the use of laboratory - scale fermentation

0960–3085/03/$23.50+0.00# Institution of Chemical Engineers

www.ingentaselect.com=titles=09603085.htm Trans IChemE, Vol 81, Part C, March 2003

THE USE OF LABORATORY-SCALE FERMENTATIONS ASA TOOL FOR MODELLING BEER FERMENTATIONS

N. HEPWORTH1, A. K. BROWN2, J. R. M. HAMMOND2, J. W. R. BOYD1 and J. VARLEY1

1Department of Chemical Engineering and Chemical Technology, Imperial College London, London, UK2Brewing Research International, Nut� eld, Surrey, UK

T here have so far been relatively few attempts reported in the literature to developmodels for prediction of beer fermentation at large scale as a function of key processconditions. Important outputs would be concentrations of key � avour components,

which are important determinants of product quality. Such models would be useful for theirpredictive power, and in the longer term for process optimization. In this paper, an approach forlinking the effect of mixing, based on power input, to kinetic models based on small-scalehomogenous fermentations is presented. The kinetic models themselves are useful as they canbe used for prediction of ethanol, substrate, ester and higher alcohol yield coef� cients, as afunction of temperature, pitching rate, gravity and initial dissolved oxygen concentration in thewort, based on on-line measurements of CO2. On-line measurement of CO2 is relatively easyand inexpensive and so models of this kind should provide a useful � rst stage towardsdeveloping more rigorous models for the brewing industry.

Keywords: beer; kinetics; effectiveness; hydrodynamics; mathematical modelling.

INTRODUCTION

Considering the established nature of the brewing indus-try, there is surprisingly little published information on themodelling and control of industrial-scale beer fermenta-tions. Models which could be used to predict, over arange of scales of operation, the development of yeastgrowth, ethanol and � avour production, particularly as afunction of key process parameters, should be of greatvalue to the brewing industry. Such models would,together with appropriate control strategies, allow formore consistent production and could be used for processoptimization.

The utility of modelling approaches for beer fermentationproposed to date has been restricted because:

° most models have been based on data from bench scalefermenters, in which there are few mass transfer andmixing limitations, unlike processes at industrial scale(¹400 m3);

° those models which have been developed have beenvalidated for only a narrow range of process conditions;

° data used for model development have primarily beenlimited and taken off-line;

° models which allow rigorous optimization would beextremely complex, as full account would have to betaken of kinetics (including effect of key process vari-ables) and of the three-phase hydrodynamics, which areparticularly complex because the � ow is driven by time-varying CO2 evolved during the process.

The key elements of a successful model will be:

(1) accurate prediction of cell growth, substrate uptake andethanol production;

(2) accurate prediction of the main beer � avourcompounds;

(3) robustness of model predictions to changes in the keyprocess conditions (e.g. temperature, pitching rate, pH)

(4) dependence on input parameters, which can bemeasured relatively easily and on-line;

(5) applicability of models over a range of fermenterscales, from laboratory to industrial scale.

In this paper a systematic approach towards developmentof a rather simplistic model, which could allow prediction ofkey characteristics of beer fermentations, is described.Importantly, those in the brewing industry could use thistype of approach readily without the need for complexmathematical modelling of � ow patterns in large-scalefermenters. This approach involves:

(1) A kinetic model based on laboratory experimental datafor impeller agitated fermentations, which are assumedto be well mixed. These models build on thosepublished previously for fermentations driven by CO2

evolution only (no mention is made by these authors ofany additional agitation during fermentation; Treleaet al., 2001; Titica et al., 2000).

(2) Linkage of this kinetic model to larger-scale processesthrough the development of a relationship between

50

(i) the reaction rate in the well-mixed homogenousbioreactor with no diffusional limits and (ii) reactionrates in larger-scale processes.

Alternative approaches have been proposed, for example,a scale-down approach has been described as part of amethodology for optimizing fermenter dynamics anddesign, which included the following steps: (1) regimeanalysis of the (proposed) process on a product scale; (2)simulation of the rate-limiting mechanisms on a laboratoryscale; (3) optimization and modelling of the process on alaboratory scale; and (4) implementation of the process on aproduction scale by transformation of the optimised labora-tory conditions (Luckiewicz, 1978). Other models, forexample, for predicting CO2 generation and CFD modelsapplicable to beer fermentations, have also been described,with the focus on modelling hydrodynamics rather thanintegrating kinetic and hydrodynamic models (Luckiewicz,1978; Luyben, 1997).

The development of kinetic models for well-mixed reac-tors with no diffusional limits will � rst be described,followed by consideration of methods for utilising thesemodels for larger-scale processes.

Monitoringof beer fermentations typically includes off-linemeasurement of wort density, ethanol concentration and aselection of other fermentation products including key � avourcompounds. The maintenance of a particular � avour pro� le isobviously very important in beer production. Typically, pH,temperature, dissolved oxygen and pressure are the onlyvariables measured on-line. It is generally accepted that thekineticmechanisms underlyingethanol and � avour productionin beer fermentations are relatively well understood. Yeastgrowth is generally described in terms of Monod kinetics, i.e.

dX

dtˆ mX (1)

where X is the yeast concentration, t is time and m is aspeci� c growth rate constant. The form of this equation maybe modi� ed to take account of, for example, product(ethanol) inhibition, substrate inhibition and self-inhibition(for a review of kinetics of wine fermentation see Mar‡́n,1999). The production of ethanol and various � avourcompounds including esters and fusel alcohols has beeninvestigated; the production of these � avour compounds islinked to yeast growth (Garc‡́a et al., 1994a).

Recently, kinetic models have been written in terms ofevolution of CO2; this is particularly valuable because CO2evolution can be measured relatively easily on-line. Linearrelationships between the production of higher alcohols andCO2 have been reported (Titica et al., 2000). A two-stagerelationship between the production of esters and CO2 wasfound, with a slow � rst phase of synthesis, followed by asecond accelerated phase. The concentrations wereexpressed through the use of different yield coef� cientsfor the two phases. The transition from slow to acceleratedphase corresponded to the time at which the rate of CO2production was a maximum, regardless of the operatingconditions. This work was extended to include a model forthe fermentation pro� le including ethanol production andsubstrate consumption (Trelea et al., 2001). Relationshipsbetween CO2 production and ethanol production andsubstrate consumption have been developed and yieldcoef� cients have been modelled for a range of operating

conditions at laboratory scale (Trelea et al., 2001; Titicaet al., 2000). The operating conditions they consideredwere: fermentation temperatures of 13, 10 and 16¯C; pres-sures of 800, 450 and 50 mbar; and initial yeast concentra-tions of 20 £ 106, 10 £ 106 and 5 £ 106 million cells per ml.The following relationships were developed for ethanol,substrate, higher alcohol and ester concentration as afunction of time:

Ethanol

E(t) ˆ YE=C £ Cp(t) (2)

Substrate

S(t) ˆ S0 ¡ YS=C £ Cp(t) (3)

Higher alcohols

Alc(t) ˆ YAlc=C £ Cp(t) (4)

Esters

If Cp(t) µ Cdc,m (phase 1)

Est(t) ˆ YEst=C,1 £ Cp(t) (5)

If Cp(t) ¶ Cdc,m (phase 2)

Est(t) ˆ YEst=C,1 £ Cdc,m

‡ YEst=C,2 £ [Cp(t) ¡ Cdc,m] (6)

where E(t), S(t), Alc(t) and Est(t) are ethanol, substrate,higher alcohol and ester concentrations, respectively, Cdc,mrepresents the concentration of CO2 produced correspond-ing to the maximum CO2 production rate, Cp(t) representsthe total amount of produced CO2; S0 is the initial substrateconcentration and YE=C, YS=C, YAlc=C, YEst=C,1 and YEst=C,2 arethe yield coef� cients for ethanol, substrate, higher alcohol,ester (phase 1) and ester (phase 2), respectively. YAlc=C wasconsidered to vary with temperature, the dissolved frac-tion of CO2 and X0 and YEst=C,1 and YEst=C,2 to varywith temperature, pressure and X0

2.In addition to the individual component relationships

described above, the relationships for ethanol and substratewere combined to give the following equation for the rate ofproduction of CO2 as a function of time:

dCp(t)

dtˆ umax

S[Cp(t)]

KS ‡ S[Cp(t)]1

1 ‡ KIE[Cp(t)]2

£ [Cp(t) ‡ C0X0] (7)

where umax is the maximum speci� c CO2 production rate,KS is the substrate limitation coef� cient, KI is the productinhibition coef� cient, C0 is the initial production ratecoef� cient and X0 is the initial yeast concentration, umaxbeing a function of temperature, pressure and X0.

The effect of liquid mixing and fermenter scale has beenconsidered previously (Garc‡́a et al., 1993, 1994b, 1995).The degree of mixing (or homogeneity) throughout thefermentation process has been correlated in terms of CO2

production rate (Garc‡́a et al., 1994b). The work wasextended by introduction of the concept of an effectivenessfactor Z, which was de� ned as the ratio of the rate of reactionin reactor under consideration to the rate of the reaction in ahomogeneous reactor (i.e. a reactor with no diffusionallimits; D‡́az et al., 1996).

LABORATORY-SCALE FERMENTATIONS 51

Trans IChemE, Vol 81, Part C, March 2003

In this paper, research is described in which, the kineticmodels discussed above have been applied to data collectedfrom 1 l fermentations at Brewing Research International(BRi, Surrey, UK) including on-line CO2 data to predictsubstrate uptake and ethanol, higher alcohol and esterproduction for a range of temperatures (12–28¯C), pitchingrates (0.11–2.18 g l¡1), gravities (13–19.25¯Plato), andinitial dissolved oxygen concentration in the wort(0–100% air saturation).

A second part of the model is to link the kinetic dataobtained on small-scale experiments to industrial large-scalefermentations. This will be through the use of an ‘effective-ness factor’ based on CO2 emissions, which due to itsrelative simplicity has the potential to be used widely bythose in the brewing industry.

METHODS AND MATERIALS

Yeast Strain

The lager strain NCYC 1324, was used in this study.Permanent stocks are kept in the BRi Yeast Culture Collec-tion at ¡196¯C in liquid nitrogen. Working cultures aremaintained on MYGP agar slopes at 4¯C.

Yeast Propagation

All wort (standard BRi lager wort, 16¯Plato) was producedin the BRi pilot brewery. Yeast propagation was initiated byinoculating 10 ml of fresh lager wort with a sterile loop ofyeast from an agar slope. This culture was shaken at150 rpm at 25¯C for 24 h. Subsequently, the culture wastransferred into a � ask containing 100 ml lager wort andshaken (150 rpm) at 25¯C for 24 h. Yeast cells were thenenumerated using a haemocytometer and a methylene bluestain using the standard Institute of Brewing (IOB) method.The desired pitching rate for the fermentation was obtainedby diluting the inoculum with fresh lager wort. An inoculumvolume of 100 ml was used for all fermentations.

Batch Yeast Fermentation

Two litre Applikon fermenter systems (sterilized prior touse at 121¯C for 15 min) were used in this study. All processdata including pH (Applikon, UK), dissolved oxygen(Broadley James, USA), carbon dioxide evolution (SierraInstruments, USA) and temperature were logged on-lineusing BioXpert software (Applikon, UK) with an ApplikonADI 1035 BioConsole controlled by an Applikon ADI 1030BioController. Temperature was controlled throughout thefermentations via continuous circulation of water throughthe fermenter outer jacket, employing a B. Braun (Reading,Berks, UK) heater=chiller unit. Dissolved oxygen and pHwere not controlled at any set-point values. A 900ml sampleof fresh sterile wort was pumped into the fermenter and100 ml of inoculum (diluted to the required yeast concen-tration) added at the onset of the fermentation. The fermen-tations were stopped once the speci� c gravity had reached2.5¯Plato. Thirty-four fermentations were run for a range offour process variables (temperature, pitching rate, gravityand initial dissolved oxygen concentration in the wort); runnumbers and process conditions used are shown in Table 1.

Speci� c Gravity and Substrate Measurement

Speci� c gravity was measured using a Kyoto InstrumentsDA-300 Speci� c Gravity Meter. Cell counts and viabilitymeasurements were performed as described in the IOBMethods of Analysis. All speci� c gravity and cell measure-ments were taken during the course of the fermentation;speci� c gravity measurements were converted to density andthen to ¯Plato according to:

¯Plato ˆ (1000 £ density) ¡ 9994484:08745

The sugar (substrate) concentration was taken as the differ-ence between the measured density and the density at theend of the fermentation (2.5¯Plato).

Chemical Analysis

Samples were taken at the end of the fermentation(once speci� c gravity reached 2.5¯Plato) and analysed for� avour volatiles and ethanol. Vicinal diketones weremeasured by GLC as described in the European BreweryConvention Recommended Methods of Analysis using a50 m £ 0.22 mm internal diameter SGE BP20 0.25 (WCOT)fused silica column. Higher alcohols and esters weremeasured by GLC as described in the IOB Methods ofAnalysis using a 60 m £ 0.25 mm internal diameter CP WaxS7-CB (WCOT) fused silica column. These analyses were

Table 1. Run numbers and conditions for all 1 l fermentation experiments.

Runnumber

Temperature(¯C)

Pitchingrate

(g L¡1)Gravity(¯Plato)

Initial DO levelin the wort

(% air saturation)

2 12 0.80 13 503 21 0.36 19.25 04 21 0.30 15.25 505 28 0.30 14.75 1006 28 0.35 19.5 507 21 0.32 14.5 08 21 0.40 10.75 509 21 0.14 14.5 50

10 28 0.36 13.75 5011 12 0.20 14.75 10012 12 1.04 10 5013 21 0.42 14.75 10014 21 0.11 18.75 5015 21 0.50 19 5016 12 0.07 15.25 5017 21 0.84 14.5 5018 21 0.58 14.75 10019 28 0.21 10.75 10020 12 0.18 15 021 21 0.61 14.5 022 12 1.22 17.25 5023 21 0.88 9.75 5024 28 0.88 13.75 5025 21 2.11 9.75 026 21 1.92 17.25 10027 28 0.89 18.5 028 28 1.06 14.75 5029 28 0.21 10.75 5030 21 1.00 18.75 031 21 1.18 15.25 5032 28 0.21 15 10033 28 0.37 18.75 5034 28 2.18 17.75 5035 12 2.03 14.75 50


52 HEPWORTH et al.

performed using a Perkin Elmer Autosystem XL GasChromatograph � tted with a HS40 Headspace Analyserand a FID. Ethanol was measured essentially as describedin the IOB Methods of Analysis on a 15 m £ 0.53mminternal diameter HP-Wax cross-linked polyethylene glycolcolumn using a Hewlett Packard 5890A Gas Chromatograph� tted with a HP6890 Series Injector and an FID.

Pilot-scale Fermentations

The only larger scale data available and which includedon-line CO2 measurements was for 11 litre cylindrico-conicalfermentations run at BRi. The process conditions for thefermentation considered here were initial dissolved oxygenconcentration in the wort ˆ 100% air saturation; pitchingrate ˆ 2.5 g l¡1, gravityˆ 9.25¯Plato and temperatureˆ 20¯C.

RESULTS AND ANALYSIS

The fermentation runs with values for the four processvariables (temperature, pitching rate, gravity and initialdissolved oxygen concentration in the wort) under consid-eration here are shown in Table 1.

For comparison of the data runs, the pitching rate, gravity,temperature and dissolved oxygen level (DO) were normal-ised according to the following equations:

In ˆ 1 ¡ bc

with b ˆ Imin ‡ Imax

2and

c ˆ Imax ¡ Imin

2(8)

where In represents the normalized value of the factor(I varies between Imin and Imax). The normalized valuestherefore ranged from ¡1 to 1.

For each run, the yield coef� cients for ethanol, substrateand � avour compounds were identi� ed from experimentaldata by regression analysis, using equations (2)–(6). (Theexperimental data for CO2 evolution was converted to acumulative CO2 pro� le. From this pro� le, values of Cp foreach sampling time point were available; from these valuesand concentration data, yield coef� cients could then becalculated for each run).

For each measurement of CO2 evolution (every 10 min),the residual between the experimental evolution rate(dCp=dt) and the predicted evolution rate [using equation(7)] was calculated [i.e. (experimental¡ predicted)2]; these

time point residuals were summed and averaged and thevalues of umax, KI and KS were found which minimized thistotal residual (using a Newton–Raphson optimization tech-nique within the package Excel). It was assumed that KI andKS do not vary with operating conditions as has beenreported previously (Trelea et al., 2001); the values takenwere those calculated for run 31 (this being the run closestto central values of all variables); values for this run werefound to be KIˆ 0.2431 and KSˆ 17.0886. In all analysishere it was assumed that C0ˆ 0. Also, as describedpreviously (Titica et al., 2000), account was taken of CO2that would be produced initially but would not be evolveduntil saturation is reached, as it would initially be dissolvedin the wort.

For runs 2–30 and 32–35, the yield coef� cients for the� avour components under consideration and umax weredetermined as linear functions of temperature (T), pitchingrate (P), substrate concentration (S) and initial dissolvedoxygen concentration in the wort (D) and pairwise inter-actions as described in equation (9):

Y ˆ a0 ‡X

aIIˆT ,P,S,D

In ‡X

IˆP,S,D

aT ,ITn, In

‡X

IˆS,D

aP,I Tn, In ‡ aSDSnDn (9)

where subscript ‘n’ denotes normalized value of factor[normalized according to equation (8)] and a values arethe coef� cients with respect to variables given in thesubscript. Where the subscript for a is a product of twovariables, this indicates the coef� cient is for an interactionbetween these two process variables (higher than pairwiseinteractions were found to be insigni� cant).

The calculated coef� cients for umax and � avourcompounds: ethyl acetate, iso butyl acetate, iso amyl acetate,ethyl hexanoate, n-propanol, iso-butanol and iso-amyl alco-hol are shown in Tables 2 and 3. Factor normalizationis valuable as it allows determination of relative importanceof factors on yield coef� cients. The larger the coef� cient,the more in� uential the factor. The value of the sign forthe coef� cient indicates either an increase in the coef� cientwith an increase (positive sign) or decrease (negative sign).

For run 31 values, yield coef� cients and umax calculatedusing equations (2)–(7) (as described above) were comparedwith a second set of values for yield coef� cients and umaxcalculated using equation (9) and the values of coef� cientsgiven in Tables 2 and 3. These two sets of values of yield

Table 2. Yield coef� cient parameters for fermentation pro� le and higher alcohols.

CO2 pro� le Ethanol Substrate n-Propanol Iso-butanol Iso-amyl alcoholvmax (h¡1) Yeth=C [l(100 l¡1)] Ysubs=C (g l¡1) Yalc=C (mg l¡1) Yalc=C (mg l¡1) Yalc=C (mg l¡1)

a0 0.4814 0.5914 ¡5.3363 2.599 2.814 11.845aT 0.1088 ¡0.3770 4.2316 ¡1.523 ¡1.546 ¡7.035aP ¡0.0964 ¡0.2529 3.6863 ¡0.497 ¡0.548 ¡4.463aS 0.1391 0.0007 ¡0.8572 ¡0.612 ¡0.948 ¡4.090aD ¡0.1581 ¡0.0080 0.7585 0.263 0.891 1.469aTP ¡0.0646 0.3592 ¡4.9073 0.949 0.973 7.084aTS 0.2280 0.0514 ¡0.5159 0.396 0.396 4.429aTD ¡0.1559 0.0434 ¡0.8992 ¡0.245 ¡1.313 1.959aPS 0.1653 0.1122 ¡1.8500 0.329 ¡0.039 0.321aPD ¡0.1096 ¡0.1473 2.2612 ¡0.553 ¡0.808 ¡0.754aSD 0.0445 ¡0.0450 0.1439 ¡0.496 ¡1.004 ¡3.111

Units for coef� cient parameters can be determined from equation (9).



coef� cients and umax are compared in Tables 4 and 5. It isclear from the values in Tables 4 and 5 that in general thereis reasonably good agreement between the two sets of yieldcoef� cients, thus indicating that the model can be used topredict these parameters as a function of the process condi-tions considered here. Agreement between experimental andpredicted values is not as close for yield coef� cients withlow absolute values; this may be as much a result ofaccuracies in experimental determination of these coef� -cients as with predictive values. It is important to note that awider range of process conditions has been considered herethan by previous researchers. It is dif� cult to compare valuesof yield coef� cients with values reported previously in theliterature, because of differences in the process and condi-tions used here as compared to those from other studies.However, yield coef� cients for ethanol, for example, are inrelatively good agreement with those quoted previously(Titica et al., 2000).

As described above, a longer-term objective is to developmodels for prediction of fermentation behaviour at commer-cial scale. In a � rst step towards this goal, the kinetic modelsdeveloped here were used to evaluate fermentation perfor-mance at pilot scale. For the pilot scale data available, onlyCO2 evolution and wort density (substrate uptake) values

had been collected, i.e. there was no � avour data. A CO2evolution pro� le was calculated for the pilot-scale processconditions, assuming solution homogeneity and using themodels described above, for comparison with the measuredevolution pro� le, using the following procedure. Initiallyequation (7) [and yield coef� cient equations for substrateand ethanol, which are needed to determine values for S andE in equation (7)] was integrated using values of umax, KI, KS

(calculated as described above for laboratory scale as afunction of process conditions) to give variation of Cp withtime; dCp=dt could then be calculated. Using this equation,the CO2 evolution pro� le, which would be expected fora small-scale (presumably homogenous) fermentation runat the same process conditions as used for the generation of11 litre fermentation datawas determined. This CO2 evolutionpro� le is compared with the pilot scale experimental data inFigure 1. An effectiveness factor (Z) was evaluated from thisdata as a function of time according to: (Cp)pilot=(Cp)laboratory;this is shown in Figure 2. Also shown in Figure 2 is theeffectiveness factor calculated according to the followingequation, presented by D‡́az et al. (1996):

Z ˆ ben (10)

Table 3. Yield coef� cient parameters for esters.

Ethyl acetate Iso-butyl acetate Iso-amyl acetate Ethyl hexanoate

YEst=C,1

(mg l¡1)YEst=C,2

(mg l¡1)YEst=C,1

(mg l¡1)YEst=C,2

(mg l¡1)YEst=C,1

(mg l¡1)YEst=C,2

(mg l¡1)YEst=C,1

(mg l¡1)YEst=C,2

(mg l¡1)

a0 0.961 4.189 0.002 0.013 0.056 0.367 0.011 0.033aT ¡0.401 ¡4.349 ¡0.002 ¡0.014 0.008 ¡0.263 ¡0.003 ¡0.026aP ¡0.258 ¡2.130 ¡0.006 ¡0.015 ¡0.034 ¡0.187 ¡0.001 ¡0.017aS 0.106 ¡3.859 0.003 ¡0.007 ¡0.009 ¡0.237 0.006 ¡0.016aD ¡0.467 0.100 ¡0.001 ¡0.019 ¡0.002 0.013 0.001 ¡0.003aTP 0.458 2.161 0.001 0.024 0.024 0.224 ¡0.002 0.036aTS 0.128 7.401 ¡0.001 0.019 ¡0.008 0.417 ¡0.005 0.023aTD 0.737 3.088 ¡0.006 0.059 ¡0.022 0.248 ¡0.012 0.027aPS ¡0.232 ¡0.219 0.005 0.003 ¡0.069 ¡0.076 0.005 0.001aPD 0.298 1.300 ¡0.004 0.018 0.053 0.086 ¡0.004 0.000aSD ¡0.046 ¡3.238 0.007 0.003 ¡0.087 ¡0.178 ¡0.001 ¡0.012

Table 4. Yield coef� cient parameters for the fermentation pro� le and higher alcohols experimental and predicted for run 31.

CO2 pro� le Ethanol Substrate n-Propanol Iso-butanol Iso-amyl alcoholvmax (h¡1) Yeth=C [l(100 l¡1)] Ysubs=C (g l¡1) Yalc=C (mg l¡1) Yalc=C (mg l¡1) Yalc=C (mg l¡1)

Experimental 0.4601 0.5111 ¡4.0042 1.9995 2.8056 9.6397Predicted 0.5346 0.5120 ¡4.7702 2.3176 2.4824 10.3181Percentage error 13.9 0.2 16.1 13.7 13.0 6.6

Table 5. Experimental and predicted yield coef� cient parameters for esters: run 31.

Ethyl acetate Iso-butyl acetate Iso-amyl acetate Ethyl hexanoate

YEst=C,1

(mg l¡1)YEst=C,2

(mg l¡1)YEst=C,1

(mg l¡1)YEst=C,2

(mg l¡1)YEst=C,1

(mg l¡1)YEst=C,2

(mg l¡1)YEst=C,1

(mg l¡1)YEst=C,2

(mg l¡1)

Experimental 0.8124 2.8708 0.0000 0.0183 0.0000 0.3288 0.0140 0.0329Predicted 0.9140 3.1662 0.0022 0.0101 0.0538 0.3011 0.0109 0.0271Percentage error 11.1 9.3 100 81.2 100 9.2 28.4 21.4


54 HEPWORTH et al.

where b and n are constants, which were reported to betypically 0.4 and 0.2, respectively, for a Saccharomycescerevisiae fermentation of 200m3 (D‡́az et al., 1996). e isthe power input per unit volume which was calculated forthe pilot-scale fermenter using the following equation:

e ˆ PV

ˆ QCO2g Hf r ln

Hf ‡ 12 H

Hf

³ ´(11)

where QCO2is the CO2 evolution rate, g is acceleration due

to gravity, r is density of the � uid, Hf is atmosphericpressure expressed in terms of meters of � uid in thefermenter and H is the height of liquid in the fermenter. Itis clear from Figure 1 that the larger scale fermentation is

less ‘effective’ than predicted based on an assumed homo-genous 1 litre fermentation. However, from Figure 2 it isclear that the effectiveness factor predicted by equation (10)is not in close agreement with (Cp)pilot=(Cp)laboratory

calculated for this case. However, it should be rememberedthat the constants used in equation (10) to calculate theeffectiveness factor were determined for a much larger scalevessel than is under consideration here; ideally values forthese constants should be determined as a function of scale,but much more large-scale data would be required to achievethis. The large discrepancy at shorter time intervals issomewhat misleading as it arises because of a time lag inthe CO2 pro� le predicted by the model; this could beexplained if in the experimental case the wort was saturatedwith CO2 at the start of the fermentation. The agreementbetween experimental and predicted effectiveness is closertowards the end of the fermentation.

DISCUSSIONS AND CONCLUSIONS

A mathematical model has been developed for predictingyield coef� cients for ethanol, substrate, esters and higheralcohols from on-line measurements of CO2 productionrates, as a function of temperature, pitching rate, gravityand initial dissolved oxygen concentration in the wort, for1 litre laboratory impeller agitated fermentations in whichmixing is assumed to be homogenous. This model is basedon an approach reported for fermentations agitated solely byCO2 evolution by previous researchers (Trelea et al., 2001;Titica et al., 2000), who primarily considered the effect oftemperature, yeast inoculum and pressure on yield coef� -cients. These previous researchers consideredthe dependence on process conditions of yield coef� cientsfor key � avour compounds only, assuming that yieldcoef� cients for substrate and ethanol were independent ofprocess conditions; results here, however, clearly show thatyield coef� cients for ethanol and substrate do vary withprocess conditions investigated. This type of model shouldbe valuable to the brewing industry as CO2 is a relativelyeasy and inexpensive parameter to measure continuouslyon-line. Such models could be used for optimization interms of process conditions to achieve a speci� ed set ofyield coef� cients. It is also suggested here that this kineticmodel can be used to predict yield coef� cients at largerscale, as a function of process conditions considered here,by means of the effectiveness factor approach proposedpreviously (D‡́az et al., 1996). This approach has beenused to compare CO2 evolution predicted for homogenoussmall-scale fermentation with measured values for an11 litre scale fermentation. Demonstration of this approachfor other scenarios, e.g. to predict yield coef� cients as afunction of process conditions at a range of scales, is limitedby the current lack of availability of large-scale � avour andCO2 data. It is suggested here that, as a � rst stage towardsdeveloping models for beer production at larger scale, thisapproach may provide useful information regarding effect ofchanging process conditions and mixing input on yieldcoef� cients for key � avour components. Whilst it is appre-ciated that this approach is relatively simplistic, it has valuein relying on measurable parameters. It is hoped that thisbasic demonstration of this approach will encourage collec-tion of relevant large-scale process data to allow moreextensive model validation. More complex computational

Figure 1. Variation of measured carbon dioxide production rate for the11 litre fermentation as a function of time ( j£), compared with therate predicted from the model equations for an homogeneous 1 litrefermentation (—).

Figure 2. Variation of effectiveness factor for the 11 litre fermentation, as afunction of time, calculated (i) as (Cp)pilot=(Cp)laboratory (£), and (ii) usingequation (10) (‡).



models are likely in the long term to provide more accuratepredictions; however, the development of such models,in integration with kinetic models, is far from trivial.Furthermore, methods for validation of such models wouldneed to be developed.

NOMENCLATURE

Alc higher alcohol concentration, mg l¡1

C0 initial CO2 production rate coef� cient, l g¡1

Cdc,m CO2 concentration at maximum CO2 production rate,l l¡1 wort

Cp total volume of CO2 at time t per litre of wort, l l¡1

D initial dissolved oxygen concentration in the wort,% air saturation

E ethanol concentration, l (100 l¡1) i.e. % v=vEst ester concentration, mg l¡1

g acceleration due to gravity, m s¡2

H height of � uid in fermenter, mHf atmospheric pressure in terms of meters of � uid in

fermenter, mIn normalised factor value, varying between Imax and Imin

KI product inhibition coef� cient, (100 l)2 l¡2

KS substrate limitation coef� cient, g l¡1

P pitching rate, g l¡1

P power input, WQCO2

CO2 evolution rate, l l¡1s¡1

S substrate concentration, g l¡1

S0 initial substrate concentration, g l¡1

t time, hT fermentation temperature, ¯CV volume, m3

YAlc=C yield coef� cient for higher alcohols based on CO2

production, mg l¡1

YE=C yield coef� cient for ethanol based on CO2 production,l (100 l¡1)

YEst=C,1 yield coef� cient for esters based on CO2 productionfor phase 1, mg l¡1

YEst=C,2 yield coef� cient for esters based on CO2 productionfor phase 2, mg l¡1

YS=C yield coef� cient for substrate based on CO2

production units, g l¡1

X yeast concentration, g l¡1

X0 initial yeast concentration, g l¡1

Subscriptn normalized factor value [according to equation (8)]

Greek symbolse power input per unit volume, W m¡3

m speci� c growth rate constant, h¡1

r wort density, g l¡1

Z effectiveness factorumax maximum speci� c CO2 production rate, h¡1

REFERENCES

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Titica, M., Landaud, S., Trelea, I.C., Latrille, E., Corrieu, G. andCheruy, A., 2000, Modelling of the kinetics of higher alcohol and esterproduction based on CO2 emissions with a view to control of beer� avour by temperature and top pressure, J Am Soc Brewing Chem,58(4): 167–174.

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ACKNOWLEDGEMENTS

The authors would like to thank EPSRC for providing funding for thiswork. The agreement of the Chief Executive Of� cer of BRi to thepublication of this work is gratefully acknowledged.

ADDRESS

Correspondence concerning this paper should be addressed toDr J. Varley, Department of Chemical Engineering and ChemicalTechnology, Imperial College London, South Kensington Campus,London SW7 2BY, UK. E-mail: [email protected]

The manuscript was received 8 November 2002 and accepted forpublication after revision 6 March 2003.


56 HEPWORTH et al.

the use of laboratory - scale fermentation

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