Chemical Engineering Science 66 (2011) 6209–6219

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Science

0009-25

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/ces

Design of continuous ion exchange process for the wastewater treatment

Roman Bochenek, Robert Sitarz, Dorota Antos n

Department of Chemical Engineering and Processing, Rzeszow University of Technology, ul. W.Pola 2, 35-959 Rzeszow, Poland

a r t i c l e i n f o

Article history:

Received 18 May 2011

Received in revised form

28 August 2011

Accepted 30 August 2011Available online 7 September 2011

Keywords:

Dynamic simulation

Ion exchange

Optimization

Pollution

Wastewater treatment

Zeolites

09/$ - see front matter & 2011 Elsevier Ltd. A

016/j.ces.2011.08.046

esponding author.

ail address: dorota.antos@prz.edu.pl (D. Anto

a b s t r a c t

A generic design procedure for the continuous ion exchange process is proposed. The procedure is

based on the optimized arrangement of parallel batch columns. The continuity of the process is

achieved by proper shifting of the inlet conditions. The method for the optimization of the process

variables is presented.

The concept is demonstrated on the example of ammonia removal from wastewaters. Two

flowsheet schemes are considered utilizing fresh or recycled regenerating agent.

The superiority of the optimized process over the periodic operation is demonstrated.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Ion exchange has numerous applications for industry as well aslaboratory research. It is used in production of various acids, bases,salts, for industrial drying and treatment of gases, in biomolecularseparations as well as in the food industry. Ion exhange processes isalso commonly used in treatment of drinking and wastewater incommercial and industrial applications such as water softening,demineralization and decontamination (Spiro, 2009).

The ion exchange process comprises of the interchange of ionsbetween a solution and an insoluble solid, i.e., polymeric ormineralic ion exchangers such as ion exchange resins (functiona-lized porous or gel polymer), natural or synthetic zeolites,montmorillonite, clay, etc. In a water treatment system undesir-able ions in the water supply are replaced with more acceptableions. Water decontamination consists of removal of ionic pollu-tans such as phosphate, nitrate, ammonia, which appear invarious types of agricultural, domestic and industrial wastewatersor heavy metals discharged in effluent from electroplating plants,metal finishing operations, as well as a number of mining andelectronics industries (Pintar et al., 2001; Dabrowski et al., 2004;Spiro, 2009).

Although other physicochemical methods of water purificationsuch as chemical reactions, electro-flotation, reverse osmosis andadsorption may be under given conditions more effective thanion exchange (Flores and Cabassud, 1999), the latter process is

ll rights reserved.

s).

considered attractive because of the relative simplicity of applica-tion (Blanchard et al., 1984) and in many cases is proven to beeconomic and effective technique to remove ions from waste-waters, particularly from diluted solutions (Pintar et al., 2001;Valverde et al., 2006).

The operating cycle of ion exchange fixed bed (column)consists of two working modes: saturation and regeneration. Inthe first mode the feed stream containing wastewater is deliveredinto the column inlet and the effluent free of the polluting ion iswithdrawn at the column outlet. The saturation is interruptedwhen the concentration of the polluting ion in the effluentexceeds a permissible limit. The bed is regenerated in two stages:elution and re-equilibration. Elution consists of replacing theretained ions with ions of a regenerant. It is followed by thecolumn re-equilibration where the regenerant is washed out andthe column is brought back to the initial conditions. The alternatemodes of saturation and regeneration result in a periodic dis-tribution of concentration in the effluent stream characteristic forprocesses of concentration swing adsorption. After a number ofcycles the process attains the cyclic steady state (CSS) in whichdistribution of concentration in each cycle is identical.

The process can be realized using a single bed as well as a systemof interconnected beads based on variation of upstream and down-stream conditions (Nilchan and Pantelides, 1998). The performance ofsuch a periodic operation is strongly affected by a number ofoperating variables. Therefore, the design of effective process requiressolving an optimization problem aimed at minimizing operating costsof the process subject to the constraints of the product purity(Nilchan and Pantelides, 1998; Cruz et al., 2003; Jiang et al., 2004;Cruz et al., 2005; Agarwal et al., 2010).

R. Bochenek et al. / Chemical Engineering Science 66 (2011) 6209–62196210

The design procedures for various periodic processes of ionexchange have been discussed in several publications concerning abatch system based on a single column operating periodically (Sunet al., 1990; Lewus et al., 1998; Castel et al., 2000) as well as acontinuous system utilizing multicolumn setups such as the carouselsystem (Softening et al., 1990; Ernest et al., 1997; Hritzko et al., 2000;Huckman et al., 2001; Rochette, 2006). The carousel process refers tothe operation systems in which feed and regenerating streams aredelivered subsequently through the columns mimicking counter-current movement of the fluid flow and the columns. The movementis realized by switching regenerant and feed ports in equal timeintervals. However, the volume of the feed stream used for thecolumn saturation typically is much larger compared to that requiredin the regenerating stages. The equality of switching intervals maycause that the flowrate of streams delivered in the regeneration modehas to be set lower compared to that used during the saturation. Sucha forced flowrate adjustment is a serious drawback of the carouselprocess limiting the process performance.

In this study an alternative procedure for the design of thecontinuous ion exchange process in a multicolumn setup has beenproposed. The procedure is based on the parallel delivery of feed andregenerating streams into the column inlets in such a way that in thesame time interval a certain number of columns operate in thesaturation mode while the rest of them are regenerated. The numberof columns operating in the saturation mode is time-invariant, whichassures the continuity of the process. The operating cycles ofconsecutive columns are sequentially shifted in time. The length ofthe time intervals for the saturation and regeneration can be adjustedto assure optimal performance of the overall process.

To verify the concept suggested a model system of ion exchangeprocess has been selected, i.e., the removal of ammonia ions fromwastewaters on a synthetic zeolite has been analyzed. Two flowsheetschemes have been considered differing in the manner of the columnregeneration—in the first one a fresh solution of the regenerant wasused for the column regeneration whereas in the second one theexhausted regenerant was partly recycled and reused in the regen-eration mode. For the process design and optimization a dynamicmodel was employed based on the equation of the linear driving forcein the solid phase (i.e., LDF model). The Differential Evolution (DE)procedure was adopted for the process optimization based on a

Fig. 1. Flowsheet scheme for complete operating cycle on a single column without rege

III, respectively, Qrecov is the streams of purified water, V IIw , V III

w are the volumes of the

re-equilibration stages, respectively.

simple evolutionary strategy (Storn and Price, 1997) for non-linear,non-differentiable and non-convex problems with continuousvariables.

The production rate of purified water (process product) wasused as the performance criterion and the goal function of theoptimization procedure.

It has been shown that the optimized continuous process cansignificantly outperform the periodic operation.

2. Principles of the process

2.1. Cyclic process of ion exchange in a single column

In the simplest case, the cyclic ion exchange system comprises asingle batch column operating in a periodic manner, which is basedon alternate stages of the column saturation and regeneration.

The flowsheet scheme of the process is presented in Fig. 1.During the saturation period (stage I) the column is loaded

with wastewater (i.e., with the feed stream), the ionic pollutantsare retained on the stationary phase and the purified waterstream is withdrawn at the column outlet. The operation ofsaturation is stopped when the pollutant concentration in the

purified water, Cout,I

P , exceeds permissible upper limit, EpsI.

In the next stage the column has to be regenerated. Theregeneration comprises two operations: elution (stage II) where theregenerant is delivered into the column to elute the retained ions inthe form of concentrated solutions, and the column re-equilibration(stage III), where the column is rinsed out to remove the regenerantand restore initial conditions. The elution stage is stopped when theconcentration of the ionic pollutant in the column effluent, Cout,II

p ,drops below a threshold concentration, EpsII.

The last stage, i.e., of re-equilibration is interrupted when theconcentration of the regenerant in the effluent stream, Cout,III

r ,decreases below the threshold concentration, EpsIII.

The stream of the wastewater purified in the saturation modeis partly consumed for the preparation of regenerating solutionsin the elution and re-equilibration stages (V II

w, V IIIw , see Fig. 1).

To improve the process performance, i.e., to reduce the waterconsumption, the effluent from the elution stage (stage II)

nerant recycling, QI, QII, QIII are the flowrates of the inlet streams in the stages I, II,

purified water consumed for supplementing the streams in the elution and the

Fig. 2. Flowsheet scheme for complete operating cycle on a single column with regenerant recycling.

Fig. 3. Gantt chart for a setup of eight parallel column operating in a periodic node.

R. Bochenek et al. / Chemical Engineering Science 66 (2011) 6209–6219 6211

containing exhausted regenerant can be partly recycled (seeFig. 2). The recycled part is collected and temporarily stored ina buffer tank to be completely used up in the initial period of theelution stage II of the consecutive cycle. The exhausted regenerantis collected within a certain time interval, whose length isrestricted by the threshold concentration of the pollutant in thebuffer tank, C

rec

P rEpsrec . Subsequently, in the same stage, thecolumn is regenerated with a portion of fresh regenerant.The contribution of the exhausted regenerant to the wholeregeneration stream used in the elution stage is determined bythe recycling ratio U.

Since the last step of re-equilibration is designed for washingout the regenerant as well as other impurities clogging the bed,the effluent of the step III is discharged; it is not recycled to theprocess.

2.2. Continuous process of ion exchange

The throughput of the ion exchange process can be increasedby utilizing a system of several identical columns arranged inparallel. If all these columns are simultaneously operated underthe same conditions the node works periodically. The values of

the feed and product flowrates of the node are multiplication ofthe corresponding flowrates of the single column.

The operating cycles for a setup of eight parallel columns areillustrated in Gantt chart in Fig. 3.

Large-scale processes, which require large amounts of product,are usually more cost-effective for continuous operations. There-fore, in this study a continuous process of the wastewatertreatment was considered. In this process the operating cyclesof subsequent columns are shifted in time so that in each timeinterval a certain number of columns could operate in thesaturation mode while remaining ones in the regeneration mode.Because the time length necessary for accomplishing the satura-tion and regeneration stages are different to assure the processcontinuity some of the columns have to wait for the use in asubsequent cycle in the work stoppage. Therefore, a completeoperating cycle for each column of the continuous node com-prises four stages: saturation, elution, re-equilibration and thework stoppage. Gantt chart for an eight-column continuous setupis presented in Fig. 4. It can be observed that after the startup ofthe operation in each time interval four columns are loaded withthe feed stream, i.e., they work in the saturation mode, four areregenerated or remain in the work stoppage. In this case theprocess conditions are optimized for the column operating

Fig. 4. Gantt chart for a setup of eight column operating in the continuous mode; individual column optimization.

Fig. 5. Gantt chart for continuous system of eight-column system, node column optimization.

R. Bochenek et al. / Chemical Engineering Science 66 (2011) 6209–62196212

individually but not optimized for the column operating jointly inthe multicolumn node.

The work stoppages cause lengthening of the cycle time, whichreduces the process effectiveness. Therefore, optimizing theprocess parameters for individual columns (individual columnoptimization) and synchronizing their cycles to achieve contin-uous operation is not sufficient; to upgrade the process perfor-mance, optimization of the process parameters for the columnoperating jointly in the system (node optimization) is required.

Gantt chart for an optimized eight-column node is presentedin Fig. 5.

The throughput of the optimized node is significantly highercompared to that obtained for the individual column optimiza-tion. In the case illustrated in Fig. 5, five columns are running inthe saturation mode, three in the regeneration mode or in thework stoppage. In this case the length of the work stoppages is soshort that they are not noticeable in the chart.

To synchronize the runs of columns assembled in the contin-uous system the shift time between the cycles of consecutivecolumns has to be adjusted in such a way that the number ofcolumns operating simultaneously in each of two modes (i.e.,saturation and regeneration) is time-invariant, which assurescontinuity of the feed delivery and the product withdrawal. Theshift time corresponds to the switching time of the inlet condi-tions. It can be determined based on the concept of time unit,which is elucidated as follows.

Each stage consists of a certain number of the time units; thetotal number of the time units for all the stages is equal to thenumber of columns in the node.

The time units can be divided into two categories: productive units,NP, corresponding to the saturation mode, and non-productive units,NR, corresponding to the periods of elution, re-equilibration and the

work stoppage. The sum of the productive and non-productive unitshas to be equal to the number of the column in the node:

NPþNR ¼Ncol ð1Þ

The number of productive time units can be calculated asfollows:

NP ¼ INTtI

tcNcol

� �ð2Þ

where INT is an integer function rounding down; tc is the totalworking cycle time given by the following equation:

tc ¼ tIþtIIþtIII ð3Þ

where tI, tII, tIII are the lengths of the time periods for saturation,elution and re-equilibration, respectively.

The length of the time unit is expressed as

tj ¼tI

NPð4Þ

The stoppage time can be calculated as follows:

tstop ¼NRtj�ðtIIþtIIIÞ ð5Þ

For the total operating time in the node it holds:

ttot ¼ tIþtIIþtIIIþtstop ð6Þ

Additionally, the following dependence is fulfilled:

Ncoltj ¼ tIþtIIþtIIIþtstop ð7Þ

The length of the periods of saturation, elution and re-equilibration, tI, tII, tIII, can be determined on the basis ofsimulations of operation cycles for a node column running underCSS conditions.

R. Bochenek et al. / Chemical Engineering Science 66 (2011) 6209–6219 6213

3. Process optimization

3.1. Optimization procedure

To solve the optimization problem the Differential Evolu-tion (DE) method was used. It utilizes the evolutionaryalgorithm belonging to the class of stochastic population basedmethods that proved their efficacy in solving hard nonlinearglobal optimization problems involving noncontinuous,nondifferentiable and nonconvex functions in the optimiza-tion models (Michalewicz and Fogel, 2002; Onwubolu andBabu, 2004).

The evolutionary techniques had found wide application forsolving various problems of chemical and process engineeringsuch as batch operation scheduling, designing various subsys-tems, e.g., heat exchanger network or water network, moleculardesign, designing processes and apparatus (Deb, 2001; Babu et al.,2005; Jezowski et al., 2005, 2007; Babu and Angira, 2006;Bochenek et al., 2007; Srinivas and Rangaiah, 2007).

The DE method is a simple evolutionary strategy proposed byStorn and Price (1997) for solving nonlinear, nondifferentiableand nonconvex optimization models with continuous variables. Itcan handle both unconstrained and constrained optimizationproblems and was proved for its high performance for solvingmulti-modal problems (Price et al., 2005). The algorithm of themethod is illustrated in Fig. 6.

3.2. Formulation of optimization problem

The problem of the optimal design of the water purificationnode that consists of a given number of columns relies on

Fig. 6. Algorithm of the DE method,

determining the following process variables:

�

see

volumetric flowrates Q in the stages I, II, III, which are relatedto the time lengths: tI, tII, tIII. Increasing the flowrates results inreducing the operation time, which improves the processperformance. On the other hand, it alters the HETP value, i.e.,it can reduce the column efficiency due to worsening condi-tions for the mass transport. Therefore, determining the valuesof flowrates for each stage requires solving an optimizationproblem.Typically, the regenerant is not adsorbed; therefore, in the re-equilibration stage (stage III) the mass transport kinetics doesnot affect the process efficiency. In such a case the flowrate QIII

can be limited only by the pressure drop in the system or thepump capacity;

� shift time of cycles of subsequent columns (i.e., the switching

time) and the number of columns operating in individualmodes in each time unit. These variables can be calculatedon the basis of the model simulations if the flowrates Qk (k¼ I,II, III) are known;

� threshold concentration of the polluting ion in the column

effluent in the saturation stage, i.e., the water purity, EpsI. Thisvalue can be set arbitrarily according to the permissibleconcentration limit;

� threshold concentration of the polluting ion at the end of the

elution stage, EpsII.The value EpsII should be considered as an indicator of theregeneration efficiency. Complete regeneration, i.e., completeremoval of the ionic pollutant from the column (EpsII

�0)usually requires long elution time, which reduces the processeffectiveness. On the other hand incomplete regenerationcauses reduction of the loading capacity of the bed. Therefore,the value of EpsII should be optimized;

details in (Price et al., 2005).

R. Bochenek et al. / Chemical Engineering Science 66 (2011) 6209–62196214

�

threshold concentration of the regenerant at the end of the re-equilibration stage, EpsIII;the threshold concentration, EpsIII, can be selected on a levelthat mimics the effect of the hardness of the wastewatercontained in the feed stream; � additionally, for the system involving recycling: the recycling

ratio U and the threshold concentration of the pollutant in therecycled stream, Esprec;The threshold concentration Epsrec should be selected properly;low value of Epsrec results in higher water consumption whereastoo high Epsrec causes reduction of the regeneration efficiency.Finding the best values of Epsrec and U is an optimization problem.

As a criterion of the process performance the productivity ofpure water can be taken into account. The productivity can bedefined as the volume (or mass) flow of the recovered water,Qrecov:

Pr¼Qrecov ¼Q I

wtI�V IIw�V III

w

ttotð10Þ

where V IIw and V III

w are the volumes of the purified water consumedin the stages II and III, respectively, to supplement the streams QII

and QIII (see Figs. 1 and 2).To optimize the process performance the following problem

can be solved:

max ½PrðvÞ� ð11Þ

where v is a vector of the decision variables.The optimization problem is solved subject to the constraint

concerning the purity of the recovered water:

Cout,I

P rEpsI ð12Þ

Cout,I

p ¼

Z tI

0

Cout,Ip dt

t

In the recycling mode additional constraint should be addedthat is related to the concentration of pollutant in the recycledstream collected at the column outlet:

Crec

p rEpsrec ð13Þ

The following decision variables can be taken into account:v¼[QI, QII, EpsII, Epsrec, U]

The two last variables Epsrec, U are active for the processinvolving the regenerant recycling.

The optimization problem should be solved for the systemoperating under CSS conditions, which correspond to repeatabil-ity of the concentration profiles at the column outlet for eachconsecutive cycle.

3.3. Modeling of the process dynamics

To predict the process performance a simplified dynamicmodel based on the equation of linear driving force (LDF model)was used (Ruthven, 1984).

The LDF model consists of the mass balance equation in themobile phase:

et@Ci

@tþð1�etÞ

@qi

@t¼ eeDL

@2Ci

@x2�u

@Ci

@xð14Þ

Eq. (14) is coupled with the following kinetic equation:

@qi

@t¼ km,iðq

n

i �qiÞ ð15Þ

where i denotes the system component, e.g., eluite (pollutant) ioni¼p, and co-ion i¼co, t, x are the time and the axial coordinates,respectively; Ci(t, x) is the concentration in the mobile phase; qi(t, x),qn

i ðt,xÞ are the solid phase concentration and the equilibrium solid

phase concentration, respectively; u is the superficial velocity; ee andet are the external, internal and total porosity; DL is the dispersioncoefficient, and km,i is the overall mass transport coefficient.

The coefficient km,i lumps the contribution of external andinternal mass transport kinetics to the overall mass transportmechanism. It also depends on the isotherm course as follows(Kaczmarski et al., 2001; Antos et al., 2003):

1

kmi¼

k00i

ð1þk00iÞ2

1

k1iþ1

� �2 eeFe

et

dp

6keff ,iþ

d2p

60Dintra,i

!ð16Þ

k00i ¼ Ftdqn

i

dCið17Þ

k1i ¼ Fe epþð1�epÞdqn

i

dCi

� �ð18Þ

where Fe ¼ 1�ee=ee and Ft ¼ 1�et=et are the phase ratio:

Dintra, i ¼ epDpeff , iþð1�epÞDseff , i

dqn

i

dCið19Þ

where keff is the effective external mass transport coefficient inionic solutions; Dpeff, Dseff are the effective coefficients of diffusionin macropores and micropores, respectively; ep is the internalporosity. For a linear isotherm dqn

i =dCi is the Henry constant.For self-sharpening fronts the equations presented above can

be used, provided that the isotherm slope dqn

i =dCi is replaced withthe isotherm chord Dqn

i =DCi (Lapidus and Amundson, 1952;Kaczmarski et al., 2001; Antos et al., 2003).

The model is solved with the boundary and initial conditions:Initial conditions:

Ciðt¼ 0,xÞ ¼ C0i ð20Þ

qiðt¼ 0,xÞ ¼ q0i ð21Þ

Typically, the column is free of the polluting ions in the initialstate C0

i ¼ 0; q0i ¼ 0 (i¼p).

Boundary conditions

At the column inlet the Danckwerts-type boundary conditionscan be assumed:

uðCFi ðtÞ�Ciðt,x¼ 0ÞÞ ¼�eeDL

@Ciðt,x¼ 0Þ

@xð22Þ

where CFi ðtÞ is the profile of concentration at the column intlet. In

the saturation stage CFi ðtÞ stands for the feed concentration for the

eluite ion as well as the regenerant ions while in the regenerationstage it describes the regenerant profile. For step changes of theinlet concentration in k stage it holds:

CFi ðtÞ ¼ Cin,k

i k¼ I, II, III ð23Þ

where Cin, Ii ¼ CF

i

At the column outlet continuity of the concentration profile isassumed:

@Ciðt,x¼ LÞ

@x¼ 0 ð24Þ

The model has to be coupled with the isotherm equation, e.g.,for the Donnan isotherm model it holds:

qn

i

Ci¼ Ki

qnc

Cc

� �zi=zc

, Ki ¼gm

i

gsi

gsc

gmc

� �zi=zc

ð25Þ

Eq. (25) is combined with the conditions of electroneutrality inthe mobile phase:

ziCiþzcCcþzcoCco ¼ 0 ð26Þ

and in the solid phase:

ziqn

i þzcqn

cþzmG¼ 0 ð27Þ

R. Bochenek et al. / Chemical Engineering Science 66 (2011) 6209–6219 6215

where z is the ionic charge, m denotes the solid matrix (zm¼�1for the cation exchanger); and G is the exchange capacity.

The coefficient K lumps contribution of activity coefficients ofions in the mobile gm and the solid phase gs.

Typically, the coefficient K is a function of the regenerantconcentration, r, i.e., salt supplying counter- and co-ions. Thesame can holds for G, which can decrease with the increase of theionic strength due to the reduction of the electrostatic potential ofthe solid matrix. Therefore, additional dependencies should bequantified (Gorka et al., 2007).

K ¼ f ðCrÞ ð28Þ

G¼ f ðCrÞ ð29Þ

4. Results and discussion

4.1. Model parameters

The model parameters used for the simulations were the sameas determined in our previous study for the system of ammoniaremoval on a zeolite ion exchanger with NaCl salt as theregenerant (Gorka et al., 2007).

The bed parameters were assumed as follows:the column dimensions: column length L¼25 cm, column dia-

meter dcol¼10 cm; the bed porosities were et¼0.7, ee¼0.5, ep¼0.3.The following values and dependencies of the isotherm and

kinetic coefficients were used:

–

empirical dependencies of the isotherm and kinetic coefficientsfor the eluite ion, p, on the concentration of counter-ions, Cc,supplied by the regenerant, i.e.,� for the isotherm coefficients:

GðCcÞ ¼ 2:45þ3:07expð�Cc=0:02Þ

KpðCcÞ ¼ 16:42�15:41expð�Cc=0:07Þ

To quantify these concentration dependencies the isothermcourse was determined for different contents of the regen-erant in the mobile phase. For each set of equilibrium datathe isotherm coefficients G and Kp were estimated. Next, Gand Kp were appropriately correlated with the regenerantconcentration (see details in Gorka et al., 2007).Because co-ions were not adsorbed, the coefficient, Kco wasset equal to zero (Kco¼0).� for the effective external mass transport coefficient:

keff ,p ¼ 1:0� 10�5ðCcÞ

�0:37

The influence of flowrate variations on the keff value wasaccounted for by the relation of Wilson and Geankoplis(1966), i.e.:�

0:333

keff ,p ¼ f ðwÞ

For co-ions the mass transport resistances were neglected.Note that for non-absorbable species the mass transportresistances are negligible (see Eq. 16 at k00i-0).

Diffusion coefficients:

Dseff ,p ¼ 4:97� 10211½m2=s�

The contribution of the pore diffusion Dpeff,p to the masstransport mechanism could be neglected (Gorka et al., 2007).

Dispersion coefficient:the dispersion coefficient was calculated according to the

Gunn equation (Gunn, 1987).All the model parameters were assumed to be time invariant,

i.e., gradual bed destruction or deactivation due to clogging,ageing, etc., was not taken into account.

The remaining operating variables were set as describedbelow:

-

feed composition, i.e., the inlet composition in the stage I:

CFp ¼ NHþ4

¼ 0:0153mol=L

CFr ¼ NaCl ¼ CF

co ¼ Cl ¼ 0:0017mol=L

A relatively low inlet concentration of the ionic pollutant,CF

p ¼ NHþ4, was selected for the simulations. It corresponded to

weakly non-linear range of the isotherm for which ion-exchange process can be effective; the use of concentratedsolutions is unprofitable due to the fast saturation of the bedloading capacity. Nevertheless, the principles of the optimiza-tion procedure presented here are valid for any initialconcentration.

-

concentration of the regenerant (salt NaCl) in the stage II:

Cin,IIr ¼ 0:5mol=L ð3%wt=vÞ

-

threshold concentrations:pollutant concentration in the collected stream (i.e., permis-sible limit):

EpsI ¼ 1� 1024 mol=L

threshold concentration of the regenerating agent:

EpsIII ¼ CFR ¼ 0:0017mol=L

-

flowrate of the water stream in the re-equilibration stage III:Q III ¼ 6L=min

The value of QIII was set as maximal regarding the systemcapacity limitation.

4.2. Process simulation

To simulate the process dynamics the model described by Eqs.(14)–(29) was employed with parameters reported above inSection (5.1). The model was solved for the eluite ion, i.e.,ammonia ions, NHþ4 , and for co-ions, Cl�. The concentration ofthe counter-ions was calculated using the electroneutrality con-ditions (Eqs. (26) and (27)). Note that because the ionic charge ofco-ions was 9zN9¼1 the inlet co-ion concentration was equal tothe concentration of the regenerant salt Cin,k

co ¼ Cin,kr (k¼ I, II, III).

Local values of the isotherm and kinetic coefficients werecalculated according to the temporal concentration profile ofthe counter-ion using Eqs. (28) and (29).

To simulate the breakthrough profiles in the saturation modethe isotherm chord was used in Eqs. (17)–(19), whereas forpredicting the regenerating profiles the isotherm slope wascalculated. Details of the procedure can be found elsewhere(Gorka et al., 2007).

The simulation of consecutive stages of the process relied onproper exchanging the boundary conditions (Eqs. (22) and (23)).

To simulate the process including regenerant recycling theadditional sub-stages in the regeneration mode had to be taken

R. Bochenek et al. / Chemical Engineering Science 66 (2011) 6209–62196216

into account. The effluent containing exhausted regenerant wasassumed to be discharged to the waste within the period (tI,tcollect). At the time point, tcollect, the effluent started to be collectedin a buffer tank. The whole storage is used up in stage II of a nextcycle. The value of tcollect was calculated according to the averageconcentration C

rec

P using the following mass balance equation:

Q IICrec

p trec ¼�Q II

Z tcollect

tII

Cout,IIp ðtÞdtþQ IIEpsIðtII�tcollectÞ ð30Þ

where trec is the recycling duration. The last term on the left handside of the equation corresponds to the mass of the pollutant inthe stream of purified water coming from stage I (see Fig. 2).

The recycling duration trec is determined by the choice of therecycling ratio U that was defined as follows:

U ¼Cout,II,max

p �CUp ðt

recÞ

Cout,II,maxp �EpsII

ð31Þ

where Cout,II,maxp is the maximum of pollutant concentration in the

regeneration profile, CUp is the concentration corresponding to the

end of the recycling period.

Fig. 7. Concentration profiles of ammonia at the column outlet after two cycles,

for the column without recycling; the re-equilibrating stage III is very short,

therefore not visible on the plot.

Fig. 8. Concentration profiles of ammonia in CSS for first four cycles (column without

saturation stage I.

When U is set the outlet concentration CUp can be calculated

according to Eq. (31) and the corresponding time for the elution ofconcentration CU

p , i.e., trec, can be found.As mentioned above the optimization problem should be

solved for the system operating in the cyclic steady state. TheCSS was attained after few cycles, i.e., after second cycle for thecolumn operating without recycling and after fourth for therecycling mode. The simulation of the start up of the process isdemonstrated in Figs. 7 and 8.

4.3. Optimization results

4.3.1. Single column optimization

The cyclic process of ion exchange was optimized for an singlecolumn operating according to the flowsheet scheme involvingthe regenerant recycling as well as without recycling. Theobjective function was defined by Eq. (10), the consumption ofwater V II

w, V IIIw was determined by the water demand in the

regenerating and re-equilibrating streams.The optimization results are summarized in Table 1. It com-

prises the parameters of the optimization procedure, the searchingrange of the decision variables and the optimal solution. It is evident

recycling): (a) complete concentration profile and (b) concentration profile for the

Table 1Optimization results for the single column optimization.

Without recycling With recycling

Parameters of the optimization procedureCRa 0.3 0.3

Fa 0.8 0.8

Number of generation 120 150

Number of individuals 10 15

Searching range of the decision variablesQI (L/min) 0.3–10 0.3–5

QII (L/min) 0.3–10 0.3–5

EpsII (mol/L) 10�4–3�10�3 10�4–4�10�3

Epsrec (mol/L) – 10�4–4�10�3

U – 0–1

Best solutionObjective function OF (L/min) 1.14 1.46

QF¼QI (L/min) 2.16 2.67

QII (L/min) 1.38 2.88

EpsII (mol/L) 8.06�10�4 5.06�10�4

Epsrec (mol/L) – 1.33�10�3

U – 0.710

a See Fig. 6.

TaO

th

R. Bochenek et al. / Chemical Engineering Science 66 (2011) 6209–6219 6217

that the process involving recycling performs better compared to thatrealized without recycling. The performance improvement for theprocess being investigated was ca. 28%.

4.3.2. Node column optimization

As described above, to increase the throughput a multicolumnnode can be used. The node can operate periodically—it thencomprises a setup of parallel columns operating periodicallyunder the same conditions (Fig. 3) or continuously, where theinlet conditions for each column are sequentially changed in time(Figs. 4 and 5).

The productivity, Pr, of the periodic node is just a multi-plication of that for a single column presented in Table 1.

The performance optimization for the continuous multicolumnnode was done for three setups comprising 3, 6 and 8 columns.

ble 2ptimization results for the process of ion exchange in a multicolumn node. Parameters of

e same as reported in Table 1.

Without recycling

3 Columns 6 Columns

QI (L/min) 2.01 1.99

QII (L/min) 1.59 1.54

EpsII (mol/L) 7.97�10�4 8.24�10�4

Epsrec (mol/L) – –

U – –

OF (L/min), node column optimization 3.39 6.78

OF (L/min) individual column optimization 1.85 5.54

Fig. 9. Comparison between the optimization results (a) productivity obtained for the in

scheme without regenerant recycling; (b) productivity obtained for the individual colum

regenerant recycling; (c) comparison between productivity of the nodes with and with

Two optimization approaches for the optimization were com-pared: the operating parameters were optimized for a singlecolumn operating individually in the node (individual columnoptimization) and for the column operating jointly in the node(node column optimization).

The optimization results are summarized in Table 2.It can be observed that for the node column optimization the

system performs markedly better compared to that for theindividual column optimization. The performance differencesresult from unproductive gaps in the operating cycles, i.e., thework stoppages occurring in the continuous operation. The nodecolumn optimization allows minimizing gaps between cycles. Thesuperiority of the performance of the optimized mode is visua-lized in Fig. 9a and b.

An important observation is the upgrade of the processefficiency for the system based on the regenerant recycling (even

the optimization procedure and the searching range of the decision variables are

With recycling

8 Columns 3 Columns 6 Columns 8 Columns

2.15 2.26 2.27 2.49

1.39 2.63 2.79 2.80

8.19�10�4 5.14�10�4 4.88�10�4 4.75�10�4

– 1.12�10�3 1.25�10�3 1.36�10�3

– 0.679 0.715 0.744

9.12 4.19 8.54 11.2

7.39 2.41 7.22 9.62

dividual column optimization and the node column optimization for the flowsheet

n optimization and the node column optimization for the flowsheet scheme with

out recycling.

R. Bochenek et al. / Chemical Engineering Science 66 (2011) 6209–62196218

up to 83% for the three columns system) as demonstrated inFig. 9c.

The productivity achieved in the continuous system with nodecolumn optimization is slightly lower than that for the periodicnode (compare Tables 1 and 2). It results from the necessity ofadjustment of the process parameters to achieve the continuousoperation, which reduces the number of degree of freedom in theoptimization procedure. Increase of the column number benefitsin a reduction of the time of the work stoppages. Therefore, thedifferences between productivity for the periodic and the con-tinuous setups disappear with the increasing column number.

Nevertheless, the observed superiority of the periodic setupover the continuous one is only apparent. The periodic systemoperates more efficiently only if the throughput is also periodic,i.e., water to be treated is stored in a large amount and isprocessed in the purification node in any time.

If the wastewater delivery is continuous the periodic nodeperforms much worse compared to the continuous system. Toillustrate the problem one can consider a certain wastewaterstream (throughput) to be processed in a purification node. Accord-ing to the given throughput the number of column has to beadjusted so that they could operate under optimal conditions. Forinstance, for the throughput (feed flowrate) 4 L/min a set of threecolumns can be used, for 8 L/min six columns while for 10 L/mineight columns. In the continuous node the given throughput streamcan be processed without storage, i.e., in 3-columns system twocolumns are always in the saturation mode, in 6-column systemfour columns while in 8-column system five columns that areprocessing required stream of wastewater.

For a periodic node a part of the throughput has to be stored ina buffer tank and can be processed in a next cycle. In the examplebeing studied the given throughput can be is processed withoutstorages only in cycles with even numbers. For cycles with oddnumbers the throughput delivered into the node is in an excesswith respect the column capacity and has to be partly stored (e.g.,the throughput 4 L/min can be split into the three columnsworking parallel into the amount of ca 1.33 L/min per column,which can be processed within the saturation period making ca.62% of the total cycle time that gives ca. 2.5 L/min of effective feedflowrate for each odd cycle). The amount of feed stored duringnon-productive period of the cycle can be consumed in the next(even) cycle with maximal productivity.

It is obvious that the operation of storing reduces the effectivethroughput of the system. The difference of productivity betweenthe periodic and optimized continuous node is demonstrated forthe system without recycling in Table 3.

Similar results can be achieved for the columns operating in asetup involving recycling (not shown here).

As it can be observed, the advantage of the continuous systemsenhances with increase of the column number (see Table 3).

It should be noted that for the simulations presented an idealion-exchange system was assumed; no changes of bed propertiesprogressing during a long-time operation was assumed. In a realsystem a gradual loss of the loading capacity due to the bedcontamination can often be observed. If the isotherm coefficientsare changing from cycle to cycle in a systematic manner, theirvalues could be correlated with the cycle number. Implementation

Table 3Performance of different continuous multicolumn setups.

40(L/min)

80(L/min)

100(L/min)

OF, optimized continuous node 3.39 6.78 9.12

OF, periodic node/periodic throughput 3.42 6.84 9.12

OF, periodic node/continuous throughput 2.74 5.48 7.31

of such additional empirical correlations into the dynamic modeland the optimization procedure is straightforward. In such a casethe operating parameters can be periodically adjusted accordingto the predicted changes of the bed properties and the process canbe interrupted to discard the adsorbent bed as it approachessaturation with the contaminant. If an unpredictable bed destruc-tion is expected, the process controlling has to be used based onthe monitoring of the concentration profiles and adjusting accord-ingly the operating variables. The procedure of the processmodeling and optimization developed in this work could be usefulfor the process design also in this case. However, a detailedanalysis of this problem is outside the scope of this study.

5. Conclusions

A design procedure of the continuous ion exchange process forthe wastewater treatment has been proposed. The node for thewastewater treatment consisted of a multicolumn setup arrangedin such a way that the time-invariant number of columns couldoperate in the productive mode (saturation). The operating cyclesof consecutive columns in the node were shifted in time; properadjustment of the shift time assured continuity of the operation.

For the process design a model of the process dynamic wasused, i.e., the LDF model, which was incorporated into theoptimization procedure based on the differential evolutionmethod.

The process conditions were optimized subject to the con-straint of the pollutant concentration in the output water streamfor the periodic as well as continuous system.

The best results in terms of the process performance wereachieved in case of optimization of the operating conditions forthe columns operating jointly in the purification node.

The optimization results indicated that continuous process cansignificantly outperform the periodic operation.

Additionally, the possibility of the improvement of the processproductivity was analyzed for the flowsheet scheme involvingrecycling of the exhausted post-regenerating stream. Introducingthe regenerant recycling resulted in reduction of the consumptionof purified water in the regeneration mode and increased theprocess performance.

The procedure of the process design suggested in this studywas developed for an ideal ion-exchange system for whichgradual changes of bed properties were neglected. However, afterproper adjustments, it can potentially be used for real systems.

Nomenclature

C concentrations in the mobile phase (mol/L)DL dispersion coefficient (m2/s)Dpeff effective coefficients of diffusion in macropores (m2/s)Dseff effective coefficients of diffusion in micropores (m2/s)keff effective interparticle mass transport coefficient (m/s)km lumped mass transport coefficient (1/s)K isotherm coefficient (dimensionless)L column length (m)N number of time unitsOF objective function (mol/(Lmin))Pr productivityq solid phase concentration (mol/Lsolid)qn solid phase concentration in equilibrium with the liquid

phase (mol/Lsolid)Q volumetric flow rate (L/min)u superficial velocity (m/s)V column volume (m3)

R. Bochenek et al. / Chemical Engineering Science 66 (2011) 6209–6219 6219

x axial coordinate (m)z ion charge

Greek letters

g activity coefficientG exchange capacity (mol/Lsolid)ee external porosityep internal porosityet total porosity

Subscripts

c counter-ionsco co-ionsp eluite (pollutant) ionr regenerant

Superscripts

0 initial conditionsin the column inletk stage indexF feedm mobile phaseout column outletrec recyclings solid phase

Acknowledgment

The financial support of Polish Scientific Committee within thegrant no. N N209 033538 is greatly acknowledged.

References

Agarwal, A., Biegler, L.T., Zitney, S.E., 2010. A superstructure-based optimalsynthesis of PSA cycles for post-combustion CO2 capture. AIChE J. 56 (7),1813–1828.

Antos, D., Kaczmarski, K., Piatkowski, W., Seidel-Morgenstern, A., 2003. Concen-tration dependence of lumped mass transfer coefficients—linear vs. nonlinearchromatography and isocratic vs. gradient operation. J. Chromatogr. A. 1006,61.

Babu, B.V., Pallavi, G.C., Syed Mubeen, J.H., 2005. Multiobjective differentialevolution (MODE) for optimization of adiabatic styrene reactor. Chem. Eng.Sci. 60 (17), 4822–4837.

Babu, B.V., Angira, R., 2006. Modified differential evolution (MDE) for optimizationof nonlinear chemical processes. Comput. Chem. Eng. 30, 989–1002.

Blanchard, G., Maunaye, M., Martin, G., 1984. Removal of heavy metals fromwaters by means of natural zeolites. Water Res. 18, 1501–1507.

Bochenek, R., Jezowski, J., Bartman, S., 2007. Optimization of heat exchangernetwork with fixed topology by genetic algorithms. Chem. Eng. Trans. 12,195–200.

Castel, C., Schweizer, M., Simonnot, M.O., Sardin, M., 2000. Selective removal offuoride ions by a two-way ion-exchange cyclic process. Chem. Eng. Sci. 55,3341–3352.

Cruz, P., Magalh~aes, F.D., Mendes, A., 2005. On the optimization of cyclicadsorption separation processes. AIChE J. 51 (5), 1377–1395.

Cruz, P., Santos, J.C., Magalhaes, F.D., Mendes, A., 2003. Cyclic adsorption separa-tion processes: analysis strategy and optimization procedure. Chem. Eng. Sci.58 (14), 3143–3158.

Dabrowski, A., Hubick, Z., Podkoscielny, P., Rubens, E., 2004. Selective removal ofthe heavy metal ions from waters and industrial wastewaters by ion-exchangemethod. Chemosphere 56, 91–106.

Deb, K., 2001. Multi-objective Optimization Using Evolutionary Algorithms. JohnWiley, Singapore.

Ernest, M.V., Bibler, J.P., Whitley, R.D., Linda- Wang, N.H., 1997. Development of acarousel ion-exchange process for removal of Cesium-137 from alkalinenuclear waste. Ind. Eng. Chem. Res. 36, 2775–2788.

Flores, V., Cabassud, C., 1999. A hybrid membrane process for Cu(II) removal fromindustrial wastewater, comparison with a conventional process system.Desalination 126, 101–108.

Gorka, A., Bochenek, R., Warcho", J., Kaczmarski, K., Antos, D., 2007. Ion exchangekinetics in removal of small ions. effect of salt concentration on inter- andintraparticle diffusion. Chem. Eng. Sci. 63, 637.

Gunn, D., 1987. Axial and radial dispersion in fixed beds. Chem. Eng. Sci. 42,363–373.

Hritzko, B.J., Walker, D.D., Linda- Wang, N.H., 2000. Design of a carousel processfor cesium removal using crystalline silicotitanate. AIChE J. 46 (3), 552–564.

Huckman, M.E., Latheef, I.M., Anthony, R.G., 2001. Designing a commercial ion-exchange carousel to treat DOE wastes using CST granules. AIChE J. 47 (6),1425–1431.

Jiang, L., Fox, V.G., Biegler, L.T., 2004. Simulation and optimal design of multiple-bed pressure swing adsorption systems. AIChE J. 50 (11), 2904–2917.

Jezowski, J., Bochenek, R., Ziomek, G., 2005. Random search optimization approachfor highly multi-modal nonlinear problems. Adv. Eng. Software 36 (8),504–517.

Jezowski, J., Bochenek, R., Poplewski, G., 2007. On application of stochasticoptimization techniques to designing heat exchanger- and water networks.Chem. Eng. Process.: Process Intensification 46, 1160–1174.

Kaczmarski, K., Antos, D., Sajonz, H., Sajonz, P., Guiochon, G., 2001. Comparativemodeling of breakthrough curves of bovine serum albumin in anion-exchangechromatography. J. Chromatogr. A. 925, 1.

Lapidus, L., Amundson, N.L., 1952. Mathematics of adsorption in beds. the effect oflongitudinal diffusion in ion exchange and chromatographic column. J. Phys.Chem. 56, 984.

Lewus, R.K., Hakan Altan, F., Carta, G., 1998. Protein adsorption and desorption ongel-filled rigid particles for ion exchange. Ind. Eng. Chem. Res. 37, 1079–1087.

Michalewicz, Z., Fogel, D.B., 2002. How to Solve it: Modern Heuristics. SpringerVerlag, Berlin.

Nilchan, S., Pantelides, C.C., 1998. On the optimisation of periodic adsorptionprocesses. Adsorption 4 (2), 113–147.

Onwubolu, G.C., Babu, B.V., 2004. New Optimization Techniques in Engineering.Springer-Verlag, Heidelberg.

Pintar, A., Batista, J., Levec, J., 2001. Integrated ion exchange/catalytic process forefficient removal of nitrates from drinking water. Chem. Eng. Sci. 56,1551–1559.

Price, K.V., Storn, R.M., Lampinen, J.A., 2005. Differential Evolution—A PracticalApproach to Global Optimization. Springer Verlag, Berlin.

Rochette, F., 2006. Novel technology: fresh approach to countercurrent ionexchange. Filtration and Separation 43 (7), 18–19.

Ruthven, D.M., 1984. Principles of Adsorption and Adsorption Process. John Willey,New York.

Softening, Y.S., Grevillot, G., Tondeur, D., 1990. Modelling and optimization of thecyclic regime of an ion-exchange process for sugar juice. Chem. Eng. J. 43,B53–B66.

Spiro, D.A., 2009. Ion exchange resins: a retrospective from industrial andengineering chemistry research. Ind. Eng. Chem. Res. 48, 388–398.

Srinivas, M., Rangaiah, G.P., 2007. Differential evolution with tabu list for solvingnon-linear and mixed-integer non-linear programming problems. Ind. Eng.Chem. Res. 46, 7126–7135.

Storn, R., Price, K., 1997. Differential evolution—a simple and efficient heuristic forglobal optimization over continuous spaces. J. Global Opt. 11, 341–359.

Sun, Y., Grevillot, G., Tondeur, D., 1990. Modelling and optimization of the cyclicregime of an ion-exchange process for sugar juice softening. Chem. Eng. J. 43,53–66.

Valverde, J.L., De Lucas, A., Carmona, M., Perez, J.P., Gonzalez, M., Rodrıguez, J.F.,2006. Minimizing the environmental impact of the regeneration process of anion exchange bed charged with transition metals. Sep. Purif. Technol. 49,167–173.

Wilson, E.J., Geankoplis, C.J., 1966. Liquid mass transfer at very low Reynoldsnumber in packed beds. Ind. Eng. Chem. Fund. 5, 9–14.