Abstract— Evolution of a cup of coffee consist of 24 steps, with roasting as one of the most important steps since it establishes the
organoleptic properties of coffee. The coffee roasting process is an exothermic reaction, characterised by a change in colour, aroma, expansion and crack of the green coffee beans. In this study, heat transfer parameters that play a role in the coffee roasting process and roasting profile were investigated. Ten models were developed and published up to date to predict the coffee bean roasting profile, and all of the investigations on this topic use heat and mass transfer parameters as constants given by reference [7]. The aim of this study is to evaluate the heat transfer parameters; air to bean heat transfer
coefficient, specific heat capacity of the bean and thermal conductivity of the bean, and validate an improved model that predicts the roasting profile. The roasting profiles were investigated with four different roasting temperatures, i.e. 170 ºC, 190ºC, 210ºC and 230ºC. MATLAB® Simulink was used to simulate Schwartzberg‟s model to estimate the coffee roasting profile. The effect of heat transfer parameters on the roasting profile was investigated and the roasting profile predicted by the model was validated with experimental data.
The model was then improved by varying the specific heat capacity of the bean, thermal conductivity of the bean and heat transfer coefficient. It was found that the effect of thermal conductivity of the bean on the roasting profile is very small and therefore negligible. Increasing the specific heat of the bean or decreasing the heat transfer coefficient decreases the mean squared error between predicted roasting profile and experimental roasting profile.
Index Terms— coffee beans, heat transfer, roasting profile,
Simulink modelling.
I. INTRODUCTION
Coffee roasting is one the most trending processes that can
be considered as both art and science with many citizens
practicing the procedure at home as a hobby and also for
commercial purposes. There are three common types of bean
species used (as raw material) to produce coffee namely (i)
Arabica with earliest plantation in the 6th century, originating from Ethiopia in East Africa, (ii) Liberica originating in West
Africa with earliest plantation during the period 1864-1881 and
(iii) Robusta planted as early as the year 1900-1910 in central
and west Africa. Each coffee plant type grows at a specific
favourable altitude with the bearing age ranging from 3-5 years
at most [1].Evolution of a cup of coffee consists of twenty-four
steps with roasting followed by grinding and brewing, the
operations required to convert selected green coffee beans into
Manuscript received October 31, 2016. This work was supported in part by the
North West University (POTCHEFSTROOM campus).
Faculty of Engineering, School of Chemical and Minerals Engineering,
North-West University, Potchefstroom Campus, Calderbank Avenue,
Potchefstroom, 2531, South Africa
N.F Bopape is with school of chemical and mineral Engineering, North
West University
a consumable beverage [2]. Coffee characteristics such as
flavour, colour and aroma are developed during the roasting
process. Roasting is a time temperature dependent process
whereby chemical changes are induced to green coffee beans
without evidence of changes in structure. The roasted beans are
characterised by the roasting process itself, degree of roast
reflected by their external colour, developed flavour, loss of dry
mass and the chemical changes in selected components [3]. The
roasting process is divided into two phases. Firstly the drying
phase where the moisture content is lowered to approximately 12% which is done by either evaporating water as temperature
of the bean is increased or by exposing the beans to the sun [4].
One reason that emphasises the importance of moistures
content in coffee parchment is that too high or too low moisture
content will result in coffee not reaching its optimum cupping
quality [5]. The second phase is roasting wherein pyrolysis
causing chemical changes such as oxidation and reduction
results at a starting temperature of 190ºC [6]. About ten known
models (with one succession and improvement on the other)
has been developed, proposed, analysed and evaluated to
investigate and predict the effect of temperature on the coffee
bean roasting profile with regard to the heat and mass transfer during roasting of green coffee bean. Reference [7] developed
a heat and mass transfer model that predicts the bean
temperature profile and the moisture content in a batch process
with the assumption that the initial moisture content and
roasting temperature are constant, which is non ideal in a real
world. The model also accounts for exothermic reactions with
the assumption that there is a proportional relationship between
heat generation rate and production reaction rate [8]. With the
shortcoming of the physical model mentioned above, reference
[6] evaluated and analysed a dynamic model that predicts
temperature of the bean and the moisture content during roasting and therefore pointed out that the bean temperature
profile against time can be a roast-degree indicator; a
phenomenon that [7] did not observe.
Reference [9] proposed a physical dynamic model that
accounts for heat and mass transfer at both the surface and
inside of the bean with water diffusivity adjusted in the study.
However lack of knowledge in roasting mechanism and
insufficient knowledge on high temperature drying
mechanisms is a drawback on the model proposed. A model
proposed by [10] describes the temperature and moisture
profile inside the bean in 3D and also accounts for diffusivity of
water. A dynamic model that predicts non-stationary thermal profile of coffee during roasting, assuming lumped specific
heat parameters of thermal effects was proposed by [11].
Improved knowledge of heat and mass transfer during coffee
drying and industrial application optimisation by determining
transport coefficients and coffee properties, was suggested by
[12] and conclusion was made that internal mass transfer
Validation and Improvement of Heat and Mass Transfer
Model in Predicting the Coffee Roasting Profile
Ntsitlola F. Bopape, Abraham F. van der Merwe, Johandri Vosloo, RG Ross
International Conference on Advances in Science, Engineering, Technology and Natural Resources (ICASETNR-16) Nov. 24-25, 2016 Parys (South Africa)
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diffusivity controls the drying process, resulting in the first
drying stage not being observed. It was also recommended that
a high gas temperature should be used at the beginning of the
process and low temperatures at the end, to optimise the
process. Performance of a coffee roaster in terms of pressure,
temperature, mass flow rate and fuel consumption has to be predicted.
A numerical model that describes the transfer of heat and
moisture during roasting process of coffee was proposed by
[13]. The model based on a 3D geometry that describes the
heat and moisture transfer inside a coffee bean roasted
singularly was then simulated and validated by [14] using
Computational Fluid Dynamics (CFD). A numerical model
based on the lumped and distributed parameter approaches that
simulates the behaviour of all the components of a batch roaster
including the roasting process of the coffee bean was proposed
by [15]. This model accounts for variation of coffee properties
during the roasting cycle as well as the fluid dynamics of air flow.
The Schwartzberg model forms the base for all the other
models‟ development, but the model does not clearly indicate
how heat transfer parameters affects the roasting profile. The
aim of this study is to validate the model proposed by [7], to
evaluate the heat transfer parameters, including the heat
transfer coefficient, the specific heat capacity of the bean and
the thermal conductivity of the beans and to propose an
improved model for the prediction of the roasting profile.
II. MATERIALS AND METHODS
A. Roasting process
Arabica coffee beans were roasted using a Genio 6
intelligence roaster. The temperature of the green beans was measured using a type K thermocouple and the relative
humidity was measured using a Fluke 975 Air meter. Roasting
temperatures were set as prime temperatures on the control
panel. The roasting temperatures used for this investigation
were 170°C, 190°C, 210 °C and 230°C. The gas flow was set to
50 kg/s. Four kilograms (4 kg) of green coffee beans were
weighed and the first sample was taken from the weighed green
beans before roasting. After the prime temperature was
reached, roasting was initiated by pressing the “roast” button on
the control panel. Green beans were dropped into the roaster
through a funnel and after every minute a sample was taken from the roasting beans. The roasting process took about 10 to
15 minutes to go through both first and second crack stages and
the roast was stopped. The roasted beans were cooled. Gas flow
was measured using Pitot tube and Fluke 975 Air meter at the
ducting leaving the roaster. After the beans have cooled,
roasted beans are weighed. Chaff, as collected by a gas cyclone
situated in the exit ducting of the roaster, was also weighed at
the end of every batch. The chaff and roasted beans were
weighed to calculate mass loss during the process. Fig 1 shows
a schematic representation of the roaster used for the
experiments.
Fig 1 - Genio 6 series intelligence roaster
To investigate moisture content and loss, samples taken
during the roasting process were first weighed to get the total
weight of the sample, then ground to increase surface area and
weighed again to get the mass before moisture loss. Ground
coffee beans were then put in an oven for twenty-four (24)
hours and weighed again to get the mass after moisture loss.
Genio roaster has a built in software that plots the roasting temperature profile.
B. Heat and mass transfer modelling
Development of the heat and mass transfer model follows the
models proposed by [6] and [14]. MATLAB® Simulink was
used for the simulation of the equations below. The specific heat capacity of the bean is one the three
parameters investigated in this study. According to [14],
specific heat capacity of the bean is calculated by
The moisture loss (X) is dependent on the temperature of the
bean and the diameter of the bean. This is empirically described
by the equation below [6]:
[
]
The temperature of the bean changes with time and it is
modelled by the equation;
[ ]
The difference in air temperature is determined by
[
]
According to [14] the global heat transfer coefficient between
air and the coffee bean is calculated by:
International Conference on Advances in Science, Engineering, Technology and Natural Resources (ICASETNR-16) Nov. 24-25, 2016 Parys (South Africa)
http://doi.org/10.15242/IAE.IAE1116440 226
When water contained in a coffee bean is allowed to
evaporate partially, an amount of energy is released.
Exothermic heat production rate was calculated by [6],[7] and
[16] as:
[
]
The heat transfer coefficient was calculated using the
Ranz-Marshall correlation [14]. After rearranging, the equation
below was used:
[ (
)
]
Thermal conductivity of the coffee bean, given by [16] is:
The roasting temperature is predicted by the model of
Schwartzberg and it is described by:
The table below contains the constant values used for model
development and simulation. TABLE I
CONSTANTS USED FOR MODEL SIMULATION
Variable constant reference
db 6.8686 (mm) User defined
ΔHvap 2790 kJ/kg Schwartzberg (2002)
A 116 200 kJ/kg dry
coffee
Schwartzberg (2002)
Ha/Rg 5500 (° K) Schwartzberg (2002)
Agb 3.7 m2 User defined
Vg 0.7 m/s User defined
G 0.047kg/s User defined
Kt 0.016 calculated
mbs 4 kg User defined
III. RESULTS AND DISCUSSION
a) Simulink model.
In the following, the key results from the model are
discussed and validated based on experimental data.
Firstly, the roasting profile and bean temperature profile
were obtained from the simulation with the model proposed by
Schwartzberg. Fig.2 shows the profiles developed during the
roasting process for a 10 minutes roast of a 4 kg batch at
roasting temperatures of 170ᵒC, 190ᵒC, 210ᵒC and 230ᵒC. The
yellow line and blue line represents the roasting temperature profile and bean temperature profile respectively.
Fig 2a - Roasting temperature and bean temperature profile as
modelled at Tr = 170 degrees
Fig 2b - Roasting temperature and bean temperature profile as
modelled at Tr = 190 degrees
Fig 2c - Roasting temperature and bean temperature profile as
modelled at Tr = 210 degrees
Fig 2d - Roasting temperature and bean temperature profile as
modelled at Tr = 230 degrees
It was observed that roasting profiles obtained from the
model agrees with the roasting profile obtained by [7]. Secondly, the effect of heat transfer parameters were
investigated. The values obtained in the model for the heat
transfer coefficient, the specific heat capacity of the bean and
the thermal conductivity of the bean were altered using 10%
increments. Linear regression was performed each time to
investigate the “goodness of fit” between the modelled roasting
profile and the roasting profile obtained from experimental
data. Tables 2 contains the numerical values of the coefficient
of multiple determination (R2)
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TABLE II
COEFFICIENT OF MULTIPLE DETERMINATION BETWEEN MODELLED AND
OBSERVED HEAT TRANSFER PARAMETERS
R2
Tr=170 °C Tr=190°C Tr=210°C Tr=230°C
paramet
er
varied
Deviation (%) Deviation
(%)
Deviation
(%)
Deviation
(%)
-10 +10 -10 +10 -10 +10 -10 +10
Cpb 0.91 0.95 0.94 0.97 0.91 0.95 0.87 0.92
kb 0.93 0.93 0.96 0.96 0.93 0.93 0.90 0.90
he 0.93 0.93 0.96 0.96 0.93 0.93 0.90 0.90
It was found that increasing the specific heat of the beans
increases the “goodness of fit”. Decreasing the heat transfer
coefficient from air to bean has similar effect on the roasting
profile as increasing the specific heat capacity of the bean, i.e.
increasing the “goodness of fit”. Variations of the thermal
conductivity of the bean has a significantly small effect on the
roasting profile, with no effect on the “goodness of fit”.
Table 3 contains the mean squared error and coefficient of multiple determination for the 0% percent deviation predicted
data TABLE III
MSE AND R2 OF THE 0% DEVIATION DATA
Tr(°C) MSE R2
170 766 0.93
190 402 0.96
210 741 0.93
230 1022 0.9
b) Model validation
Experimental data obtained from the Genio 6 intelligence
roaster's Pro-roast data log was compared to the results
obtained from the MATLAB® Simulink model. In this section,
values for the heat transfer coefficient, the specific heat
capacity of the beans and the thermal conductivity of the beans
are based on literature. Fig 3 shows roasting profiles for
roasting temperatures of 170°C, 190°C, 210°C and 230°C. The
blue line represent the roasting profile obtained from the
simulation, referred to as predicted roasting profile (Tr,pred)
and the orange line represents the roasting profile from
experimental data (Tr,exp). Temperature deviations for all roasting temperatures shows
an initial difference being small and an increase observed over
time. Fig3a represents the roasting profiles for Tr=170°C. The
shape of both roasting profiles indicate correspondence
although the goodness of fit is very low and the MSE is high at
a value of 766.87. The predicted roasting profile increases
drastically at time around 100 seconds.
Fig 3b and Fig 3c represent the roasting profiles for Tr
=190°C and Tr =210°C respectively. For both roast
temperatures, the roasting profiles initially have small errors.
The predicted roasting profile increases drastically after
approximately 175 seconds, increasing the error between the roasting profiles.
Fig3a - Comparison between experimental and predicted roasting
profiles for Tr =170 degrees.
Fig 3b: Comparison between experimental and predicted roasting
profiles for Tr =190 degrees.
Fig 3c - Comparison between experimental and predicted roasting profiles for Tr =210 degrees.
Generally, the model represents the roasting profiles of Tr
=190°C and Tr =210°C better. As can be seen on Fig 3d below,
the error between roasting profile is high and results in a MSE
of 1022.68. The coefficient of multiple determination is 0.90,
which is low compared to values obtained for other roast
temperatures.
International Conference on Advances in Science, Engineering, Technology and Natural Resources (ICASETNR-16) Nov. 24-25, 2016 Parys (South Africa)
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Fig 3d - Comparison between experimental and predicted roasting
profiles for Tr = 230 degrees.
c) Model enhancement
Due to high MSE and low R2 values obtained during model
validation, an enhancement to the model for predicting the
coffee roasting profile was investigated. Firstly, the specific
heat capacity of the bean was increased with 10% increments. It
was found that the best predictability of the model is observed
with a 50% increase in the value published for the specific heat
capacity of the beans, and at only 50% of the literature value
published for the heat transfer coefficient. The graphs in Figure
4a-d show the predicted roasting profile with a 50% increase in
specific heat capacity and with a 50% decrease in the heat
transfer coefficient.
By increasing the specific heat capacity with 50% and by decreasing the heat transfer coefficient by 50% relative to
published values for these parameters resulted in a predicted
roasting profile that is closer to the experimental roasting
profile in all cases. The proposed model enhancement with
Cpb*1.5 and he*0.5 resulted in a decrease in MSE to values of
94, 176, 163 and 206 from original values 766, 402,741 and
1022 for the roasting temperatures of 170°C, 190°C, 210°C and
230°C respectively.
Fig 4a - Roasting profiles from enhanced model for Tr =170 degrees
The figure above indicates that the enhanced roasting profile
presents a better fit than the initially predicted roasting profile.
Fig 4b - Roasting profiles from enhanced model for Tr =190 degrees
From Fig 4b it is observed that the deviation between the
improved model roasting profile and experimental roasting
profile maintain a smaller error towards the end of the roast.
Fig 4c - Roasting profiles from enhanced model for Tr =210 degrees
Figures 4c and Fig 4d show an improved relationship
between the experimental roasting profile and the improved
roasting profile model.
Fig 4c - Roasting profiles from enhanced model for Tr =230 degrees
Fig 5a-d represents the regression performed for the
enhanced model. Experimental roasting profiles were plotted
against the improved roasting profiles and the trend line was
fitted to determine the coefficient of multiple determination.
International Conference on Advances in Science, Engineering, Technology and Natural Resources (ICASETNR-16) Nov. 24-25, 2016 Parys (South Africa)
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Fig 5a - Regression on the enhanced roasting profile at Tr =170
degrees
Fig 5b - Regression on the enhanced roasting profile at Tr =190
degrees
Fig 5c - Regression on the enhanced roasting profile at Tr =210
degrees
Fig 5d - Regression on the enhanced roasting profile at Tr =230
degrees
It was observed from the above figures that the proposed
model enhancement increases the goodness of fit for the four roast temperatures. The enhanced model fits the experimental
data for Tr =170°C effectively. Comparing the enhanced
model‟s roasting profile prediction with the initial predicted
roasting profile, it can be clearly seen that for the four roast
temperature, the R2 value increased significantly.
The proposed enhanced model was tested and validated using
experimental data for Tr =200°C. The comparison between the
predicted roasting profile from the original (unenhanced) model and experimental roasting profile resulted in R2=0.47,
obtained from the linear regression represented in Fig 6b. The
MSE was calculated to be 1343 which is very high.
Fig 6a - Comparison of the roasting profile at a roasting temperature of
200 degrees
The roasting profiles for the experimental data, predicted
data from the unenhanced model and predicted data from the
enhanced model are represented in fig 6a above. It is observed
from the plot that the enhanced model is significantly more
successful in reducing the deviation between Tr,exp and
Tr,pred.
Fig 6b - Regression between predicted roasting profile and
experimental roasting profile
Fig 6c - Regression between improved predicted roasting and
experimental roasting profile
Fig 6b and Fig 6c represent the regression performed to
evaluate the fitting efficiency of the roasting profile, and it can
International Conference on Advances in Science, Engineering, Technology and Natural Resources (ICASETNR-16) Nov. 24-25, 2016 Parys (South Africa)
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be seen that the coefficient of multiple determination obtained
for the enhanced model is much larger than that of the roasting
profile predicted by the unenhanced model. The MSE was
calculated to be 454 for the improved model which is also
significantly lower than the value determined for the prediction
from the unenhanced model.
IV. CONCLUSION
The predicted roasting profiles obtained from simulations
shows good agreement to the roasting profiles obtained by
Schwartzberg. The model proposed by Schwartzberg can
successfully be used to predict the coffee roasting profile. The
model requires alterations to better fit various roasting
conditions. The proposed enhanced model proved the
capability of improving the roasting profile for other roasting temperatures desired by the user. The effects of the bean
thermal conductivity on the coffee roasting profile is found to
be negligibly small. The differences observed between roasting
profiles are due to the fact that the model does not account for
other factors affecting heat and mass transfer. For example, the
initial temperature of the gas flow is assumed to be constant
throughout the roasting process. Another reason is that roasting
does not always start at the exact roasting profile due to
equipment and measurement error. Therefore it is
recommended that a better strategy is implement to reduce
experimental error and the model be improved upon to account for such factors.
V. LIST OF SYMBOLS
A Arrhenius pre-factor (kJ/Kg.s)
Agb contact surface area between air and coffee beans (m2)
Bi Biot number
Cpb Specific heat capacity of the bean (J/kgK)
Cpg Specific heat capacity of gas (J/kgK)
db Diameter of coffee bean (m) G Air mass flow (kg/s)
Ha Activation energy (J)
he heat transfer coefficient (W/mK)
He Amount of heat produced from beginning until time
t(kJ/kg dry coffee)
Het total amount of heat produced (kJ/kg)
kg thermal conductivity of gas (W/mK)
kb thermal conductivity of beans (W/mK)
Lv latent heat of vaporisation (j)
MSE Mean squared error
mbs dry weigh of coffee beans (kg) Nu Nusselt number
Pr Prandtl number
Rg ideal gas low constant
Qr Exothermic heat production rate (kJ/kg dry coffee.s)
R2 Coefficient of multiple determination
Tb coffee beans temperature (°C)
Tgi inlet gas temperature (°C)
Tgo outlet gas temperature (°C)
Tr Roasting temperature (°C)
Tr,exp Roasting profile from experimental data (°C)
Tr,pred Roasting profile from simulation (°C)
X mass or moisture loss (g) Vg Relative speed of flow of gas (m/s)
α Global heat transfer coefficient
ρg Density of gas (kg/m3)
µg Viscosity of gas (kg/m.s)
ACKNOWLEDGMENT
The author would like to thank School of Chemical and
mineral engineering, North West University for the
sponsorship, Mr. R.G. Ross, student at the University for
Assistance with experiments, Ms. Johandri Vosloo for
assistance with experiments and modelling and Mr Frikkie Van
Der Merwe, supervisor with the university.
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International Conference on Advances in Science, Engineering, Technology and Natural Resources (ICASETNR-16) Nov. 24-25, 2016 Parys (South Africa)
http://doi.org/10.15242/IAE.IAE1116440 231
N tsitlola F Bopape was born on 29 October 1992 in
Mashashane Limpopo. She matriculated in 2010 and
became a student at North West university in January
2011 studying towards a Bachelor‟s degree in
Chemical Engineering. She was employed by Sedibeng
Brewery, Heineken for experiential work for a period
of six weeks and continued studying towards obtaining
her degree.
International Conference on Advances in Science, Engineering, Technology and Natural Resources (ICASETNR-16) Nov. 24-25, 2016 Parys (South Africa)
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