20320140501017

International Journal JOURNAL OF ADVANCED RESEARCH Technology (IJARET),
INTERNATIONAL of Advanced Research in Engineering and IN ENGINEERING
ISSN 0976 – 6480(Print), ISSNAND – 6499(Online) Volume 5, Issue 1, January (2014), © IAEME
0976 TECHNOLOGY (IJARET)

ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 5, Issue 1, January (2014), pp. 154-163
© IAEME: www.iaeme.com/ijaret.asp
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IJARET
©IAEME

EXPERIMENTAL STUDY OF COCOA DRYING KINETICS WITH A VIEW
TO MODELLING A DRYER
Abraham Kanmognea*,
a

Oumarou Hamandjodaa,

Jean Nganhoua,

Bienvenu Kenmeugnea

Laboratoire d’Energétique (Energy Systems Laboratory), Ecole Nationale Supérieure
Polytechnique, P.O. Box 8390 Yaounde, Cameroon

ABSTRACT
Kinetic drying measurements make it possible to determine the influence of various
parameters (temperature, thickness of the layer of the product, speed of drying air) on the behaviour
of the product when it is being dried and thus deduce from it a characteristic curve of the product
including the maximum parameters. In this paper, we have studied through experiment the drying of
cocoa in several layers and defined the correlations that make it possible to find the characteristic
cocoa drying curve for a group of given parameters. The graphic determination of the characteristic
drying curve made it possible to obtain results that conform to the direct method. Tests were
conducted in the Laboratoire d'énergétique (Energy Systems Laboratory) of the Ecole Nationale
Supérieure Polytechnique of Yaounde (ENSPY). The atmospheric conditions in the laboratory are
relatively constant: average room temperature of 28°C ; average humid temperature of 23°C ;
average absolute humidity: 15,5 g water/kg dry air; average relative humidity of 65%
Keywords: drying kinetics, parameter, cocoa, characteristic curve, laboratoire d’énergétique
(energy systems laboratory).
1. INTRODUCTION
The economy of developing countries is based generally on agriculture and particularly on
cash crops such as: coffee, cotton, cocoa etc… In sub-Saharan Africa, cocoa occupies a pride of
place in the exports of many countries of the sub-region. However, in the world market the price is
compatible with the quality of marketable cocoa. Cocoa producing countries must take special
measures to ensure that the product put in the market is of quality. Drying seems like an economic
and essential means adapted to the improvement of the quality of cocoa and its preservation. Cocoa
dried up to 7% water content allows for its proper preservation [1]. In Cameroon, losses after harvest
154

International Journal of Advanced Research in Engineering and Technology (IJARET),
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 1, January (2014), © IAEME

due to the drying of cocoa are estimated at 15 % [2]. The building of appropriate dryers aimed at
transforming cocoa with a view to improving its quality, its preservation requires a perfect
knowledge of its behaviour during drying. Knowledge of the behaviour of solid products during
drying is an essential element in calculating the dimension or size of a dryer and/or defining its
conditions of use [3]. At the Energy Systems Laboratory (LAEN) of the Ecole Nationale Supérieure
Polytechnique (ENSP), research works have been undertaken to study experimentally the kinetics of
the drying of cocoa. It is impossible to estimate the drying curve of a product by a calculation that
would take into account the influence of phenomena (transfer of water and heat in the product,
deformation of the product) that are described in the current state of knowledge in the domain of
drying. The only means to know the kinetics of drying is thus to measure it [4]. The purpose of this
study consist in making measurements of loss of mass of cocoa in a test section (small scale dryer) in
the laboratory and drawing or plotting the drying kinetics with a view to modelling a large scale
dryer.
2. MATERIAL AND METHOD
2.1 Principle
A quantity of cocoa that has a determined density or a thickness is placed in the test section,
under a hot current air of fixed temperature and known speed. The product is weighed at regular time
intervals. These measurements make it possible to obtain the variation of the mass of the product
depending on time and thus the variation of the water content of the product depending on time.
2. 2 Description of the device
A thermostatically-controlled drying vein makes it possible to have an air flow that has well
controlled areothermic characteristics [5].
The entire device assembled on a frame comprises (figure 1)
•
•
•
•
•
•

•
•

An axial fan driven by a 750 watts engine
An alternostat that allows for the regulation of the heating power of resistances
A Plexiglas test section of 125 mm x 125 mm and 200 mm long
A convergent at the entrance of the sheath to ensure proper canalization of air flow
A diaphragm placed at the air outlet that enables the regulation of its deficit,
Three deflectors installed respectively downstream of the heating battery, between the heating
battery and the vein upstream of the test section for a better distribution of the speed of air at the
section of the vein,
A thermometer that gives digital readings to ensure a constant indication of the temperature in
the test section,
10,5 cm x 10,5 cm x 4 cm 10,5 cm x 10,5 cm x 3 cm et 10,5 cm x 10,5 cm x 2 cm aluminium
plated trays introduced in the vein and connected to an electronic balance of precision ± 0,01 g
by a screw-nut system.

155


Diaphragm
Thermometer
Vein

Resistances
chauffantes

Sheath

Fan
Balance

Figure 1: Drying test bench

2. 3 Measurement devices
The installation is rounded off with a certain number of measuring devices:
• A Platinium Pt sensor electronic thermometer 100 (- 100 °C to 500°C) makes it possible to
measure the dry air temperature in the test section, a Sartorius electronic balance is used to
measure mass losses during the drying process. The measurements are made with the help of
intermittent weighing hours,
• A TESTO 425 thermo-anemometer measures the speed and air temperature in the test section.
Measurement takes place inside the vein. Air speed can be adjusted by creating pressure
drops on the diaphragm located at the fan outlet.
• An H27O electronic thermo-hygrometer to measure the room temperature and relative
humidity of the ambient air.
• A Chromel-Alumel type thermocouple connected to a Digi-Sense electronic thermometer
provides temperature control in the vein.
• A drying oven at 103 ° C ± 2 ° C to determine the dry mass of cocoa. [6]
2.4 Experiment Method
Sample Preparation
After opening the pod, the cocoa beans are put into clusters in a one-litre plastic bowl. They
are then covered with banana leaves. After 3 to 7 days of fermentation, the beans are placed in the
aluminium tray with a dimension of 10.5 cm x 10.5 cm and a height of 4, 3 or 2 cm, which is put into
the test section. At the same time, other beans are placed in three cups that are tared beforehand. The
samples are ready for testing in the drying oven.

156


Experiment Protocol
The air speed is set using a diaphragm and the heating system is adjusted to the desired
temperature using an alternostat. The product to be dried is arranged in a thick layer in the tray,
placed in the test section, parallel to the flow of hot air. The mass of the sample, the ambient relative
humidity and the room temperature measurements are taken at regular time intervals (15 m at the
beginning of the test and 30 to 45 mm towards the end of the test). During the tests, temperature
control in the test section is done by using the platinum sensor electronic thermometer. The control
of the drying air-speed is done through a thermo-anemometer.
The three previous cups are placed in the drying oven after weighing. Weighing of the cups is
done after every 24 hours. At the end of 72 hours, the weight of each cup becomes constant and we
can then determine the dry mass of cocoa which enable us to determine the initial water content of
the cocoa.
The experimental curves were obtained following the test plan shown in Table 1.

Test n°
1
2
3
4
5
6
7
8
9

Table 1: Parameter values for the various tests
T (°C) V (m.s-1) e (mm) Test n° T (°C) V (m.s-1) e (mm)
0.25
10
0.25
0.5
20
11
0.5
20
1.0
12
1.0
0.25
13
0.25
40°C
55°C
0.5
30
14
0.5
30
1.0
15
1.0
0.25
16
0.25
0.5
40
17
0.5
40
1.0
18
1.0

3. RESULTS AND DISCUSSION
3.1 Determination of the equilibrium water content Xeq
The dry mass is used to calculate the equilibrium water contents on a dry basis (Xeq) of each
sample under each condition set in advance using the following relations:
X0 =

m0
−1
ms

(1)

X eq =

m (1 + X 0 )
−1
m0

(2)

where m is the sample mass, X0 the initial water content of the sample and m0 its initial mass.

3.2 Determination of the water content X(t)
An m0 mass of the fresh product is placed on a support which mass M0 is determined by
weighing. The whole mass (M+m)0 is measured before putting into the drying section. The mass
value (M+m)i is then measured at different times ti until the product reaches the final desired water
content. This is calculated as follows:

157


X i = mi − ms
ms

(3)

plus ms dry mass of the sample. Figure 2 shows the variation in the cocoa water content depending
on the drying time for a 3 cm-layer thickness.

Figure 2 : Experimental curves for cocoa drying of a 3 cm-layer
3.3 Determination of the drying speed
The drying curves are determined from measuring the sample mass variation over time. They
represent either variations in the average water content (X) depending on time, or the drying speed
( − dX ) depending on (X). Determination of curve ( − dX )=f(X) is obtained by calculating the
dt
dt
derivative directly from the experimental points using the following formulae:

1  ( X i +1 − X i ) ( X i − X i −1 ) 
 dX 
−
+
 =− 
 i ≠ 0, n
2  ti +1 − ti
ti − ti −1 
 dt  X i

(5)

X1 − X 0
 dX 
−
 =−
t1 − t0
 dt  X 0

(6)

X n − X n −1
 dX 
−
 =−
tn − tn −1
 dt  X n

Where n is the number of experimental points, Xi is the instant average water content. The
humidity transfer between the air and the product can be represented in a curve describing the
evolution in water content depending on time or evolution in drying speed depending on the water
content.

Influence of temperature on drying speed
Figure 3 shows drying kinetics at different temperatures. An increase in air temperature
causes an increase in drying speed including a drop in drying time.

158


1

X (kg.kgms-1)

0.8
X 40°
C

0.6

X 55°
C

0.4
0.2
0
0

20

40

60

80

t (h)

Figure 3: Influence of temperature on Cocoa drying speed
(V = 0,5 m.s-1, layer thickness = 3 cm)

Influence of air speed on drying speed
An increase in air speed causes an increase in drying speed.
Influence of Cocoa layer thickness on drying speed
The influence of the product’s thickness is obtained by modifying from one test to the other
the product’s loading density and characteristics of the air remained constant. Figure 4 presents this
effect on the growth of the average water content that drops as time changes. The product’s drying
speed drops as the product’s layer thickens.

1
0.8

e = 20 mm
X/X0

0.6

e = 30 mm
e = 40 mm

0.4
0.2
0
0

10

20

30

40

t (h)

Figure 4: Influence of Cocoa layer’s thickness on drying speed
(V=1 m.s-1, T = 55°C)

159

50


3.4 Modelling drying kinetics
Several theories and models have been formulated to illustrate drying kinetics and to
understand the physical laws that control transfers. The complexity of the mechanisms employed and
the variable nature of the products (type, form, and physical properties) hamper the formulation of a
unique model that can represent all situations. The drying characteristics curve method (CCS)
consists in representing drying kinetics in the following form:

Vr = V = f (φ)

(7)

 X − X eq 
Where: φ = 

 X 0 − X eq 



(8)

V0

And:
Vr is reduced drying speed
V0 is initial drying speed (kgeau.kgms-1.h-1)
Xeq is product’s water content in harmony with its milieu (kgeau.kgms-1)
X is product’s average water content (kgeau.kgms-1)
X0 is initial water content (kgeau.kgms-1)

Direct Method
This method is based on the processing of raw experimental data, which helps to determine
the value of V0 following the drying curve ( − dX )=f(X). This method assumes that at the start of the
dt

drying, the product’s humidity level is below or equal to the critical humidity. The function f(φ) is a
function that, in principle, is characteristic of the environment under study. It can be a polynomial
function or power function. To process our data, we will use the following power characteristics
curve:
f(φ)=φα

(9)

From the curve m=f(t), we will determine the curve X=f(t) and the curve:
V=( − dX )=f(X)

(10)

dt

Equations 7, 8 and 12 will give the following formula:
X − X eq   X − X 0 
Vr = V = f 
 X 0 − X eq  =  X 0 − X eq 
V0

 


α

(11)

Where α is positive or nil.
The process to determine α is as follows: points (X, V) and values X0, V0, Xeq are known for
each test and are used to calculate Vr and φ at instant t. For each experimental point we deduce an
instant value αt as follows:

160


αt =

[

Ln ( Vr )
Ln (φ)

]

(12)

For a test performed on a specific product under defined drying conditions, the average value
αi is calculated using the formula:
P
αi = 1 ∑ α t
P

(13)

i =1

Where P is the number of points per test. The average value retained for the α parameter is
calculated using the formula:
K
α = 1 ∑ αi
K

(14)

i =1

Where K is the number of the drying test conducted. This final α value, characteristic of the
product, does not depend on the test conditions or a group of test parameters. The values from Xeq to
40°C and to 55°C are determined by desorption isotherms at 40 and 55°C [8]. The estimated values
of the initial rate of drying V0 and the exponent α are shown in table 2. The average values of
α obtained for the different thicknesses are: α20µµ = 1.61; α30µµ = 1.47 ανδ α40µµ = 1.485

Table 2: Values of α, characteristic parameter of the characteristic curves of cocoa
Test n°
V0 (kg.kgms-1.s-1)
Test n°
V0 (kg.kgms-1.s-1)
α
α
-5
-5
1
16,6.10
1,77
10
1,3.10
1,28
2
8.10-5
1,58
11
1,8.10-5
1,51
1,55
3
8,3.10-5
12
3,7.10-5
1,25
4
5,3.10-5
1,45
13
3,3.10-5
1,41
-5
5
7,5.10
1,64
14
1,6.10-5
1,45
-5
-5
6
3,2.10
1,71
15
2,4.10
1,53
1,72
7
2.10-5
16
2,2.10-5
1,82
8
3,8.10-5
1,23
17
1,3.10-5
1,49
-5
-5
1,52
9
3,5.10
18
1.10
1,48

The model presented by formula (9) is used to describe the change in the reduced speed
depending on the reduced water content. It makes it possible to increase the water content value
depending on time from the following correlation:


V (1 − α )
X = X eq + ( X 0 − X eq )1−α − 0
( X 0 − X eq )α



1

 (1−α )
[9]
t



(15)

Considering the different α values, the modelled curves agree with the experimental results as
exemplified in figures 5 representing the simulated experimental curve corresponding to test n°6.

161


Figure5: Comparison of the theoretical model with experimental results: example of the
change in the reduced rate of drying for test n°6
Graphical determination of the characteristic drying curve
We sketched the experimental curves (Vr,Xr) for different drying parameters and identified
the value that is closest to the experimental points in order to deduce the expression of the water
content depending on time. Figure 6 shows curves for three values of α and the experimental points
for a cocoa layer thickness of 4 cm. Some dispersion is observed in the experimental points as
compared to the identified theoretical patterns. The identification is quite precise when the
experimental points obtained are considered for Xr values lower than 0.4.

Figure 6: Graphic determination of parameter α
The average value of α determined using the direct method is 1.485 and the value of α
determined using the graphic method is 1.55, which clearly conforms to the former value.

162


4. CONCLUSION
A series of experimental drying curves for different operating conditions (air speed, air
temperature, cocoa layer thickness) were sketched. An equation deduced from these curves enables
the identification for each product layer thickness a characteristic drying graph. Based on the
correlations obtained, a good reconstitution of the results of the experiments can be made. Thus, we
can calculate the drying time, an important parameter for the sizing of dryers, as per the conditions
adopted.

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[1]

[2]
[3]
[4]
[5]

[6]

[7]

[8]

[9]

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Ph.D, Université de Yaoundé I, 142 p.
Kanmogne A., Jannot Y. et Nganhou J., 2012, Description concise et analyse des systèmes
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J.J. Bimbenet, 1978. Le séchage dans les industries agricoles et alimentaires. Cahier du GIA,
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