Kinetics of adsorption from liquid phase on activated carbon

Kinetics of adsorption from liquid phase on activated carbon

Citation for published version (APA):

Kouyoumdjiev, M. S. (1992). Kinetics of adsorption from liquid phase on activated carbon. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR387873

DOI:

10.6100/IR387873

Document status and date: Published: 01/01/1992

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KINETICS OF ADSORPTION

FROM LIQUID PHASE

ON ACTIVATED CARBON

FROM LIQUID PHASE

ON ACTIVATED CARBON

PROEFSCHRIFf

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof. dr. J.H. van Lint, voor een commissie aangewezen door het College van Dekanen in het openbaar te verdedigen op

vrijdag 18 december 1992 om 16.00 uur

door

Marcho Stefanov Kouyoumdjiev

geboren te Sofia

Dit proefschrift is goedgekeurd door de promotoren: prof.dr.ir. P.J.A.M. Kerkhof

KINETICS OF ADSORPTION FROM LIQUID

PHASE ON ACTIVATED CARBON

THESIS

to obtain the degree of doctor at the Eindhoven University of Technology by the authority of the Rector Magnificus, prof.dr. J.H. van Lint, to be defended in public in the presence of a committee nominated by the council of Deans on

Friday, December 18th 1992 at 16:00 hrs

by

Marcho Stefanov Kouyoumdjiev

This thesis has been approved by the promoters: prof.dr.ir. P.J.A.M. Kerkhof

ACKNOWLEDGMENTS

The research work presented in this thesis was carried out in the Laboratory of Chemica! Process Technology at the Eindhoven University of Technology. I would like to thank all memhers of this laboratory, working in the Fr-hal, for their support and contributions to this thesis.

I would like to express my gratitude especially to prof. Kerkhof for the opportunity he gave me to work at the Eindhoven University of Technology and for the regular discussions and valuable comments during my work on the thesis. I am particularly indebted to Marlus Vorstman for his kindness and help in the four years of the research study. The on-line constructive discussions which I had almost daily with Marlus were an invaluable souree of ideas and a solid support during my work.

The assistance of all the technica! staff of the Fr-hal is greatly appreciated and I want to mention especially Chris Luyk who contributed substantially to the construction of the experimental installation.

Significant contributions to this work were made by the graduale students Sandra Vedder, Paul Steenbergen, Paul Laimböck, Heinie Voncken, Marc Donker and Marco Ligthart, for which I sincerely thank them.

During the course of this thesis many other people have helped or advised me about my work and have contributed directly or indirectly to its successful completion and I want to mention especially Toine Ketelaars, Gerben Mooiweer, S. Rienstra and Kostadin Paev.

Thanks are due to Norit BV for the more-than-enough supply of activaled carbon with which I performed all experiments described in this thesis. I would also like to thank Wim van Lier for the valuable advise and remarks during our frequent discussions.

Last but not least I want to thank Unilever Research Laboratorium in Vlaardingen for the onderstanding and technica! support during the last weeks of the completion of this thesis.

Marcho Kouyoumdjiev 22 October 1992

Adsorption is one of the most important processes used in industry for the separation of solutes from a fluid stream. To design adsorption equipment it is very important to know the adsorption capacity and the rate of adsorption. Usually the capacity is represented by an isotherm based on measured data. The rate of adsorption depends, among others, on the rate of transport to the outer surface of the carbon particles and also on the rate of transport inside the particles.

In this thesis the kinetics of adsorption on activated carbon are investigated and single-solute kinetic parameters are used to describe (predict) multisolute kinetics. This is achieved by studying the overall rate of adsorption of several organic compounds from dilute aqueous solutions on granular activaled carbon in a batch system with special focus on the dependenee of diffusion inside the partiele on initial organic compound(s) concentration, amount of carbon added, type of organic compound used, type of adsorption system (single- or two-solute) and partiele size (for a limited number of experiments). Several mathematica! models are developed and the simulation results are compared to experimental data.

In order to obtain experimental data kinetic experiments were performed. This was done by means of adding a certain amount of carbon to a fixed volume of solution and following the concentration change of the component(s) in time. The shape of the concentration decay curve curve depends on several factors, some of which (mentioned in the previous paragraph) were chosen for variations in this study.

Three single-solute systems (4-isopropylphenol, p-nitroaniline and nitrobenzene) and the combined two solutes systems (4-isopropylphenoV p-nitroaniline and nitrobenzene/p-nitroaniline) are used. These compounds were chosen because they are representative for pollutants occurring in industrial waste water streams and because their concentrations could be accurately measured by the analytical metbod used (UV-spectrophotometry).

Equilibrium experiments were also performed, for all systems under investigation. The single-solute data is successfully fitted with a Radke-Prausnitz isotherm. An improved version of the Fritz & Schlünder isotherm equation, proposed in this study, is correlated to the two-solute equilibrium data and is used for calculating local equilibrium in the multisolute kinetic models.

Two basically different diffusion models are developed to predict the behavior of the investigated adsorption systems under different conditions. Both models take into account an extemal film resistance and inside the partiele two-intraparticle diffusion mechanisms in parallel: pore liquid diffusion and surface diffusion. The rate of the adsorption step is considered fast compared to the rates of the diffusional steps and local equilibrium is assumed between pore liquid and adsorbent.

In literature the intra-partiele kinetics of adsorption has been described most often with a Fick diffusion equation which is the basis of one of the models used in this study.

Another way of descrihing intra-partiele kinetics of adsorption is based on the generalized Maxwell-Stefan formulation in which the gradient of the chemical potential is taken as the driving force for diffusion. Such a model, derived for adsorption from the gas phase, was recently proposed by Krishna and has already been successfully applied by Hu and Do. The main advantage compared to the Fickian description is, apart from being thermodynarnically correct, the potential to apply single-solute diffusivities in multisolutekinetics. The second basic model used in this thesis extends the model of Kris~a to liquid phase adsorption.

Apart from the two basic diffusion models a third, more simple model was also used in this thesis. In this model mass transport inside the partiele is modeled by means of a constant effective diffusivity. This constant diffusivity is a lumped parameter and does not depend on the driving force formulation (Fickian or Maxwell-Stefan). Although this model is clearly far from the real physical picture inside the carbon particle, it is quite often encountered in literature and therefore was used for comparison with the other models in this study.

curves with the help of an optimization procedure and from the best-fit model curves the values of the different types of diffusivities were determined.

In the case of single-solute systems model simulations showed that the spread in diffusivity values for the constant diffusion model is too big for the model to have any predictive value. The Fickian model showed a relative standard deviation of the average diffusivity value similar to the one for the constant diffusivity model which indicates that this model has no predielive value either.

The Maxwell-Stefan model, applied for the first time to adsorption from liquid phase, showed a significantly smaller spread around the average diffusivity value than the other two models. This means that the model bas a real predictive value for the single-component adsorption systems and may have the potential to apply single-solute diffusivities in multicomponent kinetics.

In the case of two-solute systems the constant diffusion model fits reasonably well the experimental 4-isopropylphenol/p-nitroaniline results and to a lesser extent the nitrobenzene/p-nitroaniline ones. It can be used for simulations, however, as the values of the constant diffusivities clearly deviate from the single-solute values two-solute experiments will be needed to make model predictions.

The multisolute Maxwell-Stefan model gives a fair predietien of the experimental concentration decay curves and gives ranges for the diffusivity values close to the single-solute ones for components 4-isopropylphenol and p-nitroaniline. The diffusivity range for nitrobenzene, although not large, is rather different from the single-solute diffusivity range. This model can be used to predict fairly well multisolute kinetics based on single-solute diffusivity data.

SAMENVATTING

Adsorptie is een van de belangrijkste processen voor het (af)scheiden van opgeloste stoffen uit vloeistofstromen. Voor het ontwerp van adsorptieapparatuur is kennis omtrent de adsorptiecapaciteit en de snelheid van adsorptie een vereiste. Gewoonlijk wordt de capaciteit beschreven door een adsorptie-isotherm welke verkregen is uit metingen. De snelheid van adsorptie wordt onder meer bepaald door de transportsnelheid aan de buitenzijde van de absorbensdeeltjes en van de transportsnelheid binnen de deeltjes.

In dit proefschrift wordt een studie beschreven naar de kinetiek van adsorptie op aktieve kool met als doel te komen tot een zodanige beschrijving van de kinetiek dat de difffusiecoëfficiënten verkregen uit experimenten met één opgeloste component gebruikt kunnen worden voor het voorspellen van de van de kinetiek in meercomponenten systemen. Daartoe zijn ladingsgewijs metingen van de adsorptiesnelheid aan granulaire aktieve kool uitgevoerd vanuit verdunde oplossingen van verschillende organische componenten in water. Hierbij wordt gekeken naar de invloed van een aantal factoren op de diffusie binnen het deeltje: de beginconcentratie(s) van de opgeloste component(en), de hoeveelheid toegevoegde kool, soort van organische component, keuze van één-of tweecomponentensysteem en - bij een beperkt aantal experimenten- de deeltjesgroottte . Er zijn verschillende wiskundige modellen ontwikkeld en de uitkomsten van de berekeningen met deze modellen zijn vergeleken met de experimentele gegevens.

Ter verkrijging van experimentele gegevens zijn kinetische experimenten uitgevoerd. Daarbij werd een bepaalde hoeveelheid kool toegevoegd aan een vast volume oplossing en werd het concentratieverloop als functie van de tijd gemeten. De vorm van de zogenaamde concentratievervalcurve hangt af van een aantal factoren waarvan er een aantal (genoemd in de vorige alinea) gekozen werden als te onderzoeken variabelen.

Onderzocht zijn drie systemen met één opgeloste component (4-isopropylfenol, p-nitroaniline en nitrobenzeen) en twee gecombineerde tweecomponentensystemen

die in industrieel afvalwater voorkomen en omdat hun concentraties nauwkeurig

te meten zijn met de toegepaste analysemethode (UV-spectrofotometrie). Naast kinetische experimenten zijn voor alle betrokken systemen ook evenwichtsexperimenten uitgevoerd. In dit onderzoek is een verbeterde versie van de Pritz & Schlünder vergelijking voor de evenwiehts isotherm voorgesteld. Deze vergelijking is gebruikt voor het beshcfijven van de 'twee-componenten' systemen en toegepast voor het berekenen van het lokaal evenwicht in de kinetische modellen.

Er zijn twee wezenlijk verschillende diffusiemodellen ontwikkeld om het gedrag van de onderzochte adsorptiesystemen onder verschillende condities te kunnen beschrijven(voorspellen). Beide modellen gaan uit van een uitwendige filmweerstand en binnen het deeltje twee parallel verlopende diffusiemechanismen: diffusie in de porievloeistof en oppervlaktediffusie. De snelheid van de eigenlijke adsorptiestap wordt groot verondersteld ten opzichte van de diffusiesnelheden; daarom is er in alle modellen van uitgegaan dat binnen het deeltje evenwicht bestaat tussen porievloeistof en het adsorbans op die plaats.

In de literatuur wordt de adsorptiekinetiek binnen het deeltje meestal beschreven met behulp van de diffusievergelijking van Piek; deze vormt ook de grondslag voor een van de in deze studie gebruikte modellen.

Een andere wijze van beschrijven van de kinetiek is gebaseerd op de veralgemeende Maxwell-Stefan formulering waarbij de chemische potentiaal als drijvende kracht voor diffusie wordt genomen. Krishna heeft recent een hierop gebaseerd model voorgesteld voor diffusie uit de gasfase; dit model is inmiddels met succes toegepast door Hu en Do. Het belagrijkste voordeel van de Maxwell-Stefan beschrijving in vergelijking tot die volgens Piek is - naast de thermodynamische fundering dat diffusiecoëfficiënten verkregen uit experimenten met een enkele opgeloste stof gebruikt kunen worden voor het beschrijven van de kinetiek in meercomponent systemen. Het tweede model dat in dit proefschrift wordt toegepast kan worden gezien als een uitbreiding van het

model van Krishna tot adsorptie vanuit oplossingen.

Naast de twee bovengenoemde modellen is ook nog een derde, eenvoudiger, model toegepast. In dit model wordt het massatransport binen het deeltje beschreven met behulp van een constante effectieve diffusiecoëfficiënt. Deze constante diffusiecoëfficiënt is een 'lumped parameter' en hangt niet af van de keuze van defmitie van de drijvende kracht (volgens Fick of Maxwell-Stefan). Omdat het model vaak in de literatuur wordt gebruikt is het in deze studie ter vergelijking met de andere twee modellen meegenomen, ondanks het feit dat het model duidelijk ver afstaat van de fysische realiteit binnen het deeltje.

De modellen zijn numeriek opgelost door middel van een 'fmite-difference' methode. Alle modelresultaten zijn met behulp van een optimalisatieprogramma vergeleken met de bijbehorende experimentele curves van het concentratieverloop . De diffusiecoëfficiënt behorende bij de curve die het beste overeen kwam met de experimentele curve geldt als waarde voor dat experiment volgens het betreffende model.

Voor de 'ééncomponentsystemen' bleek uit de modelsimulaties dat de spreiding in de waarden van de diffusiecoëfficiënten erg groot was voor zowel het model met constante effectieve diffusiecoëfficiënt als voor het model gebaseerd op de wet van Fick. Dit betekent dat beide modellen geen voorspellende waarde hebben.

Het Stefan-Maxwell model, dat hier voor het eerst op adsorptie vanuit vloeistoffen is toegepast, vertoonde een veel kleinere relatieve spreiding rond de gemiddelde waarde van de diffusiecoëfficiënt. Dit betekent dat dit model wel degelijk voorspellende waarde heeft voor de systemen met slechts één opgeloste component en het opent de mogelijkheid de gevonden waarden van de diffusiecoëfficiënt toe te passen in systemen met meer componenten.

Voor de 'meercomponentensystemen' blijkt het model met de constante diffusiecoëfficiënt de experimentele resultaten redelijk goed te kunnen beschrijven in het systeem 4-isopropylfenol/p-nitroaniline en in iets mindere mate in het systeem nitrobenzeen/p-nitroaniline. Het model zou dus gebruikt kunnen worden voor simulatieberekeningen. Aangezien de waarden van de gevonden diffusiecoëfficiënten echter duidelijk afwijken van de (niet

Het meercomponenten Maxwell-Stefan model geeft een redelijke voorspelling van het experimentele concentratieverloop en levert waarden voor de diffusiecoëfficiënten die dicht in de buurt liggen van de waarden uit het ééncomponenten systeem voor zowel 4-isopropylfenol als p-nitroaniline. De waarden van de diffusiecoëfficiënt voor nitrobenzeen in het tweecomponenten systeem verschillen onderling niet veel maar wijken wel af van die in het ééncomponentsysteem.

Dit model maakt het mogelijk het kinetische gedrag van meercomponenten systemen redelijk te voorspellen met behulp van diffusiecoefficienten die zijn verkregen uit experimenten met één opgeloste component.

CONTENTS

Chapter 1. Introduetion

1.1 Activated carbon 1.2 Historica! background 1.3 Liquid phase applications 1.4 Objectives of this study

Chapter 2. Equations for liquid phase adsorption equilibria

2.1 Introduetion

2.2 Adsorption isotherrns for single-component systems 2.3 Adsorption isotherrns for multicomponent systems 2.4 Some remarks on irreversibility of adsorption

Chapter 3. Model formulation for adsorption kinetics 3.1 Introduetion

3.2 Basic adsorption models - literature review 3.3 Models based on Pickian diffusivity

3.3.1 Introduetion

3.3.2 Physical description of general model 3.3.3 Matbematkal description of Pickian model 3.3.4 Pull set of equations for constant

diffusivity (HPMC) model

3.3.5 Pull set of equations for Pickian model 3.3.6 Two-solute constant diffusivity model 3.4 Models based on Maxwell-Stefan diffusivity

3.4.1 Introduetion

3.4.2 Theoretica! background 3.4.3 Maxwell-Stefan pore diffusion

3.4.4 Relation between Pickian and Maxwell-Stefan diffusivities 1 1 2 3 4 7 7 8 11 18 20 20 21 23 23 24 27 34 34 36 36 36 37 40 45

3.4.7 Two-solute model equations

Chapter 4. Experimental methods and results for equilibria

4.1 Matenals and instanation

4.1.1 Adsorbates and adsorbate mixtures 4.1.2 Water

4.1.3 Adsorbent

4.1.4 Equipment for equilibrium experiments 4.2 Experiments and analytica! methods

4.2.1 Preparation of standard solutions 4.2.2 Carbon pretreatment and preparation 4.2.3 Procedure for absorbance measurements 4.2.4 Procedure for obtaining equilibrium data

4.2.5 Remarks on experimental and instrumental errors 4.3 Correlation of adsorption equilibrium data

4.3.1 Single-solute systems 4.3.2 Two-solute systems

4.4 Some notes on irreversibility of adsorption 4.5 Conclusions

Chapter 5 Experimental and numerical methods for kinetics

5.1 Batch kinetic experiments 5.1.1 Experimental setup

5 .1.2 Procedure for obtaining kinetic adsorption data 5 .1.3 Ex perimental results

5.1.4 Some remarks on experimental reproducibility 5.2 Numerical solution, parameter fitting and optimization

5.2.1 Numerical salution and algorithms

5.2.2 Comparison of analytica! and numerical solutions 5.2.3 Parameter fitting and optimization

5.2.4 Influence of equilibrium on parameter fitting

59 62 62 62 64 64 65 66 66 67 67 68 70 72 72 78 88 90 92 92 92 96 98 103 104 104 106 109 118

5.3 Conclusions

Chapter 6. Estimation of rate parameters for single-solute systems

6.1 Estimation of external mass transfer coefficient 6.2 Model calculations for single-solute systems

6.2.1 Introduetion

6.2.2 Model with constant diffusivity

6.2.3 Fickian model with variabie diffusivity 6.2.4 Transition model based on the pore liquid

concentration gradient

6.2.5 Maxwell-Stefan model with variabie diffusivity 6.3 Some additional remarks and discussions

6.4 Conclusions

Chapter 7. Estimation of rate parameters for two-solute systems

7.1 Estimation of external mass transfer coefficient 7.2 Model calculations for two-solute systems

7.2.1 Constant diffusivity model

7.2.2 Maxwell-Stefan model without cross-diffusion coefficients

7.3 Conclusions and recommendations

Chapter 8. Epilogue

8.1 General conclusions

8.2 Recommendations for future work

Appendix 4.1 122 123 123 127 127 128 134 140 142 150 157 159 159 160 160 164 168 170 170 170

Appendix 5.1

Experimental conditions for kinetic single-solute systems

Appendix 5.2

Experimental conditions for kinetic two-solute systems

Appendix 5.3

Some important experimental errors and reproducibility measurements

Appendix 5.4

Numerical solution of differential equations used in this stud y

Appendix 5.5

Flowsheet of general algorithm for single-solute model with variabie diffusion coefficient

Appendix 5.6

Pascal program for two-component Maxwell-Stefan model

Appendix 5.7

Comparison of analytica} and numerical solutions for special cases of the constant diffusivity models (some additional details)

Appendix 6.1

Experimentally determined values for extemal mass transfer coefficient

Appendix 6.2

Transition model based on the pore concentration gradient (see also section 6.2.4)

176 179 181 186 192 195 208 214 216

Appendix 7.1

Experimental values for extemal mass transfer coefficients

References List of symbols Curriculum vitae

INTRODUCTION

Adsorption is a surface phenomenon by which a solute is removed from one phase and accumulated at the surface of a second phase. The material being adsorbed is the adsorbate, and the adsorbing material is called the adsorbent.

1.1. ACTIV ATED CARBON

Some of the most widely used types of adsorbents nowadays are activated carbons. They are non-hazardous, processed, carbonaceous products, having a porous structure and a large intemal surface area. These materials cao adsorb a wide variety of substances, i.e. they are able to attract molecules to their intemal surface and are therefore often used in processes of purifying, decolorizing, deodorizing, detoxicating and separating.

Although it is now recognized that the pore structure is the most important property of activated carbon, it was formerly believed that the carbon had to he activated by chemica! and heat treatment before it could remove color, hence the name activated carbon. It is now known that the removal of impurities from gases and liquids by activated carbon is by adsorption, and the activation process simply increases the intemal surface area of the carbon and hence the number of sites available for adsorption.

Activated carbons cao he prepared in the laboratory from a large number of materials but those most commonly used in commercial practice are peat, coal, lignite, wood and coconut shell. The residues from carbonization have a large pore volume, and as this is derived from very small diameter pores the intemal surface area is high. Activated carbons have internat surface areas in the range 500 1500 square meters per gram and it is this large area which makes them effective adsorbents.

Th ere are two main types of activation processes: steam activation and chemica! activation.

Steam activated carbons are produced by a two-stage process. Firstly the material is carbonized and a coke is produced, the pores of which are either too small or constricted for it to he a useful adsorbent. The next stage is a

Chapter I 2

process of enlarging the pore structure so that an accessible internat surface is created. This is achieved by reacting the semi-product with steam between 900°C and I000°C. At this temperature the rate determining factor is the chemical reaction between carbon and steam. This reaction takes place at the internat surface of the carbon, removing carbon from the pore walls and thereby enlarging them.

Chemically activated carbons are produced by mixing a chemical with a carbonaceous material, usually wood, and carbonizing the resulting mixture. The carbonization temperature is relatively low, e.g. 400°C 500°C and the chemical is usually reeavered for use after carbonization. The chemieals normally used are phosphoric acid and zinc chloride solutions which swell the wood and open up the cellulose structure. On carbonization the chemica! acts as a support and does not allow the resulting char to shrink.

The majority of activated carbon used throughout the world is produced by steam activation.

1.2. HlSTORICAL BACKGROUND

Activated carbon is one of the oldest and best known adsorbents with a wide range of dornestic and industrial applications. Charcoal, the forerunner of modern activated carbon was used by ancient Egyptians for medicinat purposes. The properties of carbon to adsorb gases were first reported by Scheele in the 18th century. In 1790 Lowitz established the first use of powdered charcoal for the removal of bad tastes and odors from water on an empirica! basis. The first application of activated carbon in a water treatment plant, for removing chlorophenolic substances, was reported in the United States, in 1929. By some estimates by 1939 there were already 400 such plants, using powdered carbon to reduce odors in drinking water [Faust, 1987].

Nowadays activated carbon is used for solvent recovery and air purification, in food processing and chemica! industries; in the purification of many chemical and foodstuff products; for the recovery of gold, silver and other inorganic products and in the treatment of dornestic and industrial waste waters. Nearly 80% (220 000 tons/yr) of the total world production of activaLed carbon is consumed for liquid phase applications where both granular and powder activated carbons are used [Bansal, 1988].

1.3. LIQUID PHASE APPLICATIONS

Since 1930 powdered activated carbon has been used as the main adsorbent for cleaning ground water and thus making it suitable for drinking. However, during the last hundred years the consumption of potable water bas significantly increased and so it became necessary to use other sources, such as surface waters and process them into a form suitable for drinking purposes. The presence of pesticides and other toxic substances in the surface waters led to the need for much larger amounts of activated carbon and for radkal improvement of the existing methods and technologies for potable water treatment. At the same time it became clear that not only the water for drinking had to be purified, but also the enormous amounts of waste waters produced had to be processed, before being discharged into the environment. Using granular instead of powdered activated carbon proved out to be an economically viabie and efficient solution. This led to the building of numerous granular carbon treatment facilities in many parts of the world. To make them work efficiently it was necessary to define and develop suitable design parameters and to study the kinetics of adsorption from dilute solutions.

In many cases the use of granular carbons, unlike powdered carbons, involves the regeneration of the carbon. Regeneration is the treatment of the carbon to remove the adsorbed impurities so that it can be re-used. The three most commonly used ways to regenerale used carbons are: steam regeneration this can be used if the adsorbed products are volatile, i.e. if they can be steam distilled; chemical regenerafion in certain cases the adsorbed impurity can be desorbed from the surface by treatment with a chemical. Caustic soda has been used successfully with eertaio organic acid purification systems; thermal

regeneration this is the most widely used metbod particularly in the large tonnage outiets in the sugar, glucose and water industries. This involves the removal of the carbon from the packed column and buming off the impurities under controlled conditions in a regeneration kiln.

There are several important design parameters in the construction of a granular carbon plant used for potable water production or waste water treatment (EPA report, 1973]:

Chapter I 4

- mode of operation of the filters (fixed bed, fluidized, etc.) - contiguration of the filters (in series, in parallel, etc.)

- contact time between treated liquid and carbon, fluid velocity, pressure drop

- type of carbon used (particle size, pore structure) - reactivation facilities (local or extemal)

The overall rate of adsorption can be defined as the rate at which the adsorbable component is transferred from the bulk phase outside the carbon particles to the intemal adsorption sites [Van Lier, 1989]. The overall rate of adsorption depends on such factors as:

- the type of carbon which is used

- the nature and relative concentrations of the substances to be removed - the pH and temperature of the water

- the presence of compounds which have an influence on the adsorption process, although they do not have to be removed

The overall rate of adsorption is very important for the design because it determines the optimal values of the linear liquid velocity and contact time.

1.4. OBJECTIVES OF TUIS STUDY

The main objective of this study is to investigate the kinetics (i.e. overall rate) of adsorption on activated carbon and to try to use single-component kinetic parameters to describe (predict) multicomponent kinetics. This objective is achieved by studying the overall rate of adsorption of several organic compounds from dilute aqueous solutions on granular activated carbon in a batch system, with special focus on the dependenee of diffusion inside the partiele on initial organic compound(s) concentration, amount of carbon added, type of organic compound used and type of adsorption system (single- or two-component). Several mathematica! models are developed and the simulation results are compared to experimental data.

For all experiments only one type of activated carbon is used. In several cases the influence of the partiele size and partiele size distribution are

also investigated. The one-component experimental systems used are nitrobenzene(NBZ)/water, p-nitroaniline(PNA)/water and 4-isopropylphenol(IPP)/ water. The two-component systems are nitrobenzene/p-nitroaniline/water (NBZ/PNA) and 4-isopropylphenol/p-nitroaniline/water (IPP/PNA).

The above-mentioned organic compounds and respective mixtures were chosen because they are often present m waste waters and because their concentrations (absorbances) could be accurately measured by the analytical metbod used (UV-spectrophotometry).

A review of existing equilibrium models is presented in chapter 2. Empirica! and theoretically based isotherm equations are discussed and several improved versions for some of the isotherm equations are being proposed. In the last part of the chapter some remarks are made on adsorption irreversibility

In the first part of chapter 3 a literature review of kinetic batch models is given. Later in the same chapter a detailed denvation and explanation of the mathematica! models used in this study is presented.

Chapter 4 contains a description of the experimental methods and matenals used for equilibrium experiments. The correlations of the obtained data with different isotherm models are also presented in this chapter.

Chapter 5 is dedicated to estimation of single-solute kinetic parameters. In the beginning of the chapter , the experimental methods and results from the kinetic experiments are given and also some remarks are made on experimental errors and reproducibility. Later in the same chapter results from the numerical model calculations are compared with analytica! solutions from literature. The last part of chapter 5 includes a description of the optimization procedure used and a discussion of the sensitivity of different fitting parameters.

Chapter 6 contains the results of all model calculations for the three single-component systems used in this study. Comparisons between the different models and between the experimental systems are made and the validity and predictive value of the models are discussed.

Chapter I 6

In chapter 7, some data and discussions are presented about the two-component model calculations, tagether with comparisons between model and experimental curves.

Finally, chapter 8 contains general conclusions and recommendations for future work.

Some chapters have Appendices which contain additional information and details about the subjects under discussion. The Appendices carry the number of the respective chapter, but are all placed at the end of this thesis.

EQUATIONS FOR LIQUID PHASE ADSORPTION EQUILIBRIA

2.1. INTRODUCTION

In order to describe the overall rate of adsorption on activated carbon it is necessary to understand the mass transfer processes, and also the equilibrium behavior of the systems involved. This chapter deals mainly with liquid phase adsorption equilibrium to the extent necessary to describe the rate behavior of the single- and two-component systems used in this study.

In principle, the process of adsorption involves the concentration of the adsorbate on the surface of a solid or, less frequently, of a liquid. Two types of adsorption can be distinguished, depending on the nature of the forces involved. In chemical adsorption a single layer of molecules, atoms or ions is attached to the adsorbent surface by chemica! bonds. In physical adsorption adsorbed molecules are held by the weaker van der W aais' forces and multilayer formation is possible.

Physical adsorption of single-gases on solid adsorbent surfaces is well described in literature. The first serious attempt to give a fundamental description of monolayer localized adsorption was made by Langmuir in 1918. Since that time numerous other papers were published, extending the ideas of Langmuir to multilayer adsorption on homogeneous solid surfaces [Brunauer,

1938], others assuming a semi-mobile adsorption model [Patrykiejew, 1984], and still others descrihing the single-gas adsorption by statistical-mechanical means [Steele, 1974], [Sokolowski, 1981].

There is also a significant amount of publications available in the field of multicomponent gas adsorption, although here the overall physical picture is less clear. The most complete compilation of existing data on equilibrium of pure gases and gas mixtures has been publisbed by Valenzuela and Myers in 1989. This same pubHeation contains also a lot of data on liquid mixtures. On the theoretica} side, in 1965 Myers and Prausnitz applied for the frrst time solution thermodynamics to mixed-gas adsorption, foliowed by further advances in the same field [Sircar, 1973], [Myers, 1987]. An alternative thermodynamic

Chapter !I 8

description of mixed-gas adsorption is based on the vacancy solution theory [Suwanayuen, 1980a,b], [Fukuchi, 1982], [Talu, 1987].

In many theoretica! studies in literature it is assumed that the surface of the adsorbent is homogeneaus and that there are no lateral interactions between the adsorbed molecules. This is not the case for such a strongly heterogeneaus adsorbent as activated carbon and it makes the task of finding a fundamentally correct and at the same time universally applied isotherm equation very difficult.

A different type of adsorption is the adsorption from liquid solutions. Here it is much more complicated than for gases to formulate a unified theory, because there are many liquid mixtures with very different physical and chemical properties. Another complication arrises from the strong possibility for interactions in the liquid phase between different components, as well as the complex structure of the adsorbent [Jaroniec, 1985].

Adsorption from dilute solutions is a special case of liquid adsorption. In principle, the isotherm equations for adsorption from dilute solutions can be derived from the general isotherm equations in liquid solutions which describe the whole concentration range (Jaroniec, 1988]. It often happens, however, that researchers use gas-adsorption isotherm equations and change the relative pressure into solute concentration. From a mathematica! point of view the isotherm equations can be identical, which does not necessarily meao that the mechanisms involved in the two processes are the same (Jaroniec, 1983]. In spite of these difficulties, there are several empirica! and semi-empirica! isotherm equations which give in many cases a good description of experimental liquid-phase adsorption results [Radke, 1972a], [Jossens, 1978], (McKay,

1989].

Further in this chapter a short description will be given of several commonly used isotherms, some of which have been applied in this study. As noted, most discussions will be in terros of liquid phase adsorption.

2.2. ADSORPTION ISOTHERMS FOR SINGLE-COMPONENT SYSTEMS

The Henry isotherm

law. At very low sol u te concentrations the molecules of the adsorbate do not interact with each other and do not compete for adsorption sites. In that case the equilibrium relationship between the concentrations in the fluid and in the adsorbed phases will have a linear form. This is referred to as Henry's law, where the constant of proportionality is the adsorption equilibrium constant Kh [Ruthven, 1984]:

Q

=KC

h p' (2.1)

where Q and C can be expressed as molecules or moles or weight per weight

p

or per unit volume in the adsorbed and fluid phases.

TheLangmuir isotherm

The first isotherm model which assumed monolayer coverage of the adsorbent surface was proposed by Langmuir in 1918. It contains several very important assumptions:

1. All molecules are adsorbed on definite sites of the adsorbent surface. 2. Each site can be occupied by only one molecule.

3. The adsorption energy of all sites is equal.

4. When adsorbed molecules occupy neighboring sites there is no interaction between them.

Initially this isotherm was derived by Langmuir kinetically while later, it was also derived on basis of statistica} mechanics, thermodynamics and the Maxwell-Boltzmann distribution law [Young, 1962].

The most commonly used form of the Langmuir isotherm is the following:

Q= Q b

c

m P 1 + b

c

p (2.2)

where C is the equilibrium concentration of the component; Q is the

p m

concentration in the adsorbed phase required to have monolayer coverage of the whole surface; and b is a constant related to the heat of adsorption.

At very low concentrations the term b·C is much smaller than unity and then

p

Chapter ll JO

Q Q _m b

c'

P (2.3)

which is exactly the form of Henry's law. On the other hand from Eq. (2.2) it follows that Q approaches Q asymptotically as C goes to infinity which is

m p

the expected behavior for monolayer adsorption.

Although for many systems the assumptions of the Langmuir isotherm do not hold it can be still very useful as a theoretica! basis for studying adsorption equilibrium.

The Freundlich isotherm

The Freundlîch equation [Freundlich, 1926] is one of the best known mathematica! descriptions of adsorption equilibrium. lt bas the following general form:

(2.4)

where Fr and Nf (Nf > 0) are constants characteristic of the system.

Although this is an empirica! isotherm it still gives some information about the heterogeneity of the adsorbent surface [Jaroniec, 1983]. A drawback is that it does not reduce to a straight line (that is, to Henry's law) at very low concentrations.

The BET isotherm

The isotherm model developed by Brunauer, Emmett and Teller (BET) in 1938 extends the concept of monolayer adsorption to the formation of multilayers on the adsorbent surface. It makes several basic assumptions, the most important of which is that each molecule in the frrst adsorbed layer is providing one site for the. second and subsequent layers. The molecules of these layers are considered to behave as the saturated liquid while the equilibrium constant for the first layer of molecules in contact with the surface of the adsorbent is different [Ruthven, 1984]. The most widely used form of the BET equation reads as follows:

Q B C

Q= m p _(2.5)

(C-C) [1+ (B-l)C /C]

where

c

is the solubility of the component in water at the relevant

s

temperature and B is a constant.

The BET isotherm model is applied in one of the main methods for the determination of the specific surface area of microporons solids.

The Radke-Prausnitz isotherm

An empirica! relation with three parameters was proposed by Radke and Prausnitz [1972a] to describe equilibrium data from liquid phase over a wide concentration range:

KC

Q

= ___

r__,_p _ _ _ 1 + ( K /F )C1-Nr r r p (2.6)

where K , F and N are constants and N < 1.

r r r r

Although empirical, the Radke-Prausnitz equation bas several important properties which make it suitable for use in many adsorption systems. As already mentioned it can describe fairly well the equilibrium dependenee over a very wide concentration range. At low concentrations it reduces to a linear isotherm, described by Bq. (2.1). At high solute concentrations it becomes the Freundlich isotherm, Bq. (2.4), and for the special case of N

=

0 it becomes

r

the Langmuir isotherm (Bq. (2.2)). The three parameters are estimated by a non-linear statistica! fit of the equation to the experimental data.

The Radke-Prausnitz isotherm was used in this study to correlate the single-component experimental equilibrium data.

2.3. ADSORPTION ISOTHERMS FOR MULTICOMPONENT SYSTEMS

Many practical adsorption systems, especially those in potable and waste water treatment, contain more than one component. That is why the problems of correlating and predicting multisolute equilibria from single-solute data is of primary importance when dealing with such systems. Several isotherm models will be considered in this section.

Chapter IJ 12

Models based on the isotherm

The classica! Langmuir model for multicomponent adsorption is based on the same assumptions as the single-component model. The resulting equation has been derived for the first time by Butler and Oclcrent [1930] and reads as follows: Q ' b,

c'

Q.

= ___

m_:_, • _ _ •_P'-'·-'-1 k (2.7) +:Eb,

c '

j l I p,t

where k is the number of components, i is the component number and the constants b are obtained from single-component data. This model is still often used although recent studies [McKay, 1989] show that in many cases it can not give a good correlation of the experimental data.

In 1973 Jain and Snoyeink introduced a two-component model, which is a modified version of Langmuir's model:

(Q - Q ) b

c

Q = rn,l m , 2 I p,l + l 1 + b

c

I p, I Q b

c

m,2 l p,l (2.8) 1 +bC +bC I p, 1 2 p,2

(2.9)

It is a semi-competitive model as it assumes that part of the adsorption takes place without competition due to the fact that not all adsorption sites are available to all solutes. In quantitative terms this means that a number of sites corresponding to Q Q (where Q > Q ) can accept only

m,l m,2 m,l m,2

molecules from component 1 while all components compete for the remaining sites, which are equal to Q . These equations can be very suitable for

m,2

components with different molecular sizes or with different chemica! properties relative to the adsorbent. A drawback of this model is that it is valid only for two-component systems.

The above described roodels use only single-component data and do not take into account the possible interactions between the components while the adsorption

takes place. It is very probable that in real adsorption systems there are various interactions which have to be accounted for when modeling the process. This reasoning was the basis for the introduetion of another, modified version of the Langmuir model, in which an interaction term, 11, appears. In this model, proposed by Schay [1957] the interaction terrus 11. are evaluated by

I

correlating the model to multicomponent experimental data. He proposed the following correlation: Q Q . _m, b. (C . I

'llJ

1 1 p, 1 t k (2.10) +

I

b. (C . I 11) j=l J p.j J

where 11 is a term which accounts for possible interactions between the components and is specific for each solute.

Models based on the Radke-Prausnitz isotherm

Mathews [1975] extended the Radke-Prausnitz isotherm to multicomponent adsorption and proposed the following equation:

Q'

=

~----,.--~----"--···--1 k (2.11)

1

+I

(K , I F ,) C ~-Nrj j=

1 r,J r,J p,J

In this equation the constants are calculated from the single-component systems which are described by Eq. (2.6).

Por some of the systems used, Mathews achieved better results by using Eq. (2.11) than by using Eqs. (2.8) - (2.9). However, other systems could not be adequately described even by Eq. (2.11), so he applied an interaction term and proposed another equation:

(2.12)

k

+

L

(K ,/ F .) (C . I '11)1-Nrj

j I r ,J rJ p,J J

The constants K , F, N for each component are obtained in the same way as

r r r

for Eq. (2.11). The terrus 11. are determined by miniruizing the sum of squares

Chapter /1 14

(SOS) of the difference between the relative experimental and calculated adsorbed phase concentrations for each component.

One of the basic conditions a multicomponent equilibrium model should fulfill is that when the concentrations of all but one components are zero it should reduce to the single-component form of the equation. This is not the case with the isotherm model described by Eq. (2.12) which raises questions about its validity, especially in systems where some solute concentrations in the adsorbed phase can be very low. lt may also lead to erroneous results when using the equation in a ldnetic model where the calculations always start with a zero adsorbed phase concentration.

Due to the above reasons, an improved version of Eq. (2.12) is proposed in this study: K r i (2.13) k 1 + (K . I F .) C . +

L

(K

.I

F .) (C . I TJ/-NrJ r,1 r,1 p,1 j = 1 r ,J r,J p,J J ( j

*

î)

In contrast to Eq. (2.12), Eq. (2.13) reduces to the single-component form when all but one concentrations are zero. A discussion and correlation with some experimental results are given in chapter 4.

Models based on the Freundlich isotherm

Fritz and Schlünder [1974] proposed a general empirica! multisolute equation, which has the following form:

A.

C . Bio Q.

=

1 10 p t 1 (2.15) k E +

LA ..

c

Bij I IJ PJ

where A, B and E are constants.

For specific values of the constants Eq. (2.15) reduces to the Mathews equation (Eq. (2.11)) or to the Langmuir muitkomponent model (Eq. (2.7)). Fritz and Schlünder showed a method for evaluating the constants for a two-component system when the single-component data could be fitted with the

Freundlich isotherm. In this case the equations are: F C Nf, I + B I I Q _I

=

f, I p,l (2.16a)

c

B +A

c

B I 1 12 p • I 1 2 p,2 N ₊ 8 22 f. 2 ~= (2.16b)

c

8 2 2 + A

c

B 21 p,2 21 p • I

where Ff and Nr are the single-solute Freundlich constants, while the A and B constauts are determined by correlating the multicomponent equilibrium data. The use of Eqs. (2.16) in kinetic models calculations presents eertaio · difficulties. As mentioned the Freundlich isotherm does not reduce to a linear form at low concentrations and this is also valid for its multicomponent form, i.e. Eqs. (2.16). This may lead to erroneous results when calculating the profiles inside the partiele in the multicomponent kinetic models and consecutively to the deterrnination of the wrong diffusion coefficients. For this reason a new, extended form of Eqs. (2.16) is proposed in this study in which an additional term is introduced, accounting for the linear part of the isotherm at concentrations close to zero:

c

B A

c

D 1 1 p ,I I + I p,2 I :::: _{+ (2.17a)} Ql K r, I

c

p,l _F

c

N r , I + B I r, I _{p • I}

c

B + A

c

D 1 1 p,2 2 2 p • I 2

=

+--··· (2.17b) Q2 K _{r, 2}

c

_{p,2 F}

c

N _{r , 2} + B2 r, 2 p,2

The transformation from Eqs. (2.16) to (2.17) is analogous to the one from Freundlich to Radke-Prausnitz isotherm for a single-solute system. Note, however, that in Eqs. (2.17a) - (2.17b) all the single-solute parameters used are from the Radke-Prausnitz isotherm, while Eqs. (2.16) are based on

Chapter IJ 16

Freundlich single-solute parameters.

lsotherm Eq. (2.17) was used in this study for calculating the local equilibrium in the kinetic models. Details are presented in chapter 4.

Model based on the ideal adsorption salution theory (lAST)

The technique of predicting multisolute data on the basis of single-solute experiments using the concept of an ideal adsorbed solution was proposed for the first time by Myers and Prausnitz [1965]. The main idea is that in an ideal salution the partial pressure of an adsorbed component is given by the product of its mole fraction in the adsorbed phase and the pressure which it would exert as a pure adsorbed component at the same temperature and spreading pressure as those of the mixture. This thermadynamie spreading pressure can be calculated from the experimental adsorption isotherms and does not depend on any particular physical model of the adsorbed phase. lnitially this model was derived for gas mixtures and was extended later to dilute liquid mixtures by Radke and Prausnitz [ 1972b]. Si nee that time the lAST has been used by numerous researchers to predict multicomponent equilibria from single-component isotherm parameters [ûkazaki, 1980], [Fritz, 1981], [Crittenden, 1985], [Baudu, 1989]. However, predicted adsorption equilibria are not always found to be in good agreement with experimental data. Extensions and modifications of the lAST were proposed, where more pronounced deviations from ideality were taken into account [Lee, 1988], [Seidel, 1989], [Gamba, 1990], [Myers, 1991].

The basic assumptions made in the ideal adsorption salution model in the case of liquid mixtures are: 1) the liquid solution in question is dilute, 2) the adsorbed phase forms an ideal solution, 3) the adsorbent is thermodynamically inert, and 4) the available surface area is identical for all solutes. For these systems the model is based on the assumption of a hypothetical ideal adsorbed phase salution which contains only one component i, and this salution has the same spreading pressure

n

as the adsorbed phase solution containing all the components.

n

is defrned as the difference between the interfacial tension of the pure solvent-solid interface and that of the solution-solid interface at the same temperature:

0=0"

The model can be described by several basic equations and can predict muitkomponent behavior from single-component data [Radke, 1972b]:

where n

<2r

=

:L

Q. i = l 1 z. ₁ = Q. _I

I

o

_"'î

c

= z C0 i i i n z.

=

L-1-. Qo I l . 1 TI A TI0 A m s i = -RT RT Co Qo =

J

i _ i dCo 0 . 0

c

TI0 :spreading pressure of single solute [N·m-1]

I

I1 :spreading pressure of mixture [N·m-1]

m (2.19) (2.20) (2.21) (2.22) (2.23)

The two basic equations needed to calculate multi-solute equilibria are (2.21) and (2.22). Equation (2.22) indicates that the total invariant adsorption is determined by the adsorptions of the single solutes at identical values of spreading pressure and temperature. Equation (2.21) results from consiclering the equilibrium between the adsorbed and liquid phases.

In order to apply Eqs. (2.21) and (2.22) it is necessary to know the spreading pressores of the different singly-adsorbing solutes in the mixture. These pressores are calculated from Eq. (2.23) using the data from experimental single-component isotherms. As I1 is determined only by these isothenns no theoretica! model is needed to describe the adsorption equilibria.

There is, however, an important condition to be fulfilled. As the integration in Eq. (2.23) begins at zero concentration it is necessary to have experimental data for the whole range of loadings from zero to

Q?

in order to calculate TI accurately enough.

The lAS theory is applied most often to two-component systems, but extending it to multicomponent systems is straightforward and easy. There is no

Chapter 11 18

restrietion whether the components are below or above their melting points, or whether or not they are miscible in all proportions with the solvent [Radke, 1972b].

Although the lAS model is thermodynamically consistent and extensively used, its assumptions have limited applicability and its theory cannot provide a general method for the prediction of binary or multicomponent equilibria from single-component data [Ruthven, 1984]. In addition to that, as already pointed out, it is necessary to have single-component data at very low concentrations in order to calculate the spreading pressure. The model requires extensive computational effort, especially in the case when the spreading pressure integration (Eq. (2.24)) cannot be solved analytically. Another objection 1s that at high surface loadings the assumption for an ideal adsorbed phase is probably not correct.

In view of the foregoing the lAS model was not used in this study and more simple, empirica! relations were applied in the kinetic models.

2.4 SOME REMARKS ON IRREVERSIBILITY OF ADSORPTION

All isotherm equations discussed so far are based on the assumption that adsorption is a physical process and no chemica} reactions occur on the adsorbent surface. However, all carbonaceous materials, even graphite and diamond, contain surface functional groups. On activaled carbon these surface groups are mostly located at the edges of graphite-like basal planes and there are probably electronk interactions between them [Rivin, 1971]. Therefore, it is possible that under certain conditions, the components which are adsorbed on the activated carbon would react with these surface groups, leading to the formation of strong chemica! honds. In 1969 Mattson proved the formation of charge-transfer complexes between adsorbates and surface functional groups.

In adsorption literature most authors use the term "irreversibility" to designale the occurrence of chemisorption [Suzuki, 1978], [Yonge, 1985], [Vidic, 1990]. There are various studies which strongly suggest the existence

of strong irreversibility (chemisorption). Recently, Grant [1990], through systematic sequence of experiments, determined that oxidative coupling of phenolic compounds on carbon surfaces is a plausible explanation for irreversible adsorption. Earlier Coughlin [1968] showed that oxidation of the activated carbon surface prior to adsorption lowered the capacity of the carbon for phenol and nitrobenzene. Other researchers however [Thakkar, 1987] succeeded in fully recovering several phenolic compounds from activated carbon and thus concluded that there was little, if any, irreversible adsorption in this case.

A different concept for irreversibility was proposed in 1988 by Kerkhof. He suggested that in some cases physical rather than chemical adsorption can be the cause for irreversibility and that capillary crystallization may be the mechanism by which it is occurring. However, forther studies are necessary in order to get more conclusive evidence about this model.

In the present study limited attention is given to the problems of irreversibility. The kinetic models developed are based on the assumption that adsorption is fully reversible and there is no special term accounting for possible chemica} reactions. Although the discussed literature sourees offer some evidence about irreversible adsorption it is still the case that almost all existing models do not take it into consideration and for most practical applications these roodels can predict fairly well the process.

A very limited amount of desorption experiments were performed with 4-IPP to try to determine the extent of irreversibility, if any, at different temperatures. Details are given in chapter 4.

Chapter III 20

MODEL FORMULATION FOR ADSORPTION KINETICS

3.1. INTRODUCTION

Descrihing adsorption on a porous solid requires an understanding not only of equilibrium behavior but also of mass transfer (transport) phenomena.

In principle, adsorption kinetics can be determined by several processes: - transfer of molecules from the bulk phase to the outer surface of the

partiele through a fluid boundary layer surrounding the partiele (external mass transfer).

- diffusion of molecules in the liquid in the pores (pore diffusion) - diffusion of already adsorbed molecules along the surface of the pores

(surface diffusion).

- the elementary processes of adsorption and desorption.

One or several of these processes can be much slower than the others and in that case they determine the overall rate of adsorption. On the other hand since adsorption is exotherrnic and the heat of sorption must be removed by heat transfer there is, in general, a difference in temperature between the adsorbent partiele and the bulk fluid when adsorption takes place. How important this temperature difference is depends on the relative rates of heat and mass transfer. However for adsorption from liquid systems it will be fairly accurate to assume that heat transfer is sufficiently rapid, so that temperature gradients in and around the partiele are negligible [Ruthven,

1984].

A convenient way to describe the intrapartiele transport in an adsorbent like activated carbon is to consider it as a diffusive process and to express it according to Fick's 1 s 1 and 2"d laws, which will be considered in more detail later in this chapter. This is the most widely used form and almost all models in literature are based on Fick's mathematica! representation. However, since the true driving force of a diffusion process is the gradient of the chemical potential and not the concentration gradient an alternative model is discussed in Section 3.4, based on the Generalized Maxwell-Stefan equations.

homogeneaus and isotropie pore structure. However, in order to distinguish between the two types of flux-driving force defmitions, the Fickian model will be referred to as Homogeneaus Partiele Fickian Model (HPMF) and the MS model will be referred to as Homogeneaus Partiele Maxwell-Stefan Model (HPMS). As it will become elear from the mathematica! derivations in this chapter both types of models inelude a variabie apparent diffusivity (D ), but constant

app

pore (D ) and surface (D ) diffusion coefficients.

p s

In addition, two other models are also used in this study. The first one, named Homogeneaus Partiele Constant Diffusivity Model (HPMC) assumes a constant D . The second one, called Homogeneaus Partiele Transition Model

app

(HPMT) assumes a variabie D and is based on rather empirica! app

considerations. This latest HPMT model is discussed in chapter 6 and Appendix 6.2.

3.2. BASIC ADSORPTION MODELS LITERATURE REVIEW

Extensive efforts were made during the last few decades to try to model the adsorption of single and multicomponent systems of gases and, to a lesser extent, of liquids. This short review will deal mainly with studies of mass transfer on activated carbon from aqueous solutions, however, work of a more general nature, ineluding other adsorbents and solvents, have also been included where they are relevant to the present study. A much more extensive literature review on kinetics of adsorption on activated carbon has been published by Van Lier [1989].

The models reviewed in this survey are classified on basis of the type of mass transfer resistances (one or more) that they take into account. This elassification is commonly used in adsorption literature and gives a good basis for comparison between different classes of models.

In earlier adsorption studies models were proposed which considered only the resistance to extemal mass transfer as important. One such model was published by Misic [1971]. There, adsorption of benzene in carbon slurries was modeled and the intrapartiele transport resistance was considered negligible (for the specific system conditions), while the resistance to mass transfer through the liquid immediately surrounding the partiele appeared to be