validation and improvement of heat and mass transfer...

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)

http://doi.org/10.15242/IAE.IAE1116440 225

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:



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


Fig 2c - Roasting temperature and bean temperature profile as


Fig 2d - Roasting temperature and bean temperature profile as


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)



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.



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.



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



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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[9] B Heyds,.et al ,”physical model of heat and mass transfer in spouted bed

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[13] A Fabbri,.et al, “Numerical modelling of heat and mass transfer during

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[14] B Alonso-Torres, .et al, “Modelling and validation of heat and mass

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[16] J.A Hernandez, “Study of roasting; modeling determination of the degree

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https://doi.org/10.1002/9783527619627

https://doi.org/10.1002/9783527619627

https://doi.org/10.1002/9783527619627




https://doi.org/10.1080/07373930701438683

https://doi.org/10.1080/07373930701438683

https://doi.org/10.1080/07373930701438683





















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.



validation and improvement of heat and mass transfer...

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