Mass transfer to activated carbon in aqeous solutions

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^'«tlte-MASS TRANSFER TO ACTIVATED CARBON

IN AQUEOUS SOLUTIONS

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MASS TRANSFER TO ACTIVATED CARBON

IN AQUEOUS SOLUTIONS

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR AAN DE TECHNISCHE UNIVERSITEIT DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS, PROF. DRS. P.A. SCHENCK IN HET OPENBAAR TE VERDEDIGEN TEN OVERSTAAN VAN EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN OP MAANDAG 12 JUNI 1989 TE 14.00 UUR

DOOR

WILLEM CORNELIS VAN LIER

GEBOREN TE EDE SCHEIKUNDIG DOCTORANDUS

DRUKKERIJ ELINKWIJK BV - UTRECHT 1989

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DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOR PROF. IR. J.A. WESSELINGH

EN DE CO-PROMOTOR PROF. DR. A.I. LIAPIS

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I

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Chapter 1 Introduction

The historical background to the present study will be outlined in the first section. The second will deal with the role played by the rate of adsorption in designing a granular carbon plant for water treatment. The objectives of the present study will be discussed in the third section.

1.1 Historica! background

Powdered activated carbon has been used for more than fifty years to remove substances imparting taste and/or odour in the preparation of potable water from surface water (ref. 1). Following the second world war, the increase of population and rapid industrialisation caused a swiftly increasing demand for potable and clean process water in many countries. In many cases the amount of ground water available was insufficiënt to satisfy the increasing demand. For this reason, surface water became more important as raw water source for the production of potable water. At the same time, the quality of this surface water had deteriorated sharply. This was because the installation of waste water treatment plants lagged far behind the increases in population and in industrialisation. Moreover, many of the existing treatment plants were unable to cope with the non-biodegradable compounds present in the waste water being treated. The development of techniques for isolation and the qualitative and quantitative analysis of the inorganic and organic compounds in water, lead to the discovery that many rivers and lakes contained tracé amounts of substances toxic to humans. These substances, originating from discharge of waste water and agricultural run-off (e.g. pesticides), had to be removed from the water in order to make it safe for human consumption. The classical dosing of powdered activated carbon could not cope with these problems, at least not economically.

It was soon realised, and demonstrated, that these (toxic) compounds could be removed economically by using granular activated carbon.

In the seventies many potable water works, especially in Western Europe, installed granular carbon plants. At the same time several waste water treatment plants (USA, South Africa, Europe) incorporated a granular carbon treatment step. It was discovered a little later that the groundwater was also polluted in many places with compounds which made the water unsafe for human consumption. In many of these cases treatment with granular activated carbon proved a succesful treatment technique.

These developments produced a need for design parameters for granular carbon plants. They stimulated the study of the rate of adsorption from dilute aqueous

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solutions onto activated carbon. A comparable phenomenon occurred after the first world war. The use of war gases stimulated research on the rate of adsorption from the gas phase.

1.2 The rate of adsorption as a design variable

The following design variables are important in the construction of a granular carbon plant used for potable water production or waste water treatment (ref. 2):

1. The type of carbon filters used (open gravity filters or closed pressure filters).

2. The mode of operation of the filters (fixed bed, fluidised bed, upflow, downflow etc).

3. The configuration of the filters (in series, in parallel, or a combination). 4. The values of superficial liquid velocity, contact time between the liquid to

be treated and carbon, and the height of the carbon layer (only two of these three parameters can be chosen freely).

5. The carbon type (partice size, pore structure). 6. Reactivation facilities (local or external).

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 internal adsorption sites. This rate plays a decisive role in the design, because it determines the optimal values of the linear liquid velocity and contact time. The rate of adsorption depends on:

— the nature and relative concentrations of the substances to be removed. — the presence of compounds which need not be removed, but which

interfere with the adsorption of the compound to be removed. — the pH and temperature of the water.

— the carbon type used.

For economie reasons, a high overall rate of adsorption is desirable, since it uses the carbon most efficiently (ignoring any loss of efficiency due to axial dispersion effects). In many respects, there is a conflict of economie interests when designing for the optimum rate of adsorption. Two examples will be discussed here.

The first relates to carbon partiele size. While the rate of adsorption increases as partiele size decreases, the head loss over the carbon layer increases. If closed pressure filters are used, pumping costs will increase as partiele size decreases, as also will the backwash frequency. In open gravity filters the backwash frequency will increase, resulting in an increased requirement for backwash water.

Backwashing always is done with treated water i.e. water which has been subjected to all treatment steps, and which has an economie value.

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The second example of conflicting economie interests relates to the influence of the degree of activation (DOA) of the carbon on efficiency. In this case the gain in carbon efficiency from an increased rate of adsorption is counteracted by decreased adsorption on a volume basis as explained below.

A series of activated carbons produced from the same raw material, using the same basic production techniques, but with variation in one of the process parameters (e.g. residence time in the activation kiln), will show differences in pore structure. These differences are progressive and gradual in character.

Such carbons are considered to differ in degree of activation.

If two carbons are produced from different raw materials using the same production technique, or from the same raw material using different production techniques, the pore structure of the two carbons will generally be fundamentally different. Such carbons are said to differ in pore structure.

If the process residence time is increased, so too do the DOA and the degree of carbon burn-off. Increased burn-off implies a decrease in the density of the carbon. The following discussion will be limited to systems containing only one component in order to minimise complication. Consider a filter containing Vf m3 of an activated carbon with a bed density of QB kg.m"3. It is assumed that the carbon has to reduce the concentration of the compound by 90%. If the concentration of the compound in the filter effluent is 10% of that of the filter influent, then the carbon in the filter has taken up on average QD (kg.kg') of the compound. The total amount removed from the water will therefore be equal to

VfoBQD(kg)

The value of QD will be lower than that of QE, the equilibrium loading of the carbon, because of the finite rate of the mass transfer processes. For a substance with molecular dimensions appreciably smaller than those of the micro- and mesopores, the values of QD and QE will not be very different if the design parameters have been chosen properly. As molecular size increases, so too does the difference between QE and QD, the values of all other variables remaining constant. An increase in the DOA reduces this difference, because it increases the overall rate of adsorption. This applies to both large and small molecules. So long as the rate of internal transport is one of the mechanisms contributing to the overall rate of adsorption, an increase in DOA implies an increase in the steepness of the breakthrough curve (see fig. 1). An increasing DOA always results in a decreasing value of QB, the bed density. At a certain DOA, the relative rate of increase of QD will be equal to the relati ve decrease of

QB-The product Vf gBQD will attain a maximum value at this DOA of the carbon used. Beyond this maximum value the relative rate of decrease of pB will be greater than the relative rate of increase of QD as DOA increases.

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time

Figure l.l.A Breakthrough curves for single component systems as a function of the degree of

activation (DOA) of the carbon. Case A: 'Small' adsorbate molecules.

time ■

Figure l.l.B Breakthrough curves for single component systems as a function of the degree of

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increase in the steepness of breakthrough. This stituation is depicted in fig. IA, where breakthrough curves are shown for a relatively small sized model substance, for three carbons differing only in degree of activation, all other parameters remaining constant. Fig. 1B shows the breakthrough curves for the same three carbons against a solution of compound of the larger molecular size. In this case the maximum value of Vf QBQD has not yet been attained, i.e. the relative f ate of increase of QD is still larger than the relative rate of decrease of QB. The consequence is that the gradiënt of the breakthrough curve and the breakthrough time both increase with increasing DOA. These phenomena have been demonstrated by comparing breakthrough curves of aqueous solutions of p-nitrophenol with those of aqueous solutions of carminic acid (ref. 3).

The picture presented above is highly simplified, even for systems containing only one component. The value chosen for C0, the initial concentration of the compound, also plays a role because QE will also change if the DOA changes. Physical reality is more complex, as there will generally be many compounds present in the water to be treated, and which will compete for the available adsorption sites. Despite this, some of the picture will be retained since is is based on the accessibility of the micro- and mesopores, which make up almost all adsorptive capacity of the carbon. If the DOA is changed, the macroporous system of the carbon is generally little changed. An increase in the DOA has a marked influence on micropore size (ref. 4).

The above example demonstrates the very complex role played by the overall rate of adsorption in designing the activated carbon step of a water treatment plant. In the next chapter it will be argued that this complex role is only party understood.

1.3 Objectives of the present study

The main objective of this study is to investigate the influence of carbon type on the rate of adsorption. The following variables have been studied:

— size and shape of the carbon particles. — pore structure.

— degree of activation.

This has been done by carrying out batch studies using nitrobenzene as a model substance. The rate of adsorption of this substance on 30 different carbons has been determined under exactly the same conditions, viz.,:

— amount of carbon, W.

— initial concentration of the nitrobenzene, C0. — the hydrodynamic conditions.

— temperature.

Some experiments have been done using other values for W and/or C0.

Experiments have been carried out with a larger model substance (azosulfamide) on 10 of the carbons.

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The results of these batch studies are interpreted applying 10 different mass transfer models, which can be divided in two different groups, viz.,:

1. Homogeneous partiele models (HPM) characterised by the assumptions that the particles are isotropic and homoporous regarding pore structure. 2. Bi-porous partiele models (BPM) characterised by the assumption that the particles basically contain two pore sizes viz. homoporous micropores and homoporous macropores.

Both groups are based on the assumption, among others, that the overall rate of adsorption is only dependent on the rate of several possible diffusion steps in various combinations.

From a survey of literature, it appears that the results reported by the various authors using activated carbon as adsorbent conflict when applying the HPM models mentioned above (see chapter 2). These conflicting results refer to model prediction regarding the role of:

— partiele size of the carbon. — pore structure of the carbon. — the values of W and C0.

It does not appear possible to explain these phenomena with the homogeneous partiele models.

An objective of the present study is to offer an explanation for the conflicting results mentioned above.

By a systematic comparison of the two groups of models above, it will be argued that a consistent picture can be obtained by postulating a multi-porous model. A lack of fundamental knowledge on the pore geometry of activated carbons and the absence of a correct theory of liquids prevents a quantitative model formulation.

The results obtained from the batch studies indicate a large variation in the overall rate of adsorption among the individual particles from the same batch of a commercial carbon. These variations can be attributed to variations of partiele size and degree of activation within commercial activated carbons.

In most cases, the carbon bed must be backwashed with varying frequencies, when granular activated carbon is used in potable water purification or waste water treatment. A difference in DOA means a difference in carbon burn-off i.e. the density of the carbon partiele.

During backwashing, particles are classified by size and density. This classification may influence breakthrough behaviour. Some column studies have been carried out to investigate the effect of this classification phenomenon, using a nitrobenzene solution and a solution of humic acid.

Following a literature survey in chapter 2, a chapter follows in which the mathematical equeations describing the several models are derived.

In chapter 4 the equipment used and the experimental techniques applied are discussed. The results are presented in the fifth chapter, without extensive comment.

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These results are discussed in chapter 6 (the homogeneous partiele models) and chapter 7 (the bi-porous models).

References

1. Baylis, J.R., Elimination of taste and odor in water, New York (1935).

2. US Environmental Protection Agency, Process Design Manual for Carbon Adsorption, Cincinnati (Ohio), 1973.

3. Seiler, H., "Zur Adsorptionskinetik organischer Moleküle in mit wassrigen Lösungen durchströmten Aktivkoksschüttungen unter den Bedingungen der Wasseraufbereitung", Thesis, Techn. Hochschule, Aachen (1971).

4. Wigmans, T., Comparison of activated carbons produced by partial steam gasification of various carbonaceous material in "Activated carbon . . . A fascinating material", Capelle, A. and F. de Vooys (Eds.), Amersfoort, 1983.

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Chapter 2 Literature

This survey will deal mainly with studies of mass transfer on activated carbon from aqueous solutions. However, work of a more general nature and studies with other adsorbents and solvents (both liquids and gases), have been included where they are relevant to the present study.

This chapter is divided in three sections and particular attention is given to systems with only one well-defined adsorbable component. The first section is devoted to studies of batch systems, and the second one to column processes (mainly fixed beds). The last section deals with simulations of practical conditions.

These studies refer to:

— systems with more than one well-defined adsorbable component.

— systems with one well-defined adsorbable component against a background of e.g. humic acid.

— column experiments with deliberate fluctuations in the initial concentration of the adsorbable component or in the liquid velocity.

2.1 Batch studies on single component adsorption

All studies considered in this section are summarised in table I. This table may be considered as an extension of earlier reviews (ref. 41 and 47). However it contains more information on the variables studied.

Unless explicitly mentioned, the studies refer to the finite bath mode, -in which a limited amount of adsorbent is contacted with a limited amount of a liquid solution of the adsorbate. In the infinite bath mode the concentration of the adsorbate in the bulk solution is kept constant.

Except at very low concentrations, the equilibrium relationship for the adsorption on activated carbon from aqueous solutions is non-linear. For this reason the mathematical equations of models which account for diffusional mass transfer resistances, cannot be solved analytically, and numerical methods have to be used. The rise of modern computational techniques, and especially the widespread availability of these techniques at the end of the "sixties", mark a kind of breaktrough in the study of this subject.

At the same time the role of powdered activated carbon in water treatment was taken over by granular carbon, creating an urgent need for design concepts and stimulating research in this field of engineering.

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Prior to the "seventies", numerical techniques were seldom applied, and even when used, they were mainly explorative or demonstrative in character.

In most single component adsorption studies the adsorption isotherm was assumed to be linear. With increasing application of numerical techniques, the mass transfer models used slowly became more complicated. Models taking into account both external and internal mass transfer resistances were developed. In a later phase, two different contributors to internal resistance were distinguished viz.:

— pore diffusion, i.e. diffusion of non-adsorbed species in the fluid inside the pore, characterised by a pore diffusion coëfficiënt, Dp,

— surface diffusion, i.e. diffusion of adsorbed species along the pore walls, characterised by a surface diffusion coëfficiënt, Ds.

In earlier studies mass transfer was considerded to be governed by pore diffusion. The value of Dp would than be expected to have a maximum value of DF (the coëfficiënt for

free diffusion in Iiquids). Generally Dp is found to be larger (ref. 20,22,28,29,32 and

51), although there are exceptions (ref. 4, 10, 20, 22, 28, 32 and 44).

Electrochemical effects seem to play a role, since for p-nitrophenol, a neutral molecule, Dp >DF, whereas Dp< DF for the anion (ref. 22).

These observations resulted in an increasing interest in models based on surface diffusion.

In most studies the diffusion coefficients are supposed to be independent of concentration. The validity of this assumption can be examined by determining Dp or

Ds at different values of Co; the initial concentration of the adsorbable component or

of W, the amount of adsorbent in the system. Results of such studies are contradictory.

For the majority of systems studied, the value of Dp indeed appears to be independent

of the values of C0 and W, when a pore diffusion model is applied, (ref. 28, 32, 51),

although a few exceptions exist (ref. 44, 61).

The values of Ds, however generally depend on C0 (ref. 40,46, 49, 51, 54, 61), but

again with a few exceptions (ref. 60, 65). The dependency of Ds on the C0 value

stimulated the development of models in which Ds is supposed to be a function of

adsorbent loading. This dependency of Ds on concentration has long been known for

adsorption from the gas phase. Therefore it is not surprising to see that the relation between Ds and the isosteric heat of adsorption, proposed for adsorption from a gas

(ref. 73), has been applied to models describing adsorption from dilute aqueous solutions (ref. 40, 43, 47, 53, 54).

Others (ref. 33) have criticised the application of gas models to adsorption from liquid solution and proposed a model in which the interaction between solvent and adsorbent is also taken into account.

More evidence for a concentration dependent surface diffusion coëfficiënt is given by the shape of the adsorption wave penetrating into the partiele.

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Table 1

Author Ref. Model lsoth. Phase Mat hem. Adsorbent Remarks, variables. Internal Film soln.

1948 1950 1952 1954 196(1 1961 1961 1962 1963 1965 1966 1967 1967 1968 1968 1970 1971 1971 1971 1971 1972 1973 1973 1973 1973 1974 1974 1974 1974 1974 1974 1974 1974 1975 1975 1975 1975 1976 1976 1976 1976 1976 1978 1978 1978 1978 Wilson Eagle et al. Edeskuty el al. Dryden el al. Tien Tien Mingle et al. Carberry Weber et al. Weber et al. Schwuger Brecher et al. Dedrick et al. Snoeyink Knoblauch Miller el al. Wille Rückenstein et a Misic et al. Heil Digiano et al. Digiano et al. Furusawa et al. Furusawa et al. Kocirik et al. Kocirik et al. Komiyama et al. Suzuki et al. Furusawa et al. Erashko et ül. Voloschchuk et al. Spahn Komiyama et al. Spahn et al. Dubinin et al. Hashimoto et al. Suzuki et al. Neretnieks Neretnieks Neretnieks Buchholz Ma et al. Neretnieks Fritz Avramenko et a Sudo et al. ( 1) ( 2) ( 3 ( 4 ( 5) ( 0) ( 7 ( x ( 9 (10 ( H (12 (13 (14 ( ' 5 (16 ( ' 7 .(18 (19 (20 (21 (22 (23 (24 (25 (26 (27 (28 (29 (30 (31 (32 (33 (34 (35 (36 (37 (38 (39 (40 (41 (42 (43 (44 .(45 (46 HPDM HSDM HPDM HSDM HSDM HSDM BPM BPM — HPDM HDPM/HSDM HSDM HPDM HPDM/HSDM HPSDM HSDM HPDM BPM -HPDM/HSDM HPDM HPDM HPDM HPDM HPDM BPM HSMD HPDM/HSDM HPDM BPM BPM HPDM HPSDM HPDM BPM HPDM/HSDM HSDM HPDM/HSDM HPDM/HSDM HSDM HPDM/ HSDM/BPM BPM HPDM/HSDM HPDM/HSDM HSDM HSDM _ -+ -" " " -— -~ ~ + -+ + + + + + -— + -+ -+ ~~ -+ + + -+ + -lin. lin. lin. lin. non-lin. fr. non-lin. la. fr. BET lin, irr. fr. la. BET fr. lin. lin. fr. irr. la. lin. la. la. lin. fr. irr. lin. lin. lin. irr. fr. irr. lin. fr.,la. fr. fr.,la. fr.,irr. te. fr. lin. te. fr. te. fr. L L L L L L G G L L L G L L L L L G L L L L L L -G L 1. L G G L L L G L L -L L G L L L L anal anal anal. anal anal. num. appr. appr, emp. num. appr. num. appr. num. num. num. emp. num. appr. num. anal. num. mm num. appr. mm anal. num. num. appr. appr. num. num. num. mm num. num. num. num. num. num. num. num. num. appr. num. _ several activ. carbon acliv. carbon permutite ~ — -activ carbon activ. carbon activ. carbon silica activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon macroret. resin activ. carbon acliv. carbon acliv. carbon acliv. carbon acliv. carbon activ. carbon -activ. carbon amberlite activ. carbon two adsorbenis activ. carbon activ. carbon activ. carbon amberlite activ. carbon activ. carbon activ. carbon activ. carbon -activ. carbon activ. carbon zeolite activ. carbon activ. carbon activ. carbon activ. carbon model development comparison adsorbents C,„ R and T R

polynomial function for equil. isotherm used model development (only for N - 0 . 5 )

model developm., catalyst effectiveness factor catalyst effectiveness factor phenomenological description adsorbate (several alkylbenzenes) carbon type, adsorbate R

inifite balh C„, W, T, pH degree of activation, approxim.

comparison num. soln. with appr.

R

model development slurry reactor (GL) model comparison, adsorbale semi-anal. soln.

impellêr speed, pH, influence buffer

slurry reactor (GL) slurry reactor (GL) appr. soln. for plane sheet uses anal. soln. lin. isoth.: solvent

carbon type

activ. carbon vs. amberlite model development model confirmation carbon type, C„ D, - D,(q)

exp. determination profile inside partiele exp. determination profile inside partiele carbon type, C„ interpretation Ds model comparison model comparison C„,DS-Ds(q) model comparison, R. model development model comparison, D. = D,(q)

model comparison, carbon type, C,„ W

T

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Author Ref. Model Isoth. Phase Mathem. Adsorbent Remarks, variables. Inlernal Film soln.

1978 1978 1979 1981 1981 1981 1982 1982 1982 1982 1983 1983 1983 1983 1983 1983 1983 1983 1984 1985 1985 Bruin et al. Chihara et al. (47) (48) Mamchenko et al.(49) Thacker el al. Leyva Ramos Peel et al. Suzuki et al. Muraki et al. Misic et al. Zolotarev et al. Hand et al. Zolotarev et al. Zolotarev et al. Mathews Moon et al. Beverloo et al. Lee et al. Cornel McKay et al. Leyva Ramos et al. Smith et al. (50) (51) (52) (53) (54) (55) (56) (57) (58) (59) (60) (61) (62) (63) (64) (65) (66) (67) HPDM/HSDM BPM HSDM HSDM H P D M / H S D M BPM HSDM HSDM -BPM HSDM BPM BPM HSDM H P D M / H S D M HSDM MPM HPDM HSDM HPDM/HSDM HPDM + -+ + + ~ + + + + -+ + + -+ + + — jo. lin. fr. fr. rp. fr. rp. fr. fr. lin. fr. (non-)lin. la. rp. fr. fr., irr. lin. fr. rp. fr. sev. L G L L L L L L L L L -L L L -L L L — num. mm num. num. num. num. num. num. num. num. num. num. num. num. num. num. num. num. appr. num. num. activ. carbon mol.sieve activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon -macr.ret.resins several model comparison, D, - D,(q) Dm - D„(q) C,„ empir. relation D, - D,(C„) carbon type role solvent, model comparison use rate equations porous plug system, DN = Ds(q) C„, W, Ds = Ds(q) study film diffusion model development study minimal Biot model development also calcul. internal profile R, C,„ best choise of R

C„

model comparison model development comparison with activ. carbon (ref. 44) comparison adsorbent type on dyestuffs

param, study, also D, = D,(q)

isotherm comparison

Caption

Model, internal HPDM, HSDM, based on homogeneous partiele model with pore or surface diffusion respectively. HPSDM, pore and surface diffusion acting in parallel.

HPDM/HSDM, both models investigated. BPM, bi-porous model.

MPM, multi-porous model

Model, film + indicates film diffusion taken into account. — indicates film diffusion not taken into account. Isotherm abbreviations used,

lin. linear isotherm irr. irreversible isotherm la. Langmuir isotherm fr. Freundlich isotherm te. Temkin isotherm

rp. isotherm proposed by Radke and Prausnitz (ref. 80). jo. isotherm proposed by Jossens et al (ref. 81) Phase L, liquid phase; G, gaseous phase

Mathem. solution mathematical solution abbreviations used anal. analytical appr. approximation

mm method of moments (see section 2) num. numerical

Remarks, variables GL gas-liquid system

D, = Ds(q) model with a coverage-dependent surface diffusion coëfficiënt C„ initial concentration of adsorbable component

W amount of adsorbent in the system R radius of adsorbent partiele

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Independently of each other, two groups of investigators have measured the shape of this wave. One group (ref. 35) measured the rate of adsorption of bromo-benzene from an inert carrier gas, and the other group (ref. 129) that of phenyl-acetic acid from aqueous solution. Both groups used activated carbon as adsorbent. On penetration into the partiele the adsorption wave retained a steep character and this profile was calculated for several models. It has been demonstrated (ref. 47) that the adsorption wave remains steep for:

— pore diffusion acting alone

— surface diffusion with a coverage-dependent diffusion coëfficiënt. For surface diffusion with a constant diffusion coëfficiënt, the adsorption wave flattens out on penetration of the adsorption wave.

Despite this compelling evidence, several authors (ref. 44, 50, 51, 57, 60, 62, 65) implicitly deny the dependency of the surface diffusion coëfficiënt on coverage. It would be of interest to compare studies in which the carbon type is varied. This subject is complicated because the carbons investigated may differ in more than one respect.

In one of the studies, using ten different carbons and with phenylacetic acid as the adsorbate, roughly the same value was found for Dp (ref. 32), while in other studies (ref. 11, 15, 50) the values found for Dp or Ds varied strongly with carbon type. The partiele size of the carbon provides a parameter for model examination. The values of Dp or Ds found for a series of carbons differing only in partiele size should be independent of that size. Several authors (ref. 3, 4, 15, 23, 29, 51) indeed report this independence, while others have found a dependency of the diffusion coefficients on partiele size (ref. 11,12, 41). In some cases this dependence may be attributed to the fact that the wrong model has been used e.g. neglecting film diffusion (ref. 11), but in other cases (ref. 41) the explanation is less obvious and will be discussed in depth in chapter 6. The models described so far can be called homogeneous partiele models, as it is assumed that the pore size distribution is very narrow. It is therefore assumed that all pores in the partiele have the same radius, and that there is no preferential pore direction. This concept will be discussed in more detail in section 3. of the third chapter. Several investigators (ref. 18, 35,41) haver proposed a model which differs completely from the preceding ones. In this model, developed originally for the description of heterogenous catalysis (ref. 7, 8, 68, 69), two distinct regions are distinguished viz. microporous zones inter-connected by a macroporous network, in which the transport mechanisms are different. This model (denoted bij BPM, "bi-porous model" in the table) has found widespread application for the description of mass transport inside zeolites (ref. 76), and has been applied also to activated carbon (ref. 35, 41).

A critical survey and comparison of the several variations of this model was made ten years ago (ref. 70). Besides the allowance for different modes of transport in pores of different size, the model describes the role of partiele size in a different way, which may explain the contradictory results on the influence of partiele size, mentioned above (ref. 41).

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Additonal information on the transport mechanisms inside the adsorbent partiele can be obtained by choosing different solvents.

This has been done for a macroporous resin adsorbent, using both water and mixtures of water and methanol (ref. 27).

In a study with activated carbon the solvents were water and cyclohexane (ref. 51). A variant on this theme is a comparison of two different adsorbents (macroporous resin versus activated carbon) using the same adsorbate (ref. 64, 44).

In almost all studies the internal diffusion is described by modifications of Fick's law of diffusion. In one study (ref. 32) the solution using Fick's law has been compared with the solution obtained by using a rate equation for the description of internal transport (linear driving force type). Whereas the Dp value appeared to be constant along the kinetic curve, the value of the internal mass transfer coëfficiënt varied strongly along the curve.

As already has been mentioned, most of the studies refer to batch experiments. A technique that is extensively applied in studying transport from the gaseous phase is where the flow of the adsorbate is measured over a porous plug of the adsorbent (ref. 71, 72). This technique has been applied sporadically in measuring mass transfer in liquid systems (ref. 53). Some of the results obtained from studies in the gas phase can be used however, for interpretation of the results obtained for aqueous systems, as will be argued in chapter 6. of the present study.

Table I summarises the literature on single component batch studies.

The table is the best one that the present author could compile, completeness is not guaranteed. The concept 'homogeneous partiele model' will be discussed in section 3. of chapter 3. It refers to particles in which the pore size distribution is very narrow, is constant throughout the particles and where the pores have no preferential direction.

2.2 Column studies of single component adsorption

The literature survey in this section is also presented in a tabular form. For several reasons the number of column studies is much larger than that of batch systems. This review is therefore limited to those studies necessary to obtain an outline of the development of the subject. The studies covered mainly concern adsorption from a liquid in a bed of a conventional solid adsorbent. In some cases, new concepts in this field had their origins elsewhere. That is why some studies have been included on adsorption in ion exchange, gas-solid chromatography and heterogenous catalysis. The presentation of an exhaustive survey is not therefore possible in the present study, an excellent survey on mass transfer to and in solid adsorbents is given by Vermeulen et al. (ref. 75). The survey in this section tries to present a historie outline for the objective of this study as defined in the preceding chapter.

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The development is more or less the same as the one in the preceding section and can be summarised as follows. After an inital phase, characterised by the use of approximatipns (linear equilibrium, description of internal transport by rate equations instead of Fick's law), the development of numerical techniques stimulated the construction of more complicated models. In this way the three basic models from the preceding section:

— the homogeneous pore diffusion model (HPDM), — the homogeneous surface diffusion model (HSDM), and — the bi-porous model (BPM).

were also used for the description of column behaviour.

Several authors have used data on internal transport, obtained from batch studies, for the prediction of column behaviour (ref. 125, 132, 133, 139). There are many examples where the models used in the batch experiments are suspect. Even so, good results are often claimed. For example in ref. 32 the Dp-values are unrealistically high. Another example is given by studies applying the HSDM model with a coverage-independent surface diffusion coëfficiënt (e.g. ref. 133) despite the strong evidence (see the preceding section) that Ds depends on the degree of coverage.

In many studies the breakthrough curve is fitted directly to a number of calculated curves without the preceding step of a batch study. When applying these procedures the contribution of external mass transfer is estimated from existing correlations (a survey is presented in ref. 77). As an alternative to batch studies the so-called mini column has been proposed, a technique in which a small column (with a short service time) is used to obtain data on external and internal transport (ref. 136, 146). A special case of breakthrough behaviour is the constant pattern which develops for "favourable isotherms" (i.e. isotherms for which d2q/dc2 < 0) after the adsorption front has travelled a certain distance through the adsorbent bed. In this case column length disappears as an independent variable, and systematic numerical analysis is much simpler than for the general case. Numerical solutions are given in several studies (ref. 100, 119).

For the HSDM with the Freundlich isotherm the conditions for the development of a constant pattern have been formulated as a function of three dimensionless numbers viz. the Biot number, the Stanton number and the reciprocal value of the isotherm slope. The same authors have developed a simplified method to predict breakthrough behaviour from data obtained from batch studies (and existing correlations for film diffusion), by using a relative simple empirical relation developed from their numerical results (ref. 145, 159).

A fairly powerful method for obtaining kinetic data for adsorption from the gas phase is the GS-chromatography theory, developed by Kubin and Kucera (ref. 78, 79). In this theory, which only strictly applies to systems exhibiting linear adsorption

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isotherms, the system of mathematical equations describing the shape of the pulse travelling through the column is subjected to a Laplace transformation, and the resulting set of equations is solved analytically. Although it is impossible to execute the reverse transformation, it is possible to derive a relation between the first, second and third moment of the peak on one hand, and the mass transfer coefficients (axial dispersion, film diffusion and internal diffusion coëfficiënt) on the other, from the Laplace solution.

This technique has been applied several times to describe systems with activated carbon as adsorbent (ref. 105, 155-158). A group of authors have modified the technique to describe adsorption from liquid solutions (ref. 23). A non-chromatographic analogue has been proposed for non-linear isotherms in which the mass transfer parameters are also obtained from the moments (ref. 147, 148). Much theoretical work has been done on adsorption kinetics (especially from the gas phase) by several groups of authors from the Soviet Union.

Much attention has been paid to bi-porous models, as the HPDM was found to give a partiele size effect that differed from that expected. The lack of modern computer facilities probably forced these investigators to use approximations instead of numerical techniques e.g. linear of irreversible isotherms. These studies are not all included in table II. Some examples are ref. 149-154. The literature summarised in table II all refers to single component adsorption studies.

Table 2 1948 1950 1951 1952 1952 1952 1952 1953 1954 1959 1960 1965 1965 1965 1965 1966 1966 Author Amundson Amundson Thomas Rosen Michaelis Kasten et al. Lapidus et al. Vermeulen Rosen Tien et al. Tien et al. Masamune et al. Masamune et al Tien et al. Cooper Chao et al. Carter Ref. ( 82) ( 83) ( 8 4) ( 85) ( 86) ( 8 7) ( 88) ( 89) ( 90) ( 91) ( 92) ( 93) ( 94) ( 9 5) ( 96) ( 97) ( 98) Bed Fix Fix Fix Fix Fix Fix RD Fix Fix Fix Fix Fix Fix Fix Fix Fix Fix Model Internal HPDM HPDM HSDM HSDM " HPDM HSDM HSDM HSDM HSDM HSDM HPSDM HPSDM HSDM HSDM HPDM HPDM/HSDM D,. -" — -— ~ -— +2> -k„ -" — + + + + + + + + + + — + + Isoth. lin. lin. lin. lin. lin. lin. la., irr. lin. fr. lin. lin. lin. fr. irr. lin. non-lin Phase -G L L G L L L G G L L G G Mathem soln. anal. anal. anal. anal.11 emp. anal. anal. appr., anal. anal.') num. anal. num.4) num.4' num. num. mm num. Adsorbent -~ -ion exchange -several ion exchange ion exchange -sifica ion exchange ion exchange -alumina Remarks, variables.

rale equations, model development rate equations, model comparison model development model development length of mass transfer zone concept model development rate equations, model comparison rate equations, model comparison model development also constant-pattern also actual ads. step model confirmation extension of ref. 92 comparison with driv. force equations model development model development

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Author Ref. Bed Model Inlemal

Isoth. Phase Mathem. Adsorbent Remarks, variables.

DL k,.- soln. 1966 1966 1967 1968 1968 1968 1969 1969 1969 1969 1969 1969 1970 1970 1970 1971 1971 1971 1971 1971 1973 1973 1973 1973 1974 1974 1974 1974 1975 1975 1975 1975 1975 1976 1976 1978 1978 1978 1979 1980 1980 1980 1980 C o l w e l l el a l . H a l l et al. M e y e r et al. K e i n a t h et al. R i m p e l et al. Z i k é n o v ó et a l . Z i k a n o v a ei a l . D u b i n i n et a l . C o l w e l l et al. L e e ét al. L e e et al. A n t o n s o n et a l Marcussen C o o p e r er al. K a c h a n a k et al C o l w e l l et a l . L e e et al. Seiler K a c h a n a k et al K a c h a n a k et a l R e e k et al. K a c h a n a k et al K a c h a n a k et al I k e d a et al. K a w a z o e et al. Neretnieks B r a u c h W e b e r et al. W e b e r et al. W e s t e r m a r k B r a u c h et al. Jonas et al. G a n h o et al. N e r e t n i e k s N e r e t n i e k s C r i t t e n d e n et a ( W ) ( 1 0 0 ) ( 1 0 1 ) ( 1 0 2 ) ( 1 0 3 ) ( 1 0 4 ) ( 1 0 5 ) ( 1 0 6 ) ( 1 0 7 ) ( 1 0 8 ) ( 1 0 9 ) ( 1 1 0 ) ( 1 1 1 ) ( 1 1 2 ) ( 1 1 3 ) ( 1 1 4 ) ( 1 1 5 ) ( 1 1 6 ) ( 1 1 7 ) ( 1 1 8 ) ( 1 1 9 ) ( 1 2 0 ) ( 1 2 1 ) ( 1 2 2 ) (-123) ( 1 2 4 ) ( 1 2 5 ) ( 1 2 6 ) ( 1 2 7 ) ( 1 2 8 ) ( 1 2 9 ) ( 1 3 0 ) ( 1 3 1 ) ( M ) ( 3 9 ) . ( 1 3 2 ) C r i t t c n d e n e t a l . ( l 3 3 ) R i c h t e r et al. W i l s o n W e b e r et al. F a m u l a r o et al Basmadhyan Peel et a l . ( 1 3 4 ) ( 1 3 5 ) ( 1 3 6 ) ( 1 3 7 ) ( 1 3 8 ) ( 1 3 9 ) Fix Fix Fix F I b Fix Fix Fix Fix Fix Fix Fix F i x Fix Fix Fix Fix Fix Fix Fix Fix Fix Fix Fix Fix Fix C C Fix H S D M H P D M / H S D M H P D M 2 n d o r d e r k i n . H P D M H P D M H P D M H P D M H S D M H P D M H P D M H S D M H P D M H P D M H P D M H S D M H P D M H P D M H P D M H P D M H P D M / H S D M H P D M H P D M H S D M B P M H S D M H P D M + -+ + + + — ~ — -+ -— -+ -extensive survey ot l i t e r a l u r e Fix Fix Fix Fix F I B C C C C Fix Fix Fix Fix Fix Fix Fix Fix H S D M H P D M H P D M ~ — H S D M / H P D M H S D M / H P D M H P D M / H S D M H S D M Several L P M H S D M B P M — B P M — -~ — -— -— + (+) — + — + -+ + + + + + — + + — + -+ ~ -+ + + + + + -+ + + + + + + + + + + + + + + + la. rep. la. la. d u b . d u b . , l i n . l i n . n o n - l i n . n o n - l i n . n o n - l i n . la. fr..la. irr. n o n - l i n . n o n - l i n . irr. la. Ia..fr. la. Ia.,fr. Ia..fr. la. la..irr. l i n . irr. irr. la. n o n - l i n . irr. d u b . la. fr..la. fr,,irr. n o n - l i n n o n - l i n . sev. la. fr. r p . la. fr. L -G L G G G G L G G G G L -L G L -G -G G G C -L L L L G L -" L L — L L L G L n u m . n u m . n u m . n u m . num.-'1 appr. m m appr. n u m . n u m . n u m . n u m . n u m . anal. appr. a n a l / n u m . empir, n u m . appr. appr. n u m . appr. appr. n u m . appr. n u m . n u m . n u m . n u m . n u m . appr. anal. n u m . n u m . n u m . n u m . n u m . n u m . n u m . appr. n u m . i o n exchange -activ. carbon activ. carbon activ. a l u m i n a activ. carbon activ. carbon activ. carbon ~ " activ. carbon zeolite activ. a l u m i n a -ion exchange m o l . sieve activ. carbon -— -activ. carbon m o l . sieve activ. carbon -activ. c a r b o n activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon -" activ. carbon activ. carbon activ. carbon activ. carbon activ. carbon ~~ activ. carbon m o d e l verification constant-pattern also n o n - i s o t h e r m a l R, v, C „ as variables R, v, C „ , pore size R E , length of M T Z R E R E , c o n s t a n t - p a t t e r n , M T Z comparison w i t h linear isoth. case

four isotherm types investigated isothermal and n o n -isothermal partiele shape, c o m p a r . with R o s e n ( 1 9 5 2 ) v, C „ . R R E compar. linear a n d non-linear soln. soln. f o r l i n . isoth. used R E

R E w i t h variable mass transf. coeff. constant-pattern case R E . M T Z exp. verif. of previous ones R E also for i n t e r n a l step R model d e v e l o p m e n t C „ , v. adsorbate comparison w i t h T h o m a s model c o l u m n o p t i m i z a t i o n C „ . v. adsorbate reactiun kinetic treatment reaction kinetic treatment. R. v D , * Ds( q ) a n d I X - DM model d e v e l o p m e n t v, exp. ver. o f ref. ( 1 3 2 ) detailed survey l u m p e d p a r a m , m o d e l development m i c r o column techn. R E for internal a n d external use R E and graphical soln. m e t h o d

m i c r o p o r e diff. description by R E

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Author Ref. Bed Model Isoth. Phase Mathem. Adsorbent Remarks, variables. Interna! DL k,.- soln. 1982 1983 1983 1984 1984 1984 1984 Weber et al. Hasanain et al. Weber et al. Weber Mathews Crittenden et a Aguwa et al. (140) (141) (142) (143) (144) .(145) (146) Fix Fix Fix Fix Fix Fix Fix HSDM HSDM BPM BPM HSDM HSDM HSDM Capt -~ ~ ~ on + -+ + + + fr. rp. fr. fr. rp. fr. fr. L G L L L L L

and additional notes num. num. num. num. num. num. anal. activ. carbon -activ. carbon activ. carbon activ. carbon activ. carbon model confirmation model developmenl model development model development and confirmation influence polydispersity adsorbent

also desorption and re-adsorption

macr.ret. resins mini-column study

The same notation has been used here as in table 1, however some new concepts are required. D, +axial dispersion taken into account

RE rate equations (e.g. iinear driving forcc equation used) MTZ mass transfer zone

Additional notcs:

1. analytical solution with numerical results. 2. axial dispersion was considered in an infinite bed. 3. author uses numerical result of Rosen (ref. 85. 90).

4. analytical solution in the form of an integral which must be solved numerically.

2.3 Multi-component systems - the approach to practical reality

The preceding sections dealt with studies on dilute solutions of one well-defined adsorbable component. As a first step toward more practical conditions, studies on systems with two well-defined adsorbates will be reviewed. In multi-component systems two complications arise, both due to the mutual interaction of the components. First, the amount of each component adsorbed is influenced by the adsorptive behaviour and the amount of all other components present. A mathematical description of the behaviour of each component present in the mixture requires a description of equilibrium behaviour which accounts for their interaction. Fritz and Schlunder (ref. 160) proposed a general empirical equation for multi-component equilibrium adsorption, after they had tested and rejected a number of other descriptions (ref. 161-163). Meyers and Prausnitz (Ref. 164) developed a method to calculate mixed gas equilibrium isotherms from the individual isotherms. Radke and Prausnitz (ref. 165) adapted this method for multi-component solutions. The method is based on assumptions of ideal thermodynamic behaviour of the adsorbed solution (Ideal Adsorbed Solution - IAS), and that the internal surface area of the adsorbent is accessible to all components. Crittenden et al. (ref. 166) extended the IAS-theory to the case where the equilibrium adsorption of the pure components is described by the Freundlich isotherm. Digiano et al. (ref. 167) proposed a simplified version of the IAS-theory.

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The second complication concerns the diffusion processes in multicomponent systems. Diffusion takes place under the influence of a gradiënt of the thermodynamic potential (see section 3.9). Since the chemical potential of an individual component will change if the amounts of the other components change, all components are expected to excercise some influence on each others diffusional behaviour. A generalisation of Fick's law for a system containing n components reads (ref. 168):

- n-1

-n j= 2 DJJVCJ

1=1 i = 1, 2, 3 . . . n

in which n( presents the molar flux of component i.

Each off-diagonal term (or cross-term), D^: i # j , reflects the contribution to the flux of one component, on the concentration gradients of the other components. For bulk diffusion in dilute systems, the diagnoal terms, D^ : i = j , are generally much larger than the cross-terms (ref. 168)

In the early phases of research into binary systems, much attention was paid to constant-pattern behaviour. Cooney and Lightfoot (ref. 169) proved the existence of asymptotic solutions for fixed bed operations.

In a later study, Cooney and Strusi (ref. 170) developed analytical solutions for the breakthrough curves of both components, but these solutions can only be applied to mixtures of components having almost equal mass transfer parameters. Miura et al. (ref. 171, 172) extended this method and developed numerical solutions for the constant-pattern case, but also more general solutions based on the HPD- and HSD-models using the Langmuir and Freundlich isotherms.

For an aqueous solution containing dodecyl-benzenesulphonate and p-nitrophenol, they could predict the breakthrough curve for the first component fairly well, but not that of the other component. Crittenden and Weber (ref. 173) applied the HSD-model (which film diffusion) to two binary systems. If the two components differed strongly in diffusional behaviour, the Ds-value of the "slower" component appeared to be much higher than the value found in single solute experiments. Liapis and Rippin (ref. 174), using the isotherm proposed by Fritz and Schlünder (ref. 160), conducted batch studies of a binary system applying the HPD- and HSD-models (including film diffusion). In later studies (ref. 175 and 204) they used the parameters obtained from the batch data to predict the breakthrough behaviour in columns, applying the same models and taking account of both film diffusion and axial dispersion. The correspondence between experimental and predicted curves was reasonably good.

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Fritz (ref. 44) conducted batch studies on several binary systems, applying the HPSD-and HSD-models (film diffusion included). He used both the multi-component isotherms discussed earlier (ref. 160) and the IAS-theory. The values of Dp and Ds used for the binary predictions had been determined in advance for single solute systems.

He observed differences between experiment and prediction for both models where the two components differed in adsorptive or diffusional behaviour, the difference between experiment and prediction depending on the ratio of the initial concentration of the two components. Merk (ref. 176) used the batch data generated by Fritz to predict breakthrough behaviour. As these two studies seem to bee the most extensive ones published to date, and since they contribute appreciably to the understanding of the interactions in binary systems, they will be discussed in more detail later (chapter 6.).

Takeuchi and Suzuki (ref. 177) applied the HSDM to three different binary stystems, and compared the results with those obtained from the corresponding single solute systems. They found that the preferentially adsorbed component exerted a strong influence on the more weakly adsorbed one. The Ds-value of the latter being higher while that of the former is lower, relative to the single solute data. Friedman (ref. 178) predicted breaktrough behaviour from batch data for a mixture of chloroform and trichlorethylene using IAS-theory. The prediction using the HPSDM appeared slightly better than that using the HSDM. From a sensitivity analysis, variations in the isotherm parameters proved to exert a much stronger influence on breakthrough than variations of mass transfer parameters. Fettig (ref. 179), using the simplified IAS-theory (ref. 167) investigated two binary systems. Applying the HSDM, the Ds-value found for the more weakly adsorbed component appeared to be higher in the binary system than the corresponding value for the one-component system. If the carbon was pre-loaded with one component, and the second component added once equilibrium had been attained for the first one, the Ds-values found for both components appeared to differ from the bi-solute and single solute experiments. A comparable result was been obtained by Takeuchi and Suzuki (ref. 177).

In the studies discussed so far, it has been assumed that the cross-coefficients, D^: i ¥='), can be neglected with respect to the diagonal terms, D^: i = j . In that case the diffusion equations are not self-consistent, as has been demonstrated by Toor and Arnold (ref. 180). Liapis and Litchfield (ref. 181) re-considered the batch study discussed earlier (ref. 174) applying the HPD model and including the cross coefficients.

The values of the off-diagonal terms proved to be two orders of magnitude smaller than those of the diagonal terms. Merk (ref. 176), applied the HSD model to the batch data of the system p-nitrophenol-phenol, and found almost the same order of magnitude, for both types of diffusion coefficients. In this instance, the cross terms were only 20 to 30% smaller than the diagonal terms. A comparison between the two

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different models, HPDM and HSDM, seems to indicate that the cross coefficients cannot be neglected for surface diffusion. The strong effect on the value of Ds produced by pre-loading the carbon with one component prior to addition of the second one, also points in the direction of large interactive effects in surface diffusion. Merk (ref. 176) ascribes these effects to the much higher density of the molecules in the adsorbed state, in comparison with their state when dissolved in a liquid. All studies discussed so far refer to systems containing two well-defined adsorbable components. A few studies have been carried out on systems with more than two (well-defined) components (ref. 176, 178, 182 and 205). In real conditions the number of components is generally so large that the equations are unmanageable. There is also a lack of sufficiënt data. In other cases the constituents of the water to be treated are unknown or cannot be defined - such as humic acid.

Where the number of components is too great, Tien and co-workers (ref. 183-186) have proposed the so-called "species-grouping method" in which the number of components is reduced by grouping together components with similar adsorption characteristics and treating the group as one pseudo-species. The adsorption equilibrium is calculated by application of the IAS-theory to all pseudo-species. The limitations of the pseudo-species approach taken by Tien and co-workers have been exposed by the results of Balzli et al. (ref. 204).

Crittenden et al. (ref. 182) have studied a modification of this technique by aggregating a number of well-defined volatile halogenated organic compounds as one parameter (TOX, total organic halogen compound), as proposed by Frick et al (ref. 188, 189).

Volker et al. (ref. 187), using the simplified IAS-theory (ref. 167), applied this technique to many different samples of industrial waste water. The unknown organics are characterised by a group parameter like TOC (total organic carbon). The TOC-value of the non-adsorbable fraction is estimated first, then the adsorbable fraction is subdivided into 4 to 7 pseudo components (in terms of TOC) with the same value for the Freundlich exponent. The pre-exponential factor of the isotherm for each pseudo-component is treated as a free parameter, the values of which are calculated via a non-linear regression analysis, by matching the overall TOC-isotherm using the IAS-theory. With the exception of the studies carried out by Tien and co-workers, all these studies are equilibrium studies. In most rate studies, the unkown organics are aggregated as one parameter. As an example see Lee (ref. 190) and Lee et al. (ref. 191, 192) on the adsorption of humic acid in batch and column studies. Hsieh et al. (ref. 193) conducted batch studies on a domestic waste water during several treatment steps. Cannon and Roberts (ref. 194) and Summers and Robers (ref. 195) conducted batch and column studies on biologically treated water, applying the HPDM (including film diffusion). Fettig and Sontheimer (ref. 196) studied the rate of adsorption of a humic acid in a differential bed adsorber.

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values of Ds for the various pseudo components, applying the technique proposed by Frick et al. (ref. 188). Roughly the same result has been obtained by Fettig (ref. 179) studying fulvic acids in batch reactors.

An application of activated carbon which is becoming increasingly important is the removal of one or a few, man-made toxic compoünds from ground water. Sevéral model studies have been carried out on this subject. Weber and Pirbazari (ref. 197, 198) compared the removal of several of these compoünds from tap water (containing humic acid), with that from organic-free water, using the HSDM in column studies. They concluded that the rate of removal of the small compoünds studied was not affected by the presence of the humic acid. Fettig (ref. 179) applied the same model to batch data of a mixture containing fulvic acid and p-nitrophenol. If the carbon had been pre-Ioaded with the fulvic acid, the rate of adsorption of the p-nitrophenol proved to be much lower than where both "components" were adsorbing simultaneously.

This behaviour corresponds with that shown in systems containing two well-defined components (ref. 44 and 177). This effect, as Fettig points out, is expected to play a role when using long carbon columns, because the more slowly adsorbed humic acid move ahead of the adsorption front of rapidly adsorbed compoünds like p-nitrophenol.

This, however, contradicts the results discussed above and obtained by Weber and Pirbazari.

From this limited survey it becomes clear that the modeling of multicomponent adsorption systems is still not well founded, because of the problems of coping with the influences of mutual interaction of the components on the adsorption equilibria and on the kinetic behaviour.

One of the founders of the IAS-theory, Myers, has seriously criticised the IAS-theory, proposing the more complicated Heterogenous Ideal Adsorbed Solution theory, since the effect of heterogenicity of the adsorbent, with respect to the adsorption energy, on the behaviour of mixtures is very strong (ref. 199). Jaroniec et al. (ref. 200) found that heterogenicity of the micropore system showed large differences between different compoünds, thus violating one of the basic assumptions of the IAS-theory (the internal surface area should be accessible to all components of the mixture). Evidence from the literature that surface diffusion plays a major role in the internal diffusion, and that the surface diffusion coëfficiënt is a function of carbon loading, is overwhelming (see section 2.1). Merk (ref. 176) has shown that the surface diffusion cross-terms, which can be considered to be a measure of mutual interaction in the rate of diffusion in the adsorbed phase, cannot be neglected with respect to the surface diffusion diagonal terms. These factors suggest that the modeling of systems containing more than one adsorbable component is extremely complicated.

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account. One problem (ref. 201, 202) is provided by fluctuations in initial inlet concentrations. Another problem is the fact that backwashing a commercial carbon bed, in many circumstances a necessity, produces classification to partiele size, which may influence the adsorption rate behaviour as has been demonstrated by the present author (ref. 203).

This will be discussed in more detail in chapters 5 and 6.

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Mass transfer to activated carbon in aqeous solutions

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MASS TRANSFER TO ACTIVATED CARBON

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WILLEM CORNELIS VAN LIER

Table of contents

Chapter 1

Introduction

1.1 Historica! background

1.3 Objectives of the present study

References

Chapter 2

Literature

2.1 Batch studies on single component adsorption

2.2 Column studies of single component adsorption

2.3 Multi-component systems - the approach to practical reality

References