Design models for adsorption systems in wastewater treatment

Adsorption systems It is important to consider the modes of contacting the solid adsorbent and the wastewater when applying the adsorption system to large-scale treatment.. Batch-type p

Design Models for Adsorption Systems

in Wastewater Treatment

Gordon McKay

Department of Industrial Chemistry, The Queen's University of Belfast, 21 Chlorine Gardens, Belfat BT9 5DL (Paper received 27 February 1981 and accepted 19 June 1981)

The application of mathematical models to the design of adsorption systems as a method of purifying wastewaters is considered The design of batch, fixed-bed, pulsed- bed, moving-bed and fluidised-bed systems for effluent treatment is discussed A brief review of the wide range of industrial effluents and adsorbents that may be utilised

in such systems is considered Reactivation procedures are presented and the principles

of minimising design costs by optimising design are given

1 Introduction

Adsorption operations exploit the ability of certain solids to concentrate specific substances from solution onto their surfaces Typical liquid separations include the removal of moisture dissolved in gasoline, decolorisation of petroleum products and aqueous sugar solutions, removal of objection- able taste and odour from water, and the fractionation of mixtures of aromatic and paraffinic hydrocarbons The treatment of wastewaters by adsorption techniques is receiving growing attention since the standards for the quality of a waste effluent are gradually becoming more rigid, and new methods of treatment are continuously being developed Certain industrial wastes cannot be treated

by conventional methods of aerobic digestion and adsorption offers an attractive method for solving these problems

Most of the work has been based on studies with activated carbonl-14 which has found wide application in wastewater treatment operations Activated carbon is available in powdered or granular form; the powder is usually dry-fed or slurry-fed to the water undergoing treatment, whereas the granular material is normally used in pressure-fed adsorption units similar to pressure filters

Specific applications of adsorption include the removal of dialysable organic compounds in solution in sewage effluents.15 Other examples of the adsorption of organic compounds from dilute solutions are available, sucb as butanol adsorption on carbonla and detergents with carbon and macroporous zeolites and gel-type resins.l7.1* The substances which are most necessary to remove, for example pesticides, tastes and odours, generally constitute only a small fraction of the organic matter in the ~ a t e r 1 ~

Treatment of textile wastes by adsorption techniques has received considerable attention An activated carbon plant,20 designed to treat 2.52 dms s-1 (40 g.p.m.), incorporates a continuous on-line operation for the treatment of textile effluent and has two sets of three adsorption columns

in series While one set of columns is in operation for the effluent treatment, the remaining columns are undergoing regeneration

The use of other adsorbents in treating textile effluents is continually being investigated Activated silica made from sodium silicate has been usedal-2s as an important adjunct in the treatment of water supplies as well as waste effluents from many industrial processes Silica gel has been shown

to be an effective adsorbent for basic dyes24325 in fixed-bed and fluidised-bed systems Some workers 28-28 have found Fuller's earth and bauxite successful as adsorbents for textile effluent

0142-0356/81/1200-0717 $02.00 0 1981 Society of Chemical Industry

717

718 G McKay

treatment, but considerable flow problems wereencountered in the fixed-bed operation Williamson29 tested several cheap commercially available materials for the treatment of wastewaters The use of peat and wood for wastewater treatment is of considerable intere~t.~O-~O

2 Adsorption systems

It is important to consider the modes of contacting the solid adsorbent and the wastewater when applying the adsorption system to large-scale treatment Five types of contacting systems are usually encountered: (i) batch-type contact; (ii) fixed-bed type process; (iii) pulsed beds; (iv) steady- state moving beds; (v) fluidised-bed type contact

Batch-type processes are usually limited to the treatment of small volumes of effluent, whereas fixed-bed systems have an advantage because adsorption depends on the concentration of solute

in the solution being treated The adsorbent is continuously in contact with fresh solution; thus the concentration in the solution in contact with a given layer of adsorbent in a column is relatively constant Conversely, the concentration of solute in contact with a given quantity of adsorbent is continuously changing due to the solute being adsorbed Fluidised beds for effluent removal result

in high mass-transfer rates, but suffer from relatively short residence times

2.1 Batch adsorption

The schematic diagram for a single-stage adsorption process is shown in Figure 1 The solution to

be treated contains G kg of solvent and the pollutant concentration is reduced from YO to Y1 kg

of solute kg-1 of solvent The amount of adsorbent added is L kg of adsorbate-free solid and the

solute concentration increases from XO to X1 kg of solute kg-l of adsorbent If fresh adsorbent is used, Xo=O The mass balance equates the solute removed from the liquid to that picked up by the

solid

G( Yo - Y l ) = L ( X 1 - XO) = L X 1 (1)

The Freundlich isotherm data from equation (2) may now be applied to (1)

L g of adsorbent

X , g of solute g-' of adsorbent

G g of solvent

C, g of solute g-' of

G g of solvent

C, g of solute 9-l of

L g of adsorbent

Figure 2 Contact filtration

Schematic arrangement for single-

stage batch adsorption A, Agitated

contacting tank; B, filter press;

C, filtrate storage tank; D, steam

where k and n are the Freundlich constants, Xe represents the equilibrium concentration of solute (kg) on adsorbent (kg) and Ye is the equilibrium solute concentration Substituting equation (2)

into (1) for unit mass of adsorbent gives equation (3)

L YO- Ye

Equation (3) permits calculation of the adsorbent, solution ratio for a given change in solution

concentration, YO- Ye

A typical batch process is shown in Figure 2 The effluent to be treated and the adsorbent are intimately mixed in the treating tank for a set time t o enable the system to approach equilibrium, following which the thin slurry is filtered to separate the solid adsorbent and adsorbate from the liquid The equipment may be made multistage by providing additional tanks and filters If the operation is to be made continuous, centrifuges or a continuous rotary filter may be substituted for the filter press The adsorbent is usually applied in the form of a finely ground powder and the time required for the adsorbent and liquid to come to substantial equilibrium depends primarily

on the concentration and particle size of the solid, the viscosity of the liquid and the extent of agita- tion Agitation should be vigorous to ensure rapid contact of the adsorbent particles with the liquid

2.2 Fixed-bed adsorption

Normally, in practical cases, the concept of fixed-bed adsorbers is expressed in graphical terms, to allow for deviation from the ideal case The dynamic adsorption system is represented in Figures

3 and 4, where the wavefront length (mass-transfer zone or MTZ) can be expressed in terms of time, 8 In the MTZ the concentration of solute in the effluent will change from YO to Ye In Figure 3

the area below the wave (a, g, d, e, a) reflects unused adsorbent capacity and the (a, g, d, e, a)/ (a, b, d, e, a) ratio is the fraction of unused adsorbent in the MTZ

I

I / I

I I I / I

V

Figure 3 The Mass-transfer zone

720 G McKay

Effluent v 1 - - - - - - 7 v 1 - - - - y-

breakthrough

Onstream t i m e ( 0 )

Figure 4 Progress of a stable mass-transfer front through an absorbent bed(a) and position of the stoicheio-

metric front relative to the stable mass-transfer front during dynamic adsorption (b)

A vertical straight line drawn through g, the 50% breakthrough point, such that area (a, f, c, b, a)

=(a, g, d, b, a) and (f, e, d, c, f) = (a, g, d, e, a), yields an equivalent stoicheiometric front for the

system at time, 0, The rectangle (h, f, c, k, h) corresponds to adsorbent at its equilibrium loading,

X , ; it is defined as the equivalent equilibrium section and is specified in terms of the length of this

section, ZE The area (f, e, d, c, f) corresponds to adsorbent at its initial loading, X O ; it is specified

in terms of the length of unused bed, Z,

The adsorbent bed at breakthrough is actually comprised of an equilibrium zone and a mass-

transfer zone The system is shown schematically in Figure 4 where (a) depicts a stable MTZ moving

at uniform velocity, U, through an adsorber and (b) shows the stoicheiometric transfer front super-

imposed over the actual transfer front

The total amount of solute removed, w, from the bulk fluid between time 8 and time (0+ A0)

is expressed in equation (4)

As w kg of soluted are adsorbed, the shape of the MTZ is unaltered although its position changes

and there is an increase in bed length, AZ, and

where p is the bulk density of the adsorbent and a is the surface area for adsorption

Combining equations (4) and ( 5 ) and rearranging gives equation (6)

apAX

During steady-state operation, the values of G, p, AX and A Y are fixed and so at any time, 0,

the position of the stoicheiometric front, Z,, is given by equation (7)

and by definition at the breakthrough time, 0b,

z s = z E

Therefore

At the stoicheiometric time, 0,,

Therefore

zE= u8b

z, = zo

z o = ue,

Combining equations (9), (11) and (12) and eliminating U gives

z u = z o ( l + )

Thus simple breakthrough curves provide the data required for the correlation of rate data in dynamic systems and equation (8) is the basic equation which may be used for the analysis of

breakthrough data Several examples of the use of the MTZ theory33-37 may be found in the

literature

A simplified approach for fixed-bed adsorbers is available to correlate the Service time with the operation variables One such model is the Bed-Depth Service Time (BDST) modelas (a simplified form of a previous theory)3g and states that the Service time of a column is given by the following equation (14):

e,=" [Z-mln V ($-I)]

xo v

where NO is the adsorption capacity, k the rate constant of adsorption and V the superficial volu- metric flow rate

At 50% breakthrough, Xo/X=2 and 8= 80.5, the final term in equation (14) becomes zero giving the relationship:

No

xo v

80.5= ~ Z= constant Z

Consequently a plot of BDST at 50% breakthrough against bed height should be a straight line passing through the origin The model has been applied successfullys~3s provided certain conditions apply; namely, that the MTZ is small compared with the adsorbent bed height and also that the breakthrough curve is symmetrical about the stoicheiometric front

A further column-design method38 is based on two concepts: the height of an equivalent transfer unit (HETU) and the maximum permissible space rate at which full adsorption takes place (R) The HETU unit is based on the variation in the void fraction, E , with variation in mean equivalent particle diameter, dp, and packing density It reaches a maximum of 0.12 m when E is 0.50 and dp

is 0.008 m and methods for estimating HETU for any adsorbent are a ~ a i l a b l e ~ ~ - ~ ~ The HETU for

any adsorbent can be determined from Figure 5 and the minimum adsorbent bed height for

maximum product quality is 55-60 HETU; thus

Equation (16) normally results in minimum bed heights between 3 and 6 m Bed heights>Zmin are desirable economically for longer on-stream lifetimes, but values of Z> 10 m should not be used because of difficulties in maintaining packing stability

Column diameters are limited to constructional details For diameters c 1 m columns are usually made from pipes and for diameters 1-4 m (a maximum value for stable packing) plate fabrication

is normally used

The maximum flow rate, R (m3 of solution per m3 of adsorbent h-1) may be calculated from equations (17) and (18) with certain limitations as described by Johnston (See reference49.)

log R=2.0896-38.7 p + b g (0.00308-0.305 dp)

For

p > 0.5 x 10-3 Nsm-2 and dp < 0.00305 m For

R=101.2-3.08~ 1 0 S p + 2 2 9 ~ 10gp2-219.5dp

0.05 x lO-3< p < 0.50 x 10-3 Nsm-2 and dp up to 0.008 m

122 G McKay

Void fraction 6 ( D ~ packed density )

Figure 5 HETU against void fraction

However, if a value of 0.40 x Nsm and dp=0.61 x m are substituted into equation (18)

a value of -779 m3 of feed per m3 of adsorbent h-l is obtained Furthermore suitable values of

p and dp in equation (17) give low results [Limited information in reference 38 makes it impossible

to derive the correct equations for Rx; the author therefore does not recommend the use of

equations (17) and (18).]

The volume of bed is obtained by dividing the throughput by R and thus the amount of adsorbent, diameter and height of bed can be determined

The maximum permissible space rate is a function of the feed absolute viscosity, the pressure drop and dp Pressure drop and flow distribution problems have been di~cussed.~l 42

Figures 6 and 7 showed schematically the operation of fixed-bed adsorbers in series and in parallel

respectively

2.3 Pulsed beds

A moving or pulsed-bed system may be used, where some carbon is removed at intervals from the bottom of the column and replaced at the top by fresh adsorbent, when the adsorption wave front

In

Figure 6 Fixed adsorption

t

Figure 7 Fixed adsorption beds in

o u t series

L

begins to leave the system Consequently, the rate at which the wave front moves through the bed will be the rate for determining when a ‘pulse’ of fresh adsorbent must be removed

The BDST equation may be varied to cover pulse systems by determining the wave-front rate from pilot-plant tests The modified equation is developed by assuming that the moving bed is pulsed just as the wave front begins to leave the column The design equation based on equation

(14) may be expressed as:

where the constants

e b = U Z - /I

No

-

Yo v

and

1

/I= k -1n Yo (;-I)

Effluent Freeboard

Media

Figure 8 Schematic diagram of

pulsed-fed adsorption unit

Influent

Air inlet

124

For changes in flow rate, VI, then the constant a is replaced by al, where

G McKay

(20)

and for changes in feed concentration, XI* then a and b are replaced by u1 and where

and YA is the new effluent concentration

A typical process configuration which has been developed43 is shown in Figure 8 The system uses a column or bed of a fine medium with wastewater and air flowing concurrently upward through the bed The air supplies oxygen for biological oxygen demand (BOD) and also provides a pulsing agitation action to the bed to prevent clogging

1

tact moving-bed adsorption

Steady-state conditions require continuous movement of both fluid and adsorbent through the equipment at a constant rate, with no change in composition at any point in the system with passage of time If parallel flows of solid and fluid exist, the net result is at best a condition of equilibrium between effluent streams or the equivalent of one theoretical stage However, counter- current operations of such systems enable separations equivalent to many stages to be developed

A schematic diagram of a continuous counter-current adsorption system is shown by Figure 9

A solute balance around the entire tower is given by equation (21)

(21)

G( Yo - Y I ) = L( Xo - XI)

The mass balance around the upper part of the column is,

G( Y - Y I ) = L ( X - X I )

From the mass-balance equations, the operating line can be constructed on the equilibrium curve

(Figure 10) The operating line is the straight line of slope L/G, joining the terminal conditions

v,

Y

Figure 10 Operating diagram

for continuous-contact adsorp-

tion

R

will lie on this line

By assuming that the column operates under approximately isothermal conditions and that film and internal diffusional resistances can be represented by an overall mass-transfer term, ky, then the incremental mass-transfer rate is,

where d Z is an incremental height in the adsorber, a is the external surface of the adsorbent particles

and Ye is the equilibrium solute concentration in liquid corresponding to composition X The

driving force, A Y = Y - Ye, is obtained from the vertical distance between the operating line and the equilibrium curve in Figure 10 The number of mass-transfer units, N, may be defined by equa-

tion (24)

(24)

726 McKay

The number of mass-transfer units may be obtained by graphical integration and the height of the bed, 2, is obtained by combining equations (23) and (24) to give,

l 0 d Y kyadZ - _ - 2

Y - Ye G Ht

where the height of the mass-transfer unit, H, is defined by

Mass-transfer correlations, for evaluating k,, have been reviewed.44

Large-scale devices for the continuous contacting of granular solids and fluids have been developed after certain operational problems had been overcome These difficulties included obtaining uniform flow of solid particles and fluid without channelling or local irregularities, as well as those of intro- ducing and removing the solid continuously into the vessel to be used Such devices include the

h y p e r ~ o r b e r ~ ~ - ~ ~ and the Higgins contactor,*8~49 the latter being specifically designed for solid- liquid ion-exchange operations The previous systems utilise the principals of fluidisation and recent work on fluidisation has been applied specifically to colour removal

2.5 Fluidised beds

In wastewater treatment systems it is advantageous to keep the particle size as small as possible,

so that high rates of adsorption may be achieved Columnar operation, in which the solution to be treated flows upward through an expanded bed of the particulate adsorbent, is one method of taking advantage of small particle size The main problems of the use of small particles in fixed beds are excessive head loss, air-binding and fouling with particulate matter The design of a continuously operating counter-current fluidised bed is relatively ~imple,~O-52 although the solution

of the design equations can become quite ~ o m p l e x ~ ~ - ~ ~

Determination of the mass-transfer coefficient, k,, provides the fundamental design parameter

for fluidised-bed systems An intraparticle diffusion-controlled adsorption model has been pro- p0sed5~~59 and also a ‘completely mixed column’ model has been used for the removal of alkyl- benzene sulphonate from wastewater,OO with a fluidised bed of carbon, and of basic dye from effluent,24 with a fluidised bed of silica

By assuming steady-state conditions, the rate of mass transfer to the adsorbent across a film is,

Driving force Resistance Rate=

The driving force is the product of the concentration gradient between adsorbent and solution and the total area across which transfer is taking place The resistance is assumed to be uniform throughout the system and the reciprocal of this resistance is the transfer coefficient, k y Therefore

where : A =effective transfer area per unit mass of adsorbent; M = mass of adsorbent; Ay = con- centration difference across the film; r = rate of transfer

Since the investigations 24, 60 were performed under non-steady-state conditions, the rate of trans- fer may be expressed in tcrms of the concentration in solution at any time and the eon&khtkdtioh gradient across the film at that time Due to the strong affinity of the adsorbate for the adsorbent a partition coefficient, P, is incorporated to increase the concentration gradient term Its value is the mass concentration of adsorbate in solution, at time 0, divided by the mass concentration in the adsorbent at time 0, at equilibrium:

P= Y - equilibrium

Y s