Biochemical Engineering Journal 13 (2003) 43–52

An original kinetic model for the enzymatic hydrolysis ofstarch during mashing

C. Brandama,∗, X.M. Meyera, J. Prothb, P. Strehaianoa, H. Pingaudca Laboratoire de Génie Chimique (LGC UMR-CNRS 5503), 5 rue Paulin Talabot, 31106 Toulouse, France

b TEPRAL Research, Centre de Recherche des Brasseries Kronenbourg, 67 route d’Oberhausbergen, 67037 Strasbourg, Francec Centre de Génie Industriel, Ecole des Mines d’Albi Carmaux, Campus Jarlard, Route de Teillet, 81013 Albi CT Cedex 09, France

Received 7 March 2002; accepted after revision 25 July 2002

Abstract

This paper presents a kinetic model for the enzymatic degradation of the starch during mashing for beer production. Based on anew set of experiments, an original reaction scheme for the hydrolysis of starch by�- and�-amylases has been proposed. Here, thekinetics of the reactions involved in this scheme are described: starch gelatinisation, amylase activities and carbohydrate production. Oneoriginality of this model is the mathematical representation of the amylase activities temperature dependency. The model requires to knowthe initial composition of malt (starch concentration and amylase potential which are classically measured to qualify the raw material)and the operating conditions (temperature chart) to predict the evolutions of amylase activities, dextrins and fermentable carbohydrateconcentrations during mashing.

The model parameters have been estimated by fitting nine experiments performed on one malt variety. Five other experiments validatethe model for different malt varieties.© 2002 Elsevier Science B.V. All rights reserved.

Keywords: Beer; Mashing; Enzyme activity; Modelling; Starch; Enzyme bioreactor

1. Introduction

Beer is produced from barley through successive opera-tions: malting transforms barley into malt, mashing extractsmalt grain components and fermentation performs sugarconversion into the alcohol. Among these main steps ofbrewing, the mashing remains relatively unexplored com-pared to fermentation. Yet, it determines the wort compo-sition and so, strongly influences the fermentation step andthe final beer quality and production.

The mashing tank can be considered as an enzymatic re-actor where enzymes and substrates are recovered from maltgrains. The three main enzymatic reactions occurring dur-ing mashing are the hydrolysis of the gelatinised starch intofermentable carbohydrates (glucose, fructose, sucrose, mal-tose and maltotriose), the hydrolysis of proteins into freeamino acids and the degradation of�-glucan chains. Theseconversions happen under the action of amylases, proteases

∗ Corresponding author. Tel.:+33-5-62-88-58-43;fax: +33-5-62-88-56-00.E-mail addresses: cedric.brandam@ensiacet.fr (C. Brandam),xuan.meyer@ensiacet.fr (X.M. Meyer).

and�-glucanases, respectively. To cover the optimal activitytemperature range of each enzyme, mashing is usually op-erated by successive rests at increasing temperatures: a firstrest at 50◦C for proteinisation and�-glucan hydrolysis, asaccharification rest at 65◦C and a final rise up to 76◦C toensure an ultimate dissolution of small starch grains.

The most important reaction for the brewer is certainlythe hydrolysis of starch, since it determines the quantity offermentable carbohydrates in the wort and so the alcohol de-gree of the final beer. As regards this reaction, the objectiveof mashing is to reach the maximal fermentable carbohy-drates productivity, while respecting a specification on thefinal dextrin concentration (non-fermentable carbohydrates)to ensure the organoleptic qualities of the final beer. Indus-trially, this objective is faced with two main difficulties: themalt composition variability due to the annual barley qualityand malting, and the large range of recipes resulting fromthe development of new products. Process operating condi-tions and particularly mashing temperature chart need to bealways finely adapted to ensure the best wort composition.Yet, the effects of temperature on starch hydrolysis are verycomplex and it is often very difficult for the brewer to predictthe result with a good accuracy. As laborious laboratory and

1369-703X/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S1369-703X(02)00100-6

44 C. Brandam et al. / Biochemical Engineering Journal 13 (2003) 43–52

Nomenclature

a(T) global enzyme activity (U/kg of maısche)a(Tref) enzyme activity measured by the

Megazyme method (U/kg of maısche)as(T) relative specific enzyme activity (–)a�, a� global activity of�- and�-amylases

(U/kg of maısche)[D] dextrins concentrations (g/kg of maısche)[E] active enzyme site concentration

(U/kg of maısche)Ede activation energy for enzyme

denaturation (J/mol)Egi activation energy (J/mol),i = 1 for

T < Tg, i = 2 for T > TgEsg activation energy for small starch

granules gelatinisation (J/mol)kde pre-exponential factor for enzyme

denaturation (s−1)kgi pre-exponential factor (s−1), i = 1

for T < Tg, i = 2 for T > Tgkgl, kmlt,k�,mal,k�,mal,kdex,k′

gl, k′mlt,

k′�,mal

andk′�,mal kinetic factors for sugar production

(kg/U s)ksg pre-exponential factor for small starch

granules gelatinisation (s−1)rac reaction rate for global enzyme activity

(U/kg s)rde reaction rate for enzyme

denaturation (U/kg s)rg reaction rate for starch gelatinisation

(g/kg s)rgl, rmlt,rmal, rdex,r ′gl, r ′

mltandr ′

mal reaction rate for sugar production (g/kg s)rsg reaction rate for small starch granules

gelatinisation (g/kg s)R the gas constant (8.31 J/mol K)[Sg] gelatinised starch concentration

(g/kg of maısche)[Ss] ungelatinised starch concentration

(g/kg of maısche)[Sss] ungelatinised small starch granule

concentration (g/kg of maısche)T temperature (K)Tg threshold temperature for gelatinisation

kinetic (K)

v(T ) consumption rate of enzyme specificsubstrate at the temperatureT(U/kg of maısche)

v(Tref) consumption rate of enzyme specificsubstrate at the reference temperature ofthe Megazyme method (U/kg of maısche)

pilot scale experiments cannot be realised to choose suitableprocess conditions for all raw materials used in breweries, amathematical model able to describe the mashing phenom-ena is necessary. It will help to improve the process perfor-mances, to control the final wort sugar composition and toincrease the productivity.

Two models for the starch hydrolysis during mashing havealready been proposed[1,2]. These models suffer from aninaccurate representation of starch gelatinisation and a badsensitivity to the temperature. So, a new kinetic model basedon an original reaction scheme has been developed to over-come this problem and to control better the starch hydrolysisduring mashing.

2. Materials and methods

2.1. Experimental strategy

Mashes were produced in the 100 l microbrewery ofTEPRAL Research (KRONENBOURG breweries researchcentre) by mixing 20 kg of malt with 70 kg of water.

A first set of nine experiments was performed with maltfrom Scarlett variety referenced here as S1. These exper-iments were designed to study the effects of temperature.Seven experiments consisted of four successive rests sep-arated by linear temperature increases: 10 min at 37◦C,increase at 2◦C/min to reach 50◦C, 30 min at 50◦C, avariable length increase at 2◦C/min to reach the desired sac-charification temperature, a saccharification rest at differenttemperatures and lengths, increase at 0.5◦C/min until 76◦Cand 10 min at 76◦C to ensure the total starch gelatinisation.For the first four experiments, the saccharification rest wasperformed at 60◦C (E1), 63◦C (E2), 65◦C (E3) and 70◦C(E4) for 15 min, respectively. The next three experimentswere designed to study the effect of the saccharification restduration: 0 min (E5), 60 min (E6) and 180 min (E7) at 63◦C.The two last experiments were isothermal mashing: one at63◦C for 90 min (E8) where both�- and �-amylases areactive and one at 70◦C for 90 min (E9) to study�-amylaseaction when�-amylases are completely denatured.

A second set of five experiments (E10–E14) was thenrealised using five different malts submitted to the sametemperature chart with a saccharification rest at 63◦C during15 min. The main characteristics of these malts are presentedin Table 1. They correspond to those usually encountered inbrewing.

C. Brandam et al. / Biochemical Engineering Journal 13 (2003) 43–52 45

Table 1Characteristics of the malts used in the set of experiments

Scarlett S1 Scarlett S2 Scarlett S3 Mixing M1 Mixing M2 Mixing M3

Humidity (%) 4.8 4.3 5.4 5.5 4.0 5.1Extract (% MS) 84.4 83.8 84.9 81.4 82.6 81.7Starch (g/kg) 113.5 123.0 117.0 115.0 113.0 120.0Glucose (g/kg) 4.0 3.7 2.4 3.8 5.3 5.3Maltose (g/kg) 5.0 3.1 2.2 8.8 5.4 5.8Maltotriose (g/kg) 0.0 0.0 0.0 1.5 0.0 0.0Dextrins (g/kg) 0.0 0.0 0.0 0.0 0.0 0.0Total �-glucans (% MS) 0.26 0.14 1.50 1.21 0.7 0.3Soluble�-glucans (mg/l) 80 70 480 650 169 44Modification (%) 96 98 82 78.8 87 97Total proteins (% MS) 10.1 8.5 10.9 10.5 9.3 9.8Soluble proteins (% MS) 4.3 4.0 3.7 3.8 4.1 5.5�-Amylase (U/kg MS) 210 230 290 110 210 230�-Amylase (U/kg MS) 380 450 346 345 550 390�-Glucanase (U/kg MS) 98 110 115 110 78 70

2.2. Analytical methods

Samples were withdrawn at different processing times,rapidly cooled at 4◦C in carbo-ice to stop enzymatic activ-ities and centrifuged for 12 min at 4000g. The solid phasewas lyophilised and the liquid phase was frozen before anal-ysis.

Starch in the solid phase was measured with the “totalstarch determination kit” commercialised by the Megazymesocietyhttp://www.Megazyme.com. The gelatinised starchquantities were calculated by differences between initialmalt starch and measured solid residual starch.

Fermentable carbohydrate concentrations were deter-mined by HPLC using WATERS HPLC equipment with anautomatic injector 717, a gradient pump and a refractomet-ric detector. Glucose, fructose, sucrose, maltose and mal-totriose were separated on a SHODEX NH2P-50 4E columnwith acetonitrile/H2O (70:30) at a 1 ml/min flow rate.

Final dextrin concentration was measured by evaluation ofglucose concentration after wort fermentation and treatmentwith amyloglucosidase which hydrolyses all the dextrins intoglucose.

2.3. Enzymatic activity

The activities of the endogenous�- and �-amylaseswere measured with the Megazyme kits based on specificcoloured substrate consumption (AMYLAZYME and BE-TAMYL). These methods measure the amylase activities ata reference temperature: 30◦C for �-amylases and 40◦Cfor �-amylases. They indicate the residual enzymatic poten-tial after the mashing temperature treatment. These valuescan be assimilated to the quantity of still active enzymesbut they do not represent the real enzymatic activity at theconsidered mashing temperature[3].

In fact, the global enzymatic activity depends not onlyon the quantity of active enzymes, but also on the enzyme

capability to perform the chemical bounds degradationwhich is highly temperature dependent. So, to get the realenzymatic activity at the mashing temperatures, relation ofthe specific activity to temperature has been determined.From the same active enzyme quantity, isothermal labo-ratory experiments have been carried out at temperaturesranged between 30 and 75◦C. The initial rate of specificsubstrate consumption for�- and �-amylases gives theactivity with respect to temperature.

Then, the relative specific activityas(T) has been definedas the ratio of the initial rate of specific substrate consump-tion v(T ) measured at temperatureT to the initial rate mea-sured at the reference temperaturev(Tref):

as(T ) = v(T )

v(Tref)(1)

For each mashing experiment, the real enzymatic activityhas been calculated by the formula:

a(T ) = a(Tref)as(T ) (2)

where a(Tref) is the activity measured by the Megazymemethod andas(T) is the relative specific activity.

3. Reaction scheme

Drawing up a reaction scheme constituted the first stepfor the development of a mathematical model to repre-sent the mashing process. The qualitative analysis of theseexperiments has brought to the fore the starch hydrolysismechanisms[4].

In cereals, starch consists of two glucosic polymers,amylose and amylopectin granules. In solution, when tem-perature increases, the structure of the granules changes:they are swollen with water and burst forming a starch gel.This gelatinisation occurs at different temperatures accord-ing to the cereal and the granule size. For barley malt, it

46 C. Brandam et al. / Biochemical Engineering Journal 13 (2003) 43–52

Fig. 1. Starch hydrolysis scheme.

occurs between 55 and 80◦C. The smaller the granules are,the higher the gelatinisation temperature is.

Enzymes cannot act directly on solid starch grains. Theenzymatic catalysis only affects the gelatinised starch. Thespecific role of each enzyme has been determined and it en-ables to suggest a new scheme for starch hydrolysis (Fig. 1).Table 2synthesises and compares three reaction schemes:Marc [5], Koljonen[6] and Brandam et al.[4]. The last onediffers from the others insofar as the carbohydrate produc-tion was find to result from two reactions: a rapid degra-dation of gelatinised starch into fermentable carbohydratesand dextrins by enzymatic catalysed breakage of the easilyaccessible�-1,4 bonds of amylose and amylopectin, and aslower degradation of dextrins formerly produced. The pro-duction occurs as soon as starch begins to be gelatinisedunder the temperature effect. The dextrin degradation takesplace as soon as some starch has been hydrolysed and bothreactions occur simultaneously. Moreover, the experimen-tal results indicate the preponderant role of�-amylase inthe production of glucose, maltose and maltotriose, whereasMarc [5] and Koljonen[6] favoured the�-amylase action.

The main conclusions drawn from the qualitative analysisof our experiments are:

• �-Amylases,�-amylases and initial carbohydrates in maltgrains can be considered as immediately dissolved in liq-uid phase.

• Starch is gelatinised under the temperature effect.

Table 2Comparison of the amylase actions in the reaction scheme of Marc[5], Koljonen [6] and Brandam et al.[4]

Production �-Amylase �-Amylase

Marc [5] Koljonen [6] Brandam et al.[4] Marc [5] Koljonen [6] Brandam et al.[4]

Dextrins√ √ √ √ √

Glucose√ √ √

Maltose√ √ √ √

Maltotriose√ √ √ √

• Enzymes can only act on gelatinised starch and in liquidphase.

• �-Amylase action on gelatinised starch leads to the pro-duction of glucose, maltose, maltotriose and dextrins.

• �-Amylase action on dextrins leads to the production ofglucose, maltose and maltotriose.

• �-Amylase acts on gelatinised starch and dextrins to onlygive maltose.

• Fructose and sucrose concentrations can only vary underthe invertase action that is minor compared to amylaseactions. These two compounds were not included in ourmodel.

• Temperature denatures the enzyme sites but increases therate of catalysis.

4. The stoicheo-kinetic model

4.1. Starch gelatinisation

The gelatinisation is not an instantaneous phenomena: itdepends on temperature, time and grain size. The size distri-bution of malt starch is not a routine analysis in breweries.It has not been measured in this work. In fact, we supposedthat starch consists only of big grains of homogeneous size.

In the literature, the starch gelatinisation kinetic is oftenrepresented as a first-order reaction[7–10]:

rg = Kg[Ss] and Kg = kgexp

(−Eg

RT

)

Our experimental values of ln(Kg) plotted versus tempera-ture (T) show a discontinuity between 60 and 63◦C (Fig. 2).Pravisiani et al.[11] have already observed a similar dis-continuity at 67.5◦C for potato starch. They explained it bythe fact that starch granules consist of several amorphousregions and crystalline regions, the gelatinisation occurringdifferently (temperature threshold and rate) according to theregion. As Verlinden et al.[12], they represented the potatostarch gelatinisation dynamic by a first-order kinetic modelwith a rate constant expressed by an Arrhenius law with twodifferent activation energies based on whether the tempera-ture is under or above 67.5◦C.

To draw up a more detailed model, a microscopic studyof the crystallographic structure of the malt grain wouldbe necessary. To stay at a macroscopic level, we keep on

C. Brandam et al. / Biochemical Engineering Journal 13 (2003) 43–52 47

Fig. 2. Relation between temperature and kinetic parameter logarithm of the starch gelatinisation reaction.

modelling the starch gelatinisation considering a globalstructure of the starch:

[(C6H10O5)n]ungelatinised→ [(C6H10O5)n]

The starch gelatinisation rate (rg) expressed in g/kg s ismodelled by a set of twoEqs. (3) and (4):

rg = kg1exp

(−Eg1

RT

)[Ss] for T < Tg (3)

rg = kg2exp

(−Eg2

RT

)[Ss] for T >Tg (4)

where [Ss] is the ungelatinised starch concentration (g/kg ofmaısche);Egi the activation energy (J/mol),i = 1 for T <

Tg, i = 2 for T > Tg; kgi the pre-exponential factor (s−1),i = 1 for T < Tg, i = 2 for T > Tg; T the temperature (K);Tg the threshold temperature (K) andR is the gas constant(8.31 J/mol K).

4.2. Amylase activities

Relation between global enzymatic activity and tempera-ture may be represented as the contribution of two terms[3]:

• Temperature effect on the specific activity of one enzymesite.

• Couple ‘time–temperature’ effect on the denaturation ofactive sites.

The two terms are modelled separately. The same modelstructure is used for�- and�-amylases. Kinetics of thermaldenaturation are classically represented by a first-order rateprocess:

one active site→ one inactive site

rde = kdeexp

(−Ede

RT

)[E] (5)

where rde is the reaction rate of denaturation (U/kg s),[E] the active site concentration (U/kg of maısche),Ede

the activation energy for the denaturation (J/mol),kde thepre-exponential factor (s−1), T the temperature (K) andRis the gas constant (8.31 J/mol K).

The enzymatic site specific activity, only temperature de-pendent, is modelled by four polynomial laws (as(T)) ac-cording to the temperature range (Fig. 3). The global enzymeactivation rate (rac expressed in U/kg s) can be mathemati-cally represented by the product of both terms:

rac = kdeexp

(−Ede

RT

)[E]as(T ) (6)

4.3. Carbohydrate production

Starch and dextrin are glucosic polymers more or lessbranched and long. Building a model considering the struc-tural aspects of these polymers is nearly impossible. To stayat a macroscopic level, these compounds are representedas a homogeneous glucosic polymer class with an averagechain length. This representation permits to write chemicalreactions that verify the mass balances for the hydrolysis ofstarch and dextrins into glucose, maltose, and maltotriose:

(C6H10O5)n + n(H2O) → n(C6H12O6)

(C6H10O5)n + 12n(H2O) → 1

2n(C12H22O11)

(C6H10O5)n + 13n(H2O) → 1

3n(C18H32O16)

(C6H10O5)n → x(C6H10O5)n/x

(C6H10O5)n/x + n

x(H2O) → n

x(C6H12O6)

(C6H10O5)n/x + n

2x(H2O) → n

2x(C12H22O11)

(C6H10O5)n/x + n

3x(H2O) → n

3x(C18H32O16)

It has been checked that values ofx andn do not influencethe simulation results when the system is treated with massic

48 C. Brandam et al. / Biochemical Engineering Journal 13 (2003) 43–52

Fig. 3. Polynomes for the relation between temperature and the relative specific activity for�- and �-amylases.

concentrations. For instance, coherent physical values canbe 12 000 forn and 1000 forx.

Starch and dextrin enzymatic hydrolysis are consideredas second order reactions, first-order regarding the substrateand first-order regarding the enzymatic activity. Accordingto the reaction scheme and the specific action of�- and�-amylases, kinetics (expressed in g/kg s) for the gelatinisedstarch hydrolysis into glucose, maltose, maltotriose and dex-trins are, respectively, represented by

rgl = kgla�[Sg] (7)

rmal = k�,mala�[Sg] + k�,mala�[Sg] (8)

rmlt = kmlta�[Sg] (9)

rdex = kdexa�[Sg] (10)

Kinetics for the dextrins hydrolysis can be similarly repre-sented by the following relations:

r ′gl = k′

gla�[D] (11)

r ′mal = k′

�,mala�[D] + k′�,mala�[D] (12)

r ′mlt = k′

mlta�[D] (13)

wherekgl, kmlt, k�,mal, k�,mal, kdex, k′gl, k

′mlt, k

′�,mal andk′

�,malare the kinetic factors (kg/U s), [D] and [Sg] the dextrins andgelatinised starch concentrations (g/kg of maısche), anda�

anda� are the real activity of�- and�-amylases (U/kg ofmaısche).

The following ordinary differential equations express thecarbohydrate concentration evolutions:

d[Ss]

dt= rg

d[Sg]

dt= rg − rgl − rmal − rmlt − rdex

d[D]

dt= rdex − r ′

gl − r ′mal − r ′

mlt

d[gl]

dt= rgl + r ′

gl

d[mal]

dt= rmal + r ′

mal

d[mlt]

dt= rmlt + r ′

mlt

Temperature effect on carbohydrate production kinetics hasbeen previously described in literature with a rate constantfollowing an Arrhenius law[1,2]. This formulation was co-herent with the fact that the temperature kinetic contributionwas not taken into account by these authors in the represen-tation of the enzymatic activity. In the new formulation thatwe suggest,k andk′ are considered as independent of tem-perature. The temperature effect is only taken into accountthrough the amylase activities that are modelled at effectivemashing temperatures. Consequently, less parameters haveto be estimated compared to previous models.

Finally, the mathematical model representing the starchhydrolysis during mashing consists in a set of 10 ordinarydifferential equations with 17 parameters. Model inputs arethe starch concentration in grist, the initial quantities of glu-cose, maltose and maltotriose (quantities immediately dis-solved from grist to wort during the dilution water/malt) andthe initial enzymatic potential of�- and�-amylases of themalt. These values are malt characteristics classically mea-sured in breweries to control malt quality after malting.

The system is solved by a Gear method implemented inProsim Batch® [13]. The 17 parameters of the model wereestimated by a least-square method using Prosim Batch®

identification software[14] assuming an experimental rela-tive error of 2, 7 and 2% for starch, amylases and fermentablecarbohydrates, respectively.

5. Modelling results

Before proposing a new kinetic model, the Koljonenmodel have been reproduced to be sure that is not adequate

C. Brandam et al. / Biochemical Engineering Journal 13 (2003) 43–52 49

Table 3Comparison between experimental values and predicted values byKoljonen’s model[6]

Glucose Maltose Maltotriose

Model Experiment Model Experiment Model Experiment

E1 7.5 10.8 73.5 73.2 15.6 17.5E2 7.5 10.4 73.5 76.9 15.6 15.9E4 7.5 9.3 73.3 69.8 15.6 16.4E4 7.5 9.4 73.5 73.4 15.6 15.4E6 7.5 11.7 73.2 86.3 15.6 18.2

for our experiments. Comparison between experimental val-ues obtained during experiments E1–E6 and predicted val-ues by Koljonen model (Table 3) shows the lacunas of thismodel. The variations of predicted values for fermentablecarbohydrate did not exceed beyond 0.5% with the differenttemperature charts whereas the variations are superior to20% for the measured values. If Koljonen’s model repre-sents the global allure of carbohydrate apparition well, it isnot sensible enough for the temperature chart to represent,with sufficient accuracy, the final fermentable carbohydrateconcentrations. Therefore, a new kinetic model is necessary.

5.1. Starch gelatinisation

As previously explained, experimental results have en-lightened a temperature threshold ranging between 60 and63◦C. The rate of gelatinisation is different under or abovethis threshold. Consequently, two sets of gelatinisationparameters (Eg and kg) were determined from E1 to E9experimental values of solid starch concentrations: one setfor temperatures under this threshold and one for temper-atures above. The kinetic parameters and the temperaturethreshold were identified with a good confidence level. Theparameter values are reported onTable 4.

The adequacy of the starch gelatinisation model with theexperimental values is presented onFig. 4for two mashes re-alised with the malt (S1). On the figure but also for all otherexperiments, starch gelatinisation is represented with a good

Fig. 4. Comparison between experimental values (points) and predicted values (lines) for solid starch concentration. Consideration of one starch granulesize (solid and thick lines) and two starch granule sizes. Experiments realised with the same malt S1.

Table 4Parameter values and confidence levels determined from experimentalvalues

Parameters Values Confidence level Confidencelevel (%)

Gelatinisation:T < Tg

Kg1 (s−1) 5.7 × 1031 ±8.0 × 1012 –Eg1 (kJ/mol) 220.6 ±7.8 × 10−5 –

Gelatinisation:T > Tg

Kg2 (s−1) 3.1 × 1014 ±8.0 × 1012 –Eg2 (kJ/mol) 108.3 ±5.9 × 10−5 –Tg (◦C) 60 – –

Small granule gelatinisationksg (s−1) 4.18× 1035 – –Esg (kJ/mol) 253.6 – –

Amylaseskd� (s−1) 6.9 × 1030 ±59 –Ed� (kJ/mol) 224.2 ±1.4 × 10−3 –kd� (s−1) 7.6 × 1060 ±92 –Ed� (kJ/mol) 410.7 ±6.6 × 10−4 –

Sugarskgl (kg/U s) 0.023 ±0.009 39.1kmlt (kg/U s) 0.117 ±0.026 22.3kdex (kg/U s) 0.317 Fixed –k�,mal (kg/U s) 0.389 ±0.120 30.8k�,mal kg/U s) 0.137 ±0.154 112.2k′

gl (kg/U s) 2.9 × 10−8 ±1.2 × 10−8 42.4k′

mlt (kg/U s) 1.5 × 10−8 ±1.1 × 10−8 73.3k′

�,mal (kg/U s) 1.2 × 10−7 ±4.9 × 10−8 42.0k′

�,mal (kg/U s) 8.4 × 10−8 ±3.4 × 10−7 400.1

accuracy by our kinetic model except for the end of 63◦Crest. Model predicts the total gelatinisation of starch gran-ules at this temperature after a 15 min rest. Experimentally,a residual concentration of about 3 g/kg of starch in solidphase is observed, even after 60 min of rest (E6). This resid-ual starch quantity is only gelatinised when temperature in-creases to 76◦C (E3). This discrepancy comes from the factthat small grains were not taken into account in the model.

To represent this physical limitation, specific analysison starch granules would be necessary to distinguish smallfrom big granules, amorphous from crystalline regions, etc.

50 C. Brandam et al. / Biochemical Engineering Journal 13 (2003) 43–52

Fig. 5. Comparison between experimental values (points) and predicted values (lines) for real�-amylase (�) and�-amylase (�) activities. Experimentsrealised with the same malt S1.

however these analyses require important experimental ef-forts which we cannot be systematically performed in in-dustry unless demonstrating that it is worth doing it.

Nevertheless, to improve the model, we can suppose thatsmall starch granules represent a constant proportion of thetotal starch mass. Assuming that their gelatinisation occursabove 60◦C according to a kinetic law similar to big grains,we can identified an activation energy for small starch gran-ule gelatinisation (Esg in J/mol) and a pre-exponential factorfor small starch granule gelatinisation (ksg in s−1).

[(C6H10O5)n]small ungelatinsed→ [(C6H10O5)n]

rsg = ksgexp

(−Esg

RT

)[Sss] (14)

where [Sss] is the ungelatinised small starch concentration(g/kg of maısche)

In the literature, the proportion of small grains is evaluatedto range between 5 and 10% in mass.Esg and ksg wereidentified for a 8% small grain proportion (Table 4). Resultsfor the new global starch gelatinisation are also presentedon Fig. 4 for experiments E3 and E6 (dotted line). Starchgelatinisation on the end of 63◦C rest are better represented.It will also be necessary to evaluate the influence of everystarch gelatinisation on carbohydrate production to conclude

Fig. 6. Comparison between experimental values (points) and predicted values (lines) for glucose (�), maltose (�), maltotriose (�) and final dextrin (�)concentrations. No differentiation between small and big starch granules in the gelatinisation kinetic model. Experiments realised with the same malt S1.

whether the obtained gain of accuracy on the model justifiesthe introduction of complexity.

5.2. Amylase activities

The temperature kinetic contribution on amylase activityC(T) was determined from a set of experiments independentfrom mashing[3]. Other amylase activity modelling param-eters (kde, Ede) were estimated from the set of experimentsE1–E9, with the enzymatic activity values measured withMegazyme method. All values are reported inTable 4.

Calculated values for the real�- and�-amylase activitiesare confronted to experimental values onFig. 5 for two rep-resentative mashing. The model fits rather well the amylaseactivities. For all experiments, errors between experimentand model did not exceed 8%.

5.3. Carbohydrate productions

At first, starch gelatinisation was modelled consideringthat starch consists only of big granules. Carbohydrateproduction kinetic parameters were estimated from the setof experiments E1–E9. Confidence levels of carbohydrateproduction parameters are rather high (Table 4). The ab-sence of dextrin measurements during mashing can explain

C. Brandam et al. / Biochemical Engineering Journal 13 (2003) 43–52 51

Table 5Comparison between experimental values and predicted values of the final carbohydrate concentrations

Sugarsa

Experiment Model 1b Error 1% Model 2c Error 2%

E1 (60◦C/15 min) 101.5 103.7 −2.2 102.6 −1.1E2 (63◦C/15 min) 103.2 103.0 0.2 102.2 1.0E3 (65◦C/15 min) 99.9 100.2 −0.9 99.9 −0.6E4 (70◦C/15 min) 95.5 94.3 1.3 95.2 0.3E5 (63◦C/0 min) 98.2 96.0 2.2 95.7 2.5E6 (63◦C/60 min) 116.2 114.0 1.9 112.9 2.8E7 (63◦C/180 min) 124.5 123.2 1.0 122.4 1.7E8 (63◦C/100 min I) 107.5 116.6 −8.5 114.1 −6.1E9 (70◦C/100 min I) 83.8 92.5 −10.4 95.4 −13.8

a Glucose+ maltose+ maltotriose.b Starch gelatinisation kinetic considering one granule size.c Starch gelatinisation kinetic considering two granule size.

Table 6Representation of the saccharification rest duration effect on dextrin and fermentable carbohydrate concentrations

0 min/63◦C 15 min/63◦C 60 min/63◦C 180 min/63◦C

Experimental sugarsa 98.2 103.2 116.2 124.5Modelled sugarsa 96.0 103.0 114.0 123.2Experimental dextrins 29.3 24.6 12.3 4.5Modelled dextrins 31.0 24.4 14.0 5.5

a Glucose+ maltose+ maltotriose.

those bad confidence levels. Nevertheless, the adequacycalculated–experimental values confirms a good represen-tation of the sugar production by the model (Fig. 6).

Errors between the measured and predicted final carbo-hydrate concentrations are mentioned inTable 5for the setof nine experiments. Total fermentable carbohydrate repre-sentation by the model has an error average of 3.1% andnot exceeds 10.4%. Individual fermentable carbohydrateproduction error, not mentioned here, is less than 15%.

The model also represents with good accuracy the experi-mental sensibility to mashing temperature profile variations.Time and temperature effects of the ‘saccharification rest’are well-represented (Tables 6 and 7).

Another set of carbohydrate production kinetic parame-ters were estimated, assuming that starch consists of bothbig (92% in mass) and small granules (8%). Errors betweenthe measured and predicted final carbohydrate concentra-tions are also mentioned inTable 5for the set of nine experi-ments. Differences with values of fermentable carbohydrateconcentrations obtained with the other gelatinisation kinetic

Table 7Representation of the saccharification rest temperature effect on dextrin and fermentable carbohydrate concentrations

60◦C/15 min 63◦C/15 min 65◦C/15 min 70◦C/15 min

Experimental sugarsa 101.5 103.2 99.3 95.5Modelled sugarsa 103.7 103.0 100.2 94.3Experimental dextrins 26.2 24.6 28.5 31.8Modelled dextrins 23.8 24.4 27.0 32.7

a Glucose+ maltose+ maltotriose.

are weak. Some experiments are better represented (E1 orE8) but others are less well represented (E6 or particularlyE9). The average error for the total fermentable carbohy-drate representation is of 3.7%. The maximum is 13.8% forthe 70◦C isothermal experiment. Therefore, differentiatinggelatinisation kinetics for small and big starch granules im-proves the representation of the gelatinisation phenomenonbut does not lead to a significant improvement concerningthe prediction of fermentable carbohydrate production. Asfor the brewer the most important is the final fermentablecarbohydrate concentrations, it is not worth complicatingthe starch gelatinisation model by including a differentiationbetween small and big starch granules.

6. Model validation

This model has been established from nine experimentsperformed with the same malt. It was validated with exper-iments realised with other malts.

52 C. Brandam et al. / Biochemical Engineering Journal 13 (2003) 43–52

Fig. 7. Comparison between experimental values and predicted values for glucose (�), maltose (�), maltotriose (�) and final dextrin (�) concentrationsfor experiments realised with different malts.

Table 8Comparison between experimental values and predicted values of the finalcarbohydrate concentrations for experiments realised with six differentmalts

Sugarsa

Experiment Model Error (%)

E2 (malt S1) 103.2 103.0 0.2E10 (malt S2) 106.6 106.2 0.4E11 (malt S3) 100.5 101.0 −0.5E12 (malt M1) 102.9 106.2 −3.2E13 (malt M2) 102.6 104.8 −2.1E14 (malt M3) 110.4 112.8 −2.2

a Glucose+ maltose+ maltotriose.

Experiments E10–E14 realised with five other malts aresimulated with the model. Amylase activities and starchgelatinisation have the same behaviour in the different maltscompared to S1. InFig. 7, results for the carbohydrate pro-ductions are presented for two malts. Model predicts the ex-perimental values with a very good accuracy. Errors on thetotal fermentable carbohydrate concentration do not exceed3.2% (Table 8).

The six tested malt characteristics cover the industrialspecification range of the breweries. They exhibit enzymaticpotential that varies considerably (Table 1). In spite of thesevariations, the model is valid for the six tested malts even ifthe parameters have been estimated only from experimentsrealised with the malt S1.

7. Conclusions

The stoicheo-kinetic model presented in this paper enablesus to predict the evolutions of�- and�-amylase activities,starch concentration, fermentable carbohydrate and dex-trin concentrations, from three malt characteristics (starch,

�- and�-amylase potential) and from mashing temperaturechart. The kinetic parameters were determined with a goodaccuracy from nine mashes realised with the same malt. Themodel was then validated on five other experiments. Theoriginal approach to represent amylase activities tempera-ture dependency leads to a better representation of the tem-perature sensitivity during mashing compared to previousmodels[1,2] and decreases the number of parameters thatmust be estimated.

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