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Analytica Chimica Acta 595 (2007) 80–88

Scale-up of batch kinetic models

Maryann Ehly a, Paul J. Gemperline a,∗, Alison Nordon b,David Littlejohn b, J. Katy Basford b, Martin De Cecco b

a Department of Chemistry, East Carolina University, Greenville, NC 27858, USAb WestCHEM, Department of Pure and Applied Chemistry and CPACT, University of Strathclyde,

295 Cathedral Street, Glasgow G1 1XL, UK

Received 17 October 2006; received in revised form 13 February 2007; accepted 16 February 2007Available online 22 February 2007

bstract

The scale-up of batch kinetic models was studied by examining the kinetic fitting results of batch esterification reactions completed in 75 mL andL reactors. Different temperatures, amounts of catalysts, and amounts of initial starting reagents were used to completely characterize the reaction.custom written Matlab toolbox called GUIPRO was used to fit first-principles kinetic models directly to in-line NIR and Raman spectroscopic data.

econd-order kinetic models provided calibration-free estimates of kinetic and thermodynamic reaction parameters, time dependent concentrationrofiles, and pure component spectra of reagents and product. The estimated kinetic and thermodynamic parameters showed good agreementetween small-scale and large-scale reactions. The accuracy of pure component spectra estimates was validated by comparison to collected NIR

nd Raman pure component spectra. The model estimated product concentrations were also validated by comparison to concentrations measured byff-line GC analysis. Based on the good agreement between kinetic and thermodynamic parameters and comparison between actual and estimatedoncentration and spectral profiles, it was concluded that the scale-up of batch kinetic models was successful.

2007 Elsevier B.V. All rights reserved.

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eywords: Reaction modeling; Online spectroscopy; Nonlinear regression; Re

. Introduction

Batch processing is an important method in the chemicalnd pharmaceutical industries, especially in the production ofow volume high value products. Fitting of kinetic models to

ultivariate spectroscopic measurements as a function of timeas made possible new methods for monitoring and control-ing batch reactions [1–3]. Fitting of multiway kinetic modelso spectroscopic measurements using non-linear least squaresstimation of model parameters is now well established [4–7].itting of these first principles kinetic models directly to spectro-copic data is a useful, calibration free method for characterizingatch reactions [2]. The determination of reaction mechanisms

nd rate constants gives fundamental process insights and is ofignificant practical use in process analytical chemistry [1,2].nce a kinetic model is obtained, it can be used to forecast reac-

ion endpoints, predict reaction yields and can be used to controlnd optimize industrial processes [2].

∗ Corresponding author. Tel.: +1 252 328 9810; fax: +1 252 328 6767.E-mail address: gemperlinep@ecu.edu (P.J. Gemperline).

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003-2670/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.aca.2007.02.040

kinetics; Model scale-up

Scale-up of processes from the laboratory to pilot scale is aritical problem in process development [8–10]. During scale-p, mass transfer, energy transfer and agitation processes changeignificantly and can lead to significant safety concerns if notddressed properly. Only robust control models that properlyodel mass transfer, energy transfer and agitation can be suc-

essfully transferred during scale-up.In this paper, we report the scale-up of batch reaction

odels from 75 mL to 5.0 L reactors. Batch reactions wereun with calorimetry data, in-line NIR data, in-line Ramanata for small-scale batches and off-line gas chromatogra-hy analysis. Model fitting was completed using a previouslyescribed custom Matlab program called GUIPRO [11]. Theoftware performs non-linear least-squares fitting of first-rinciples kinetic models including mass balance and reagentow-in to in-situ spectroscopic measurements from batcheactors. Modeling of chemical equilibria is included in the

inetic fitting process [12]. It is the hypothesis of this paperhat a successful scale-up can be judged by successfully fit-ing the same first-principles model to measurements frommall-scale and large-scale batch reactions and obtaining very

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M. Ehly et al. / Analytica C

imilar kinetic, equilibrium, and other thermodynamic modelarameters.

According to the Beer–Lambert Law, multivariate spectro-copic data measured as a function of time can be represented inatrix notation where Y (n × m) is a matrix of reaction spectraeasured over n time intervals, one spectrum per row, digitized

t m wavelength or frequency intervals. It is assumed that Yan be expressed as a product of pure component concentrationrofiles, C (n × k), and pure component spectra of the absorbingpecies, A (k × m). Small, random experimental errors, R, in theeasurements are defined as the difference between the mod-

led reaction spectra, C × A, and the measured reaction spectra,.

= CA + R (1)

Using the least squares criterion, the task of the model fittingrocess is to find the best rate constants and equilibrium con-tants that define matrix C, and the best molar absorptivities thatefine matrix A, for a given data set, Y. Given the estimates of theoncentration profiles, C, calculated by numerical integration,stimates of the pure component spectra, A, can be calculatedn a single step as they are linear parameters and do not need toe passed through a non-linear integration routine [13].

ˆ = C−1

Y (2)

Knowing the initial concentration of all reagents and a func-ionally adequate kinetic model, calibration-free fitting can beccomplished [2,11]. A significant advantage of this approachs that there is no need for multivariate calibration with methodsike partial least-squares (PLS) and costly and time-consumingeference methods such as off-line GC.

Under non-isothermal conditions the custom kinetic fittingoftware used in this project is able to model the effect ofemperature on kinetic rate constants and chemical equilibriumonstants. This is accomplished by the incorporation of temper-ture measurements into the numerical integration routines, andsing an Arrhenius model for rate constants and a van’t Hoffodel for equilibrium constants [1,2,14–16]. In order to avoid

igh correlation between the parameters A and EA, the reparam-terized form of the Arrhenius equation shown in Eq. (3) is usedhere kref is the rate constant at temperature Tref. This approach

equires fitting of two parameters, kref and Ea, for each kinetictep in a model instead of one parameter, k.

= krefe−(1/T−1/Tref)Ea/R (3)

The temperature dependence of the equilibrium reaction isodeled by fitting the van’t Hoff equation

og(K) = log(Kref) −(

1

T− 1

Tref

)ΔHf

2.303R(4)

here log(K) is the value of the equilibrium constant at some

xperimental temperature, T; log(Kref) is the value of the equi-ibrium constant at some reference temperature, Tref; �Hf is thetandard enthalpy of formation in joules per mole of the equi-ibrium reaction at Tref. Compared to fitting iso-thermal models

dpli

a Acta 595 (2007) 80–88 81

nd one model parameter, log(K), two parameters, log(Kref), andHf, are estimated here.It is usually not feasible to study complex reaction mecha-

isms by only fitting a model to one batch reaction, as is done iningle batch analysis [4,17]. When the analysis is restricted tosingle batch, some experimental factors such as the effect of

emperature, different amounts of catalyst, different initial con-entration of reagents, etc., may not be adequately represented inhe measurements. Instead it is often necessary to study batcheserformed under different conditions to completely characterizereaction at different conditions including temperature, amountf catalyst and initial mole ratio of reactants using a processeferred to as second-order analysis [4,17], In multi-batch anal-sis, one model is simultaneously fit to two or more experimentsr batches.

The multi-batch approach to fitting one model to multiplexperiments offers many benefits including more robust esti-ates of parameters, validation of the model, breaking rank

eficiencies and guarding against over-fitting [2,18]. For exam-le, a more robust model may be obtained if multi-batch analysisroduces a model that gives a useful fit over a wider rangef experimental conditions such as temperature or amount ofatalyst. Rank deficiencies can occur in some kinetic modelshere two or more species are consumed or produced at the

ame rate, as in the model for the mechanism A + B → C + D.ulti-batch analysis of two or more experiments with different

nitial ratios of A/B and C/D helps resolve this type of rank defi-iency. In single batch analysis, different mechanistic models ofncreasing complexity may be found that are statistically suffi-ient for a series of experiments (over-fitting); however, whenulti-batch analysis is applied to simultaneously fit two or more

xperiments with different experimental conditions, is likely thatnly one model will be found to be statistically sufficient forll experiments simultaneously, thus helping to guard againstver-fitting.

Multi-batch analysis was used in this project to performimultaneous fitting of one model to data of multiple batchesperated at different conditions including temperature, amountf catalyst and initial mole ratio of reactants. All the previ-usly described procedures can be applied to multi-batch data,roducing a multi-batch kinetic fit.

Multi-batch kinetic models can be used to calculate a singleatrix of molar absorptivities, A, known as a global spectralt, or to calculate individual A for each experiment, known aslocal spectral fit. In other words, local spectral models allowifferences in estimated pure component spectra from batch toatch. Both are very powerful techniques. The choice to use localr global spectral models often depends on the type of analysisnd the degree of spectral variation from batch to batch [2]. Localpectral models provide more flexibility in the fitting process toccommodate for spectroscopic changes between batches suchs, baseline offsets. A drawback of this approach is that theoncentration matrices of the batches, Ci, are often rank deficient

ue to the presence of linear combinations in the concentrationrofiles of e.g. products [2], which requires solving Eq. (2) atower rank. Conversely, in multi-batch analysis, the matrices ofndividual batches are row-wise concatenated, and with properly

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esigned batches, the concatenated matrix may have full rank,aking the solution of Eq. (2) more complete.

. Experimental

In order to study model scale-up, a series of batch reactionsere conducted using a 75 mL reactor at East Carolina Univer-

ity in Greenville, NC and a 5 L reactor located at the Universityf Strathclyde in Glasgow, Scotland. In-situ calorimetry data,IR data and off-line GC data were collected for all batches.aman data were also collected for small scale batches. The

ame chemical reaction, experimental design, and conditionsere used at both scales. The reaction studied was the esteri-cation of 1-butanol (BuOH) using acetic anhydride (AA) andatalyst 1,1,3,3-tetramethylguanidine (TMG).

.1. Reactors and process control

The small-scale reactions reported in this study were per-ormed in a custom jacketed 75 mL reaction vessel maden-house at East Carolina University. The reactor and lid werepecially designed to accept an NIR probe, a temperature probe,n electrical heating element and two PTFE feed lines. The reac-or was thermostated using a MGW Lauda RMS6 heater/chillernd the PTFE feed lines were connected to two syringe pumps.he reactor temperature, jacket temperature, heater power, and

eagent addition from the pumps were monitored and controlledy WinISO software from H.E.L. Inc. (Lawrenceville, NJ).tirring was controlled by an IKA Labortechnik RCT Basicagnetic stirrer and a PTFE coated stir bar placed in the reaction

essel.The large-scale reactions reported in this study were per-

ormed at University of Strathclyde in a reactor system suppliedy H.E.L., UK. The reactor included a 5 L glass reaction ves-el with two jackets: an inner oil jacket connected to a JulaboP50-HD heater-chiller and an outer vacuum jacket. A stirrerontrolled by a Paar air motor with a PTFE impeller, a tem-erature probe (Cowie PT100) and two PTFE feed lines werenserted directly into the reaction vessel through B29 ports in theeactor lid. The two feed lines were used to pump in reagentssing ProMinent diaphragm metering pumps. The pumps wereonnected via PTFE convoluted tubing to 5 L flasks, whichere set upon two balances. Two different pump models weresed, a Gamma G/5b and a Gamma L. Another B29 port wassed to connect a glass condenser to the reactor. Process condi-ions, including condenser flow, stir rate, oil jacket temperatureinlet and outlet), reactor temperature, and mass of reagents fedhrough the pumps, were monitored and controlled by WinIsooftware supplied by H.E.L., UK.

The temperature was controlled differently in the small- andarge-scale reactors. Temperature control for the small-scaleeactor was carried out by power compensated calorimetry [19].efore a reaction was initiated, the jacket temperature was set

o a precisely controlled constant value, usually 5–10 ◦C belowhe desired reaction temperature. The reaction temperature was

aintained by a controller that monitored the reaction mixtureemperature using a stainless steel temperature probe in the

aiw1

a Acta 595 (2007) 80–88

eactor and adjusted the power to a hastalloy electrical heatermmersed in the reaction mixture. To achieve temperature con-rol in the large-scale reactor, a controller responded to changesn temperature of the reaction mixture by adjusting the tem-erature of the oil flowing into the jacket. Power compensatedeating was a more effective method for maintaining isother-al conditions, whereas, the response time was much slower

or heating and cooling the large-scale reactor.

.2. Spectroscopic equipment and data acquisition

NIR spectra were collected in the batch reactors using similarnstruments and acquisition parameters. In the small-scale reac-or, NIR measurements were made using a FOSS NIRSystemsSIlver Springs, MD) model 6500 scanning spectrophotome-er with a resolution of 4 nm in the 1100–2500 nm region, and

transflectance fiber optic probe of 1 mm path length. Timeveraged spectra (10 per 30 s intervals) were recorded usingision software designed by Foss NIRSystems. The NIR spec-

rometer used to monitor the large-scale batches was a BomemB155 FTIR/NIR (Clairet Scientific, Northampton, UK) withtransmission probe of 1 mm path length. NIR spectra were

cquired with a resolution of 16 cm−1 in the 4000–12000 cm−1

egion using GRAMS/32 software. For all small- and large-scaleatches, a background spectrum of air was acquired before thetart of each experiment and NIR spectra were measured every0 s during the course of each batch reaction.

Raman spectra were acquired in small-scale batches usingKaiser Optical Systems, Inc. (Ann Arbor, MI) RamanRxn1nalyzer equipped with a 785-nm excitation laser. The spec-

rophotometer was coupled to the reactor using fiber optics and1/4 in. immersion probe with a sapphire window. Spectra wereollected every 30 s using HoloGrams and an exposure time of0 s. A dark current spectrum was acquired of the CCD beforeach reaction, and a cosmic ray filter was employed to removeoise.

.3. Reaction conditions

In order to completely characterize the reaction an experi-ental design was employed that varied temperature, amount

f catalyst, and amount of initial reagents. Operating conditionsor reactions at both scales are shown in Table 1.

This experimental design allowed multivariate kinetic fittingesults to be compared to a conventional Arrhenius plot of 1/Tersus ln(k). For each small-scale reaction, the process was ini-iated by adding 25 mL of pure acetic anhydride (AA, Fishercientific, Fair Lawn, NJ) into the dry reactor at room tempera-

ure. Power was applied to the internal heater to warm the AA tohe temperature specified in the experimental design. Data acqui-ition began when the desired temperature was reached. Catalyst,1,3,3-tetramethylguanidine (TMG, 99%, Sigma Aldrich, Saintouis, MO) was added to the warm AA via a syringe pump over

period of about 3–5 min. When the temperature of the result-

ng mixture equilibrated, 1-butanol (BuOH, Fisher Scientific)as added to the reactor using a second pump at a flow rate of.0 mL min−1. Doses of 25–35 mL thus took 25–35 min to com-

M. Ehly et al. / Analytica Chimica Acta 595 (2007) 80–88 83

Table 1Experimental design and reaction conditions for 75 mL (sm) and 5 L (lrg) reactorsa

BuOH: AA molar ratio Volume BuOH (mL) Batch Volume TMG (mL)

sm lrg sm lrg

0.8:1 20 1400 1 1.4 701:1 23 1680 2 0.7 351:1 23 1680 3 4, 5, 6 7 1.4 701:1 23 1680 8 2.8 1401:0.8 31 2170 9 1.4 70

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emperature (◦C)

a Initial volume of acetic anhydride (AA) for all small and large scale reactio

lete. The reaction was allowed to proceed for approximately 2 hfter BuOH addition and data acquisition continued until ceasedy the operator.

Operation of the large-scale reactor was adjusted accord-ng to the following procedure. Acetic anhydride (AA, GPR98%, BDH, UK) was added to the reactor via the Gamma/5b pump, data acquisition was immediately initiated and

he reactor was heated to the set point temperature. 1,1,3,3-etramethylguanidine (TMG, 99%, Sigma–Aldrich, UK) wasound to corrode the viton tubing that was employed with theeristaltic pumps so it was added manually via a glass funnel.hen the reactor temperature returned to the set point afterrise in temperature caused by catalyst addition, 1-butanol

BuOH, GPR ≥98%, BDH) was pumped into the vessel usinghe Gamma L pump at a flow rate of about 55–60 g min−1. Dosesf 1200–2100 g thus took 25–35 min to complete. Data wascquired continually for approximately 3 h after BuOH addition.

.4. Off-line GC analysis

During each large-scale reaction, aliquots of the reactionixture (200 �L) were taken at specified times throughout the

ourse of the reaction. For the first 30 min, aliquots were with-rawn every 5 min. Thereafter, the time between sampling wasrogressively increased to 30 min. Each aliquot was diluted to0 mL with methanol (CHROMASOLV HPLC grade >99.9%igma–Aldrich, UK) in a volumetric flask to which 200 �L 4-ethyl-2-pentanone (MIBK, Spectrophotometric grade, 99.5%,igma–Aldrich) was added as an internal standard. Calibrationtandards were prepared for one of the products, butyl acetate,y pipetting 25, 50, 75, and 100 �L of >99% anhydrous butylcetate (BuOAc, Sigma–Aldrich) into 10 mL volumetric flaskso which 200 �L MIBK was added. The mixtures were diluted toxactly 10 mL with methanol. Reaction samples and calibrationtandards were analyzed using a Hewlett-Packard model 5890C instrument equipped with a 25 m × 0.22 mm CP-SIL 19 col-mn operated at 50 ◦C. An injection volume of 1 �L was usedn a split injection mode at a split ratio of 11:1 with nitrogen ashe carrier gas at a flow of 5.8 mL min−1.

. Results and discussion

Using the custom kinetic fitting program, GUIPRO, first-rinciples kinetic models were fitted directly to collected NIR

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nd Raman spectroscopic data. Before modeling was attempted,he collected NIR spectra were truncated to the region from100–2200 nm. The time range was set to include spectra fromhe time after catalyst was added to AA when the BuOH pumpas turned on, until the experiment was stopped. All spectraere baseline corrected using a zero average offset.Raman spectra were preprocessed in a similar manner. The

aman shift range was truncated to the fingerprint region of00–1875 cm−1. The time range was set to include spectra fromhe time when the BuOH pump was turned on, until the exper-ment was stopped. All spectra were baseline corrected using aero average offset. In addition, the spectra were normalized toband at 419 cm−1 from the sapphire ball window to correct

or fluctuations in laser intensity and light collection efficiencyrom batch to batch.

The model fitting procedure was carried out in stages. Therst stage consisted of fitting a variety of mechanisms to singleatches. Several models fit reasonably well to single batch data;owever, when they were tested on multiple batches, poor qualityts were produced. In stage 2, modeling was done on subsets of

hree to five batches to examine separately the effect of temper-ture, catalyst and the mole ratio of AA to BuOH. This strategyelped build a fundamental understanding of each experimentalffect. Once multi-batch kinetic models were completed for sub-ets of three to five batches, stage 3 work focused on integratinghe model features for each individual effect into one multi-batchinetic model that accounted for all three effects in all batches.echanism (5) was found to produce the best quality fits in

tage 3 of the modeling procedure. This mechanism includes anquilibrium reaction between AA, and a catalyst TMG, to yieldcatalyst activated reagent. The activated AA:TMG complex

eacts with BuOH to liberate the catalyst and yield products,utyl acetate BuOAc, and acetic acid, HA.

AA + TMGlog(K)� AA : TMG

AA : TMGk−→BuOAc + HA + TMG

(5)

Using mechanism (5) non-isothermal local and global multi-atch kinetic models were developed and fit to the batches atll points of the experimental design to produce estimates of

inetic and thermodynamic parameters, concentration profiles,nd pure component spectra. The model fitting process con-erged smoothly to the same parameter values for a reasonablyide range of initial parameter estimates. Selection of very poor

84 M. Ehly et al. / Analytica Chimica Acta 595 (2007) 80–88

Table 2Comparison of NIR and Raman kinetic model fitting results for large- and small-scale batches and estimated uncertainties (±2 std. dev.)

Large-scale fits Small-scale fits Raman small-scale fits

log(K) −1.838 ± 0.001 −2.237 ± 0.002 −2.257 ± 0.002�Hf (kJ mol−1) −12.88 ± 0.07 −12.65 ± 0.03 −14.81 ± 0.07kref (L mol−1 s−1) 0.03996 ± 0.00004 0.0863 ± 0.0004 0.0556 ± 0.0002ES

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A (kJ mol−1) 46.39 ± 0.02td. dev. (Y) 0.0013

nitial starting values resulted in convergence failure, divergence,r estimation of spectral profiles with unreasonable negativeeaks in the estimated pure component spectra.

The results of fitting are shown in Table 2 using local spectralodels. The fit results for the large-scale reactions show param-

ters estimated by fitting all nine large-scale batches. Due to annmeasured pathlength change in the fiber optic probe, not allmall-scale batches in the experimental design were includedn the model. The batches left out of the model fitting processnclude batches 2, 5 and 6 shown in Table 1. The kinetic param-ters log(K) and k correspond to the first and second step inhe reaction mechanism, respectively. Estimates of the reactionnthalpy and activation energy are shown as �Hf and EA, respec-ively. The overall quality of fit was determined by the standard

eviation in the estimated spectral absorbance values, yij (showns Std. Dev. Y in Table 2).

Using identical models for the small-scale and large-scaleatch reactions, nearly the same kinetic parameters were found,

ig. 1. Temperature profiles of two selected batches run at a set point of 40 ◦CA) large-scale batches exhibit large temperature variation from the set pointanging from 35 to 63 ◦C (B) small scale batches exhibit excellent temperatureontrol throughout the entire run.

F(

40.68 ± 0.08 56.6 ± 0.20.0013 0.033

ndicating the model scale-up was successful. The estimatedhermodynamic parameters �Hf and EA were not as precisen the small-scale batch reactions; however. This may possiblye due to a lower amount of variability in the temperature inhe small-scale batch reactions. As discussed in the Section 2,

ig. 2. Measured (· · ·) and estimated(—) spectra for: (A) AA (B) BuOH andC) product.

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wauacage spectrum of pure BuOAc and pure HA. The estimated andaveraged spectral profiles show good agreement.

Fig. 3 shows model estimated concentration profiles forAA, BuOH and product for a large-scale batch at the cen-

ig. 3. Model estimated concentration profiles as a function of time for AA (—),uOH (· · ·) and product (- - -) in large-scale batch 4.

f an immersion heater with much shorter response times, ands a result, much better thermal regulation. The large range ofemperature variations (ca. 25–80 ◦C) in the large scale batcheseem to produced better estimates of thermodynamic parametersith corresponding smaller estimated errors compared to the

maller range of temperature variations (ca. 27–53 ◦C) in themall scale batches. Sample temperature profiles are shown forlarge-scale batch (Fig. 1A) and a small-scale batch (Fig. 1B)

or visual comparison of batch temperature variation.The model allowed for calibration free estimates of spec-

ral and concentration profiles for reactants and products. Underhe conditions in this paper, the concentrations of TMG andhe AA:TMG complex were too low to reliably estimate theirpectra, although their kinetic effects were adequately modeled.ig. 2 shows a comparison of measured to fitted AA, BuOH androduct spectral profiles produced from the large-scale multi-atch kinetic model.

Good agreement was observed between the estimated AApectrum and measured spectrum of neat AA. The addition ofuOH to AA gave rise to a strong OH stretching band in therst overtone region at approximately 1420 nm. This band isost likely due to a change in the intermolecular hydrogen

onding of BuOH induced by the addition of AA. Because of

his band, there is poor agreement between estimated and mea-ured BuOH spectrum in the first overtone stretching region from390–1650 nm.

ig. 4. Large-scale GC calibration results: overlay of GC concentrations fromeplicate large-scale batches (center points of experimental design).

Fb(E

a Acta 595 (2007) 80–88 85

Only one product concentration profile and spectral profileas estimated because BuOAc and HA form at equal rates

nd are mathematically equivalent. The model estimated prod-ct spectrum represents a pseudo species which is actually theverage spectrum of the actual products. The plot in Fig. 2Compares the model estimated product spectrum with the aver-

ig. 5. Comparison of BuOAc concentration profiles of replicate large-scaleatches 4, 5 and 6 (center point of experimental design) found by GC analysis©) to the concentrations predicted from the multi-batch kinetic model (—).rror bars are shown at two times the standard deviation of the GC results.

8 himica Acta 595 (2007) 80–88

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er point of the experimental design (batch 4). In order tossess the accuracy of the model estimated concentration pro-les, the calculated product concentrations were compared touOAc concentrations determined by GC analysis of reactionliquots.

.1. GC Validation

BuOAc standards were prepared and analyzed each day aarge-scale batch was run to create a total of 11 sets of stan-ards. Two batches from the nine batch experimental designere repeated due to faulty NIR spectra, giving a total of elevenays of GC data. A global calibration curve was constructed byombining the GC data from all eleven daily calibrations. Fig. 4llustrates good precision was obtained in the GC analysis byomparing concentration profiles of replicate batches with thexception of two apparent outlying points at 30 min.

The resulting GC calibration was used to estimate the concen-ration of BuOAc over time for each large-scale batch reaction.

igs. 5–8 show comparisons of the GC measured and modelstimated concentrations of BuOAc for all large-scale batcheactions. Error bars have been included at two times the stan-ard deviation of the GC results.

ig. 6. Comparison of BuOAc concentration profiles for batches run at differ-nt temperatures. Profiles found by GC analysis (©) and the concentrationsredicted from the multi-batch kinetic model (—) are shown for large-scaleatches 3 and 7 run at 30 and 50 ◦C, respectively. Error bars are shown at twoimes the standard deviation of the GC results.

Fig. 7. Comparison of BuOAc concentration profiles for batches with differentamounts of initial reagents. Profiles found by GC analysis (©) and the con-clE

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entrations predicted from the multi-batch kinetic model (—) are shown forarge-scale batches 1 and 9 run with 1400 and 2170 mL of BuOH, respectively.rror bars are shown at two times the standard deviation of the GC results.

Good agreement was observed between the calibration-freeodel estimated concentration profiles and the GC concentra-

ion profiles shown in Figs. 5–7. The magnitude scale of theoncentration profiles and GC profiles match well without anyeed for numerical adjustment. The model estimated productoncentration matches the GC estimated concentration with suf-cient accuracy to provide calibration-free estimates of productield. In Fig. 8, there is a slight mismatch between the modelnd GC estimated profiles; it is believed that the NIR kineticodel is more accurate. The GC determinations are subject to

rrors introduced during sampling (aliquot withdrawal), quench-ng, addition of the internal standard, dilution and subsequentnalysis. Quenching was performed by diluting the withdrawnliquot in methanol as quickly as possible, but this may possi-ly be a significant source of variability, and can be observedn Fig. 4, where GC results from replicate batches are overlaidn one plot. The shape of the model estimated product profileso not follow a traditional exponential growth curve because ofeagent flow in conditions. Early in the batch, the concentration

f BuOH is low, and the product curve begins to increase slowly.fter about 5 min into the reaction, the rate of product forma-

ion increases substantially owing to the presence of significantlyreater BuOH delivered by the pump.

himica Acta 595 (2007) 80–88 87

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M. Ehly et al. / Analytica C

Agreement between three replicate batches (4, 5 and 6) athe center of the experimental design can be observed in Fig. 5.lthough not readily observed in Fig. 5, slight differences in

he shape of the model estimated concentration profiles cane observed when they are overlaid (not shown) due to differ-nces in the temperature profiles from batch to batch. In Fig. 6,he effect of temperature on the rate of reaction can be readilybserved. The use of an Arrhenius model for rate constants andvan’t Hoff model for the equilibrium constant in the model

learly provides a useful estimation of concentration profiles,ncluding the initial rate and final product yield. In Fig. 7, theffect of different initial concentration of reagents is accuratelyodeled. For example, in batch 1, the initial concentration ofA is high. As BuOH is added, the rate of product formation

s correspondingly high. In batch 9, the initial concentrationf AA is much lower, and the rate of product formation isorrespondingly lower. In Fig. 8, the effect of catalyst can beeadily observed, although the model seems to have somewhatower apparent accuracy than the effects previously described.

t low catalyst concentration the initial rate of product formation

nd the product yield are substantially lower compared to highatalyst concentration. Most importantly, the one multi-batchinetic model described here adequately explains simultane-

ig. 8. Comparison of BuOAc concentration profiles for batches with differentmounts of catalyst. Profiles found by GC analysis (©) and the concentrationsredicted from the multi-batch kinetic model (—) are shown for large-scaleatches 2 and 8 run with 35 and 140 mL of TMG, respectively. Error bars arehown at two times the standard deviation of the GC results.

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ig. 9. Measured (- - -) and estimated (—) pure component AA Raman spectra.he estimated spectrum was produced using the small-scale multi-batch kineticodel.

usly the effect of catalyst, temperature and initial reagentatio.

The use of Raman spectroscopy to monitor the small scaleatch reactions allowed comparison of models fitted to NIR andaman spectroscopic data and demonstrated model robustness.he same multi-batch spectral model used to fit NIR spectro-copic data was successfully used to fit Raman spectroscopicata. The model fitting process converged smoothly to the samearameter values for a reasonably wide range of initial parame-er estimates. The Raman results reinforce the adequacy of theatch kinetic model. Fig. 9 shows a comparison of a measuredeat spectrum of AA to the model estimated Raman spectrumf AA.

Excellent agreement was observed between the estimatedaman spectrum of AA and measured Raman spectrum ofeat AA. Table 2 shows comparisons of estimated kinetic andhermodynamic parameters found by fitting NIR and Ramanpectroscopic data to the same model. The same six batchessed to fit the small-scale NIR model were used to fit the Ramanodel. The parameters were close agreement, supporting the

onclusion that an adequate calibration-free model was foundhat accurately predicts the concentration profiles of the reactantsnd products in this reaction.

cknowledgements

This research was supported in part by the National Scienceoundation under Grant Number EEC-0332330. Any opinions,ndings, and conclusions or recommendations expressed in thisaterial are those of the author(s) and do not necessarily reflect

he views of the National Science Foundation. The support ofPSRC through research grant GR/R/1966/01 is also acknowl-dged. Alison Nordon thanks the Royal Society for a Royalociety University Research Fellowship and Martin De Ceccocknowledges support provided by the Carnegie Foundation.

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