optimal economic design and operation of single- and multi-column chromatographic processes

Optimal Economic Design and Operation of Single- and Multi-columnChromatographic Processes

Sharon Chan,† Nigel Titchener-Hooker,‡ and Eva Sørensen*,†

Centre for Process Systems Engineering, Department of Chemical Engineering and Advanced Centre for BiochemicalEngineering, Department of Biochemical Engineering, University College London (UCL), Torrington Place,London WC1E 7JE, U.K.

Single-column chromatography is widely used in the biopharmaceutical industries, althoughmulti-column alternatives in the form of simulated moving bed (SMB) processes are nowemerging. It may be difficult, however, to determine which column alternative will be bestsuited for a given application, and this work sets out to address this issue. A systematic approachis presented that is based on a full economic appraisal of each process alternative based on anoptimization of the net annual profit. Single-column processes with and without recycling areconsidered, as are both the SMB and the Varicol process. The cyclic steady state for the SMBand Varicol processes is determined directly by complete discretization. The approach is appliedto a case study based on a linear isotherm where it is found that for this particular system, arecycling policy is not necessary for the single column. When comparing the single-columnprocess with the multi-column alternatives, the single column is the most economical providedthe life time of the project is short; however, the economic benefits of the more capital-intensivemulti-column processes are greater if the life time of the project is over 5 years. The SMBprocess is found to perform marginally better than the Varicol process over 15 years; however,this may be because not all extra degrees of freedom for the Varicol process were considered.

Introduction

Chromatography is an increasingly important separationtechnique in the fine chemical, pharmaceutical and biotechno-logical industries. Over the years, the operation of the chro-matographic process in these industries has undergone manydevelopments and it is no longer limited to batch processing.While the single column is still popular in preparative chro-matography, multi-column processes, such as simulated movingbed (SMB) chromatography, are now becoming increasinglypopular in industrial-scale chromatography as a continuousmeans to produce large amounts of highly purified products.From the literature, it is not evident how one can determinewhich is the most suitable chromatographic process for a givenseparation, given the vast range of column and multi-columnchromatographic processes now available, and this work seeksto address this issue.

Different operating strategies and techniques can be used toimprove the throughput of the process for single-columnchromatography. These include gradient elution, recycling withor without peak shaving and sequential injection (1-5).

Of the multi-column chromatography operations available,the technology of the simulated moving bed (SMB) process isperhaps the most prolific and best known. In the SMB process,fixed adsorbent beds are used, where feed and product positionsare simultaneously switched at regular timed intervals tosimulate the counter-current movement of the bed against theflow of mobile phase. More recent, however, is the extension

from SMB to the Varicol process, which instead employs non-synchronous switching of the inlet and outlet ports in itsoperation. Other variants of the SMB process include Power-Feed, where flow rates in the unit are allowed to change duringthe switching period (6, 7), ModiCon, in which the feedconcentration is modified periodically (8) and open loop SMB(9).

In recent years, some work has been done to compare thedifferent chromatographic systems available (10-12). Most ofthese comparisons are based on productivity or separationefficiency of these systems, which does not necessarily reflectthe economic optimum of these systems. Papers consideringchromatographic systems from an economic perspective arerelatively few, one of the more recent papers being by Jupke etal. (13), where an economic comparison is made between theoptimal design of batch and SMB chromatographic systems andwhich provides an overview of the contributions of theseparation costs between the two systems. The work presentedin this paper proposes employing a detailed economic appraisalto single- and multi-column separation systems in order to allowa fair comparison between alternatives, but to include otheroperating policies in these systems, previously not consideredby Jupke et al. (13). In this paper, we will consider the followingcolumn and operational alternatives:

1. Column (batch) chromatographya. Single columnb. Single column with recyclingc. Single column with recycling and peak shaving

2. Continuous chromatographya. Simulated Moving Bed (SMB) processb. Varicol process

We first define the column configuration and operatingpolicies we are considering. We then describe the mathematical

* To whom correspondence should be addressed: [email protected].† Centre for Process Systems Engineering, Dept. of Biochemical

Engineering.‡ Advanced Centre for Biochemical Engineering, Dept. of Chemical

Engineering.

389Biotechnol. Prog. 2008, 24, 389−401

10.1021/bp070270m CCC: $40.75 © 2008 American Chemical Society and American Institute of Chemical EngineersPublished on Web 04/04/2008

models used, particularly in terms of how we propose todetermine the cyclic steady state of the SMB processdirectly.We next describe a systematic approach for comparison ofprocess alternatives involving a full economic appraisal basedon an optimization of net annual profit. The approach isdemonstrated in a case study which clearly illustrates that thelife time of the project is the main factor which determineswhich process is the most economical.

Column Configurations and Operating Policies

Column (Batch) Chromatography. Conventional batchcolumn chromatography is a well-established technique forefficient separation for preparative purposes (14). However, theeluent costs involved can be high and the matrix usage is usuallynot very efficient. In addition, for difficult separations, therecovery yields obtained can be low for products with highpurity constraints. In such cases, other operating policies forthe column have to be examined. Employing a recycling strategyhas been found to be effective in increasing the recovery yieldof the separation and enhancing column efficiency (1, 5, 15).

In conventional (closed-loop) recycling operation, the productfrom the column is recycled back to the column several times,with the purified products collected at the end of the last cycle.The combination of increased recovery yields with reducedmatrix cost makes this an attractive option for high valueproduct(s) purification. However, for products which are difficultto separate, the technique is infeasible. The recycling actuallymakes the separation more difficult as the elution peaks becomeprogressively broader and flatter with each recycle due to thedispersive effects, thereby increasing band overlap. Thus, whilerecycling can improve the separation performance, it does notnecessarily guarantee an increment in yield.

When using a peak shaving technique, the volume of eluentcontaining sufficiently purified products is collected aftereachcycle, leaving only the off-specification fractions to be recycled.This accounts for the higher recovery yields achieved when apeak shaving technique is applied. Implementing a peak shavingtechnique with conventional recycling chromatography is foundto be most advantageous for difficult separation processes (16).The main benefit from peak shaving is that the overlapping of

peaks stemming from consecutive cycles is averted, as theoverall mass being recycled is reduced because of withdrawalof product.

Continuous Chromatography.Simulated moving bed (SMB)chromatography uses several columns, and thesynchronousswitching action of the inlet and outlet ports takes place to mimica counter-current operation. The main characteristic of the SMBprocess is its ability to produce large amounts of highly purifiedproducts using less eluent as the matrix is more efficiently used.However, the implementation of this process often requires newinvestment of equipment. Even though existing chromatographicbatch columns can be used as part of the SMB arrangement,other hardware such as multi-port or rotary valves, controlequipment, etc. will add to the cost.

The Varicol process is a recent variant form of the SMBprocess, where the switching action of the flow rates takes placeasynchronouslybased on non-simultaneous and unequal shiftsof the inlet and outlet ports (17). An example of an operationalschematic of the Varicol process is compared to that of a SMBprocess in Figure 1 for a 1/2/2/1 column configuration process(where each number indicates the number of columns in thatsection). The figure shows that within a single switching periodfor the SMB process, the column configuration for Varicol haschanged in succession: 1/2/2/1, 2/1/2/1, 2/2/1/1, 1/2/1/2 andfinally back to the original configuration of 1/2/2/1.

Both experimental and computational work has demonstratedthat the Varicol can achieve better performance than the SMB,in terms of both increased specific productivity and reducedeluent consumption but at the cost of greater complexity (6,17, 18).

Mathematical Modeling

Mathematical modeling of continuous chromatographic sepa-rations has been covered thoroughly in the works of Du¨nnebieret al. (19), Strube and Schmidt-Traub (20) and Strube et al.(21). The modeling of the SMB system has been handled bytwo main approaches: (1) as an equivalent true-moving system(TMB) where the solid and fluid velocities are involved andthe boundary conditions of the chromatography columns areindependent of time, and (2) as a simulated counter-current

Figure 1. Schematic comparison of the operations of the SMB and the Varicol process (6). (TS,start: start of switching period for SMB;TS,end: endof switching period for SMB).

390 Biotechnol. Prog., 2008, Vol. 24, No. 2

system where there are several sections with a number ofchromatography columns in each, and whose boundary condi-tions change with time (22). The SMB system is often modeledas the equivalent TMB system at steady state since the latter isless complex and the level of difficulty in the solution and thecorresponding difference in computational time is less. However,due to the simplicity of the TMB approach, this model is onlysuitable as an estimate of the operating parameters required (13).Thus, in this work, we will consider a detailed SMB model.

The simulated moving bed unit can be modeled dynamicallyby connecting the dynamic models of single chromatographiccolumns in sections with a node model in between each section.The nodal model considers the cyclic valve switching for theinlet (feed, desorbent) and outlet streams (extract, raffinate).Figure 2 illustrates how this can be modeled computationally.In addition to the inlet and outlet flow rates, the internal flowrate, or the recycle stream of section IV (the section betweenthe desorbent and raffinate nodes), must also be considered.

Column Unit Model. A number of assumptions are usuallymade to simplify the mathematical model and are also made inthis work:

1. Isothermal operation2. Isocratic elution3. Lumped axial dispersion coefficient4. No concentration gradient in the radial direction5. No local equilibrium between the macropore and stagnent

liquid phase within6. No dead-volumes in pipes, columns and connections7. No back-mixing at the nodesAssumptions are also made for the mass balances in the

column model and more details about these assumptions,including the justification for them, can be found in Guiochonet al. (23). Further improvements to the model can be made ifnecessary to take these factors into account if the assumptionsbecome invalid due to changes in operating conditions.

The chromatographic column is modeled based on a dispersedplug flow (DPF) model, giving a plug flow of the solid andaxially dispersed plug flow of the fluid. The basic differentialequation of the fluid mass balance including mass transferresistance is:

The axial dispersion coefficientDax is calculated using thecorrelations employed by Du¨nnebier et al. (19):

where

and

The particle mass balance including mass transfer resistanceis adopted from the work of Strube et al. (21):

The integration of the differential mass balances of thecomponents in chromatography requires prior knowledge of theirequilibrium isotherm which describes the distribution of thesolute between the two phases of the chromatographic system.The isotherm is a fundamental part of chromatography modelingas they define the adsorption equilibria of the system, whichcorresponds to the most important retention mechanisms usedin preparative chromatography (23). The most general isothermcan be given in the form of

Any model used to represent equilibrium isotherms, such asthe Langmuir isotherm or bi-Langmuir isotherm, can beemployed in the approach presented in this work. However, asour objective is to study the economic optimization of differentprocess alternatives, a problem which is already quite complex,a linear isotherm is employed in the case study considered later:

The Danckwerts boundary conditions are employed andmodified according to those used by Du¨nnebier et al. (19):

At the column inlet:

At the column outlet:

The initial conditions describe the state of the column whenthe operation begins:

Nodal Unit Model. The node model represents what happensat the points of switching and is illustrated by Figure 3. Theassumptions of the node model are:

Figure 2. Computational model of an SMB unit.

∂Ci(z, t)

∂t) Dax(t)

∂2Ci(z, t)

∂z2- ν(t)

∂Ci(z, t)

∂z- 1 - ε

ε

∂qi(z, t)

∂t(1)

Dax ) uLPe

(2)

Pe) 0.2ε

+ 0.011ε[Reε ]0.48

(3)

Re)2ενRpF

η(4)

∂qi(z, t)

∂t)

3keff,i

Rp(Ci(z, t) - CP,i(z, t)) (5)

qi(z) ) f(CP,i(z), ...,CP,n(z)) i ) 1, ..., NoComp (6)

qi ) KiCP,i (7)

Ci(z ) 0) ) Cin,i (8)

Ci(z ) L) ) Cout,i (9)

∂Ci(z ) L)

∂z) 0 (10)

Ci(z) ) 0 (11)

∂qi(z)

∂t) 0 (12)

Biotechnol. Prog., 2008, Vol. 24, No. 2 391

1. No holdup in the nodes2. No back-mixing at the nodes3. No loss of fluid (or mass) at the nodes, e.g., leaksAcross each node, the mass balances are:Total material balance over nodej:

Component material balance for componenti over nodej:

Since there are four main nodes, the nodes can be namedafter their respective inlet and outlet streams: feed, desorbent,extract and raffinate. For the four nodes in the system, the overallmass balance over the whole system is:

The same nodal model can be changed to an inlet (feed,desorbent) or outlet (extract, raffinate) stream depending byassigning appropriate values to the concentrations and flow ratesat the nodes.

Node j at feed point (inlet):

Node j at desorbent point (inlet):

Node j at extract point (outlet):

Node j at raffinate point (outlet):

Direct Determination of Cyclic Steady State for the SMBProcess.Cyclic processes such as adsorption swing processesand simulated moving bed (SMB) chromatographic processesoften require a number of cycles before steady-state conditionsare achieved. When optimizing such processes, each basicsimulation, of which several hundred may need to be performed,must be initialized and run until steady state as these are theconditions that determine the optimal operation. If a number ofcycles are required to achieve steady state, these optimizationsmay be very time-consuming. Being able to determine the cyclicsteady state (CSS)directly is therefore extremely useful. Thiscan be done by discretising the system of equations in bothtemporal and spatial domains and incorporating the periodicityconditions of CSS as additional boundary conditions in themodel. These periodicity conditions dictate that the state of thesystem at the end of each cycle is identical to that at the startof the cycle. A method for complete discretization was firstreported by Nilchan and Pantelides (24) for periodic adsorptionprocesses. A similar means of direct computation of periodicSMB states is discussed by Kloppenburg and Gilles (25). Intheir work, a periodic state is identified as the spatiallydistributed state of the SMB process at the end of a switchinginterval which is identical to the state at the beginning of theswitching interval, apart from a shift of exactly one column.The governing equations are:

Method 1 (Nilchan and Pantelides (24)).This method isbased on the fact that when the system is at steady state, theconditions at the end of the cycle are identical to the conditionsat the beginning of the cycle, in both the stationary and mobilephases. Here, the termcyclerefers to the inlet and outlet linesof desorbent, extract, feed and raffinate returning to the originalpositions after the time when they began to move.

The initial conditions outlined earlier (eqs 11 and 12) wouldno longer apply and are thus for columnj replaced with:

Method 2 (Kloppenburg and Gilles (25)).The second methodis based on the fact that when the system is at steady state, thestate of column (j + 1) at the end of a switching period isidentical to the state of columnj (the preceding column) at thebeginning of the switching period. In this case, the periodicityconditions are expressed as:

A comparison of these two approaches to calculating thedirect cyclic steady state (CSS) has been presented by Mincevaet al. (26) for the separation of 1,1′-bi-2-naphthol enantiomersusing the simulated moving bed (SMB) process, where theircase study showed the method by Kloppenburg and Gilles (25)to be computationally more efficient, as will indeed be con-firmed in our work, and this method is used in the case studylater.

Systematic Approach for Comparison of ProcessAlternatives

While much work in the literature has focused on themodeling and optimization of chromatographic processes, thereremains, however, a lack of a systematic approach for how to

Figure 3. Node model with the process flows.

Qin,j + QNin,j ) Qout,j + QNout,j (13)

Qin,jCin,i,j + QNin,jCNin,i,j ) Qout,jCout,i,j + QNout,jCNout,i,j

(14)

Qfeed+ Qdesorbent) Qextract+ Qraffinate (15)

QNin,j ) Qfeed (16)

CNin,i,j ) Cfeed,i (17)

QNout,j ) 0 (18)

QNin,j ) Qdesorbent (19)

CNin,i,j ) 0 (20)

QNout,j ) 0 (21)

QNin,j ) 0 (22)

QNout,j ) Qextract (23)

CNout,i,j ) Cextract,i (24)

QNin,j ) 0 (25)

QNout,j ) Qraffinate (26)

CNout,i,j ) Craffinate,i (27)

Ci,z(j, t ) 0) ) Ci,z(j, t ) Tcycle) (28)

qi,z(j, t ) 0) ) qi,z(j, t ) Tcycle) (29)

Ci,z(j, t ) 0) ) Ci,z(j + 1, t ) Tswitch) (30)

qi,z(j, t ) 0) ) qi,z(j + 1, t + Tswitch) (31)


compare the optimal performance of different chromatographicprocesses for the same separation. In this section, a methodologyis outlined which describes how to select an appropriatechromatographic process for a given separation from a selectionof process alternatives. In particular, we will consider bothsingle-column and multi-column alternatives. Figure 4 showsa flowchart of the approach which is described in the followingsections. The approach consists of a number of steps, where inthe first part (steps I-III), the separation problem is formulatedsuch that each process alternative generates an amount ofproducts that is equivalent to the product constraints. The modelparameters for each process alternative are identified fromexperimental set-ups and/or from literature. A scale-up proceduremay be necessary for some of the processes to achieve therequired quantity of products. This is followed by a second part(step IV) which involves the optimization of all the availablesingle and multi-column process alternatives using an economicobjective function. In the final part (steps V-VI), the perfor-mance of each of the processes are compared based on a fulleconomic appraisal of each in order to select the most appropri-ate alternative for the given separation. The approach isdemonstrated in detail in a case study presented later.

Step I: Separation Specification. Step I of Figure 4considersseparation specificationand refers to the formulationof the specifications of the separation that is undertaken whichwill apply to all the chromatographic alternatives:

• Step A. The requiredproduction amount for a single yearis specified.

• Step B.The total number of operating hours for a singleyear is specified (which cannot exceed 8760 h, the maximumnumber of hours in a year).

• Step C.A breakdown of the plant schedule is established,e.g., for start-up, shut-down, maintenance, etc. to determine theactual number of available operating hours for production.

Step II: Availability of Data. Step II in the approach is adecision box where required column data for modeling isidentified. If sufficient data is not available for a given processalternative, neither from the literature nor from the experimentalsetup (which is rare these days), then this alternative must bedesigned de novo. Design of chromatographic processes hasbeen covered extensively in the literature (e.g.23, 27) and willnot be covered here. (Note that without this initial collection ofdata, the subsequent optimizations are not possible.)

Some model parameters are common for both single andmulti-column processes, such as column lengthL, columndiameterDC, and particle radiusRP, although they may havedifferent values depending on the process. Other common modelparameters, like the feed concentration and the isothermparameters, may not be as readily known. For these, theapproach outlined in Chan et al. (28) for the determination ofindividual feed component concentrations, as well as estimationof isotherm parameters, may be used.

Also required are the different flow rates and operatingpolicies in each chromatographic process. For single-columnalternatives, the eluent flow rate is required and for multi-columnalternatives, the feed, desorbent, extract, raffinate and recycleflow rates as well as the switching time(s) are needed. Notethat these may all be optimized as part of the optimization instep IV, and hence only initial values are required.

Step III: Scale-Up of Operation. Each process alternativehas to be able to produce the requisite amount given thespecified production amount and the available production timefor a year and scale-up will be required in going from an existingexperimental setup to industrial scale. Without this scale-up,the different processes would not be compared on equal terms.In this work, general recommendations for scale-up based onwork in the literature (29, 30) are used. Sofer and Hagel (29)recommended the guidelines tabulated in Table 1 for scale-upof chromatographic purification. In this work, scale factors areused according to these guidelines, particularly maintaining thebed height and increasing the column diameter, sample volumeand volumetric flow rate. (Refer to the case study later forexamples of the calculation details.)

For a given scale up factor, the following equations areemployed:

Figure 4. Flowchart of the approach for comparing different chro-matographic alternatives.

Table 1. Guidelines for Scale-Up of Chromatography (29)

maintain bed heighteluent velocitysample concentrationgradient slope/bed volume (gradient elution)sample residence

increase column diametersample volume in proportion to column

cross-sectional areavolumetric flow rate in proportion to column

cross-sectional areagradient volume in proportion to column

cross-sectional areacheck reduction in supportive wall effects (increased

pressure drop)sample distribution (band broadening)piping and system dead volumes

scaled-up flow rate) base case flow rate×(scale up factor)2 (32)

scaled-up diameter) base case diameter× scale up factor(33)


The load, or injection, time (tinj) from the base case is fixed.This means that with the increased volumetric flow rate, thevolume loaded increases. To determine the production in eachbatch, the following calculations are carried out (whereCfeed isthe feed concentration):

Finally, the total annual production may be calculated usingthe following equation:

With the model specifications now consistent with theseparation specifications, the optimization of the alternativescan begin.

Step IV: Optimization. A crucial part of any optimizationis the specification of the objective function. Several objectivefunctions have been proposed in the literature (e.g.,5, 6, 13,23, 31, 32, etc). Among these, only the work of Jupke et al.(13) has consider the economic implications in the optimizationto provide a real comparison of the process economy for batch(column) and SMB chromatography. The work of Jupke et al.is extended in this work to include a recycling policy for thesingle column and also to consider the Varicol process. Anobjective function based on net annual profit and a full economicappraisal of each alternative is generated. The decision variablesconsidered for each process alternative are given in Table 2.

The choice of the objective function depends on the aim ofthe optimization. Minimization of production cost may be usedwhen seeking to lower the production cost of the process (sayfor eluent and adsorbent costs) and when the profit margin isnot a constraint. Generally, however, we would advocate theuse of a net profit objective function as it incorporates theminimization of the production costs as well as the maximizationof the sales revenue. (A summary of the calculation of net annualprofit as applied in this work is given in the Appendix.) Theobjective function may thus be described in one of the followingways:

1. Annual Net Profit. If the annual profit is maximized, thefollowing objective function is used:

subject to constraints given by

wherePannualis the annual net profit,τ is the total time horizonandu(t) is the vector of control variables. In the chromatographicprocesses considered in this work, the control variables are theflow rates and the valve switching actions (e.g., during productcollection in column chromatography, or flow rate switchingin the SMB/Varicol process) as given by Table 2.Pui andYi

are the purity and recovery yield of componenti, respectively,while ∆Pj is the pressure drop across columnj. Other constraintscan of course be used instead of these if purity and recoveryare not of major concern.

2. Annual Production Cost.If the objective is to minimizethe production costs (Ctotal) for the separation of afixed feed

amount in all the chromatographic processes, subject to thepurity and recovery yield constraints, then the following equationapplies:

where Ctotalannual is the annual net production cost, and the

optimization is subject to the constraints as given in eqs 37-39.

3. RecoWery Yield and Production Rate.The recovery yieldand production rate can be maximized simultaneously using aweighted objective function, proposed by Felinger and Guiochon(32), as the product of the productivity and recovery yield:

subject to the constraints given by eq 37-39. Generally, single-column processes have a lower recovery yield compared tomulti-column processes. Jupke et al. (13) demonstrated recoveryyields of 96% and 100% for the optimized batch and SMBchromatographic processes, respectively.

Step V: Project Evaluation. Each process alternative isoptimized separately given the chosen objective function, e.g.net profit, and the separation specifications following theprocedure outlined above to obtain the design and operation ofthat process alternative with the highest annual profit. Theseprofit estimates should, however,not be used in selecting thebest profit as the life time of the project is not taken into account.An economic appraisal is therefore carried out on each of theoptimized chromatographic alternatives, where the cash-flowof implementing each process in a plant over a number of yearsis considered. Thefixed capital inVestment(FCI) is the totalamount needed to supply the necessary plant and manufacturingfacilities, in addition to the finances required as working capitalfor operation of the facilities (33). One way of estimating thecost components in the capital investment is to assume eachcomponent as a percentage of the equipment delivery cost. Thecapital costs of each chromatographic unit are in this workestimated based on the delivered equipment costing method inPeters et al. (33). Subsequently, a basic Net Present Value (NPV)analysis of the chromatographic units over a fixed number ofyears is performed (for more details, see Sinnott (34)) and thediscounted cash flow diagram is drawn up to view the economicperformance of the different separation units over time. Notethat any economic appraisals methods, for instance, company-specific tools, may be used at this stage.

Step VI: Process Selection.The final process selection isachieved by comparing the cash flow diagrams across thedifferent chromatographic alternatives. The performance of eachunit varies over time and these must also be compared beforea final decision can be made.

Case Study

A case study will now be presented which illustrates theapproach proposed in this work. The case study is based on theparameters and operating conditions presented by Du¨nnebieret al. (19). Their work originally examined the separation of abinary mixture for an SMB process and this is now extendedto single-column processes as well as to the Varicol process.For the multi-column processes, a column configuration with atotal of 8 columns is considered with 2 columns in each section,i.e. a 2/2/2/2 configuration. The systematic approach outlinedin the previous section and illustrated in Figure 4 is employedwith each step explained in detail. All simulations, parameter

minτ,u(t) Φ(Ctotalannual) (40)

maxτ,u(t) Φ(Yi × Pri) (41)

production (g) in 1 batch) QF × tinj × Cfeed (34)

production (kg) per year) batch production (kg)×number of batches per year (35)

maxτ,u(t) ΦPannual (36)

Puimin < Pui < 1 (37)

Yimin < Yi < 1 (38)

∆Pjmin < ∆Pj < ∆Pj

max (39)


estimations and optimizations have been performed usinggPROMS (35).

Step I: Separation Specification.The procedure for speci-fying the separation is outlined as follows:

• Step A. The production amount for a single yearis aminimumof 2000 kg of product (1000 kg each of componentsA andB, respectiVely).

• Step B.The total number of operating hours for a singleyear is 8000 h.

• Step C.The start-up/shutdown/maintenance time is assumedto be 20% of the production time.

Step II: Availability of Data. The column dimensions, thefeed concentrations and isotherms are known and tabulated inTable 3. In addition, the table summarizes the model parametersacross the single and multi-column processes used in this casestudy, adapted from the work of Du¨nnebier et al. (19). (Notethat some of these will be optimized later.)

The work of Dunnebier et al. provides the dimensions forcolumns in the SMB unitonly. As there is no informationavailable on single columns for a similar separation, the columndimensions (Table 4) of the SMB unit are used for the basecase single-column process in order to calculate its annualproduction. 10mLof the feed is assumed loaded onto the singlecolumn which takes approximately 100 min to elute from thecolumn. Thus, in 1 year, the single column produces 4800batches. Table 4 shows a summary of similar calculations forthe annual production in other chromatographic processes.

In this work, the switching subintervals for the Varicol processare made equal, i.e., 0.25Tswitch, 0.5Tswitch, 0.75Tswitch andTswitch,at which the flow rates of extract, feed, desorbent and raffinateare changed, respectively (refer to Figure 2). This is becausewith a dimensionless time unitτ as used in our optimizationmodel, the time interval for each switching action must bespecified a priori.

Step III: Scale-Up of Operation. The scale-up guidelinesdiscussed earlier (Table 1 and eqs 32-35) are used to scale upthe parameters from the work of Du¨nnebier et al. (19) fromtheir production amounts in Table 4 to producing 1000 kgeachof component A and B annually. The table summarizes all thescaled-up processes and the process parameters which have beenincreased are the diameter(s) and flow rates. In the multi-columnprocesses, the same switching period is retained to maintainthe elution profiles from the base case and only the flow ratesand column diameters are scaled up. Likewise, the single columnretains the same elution profile when its diameter and eluentflow rate are scaled up. Table 5 shows the flow rates anddiameters that have been scaled up using the scale up factorsin Table 4. The product purities and recovery yields for eachscaled-up process alternative are summarized in Table 6.

Step IV: Optimization. In the following, all the objectivefunctions alternatives presented in the previous section will beconsidered and a comparison will be made between them. Threescenarios are thus explored: In Scenario I, the single-columnprocesses are optimized for a weighted objective function ofproduction rate and recovery yield for each of the components

A and B (eq 41). Closed loop recycling with peak shaving isused as basic recycling leads to recycle profiles which overlap(not shown). In Scenario II, the annual production costs acrossthe single-column and multi-column processes are minimized(eq 40). Finally, in Scenario III, the annual net profits of eachof the processes are maximized (eq 39). Table 7 shows thedifferent cost factors that make up the production costs andwhich are employed in the economic evaluations.

Scenario I: Maximizing Weighted Objective Function.Single-column processes generally have a lower recovery yieldcompared to multi-column processes. In this scenario, the designand operation of a single column and a single column withrecycling is optimized to maximize their recovery yield andproductivity. The weighted objective function proposed byFelinger and Guiochon (32), i.e., a product of the productivityand recovery yield, is used. The maximization of each compo-nent is considered separately.

Maximizing RecoWery Yield Function of Component A(Extract). The yield and production rate of component A ismaximized first based on the objective function:

subject to the constraints given by

The results of the optimization are tabulated in Table 8. Thecolumn with a recycling policy collapses to a single columnwithout recycle, as the optimal number of cycles is 1, andtherefore gives the same optimized model parameters as for thesingle-column optimization. The recovery yield of componentA is improved from 0.913 to 0.916 for the single column, while

Table 2. Optimization Decision Variables

single column single column with recycle smb process varicol process

column length column length column length column lengthcolumn diameter column diameter column diameter column diametereluent flow rate eluent flow rate eluent flow rate eluent flow ratefraction cut times fraction cut times raffinate flow rate raffinate flow rate

number of cycles extract flow rate extract flow ratedesorbent flow rate desorbent flow raterecycle flow rate recycle flow rateswitching time switching times

Table 3. Base Case Model Parameters for Single- and Multi-columnChromatographic Processes (19)a

chromatographic process process characteristics

single column eluent flow rate) 0.0166 cm3/ssingle column with recycle load (injection) time) 602.4 sSMB process, Varicol process recycle flow rate 0.0665 cm3/s

extract flow rate 0.0233 cm3/sdesorbent flow rate 0.0266 cm3/sfeed flow rate 0.0166 cm3/sraffinate flow rate 0.0199 cm3/s

SMB process switching time 618 sVaricol process 4 equal intervals totalling 618 s

a Column length: 47.5 cm. Column diameter: 1.4 cm. Feed concentration(g/cm3): A ) 0.05, B ) 0.05. Isotherm coefficients:KA ) 0.56, KB )0.23.

maxτ,u(t) Φ(YA × PrA) (42)

0.995< PuA < 1 (43)

0.995< PuB < 1 (44)

0.80< YA < 1 (45)

0.80< YB < 1 (46)

13 bar< ∆P < 100 bar (47)


for the column with recycling, the recovery yield of componentA decreases from 0.930 to 0.916. This is as a result of thesignificant increase in the productivity from US$ 5.29× 106 toUS $16.47× 106 (more than a 3-fold increase) for a singlecolumn without recycle, and the slight drop in recovery yielddoes not compromise the large increase in productivity. In bothcases, however, the recovery yields of component B dropsmarginally as the objective function is based on component Aonly. There is also a slight decrease in the total annualproduction cost and the annual net profit which is mainlybecause of the decrease in the recovery yield of component B.

Maximizing RecoWery Yield Function of Component B(Raffinate). The yield and production rate of component B ismaximized next based on the objective function

subject to constraints in eq 43-47.The results of the optimization are tabulated in Table 9.

Similarly, the optimal number of cycles for the single columnwith recycle is 1 and it thus produced identical optimizedparameters to the single column. From these results, the recoveryyield of component B improves significantly from 0.837 to 0.895in the single column (though slightly less for the single columnwith recycling from 0.867 to 0.895). The productivity of thesingle column nearly doubles (US$ 7.99× 106 to US$ 12.85

× 106), while for the single column with recycle, it increasesnearly 3-fold (similar to the previous optimization). The resultssuggest that the single column with recycle is likely to collapseto a single column when the productivity of the process isconsidered, as a single-column operation has a much greater

Table 4. Estimates for Base Case and Scaled-Up Productions (Based on Du1nnebier et al. (19))

chromatographic processproduction

per batch (g)batch

time (min)no. of batches

per yearbase

production (kg/year)scale upfactor

scaled upproduction (kg/year)

single column 0.50 100 4800 2.40 21 1060single column with recycle 0.50 170 2880 1.44 37.8 1050SMB and Varicol equivalent 0.13 618 5820 cycles 0.75 6.5 1010

Table 5. Scaled-Up Model Parameters for Single and Multi-columnChromatographic Processes

chromatographic process flow rate (cm3/s) diameter (cm)

single column eluent 8.03 30.8single column with recycle eluent 14.94 42SMB and Varicol recycle 3.740

extract 1.311desorbent 1.496 10.5feed 0.934raffinate 1.119

Table 6. Scaled-Up Case Results for Purities and Recovery Yields

component A component B

single columnpurity 0.997 0.995recovery yield 0.913 0.837

single column with recyclepurity 0.997 0.995recovery yield 0.930 0.867

SMB processpurity 0.996 1recovery yield 1 0.99

Varicol processpurity 0.9997 0.9965recovery yield 0.9998 0.9997

Table 7. Estimated Costs Factors Used To Establish ProductionCost and Net Annual Profit (from Jupke et al. (13))

parameter cost

adsorbent cost Cads 13.45 US$/geluent cost Cel 4.7× 10-4 US$/mLoperation cost Cop

h 22.4 US$/graw material cost CRM 7.17 US$/gwaste costa Cwaste 1.5 US$/g

a Estimated.

maxτ,u(t) Φ(YB × PrB) (48)

Table 8. Optimization Results for Scenario I: MaximizingComponent A

base case (scale up) optimized case

Single Columndiameter (cm) 30.8 15.76length (cm) 47.5 100a

eluent flow rate (mL/s) 8.03 4.68PuA 0.997 0.995PuB 0.995 0.995YA 0.913 0.916YB 0.837 0.8a

PrA (×10-7) 10.39 16.47functionPrA × YA (× 10-7) 9.49 15.08Ctotal

annual× 106 (US$) 1.037 0.813Pannual× 106 (US$) 3.37 2.02

Single Column with Recyclediameter (cm) 42 15.76length (cm) 47.5 100a

eluent flow rate (mL/s) 14.94 4.68cycle 2 1PuA 0.997 0.995PuB 0.995 0.995YA 0.930 0.916YB 0.867 0.8a

PrA (× 10-7) 5.29 16.47functionPrA × YA (× 10-7) 4.92 15.08Ctotal


a Optimized result on bound.

Table 9. Optimization Results for Scenario I: MaximizingComponent B

base case (scale up) optimized case

Single Columndiameter (cm) 30.8 16.69length (cm) 47.5 100a

eluent flow rate (mL/s) 8.03 4.73PuA 0.997 0.995PuB 0.995 0.995YA 0.913 0.800a

YB 0.837 0.895PrB (×10-7) 9.55 14.36functionPrB × YB (× 10-7) 7.99 12.85Ctotal


Single Column with Recyclediameter (cm) 42 16.69length (cm) 47.5 100a

eluent flow rate (mL/s) 14.94 4.73cycle 2 1PuA 0.997 0.995PuB 0.995 0.995YA 0.930 0.800a

YB 0.867 0.895PrA (×10-7) 5.29 14.36functionPrA × YA (× 10-7) 4.92 12.85Ctotal


a Optimized result on bound.


productivity. The reason for this is most likely the linearisotherm used. If the product purities were difficult to meet(common in nonlinear chromatography), the recycle may haveprobably played a role. There is a significant decrease in thetotal annual production cost and the annual net profit. This ismainly because of the large decrease in the recovery yield ofcomponent A from 0.913 to 0.800 for the single column. Notethat the costs and profit are not optimized in this scenario.

Scenario II: Minimizing Production Costs. In the secondscenario, the total annual production cost is examined for eachof the four chromatographic alternatives: single column, singlecolumn with recycle, simulated moving bed and Varicolprocesses. The objective function is the minimization of thetotaloperating costsof each process (defined in eq 40):

subject to the constraints in eqs 43-47.Table 10 shows the optimization results for the different

processes when minimizing the total production cost. Theoptimal number of cycles in the single column with recyclingis again 1, i.e., it collapses to a single column. Both single-column processes thus have the same optimized design andoperation parameters in the optimization. Compared with thecase when optimizing the recovery yield of component B, theannual production cost is lowered from US$ 1.078× 106 toUS$ 0.536× 106. At the same time, the annual net profit forthe single-column process drops from US$ 3.49× 106 to US$3.00 × 106. The lowered annual net profit suggests that thesales income is lower in the optimized case which is as expectedas the objective was to minimize the operating costs only (butnote that the yields are different). The single column shows amuch higher total production cost, just over twice that of theSMB process.

The multi-column processes have higher annual net profitsthan the single-column processes as the recovery yields aremaintained at a high value of 0.995. The high recovery yieldsare characteristic of the SMB/Varicol processes and show thateven to lower costs, these cannot be reduced or the separationis compromised in the unit. The SMB/Varicol processes havesimilar annual profits (US$ 5.36× 106 and US$ 5.37× 106,respectively) although the production costs are lower for theSMB process (US$ 0.268× 106) compared to the Varicolprocess (US$ 0.309× 106).

Scenario III: Maximizing Annual Net Profit. In the finalscenario, a full economic objective function for theannual profitis considered. In the previous section, the minimization of theproduction costs was conducted as was done in the work ofJupke et al. (13). However, the productivity of the process wasnot included in the objective function and the productivity may

therefore be compromised in order to achieve lower costs. Toavoid this, the annual profit is maximized as described explicitlyin the following objective function:

subject to the constraints in eqs 43-47.The profit values in Table 11 differ slightly from those

obtained in Table 10. In this scenario, the profit is employed inthe objective function and the productivity of the process is alsoconsidered alongside the production costs. It is evident thatminimizing the production costs (Table 10) does not necessarilylead to maximum profit for the process.

As for the previous scenario, the optimal number of cyclesin the single column with recycling collapses to a single columnand produces the same optimized results. Notably, the net profitof the single column is markedly increased, compared to thoseobtained with the optimizations in Scenarios I and II. Whilethe increment in the net profit is marginal for the SMB/Varicolprocess from the previous scenario, the annual net profit of theSMB process is now only about 8% higher than that of the singlecolumn when both are optimized in terms of annual profit whilethe difference was 44% if only the production costs wereconsidered.

Step V: Economic Appraisal.The final part of the approachis illustrated by considering an economic appraisal based onScenario III to determine the most profitable separation processafter a plant life time of 15 years based on Net Present Value(NPV) calculations. For this, the capital costs of each processalternative are needed. In this work, we have used a deliverycost percentage estimation method to determine the requireddelivered-equipment capital cost investment for both the singleand multi-column processes as shown in Tables 12 and 13,respectively. The single column and the single column withrecycling are assumed to have the same capital costs as the sameequipment can be used to allow operation in either conventionalelution or closed-loop recycling mode. Similarly, the capitalcosts for the SMB and the Varicol processes are the sameproVided the number of columns used is the same. Thedifference in operation between the two processes is controlledby computer software, hence no additional cost is assumed. Forthe multi-column processes, we have increased the percentagesfor the instrumentation and controls and engineering andsupervision sections to accommodate for the fact that theseprocesses will have higher costs that the single-column processesdue to the complexity of the multi-column arrangement.

The design and operation corresponding to the maximumannual profit of each of the four chromatographic processes aresubjected to an economic analysis where the cash flows for eachprocess is evaluated over 15 years to demonstrate the value of

Table 10. Optimization Results for Scenario II: Minimizing Production Costs

single columnsingle columnwith recycle

simulated movingbed process Varicol process

diameter (cm) 19.45 19.45 8.43 7.86length (cm) 100 100 20 35.43flow rate (mL/s) 5.45 5.45 recycle: 2.641 recycle: 2.82

extract: 1.100 extract: 1.011desorbent: 1.230 desorbent: 1.063

number of cycles 1switching time(s) 234 87 each subintervalPuA 0.995 0.995 0.995 0.995PuB 0.995 0.995 0.995 0.995YA 0.80 0.80 0.995 0.995YB 0.98 0.98 0.995 0.995Ctotal

annual(US$)× 106 0.536 0.536 0.268 0.309Pannual(US$)× 106 3.00 3.00 5.37 5.36

minτ,u(t) Φ(Ctotalannual) (49)

maxτ,u(t) Φ(Pannual) (50)


their investment to a project. It is assumed that the maximizednet profit in Table 11 is made each year of the plant life.

The cumulative discounted cash flow (DCF) diagrams forall processes using a 15% discount are shown together in Figure5. The cumulative DCF diagram reflects the value of the profitsmade over the present time, hence the cash flows appear to leveloff with time, despite a fixed annual net profit being assumedeach year. The single column with recycling was shown to havean optimum value of 1 cycle, i.e., collapsing to a single columnwithout recycling. Thus, in Figure 5, the three processes shownare the single column, SMB and Varicol processes.

Initially, the single column has the best economic performancewhich is expected, given that its capital cost is half that of themulti-column processes. This also means that the single columnhas a shorter payback time as compared to the multi-columnprocesses, although the difference is only a few months.However, by the fifth year, all three processes show the samecumulative DCF value, and the multi-column processes becomemore profitable than the single column. The SMB process isthe strongest performer at the end of 15 years (US$ 2.54×107), with the Varicol process second (US$ 2.50× 107) andthe single column last (US$ 2.42× 107). Thus, an important

Table 11. Optimization Results for Scenario III: Maximizing Net Annual Profit

single columnsingle columnwith recycle

simulated movingbed process Varicol process

diamter (cm) 22.34 22.34 7.03 8.95length (cm) 100 100 29.57 22.46flow rate (mL/s) 6.59 6.59 recycle: 3.0961 recycle: 1.72

extract: 1.509 extract: 1.45desorbent: 1.75 desorbent: 1.72

number of cycles 1switching time(s) 200 54.5 each subintervalCtotal

annual(US$)× 106 0.607 0.607 0.278 0.296Pannual(US$)× 106 5.02 5.02 5.43 5.38

Table 12. Estimated Capital Costs Based on Percentage of Delivered-Equipment Cost Method for a Single-Column Process (33)

components % of delivered equipment cost estimated cost (US$)

Direct Costspurchased equipment delivered (including fabricated equipment,

process machinery, pumps and compressors)150, 000

purchased equipment installation 0.39 58,500instrumentation (installed) 0.26 39,000piping (installed) 0.31 46,500electrical (installed) 0.10 15,000buildings (including services) 0.29 43,500yard improvements 0.12 18,000service facilities (installed) 0.55 82,500

Indirect Costsengineering and supervision 0.32 48,000construction expense 0.34 51,000legal expense 0.04 6,000contractor’s fee 0.19 28,500contingency 0.37 55,500total (FCI) 642,000working capitala 0.75 112,000total capital investment 754,500

a Approximately 15% of total capital investment.

Table 13. Estimated Capital Costs Based on Percentage of Delivered-Equipment Cost Method for a Multi-column Process (33)

components % of delivered equipment cost estimated cost (US$)

Direct Costspurchased equipment delivered (including fabricated equipment,

process machinery, pumps and compressors)300, 000

purchased equipment installation 0.39 117,000instrumentation (installed) 0.4 120,000piping (installed) 0.4 120,000electrical (installed) 0.10 30,000buildings (including services) 0.29 87,200yard improvements 0.12 36,600service facilities (installed) 0.55 165,000

Indirect Costsengineering and supervision 0.5 150,000construction expense 0.34 102,200legal expense 0.04 12,200contractor’s fee 0.19 57,200contingency 0.37 111,600total (FCI) 1,407,000working capitala 0.75 225,000total capital investment 1,632,000

a Approximately 15% of total capital investment.


consideration for the investment in a process is the life time ofthe plant. For this case study, for a long term investment (morethan 5 years), the SMB/Varicol process is a better option. Thecumulative DCF also shows that, while the net profit of theSMB process is only slightly higher than that of the Varicolprocess (US$ 5.43× 106 and US$ 5.33× 106, respectively),this difference is significant over time.

Step VI: Process Selection.Of the processes explored, thesingle column is demonstrated to be the least cost-efficient overtime, even though its capital cost is the lowest. Initially (time0 to 5 years), it has a greater cash flow than either the SMB orthe Varicol process. This is largely due to the high productioncosts associated with this process because of the size of thesingle column (and hence the amount of absorbent and the eluentconsumption required). Table 11 shows that at the optimum,the annual production cost of the single column is more thantwice that of the SMB unit.

The economic performances of the multi-column processesappear to be very similar over the first 8 years, although afterthis, the SMB process has a markedly higher cumulative DCF.This suggest that there is little difference in using either of theprocesses over the first 8 years and that SMB should evidentlybe the first choice as it is the most profitable process at the endof the plant life as well as the easier to operate.

However, the optimization has been limited for the multi-column processes in two aspects:

1. The column configuration of the multi-column processeshas not been optimized in this case study, i.e., the columnconfiguration of 2/2/2/2 is fixed, due to the difficultiesencountered in optimizing such a complex model. Literaturesuggests that the Varicol processes save on adsorbent cost (byusing fewer columns) and may hence be more attractive thanthe SMB unit.

2. The Varicol process as considered in this work is limitedto equal sub-intervals of switching times due to the limitationof the CSS model implemented. This means that the otherpotential degrees of freedom in unequal switching times havenot yet been explored.

Even with these limitations, however, the multi-columnchromatographic processes are clearly a better choice for thiscase study.

Conclusions

In this work, a systematic approach for the selection of themost suitable single- or multi-column chromatographic process

based on a full economic appraisal of a given separationspecification has been presented. Four process alternatives havebeen considered: single column, single column with recycling,simulated moving bed (SMB) process and Varicol process. Acase study has been used to demonstrate the approach whereeach process alternative was optimized for three differentscenarios: Scenario I only involved the single-column processesto demonstrate that optimization based on a weighted objectivefunction of productivity and recovery yield can improve thedesign of the column such that its results are comparable withthe multi-column processes. Scenario II and III considered allsingle and multi-column processes, and show that the minimiza-tion of the production costs of the process (Scenario II) doesnot necessarily lead to the maximum profit (Scenario III),although the results are not very different. All three scenariosshowed that the single column with recycling collapsed to asingle column as the optimal number of cycles is 1.

Some interesting results have been shown in the economicalappraisal, which was conducted for the maximum annual profitresults (Scenario III). It has been demonstrated that, while thesingle column initially showed a stronger economic performancecompared to its multi-column counterparts, this graduallydeteriorated over time due to its operating costs being twicethat of the multi-column processes. The SMB process has beenshown to be the best choice for this case study, although theVaricol process was only marginally worse. It is quite possiblethat if all the degrees of freedom of the Varicol process wereexplored, the Varicol process may come out best. If theinvestment is short-term, however, the single column may beeconomically more viable due to its relatively low capital cost.The single column with recycling may also perform better inother separations to lower production costs for single-columnoperation.

It should be noted, however, that the case study used toillustrate the systematic approach only considers a linearisotherm. The fact that the single column with recycle reducesto the single column without recycle is most likely due to thelinearity of the isotherm. If the product purities were difficultto meet (common in nonlinear chromatography) the recyclewould have probably played a role.

Acknowledgment

The authors gratefully acknowledge the financial assistanceof the UCL Graduate School (S.C.). In addition, helpfulconversations with Daniel Bracewell (UCL), Suzanne Farid

Figure 5. Discounted cumulative cash flow figure for all chromatographic alternatives.


(UCL), Derek Hill (Novasep) and Marc Bisschops (Univalid)to formulate this work are gratefully acknowledged.

Appendix: Calculation of Annual Net Profit

The net profit of a process is the difference between theamount made from the sales of the product and the cost ofprocessing the product. The latter includes not only theproduction costs, but also the costs of the raw material used tomake the product. The annual net profit for each chromato-graphic process may therefore be written as follows:

wherePannualis the net annual profit,Sincomeannual is the annual sales

income from selling the purified products produced,CRMannual is

the annual cost of the raw material andCtotalannual is the annual

total production costs.The total annual cost for each chromatographic process

depends on the operation cost, the eluent cost, the adsorbentcost and the waste cost and may be written as follows:

The individual cost items are determined as follows:1. Labour and Maintenance (Operation) Costs.The labour

and maintenance (operation) costs are assumed to be a costfactor of a certain plant size, and dependent on the operatingtime. The total annual operating costs may be written as:

where Copannual is the total annual operating cost,Cop

hl is theoperating costs per hour andtop

annualis the annual operation timeof the plant.

2. Eluent Cost. A popular comparison between single andmulti-column processes is in terms of the amount of eluent usedas the cost of the eluent is an important cost factor. The annualeluent costs,Cel

annualmay be written as:

whereEc is the eluent consumption over one cycle,Tcycle thetime taken to complete one cycle (of the column/column withrecycle/SMB/Varicol process),top

annual is the annual operationtime of the plant andCel is the cost per kilogram of eluent.

3. Adsorbent Cost. The cost of the adsorbent, or matrix, ina chromatographic column is often high. The cost is generallyspecific to the separation, i.e., the cost is fixed. However,adsorbents have a finite lifetime in which they can be used forchromatographic separations. Hence, the cost of the adsorbentis an important factor, given by:

whereCadsannual is the annual cost of the adsorbent,top

annual is theannual operation time of the plant,tlife is the lifetime of theadsorbent,VC is the volume of the column,Fapp is the apparentdensity of the adsorbent andCads is the cost per kilogram ofadsorbent. The adsorbent cost used is also assumed to take intoaccount the capital costs for the column size as both depend onthe column volume,VC.

4. Cost of Waste. In all separations, there will inevitably besome waste products arising from the separation. These includeimpurities in the feed mixture or off-specification products whereit is no longer economically viable to further purify them. Thecost of this waste needs to be accounted for, and the cost of thecrude loss of product defined in Jupke et al. (13) is used as anestimate:

where Cwasteannual is the total annual cost of the waste products

generated,Mwasteis the mass of waste products generated overone cycle,Tcycle the time taken to complete one cycle (of thecolumn/column with recycle/SMB/Varicol processes),top

annual isthe annual operation time of the plant andCwasteis the cost perkilogram of waste generated.

Notation

Cadsannual annual adsorbent (stationary phase) costs

Cads adsorbent (stationary phase) costsCi concn of componenti in mobile phaseCel cost per kg of eluent

Celannual annual eluent costs

Cextract,i concn of componenti in extractCfeed,i concn of componenti in feed

Copannual annual operation costs

Coph hourly operation costs

Craffinate, i concn of componenti in raffinateCRM cost of raw material

Ctotalannual annual production costs

Cwasteannual annual waste costs

Cwaste waste costsCin,i concn of componenti in entering process streamCout,i concn of componenti in exiting process streamCNin.i concn of componenti in entering nodal streamCNout,i concn of componenti in exiting nodal streamDax axial dispersion coefficientDC diameter of columnEc eluent consumption over 1 cyclekeff,i effective diffusivityKi Henry’s coefficient for componentiL length of columnMwaste mass of waste products generated over 1 cycleNoComp number of componentsPannual annual profitPe Peclet numberPri productivity of componenti (massi produced/(batch time

× column vol))Pui purity of componenti (massi produced/mass of total

mixture produced)qi concn of componenti at stationary phaseQdesorbent flow rate of desorbentQextract flow rate of extractQfeed flow rate of feedQraffinate flow rate of raffinateQin flow rate of process inletQout flow rate of process outletQNin flow rate of nodal inlet streamQNout flow rate of nodal outlet streamRP radius of particleRe Reynolds’ number

Pannual) Sincomeannual - CRM

annual- Ctotalannual (A1)

Ctotalannual) Cop

annual+ Celannual+ Cads

annual+ Cwasteannual (A2)

Copannual) Cop

h topannual (A3)

Celannual)

Ec

TcycletopannualCel (A4)

Cadsannual)

topannual

tlifeVCFappCads (A5)

Cwasteannual)

Mwaste

TcycletopannualCwaste (A6)


Sincome sales incometinj feed load or injection time periodtlife lifetime of stationary phasetop operation timetop

annual annual operation timeTcycle time for 1 SMB cycle periodTswitch time for 1 SMB switching periodu interstitial velocity of mobile phaseu(t) vector of control variables in dynamic optimizationVc volume of columnV velocity of the mobile phaseYi yield of componenti (massi produced/massi fed to

column)

Greek letters

ε porosity of stationary phaseη viscosity of mobile phaseF density of mobile phaseFapp apparent viscosity∆P pressure drop across columnt total time horizon

Coordinates

z axial coordinatet time coordinate

References and Notes(1) Heuer, C.; Seidel-Morgenstern, A.; Hugo, P. Experimental inves-

tigation and modelling of closed-loop recycling in preparativechromatography.Chem. Eng. Sci.1995, 50, 1115-1127.

(2) Grill, C. M. Closed-loop recycling with periodic intra-profileinjection: a new binary preparative chromatographic technique.J.Chromatogr. A1998, 796, 101-113.

(3) Grill, C. M.; Miller, L. Separation of a racemic pharmaceuticalintermediate using closed-loop recycling.J. Chromatogr. A1998,827, 359-371.

(4) Quinones, I.; Grill, C. M.; Miller, L.; Guiochon, G. Modelling ofseparations by closed-loop steady-state recycling chromatographyof a racemic pharmaceutical intermediate.J. Chromatogr. A2000,867, 1-21.

(5) Teoh, H. K.; Turner, M.; Titchener-Hooker, N.; Sørensen, E.Experimental verification and optimisation of a detailed dynamichigh performance liquid chromatographic column model.Comput.Chem. Eng.2001, 25, 893-903.

(6) Zhang, Z.; Mazzotti, M.; Morbidelli, M. Multiobjective optimisationof simulated moving bed and varicol processes using a geneticalgorithm.J. Chromatogr. A2003, 989, 95-108.

(7) Zhang, Z.; Morbidelli, M.; Mazzotti, M. Experimental assessmentof powerfeed chromatography.AIChE J.2004, 50, 625-632.

(8) Schramm, H.; Kaspereit, M.; Kienle, A.; Seidel-Morgenstern, A.Simulated moving bed process with cyclic modulation of the feedconcentration.J. Chromatogr. A2003, 1006, 77-86.

(9) Ziomek, G.; Antos, D.; Tobiska L.; Seidel-Morgenstern, A.Comparison of possible arrangements of five identical columns inpreparative chromatography.J. Chromatogr. A2006, 1116, 179-188.

(10) Nicoud, R.-M.; Fuchs, G.; Adam, P.; Bailly, M.; Ku¨sters, R.;Antia, F. D.; Reuille, R.; Schmid, E. Preparative scale enantiosepa-ration of a chiral epoxide: Comparison of liquid chromatographyand simulated moving bed adsorption technology.Chirality 1993,5, 267-271.

(11) Miller, L.; Grill, C. M.; Yan, T.; Dapremont, O.; Huthmann, E.;Juza, M. Batch and simulated moving bed chromatographic resolu-tion of a pharmaceutical racemate.J. Chromatogr. A2003, 1006,267-280.

(12) Grill, C. M.; Miller, L.; Yan, T. Q. Resolution of a racemicpharmaceutical intermediate, a comparison of preparative HPLC,steady state recycling and simulated moving bed.J. Chromatogr. A2004, 1026, 101-108

(13) Jupke, A.; Epping, A.; Schmidt-Traub, H. Optimal design of batchand simulated moving bed chromatographic separation processes.J. Chromatogr. A2002, 944, 93-117.

(14) Guiochon, G. Preparative liquid chromatography.J. Chromatogr.A 2002, 965, 129-161.

(15) Seidel-Morgenstern, A.; Guiochon, G. Theoretical study ofrecycling in preparative chromatography.AIChE J.1993, 39, 809-819.

(16) Teoh, H. K. Optimal design and operation of high performanceliquid chromatographic processes. Ph.D. thesis, University CollegeLondon, University of London, 2002.

(17) Ludemann-Hombourger, O.; Pigorini, G.; Nicoud, R. M.; Ross,D. S.; Terfloth, G. Application of the “varicol” process to theseparation of isomers of the sb-553261 racemate.J. Chromatogr. A2002, 947, 59-68.

(18) Zhang, Z.; Hidajat, K.; Ray, A. K.; Morbidelli, M. Multiobjectiveoptimisation of SMB and varicol process for chiral separation.AIChEJ. 2002, 48, 2800-2816.

(19) Dunnebier, G.; Weirich, I.; Klatt, K.-U. Computationally efficientdynamic modelling and simulation of simulated moving bedchromatographic processes with linear isotherms.Chem. Eng. Sci.1998, 53, 2537-2546.

(20) Strube, J.; Schmidt-Traub, H. Dynamic simulation of simulatedmoving-bed chromatographic processes.Comput. Chem. Eng.1998,22, 1309-1317.

(21) Strube, J.; Altenho¨ner, U.; Meurer, M.; Schmidt-Traub, H.;Schulte, M. Dynamic simulation of simulated moving-bed chro-matographic processes for the optimization of chiral separations.J.Chromatogr. A1997, 769, 81-92.

(22) Hassan, M. M.; Rahman, A. K. M. S.; Loughlin, K. F. Modellingof simulated moving bed adsorption systems: a more preciseapproach.Sep. Technol.1995, 5, 77-89.

(23) Guiochon, G.; Golshan-Shirazi, S.; Katti, A. M.Fundamentalsof PreparatiVe and Nonliner Chromatography;Academic Press,Inc.: New York, 1994.

(24) Nilchan, S.; Pantelides, C. C. On the optimisation of periodicadsorption processes.Adsorption1998, 4, 113-147.

(25) Kloppenburg, E.; Gilles, E. D. A new concept for operatingsimulated moving-bed processes.Chem. Eng. Technol.1999, 22,813-817.

(26) Minceva, M.; Rodrigues, A. E. Modelling and simulation of asimulated moving bed for the separation ofp-xylene.Ind. Eng. Chem.Res.2003, 41, 3454-3461.

(27) Storti, G.; Mazzotti, M.; Morbidelli, M.; Carra`, S. Robust designof binary countercurrent adsorption separation processes.AIChE J.1993, 39, 471-492.

(28) Chan, S.; Titchener-Hooker, N.; Bracewell, D. G.; Sørensen, E.A systematic approach for modelling chromatographic processes-Application to protein purification.AIChE J.2008, 54, 965-977.

(29) Sofer, G.; Hagel, L.Handbook of Process Chromatography: AGuide to Optimization, Scale Up and Validation.Academic Press:New York, 1997.

(30) Li, Z.; Gu, Y.; Gu, T. Mathematical modelling and scale-up ofsize-exclusion chromatography.Biochem. Eng. J.1998, 2, 145-155.

(31) Felinger, A.; Guiochon, G. Optimizing experimental conditionsin overloaded gradient elution chromatography.Biotechnol. Prog.1996, 12, 638-644.

(32) Felinger, A.; Guiochon, G. Optimizing preparative separations athigh recovery yield.J. Chromatogr. A1996, 752, 638-644.

(33) Peters, M. S.; Timmerhaus, K. D.; West, R. E.Plant Design andEconomics for Chemical Engineers, 5th ed,; McGraw-Hill: NewYork, 2003.

(34) Sinnott, R. K.Coulson and Richardson’s Chemical EngineeringVolume 6-Chemical Engineering Design, 3rd. ed,; Butterworth-Heinemann: Woburn, 2001.

(35) Process Systems Enterprise Ltd., gPROMS User Manual, 2007.

Received August 10, 2007. Accepted February 11, 2008.

BP070270M


optimal economic design and operation of single- and multi-column chromatographic processes

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