exergy analysis of chromatographic separations in a fixed-bed column

SEPARATIONS

Exergy Analysis of Chromatographic Separations in a Fixed-BedColumn

M. L. O. Maia, M. Ottens, and L. A. M. van der Wielen*

Department of Biotechnology, Delft University of Technology, Julianalaan 67 2628 BC,Delft, The Netherlands

In this work, we evaluate the use of exergy analysis on a single chromatographic column. Asensitivity analysis was done to unravel the relation between several parameters that mightinfluence the quality of separation and the associated exergy loss. From the resulting analysiswe concluded that the division of the exergy content in its components is important in revealingthe nature of process irreversibilities. In addition, results show that the dilution problem isadequately described by the exergy change of mixing. All in all, results have shown that aminimum exergy loss occurs for a high production rate while keeping purity requirementsconstant. Consequently, exergy loss can be used as a tool for chromatographic separationoptimization.

1. Introduction

Chromatography is a powerful separation techniqueused in pharmaceutical, food, and bulk chemical indus-tries. The separation of xylene isomers and fructose fromhigh fructose corn syrups are examples of the large-scaleapplication of chromatography in bulk chemicals pro-duction, whereas resolution of enantiomers and recoveryof amino acids, antibiotics, and proteins from complexbiological streams are increasing in importance in finechemicals manufacturing. In all cases, however, thetotal manufacturing costs and environmental impact ofthe chromatographic processes must be minimized.Therefore, large-scale chromatographic operations areincreasingly performed in so-called simulated movingbed (SMB) systems, where equipment size, resin inven-tory, and eluent consumption is often considerablyreduced relative to fixed-bed (FB) operation.1 The maincost contributors in chromatographic processes are,apart from equipment and resin costs, operational costssuch as net eluent consumption, recovery of the productsfrom the solvent streams, regeneration of the eluent,and energy costs related to mechanical work andthermal operations.

Optimization of any chromatographic technology is acomplex matter because many parameters affect theperformance of the system significantly. Therefore,general rules for designing and optimizing chromato-graphic processes are difficult to establish.1 It is acommon practice to group all the parameters in dimen-sionless numbers to reduce the number of variables andsimulations needed. Felinger and Guiochon2 proposedthe use of a hybrid cost function that considers the

importance of solvent use and production rate at a givenweight factor. However, no price specifications arepresented. Instead, production rate is maximized bysimultaneously changing loading factor and number ofplates (efficiency). The production costs are approxi-mately reflected using a weight that is inversely pro-portional to the ratio of the capital costs and operatingcosts. In another contribution, Felinger and Guiochon3

use the product of the production rate and recovery yieldas the objective function. They claim that in this caseboth productivity and recovery yield are optimized.Moreover, this objective function is used in the com-parison of different modes of chromatographic separa-tion.4 A detailed cost optimization can be found inJupke.5 Minimizing a cost objective function, however,inevitably has the drawback of depending on economicparameters that may be arbitrary and/or fluctuating intime.

Alternatively, optimization procedures based on ther-modynamic concepts provide an understanding of theunderlying physical phenomena in a process, and thuscan provide physical reasons for process inefficiencies.Exergy analysis is one of these optimization procedures.This sort of analysis has become increasingly importantgiven the considerable energy requirements of theprocess industry. The efficient use of the energy can beaccounted for by combining the First and Second Lawof Thermodynamics, that is, using the exergy concept.The identification of the optimal thermal condition ofthe feed of distillation columns6 is an example of theapplication of the exergy concept. Smith7 applied exergyanalysis for the determination of the optimum pressurefor supercritical carbon dioxide extraction. In addition,pressure swing adsorption (PSA) systems studied byBarnerjee,8 where the compressor work is the mainconcern, were optimized using exergy analysis. A reviewon the opportunities and limitations of the use of exergy

* To whom correspondence should be addressed.Tel.: +31-15-2782332. Fax: +31-15-2782355. E-mail:[email protected].

3183Ind. Eng. Chem. Res. 2004, 43, 3183-3193

10.1021/ie030603u CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 05/11/2004

analysis on both process synthesis and optimization canbe found elsewhere.9

The goal of exergy analysis is to minimize the exergyloss that is closely related to process’ irreversibilitiesand thus arises in any real process. Concerning chro-matography, sources of irreversibility are related to heateffects, pressure drop, mixing of solutes and eluent, andmass transfer between two phases due to finite drivingforces. These sources combined contribute to the exergyloss of this system. The thermodynamic price for theseirreversibilities is paid in energy for pumping of fluidphase, eluent use, product dilution, and thus down-stream separation costs. Bailly10 (1984) has proved thatthe reduction of entropy generation during a separationin a single chromatography column parallels the reduc-tion of the solvent consumption. Therefore, an exergyanalysis may be of use when designing and/or optimiz-ing chromatographic separations.

The optimization and design of simulated moving bedsystems is of particular importance. So far, however, noopen literature concerning the use of exergy concept infixed and simulated moving bed chromatographic sys-tems seems available. Due to the fact that SMB systemsare constituted of a number of interconnected FBchromatographic columns, the first step toward theunderstanding of the exergy analysis of an SMB systemis to evaluate the use of exergy analysis for one singlechromatographic column.

The aim of this work is to provide a methodology toperform exergy analysis on a fixed-bed chromatographiccolumn. A sensitivity analysis is used to understand therelation between several parameters that might influ-ence the quality of separation and the associated exergyloss. The separation of a binary ideal mixture was usedas a case study.

2. Exergy Analysis

An exergy balance (eq 1) for a steady flow in an opensystem is obtained by combining the First and SecondLaw of Thermodynamics.11

where

represents the exergy transfer due to heat flow (Q) fromthe system.12 The subscript “0” indicates the referencestate, which for exergy analysis is imposed by thesomewhat arbitrary environment.11 In this work, thereference temperature and pressure are, respectively,298.15 K and 1.01 bar. W is the exergy transfer due toshaft work (kJ/s) performed by the system. Finally, thelast term in eq 1, ∆Exloss (kJ/s) represents exergy lossdue to irreversibilities within the system.

Concerning the material flows, the exergy transfer isgiven by

with n being the molar flow rate (mol/s) and exout andexin (kJ/mol) the specific exergy of the material streams

outflowing and entering the systems boundaries, re-spectively. The latter is given by

Equation 1d can be divided into three terms (eq 2),those being chemical, physical, and mixing exergy.

Hinderink13 et al. present a detailed discussion aboutthe definition of each term, together with the compu-tational procedure. For separation processes, the chemi-cal exergy can be neglected because no chemical trans-formation occurs and the same components are involvedfor both inflowing and outflowing streams. Thus, onlythe mixing and physical terms of the total exergycontent are relevant.

According to Hinderink et al.,13 physical exergy of amulticomponent stream can be computed using purecomponents enthalpies and entropies. Moreover, whenno phase transitions occur on bringing multicomponentmaterial streams to the reference conditions, its exergycontent is given by eq 3.

where the subscript “actual” refers to the actual T andP of the mixture and “0” the conditions at the referencestate.

The mixing exergy is calculated using the enthalpyand entropy change of mixing.13

3. Fixed-Bed Adsorption Model

Chromatography is a separation technique where amulticomponent feed is pulsed into a column packedwith a suitable sorbent. The degree of separationdepends on the column length and the differences incomponent affinity for the sorbent. Henley and Seader14

give the convective-dispersion model (eq 5) that de-scribes the separation.

with ci and qi being the concentration of species i in theliquid and solid phase, respectively, z the axial coordi-nate, t the time, and ε the bed porosity. The first termaccounts for the axial dispersion with dispersion coef-ficient DL, the second allows for the axial variation ofthe fluid velocity (convective term), the third is theaccumulation of the solute in the liquid, and the fourthis the accumulation in the sorbent. The concentrationof the liquid and solid are coupled via a mass transferrelation:

Equation 6 describes the adsorption rate and is a partialdifferential equation when mass transfer is limited bypore diffusion.

In this contribution, we consider the exergy loss thatoccurs due to the following irreversibilities: mixing of

Exin ) Exout + ExQ + W + ∆Exloss (1)

ExQ ) ∑Q*(Tr - T0)

Tr(1a)

Exout ) ∑n*exout (1b)

Exin ) ∑n*exin (1c)

ex ) (h - h0) - T0(s - s0) (1d)

ex ) exchem + exphys + ∆mixex (2)

exphys ) ∆actualf0(∑i

xihi - T0∑i

xiSi) (3)

∆mixex ) ∆mixH - T0∆mixS (4)

-DL

∂2ci

∂z2+

∂(uci)∂z

+∂ci

∂t+

(1 - ε)ε

∂qji

∂t) 0 (5)

∂qji

∂t) f(qji,ci) (6)

3184 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004

eluent and solutes, finite driving force for mass transferbetween the phases, and pressure drop. For this pur-pose, we use a simpler model, which assumes plug flowand neglects axial dispersion effects. Furthermore, themass transfer is accounted by the common linear drivingforce relation (LDF).15 The overall mass transfer coef-ficient is divided into two parts: external mass transferfrom the bulk liquid to solid surface and internal porediffusion within the particle itself. The model used isthen given by

with ke being the film mass transfer coefficient, kintrathe intraparticle mass transfer coefficient, k the overallmass transfer coefficient, a the interfacial area, and qi*the solid phase equilibrium concentration. The relationbetween the concentration of the stationary phase andmobile phase at equilibrium is described by a suitableisotherm, which is often in liquid chromatography themulticomponent Langmuir equation.1

The set of partial differential equations are solved usingspatial discretization and fourth-order Runge-Kuttamethod for integration in time. Moreover, the pressureeffects are accounted by using the Ergun relation.

4. Exergy Balance on Fixed-Bed ColumnsMethodology

In this work, the overall exergy balance of the systemconsiders the exergy loss during one isocratic chromato-graphic cycle (Figure 1). The initial system is filled witheluent, which is pumped through the column, and the

sorbent is free of solute. The cycle starts when a pulseof the mixture to be separated replaces the eluentstream at the same volumetric flow rate. After the pulse,the eluent stream is resumed to the column until theend of the cycle. The entire cycle lasts for a period oftime called elution time (telution), which is large enoughto ensure that all solutes leave the column. At the endof this time interval, therefore, the system is back toits initial state. Therefore, its exergy content is un-changed and eq 1 can be applied. The exergy lossoccurring on each cycle is then divided by the totalamount of product that can be obtained with therequired purity.

The general procedure to perform the exergy balanceon a fixed-bed chromatographic column is describedbelow:

1. Given pulse volume, duration (tpulse), flow rates, andcomposition, use the convective-dispersion model witha suitable isotherm (eqs 7 and 8) to compute the productcomposition profile.

2. Compute the specific physical and mixing exergycontent of the feed stream using eqs 3 and 4, respec-tively. During the entire cycle the feed stream is in factthe sum of two streams: pulse and eluent. However,these two streams do not exist simultaneously. Equa-tions 9 and 10 represent the exergy content of the feedstream computed for the entire cycle duration. More-over, note that the eluent stream contains a single purecomponent and, therefore, the mixing term is null afterthe pulse.

3. Repeat step 2 for the product streams. In this case,the dynamic nature of the process causes the specificexergy content of the process streams to vary with time.Equation 12 describes the mixing exergy content of theproduct stream.

Figure 1. Chromatographic separation of binary pulse on FB. In case 1, the boundary for exergy analysis considers constant temperatureand pressure. In case 2, the system boundary is extended to include the pump.

u∂ci

∂z+

∂ci

∂t+

(1 - ε)ε

∂qji

∂t) 0 (7a)

∂qji

∂t) MTi (7b)

MTi ) ka(qi/ - qi) (7c)

1k

) 1ke

+ 1kintraεintra

(7d)

qi* ) qmax

Kici

1 + ∑j)1

nc

Kjcj

(8)Exphys

feed ) (∫t)0

t)tpulsenpulse(t) dt) * exphyspulse +

(∫t)tpulse

t)telution neluent(t) dt) * exphyseluent (9)

∆mixExfeed ) (∫t)0

t)tpulsenpulse(t) dt) * ∆mixex (10)

Exprodphys ) ∫t)0

t)telution(n*ex(t)) dt (11)

∆mixExprod ) -R‚T0‚∑j

xj(t)ln(γjxj(t)) (12)

Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 3185

4. Compute overall exergy content of the processstreams using eq 2.

5. For the particular case of chromatography, theexergy transfer due to heat flow is neglected becausethe system temperature is often too close to the refer-ence temperature. Due to the equivalence of exergyand work, the exergy transfer due to shaft work isgiven by the pump work (eq 13).

where φ is the volumetric flow rate. Pressure drop (∆P)is computed using the Ergun correlation.

6. Compute the exergy loss using eq 1.

5. Results

To illustrate the exergy analysis on batch chroma-tography, we use the separation of a binary mixture thatcan be considered a thermodynamically ideal solution.The relative concentration of the components is constantin all simulations. The details concerning column di-mensions and adsorption data16 are presented in Table1.

Several simulations were performed to investigate thecontribution to the exergy loss of parameters such asflow rates, pulse volume, and particle diameter. Resultsare presented as a function of dimensionless parameterssuch as reduced time (τ), reduced velocity (ν),17 andmodified Stanton number (St)5 given by eq 14.

For the sake of an easier understanding and simplic-ity, exergy analysis is applied to two different condi-tions. First, we consider the system to be at constanttemperature and pressure, here called case 1. In thiscase, the exergy transfer due to heat and shaft work isnot applicable. Thus, the use of eq 1 leads to theconclusion that the exergy loss is only due to change in

composition (product dilution) and is given by eq 15. Forcase 1, we have a mixing exergy loss.

The second condition accounts for the fact that inliquid chromatography both solvent and pulse streamshave to be pumped in the column. This process conditionis here called case 2. Mixing exergy loss alone does notcover energy degradation throughout the bed due topressure drop. A realistic optimization of a chromato-graphic separation process should include this problem,though. From an exergy analysis point of view, theevaluation of physical exergy content of the streams andexergy transfer due to shaft work must be used in orderto be able to deal with this problem (case 2). Equation16 describes the overall exergy balance that now in-cludes the exergy transfer due to shaft work.

In our particular case, both inflowing (in) and out-flowing (out) streams are at reference pressure P0.Therefore, the pump work is equivalent to the physicalpart of the total exergy loss, which occurs within theprocess boundary considered. Physical exergy contentof a material stream is, of course, also dependent on thetemperature. For the presented case study, the separa-tion is always carried out isothermally and thus thetemperature effect cancels out. From now on, we dividethe total exergy loss in two parts, namely, mixing exergyloss and physical exergy loss.

For batch chromatography a cut strategy (Figure 2)is needed to determine the fractions collection. Accord-ingly, the exergy output and the exergy loss depend onthe strategy used. Of course, for optimization problems,these four cut times are parameters that should beadjusted to obtain maximum productivity, yield, etc. Inthis contribution, however, two different criteria wereused to determine the four cut times (Figure 2). The first(t1) and fourth (t4) cut times are found considering thatan arbitrarily chosen amount (1% of the injected vol-ume) of the weaker and stronger binding components,respectively, can be wasted. The second (t2) and third(t3) cut times are found according to the purity specifica-tion for both products 1 and 2 (Figure 2). In this work,the product purity required is 98% for both components.

As a result of the cut strategy, two useful productstreams can be obtained as long as purity requirementsare achieved. The fraction of the outflowing stream,which corresponds to the peaks overlap, is called here

Table 1

(a) Column Characteristics

ratio length/ internal diameter (Lc/Di) 19external void fraction 0.42internal void fraction (macroporosity) 0.2solid bulk density 1.4 g/cm3

(b) Diffusion Coefficients and Parameters for the LangmuirIsotherm (Saturation Capacity and Equilibrium Ratios) at 57 °C

Dm × 105

(cm2/s)qmax × 103

(mol/g)K

(L/mol)ke × 104

(cm/s)ki × 104

(cm/s)

m-xylene 3.16 1.75 4.2 2.12 1.13p-xylene 3.16 1.75 24.0 2.12 1.13toluene 3.61 1.75 12.0 2.32 1.30

(c) Feed and Eluent Concentration

concentration(vol %)

feed 50% m-xylene50% p-xylene

eluent pure toluene

W ) φ∆P (13)

τ ) t‚uL

(14a)

ν )dp‚uDm

(14b)

Steff,i ) koverall,i‚6dp

‚Lu

(14c)

Figure 2. Chromatogram for the separation of a general binarymixture.

∆mixExloss ) ∆mixExin - ∆mixExout (15)

∆Exloss ) ∆mixExin - ∆mixExout + W (16)


waste stream (Figure 2). Concerning exergy analysis,the exergy that is carried away with the outflowingstreams can also be divided into two parts: exergy ofthe useful products and exergy of waste products. Thelatter represents the undesired exergy loss while theformer is here called desired exergy loss. Note that thetwo losses are due to internal process irreversibilities.

Apart from the exergy loss, results concerning productpurity and recovery along with solvent usage arepresented. In the authors mind, this is a way to linkthe exergy loss to parameters that will ultimately havean impact on process costs. In other words, exergyanalysis indicates potential downstream processingcosts.

According to the procedure shown in item 4, theelution time (telution) is held constant regardless of theinput variable that was changed. To account correctlyfor the eluent used, therefore, one should not considerthe fraction of solvent consumed from the cut time t4 totelution (Figure 2). This fraction is here called unusedsolvent (Vunused) and is given by eq 17.

5.1. Particle Size. Larger particles are typical forlarge-scale adsorption processes, whereas the smallerare characteristic for analytical HPLC systems. On onehand, small particles allow for higher mass transfercoefficient and thus less dilution is possibly achieved.On the other hand, mechanical energy consumption(pump work) increases due to a higher pressure drop.In this item, an analysis based on Stanton numbers isperformed to evaluate the impact of mass transfereffects on the exergy loss. Only the particle size waschanged in the simulations performed here. All othervariables such as volumetric flow rate and pulse volumeare kept constant.

The chromatograms (Figure 3), plotted with reducedtime, were obtained for two different particle sizes. InFigure 3A the peaks are much sharper and highconcentrations for both components are achieved. Inaddition, hardly any overlapping can be seen in Figure3A. Such behavior is solely due to the fact that theparticles used in Figure 3B have a radius that isapproximately 43 times larger than those used in Figure3A.

In either case, an exergy loss is expected and thereason relies on the fact that the exergy content of thepulse (equimolar binary mixture) is decreased whenmixed with the solvent. The average concentration ofthe products is lower than its initial value (C/CF < 1.0).

The same observation holds for the solvent, which isinitially a pure component.

5.1.1. Case 1: Constant Temperature and Pres-sure. For the analysis here consider the process bound-ary shown in Figure 1A. In this case, the exergy transferthrough process boundary is due to material streamsand the exergy loss is only due to changes in composi-tion, that is, mixing exergy loss (eq 15).

Figure 4 shows that decreasing Stanton number leadsto an increasing overall mixing exergy loss. Suchbehavior can be explained by the fact that peak overlapand band broadening are expected to be higher in therange of small Stanton numbers.

One limitation of analyzing the overall mixing exergyloss is that no distinction is made between the dilutionof products in the solvent and the lack of separation thatoccurs for overlapping peaks. A further division of themixing exergy loss in its two parts can help us toovercome this problem.

On the basis of the cut strategy (Figure 2), the mixingexergy loss comprises the desired exergy loss, associatedwith useful products, and the second is the undesiredexergy loss, which indicates wasted products. Thedesired exergy loss is unavoidable, even for a completeseparation, and inherent to chromatographic separation.However, it will be larger for broad peaks and lower forsharp peaks. The obvious economic penalty for thisdilution is paid in the downstream process to recoverthe products from the eluent.

The second contribution to the overall mixing exergyloss originates from the lack of separation and isstrongly related to the cut strategy used. For theseparation of a binary mixture, for example, the cutstrategy used here considers that the peaks overlap isa waste stream (between point 2 and 3 in Figure 2). Thisstream leads to low recoveries even when purity re-quirements are achieved, and could be recycled. Norecycling is, however, considered in this approach. Theexergy content of this stream is considered as a loss asit means that for this particular cycle the separationwas not achieved and thus no useful work was per-formed.

For most of the range of Stanton numbers presentedin Figure 4, hardly any change of the desired exergyloss can be observed. However, for the smallest valuesthere is a trend for this loss to decrease. The reason isthat the impact of mass transfer, which causes bandbroadening, has become stronger and therefore theproducts are highly diluted. Eventually the dilution issuch that the products (products 1 and 2) are almostpure eluent, causing the exergy loss to decrease. Con-

Figure 3. Chromatograms for different Stanton number obtainedwhen particle sizes are changed: (A) St ) 3.74 (HPLC); (B) St )0.18 (LC). Weaker binding component is represented by points (×)and stronger binding component is represented by a solid line.

Vunused ) φ*(telution - t4) (17)

Figure 4. Overall mixing exergy loss, together with its two terms,plotted against Stanton number (lines and points): (×) desiredexergy loss (useful products), (b) undesired exergy loss (wastedproducts), and (4) overall mixing exergy loss.


cerning the undesired exergy loss (waste products), anopposite trend in its behavior can be observed, due tothe increasing peaks overlap. This means that thecontribution of the lack of separation tends to be higherin the region of bigger particles with low Stantonnumbers. However, the dilution problem is reflected inboth terms of the overall mixing exergy loss.

In this work, no cost calculation is presented. How-ever, one reasonable way to show the impact of highmixing exergy loss on production costs is to plot itagainst product recovery and purity level achieved whenusing different particle sizes.

Figure 5 shows that low overall mixing exergy lossmeans high total recovery for a purity level of 98% forboth components. Conversely, product recovery de-creases dramatically (lower than 30%) when mixingexergy loss increases. Furthermore, it was not possibleto achieve the purity specification of the weaker bindingcomponent within this region.

Summarizing, mixing exergy loss is directly relatedto product dilution and thus its minimization can leadto more concentrated products as well as high recoveryrate while attending purity specification.

5.1.2. Case 2: Considering ∆P. Figure 6 shows thetotal, physical, and mixing part of the exergy loss forseveral particle sizes recalculated as Stanton numbers.The former is the summation of the two contributionsfor exergy loss, namely, mixing and physical. For mostof the range used here, mixing exergy loss has adominant impact on the total loss. As Stanton numbersdecrease, physical and mixing exergy loss shows op-

posite behavior. It can be seen in Figure 6 that thisphysical exergy loss seems to present a minimum.Although larger particle sizes allow for lower pressuredrop, the decrease in the production is such that thephysical exergy loss, which was here divided by theamount produced, increases. From this point on, onlyone product achieves purity specification and then thetotal production is dramatically decreased. Neverthe-less, for optimization purpose the total exergy loss isthe one to be used.

Adding both contributions to the exergy loss, aparticle size exists that minimizes the total exergy loss(Figure 6). In other words, larger particles allow forlower physical exergy loss while increasing productdilution, while a smaller dp allows low dilution but atthe expense of high physical exergy loss.

5.2. Pulse Volume. Pulse volume is an operatingparameter that should be adjusted when optimizing/designing chromatographic separation carried out onFB. It is important for exergy analysis, and for the sakeof a fair comparison, the input exergy to be the same inall simulations. For this reason, we consider a fixed totalvolume to be separated and then a number of cycles,with different pulse volumes, are used for the separation(Table 2).

No recycle of both eluent and waste streams, however,was accounted for. In addition, the pulse volume usedcan vary on each cycle. In our case, the total amount offeed to be separated corresponds to 37.3% of the totalvoid volume of the column. Therefore, if we start witha pulse volume of 28%, a second pulse of 9.3% will berequired.

Concerning exergy calculations, one should take intoaccount the number of cycles when computing theexergy loss. For mixing exergy loss, for instance, eq 15is rewritten as below:

Equation 18 describes the exergy loss, which occurs forthe separation of the total amount of feed. In this sense,the exergy content of the feed is constant. Conversely,the exergy content of the outflowing stream is depend-ent on both the pulse volume and the number of cycles.

The chromatograms of the two first and two last pulsevolumes used here (Table 2) are shown in Figure 7A,B.For Gaussian distribution (Figure 7A), obtained for asmall sample size, all solutes migrate with the samerate and the retention time is independent of the samplesize. However, increasing the pulse volume (Figure 7B),we move to the region of nonlinear isotherms andsolutes retention time varies with the sample size.

5.2.1. Case 1: Constant Temperature and Pres-sure. An exergy balance at constant temperature andpressure (case 1, Figure 1) was performed to investigatethe influence of the amount injected in the column onthe mixing exergy loss. In Figure 8, results are pre-sented as total mixing exergy loss, undesired exergy loss(waste products), and desired exergy loss (useful prod-ucts).

It can be observed that total mixing exergy lossdecreases with increasing pulse volumes (Figure 8). To

Table 2. Number of Cycles Depending upon the Pulse Volume

Vpulse/V0 (%) 0.187 0.935 1.869 3.738 7.475 9.344 14.950 22.425 28.032 33.638 37.375

number of cycles 200 40 20 10 5 4 3 2 2 2 1

Figure 5. Overall mixing exergy loss plotted against productrecovery for 98% purity requirement (lines and points): ([) purityweaker binding, (0) purity stronger binding, and (4) total recovery.

Figure 6. Overall exergy loss (lines and points) caused by mass-transfer effects and pressure drop over the bed: (O) mixing exergyloss, (]) physical exergy loss, and (/) total exergy loss.

∆mixExloss ) ∆mixExin - ∑j)1

Ncycle

∆mixExout( j) (18)


understand this behavior, we have to analyze the twocomponents of this loss separately. First, it is clear thatthe total mixing exergy loss is much more stronglyinfluenced by the desired loss than by the undesired one.The chromatograms (Figure 7A,B) show not only thatthe useful products concentration is increasing forincreasing pulse volume but also that peak overlap isnot significant. In fact, the Stanton number (St ) 3.74)and reduced velocity (ν ) 7.9), used in all simulations,bring the separation to a zone where purity require-ments are possible to be achieved for all pulse volumesused.

Peak overlap is the major cause for decrease in therecovery. Figure 9 shows the recovery for 98% purity ofboth components when different pulse volumes are used.The total recovery means the total amount of the twoproducts obtained regarding the purity specification and

number of cycles needed. It can be seen that, for smallerpulse volume, the recovery is high. Also, the saturationof the column, which occurs for increasing pulse vol-umes, leads to a decrease in the recovery.

Solvent usage is presented in Figure 10. Of course,the number of cycles needed plays an important role. Itis particularly interesting to see that when two cyclesare needed (Table 2), the amount injected on each cycleis very different from one another. Actually, during thefirst cycle a large amount of feed is introduced into thecolumn, while at the second one, a much smaller amountis introduced. As a result, we see in Figure 10 that inthis range the amount of solvent is practically constant,but decreases when just one cycle is used.

We now have to focus our attention in the secondcontribution for the mixing exergy loss. This term, herecalled undesired exergy loss, is the exergy content ofthe waste stream (Figure 2) itself. For very small pulsevolumes that require several cycles to separate the totalamount, this exergy loss seems to reduce. At this rangeof pulse volume, the peak overlapping is not significant.Consequently, the production is practically constant(Figure 9). Therefore, the undesired exergy loss at thisregion is mainly influenced by the number of cycles.However, when the amount injected starts to decrease,the production due to saturation of the column (moreimpressive peaks overlapping), the undesired exergyloss starts to increase. Eventually, it seems that thisterm will lead the overall mixing exergy loss to alsoincrease.

For this particular case, overall mixing exergy lossfor smaller pulse volume is practically only due to theexergy of useful products. As the pulse volume increases,the loss due to the waste stream exergy has a muchstronger impact and eventually will dominate theoverall loss (Figure 8).

From Figure 8 one can conclude that the optimumpulse volume is the highest value. This result seems tobe in agreement with classical chromatographic analy-sis. Together with product recovery, solvent consump-tion is an important parameter when computing processcosts. The conclusion here is that this particular casebenefits from higher pulse volumes. It is may be possiblethat the impact on the process costs of decreasingrecovery is not so important as the decrease in solventusage.

5.2.2. Case 2: Considering ∆P. Another importantparameter to be optimized in batch chromatography isthe mechanical energy consumption (pump work). Inthis case, eqs 15 and 16 describe the overall exergybalance.

Figure 7. (A) Chromatogram for the separation of weaker binding(line and points) from stronger binding (lines) obtained for Vpulse/Vo: 0.93% (open spheres) and 1.8% (open triangles). (B) Chro-matogram for the separation of weaker binding (line and points)from stronger binding (lines) obtained for Vpulse/Vo: 33.6% (openspheres) and 37.4% (open triangles).

Figure 8. Exergy loss due to change in pulse volumes at constanttemperature and pressure (mixing exergy loss): total loss (4),desired loss (+), and undesired loss (0).

Figure 9. Total recovery for 98% purity of both products forseveral pulse volumes: purity stronger binding (4), purity weakerbinding (×), and total recovery (0).

Figure 10. Volume of solvent used per gram of product with thespecified purity.


As mentioned before, the pressure drop over the bed,that is, a function of flow rate, particle size, etc., andnot of the pulse volume, contributes to the total exergyloss. Of course, the physical exergy loss per cycle is thesame. There is a clear trend in this part of the exergyloss to decrease as the number of cycles decreases(increasing pulse volume). However, when the amountinjected requires the same cycle number (Table 1), thephysical exergy loss is mainly a function of the amountproduced (Figure 11). It is expected, then, that thisexergy loss will increase for very small production,which occurs for a saturated column (high pulse vol-ume).

Summarizing, the pressure drop for this particularparameter is the same in all simulations. However, thebehavior of the physical exergy loss is the compromisebetween number of cycles and production.

5.3. Flow Rate. Together with pulse volume, flowrate is also one of the operating parameters that has tobe adjusted when optimizing batch chromatography.Higher flow rates allow for increasing throughput. Onthe other hand, the equilibrium between solid andmobile phase is not instantaneous and thus the solutemolecules are carried further down the column thanwould be expected in equilibrium conditions. The effectof nonequilibrium mass transfer becomes worse whenthe flow rate increases because less time is availablefor the equilibrium to be approached. The naturalconsequence of these effects is product dilution andtherefore mixing exergy loss occurs.

5.3.1. Case 1: Constant Temperature and Pres-sure. Several simulations were performed using a widerange of reduced velocities (Figure 12). In this section,we used two particle diameters and varied the flow ratesfor both cases.

Mixing exergy loss (lines and triangles curve) in-creases with increasing reduced velocity as expected.

However, a close look in Figure 12 shows that thisincrease is not significantly high. To further understandthe reason for total mixing exergy loss, the two compo-nents of this loss are also presented.

First, we consider the desired exergy loss. The dilutionof the useful products does no significantly differ whenreduced velocity is increased. For this particular case,the mass transfer coefficient is high due to the smallparticle size used. Chromatograms in Figure 13 showsharp and well-resolved peaks can be obtained for thesmallest and highest reduced velocity used here. There-fore, the desired exergy loss is not only the mostimportant contributor to the total loss but also practi-cally constant over the range here used.

The main effect of the increasing reduced velocity isthat the peaks are more overlapping and thus the wastestream exergy loss also increases. However, it is worthnoticing that for the range of reduced velocities usedthe impact of this second contribution is always lowerthan the first one. In addition, its increase is notsignificantly high as well. Again this behavior mightoccur due to the high mass transfer coefficient.

An opposite trend, however, is found when masstransfer effects are increased by using larger particles.In this case, for the same range of flow rate used in theprevious example the reduced velocities are muchlarger. The impact of changing reduced velocity (Figure14) on total mixing exergy loss is also much larger. It isimportant to address here that for reduced velocityhigher than 160 only the stronger biding component isrecovered with specified purity but at very low produc-

Figure 11. Exergy loss due to pressure drop.

Figure 12. Mixing exergy loss (lines and points) obtained forseveral reduced velocities (flow rate): (4) total mixing exergy loss,(0) undesired exergy loss (wasted products), and (]) desired exergyloss (useful products).

Figure 13. Chromatograms for the separation of a binary mixturefor two different reduced velocities. For ν ) 7.9, product 1: thickline and product 2: thin line. For ν ) 59.7: product 1 (b) andproduct 2 (0). Stanton number 3.74.

Figure 14. Mixing exergy loss (lines and points) obtained forseveral reduced velocities (flow rate): (4) total mixing exergy loss;(0) undesired exergy loss (wasted products), and (]) desired exergyloss (useful products).


tion rate. As a result, mixing exergy loss seems tochange trend but still it increases (dashed line in Figure14).

When we compare the two contributors for the totalmixing exergy loss, it is clear that in this case the wastestream is the most important reason for the mixingexergy loss. In Figure 15 it can be seen that the peaksoverlap is much larger in this case.

Concerning the desired exergy loss (useful products),there is a slight trend for this term to decrease. Thereason for this decrease is that, at increased reducedvelocities, a high degree of dilution results in a usefulproduct stream with almost pure eluent.

Up to now in our analysis we can conclude that theincrease in the reduced velocity will lead to highermixing exergy loss. In addition, we used two differentparticle sizes and thus we showed that the impact ofthe reduced velocity is higher when mass transfer effectsare stronger (larger particles). It was also shown thatthere is a need to divide the mixing exergy loss into itstwo contributions in order to understand the reasonsfor the exergy loss.

We now have to show that the lowest values for themixing exergy loss occur in the region of maximumrecovery and minimum solvent usage (Figure 16). Forthis, we use the smaller particle size. Minimizing themixing exergy loss may eventually lead to lower processcosts.

Figure 16A presents the solvent consumed for therange of reduced velocity used here. Again it can be seenthat there is a straightforward relation between mixingexergy loss and solvent used. This is so because theamount of solvent used is directly related to the productdilution when the pulse volume is held constant. More-

over, product recovery decreases with increasing mixingexergy loss while keeping the purity requirement con-stant.

5.3.2. Case 2: Considering ∆P. Fixed-bed chro-matographic separation systems require the eluent tobe pumped continuously through the column. Increasingflow rates cause the pressure drop and consequently themechanical energy consumption (pump work) to in-crease as well.

For the particular range of reduced velocities shownin Figure 17, the mixing exergy loss is almost constantand the physical exergy loss increases dramatically. Inother words, the changes in the reduced velocity havea much stronger impact on the physical term of theoverall exergy loss.

6. Discussion

In this contribution, we evaluate the use of exergyanalysis on the optimization of a chromatographicseparation. In this field of separation, simulated movingbed systems have particularly attracted much attentionin recent years. Although SMB is already a powerfulseparation technique, there is still room for furtheroptimization.

The lack of literature concerning the use of exergyanalysis of SMB units and the fact that exergy hasproved to be a useful tool for energy intensive systemshave challenged the authors to perform this study. Wedecided to start this learning process by applying theexergy balance on one single column based on the factthat SMB equipment is constituted by a series of singlechromatographic columns. A sensitivity analysis inves-tigating the influence of traditionally adjusted param-eters, namely, particle size, pulse volume, and flow rate,were carried out and then the resulting exergy loss wascomputed. The gained knowledge is the following:

1. The initial state of the column should be re-established so that the nonflow exergy (the exergychange of the bed itself) does not play a role in theanalysis.

2. Physical exergy loss equals the pump work neededto transport the fluid phase through the column.

3. There is a so-called desired exergy loss occurring,given the mixing of eluent and products. This is aninevitable loss, given the nature of the separationtechnique. However, the lack of good performance leadsto an unnecessary loss, called undesired exergy loss.

In our approach to the problem, we studied the twoterms of the overall exergy loss during a chromato-graphic separation, that is, the mixing and physicalexergy loss, separately. The former lumps together theeffect of mixing of eluent and solutes and finite driving

Figure 15. Chromatograms for the separation of a binary mixturefor two different reduced velocities. For ν ) 51.7, product 1: thinline and product 2: thicker line. For ν ) 258.5: product 1 (O) andproduct 2 (0). St ) 0.18.

Figure 16. Effect of mixing exergy loss: (A) on solvent consump-tion (0); (B) purity and recovery: (4) purity product 2, ([) purityproduct 1, (0) recovery product 1, and (×) recovery product 2.

Figure 17. Exergy loss for increasing reduced velocity: (0) mixingexergy loss and (4) physical exergy loss.


forces for mass transfer. The latter accounts for thepresence of pressure drop. Such division of the exergyloss in its components has shown to be of muchimportance in revealing the nature of process irrevers-ibilities.

Within the framework of chromatography optimiza-tion, there are two main concerns, namely, eluent useand mechanical energy (pump work). The issue ofreducing eluent use is important not only because it hasan impact on process costs but also because it leads toproduct dilution. Results have shown that when mixingexergy is lower, the dilution is also lower. This result isparticularly important when the analysis is broadenedto include the downstream process, which recovers theproducts from the eluent. Product dilution may causeunnecessary primary energy consumption if distillationcolumns are used. At this point, the traditional optimi-zation of solvent use is not enough any longer.

Exergy analysis seems also to be useful when dealingwith the problem of mechanical energy (pump work)consumption. It is well-known that mass transferresistance limits the performance of an SMB unit. Toavoid such problems, small particle sizes are recom-mended. However, the resulting pressure drop can bevery high and then mechanical energy becomes animportant issue, especially if we are dealing with large-scale processes. This latter issue can be adequatelyhandled by evaluating the physical term of the exergyloss. Having said that, the authors think that exergyanalysis may be the important tool for the improvementof the entire process.

For a proper comparison between the presented newchromatographic process optimization tool in this paperto existing ones (i.e., cost optimization2,5), both shouldyield chromatographic fixed-bed separation dimensionsin terms of column diameter, length, particle diameter,and operational settings such as solvent usage for afixed productivity at a fixed purity. When giving thesame result, confidence in the optimal setup and opera-tion is increased. Given different setup and operationalsettings, questions arise: which method is more validand why? Cost optimization uses different objectivefunctions using productivity and recovered yield as afunction of loading factor and tray number. Exergyoptimization includes mass transfer effects, dilution,convection, adsorption, and heat transfer in one singleframework. The actual optimum may change withvarying prices in cost optimization; for exergy optimiza-tion this is not the case: irrespective of prices a fixedoptimum is found. As this paper is reporting on thedeveloped exergy methodology, the actual comparisonis made only superficially.

7. Conclusion

As part of the broader research project that concernsthe use of exergy analysis as a tool to optimize chro-matographic separations, we presented here the resultsconcerning FB operation mode. Our goal is to demon-strate how to perform the exergy balance on a FBcolumn and above all to learn how to interpret theresults obtained.

A close relation between mixing exergy loss and thequality of the separation was found. That means thathigher product recoveries were achieved for low mixingexergy loss while meeting the purity specification. Toobtain some insight concerning the impact of solventregeneration and product recovery from the solvent on

the performance of the separation, a further division ofthe mixing exergy loss in two parts, that is, undesiredand desired exergy loss, was made. In addition, theenergy consumption can be minimized looking at thephysical exergy loss.

A minimum total exergy loss was found in a range ofparticle sizes that gives high product recovery andminimum energy consumption. Therefore, the operationat minimal exergy loss may lead to a reduction in theprocess costs.

Acknowledgment

This research was financially supported by TheNetherlands’ Department of Economic Affairs, theDepartment of Public Housing, Spatial Planning andEnvironmental Affairs, and the Department of Educa-tion, Culture and Sciences.

Nomenclature

a ) interfacial area (cm2)c ) concentration of mobile phase (mol/L)d ) diameter (cm)Dm ) diffusion coefficient (cm2/s)Ex ) exergy (kJ)ex ) specific exergy (kJ/mol)H ) enthalpy (kJ)h ) specific enthalpy (kJ/mol)K ) equilibrium constantk ) mass-transfer coefficient (cm/s)L ) length (cm)n ) molar flow rate (mol/min)P ) pressure (bar)q ) concentration stationary phase (mol/g)Q ) heat flow (kJ/min)R ) equivalent radius (cm)qmax ) loading capacity of the adsorbent (mol/g)T ) temperature (K)S ) entropy (kJ/K)St ) Stanton numbert ) time instant (min)V ) volume (cm3)u ) velocity (cm/s)W ) shaft works ) specific entropy (kJ/mol‚K)x ) liquid-phase mole fraction

Greek Symbols

ε ) bed porosityη ) pump efficiencyτ ) reduced time∆ ) variationφ ) volumetric flow rate (cm3/min)ν ) reduced velocity

Subscripts

0 ) ambient conditionschem ) chemicale ) externali ) componentInt ) interstitialintra ) intraparticlemix ) mixturep ) particlephys ) physicalr ) heat reservoirc ) column

Superscript

* ) equilibrium


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Received for review July 18, 2003Revised manuscript received March 22, 2004

Accepted March 26, 2004

IE030603U


exergy analysis of chromatographic separations in a fixed-bed column

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