Modelling of the kinetics of colour change in hazelnuts during air roasting

Modelling of the kinetics of colour change in hazelnutsduring air roasting

Ali Do�ggan Demir a, Jes�uus Mar�ııa Fr�ııas Celayeta a, Kevin Cronin a,*, Kamal Abodayeh b

a Department of Process Engineering, University College, Cork, Irelandb Prince Sultan College, P.O. Box 66 833, Riyadhv 11586, Saudi Arabia

Received 19 October 2001; accepted 4 March 2002

Abstract

The colour changes that occur in hazelnuts during the dry roasting process were experimentally studied in order to determine the

magnitudes of the parameters for a corresponding colour change model. Roasting times varying from 5 to 1900 min and a number

of roasting temperatures in the range from 100 to 180 �C were analysed. The order of the reaction was found by plotting isothermalcurves of colour change against time at a number of different roasting temperatures. Statistical analysis of the data demonstrated

that the colour parameter, L was best represented by a first-order process. The rate constant was assumed to have an Arrhenius-type

dependence on temperature. The activation energy (Ea) and the frequency (pre-exponential) term (k1) were determined as 64.5kJmol�1 and 33416.5 s�1 respectively for the conditions studied. Theoretical equations, based on the exponential integral function,

to predict first-order quality changes when product temperature is varying exponentially were developed. These equations were

validated by comparison with the experimental colour data extracted from the non-isothermal region of the roasting process.

� 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Hazelnut roasting; Colour responses; Quality kinetics; Exponential integral

1. Introduction

The world tree nut market is segmented into two

major categories; in-shell nuts and shelled tree nuts. The

term ‘in-shell’ describes tree nuts that are produced and

marketed with the shell intact. Their processing pri-

marily involves exterior cleaning and preparation for

seasonal market. However the most common form of

nuts used in the food-processing sector are shelled nuts.Shelled nuts undergo processes including blanching,

dicing, coating, roasting and grinding to fit product

formulation needs or give them increased consumer

appeal. Roasting is one of the most important processes

giving the product the necessary alterations to become

value-added nuts. There are two types of nut roasting:

dry and oil. Dry roasting involves the heating of nuts

using air convection or radiant microwave heat. In theoil method, raw nutmeats are immersed in boiling oil,

and then drained to remove excess oil (Somogyi, Bar-

rett, & Hui, 1996). Currently, over 4,000,000 tons ofnuts are commercially produced throughout the world.

700,000 tons of that figure is hazelnut (Corylus avellana

L.), production (€OOzdemir & Devres, 1999).There are several objectives to hazelnut roasting; one

is to ensure that the centre of every nut reaches some

minimum temperature to destroy any toxins or allergens

that may exist (M€uuller et al., 2000). Wigotzki, Stein-heart, and Paschke (2000) showed that the IgE bindingactivity of main hazelnut allergens decreased after 15

min roasting at temperatures between 100 and 185 �Cand was no longer detectable at 170 �C. Roasting at 100�C for up to 90 min had no influence on the allergenicityof hazelnut proteins. Another objective of hazelnut

roasting is to give the product surface a variety of col-

ours such as a whitened, golden yellow, dark roast or

very dark roast (€OOzdemir & Devres, 2000a). Roastingalters and significantly enhances the flavour, colour,

texture and appearance of hazelnuts. Roasting also

inactivates enzymes that speed up nutrient loss and de-

stroys undesirable microorganisms and food contami-

nants. Therefore from the quality and safety point of

view, the times and temperatures applied are very im-

portant factors in hazelnut roasting.

Journal of Food Engineering 55 (2002) 283–292

www.elsevier.com/locate/jfoodeng

*Corresponding author. Tel.: +353-21-4902644; fax: +353-21-

4270249.

E-mail address: [email protected] (K. Cronin).

0260-8774/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

PII: S0260-8774 (02 )00103-6

mail to: [email protected]

In industry, hazelnuts are generally roasted at tem-

peratures between 100 and 180 �C from 5 to 60 min withdry air as the heating medium. There is a choice between

roasting the hazelnuts at low temperatures for longtimes or high temperatures for short times. Low tem-

perature roasting can be considered as an isothermal

process because for the majority of the process, the nut

temperature is almost asymptotically equal to the con-

stant roasting air temperature after the short initial

‘come-up’ temperature period. For this schedule, the

overwhelming majority of the quality changes that occur

during roasting will take place during this ‘isothermal’period. However in high temperature roasting, as the

required process time is much shorter and air tempera-

ture considerably higher, hazelnut temperature mono-

tonically rises throughout the process and quality

changes occur over the entire temperature range. Fig. 1

illustrates the distinction between the two roasting

schedules by showing the centre temperature versus time

profiles of two hazelnuts, which were roasted in a batch

oven at air temperatures of 120 and 180 �C for 60 and 20min respectively. The Biot number for the prevailing

conditions and geometry (using the characteristic di-

mension of volume over heat transfer area) was found to

be 0.42. Therefore it was necessary to take into account

both internal and surface resistance to heat flow which is

normal in the analysis of heat transfer to food systems

with air as the heating medium.

For many roasted products browning (which can beclassified as enzymatic or non-enzymatic) is desirable.

The colour changes during roasting of hazelnuts mainly

relate to non-enzymatic browning. The non-enzymatic

browning is a complex set of reactions including the

pathways of sugar caramelization, Maillard reaction

and oxidation of ascorbic acid. Maillard reaction in-

volves the reaction between the carbonyl group of a

reducing sugar with a free, uncharged amine group of anamino acid or protein with the loss of one mol of water

(Lopez & Pique, 1997). Non-enzymatic browning has a

diminishing effect on the nutritional value due to the

decreased protein digestibility and loss of essential

amino acids (€OOzdemir & Devres, 2000b).Non-enzymatic browning reactions in food systems

are generally considered to be zero- or first-order reac-

tions. According to Heldman and Lund (1992), colourchanges can be modelled by using a first-order reaction

rate and the effect of temperature on non-enzymatic

browning reaction rate is usually expressed using an

Arrhenius-type relationship. Lopez and Pique (1997)

showed that the rate of non-enzymatic browning in-

Nomenclature

a colour dimension

an exponential integral constant

A1 equation constant

b colour dimension

bn exponential integral constantBi Biot number

C equation constant

C1 equation constant

cv coefficient of variation

Cp specific heat capacity (J kg�1 K�1)

Ea activation energy (kJmol�1)

E1 exponential integral

h overall surface heat transfer coefficient(Wm�2 K�1)

k1 frequency factor (s�1)

k thermal conductivity (Wm�1 K�1)

kR reaction rate constant (s�1)

L colour dimension (lightness)

r0 radius (m)

rc thermal rate constant (s�1)

R universal gas constant

(8:314� 10�3 kJmol�1 K�1)

R2 correlation coefficientt time (s, min)

T absolute temperature (K)

T average temperature (�C, K)

Greek symbols

b equation constantq density (kgm�3)

k1 thermal model constant

r standard deviation

Subscripts

1 asymptotic value0 initial

c centre

Fig. 1. Hazelnut temperature profiles versus time for air temperatures

of 120 and 180 �C illustrating the distinction between the two roastingschedules.

284 A.D. Demir et al. / Journal of Food Engineering 55 (2002) 283–292

creases with temperature. Browning of dried hazelnutswas described by zero-order kinetics and the reaction

rate data followed the Arrhenius equation. €OOzdemir andDevres (2000b) concluded that roasting temperature is

the main factor affecting colour development during

roasting of hazelnuts. In order to take into account in-

ternal browning, (the difference in L value between

whole nut surface colour and ground nut colour is of the

order of 20%), the roasting process should be monitoredusing the L value representing the lightness of ground

hazelnuts. A zero-order kinetic equation was applied

assuming Arrhenius-type dependence for L value of

ground state measurements of hazelnut colour.

The aim of this paper is twofold. The first is to de-

termine the order of the reaction kinetics to characterise

colour change by comparing it to other possible math-

ematical models. The second is to validate a theoreticalformula that can predict colour change during a high

temperature-short time roasting process where hazelnut

temperature cannot be considered as constant. The work

described here is applicable to the roasting of individual

hazelnuts in a laboratory batch oven.

2. Theory

2.1. Hazelnut temperature model

For the thermal geometry, the hazelnuts are regardedas solid spheres placed at the centre of a fan oven. Heat

transfer is by convection from the air to the hazelnut

and by radiation from the oven wall to the nut. Mass

transfer and shrinkage effects have been shown to be

negligible for the purpose of this work. The temperature

model consists of first term of the infinite series solution

to the Fourier field equation for a sphere undergoing

unsteady conduction. There is convective and radiativeheat transfer at the outside surface of hazelnuts, which is

modelled using an overall surface heat transfer coeffi-

cient. A zero heat flux boundary condition is imposed at

the centre. In the subsequent analysis of product quality,

average nut quality is the parameter of interest and

hence average temperature through the nut is required.

The average temperature, T of the hazelnut can thus bedefined as (Ilıcalı, 1989):

T ¼ T0ð � T1ÞA1e�rct þ T1 ð1Þ

and the centre temperature Tc can be given as (C� engel,1997):

Tc ¼ T0ð � T1ÞC1e�rct þ T1 ð2Þ

where T0 is the initial hazelnut temperature, T1 is the

process (air) temperature and rc is the thermal rateconstant. The thermal rate constant is:

rc ¼k21k

qCpr20ð3Þ

The equation constants for the average and centre

temperatures are:

A1 ¼12 sin k1 � k1 cos k1ð Þ2

k31 2k1 � sin 2k1ð Þ

C1 ¼4 sin k1 � k1 cos k1ð Þ2k1 � sin 2k1ð Þ

ð4Þ

where k1 is the function of Biot number:

1� k1 cot k1 ¼ Bi ð5Þ

The equation constants A1, C1 and k1 can be predicted asa function of the Biot number. For Bi < 3 and Bi > 5,Ilıcalı (1989) gives approximate relationships which re-

sult in an error less than 3%. The Biot Number for this

geometry is:

Bi ¼ hr0k

ð6Þ

The heat transfer to the hazelnuts in the oven is a

combination of both convective and radiative heating

and so the overall heat transfer coefficient, h is the sumof the convective and equivalent radiative heat transfer

coefficients. Note that restricting the solution to the first

term of the infinite series expansion of the Fourier

equation places a lower limit of about 90 s on solution

validity for these conditions (C�engel, 1997).

2.2. Hazelnut colour change models

The zero-order, first-order and Weibull models for

colour (lightness) change are given by the followingequations respectively:

L ¼ L0 � kRt ð7ÞL ¼ L0ð � L1Þe�kRt þ L1 ð8Þ

L ¼ L0ð � L1Þe� kRtð Þb þ L1 ð9ÞThe first-order and the Weibull models in Eqs. (8) and

(9) can be linearized into the following forms of Eqs.

(10) and (11) respectively:

lnL� L1

L0 � L1

� �¼ �kRt ð10Þ

ln lnL� L1

L0 � L1

� �� ¼ � ln kR þ b ln t ð11Þ

where L is a colour parameter (lightness) and kR is thereaction rate constant. The effect of temperature on the

reaction rate constant is expressed using an Arrhenius-type relationship:

kR ¼ k1 exp�� Ea

R1

T

� ��ð12Þ

A.D. Demir et al. / Journal of Food Engineering 55 (2002) 283–292 285

where k1 is the frequency factor, Ea is the activationenergy, and R is the universal gas constant. The term T,

in the index of the exponential function in the equation

is the absolute temperature.

Eqs. (7)–(9) can predict product quality change versus

time once product temperature is constant. For a non-

isothermal process, the reaction rate constant changes

with time (temperature changes with time) and these

equations will be invalid. Theoretical solutions for qual-ity are available for the zero- and first-order quality mod-

els where product temperature is described by Eq. (1)

and quality reaction temperature sensitivity is described

by Eq. (12). The change in a product quality parameter

with respect to time for a non-isothermal (exponential

temperature rise) first-order quality reaction can be de-

scribed by:

The derivation of Eq. (13) is given in Appendix. Thesolution of Eq. (13) is valid for Fourier numbers greater

than 0.2 (C� engel, 1997). Note the solution for a zero-order reaction is a simplified version of Eq. (13). It has

not been possible to obtain a solution for the Weibull

model. The function E1 in Eq. (13) is the exponentialintegral and can be defined by:

E1ðxÞ ¼Z 1

x

e�t

tdt ð14Þ

where x is a positive number. The exponential integral

can be directly evaluated in packages such as Mathem-

atica and a large number of different approximations,

based on simple polynomial and exponential functions,

are available for different ranges of the argument (Ab-

ramowitz & Stegun, 1970). For this work the followingapproximation based on the product of a polynomial

ratio and exponential function will be used:

E1ðxÞ ¼x4 þ a1x3 þ a2x2 þ a3xþ a4x4 þ b1x3 þ b2x2 þ b3xþ b4

e�x

xð15Þ

The error associated with the polynomial ratio in Eq.(15) will be less than 2� 10�8 for all arguments of theexponential integral greater than one. The magnitudes

of the coefficients for both quartic polynomial expres-sions are given in Table 1.

3. Materials and methods

3.1. Physical and thermal properties

Sun dried raw hazelnuts with skin were supplied. Theskins of the hazelnuts were removed by applying hot

glycerine–sodium carbonate solution before roasting. A

digital vernier and a digital analytical balance (Bosch

SAE 200) were used to measure hazelnuts radius and

mass respectively. The average density value for hazel-

nuts was found by weight and volume ratio. The thermal

properties of the hazelnuts were experimentally mea-

sured by a thermal properties meter (Thermolink SensorModel TL-1) before and after the roasting process.

Hazelnuts were placed in an incubator keeping their

initial temperature, T0 at 20 �C.

3.2. Experimental roasting procedure

A Memmert ULP 600 conventional fan oven wasused to carry out the roasting trials. Airflow in the oven

was transverse, i.e. flowing from grooves in the oven

sidewalls, across the rectangular oven compartment.

The air velocity was kept constant at the centre of the

oven by a fan operating at maximum speed throughout

the experiments.

The aim of the experiments was to obtain experi-

mental hazelnut colour versus time curves at five dif-ferent oven temperatures, T1 of 100, 120, 140, 160 and180 �C. These oven temperatures cover the commonlyused temperatures in the hazelnut industry for roasting

(€OOzdemir & Devres, 2000a; Perren & Escher, 1997). Thecorresponding roasting times for these five temperatures

are 1900, 1850, 1610, 850 and 700 min respectively. The

reason for applying very long roasting times was to be

able to observe the exact behaviour of the colour for-mation in hazelnuts over the entire colour range.

As it was not possible to measure colour on-line, an

alternative procedure was employed to obtain the colour

versus time curves. From the initial batch of hazelnuts,

sets consisting of five randomly selected hazelnuts were

assembled. Each set was placed on a small table located

at the geometric centre of the oven. Each of the five

hazelnuts was placed apart with no contact between eachother to prevent any shielding effect on the nuts during

LðtÞ ¼ðL0 � L1Þ exp k1

rcE1 Ea

RT

� � e�Ea=RT1 �

E1 EaRT

� EaRT1

� h in o� exp k1

rcE1 Ea

R T0�T1ð ÞA1þT1½

� � e�Ea=RT1ð ÞE1 Ea

R T0�T1ð ÞA1þT1½ �EaRT1

� h in o� þ L1 ð13Þ

Table 1

Magnitudes of the coefficients of the polynomial approximation for the

exponential integral function

a1 8.5733287401 b1 9.5733223454

a2 18.0590169730 b2 25.6329561486

a3 8.6347608925 b3 21.0996530827

a4 0.2677737343 b4 3.9584969228


roasting. A 1.5 mm diameter hole was drilled through

one side of one of the five hazelnuts and a thermocouple

inserted and sealed in there to measure the centre tem-

perature and data-logged by a computer. Fig. 2 shows

the placement of hazelnuts on the table at the centre of

the conventional oven. The reason for forming sets with

five nuts (all with a very similar initial colour and size)

instead of one was to minimize any unexpected colourformation that could result from using a single nut. Each

set was roasted for a given temperature-time combina-

tion to enable the colour versus time curves to be as-

sembled. Table 2 summarizes the number of sets of

hazelnuts and the times that were conducted in the ex-

periments. At the end of each experiment, the roasted

hazelnuts were removed from the oven and placed in a

freezer at 0 �C to prevent any further roasting after re-moving from the oven. They were cooled to room tem-

perature and placed in the incubator until the colour

analysis was undertaken off-line.

3.3. Colour measurement

Colour is a subjective phenomenon, which can be

expressed by visually uniform terms by CIE (Commission

Internationale d’Eclairage): International Commission

on Illumination. The colour of the roasted hazelnuts

was measured with a MINOLTA CR-300 tristumulus

colorimeter (Davidson, Brown, & Landman, 1999). Themeasuring head of the colorimeter CR-300 has an 8-mm

diameter measuring area and uses diffuse illumination

and a 0� viewing angle for accurate measurements. Theinstrument measures four specific wavelengths in the

visible range, specified by CIE. Tristumulus values give

a three-dimensional value for colour in which equal dis-

tances approximate to equal perceived colour differences.

The L, a and b values are the three dimensions of the

measured colour which gives specific colour value of the

material. In Hunter Lab Colour Space, the value L is

known as the degree of lightness or blackness. The

chromatic portion of the colour space is based on rect-

angular Cartesian coordinates (a, b); with red repre-sented byþa, green represented by�a, yellow byþb andblue by �b. The L-value gives a spectrum with a range

from 0 (black) to 100 (white). The a-value represents the

spectrum with a range from �60 (green) to +60 (red) andthe b-value from �60 (blue) to +60 (yellow) (Hutchings,1994).

Before the colour measurements, the colorimeter was

calibrated using a white surface where L ffi 100. Thesurface colour measurement of whole hazelnut kernels

was performed placing each kernel on the 8-mm diam-

eter measuring area. One reading was taken from each

of the five hazelnuts surfaces. The colours of the outside

kernels were measured for each hazelnut roasted at

different oven temperatures for different periods. The

roasted hazelnuts in each set were than ground in a

mill and kept separately in small beakers. The groundhazelnuts were spread on a plate. The colour measure-

ments were repeated by taking five readings from the

different regions in each set.

3.4. Statistical analysis of colour

The L, a and b values obtained from the experi-

ments were analysed by ANOVA, analysis of variance

Fig. 2. The placement of the hazelnuts on the table at the centre of the

conventional oven (front and elevation views).

Table 2

The times (in minutes) applied in the roasting trials of sets of hazelnuts

at different temperatures

Set number Roasting temperatures

100 �C 120 �C 140 �C 160 �C 180 �C

1 0 0 0 0 0

2 40 20 20 15 5

3 80 40 40 30 10

4 120 60 60 40 15

5 160 80 80 45 20

6 200 100 100 60 25

7 240 120 120 75 30

8 280 160 160 90 35

9 320 200 200 105 40

10 340 240 240 120 45

11 360 280 280 150 50

12 400 320 320 180 60

13 440 360 360 210 70

14 500 400 400 250 80

15 600 500 440 280 90

16 700 600 480 310 100

17 800 700 600 340 120

18 900 800 800 480 150

19 1500 1000 1440 600 200

20 1900 1850 1610 850 700


technique, to find out the effect of time and temperatureon those responses. From the ANOVA table, the more

sensitive response was selected based on the biggest

range, the highest sensitivity to temperature change ob-

tained from whole and ground hazelnut colour analysis

and the lowest coefficient of variation, cv value (Devore& Farnum, 1999). One of the colour responses between

L, a and b was selected as a significant value which is

more sensitive to time and temperature change and thusrepresenting factor of the colour change in hazelnuts

during roasting.

Hazelnut colour versus time curves available at five

different temperatures, were fitted to the three models

presented in Eqs. (7)–(9). The fit of each of the three

models to the data was assessed at each temperature

by determining the correlation coefficients, (R2) and themean square error values (MSEs), applying one-step re-gression using the package STATISTICA and checked

with EXCEL solver tool. The slopes and intercepts yield

the relevant model parameters (L0, L1 or b) for each case.The best model tomonitor the colour change in hazelnuts

were determined as the model having the highest corre-

lation coefficient, lowest MSE and the less number of

parameters required in one-step regression. The reaction

rate constants, (kR) were obtained from the slopes (Eqs.(7), (10) and (11)) of the selected model. The reaction

rate constants were then checked for the Arrhenius tem-

perature dependence in order to calculate the activation

energy, Ea and the frequency term, k1 (Eq. (12)).

3.5. Non-isothermal colour analysis

A second series of experiments were conducted in

order to assess the validity of Eq. (13). A roasting

temperature of 180 �C was selected. Twenty sets of fivehazelnuts were again assembled. The first set was roasted

for 1 min and the roasting time was incremented by1 min for each successive set. For each set again, a 1.5

mm diameter hole was drilled through one side of one

of the five hazelnuts to measure its centre temperature

and a thermocouple inserted and sealed. The centre tem-

perature profiles were data logged by a computerized

thermocouple. These experiments permitted hazelnut

temperature versus time and colour versus time curves to

be assembled for a high roasting temperature. The colourmeasurements for the roasted sets were repeated as in the

previous part. This time 10 colour measurements were

taken on the whole and ground form hazelnuts.

4. Results and discussion

4.1. Physical and thermal properties

The mean and the standard deviation, r in hazelnutradius were measured as 7.07 and 0.395 mm respec-

tively. The average density value for hazelnuts wasfound as 875 (r ¼ 17:27) kgm�3. Thermal conductiv-

ity, k of hazelnuts was measured as 0.204 (r ¼ 0:0253)Wm�1 K�1. Specific heat capacity, Cp was found to be1994 (r ¼ 188:17) J kg�1 K�1, which results in a thermal

diffusivity, a of 1:17� 10�7 (r ¼ 0:0184) m2 s�1. The

overall heat transfer coefficient for hazelnuts in the oven

was experimentally evaluated as 33.3 Wm�2 K�1. Using

this data, the Biot Number for heat transfer to thehazelnut was evaluated as 1.15 meaning that the factors

A1, C1 and k1 are 0.981, 1.31 and 1.66 respectively. Thethermal rate constant is calculated as 6:52� 10�3 s�1.

4.2. Colour data analysis

Fig. 3 gives the colour formation on hazelnuts roasted

at oven temperatures from 100 to 180 �C, for a variety oftimes ranging from 0 min (not roasted) up to 1900 min.

Due to the long roasting times these can be considered as

isothermal experiments. Fig. 4 shows the colour change

in hazelnuts during roasting at 1-min increments for aroasting time 20 min at an oven temperature of 180 �C.Table 3 shows that the effect of temperature on the col-

our response L is higher for the colour analysis on

ground form hazelnuts than that of whole nuts for the

temperatures chosen. The coefficients of variation in the

colour parameters are lower for the ground form of

hazelnuts. The highest range is in the L values of ground

form hazelnuts with an increase of 9% from whole toground form. Although the range and temperature effect

decreases in a and b values of the ground form hazelnuts

compared to whole nuts, the ratio of standard deviation

to range is smaller in the ground form. The colour re-

Fig. 3. Colour development in hazelnuts during roasting at different

temperatures and various times.


sponses L of ground form hazelnuts and b of the wholenuts demonstrate the highest sensitivity to temperature

change. Because of the lowest coefficient of variation and

the most precise response from L, L values of ground

form hazelnuts were used to quantify the colour change

in hazelnuts during roasting.

4.3. Model fitting

Having selected the L value of the ground hazelnutsas the most repeatable indicator of colour change, the

goodness-of-fit of each of the three models was assessed.

Table 4 summarizes the equation parameters, correla-

tion coefficients, R2 and the MSEs, of the three modelsapplied. As it is seen clearly in the table, the overall fit of

the zero-order model is quite poor. The Weibull model

with an offset gives a marginally better fit than the first-

order though at the expense of an extra fitting parameterb. Hence the first-order model with an offset was selectedas the best model representing the colour change in

hazelnuts during roasting. Note that all three models

have very low R2 values at 100 �C due to the relativelysmall colour change that occurs at low roasting

temperatures. Figs. 5–7 show the fit of the zero-order,Fig. 4. The experimental colour development in hazelnuts during

roasting at 180 �C with times of 1-min increments.

Table 3

F-values of the temperature effects from ANOVA factor analysis and some statistical values of the colour responses

Hazelnuts

Whole Ground

L a b L a b

F-value of temperature effect 121.76 48.37 158.12 200.1 44.85 109.9

Standard deviation, r 3.41 1.55 2.77 1.15 0.53 0.86

Range 52.36 17.86 62.13 57.06 13.53 33.95

Standard deviation/range 0.065 0.087 0.045 0.020 0.039 0.025

Coefficient of variation, cv (%) 7.07 15.94 16.36 2.55 7.66 4.21

L, a and b denotes colour responses.

Table 4

Equation parameters, correlation coefficients and MSEs of the colour models

Temperature (�C) Zero-order First-order with offset Weibull model with offset

kR R2 kR R2 kR R2

100 0.00502 0.26561 0.00010 0.25693 0.01411 0.11693

120 0.01628 0.68206 0.00044 0.76299 0.00197 0.60583

140 0.01912 0.52173 0.00101 0.70956 0.06892 0.88898

160 0.03837 0.42559 0.00321 0.70338 0.11361 0.89262

180 0.04301 0.17798 0.00798 0.72164 0.05016 0.70006

Zero-order First-order with offset Weibull model with offset

Mean R2 0.4146 0.6309 0.6409

MSE 0.7975 0.1029 0.0883

L0 72.41 65.73 71.79

L1 – 21.55 18.88

b – – 0.59


Fig. 5. Fitted profiles of zero-order model with the experimental data points of L values.

Fig. 6. Fitted profiles of first-order model with an offset with the experimental data points of L values.

Fig. 7. Fitted profiles of Weibull model with an offset with the experimental data points of L values.


first-order and Weibull models respectively with theexperimental data at each temperature.

4.4. Reaction rate constants and arrhenius temperature

dependence

The Arrhenius temperature dependence of the reac-

tion rate constants was checked with the plot of lnðkRÞversus 1=T . Fig. 8 shows that the reaction rate constantof the first-order model follows the Arrhenius equation,

in this case giving a correlation coefficient value of0.9962. From the slope and intercept of the straight line

described by the Arrhenius equation, the activation

energy, Ea and the frequency term, k1 were determinedas 64.5 kJmol�1 and 33416.5 s�1 respectively. The acti-

vation energies for non-enzymatic browning in foods are

generally between 37.7 and 167.5 kJmol�1 (Heldman &

Lund, 1992).

4.5. Validation of non-isothermal colour change formula

Fig. 9 shows the experimentally measured mean value

of the centre temperatures of the hazelnuts together with

the theoretical hazelnut centre temperature profile ver-

sus time (from Eq. (2)) at an air roasting temperature of

180 �C. The theoretical profile is given for times greaterthan 90 s corresponding to the lower limit on solution

validity. The temperature gradient inside the hazelnut is

very small and the discrepancy between the average

temperature of the nut and temperature at the centre of

the nut is negligible. The corresponding experimental

data points and theoretical hazelnut colour prediction

(Eq. (13)) are shown in Fig. 10. The initial L value, L0was measured as 73.94. As can be seen from the figure

there is a good agreement between the experimental re-

sults and theoretical predictions. The mean square root

error, values between the experimental and the theo-

retically predicted colour change values were calculated

as 0.04.

5. Conclusions

The results of this study showed that the effect of both

roasting air temperature and roasting time is more sig-

nificant for the ground form hazelnut colour analysis

than the whole hazelnuts. Among the colour parametersof L, a and b, L values had the highest sensitivity for the

time and temperature change. Thus L values of ground

hazelnuts were used to monitor the colour change during

hazelnut roasting. Colour change was analysed as a zero

order, first order and Weibull process using isothermal

analysis; the fit of the zero-order model was found to be

unsatisfactory. Although both Weibull and first-order

processes were applicable, the reaction was modelled as afirst-order process due to its greater simplicity. The re-

action kinetics sensitivity to temperature was described

well by the Arrhenius equation. The theoretical formula

(Eq. (13)) to predict the colour change during the non-

isothermal roasting resulted in good agreement with the

experimental curves. Although the work was carried out

on the roasting of single hazelnuts in a batch oven, the

results are capable of being extended to the industrialarena. The development of a validated colour model over

a large roasting temperature range should allow opti-

misation studies to be performed to determine the best

Fig. 8. Plot of reaction rate constants, lnðkRÞ against 1=T to check

Arrhenius temperature dependence.

Fig. 9. The experimental mean centre temperature and theoretical (Eq.

(2)) profiles of roasting performed at 180 �C.

Fig. 10. The profiles of L values measured experimentally and the

exponential integral prediction at 180 �C.


roasting schedule in terms of delivering required productcolour. Also the validation of the exponential integral

formula (Eq. (13)) means colour changes can be pre-

dicted theoretically during the heating up and cooling

down parts of the process.

Appendix A

The colour change in hazelnuts during roasting can

be described using a first-order model with an offset:

oLot

¼ �kR Lð � L1Þ ðA:1Þ

Replacing T, in the index of exponential function of Eq.

(12) with Eq. (1) and introducing in Eq. (A.1):

oLot

¼ �k1 exp�� EaR T0 � T1ð ÞA1e�rct þ T1½

�ðL� L1Þ

ðA:2Þ

Call

u ¼ EaR T0 � T1ð ÞA1e�rct þ T1½ ðA:3Þ

Then

ot ¼ 1

u EaR � uT1

� EaRrc

ou ðA:4Þ

Eq. (A.2) becomes:Z L

L0

oLL� L1

¼Z

�k1e�uot ðA:5Þ

Inserting Eqs. (A.3) and (A.4) in Eq. (A.5) and solving:

lnL� L1

L0 � L1

� �¼ � k1

rc

Ze�u

uou

"þ T1

Ze�u

EaR � uT1

� ou#

ðA:6Þ

From the definition of exponential integral function,

(Eq. (14)) Eq. (A.6) can be solved as:

L tð Þ � L1

L0 � L1¼ C exp

k1rc

E1EaRT

� ��

� e�Ea=RT1 �

E1EaRT

�� EaRT1

��ðA:7Þ

where C is a constant. From the initial condition:

at t ¼ 0 L ¼ L0 and T ¼ T0ð � T1ÞA1 þ T1 ðA:8Þ

C can be found as:

C ¼ exp�� k1

rcE1

EaR T0 � T1ð ÞA1 þ T1½

� ��

� e�Ea=RT1 �

E1Ea

R T0 � T1ð ÞA1 þ T1½

�� EaRT1

��ðA:9Þ

Thus, the theoretical formula predicting the colourchange in a non-isothermal process becomes:

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LðtÞ ¼ðL0 � L1Þ exp k1

rcE1 Ea

RT

� � e�Ea=RT1 �

E1 EaRT

� EaRT1

� h in o� exp k1

rcE1 Ea

R T0�T1ð ÞA1þT1½

� � e�Ea=RT1ð ÞE1 Ea

R T0�T1ð ÞA1þT1½ �EaRT1

� h in o� þ L1 ðA:10Þ


Modelling of the kinetics of colour change in hazelnuts during air roasting

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