH

molads

GCAH

moladstot

CC

Sn

CC

SnC 1111

,,+

−+

=∆ 7.8

The Helmholtz capacity is calculated with Eq. 2.20, the Gouy-Chapmancapacity is calculated with Eq. 2.5 and the various dielectric constants arecalculated with Eq. 2.18.

7.2.3. ExperimentalDuring the run in Figure 7.3 the amount of benzyl alcohol adsorbing wasdetermined using UV analysis to be 0.24 ml or 2.322 10-3 mol for each of theelectrodes (both electrodes are almost identical). For more information onconcentration measurements see section 3.3. The total potential difference of300 mV is distributed over two identical electrodes so the potential drop over asingle carbon-liquid interface is 150 mV. According to Eq. 7.8 the change incapacity after 2.322 10-3 mol of benzyl alcohol adsorbs and replaces adsorbedwater, is 104.2 F. The total charge transport is equal to 15.63 C.

Comparing the theoretical value of 15.63 C to the experimentally found value(the area under the peak) of 3.298 C shows that the peak should have been 4 to5 times higher. Only 21% of the adsorbing benzyl alcohol causes an electricalresponse. The remainder of the molecules must therefore have adsorbed on asite that is electrochemically not accessible or outside the double layer. Inchapter 5 the electrochemical not accessible part of the surface was assumed tobe about 50% of the BET area, this can account for only half the differencebetween theory and experiment.


162

2

1.5

1

0.5

0

-0.50 10000 20000

t [s]

i [m

A]

0.050.10.150.20.25

added[ml]

datapoint

13579

linetype

2

1.5

1

0.5

0

-0.50 10000 20000

t [s]

i [m

A]

0.050.10.150.20.25

added[ml]

datapoint

246810

linetype

Figure 7.4a) and b): Electrical signals after subtraction of thebaseline recorded during the electrosorption of benzyl alcohol whilea potential of –300 mV was applied.

In Figure 7.4 a) and b) the current curves generated during an electrosorptionexperiment are plotted. The amount of benzyl alcohol added to the systemincreases during the experiment. At the start of the experiment, the carbon iscompletely fresh and almost all benzyl alcohol will adsorb. At the end of theexperiment, the carbon is almost saturated and hardly any benzyl alcohol willadsorb. Increasing the pulse size means that the amount of material adsorbingis bell shaped. The adsorption is small at the start due to the small pulse, largest


163

in the middle and again small at the end due to saturation of the surface. Thesame pattern is found in these graphs.

7.2.4. ResultsFor each single measurement, the area under the graph and the height of thepeak are determined. It was found that integrating the peak area as is done inFigure 7.5 gave the best results. For the construction of each isotherm, between5 and 10 measurements were carried out. For all of these, the normalised peakareas and normalised peak heights are compared to the normalised amountadsorbing in order to compare their relative behaviour. The results are plottedfrom Figure 7.6 to Figure 7.9.

t [s]

i [m

A]

height of the peak

area ofthe peak

Figure 7.5: Two peak characteristics that are used. The influenceof the ‘negative’ peak on the height can be neglected as themaximum is very close to the left of the peak.


164

Figure 7.6a) – d): Normalised distributions of peak height, peakarea and amount adsorbed (first part).

Figure 7.7a) – d): Normalised distributions of peak height, peakarea and amount adsorbed (second part).


165

Figure 7.8a) – d): Normalised distributions of peak height, peakarea and amount adsorbed (third part).

Figure 7.9a) – d): Normalised distributions of peak height, peakarea and amount adsorbed (fourth part).


166

From these results it seems that a strong relation exist between adsorption andthe peak in the current line. Both the peak area and the peak height show thesame bell shaped pattern. Still this relation is only relative due to thenormalisation of both peak characteristics and adsorption.

The correlation between these two is less good for the phenol experiments thathave been carried out at higher potential differences. Experiments conducted athigher applied potentials were found to give more noise and relatively smallerpeaks. Due to the normalisation of all peaks, a single too high peakautomatically results in the other peaks being too low.

For a better overview of the large amount of data a parity plot was constructed(Figure 7.10). Each point represents the relation between peak area and amountadsorbing for a single measurement. Although there is a lot of scatter, mostpoints are located near the ideal line and the trend is unmistakable.

area of the peak

amou

ntad

sorb

ing

0.1 0.2 0.3 0.4

0.1

0.2

0.3

0.4

00

Figure 7.10: Parity plot relating the area beneath the relativeinitial current peak to the relative amount adsorbing.

7.2.5. DiscussionThe results so far suggest a relation between the adsorption and the current.This is of course supportive for the theoretical model. Until now only thenormalised data were examined instead of absolute values. Using Eq. 7.8 thetheoretical amount of charge that must be transported due to the adsorption of


167

benzyl alcohol can be calculated. These calculated peaks are compared to theactual peaks, Figure 7.11.

It can be seen from the graph that the peak area ratio A/Atheo rapidly decreaseswith increasing applied potentials. This means that the amount of adsorbingbenzyl alcohol giving an electrical response goes down, suggesting that theadsorption is decreasing for the polarised carbon surface area. The same patternwas found for the phenol experiments. The maximum ratio A/Atheo =0.49 wasfound for the –10 mV experiment. For the other potentials the ratio decreasedto about 5%. This means that for increasing applied potentials hardly anychanges in the dielectric are observed. Adsorption seems to occur only therewhere there is no double layer. This is also what the electrosorption theorypredicts.

φ [V]

A/A

th

eo [%

]

0

10

20

30

40

50

60

70

-1-0.8-0.6-0.4-0.20

Figure 7.11: Actual peak area related to theoretical peak areafor benzyl alcohol. For higher potentials this ratio rapidlydecreases.

7.3. Economics

7.3.1. IntroductionIn order to get a basic idea of the costs and therefore the applicability of theelectrosorption method, three in situ regeneration methods are compared to thesituation where the carbon is not regenerated, but new carbon is purchased.The carbon bed is to clean a wastewater stream of 100 L/min containing 5


168

mol/m3 phenol. The outlet stream must contain less than 0.05 mol/m3 phenol.The operating costs for a one-year operation period, including any equipmentinvestments, are determined and compared for the four methods. Allinstallations are assumed to depreciate within a period of 10 years.

The bed length is used as design parameter and ranges between 0.5 and 20 m.The bed diameter is 1 m. In the case of electrosorption this means that multiplecurrent collectors are installed so that the effective bed length for chargetransfer remains 20 mm. The volume of the bed depends on the length andvaries from 0.4 to 15.7 m3 and it contains between 248 and 9901 kg of carbon.Larger beds reduce the number of regeneration cycles needed during one year,these decrease from 340 to 17. An overview of all variables used can be foundin Appendix C.

7.3.2. No regenerationIf the carbon is not regenerated it must be replaced by fresh material once thecolumn becomes saturated. The investment associated with this method ofoperation is relatively small. A steel column is needed to contain the bed. Theprice of the column depends on its size, from 20 kЄ (20000 Euro) up to 52 kЄ(WEBCI and WUBO, 1999). These prices have to be divided by ten as allinstallations are in use for ten years. The used carbon is treated as chemicalwaste as a result of the adsorbed phenol. To get rid of it, 0.45 Є per kg carbonis charged. The price of new (regular) carbon for water purification 3.2 Є per kg(Staal, 2001). The costs for new carbon during one year are 267.7 kЄ.

7.3.3. Steam desorption at 543 KHere, steam of 543 K (270 °C) is used to desorb the adsorbed phenol. Toregenerate 1 kg of carbon, 1.5 kg of steam is needed. The steam is produced ina steam house, by burning natural gas. The efficiency of this regenerationmethod is assumed to be 90%. This is interpreted as follows: after anadsorption cycle 10% of the newly adsorbed phenol cannot be desorbed. Tocompensate for a reduced adsorption capacity, new carbon needs to bepurchased.


169

The investment includes the column and a facility for steam generation. Thecolumn is assumed to be twice as expensive as the one used in case one as theadsorption process is more complex. There are consecutive adsorption anddesorption cycles and the column must be able to handle two different fluids.The size of the steam generator depends on the bed size and the regenerationtime. Assuming an eight-hour period for regeneration and a 80% efficiency ofthe burner, the installation must deliver between 50 and 2000 kW. Theinvestment for the steam house, divided by ten, ranges from 0.32 – 12.66 kЄ(WEBCI and WUBO, 1999). Operation costs include heating costs, labourcosts and replacement carbon to compensate for the inefficiency of theregeneration.

7.3.4. Washing with methanolIn this case study methanol is used to regenerate the column. In eachdesorption cycle the column is flushed with 20 bed volumes of methanol. Themethanol is transported to a separation section where phenol and water areremoved from the methanol by heating the mixture. Ten percent of themethanol (2 bed volumes) is assumed to be lost because a substantial partremains in the bed and also the separation is not 100% effective. The methanolthat is lost must be replaced. The price of methanol is estimated at 0.16 Є perlitre for a large quantity (based on prices reported at chemical product exchangesites on the internet). A methanol storage facility must be built on-site to handlethese quantities. The efficiency of this regeneration method is assumed to be66% so the costs for buying new carbon to replace the spent carbon arereduced threefold.

The complete investment includes the adsorption column, a tank for methanolstorage and a distiller section. The costs for the column are assumed to be equalto those of case 2), between 4.14 and 10.37 kЄ. The costs of the storage tankare between 1.94 and 7.14 kЄ (WEBCI and WUBO, 1999) and the costs for theseparator are estimated between 3.9 and 14.3 kЄ. Operation costs includereplacement methanol, labour, heating costs and replacement carbon.


170

7.3.5. Electrochemical regenerationIn the fourth case study, electrosorption is used to influence the phenoladsorption equilibrium. The carbon bed is divided in two parts, the workingand the counter electrode. Each electrode is divided in 20 mm slabs by theaddition of current collectors. Based on the poor results in this work and thescarce literature data the efficiency of this method is considered to be only 50%.

The investment consists of an external electrical circuit and an adsorptioncolumn. The column is expensive due to the multiple layered structure of thebeds and the need for non-conducting construction materials. It is estimated at5 times the price of a regular column, so between 36.6 and 39.8 kЄ. Operationcosts are due to the electricity needed to polarise the electrodes and desorb thephenol labour costs and cost.

7.3.6. ResultsIn the tables below an overview of all costs associated with the four case studiesis presented. The bed size is used as variable. Equipment costs are alreadydivided by ten.

Case 1/bed size 250 kg 500 kg 1000 kg 2000 kg 5000 kg 10000 kg

Column 2.068 2.105 2.197 2.424 3.31 5.185

Labour 0 0 0 0 0 0

Waste carbon 38.27 38.27 38.27 38.27 38.27 38.27

New carbon 267.9 267.9 267.9 267.9 267.9 267.9

Total 308.23 308.26 308.36 308.58 309.47 311.34

Table 7.4: Case 1 operating costs for four different bed sizes.Prices in 1000 euro’s.

The total costs for case 1) are almost independent of the bed size. In order toremove the phenol from the water about 300.000 euro must be paid each year.


171


Column 4.136 4.21 4.393 4.849 6.62 10.371

Steam house 0.316 0.633 1.266 2.531 6.329 12.657

Labour 74.215 37.107 18.554 9.277 3.711 1.855

Waste carbon 3.827 3.827 3.827 3.827 3.827 3.827

New carbon 26.79 26.79 26.79 26.79 26.79 26.79

Steam 2.376 2.376 2.376 2.376 2.376 2.376

Total 111.66 74.942 57.204 49.649 49.651 57.875


The costs for case 2) are much lower as the costs for new and waste carbonhave decreased tenfold. The relative high costs for using small beds are due tothe regeneration labour costs.


Column 4.136 4.21 4.393 4.849 6.62 10.371

Tank 1.938 2.203 2.634 3.335 4.975 7.138

Separator 3.875 4.406 5.269 6.671 9.950 14.276

Labour 74.215 37.107 18.554 9.277 3.711 1.855

Waste carbon 12.757 12.757 12.757 12.757 12.757 12.757

New carbon 89.296 89.296 89.296 89.296 89.296 89.296

Methanol 42.502 42.502 42.502 42.502 42.502 42.502

Heat 16.099 16.099 16.099 16.099 16.099 16.099

Total 244.82 208.58 191.50 184.79 185.91 194.29


If this process were operated without methanol recovery, the process would beat least three times more expensive, and therefore twice as expensive as case 1).


172


Column 16.646 16.816 17.024 17.277 17.701 18.105

Electric 10 10 10 10 10 10

Labour 74.2115 37.105 18.554 9.277 3.711 1.855

Waste carbon 19.135 19.135 19.135 19.135 19.135 19.135

New carbon 133.94 133.94 133.94 133.94 133.94 133.94

Charging 0.088 0.088 0.088 0.088 0.088 0.088

Desorption 0.053 0.0530 0.053 0.053 0.053 0.053

Total 248.63 211.69 193.34 184.32 179.18 177.73


The total costs as function of bed size are plotted in Figure 7.12 and in Figure7.13 for two different inlet concentrations. It can be seen that the ‘noregeneration’ alternative is the most expensive in both cases. Washing withmethanol and electrosorption results in similar costs. Steam regeneration seemsthe cheapest solution for all configurations.

size of carbon bed [kg]

cost

s [1

0 eu

ro]

3

0 2000 4000 6000 8000

no regeneration

steam regeneration

methanol

electrosorption

40

60

80

100

120

Figure 7.12: Total costs of the various alternatives as function ofthe amount of carbon installed. Inlet concentration is 1 mol/m3

phenol.


173

size of carbon bed [kg]

cost

s [1

0 eu

ro]

3

0 2000 4000 6000 8000

no regeneration

steam regeneration

methanol

electrosorption

100

150

200

250

300

300

Figure 7.13: Total costs of the various alternatives as function ofthe amount of carbon installed. Inlet concentration is 5 mol/m3

phenol.

If the concentration decreases the differences between ‘no regeneration’ andthe other methods tend to become smaller, which is quite logical. The methanoland steam regeneration costs depend more strongly on the bed size than thecosts for electrosorption.

The efficiency of the regeneration method turns out to the most importantfeature as the buying of new carbon contributes most to total costs. It is for thisreason that electrosorption is less successful as alternative. The electricity costsfor charging the bed and desorbing the phenol are very low and can usually beneglected compared with the other costs. However due to the low efficiency ofthe method the costs for new carbon are too high.


174

175

C H A P T E R 8

CONCLUSIONS

In this chapter a summary of the results presented in this thesis is given withthe intention to discuss implications and suggest topics for further research.

Double layer models

• Excess charges are present in the inter-phase region. Charges in onephase induce an opposite charge in the next phase. There are two layers ofcharge, the double layer. The Helmholtz model describes the polarisedinterface as an ideal electrical capacitor. The distance between the chargedlayers is about one nm so the electrical field is in the order of 109 V/m.

• Experimental differential capacity data for mercury electrodes showsthat C is a weak function of both φ and cion. The Helmholtz model predicts acapacity that is constant.

• The Gouy-Chapman model was to be an improvement but it gravelyoverestimates the influence of φ and cion. It predicts that the capacitybecomes infinite at mild conditions already.

• The Stern model in essence combines the Helmholtz and the Gouy-Chapman models. For the high salt concentrations of 0.5 N KCl used in thiswork, the Stern model is almost identical to the Helmholtz model andtherefore it provides no real improvement.

Chapter 8: Conclusions

176

• Even if contact adsorption of ions is included in the Stern model, itremains impossible to completely predict experimental capacity versuspotential curves. This is true for both high frequency capacity measurementsand for DC methods. The differential capacities measured for graphite andAmbersorb in chapter 5 showed broad and shallow depressions around zeropotential, where the Stern model predicts a local and deeper depression (theGC contribution). Perhaps inhomogenities and surface groups in the carbonmatrix smear out the point of zero potential to a range of zero potential.The carbon materials used however are very homogeneous by nature.

• The dielectric constant decreases if a strong field is present. A limitingvalue of 5 for water is reported by Bockris and Reddy (1970b) and Kortüm(1965).

• Applying the constant limiting value for the dielectric constant ofhydration water molecules in the way it is done by Bockris and Reddy is notcorrect. These limiting values are reached only if large potentials are appliedso their model gives to low capacities if small potentials are applied.

• The alternative is to use a field dependent dielectric constant byapplying the complete Langevin equation instead of its Taylorapproximation. The Kirkwood formula was used to calculate frommolecular properties such as the dipole moment ant the polarisability thedielectric constant.

• Kirkwood constants of 5 for water and various alcohols and 2 foraceton (under normal conditions) followed from molecular properties.Molecules with large dipoles had lower constants. For use in the doublelayer model, the Kirkwood constant had to be lowered to 1.5 to be able tofit experimental capacity data. The presence of the solid surface is assumedto lower the amount of neighbours for water resulting in a lower KKW.

The mechanism of electrosorption

• It is assumed that adsorption takes place inside the double layer. Theequivalent electrical view on electrosorption is the movement of a slab of


177

material inside a charged capacitor. Using thermodynamics, changes in theadsorption constant as a function of potential can be related to changes inthe required work of adsorption.

• The difference in dielectric constants of the solute and solventmolecules is the main driving force for electrosorption. The energy of acharged capacitor is given by ½Cφ2. The system can reduce its energy byinterchanging molecules with a low dielectric constant for those with a highdielectric constant. The energy of the capacitor increases but the connectedpotential source decreases its energy to a larger extend.

• The potential dependent adsorption equilibrium is used together with aLangmuir-Freundlich isotherm to fit experimental electrosorption data. Thestandard Langmuir isotherm cannot accurately fit adsorption data of organiccompounds on activated carbon.

Electrosorption data from literature

• The complete collection of electrosorption data available in literaturecan be plotted in two small graphs without problems.

• The quality of the literature data is poor. The number of data points perseries is no more than three or four. Measurements are limited to onebranch of the potential so trend extrapolations to obtain a bell shape have alarge degree of uncertainty. It is difficult to compare data series becauserelative conditions and experimental set-ups differ.

• By introducing a bed efficiency constant and assuming a loss ofpotential in the liquid phase, the electrosorption model could fit thereported electrosorption data series.

Electrosorption data determined in this work

• The batch method for measuring adsorption equilibrium is a fastmethod as multiple points can be determined in one run. The methodcannot be used for other than open circuit conditions. Although the dataobtained from this method is in the same order of magnitude as reports


178

from literature, the experimental results are considered poor due to largescattering.

• The continuous method is slower due to smaller mass transfer and onlyone isotherm point can be measured at the same time. The results are good,scattering is relatively low (10%) and runs can be reproduced. The methodcan be used for electrosorption isotherms.

• Accurately determining the influence of the potential on the isothermhas proven a difficult task. No large effects have been measured, or at least,could not be reproduced. Small effects are hard to find due to the type of(analysing) method used. Adsorption is determined by monitoring depletionof the bulk phase. If the experimental procedures are not extremely accuratethe resulting errors are big and suppress any electrosorption effects.

• Large effects of the potential on the adsorption of benzyl alcohol onAmbersorb 572 have been measured but these turned out to be due tounaccounted for chemical reactions occurring in the system.

• Large effects of the potential on the isotherm found in literature forphenol on activated carbon (McGuire et al., 1985) and for benzyl alcohol onactivated carbon (Bán, 1998) could not be reproduced.

• Desorption experiments suggest effects up to 20%, but these are notbacked by the relevant adsorption experiments.

The physical behaviour of packed bed electrodes

• The response of two packed bed electrodes to a change in appliedpotential closely resembles that of a classic RC circuit.

• Due to its large characteristic time, charging of packed bed electrodes isa very slow process. As the charging time depends quadratically on thedistance to the current collector, thin beds are required.


179

• The response of complex RC circuits can be determined by a Laplacetransform method. This method cannot give results that contain a placedependency to account for internal electrical resistances.

• Distribution of potential in an electrode is mathematically equal to heattransfer in a slab of material (Posey and Morozumi, 1966).

• Changing the boundary conditions gives three potential distributionfunctions. The no losses model assumes that the carbon is much moreconductive than the pores and no external resistances exist. The internallosses model assumes that the carbon matrix and the pores have about thesame conductivities. The external losses model assumes that part of theapplied potential is lost due to ohmic resistances in the liquid phase.

Transient current experiments

• Only the external losses model can correctly describe experimentaltransient current experiments. The other two models are discarded.

• Reproducibility of transient current experiments is good. By fittingthem with exponential functions the values of electrical properties such asthe capacity, resistances and loss factors can be obtained.

• Direct measurement of particle and bed resistances proved to beunsatisfactory as too high values were obtained.

• Moderate mechanical pressure can significantly enhance theconductivity of packed beds of carbon granules.

• The total capacity is a weak function of the applied potential. The totalresistance is independent of the applied potential. Increasing the solventconcentration had no real influence.

Simulating a packed bed electrosorption unit

• Six characteristics times can be identified: Residence, adsorption,desorption, dispersion, mass transfer and double layer charging time. The


180

adsorption time should be larger than the charging time, the adsorption timeshould be 100 times larger than the residence time, the dispersion timeshould be 10 times larger than the residence time and the residence timeshould be 10 times higher than the mass transfer time. The second of thesefour conditions is always satisfied.

• The other three conditions can be satisfied by changing the liquid speedand the bed length, the two most important design parameters. If u = 2 10-6

m/s, L can be up to 4 m and dp to 10 mm. If u = 2 10-5 m/s, L can be up to0.4 m and dp to 1 mm. If u = 2 10-4 m/s, L can be up to 0.04 m and dp to 0.1mm. The mass transfer condition is never limiting.

• If lower concentrations are used, but the total mole flow remains thesame, lower characteristic times are obtained.

• The difference between co-current and counter-current configurationsis small. Differences occur only for the (short) time that the bed is not yetfully charged. Counter-current gives initially a faster reduction of carbonloading.

• Incorporating a potential and surface concentration dependent capacityfunction in the set of equations, instead of an empirical quadratic equationdoes not generate large differences on the packed bed performance.

Streaming current

• Streaming current is a phenomenon caused by the movement of theGC excess charge due to an applied pressure difference over the packedbed.

• A theoretical value of 8.2 mA at 1 V and 1 bar was found to be 2.5times larger in practice. A possible error in estimating the effective areacould be the cause of the difference.

• Increasing the pressure or the potential gives higher charging currents.The relation is not linear as predicted by theory. Deviations are more


181

pronounced for smaller potentials. It is assumed that increasing turbulencecauses less favourable contributions to the charging current generation.

The relation between charge and mass transfer

• The adsorption of benzyl alcohol on a polarised packed bed electrodeof Ambersorb 572 causes transport of charge. If the relative amountadsorbing (normalised) is compared to the relative amount of chargetransported (normalised) a good linear relation is found.

• Using the electrosorption model, the theoretical charge transferassociated with a certain amount of adsorption can be calculated andcompared to the experimental results. For small potentials this ratio is in theorder of 60%. For larger potentials it drops to 5-10%. If large potentials areapplied more of the adsorbing benzyl alcohol does not lead to an electricalresponse.

• A large part of the surface is covered with an electrical double layer, thisfollows from the electrical capacity measurements. Adsorption occurs insidethe double layer for small potentials and not inside the double layer for largepotentials.

Economics and feasibility

• In chapter 3 it was found that the effectiveness of electrosorption intheory could be as good as adding methanol to the mixture. Potentials didnot exceed 1.33 V to achieve the same results as rinsing with 100%methanol.

• Energy costs can be divided into two: for polarising the bed and fordesorbing the adsorbed compounds. This energy depends on systemconfiguration and conditions. It is between 4.3 and 30.7 kJ/mol and 2.6 and15 kJ/mol respectively.

• The operation costs for four cases are compared: No regeneration,steam regeneration, methanol regeneration and electrosorption. It was foundthat steam regeneration is the cheapest method. Methanol regeneration and


182

electrosorption are almost equally expensive. No regeneration is the mostexpensive option. Electricity costs can be neglected, the only problem forthe electrosorption alternative is the (probably) low regeneration efficiency.

List of symbols

183

L I S T O F S Y M B O L S

LatinA [m2] cross sectional areaa [m2/m3] interfacial areaa [-] adsorption interaction coefficient (Section 3.1.1)C [F/m2] differential capacityc [mol/m3] concentrationD [m2/s] diffusivity coefficientID [m2/s] dispersion coefficientd [m] distance between charged layersE [V/m] electrical fieldE’ [V/m] local electrical fielde0 [C] elemental charge (1.602 10-12 C)F [C/mol] Faraday constant (9.649 104 C/mol)F [N] electrostatic force (Eq. 2.31)Fo [-] Fourier number (mass)G [J/mol] Gibbs free energyg [-] association constant (Section 2.2.11)i [A] currentJ [mol/(s m2)] molar fluxj [A/m2] current densityK [F/m2] integral capacity (Eq. A.2, A.4)K [-] adsorption equilibrium constantKF [varies] Freundlich adsorption constantk [J/K] Boltzmann’s constant (1.381 1023 J/K)kads/des [1/s] rate of adsorption/ desorption (Eq. 2.33, 2.34, 3.1)kKW [-] Kirkwood’s constant (Eq. 2.18)kL [m/s] mass transfer coefficient

)(x [-] Langevin functionL [m] bed lengthM [kg/mol] molecular weightm [kg] mass (of carbon bed, Section 3.2.3)

List of symbols

184

m [-] number of resistors in infinite series modelN [mol] number of dipolesNAV [1/mol] Avogadro’s constant (6.022 1023 1/mol)n [mol] number of particlesnF [-] Freundlich adsorption constantn∞2 [-] refractive index squared (≈ 2 for liquids)o [-] number of charged rings (Eq. A.7 – A.12)P [C m] dielectric polarisationPe [-] Péclet number∆p [Pa] pressure dropQ [C] total chargeq [C/m2] charge density (Chapter 2)q [mol/kg] surface concentrationR [Ω] resistanceR [J/(mol K)] gas constant (8.314 J/(mol K))r [m] radius of molecule or ionRe [-] Reynolds numberS [m2] surface areaSc [-] Schmidt numberSh [-] Sherwood numbers [1/s] Laplace timeT [K] temperaturet [s] timeU [J] energyu [m/s] velocityV [m3] volumew [J] workXm [-] root (Eq. 4.28)x [m] place co-ordinatex [-] mole fractionx [-] auxiliary constants (Eq. 2.11, Eq. A.11)Ym [-] root (Eq.4.26)z [-] ionic charge numberz [m] position

List of symbols

185

Greekα [C2m2/J] molecular polarisabilityβ [-] angle between dipoles (in radials)χ-1 [m] Debye lengthεbed [-] porosityε0 [F/m] permittivity of the vacuum (8.854 1012 F/m)εr [-] dielectric constantη [-] efficiencyη [Pa s] viscosity (chapter 7)Φ [m3/s] volume flowφ [V] potentialφN [V] Frumkin constantϕ [-] angle in radialsγ [10-5 N] surface tension (chapter 1)γ [-] internal loss factorΚ [?] Kohlrausch constantκ [S/m] conductivityΛ [S m2/mol] molar conductivityλ [-] external loss factorλ [S m2/mol] limiting conductivity of ion (Eq. 5.4)µ [C m] dipole momentν [-] stochiometric constant (Eq. 2.22, Table 3.1)σ [C/m2] surface charge densityρ [kg/m3] densityτ [s] characteristic timeθ [-] surface coverageξ [-] dimensionless bed length

Sub- and superscripts0 initial, basic or standard conditions1,2,3… case 1,2,3…

List of symbols

186

A watera atomicads adsorptionB organic compoundbatt battery (source, potentiostat)BET indication of total surface areaCA contact adsorbed ionchem chemicalID dispersiond dipoledes desorptiondl double layerel electric/electronicext external (applied)GC Gouy-Chapman capacity modelH Helmholtz capacity modelI bulk phaseII adsorbed phasein feedint interfaceL liquidLI lateral InteractionM solid phase (originally from ‘metal’)max maximal (coverage)mol molarMT mass transferp particleR residence timeST Stern capacity modeltot total+ positive (ion)- negative (ion)

List of symbols

187

AbbreviationsAC Activated CarbonBET after Brunauer Emmet and Teller, indication of total surface areaCE Counter ElectrodeEDA Ethylene DiAmideFID Flame Ionisation DetectorGC Gas ChromatographHFL Helfand-Frisch-Lebowitz isothermIHP Inner Helmholtz PlaneIPE Ideal Polarised ElectrodeOHP Outer Helmholtz PlaneRE Reference ElectrodeSHE Standard Hydrogen ElectrodeT&N Tiedemann and Newman (plot of i(t)√t versus √t)UV Ultra VioletWE Working Electrode

List of symbols

188

References

189

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References

194

Appendices

195

A P P E N D I X A : C O N T A C TA D S O R P T I O N O F I O N S

Derivation of the triple layer model

If contact adsorption occurs, the double layer becomes a triple layer. The thirdline can be drawn through the centres of the contact adsorbed ions. It is calledthe IHP or Inner Helmholtz Plane. If it is assumed that there is no diffusedouble layer, the total potential difference across a triple layer interface (fromcarbon (M) to bulk liquid (S)) can be written as follows:

)()( OHPIHPIHPMSM φ−φ+φ−φ=φ−φ A.1

Both potential drops can be expressed in terms of the integral capacities KM-IHP

= qM/(φM – φIHP) and KIHP-OHP = qOHP/(φIHP - φOHP) that are independent ofpotential and charge. Differentiating to qM gives:

( )M

OHP

OHPIHPIHPMM

SM

dqdq

KKdqd

−−+=φ−φ 11 A.2

The electroneutrality constraint dictates that qM = qCA + qOHP. Differentiatingthis constraint gives:

M

CA

M

OHP

dqdq

dqdq −= 1 A.3

Combining Eq. A.2, Eq. A.3 and Eq. 2.2 yields:

M

CA

OHPIHPOHPIHPIHPM

M

CA

OHPIHPIHPM

dqdq

KKK

dqdq

KKC

−−−

−−

−

+=

−+=

111

1111

A.4

Appendices

196

This formula shows that the capacity of a system where contact adsorption ofions take place does not depend only on the integral capacities of the Innerand Outer Helmholtz regions, but also on the differential of contactadsorption with electrode charge. The dependence of the capacity on qM

(which is directly related to the applied potential) can hence account forasymmetric capacity-potential curves and especially for the non constantvalues at higher potentials.

The contact adsorption of ions is examined using the following equilibrium:

Empty site + ion at the OHP ↔ Contact Adsorbed ion

The transition of an ion from the OHP to the IHP can be expressed using achange in Gibbs free energy. Applying the law of mass action to thisequilibrium results in:

RTGion

sitesempty

CA renn

n /

∆−= A.5

with n the amount per surface area and ∆Gr the free energy change associatedwith the ‘reaction’. The nion is related to the concentration of ions in thesolution and nempty sites to the fraction of the surface covered with ions. Becausewe work under isothermal conditions the change in Gibbs free energy equalsthe amount of work done. The total work when transporting an ion is the sumof three contributions:

1) Chemical work arising from forces between electrode and ion.

2) Electrical work arising from interactions of the ion with the electrical field.

3) Electrical work arising from interactions of the ion with its surroundingcontact adsorbed ions.

The chemical work is accounted for by defining a change of free chemicalenergy ∆Gr,chem. The second contribution is related to the distance (x2 – x1) ourion is moved with respect to the field. The field inside the capacitor equals thepotential times the distance and the work done while transporting a charge e0

over this distance is:

Appendices

197

( )r

MIHPOHP

exxqwεε−

=−0

012 A.6

Calculating the interactions of an ion with its contact adsorbed neighbours iscomplicated. Bockris and Reddy (1970b) described the interactions of acentral ion with the surrounding ions by assuming the latter were pinneddown in a hexagonal grid (see Figure A.1) in order to simplify mathematics.By smoothing out the charges of ions at the same distance into a ring ofcharge o, they obtained a central ion surrounded by charged rings of increasingradii. In the first ring 6 ions can reside, in the second 12 and in the oth ring 6o.

r

π(r/2)2Area

2r

Site

centralion

Figure A.1: The adsorption sites for ions in the IHP according toBockris and Reddy (1970b).

The charge density σ in the oth ring is given by:

06oe=σ A.7

If r is the distance between the centres of two ions, the site area is π(r/2)2 sothere are 4/πr 2 sites per unit area. Because not all sites are filled with ions wehave:

Appendices

198

CAnr

π= 4 A.8

The potential at the central ion due to the oth ring is equal to the total chargeon the ring divided by the distance to the ring and the value for the dielectric.For the (repulsive) interaction energy we obtain:

ore

ore

rr εεσ=

επεπσ

0

0

0

0

242 A.9

This result needs to be modified due to the closeness of the carbon solidphase. The adsorbed charges induce charges on the electrode surface. Theseinduced charges are mathematically represented by image charges lying adistance 2rion inside the electrode (Bockris and Reddy, 1970b). The distance tothe reference ion is [(or)2 + (2rion)2]1/2. Thus the total interaction work takinginto account all rings both image and real becomes:

( )[ ]∞

=

+−

εεσ=

120

0

21

/21

112n ionr

LIorror

ew A.10

Using the following factorisation:

( ) ...11 283

212

1

++−=+ − xxx A.11

and incorporating the expressions for r (Eq. A.7) and σ (Eq. A.8) leads to thefinal result:

∞

=

∞

=εεπ−

εεπ=

1 14

0

20

4

20

20

2 132

918

3 25

23

23

21

n nr

CAion

r

CAionLI o

nero

nerw A.12

where the two summations are equal to π2/6 and π4/90 respectively. With theexpressions derived for the chemical, electrical and interaction contributionsthe total work is known. Substituting the results in Eq. A.6 gives the soughtafter expression for the population density of contact adsorbed ions:

Appendices

199

( )

εεπ−

εεπ−

εε−+

∆−=

kTner

kTner

kTexxq

RTG

nnn

r

CAion

r

CAion

r

Mchemrion

empty

CA

0

20

4

0

20

2

0

012,

32016

exp

25

211

23

25 A.13

If the following additional relations are used (Bockris and Reddy, 1970b):

total

iAionCA

total

emptyACACA n

rNnnn

FNqn

10002 and 1 ,max =θ−=θ= A.14

with qmax the charge density occurring at maximal adsorption, NA Avogadro’snumber and θCA the fraction of the surface covered with ions. Incorporatingthese relations in Eq. A.13, neglecting the (smaller) second term of theinteraction work and taking the logarithmic form, one obtains:

( )

232

325

max

0

220

0

012,

max

16

ln1000

2ln1

ln

CAA

r

ion

Mr

chemrion

ion

CA

CA

FNq

kTre

qkT

exxRTG

cqFr

θ

εεπ−

εε−+

∆−+

=

θ−θ

A.15

or simply:

23

ln1

ln CAMionCACA

CA BAqck θ−++=θ−

θ A.16

with kCA, A and B the appropriate constants. Eq. A.16 can be used to calculatethe differential dqCA/dqM in Eq. A.4. Because θCA and qCA are linearlydependent the differential dθCA/dqM can be used directly. However Eq. A.16cannot be differentiated directly due to the two terms containing θCA. Taking1/(dqM /dθCA) results in an equation containing only θCA, yet an equation withqCA is needed. The differential dθCA/dqM must therefore be calculatednumerically.

Appendices

200

As can be seen from Figure A.2, the occurrence of contact adsorption canlead to asymmetric potential capacity curves. It was not possible to reproduceexactly the capacity curves calculated by Bockris. The inflection point in thedifferential qCA/qM was found to occur at more negative potentials. Thisresults in the relatively high capacities (the left hump in Figure A.2) fornegative potentials contrary to the low values reported in literature.

-0.2 -0.1 0 0.1 0.2

qM [C/m ]2

10

15

20

C [

F/cm

2 ]µ

Figure A.2: Calculated differential capacity from the Triple layermodel (Eq. A.16) in series with the GC model (Eq. 2.X).Chloride ions are contact adsorbing from a bulk containing 0.5 NKCl.

Appendices

201

A P P E N D I X B : L I S T I N G O FG P R O M S I N P U T F I L E S

Program listing 1. A single current collector is used that can be put atthe begin or the end of the packed bed. The electrical capacity isconstant.

######################################################### #### gPROMS model source #### model: Langmuir-Freundlich, ext resist, 1D #### single current collector #### December 2000 #### Vincent Fischer #### #########################################################

DECLARE

TYPEVOLTAGE = 0.5 : -1E15 : 1E15 UNIT = "V"FLUX = 0 : -1E15 : 1E15 UNIT = "mol/m2.s"CONDUCTIVITY = 1.0 : -1E15 : 1E15 UNIT = "1/Ohm.m"CONCENTRATION = 1 : -1E30 : 1E15 UNIT = "mol/m3"LOADING = 1 : -1E30 : 1E15 UNIT = "mol/kg"ADSCONST = 10 : -1E15 : 1E15 UNIT = "m3/mol"SPEED = 1e-6: -1e15 : 1e15 unit = "m/s"DISPERSION = 1e-9: -1e15 : 1e15 unit = "m2/s"FLOW = 1e-6: -1e15 : 1e15 unit = "m3/s"TRANSFER = 1e-4: -1e15 : 1e15 unit = "m/s"SPECIFICSURFACE= 1E6 : -1e15 : 1e15 unit = "1/m"

END # DECLARE SECTION

####################################### #### MODELS START HERE #### #######################################

MODEL Tube

PARAMETERLength AS REAL # Reactor Length [m ]dbed AS REAL # Reactor diameter [m ]dp AS REAL # Particle diameter [m ]rho AS REAL # density particle [kg/m3 ]Ebed AS REAL # External porosity [m3/m3 ]qmax AS REAL # Maximale belading [mol/m3 ]

Appendices

202

kappaL AS REAL # Specific Conductivity [1/Ohm.m ]CAP AS REAL # Differential Capacitance [F/m2 ]A AS REAL # interaction coeff. 1 [m3/mol.V2]B AS REAL # interaction coeff. 2 [m3/mol.V ]C AS REAL # interaction coeff. 3 [m3/mol ]diff AS REAL # diffusivity coefficient [m2/s ]SBET AS REAL # specific surface area [m2/kg ]lambda AS REAL # Ohmic loss factor [- ]

DISTRIBUTION_DOMAINAxial AS (0:Length) # coordinate for the concentrationAxial2 AS (0:Length) # coordinate for the voltage

VARIABLEq AS DISTRIBUTION(Axial) OF loading # in solid phaseJ AS DISTRIBUTION(Axial) OF FLUX # adsorption fluxcB AS DISTRIBUTION(Axial) OF CONCENTRATION # in reactorV AS DISTRIBUTION(Axial2) OF VOLTAGE # Elect. potentialK AS DISTRIBUTION(Axial2) OF ADSCONST # Adsorption equil.kappa AS CONDUCTIVITY # Bulk conductivitycBin AS CONCENTRATION # Concentration in inletVzero AS VOLTAGE # External applied potentialu AS speed # interstitial velocityD AS dispersion # Dispersion coefficientkL AS transfer # mass transfer coefficientAbed AS specificsurface # surface area installedF AS flow # volume flow

BOUNDARY# @ x = 0 # At the inletcB(0) = cBin; # closed boundary# cB(0) = cBin + D/u * PARTIAL(cB(0),Axial) ; # open boundary

# V(0) = Vzero - lambda*Length* PARTIAL(V(0),Axial2) # for co-currentoperationPARTIAL(V(0),Axial2) = 0 ; # for counter-current operation

# @ x = Length # At the outletPARTIAL(cB(Length),Axial) = 0 ; # no flux condition

V(Length) = Vzero - lambda*Length*PARTIAL(V(Length),Axial2); # forcounter-current operation# PARTIAL(V(Length),Axial2) = 0 ; # for co-current operation

EQUATION# Specific interfacial areaAbed = 3*(1 - Ebed) / (dp/2);

# Interstitial liquid speed through columnu = F/(Ebed*3.1415*0.25*dbed^2);

# Dispersion coefficient

Appendices

203

D = (2*Ebed/(3-Ebed)) * diff + (u*dp/2) ;

# Mass transfer correlation of Wilson and Geankoplis, 1966kL = 1.09*diff/(Ebed*dp)*(dp * u /(Ebed*diff))^0.3333 ;

# Component B balance fluid phaseFOR x := 0|+ TO Length|- DO$cB(x) = (D * PARTIAL(PARTIAL(cB(x),Axial),Axial)) -

(u * PARTIAL(cB(x),Axial)) - (J(x) * Abed) ;# Diffusion, convection and adsorption partsEND # for loop

# Component B balance solid phaseFOR x := 0 TO length DO$q(x) = J(x) * Ebed * Abed /(rho*(1 - Ebed)) ;END # for loop

# Transport Equation to solid phase with LF isothermFOR x := 0 TO Length DOJ(x) = kL * (cB(x) - (q(x)/((qmax -q(x) )*K(x) ))^2 ) ;END # for loop

# Langmuir-Freundlich Adsorption Constant from Electric FieldFOR x := 0 to Length DOK(x) = (A * V(x)^2) + (B * V(x)) + (C) ;END # for loop

# Effective conductivity from specific conductivitykappa = ((2 * Ebed) / (3-Ebed)) * kappaL ;

# Electric potential differential equationFOR x := 0|+ TO Length|- DO$V(x) = (Ebed*kappa/(rho*SBET*(1-Ebed)*CAP)) *

PARTIAL(PARTIAL(V(x),axial2),axial2) ;END # for loop

END # Model

####################################### #### SIMULATION STARTS HERE #### #######################################

PROCESS ElecBuis

UNIT Elecbuis AS Tube

MONITOR# The variables that will be reported#Elecbuis.J(50) ;Elecbuis.cB(25) ;Elecbuis.cB(50) ;#Elecbuis.q(5) ;

Appendices

204

Elecbuis.q(25) ;Elecbuis.q(50) ;#Elecbuis.K(25) ;#Elecbuis.K(50) ;Elecbuis.V(13) ;Elecbuis.V(25) ;Elecbuis.V(37) ;Elecbuis.V(50) ;

SET # ConstantsWITHIN ElecBuis DOAxial := [BFDM, 2, 50]; # Discretization for convective flowAxial2 := [CFDM, 2, 50]; # Discretization for dispersive flowqmax := 10 ; # [mol/kg ] monolayer adsorptionLength := 0.02 ; # [m ] of the beddbed := 0.7 ; # [m ] diameter of the beddp := 5E-4 ; # [m ] particle diameterkappaL := 5.88 ; # [1/Ohm.m ] electric conductivity liquidrho := 1146 ; # [kg/m3 ] particle densityEbed := 0.45 ; # [m3/m3 ] porosity of the bedCAP := 0.15 ; # [F/m2 ] differential capacityA := -0.1 ; # [m3/mol.V2] 2th order influence potB := 0 ; # [m3/mol.V ] 1th order influence potC := 0.2 ; # [m3/mol ] 0th order influence potdiff := 9E-10 ; # [m2/s ] diffusion coefficientSBET := 1.1E6 ; # [m2/kg ] BET surface arealambda := 0.05 ; # [- ] external loss parameter potEND # within

ASSIGN # more variablesWITHIN Elecbuis DOF := 33.33E-6 ;cBin := 5 ;Vzero := 0.0 ;END # within

INITIAL # Differential VariablesWITHIN ElecBuis DOFOR x := 0|+ TO Length|- DOcB(x) = 0;END # for

FOR x := 0 TO Length DOq(x) = 0;END # for

FOR x := 0|+ TO Length|- DOV(x) = 0;END # forEND # WITHIN

SOLUTIONPARAMETERSGPLOT := ON ;REPORTINGINTERVAL := 2000 ;

SCHEDULE

Appendices

205

SEQUENCE

CONTINUE FOR 80000RESET # Desorption starts hereElecbuis.F := 33.33e-6 ;Elecbuis.Vzero := 1.0 ;Elecbuis.cBin := 0.0 ;END # resetCONTINUE FOR 320000END # sequence

END # Process

Program listing 2. The packed bed is divided into n sub regions inorder to simulate the effect of n-1 current collectors in contact with thecarbon. The electrical capacity is considered constant.

######################################################### #### gPROMS model source #### model: Langmuir-Freundlich, ext resist, 1D #### multiple current collectors #### December 2000 #### Vincent Fischer #### #########################################################

DECLARE

TYPEVOLTAGE = 0.5 : -1E15 : 1E15 UNIT = "V"FLUX = 0 : -1E15 : 1E15 UNIT = "mol/m2.s"CONDUCTIVITY = 1.0 : -1E15 : 1E15 UNIT = "1/Ohm.m"CONCENTRATION = 1 : -1E30 : 1E15 UNIT = "mol/m3"loading = 1 : -1E30 : 1E15 UNIT = "mol/kg"ADSCONST = 10 : -1E15 : 1E15 UNIT = "m3/mol"speed = 1e-6: -1e15 : 1e15 unit = "m/s"dispersion = 1e-9: -1e15 : 1e15 unit = "m2/s"flow = 1e-6: -1e15 : 1e15 unit = "m3/s"transfer = 1e-4: -1e15 : 1e15 unit = "m/s"

specificsurface = 1E6 : -1e15 : 1e15 unit = "1/m"


####################################### #### SUBMODEL STARTS HERE #### #######################################

Appendices

206

MODEL partofbed

PARAMETERLength AS REAL # Reactor Length [m ]dbed AS REAL # Reactor diameter [m ]dp AS REAL # Particle diameter [m ]rho AS REAL # density particle [kg/m3 ]Ebed AS REAL # External porosity [m3/m3 ]qmax AS REAL # Maximale belading [mol/m3 ]kappaL AS REAL # Specific Conductivity [1/Ohm.m ]CAP AS REAL # Differential Capacitance [F/m2 ]A AS REAL # interaction coeff. 1 [m3/mol.V2]B AS REAL # interaction coeff. 2 [m3/mol.V ]C AS REAL # interaction coeff. 3 [m3/mol ]diff AS REAL # diffusivity coefficient [m2/s ]SBET AS REAL # specific surface area [m2/kg ]lambda AS REAL # Ohmic loss factor [- ]


VARIABLEq AS DISTRIBUTION(Axial) OF loading # in solid phaseJ AS DISTRIBUTION(Axial) OF FLUX # adsorption fluxcB AS DISTRIBUTION(Axial) OF CONCENTRATION # in reactorV AS DISTRIBUTION(Axial2) OF VOLTAGE # Elect potentialK AS DISTRIBUTION(Axial2) OF ADSCONST # ads. constantkappa AS CONDUCTIVITY # Effective conductivitycBinlet AS CONCENTRATION # Concentration in inletVzero AS VOLTAGE # ext applied potentialu AS speed # interstitial velocityD AS dispersion # Dispersion coefficientkL AS transfer # mass transfer coeffAbed AS specificsurface # surface area installedF AS flow # volume flow

BOUNDARY# @ x = 0 # At the inletcB(0) = cBinlet; # closed boundary# cB(0) = cBinlet + D/u * PARTIAL(cB(0),Axial) ; # open boundary

# V(0) = Vzero + lambda*Length* PARTIAL(V(0),Axial2) ; # cocurrentoperation

PARTIAL(V(0),Axial2) = 0 ; # countercurrent operation

# @ x = Length # At the outlet

Appendices

207

PARTIAL(cB(Length),Axial) = 0 ; # no flux condition

V(Length) = Vzero - lambda*Length*PARTIAL(V(Length),Axial2);# countercurrent

# PARTIAL(V(Length),Axial2) = 0 ; # cocurrent



# Dispersion coefficientD = (2*Ebed/(3-Ebed)) * diff + (u*dp/2) ;


# Component B balance fluid phaseFOR x := 0|+ TO Length|- DO

$cB(x) = (D * PARTIAL(PARTIAL(cB(x),Axial),Axial)) -(u * PARTIAL(cB(x),Axial)) - (J(x) * Abed) ;

# Diffusion convection and adsorption partsEND # for loop

# Component B balance solid phaseFOR x := 0 TO length DO

$q(x) = J(x) * Ebed * Abed /(rho*(1 - Ebed)) ;END # for loop

# Transport Equation to solid phase with LF isothermFOR x := 0 TO Length DO

J(x) = kL * (cB(x) - (q(x)/((qmax -q(x) )*K(x) ))^2 ) ;END # for loop

# Langmuir-Freundlich Adsorption Constant from Electric FieldFOR x := 0 to Length DO

K(x) = (A * V(x)^2) + (B * V(x)) + (C) ;END # for loop


# Electric potential differential equationFOR x := 0|+ TO Length|- DO

$V(x) = (Ebed*kappa/(rho*SBET*(1-Ebed)*CAP)) *PARTIAL(PARTIAL(V(x),axial2),axial2) ;

END # for loop

Appendices

208

END # Model

####################################### #### MAIN MODEL STARTS HERE #### #######################################

MODEL totalbed

PARAMETERnbeds AS INTEGER : DEFAULT = 4 # number of submodels

UNITFOR i := 1 TO nbeds DO

Bed(i) AS partofbedEND # for

EQUATIONFOR i:= 1 TO (nbeds – 1) DO

Bed(i).cB(Bed(i).Length) = Bed(i+1).cBinlet ;Bed(i).F = Bed(i+1).F ;Bed(i).Vzero = Bed(i+1).Vzero ;

END # for

END # totalbed


PROCESS ElecBuis

UNIT Elecbuis AS totalbed

MONITOR# The variables that will be reportedElecbuis.B1.cB(2) ;Elecbuis.B1.cB(26) ;Elecbuis.B1.cB(50) ;Elecbuis.B2.cB(26) ;Elecbuis.B2.cB(50) ;Elecbuis.B3.cB(26) ;Elecbuis.B3.cB(50) ;Elecbuis.B4.cB(26) ;Elecbuis.B4.cB(50) ;

Appendices

209

SET # ConstantsWITHIN ElecBuis DOFOR i:= 1 TO nbeds DOBed(i).Axial := [BFDM, 2, 50]; # Discretization method for massBed(i).Axial2 := [CFDM, 2, 50]; # Discretization method for chargeBed(i).qmax := 10 ; # [mol/kg ] monolayer adsorptionBed(i).Length := 0.02 ; # [m ] of the bedBed(i).dbed := 0.7 ; # [m ] diameter of the bedBed(i).dp := 5E-4 ; # [m ] particle diameterBed(i).kappaL := 5.88 ; # [1/Ohm.m ] electric cond.liquidBed(i).rho := 1146 ; # [kg/m3 ] particle densityBed(i).Ebed := 0.45 ; # [m3/m3 ] porosity of the bedBed(i).CAP := 0.15 ; # [F/m2 ] diff capacity systemBed(i).A := -0.1 ; # [m3/mol.V2] 2th order infl potBed(i).B := 0 ; # [m3/mol.V ] 1th order infl potBed(i).C := 0.2 ; # [m3/mol ] 0th order infl potBed(i).diff := 9E-10 ; # [m2/s ] diffusion coeffBed(i).SBET := 1.1E6 ; # [m2/kg ] BET surface areaBed(i).lambda := 0.666 ; # [- ] ext loss parameterEND # for

END # within

ASSIGN # more variablesWITHIN Elecbuis DO

Bed(1).F := 33.33E-5 ;Bed(1).cBinlet := 0.5 ;Bed(1).Vzero := 0.0 ;

END # within

INITIAL # Differential VariablesWITHIN ElecBuis DOFOR i := 1 TO nbeds DOFOR x := 0|+ TO Bed(i).Length|- DO

Bed(i).cB(x)= 0 ;Bed(i).V(x) = 0 ;

END # forFOR x := 0 TO Bed(i).Length DO

Bed(i).q(x) = 0;END # for

END # forEND # WITHIN


SCHEDULESEQUENCE

CONTINUE FOR 80000

Appendices

210

RESET # Desorption starts hereElecbuis.B1.F := 33.33e-5 ;Elecbuis.B1.Vzero := 1.0 ;Elecbuis.B1.cBinlet := 0.0 ;

END # resetCONTINUE FOR 320000

END # sequence

END # Process

Program listing 3. A single current collector is used in combinationwith a variable differential capacity and a non-empirical influence fromthe capacity and the potential on the adsorption equilibrium.

######################################################### #### gPROMS model source #### model: Langmuir-Freundlich, ext resist, 1D #### single current collector, variable capacity #### October 2000 #### Vincent Fischer #### #########################################################

DECLARE

TYPEVOLTAGE = 0.5 : -1E15 : 1E15 UNIT = "V"FLUX = 0 : -1E15 : 1E15 UNIT = "mol/m2.s"CONDUCTIVITY = 1.0 : -1E15 : 1E15 UNIT = "1/Ohm.m"CONCENTRATION = 1 : -1E30 : 1E15 UNIT = "mol/m3"loading = 1 : -1E30 : 1E15 UNIT = "mol/kg"ADSCONST = 10 : -1E15 : 1E15 UNIT = "m3/mol"speed = 1e-6: -1e15 : 1e15 unit = "m/s"dispersion = 1e-9: -1e15 : 1e15 unit = "m2/s"flow = 1e-6: -1e15 : 1e15 unit = "m3/s"transfer = 1e-4: -1e15 : 1e15 unit = "m/s"

specificsurface = 1E6 : -1e15 : 1e15 unit = "1/m"


####################################### #### MODELS START HERE #### #######################################

MODEL Tube

PARAMETER

Appendices

211

Length AS REAL # Reactor Length [m ]dbed AS REAL # Reactor diameter [m ]dp AS REAL # Particle diameter [m ]rho AS REAL # density particle [kg/m3 ]Ebed AS REAL # External porosity [m3/m3 ]qmax AS REAL # Maximale belading [mol/m3 ]kappaL AS REAL # Specific Conductivity [1/Ohm.m ]K0 AS REAL # open circ ads coeff. 3 [m3/mol ]diff AS REAL # diffusivity coefficient [m2/s ]SBET AS REAL # specific surface area [m2/kg ]lambda AS REAL # Ohmic loss factor [- ]


VARIABLEq AS DISTRIBUTION(Axial) OF loading # in solid phaseJ AS DISTRIBUTION(Axial) OF FLUX # adsorption fluxcB AS DISTRIBUTION(Axial) OF CONCENTRATION # in reactorV AS DISTRIBUTION(Axial2) OF VOLTAGE # Electric potK AS DISTRIBUTION(Axial2) OF ADSCONST # adsorption constCAP, epsRA, epsRB, CGC, CHA, CHB

AS DISTRIBUTION(Axial2) OF VOLTAGE # diff capacitykappa AS CONDUCTIVITY # Effective conductivitycBinlet AS CONCENTRATION # Concentration in inletVzero AS VOLTAGE # ext applied potentialu AS speed # interstitial velocityD AS dispersion # Dispersion coefficientkL AS transfer # mass transfer coeffAbed AS specificsurface # surface area installedF AS flow # volume flow

BOUNDARY# @ x = 0 # At the inletcB(0) = cBinlet; # closed boundary# cB(0) = cBinlet + D/u * PARTIAL(cB(0),Axial) ; # open boundary

# V(0) = Vzero + lambda*Length* PARTIAL(V(0),Axial2) ; # cocurrentoperation

PARTIAL(V(0),Axial2) = 0 ; # countercurrent operation

# @ x = Length # At the outletPARTIAL(cB(Length),Axial) = 0 ; # no flux condition

V(Length) = Vzero - lambda*Length*PARTIAL(V(Length),Axial2); #countercurrent

# PARTIAL(V(Length),Axial2) = 0 ; # cocurrent



Appendices

212

# Dispersion coefficientD = (2*Ebed/(3-Ebed)) * diff + (u*dp/2) ;


# Component B balance fluid phaseFOR x := 0|+ TO Length|- DO

$cB(x) = (D * PARTIAL(PARTIAL(cB(x),Axial),Axial)) -(u * PARTIAL(cB(x),Axial)) - (J(x) * Abed) ;

# Diffusion convection and adsorption partsEND # for loop

# Component B balance solid phaseFOR x := 0 TO length DO

$q(x) = J(x) * Ebed * Abed /(rho*(1 - Ebed)) ;END # for loop

# Transport Equation to solid phase with LF isothermFOR x := 0 TO Length DO

J(x) = kL * (cB(x) - (q(x)/((qmax -q(x) )*K(x) ))^2 ) ;END # for loop

# Langmuir-Freundlich Adsorption Constant from Electric FieldFOR x := 0 to Length DO

K(x) = 0.1+0.5*K0*EXP(- ( (CHA(x)*CGC(x)/(CHA(x)+CGC(x)) )- (CHB(x)*CGC(x)/(CHB(x)+CGC(x) )) )*V(x)^2*34.092028) ;

END # for loop


# Electric potential differential equationFOR x := 0|+ TO Length|- DO

$V(x) = (Ebed*kappa/(rho*SBET*(1-Ebed)* CAP(x) )) *PARTIAL(PARTIAL(V(x),axial2),axial2) ;

END # for loop

# dielectric constants as function of V# fit function taken to describe the real functionFOR x := 0 TO Length DO

epsRA(x) = 1/(0.036245262 - 0.00031153174*V(x) +0.023023228*V(x)^2 - 0.0063672479*V(x)^3 );

END # for loop

FOR x := 0 TO Length DOepsRB(x) = 1/(0.24572379 - 0.0010757573*V(x) +0.041396901*V(x)^2 - 0.011482038*V(x)^3 );

END # for loop

# Gouy Chapman capacityFOR x := 0 TO Length DO

CGC(x) = (0.03327*epsRA(x))^0.5*COSH(19.47203*V(x));END # for loop

# Helmholtz capacities

Appendices

213

FOR x := 0 TO Length DOCHA(x) = epsRA(x)/80.49156;

END #for loop

FOR x := 0 TO Length DOCHB(x) = 1/(59.81714/epsRB(x) + 45.40607/epsRA(x));

END # for loop

# total capacity (potential and coverage dependent)FOR x:= 0 TO Length DO

CAP(x) = 0.5 *( (q(x)/qmax)/(1/CHB(x) + 1/CGC(x))+ (1 - q(x)/qmax)/(1/CHA(x) + 1/CGC(x)) );

END # for loop

END # Model


PROCESS ElecBuis

UNIT Elecbuis AS Tube

MONITOR# The variables that will be reported#Elecbuis.V(1) ;#Elecbuis.V(4) ;Elecbuis.K(1) ;Elecbuis.cB(50) ;Elecbuis.q(50) ;Elecbuis.V(1) ;Elecbuis.V(17) ;Elecbuis.V(33) ;Elecbuis.V(50) ;Elecbuis.CAP(25) ;

SET # ConstantsWITHIN ElecBuis DOAxial := [BFDM, 2, 50]; # Discretization method for massAxial2 := [CFDM, 2, 50]; # Discretization method for chargeqmax := 10 ; # [mol/kg ] monolayer adsorptionLength := 0.02 ; # [m ] of the beddbed := 0.7 ; # [m ] diameter of the beddp := 5E-4 ; # [m ] particle diameterkappaL := 5.88 ; # [1/Ohm.m ] electric conduct liquidrho := 1146 ; # [kg/m3 ] particle densityEbed := 0.45 ; # [m3/m3 ] porosity of the bedK0 := 0.2 ; # [m3/mol ] open circ equil constdiff := 9E-10 ; # [m2/s ] diffusion coefficientSBET := 1.1E6 ; # [m2/kg ] BET surface arealambda := 0.666 ; # [- ] external loss parameterEND # within

Appendices

214

ASSIGN # more variablesWITHIN Elecbuis DO

F := 33.33E-6 ;cBinlet := 5 ;Vzero := 0.0 ;

END # within

INITIAL # Differential VariablesWITHIN ElecBuis DO

FOR x := 0|+ TO Length|- DOcB(x) = 0;

END # for

FOR x := 0 TO Length DOq(x) = 0;

END # for

FOR x := 0|+ TO Length|- DOV(x) = 0;

END # forEND # WITHIN


SCHEDULESEQUENCE

CONTINUE FOR 80000RESET # Desorption starts here

Elecbuis.F := 33.33e-6 ;Elecbuis.Vzero := 1.0 ;Elecbuis.cBinlet := 0.0 ;

END # resetCONTINUE FOR 320000

END # sequenceEND # Process

Appendices

215

A P P E N D I X C : E C O N O M I C S

General data

Packed bed dataBed diameter D 0.7 mBed length L 0.02 mArea of the bed A = ¼ π D2 0.385 m2Number of layers x 10…500Volume of the bed V = A L x 0.154…3.848 m3

Density of the carbon ρp 1146 kg/m3

Porosity of the bed ε 0.45Size of the surface SBET 1100 m2/gElectrical capacity C 0.15 F/m2

Amount of carbon m = V ρp (1-ε) 97…2426 kg

Physical propertiesDensity water ρA 1000 kg/m3

Density methanol ρmeOH 791 kg/m3

Heat capacity water cp,A 4180 J/(kg K)Heat capacity steam cp,steam 2000 J/(kg K)Heat capacity methanol cp,meOH 2500 J/(kg K)Heat of vaporisation Hg 2.26 106 J/kgFor methanol Hg,meOH 1.1 106 J/kgEnergy of heating gas Egas 31.65 106 J/m3

Price of heating gas Kgas 0.159 Є/m3

Price of methanol KmeOH 0.159 kЄ/m3

Waste water dataFlow Φ 20 L/minPollutant in c 5 mol/m3

Pollutant out cout 0.05 mol/m3

Seconds in one year t 3.15 107 sAmount removed M =F t (c-cout) 5.256 104 mol

Appendices

216

Isotherm dataLF constant 1 n 0.5LF constant 2 K 0.2 (m3/mol)½

LF constant 3 qmax 10 mol/kg

Max loading n

n

KcKcqq+

=1max 3.09 mol/kg

# regeneration cycles beds = M /(m q) 340…17

Case 0) No regeneration

Investment

Column ( ) year102.2

365.194.44 31.1

⋅+= Lx 2.07…5.19 kЄ

(WEBSCI and WUBO, 1999)

Operation costsWaste carbon = 0.455 kЄ/tonne beds m 38.27 kЄ(Staal, 2001)New carbon = 3.182 kЄ/tonne beds m 267.9 kЄ(Staal, 2001)

Case 1) Steam regeneration (300 °C, 90% efficiency)

Investment

Column ( )( ) year102.2

365.194.442 31.1

⋅+= Lx 4.14…10.37 kЄ


Steam house year102.2

hr85.1

tonnehr150

⋅=

m

0.316…12.66 kЄ

(WEBSCI and WUBO, 1999)Initial bed = 3.182 kЄ/tonne m 0.788…31.502 kЄ

Appendices

217

Operation costsLabour costs = 0.027⋅4⋅2⋅beds 74.2…1.855 kЄ(27 Є/hr, 4 hr, 2 men per regeneration)Waste carbon (0.455 kЄ/tonne beds m)/10 3.827 kЄNew carbon (3.182 kЄ/tonne (beds-1)m)/10 26.71…23.64 kЄSteam needed msteam = 1.5 m beds 126.3 tonne(Suzuki, 1990) Q1 = msteam cp,A 80 K

Q2 = msteam HgQ3 = msteam cp,steam 200 K

80% efficiency heater80.0

321 QQQQtot++=

heating costsgas

gastot

EKQ

= 2.376 kЄ

Case 2) Methanol regeneration (66% efficiency)

Investment


365.194.442 31.1

⋅+= Lx 4.14…10.37 kЄ


Storage tank ( ) year102.2

20662.128.33tank7.0

⋅+= VK 1.832…5.748 kЄ

(WEBSCI and WUBO, 1999)Separation section = 2Ktank 3.665…11.5 kЄInitial bed = 3.182 kЄ/tonne m 0.788…31.502 kЄ

Operation costsLabour costs 0.027⋅4⋅2⋅beds 74.2…1.855 kЄ(27 Є/hr, 4 hr, 2 men per regeneration)Waste carbon = (0.455 kЄ/tonne beds m)/3 12.76 kЄNew carbon =(3.182 kЄ/tonne (beds-1)m)/3 89.0…78.8 kЄVolume methanol VmeOH = 20 V beds 2672 m3

Methanol costs = KmeOH 0.1VmeOH 42.5 kЄEnergy needed Q1 = VmeOH ρmeOH cp,meOH 45 K

Appendices

218

Q2 = VmeOH ρmeOH Hg,meOH

80% efficiency heater80.0

21 QQQtot+=

Heating costsgas

gastot

EKQ

= 16.1 kЄ

Case 3) Electrosorption (50% efficiency)

Investment


117.488.695 289.0

⋅+= Lx 16.65…18.11 kЄ

(WEBSCI and WUBO, 1999)Electric circuit = 100/10 10 kЄInitial bed = 3.182 kЄ/tonne m 0.788…31.502 kЄ

Operation costsLabour costs 0.027⋅4⋅2⋅beds 74.2…1.855 kЄ(27 Є/hr, 4 hr, 2 men per regeneration)Waste carbon = (0.455 kЄ/tonne beds m)/2 19.14 kЄNew carbon =(3.182 kЄ/tonne (beds-1)m)/2 133.6…118.2 kЄCharging the bed U1 = ½ (1 V)2 m SBET CDesorbing phenol U2 = ¼ (1 V)2 m SBET (0.238-0.055)

Charging costs3600kWhr2.2

101.013

⋅⋅=

− bedsU 0.088 kЄ

Desorption costs3600kWhr2.2

101.023

⋅⋅=

− bedsU 0.053 kЄ

Samenvatting

219

SAMENVATT ING

De beschikbaarheid van voldoende drinkwater kan een probleem zijn indichtbevolkte of industriële gebieden, zodat waterzuiveringsinstallatiesnoodzakelijk zijn. Adsorptie technologie kan gebruikt worden om waterigeafvalstromen te reinigen met een relatief lage concentratie aan vervuilendestoffen. Het meest gebruikte adsorptiemateriaal is actieve kool, omdat het eenzeer groot intern oppervlak heeft waaraan relatief veel vervuilende stoffenkunnen binden. Tijdens gebruik zal de kool langzamerhand verzadigd rakenen zijn werkzame functie verliezen. Er is een sterke economische drijfveer omdeze kool te regenereren zodat het opnieuw gebruikt kan worden. Dit kanbereikt worden door het zodanig veranderen van proces condities zodatgeadsorbeerde componenten zullen desorberen. De methoden die hiervandaag de dag voor gebruikt worden zijn of niet krachtig genoeg of te duur.Er is dan ook reden genoeg om nieuwe mogelijke regeneratie methoden teonderzoeken, zoals elektrosorptie. Elektrosorptie heeft te maken met deeffecten van een opgelegde elektrische spanning op het adsorptie gedrag van(in dit geval) ongeladen moleculen.

De invloed van een elektrische potentiaal op adsorptieEen elektrode in contact met een elektroliet oplossing leidt als vanzelf tot eenladingsoverschot in de vloeistof. Dit ladingsoverschot zorgt voor een identiekladingstekort in de elektrode. Samen worden deze lagen van lading deelektrische dubbellaag genoemd. Zonder de aanwezigheid van een elektrischedubbellaag zal er geen elektrosorptie optreden. Het simpelste model om het tebeschrijven is het Helmholtz model, equivalent aan een ideale parallelle plaatcondensator. Het Helmholtz model is niet in staat om de experimenteelgevonden invloeden van het elektrische potentiaalverschil en de ionconcentratie op de differentiële capaciteit te beschrijven. Een meergeavanceerd model, het Gouy-Chapman model, voorspelt dat de capaciteitzeer sterk afhangt van de potentiaal en de temperatuur en in mindere matevan de ion concentratie. Dit is niet wat er experimenteel wordt gevonden voorrelatief hogere potentialen. Beide modellen worden gecombineerd in het Sternmodel. Normaal gesproken zijn de verschillen tussen het Stern en het

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220

Helmholtz model maar klein, tenzij de ion concentratie en de opgelegdepotentiaal zeer klein zijn. Het blijkt niet eenvoudig te zijn om de elektrischedubbellaag voldoende nauwkeurig te beschrijven.

Het materiaal tussen de geladen lagen kan vergeleken worden met hetdielectricum van een condensator, waarvan de eigenschappen worden bepaalddoor de dielectrische constante. Deze is niet constant maar hangt af van(sterke) elektrische velden. Een potentiaal afhankelijke dielectrische constantekan afgeleid worden indien de complete Langevin wordt gebruikt in plaats vande Taylor benadering zoals wordt gedaan in de literatuur. Dit resulteert in eenmeer afgeronde capaciteit versus potentiaal curve.

Om het mechanisme achter elektrosorptie te kunnen verklaren, worden degeadsorbeerde moleculen beschouwd als een thermodynamisch fase, apart vande bulkvloeistof. De adsorptie evenwichtsconstante geeft de hoeveelheidgeadsorbeerde moleculen als functie van de bulk samenstelling. Omdat ergeen Faraday reacties optreden, kan het elektrische veld alleen invloeduitoefenen op dit evenwicht via de evenwichtsconstante. Binnen decondensator analogie kunnen adsorptie en desorptie worden voorgesteld alsde beweging van blokken dielectricum tussen de geladen platen. Het kanworden uitgerekend dat als de opgelegde potentiaal toeneemt, de krachtwaarmee water naar binnen wordt getrokken (en de vervuiling eruit) ooktoeneemt. Veranderingen in de Gibbs energie van het systeem kunnen wordengerelateerd aan veranderingen in de desorptie snelheidsconstante.

Electrosorptie isotherm dataTheoretisch gezien zijn Langmuir-achtige isothermen de ideale keus omelektrosorptie data te beschrijven, omdat ze de evenwichtsconstante bevatten.Hun grootste manco, de slechte fit met experimentele data, is opgelost doortoevoeging van een fitparameter aan de vergelijking.

Onze elektrosorptie theorie voorspeld een klokvormige grafiek waneer debelading wordt uitgezet tegen de potentiaal. Het maximum van de klok kanverschuiven naar positieve of negatieve potentialen als gevolg van eenspecifieke oriëntatie van - of ladingen op het adsorberende molecuul.Wanneer de schaarse data uit de literatuur wordt verzameld in een enkele

Samenvatting

221

grafiek dan blijkt deze klokvorm slechts voor een klein deel terug te vinden.Echter, de meeste data is van slechte kwaliteit en ook is er steeds slechts éénpotentiaal tak onderzocht. Wel duidelijk is dat geladen moleculen inderdaadeen sterke verschuiving van hun maximum vertonen. Fitten van een aantaldata series met het model geeft alleen zinnige resultaten indien de effectiviteitvan elektrosorptie wordt verminderd door de introductie van een bedeffectiviteit en door rekening te houden met ohmse verliezen in het systeem.

Een eerste benchmark voor elektrosorptie wordt verkregen het een vergelijkmet toevoegen van methanol aan een fenol/water systeem. De methanolbrengt net als de opgelegde spanning de isotherm omlaag. Uit de vergelijkingkan geconcludeerd worden dat (in theorie) elektrosorptie gemakkelijk dezelfdeverschuivingen teweeg kan brengen als de methanol toevoegingen.

Uitgebreid is getracht om elektrosorptie experimenten uit de literatuur tereproduceren, echter met weinig succes. Oorspronkelijk succesvolle resultatenbleken foutief door het optreden van onverwachte chemische reacties. Latereresultaten onder meer gecontroleerde omstandigheden gaven slechts weinig ofgeen invloed van de opgelegde potentiaal.

Transient elektrisch gedrag van gepakte beddenEen typische gepakt bed elektrode van AC korrels heeft eigenschappen dieniet overeenkomen met die van normale elektroden. Door zijn enormeoppervlak heeft hij een enorme capaciteit. Omdat de elektrische weerstandenin de kool en in de poriën niet verwaarloosd mogen worden, is dekarakteristieke tijd voor het opladen van de dubbellaag nog groter en zal hetsysteem zich elektrisch gezien heel traag gedragen.

De externe respons van een gepakt bed elektrode kan gemodelleerd wordenmet behulp van Laplace transformatie. De elektrode zelf blijft dan een blackbox. Meer complexe circuits kunnen en moeten vereenvoudigd worden om deuitgebreidheid van de berekeningen binnen de perken te houden. Deaanwezigheid van interne weerstanden leidt tot een potentiaal verdelingbinnenin de elektrode, in tegenstelling tot de verwachte constante waarde.Laplace kan niet gebruikt worden om lokaal de potentiaal te berekenen. Hetconcept van een oneindig aantal weerstanden in serie is daarom gebruikt voor

Samenvatting

222

de afleiding van een differentiaal vergelijking die de potentiaal distributiebeschrijft. Het resultaat vertoont veel gelijkenis met het probleem van warmteoverdracht in een vlakke plaat. Door variatie van de randvoorwaarden wordendrie verschillende oplossingen verkregen:

• Het ideale model: de kool weerstand kan worden verwaarloosd integenstelling tot de porie weerstand.

• Model met interne verliezen: de kool en porie weerstanden zijn in dezelfdeorde van grootte.

• Model met externe verliezen: een deel van de opgelegde potentiaal gaatverloren in de bulkvloeistof.

Meten van elektrische groothedenWanneer de opgelegde potentiaal plots wordt veranderd, zal er een stroomdoor het systeem lopen totdat een nieuw evenwicht is bereikt. Deze transientexperimenten zijn een goed stuk gereedschap voor de bepaling van elektrodeeigenschappen. Wanneer de i(t) data wordt omgezet in een plot van i√t tegen√t, dan worden grafieken met een specifieke vorm gevonden. Het is geblekendat alleen het model met externe verliezen in staat is om de experimenteleresultaten te beschrijven.

Gebleken is dat de capaciteit constant blijft indien de potentiaal niet meer danongeveer 10 mV wordt veranderd. Wanneer het bed volledig effectief wordtverondersteld, dan wordt gevonden dat poreus grafiet een experimentelecapaciteit heeft van 0.285 F/m2, terwijl Ambersorb 572 een capaciteit heeftvan 0.158 F/m2. Dit suggereert dat de helft van het Ambersorb oppervlak niettoegankelijk is voor dubbellaag vorming. Directe metingen van de elektrischeweerstanden van zowel bed als kooldeeltje geven resultaten die 10-100 keerhoger liggen dan de weerstanden afkomstig uit de transient experimenten. Dedirecte metingen lieten wel een sterke invloed zien van de mechanische drukop de weerstand van het gepakte bed. Hogere drukken leiden tot een betereconductiviteit.

Wanneer de ion concentratie wordt verlaagd, dan gaat de capaciteit van hetsysteem omlaag en gaat de totale weerstand omhoog. De vloeistof weerstand

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223

is direct gekoppeld aan de geleidbaarheid van het elektroliet. Het constantblijven van de capaciteit over grotere potentiaal bereiken is onzeker en isdaarom onderzocht. Voor poreus grafiet blijft de capaciteit vrijwel constantterwijl voor de Ambersorb de capaciteit ongeveer een factor of twee varieerten de overeenkomst met theoretische voorspellingen slecht is. De totaleweerstand is niet afhankelijk van de potentiaal. De in de literatuurgerapporteerde differentiële capaciteiten voor AC variëren onderling met eenfactor 5. Dit is waarschijnlijk het gevolg van de heterogene natuur van hetmateriaal. Tevens is de werkelijke grootte van het elektrisch toegankelijkeoppervlak onbekend. De aanwezigheid van organisch materiaal in het systeemgaf geen significant effect op de capaciteit of de weerstand.

Ontwerp van een elektrosorptie unitEen elektrosorptie installatie is ontworpen, geschikt voor het reinigen van eenafvalstroom van 20 L/min, met daarin 5 mol/m3 fenol. De vloeistofstromingis beschreven met behulp van een axiale dispersie propstroom model. Destofoverdrachtsweerstand is extern verondersteld en er treden geenongewenste Faraday reacties op.

Om de dimensies van de installatie te bepalen is een set van karakteristieketijden gebruikt. Sommige tijden dienen langer te zijn dan anderen, aangeziensommige processen afgerond moeten zijn voor anderen. Als aan alle hieruitresulterende ongelijkheden is voldaan, dan bevindt het ontwerp zich in hetgewenste operationele gebied. De volgende tijden zijn gedefinieerd: Degemiddelde verblijftijd van de vloeistof, de tijden nodig voor desorptie enadsorptie, de dispersietijd, de stofoverdrachtstijd en de oplaadtijd van dedubbellaag. De tijd nodig voor desorptie moet groter zijn dan die voor hetopladen van de dubbellaag. De adsorptietijd en de dispersietijd moeten groterzijn dan de verblijftijd. De verblijftijd moet groter zijn dan destofoverdrachtstijd.

De bed lengte en de vloeistof snelheid (bepaald door de kolom diameter)beïnvloeden vijf van de zes karakteristieke tijden en zijn daarmee de meestbelangrijke ontwerpparameters. Om het ontwerp in het gewenste gebied tebrengen moet de lengte van het bed ongeveer 10 mm zijn, terwijl de vloeistofsnelheid in de orde van 10-4 m/s ligt. Het complete model is geprogrammeerd

Samenvatting

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in het numerieke simulatie pakket gPROMS. Een groot aantaladsorptie/desorptie doorbraak simulaties zijn uitgevoerd, terwijl de waardenvan verschillende parameters zijn gevarieerd en hun respectievelijke invloedenzijn onderzocht.

Enkele dynamische aspectenAllereerst is het verschijnsel ‘streaming current’ onderzocht. Streaming currentwordt veroorzaakt door de beweging van de GC overschotlading als gevolgvan meesleuring door een bewegende vloeistof fase. De experimenteelgevonden stroom ligt ongeveer 2.5 keer hoger dan de waarde voorspeld doorde theorie. Dit zou veroorzaakt kunnen worden door een onderschatting vanhet actieve kool buitenoppervlak dat bijdraagt aan dit fenomeen.

Er bestaat een experimentele relatie tussen het optreden van lading- enstofoverdracht. Adsorptie van de vervuilende component veroorzaakt eenmeetbaar transport van lading. Als de relatieve hoeveelheid die adsorbeertwordt vergeleken met de relatieve hoeveelheid lading die wordtgetransporteerd, dan wordt een lineaire relatie gevonden.

De theoretisch (absolute) hoeveelheid lading die wordt overgedragen alsgevolg van een zekere mate van adsorptie kan worden uitgerekend. Dezetheoretische waarde is ongeveer 2-20 keer groter dan de experimentelewaarden. Het lijkt zo te zijn dat niet alle adsorberende moleculen bijdragenaan opwekken van stroom, doordat ze adsorberen buiten de dubbellaag. Hetverschil tussen theorie en experiment wordt sterker voor hogere potentiaalverschillen, zoals ook wordt voorspeld door ons elektrosorptie model.

De kosten voor het bedrijven van vier verschillende regeneratie methoden zijnbepaald met weloverwogen schattingen en zijn onderling vergeleken. Stoomregeneratie lijkt de meest goedkope optie, terwijl niet regenereren het duurstelijkt te zijn.

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DANKWOORD

Eindelijk, het laatste onderdeel van mijn proefschrift. Na anderhalf jaar vanschrijven en schrappen is het einde dan toch in zicht. Ik heb mijn vierpromotiejaren altijd als zeer boeiend en intensief ervaren. Zoals met zo veelandere dingen, zul je ook dit zelf meegemaakt moeten hebben om je er eenvoorstelling van te kunnen maken. Soms was het zwemmen in beton, somswas het staan op de top van de wereld. Hoogte en dieptepunten, frustratie engeluk wisselden elkaar in rap tempo af. Vier jaar lang leven voor je onderzoek.Eigenlijk was er geen moment waarop ik er niet mee bezig was. En zoalsbekend, de beste ideeën krijg je al zittende op het toilet. Ondanks het feit datik een aantal keren op het punt heb gestaan de handdoek in de ring te gooienwegens het uitblijven van enig experimenteel zinnig resultaat heb ik tochdoorgezet, waarschijnlijk omdat ik niet zo van opgeven houd. En nu zal ik hetmissen, de eenzame nachtelijke tochten naar het lab, dat donkere grote legegebouw, om toch nog even een meting op te starten. De enorme vrijheid inhet bepalen van je ritme en je werkzaamheden. De gevoelens van triomf alseen puzzelstukje op zijn plek viel. En natuurlijk ook de mensen die ik in dieperiode dagelijks om me heen heb gehad.

Allereerst wil ik mijn collegae bedanken, de sfeer op het werk en in de pauzeswas altijd fantastisch. Peter Rozendal, mijn eerste kamergenoot wist me altijdte helpen met wiskundige problemen. De vaste lunch groep, Marga Dijkstramet haar concurrerende zuiveringsproces, Vincent ‘Pantani” Verhoeven mijnstudiereisgenoot, Jasper Huijsmans met zijn uitgebreide kennis van films enveel meer chemische zaken. Han Scherpenkate die er altijd voor zorgde dat ervoldoende gespreksstof was. Linda Lucas voor de organische ondersteuning.Jaap Bosma voor zijn kruiwagen tijdens mijn sollicitatie. Arne Bollen, MichielZanting & Poeste voor de nachtelijke ‘krachtmetingen’. Cedric Thieulot voorde muzikale ondersteuning in de eindfase en verder natuurlijk Mario Cioffi,Ineke Ganzeveld, Jildert Visser, José Tijssen, Iris van Paassen, Ralf Pijpers,Rienk Hettema, Douwe van der Wal, Mook en Franscesca die zorgden vooreen zeer gezellige tijd.

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De technische ondersteuning en het pragmatisme van Marcel de Vries warenzeer waardevol. Anne Appeldoorn bedankt voor het bouwen van mijnelektrische cel. Laurens Bosgra voor de bestellingen, externe contacten en defronsende kritische blik. Alle leden van mijn IOP begeleidingscommissie voorhet leveren van feedback op mijn werk. En als laatste uit de werksfeernatuurlijk mijn promotor Hans Wesselingh die me altijd vrijliet in mijn doenen laten en die liet blijken dat hij alle vertrouwen had in wat ik nu weer aan hetuitvogelen was, om op de beslissende momenten toch een duidelijke lijn aante brengen in de chaos. Hans bedankt!

In de vrije tijd zijn er natuurlijk een hele batterij aan AMORianen. Allereerstmijn ‘eigen’ bestuursleden: Liesbeth, Joost W., Geertruida, Onne, Marjon,Marloes, we hebben het goed gedaan! Garrelt wordt extra bedankt omdat hijde scepter als voorzitter van me wilde overnemen. Heel veel teamgenoten hebik gehad: Gelijn, Sebastiaan, Erika, Sasja, Teake, Janneke, Barry-Lee, Sjula enThea. Verder waren er natuurlijk Roelof, Hans H., Harold, Wouter, Joost Q.,Oscar, Francis, Roos, Etty en Agaath voor de uitgebreide sociale contacten.

Dan de roleplayers: Hans, Alex, wederom Liesbeth, Garrelt en Roelof,Pauline, Marieke, Angelique en Jos. Ik heb erg genoten van al die fantasievollejaren.

Mijn paranimphen Marjon Roos en Jasper Huijsmans wil ik hartelijk danken.

En tenslotte mijn ouders omdat ze altijd de wetenschapper in me hebbengestimuleerd, van het voorlezen van boeken, geven van schaaklessen tottechnisch lego, hobby microscopen en chemiedozen. En de allerbelangrijksteis Ilse omdat ze toeliet dat ik haar leven zo snel een andere wending mochtgeven.

Vincent Fischer,

Eindhoven, 5 augustus 2001

Documents

In Situ Electrochemical Regeneration of Activated Carbon