Experimental and mathematical investigations of convective solar drying of four varieties of olive leaves

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 176–184

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Experimental and mathematical investigations of convective solar drying of four varieties of olive leaves Boudhrioua Nourh`ene a,∗ , Kouhila Mohammed b , Kechaou Nabil a a

Groupe de Recherche en G´enie des Proc´ed´es Agroalimentaires de l’Unit´e de Recherche en M´ecanique des Fluides Appliqu´ee et Mod´elisation, Ecole Nationale d’Ing´enieurs de Sfax, BP ‘W’ 3038, Sfax, Tunisia b Laboratoire d’Energie Solaire et des Plantes Aromatiques et M´edicinales, Ecole Normale Sup´erieure, BP 2400, Marrakech, Morocco

a r t i c l e

i n f o

a b s t r a c t

Article history:

The aim of this work is to study the drying kinetics of four varieties of Tunisian olive leaves

Received 1 June 2007

(Chemlali, Chemchali, Zarrazi and Chetoui) by using an indirect forced convective solar dryer

Accepted 15 October 2007

consisting of a solar collector, an auxiliary heater, a circulation fan and a drying cabinet used for drying experiments. Experiments are conducted at three temperatures (40, 50 and 60 ◦ C), ambient relative humidity (29–32%) and at a drying air flow rate of 0.0556 m3 /s. Three

Keywords:

models available in the literature were used to describe experimental kinetics. The exper-

Olive leaf

imental drying curves show only the falling rate period. Air temperature has a significant

Solar drying

effect on drying kinetics. The statistical parameters (correlation coefficients and standard

Kinetics

errors) show that the Page model could be used to determine the curve drying equations from

Air temperature

the experimental drying curves. The characteristic drying curves of olive leaves are deter-

Apparent diffusivity

mined empirically by using the corresponding curve drying equations. Apparent moisture

Activation energy

diffusivities of olive leaves were determined from the analytical solution of Fick’s equation. Values vary from 2.95 × 10−10 to 3.60 × 10−9 m2 /s. They depend on the olive leaves variety and on temperature. © 2008 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers.

1.

Introduction

Oleic industry generates, in addition to oil as a main product, large amounts of by-products such as crude olive cake, vegetation water, twigs and leaves. The total production of leaves and twigs per tree and per year is about 25 kg. It is thus necessary to valorize these by-products in order to avoid pollution and increase the income of oleic industry. Olive leaves and twigs were always used as animal feed. In recent studies the olive leaves are used as a natural source for extracting compounds having functional values such as biophenolic compounds (Balanehru and Nagarajan, 1991; De Laurentis et al., 1997; Gonzalez et al., 1992; Heimler et al., 1992; Zarzuelo, 1991; Tutour and Guedon, 1992; Susnik-Rybarski et al., 1983). The last compounds are recognized for their antioxidant activities which could have various applications in cosmetic, therapeutic and food industries (Zarzuelo, 1991; Fehri et al., 1994; Aziz et al., 1998). After falling in the ground, fresh olive leaves evolve

∗

rapidly and are deteriorated by dust and insects. It is very necessary to reduce the moisture content of the fresh leaves and search optimal conditions for their storage. Solar drying could be a process of great interest for stabilizing agricultural products. In fact, the drying time could be reduced compared to a simple uncontrolled sun drying. Besides, the organoleptic and hygienic qualities of the leaves could be controlled. Furthermore, solar drying process allows obtaining a safe final product without use of any chemical preservatives or other added compounds and is not treated by using any kind of harmful electromagnetic radiation or electromagnetic poles (Kouhila et al., 2002, 2003). Experimental and mathematical investigations of solar drying of olive leaves are necessary for determining the optimal conditions of preservation of the leaves. Thin layer drying modeling is always used in order to understand and estimate the drying characteristics of agricultural products (Jayas et al., 1991). Three categories of models could be distinguished: theoretical models generally based on

Corresponding author. ` E-mail addresses: [email protected] (B. Nourhene), [email protected] (K. Nabil). 0960-3085/$ – see front matter © 2008 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers. doi:10.1016/j.fbp.2007.10.001

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 176–184

Nomenclature CDC DCE f MR  dMR  − dt

characteristic drying curve drying curve equation dimensionless drying rate at any time of drying moisture ratio drying rate at any time of drying (kg moisture/kg dry basis min)  dMR  − dt initial drying rate (kg moisture/kg dry 0 basis min) r correlation coefficient S standard error t time T temperature (◦ C) initial moisture content (kg/kg d.b.) X0 final moisture content (kg/kg d.b.) Xf moisture content at any time of drying (kg/kg Xt d.b.) Xeq equilibrium moisture content (kg/kg d.b.)

diffusion equations or simultaneous heat and mass transfer equations, semi-theoretical models (approximated theoretical equations) and empirical models depending on experimental data. Many researches have been performed on drying of agricultural products (Lahsasni et al., 2004; Ait Mohamed et al., 2005; Bellagha et al., 2002). There is no literature specific to the processing and particularly the drying of Tunisian olive leaves and values of leaves physical properties (apparent moisture diffusivity, activation energy) missed in the literature. The aim of this work is to study the solar drying kinetics of four varieties of Tunisian olive leaves. An indirect forced convective solar dryer is used and the effect of air temperature on the experimental drying of olive leaf kinetics is examined. A mathematical treatment of experimental data was then applied in order to fit the experimental variations of moisture ratios versus drying time by using three empirical equations chosen in the literature and to determine the corresponding characteristic drying curve (CDC). Analytical solution of Fick’s equation was used in order to estimate apparent moisture diffusivity of the olive leaves.

2.

Material and methods

2.1.

Raw material

177

by using a muffle at 550 ◦ C up to constant weight (4 h). Carbohydrate content was estimated by difference of mean values, i.e., 100 − (Sum of percentages of moisture, ash, protein and lipids) (Al-Hooti et al., 1998; Barminas et al., 1999). The sample weight was measured by an analytical balance (METTLER-TOLEDO) having a precision of ±0.0001 g. Moisture content was expressed in wet basis (g/100 g fresh leaves) and in dry basis (kg moisture/kg d.b.). Protein, fat, carbohydrates and ash contents were expressed in wet basis (g/100 g fresh leaves). All analytical determinations were performed in triplicate. Values of different parameters were expressed as the mean ± standard deviation of repeatability.

2.3.

Experimental solar dryer

The experimental apparatus (Fig. 1) consists of an indirect forced convection solar dryer with a solar air collector (1 m × 2.5 m), an auxiliary heater, a circulation fan and a drying cabinet. A corrugated galvanized iron sheet painted black was used as an absorber plate for incident solar radiation. It was orientated southward under the collector angle of 31◦ . This angle is fixed by the control foot. A glass and plastic sheet is used as a transparent cover for the air to prevent the top heat loss. The frame is made of wood. The drying cabinet is constructed with insulated walls of 1.4 m × 0.9 m × 0.5 m and has 10 shelves. A centrifugal ventilator (0.0833 m3 /s; 80 mm CE, 220 V) connected to the north side of the drying cabinet provides a maximum air velocity of 1.7 m/s and allowed the drying air flow rate to vary from 0.0227 to 0.0833 m3 /s. The circulation fan that supplies fresh air has a power of 0.1 kW. The auxiliary heater has a power of 4 kW. The auxiliary heater was connected to the inlet of control box.

2.4.

Experimental drying procedure

A mass of ≈20 g of fresh olive leaves by tray was used for each drying experiment. In these experiments only the third shelf was used for the efficient use of drying air. The leaves were uniformly spread forming a thin layer of leaves on the drying tray that was then placed in the third shelf of the drying cabinet. The heated air enters the drying cabinet below the

Fresh olive leaves (Olea europea L.) of Chemlali, Chemchali, Zarrazi and Chetoui varieties were obtained from the farm of the Olive Institute of Sfax (Tunisia). Harvested samples were stored for 1–10 days in plastic bags at 5 ◦ C until performing the drying experiments.

2.2.

Global chemical analysis

In order to characterize the olive leaves, chemical analyses were realized according to the Association of Official Analytical Chemists (AOAC, 1984). Moisture content was measured by the gravimetric method at 105 ◦ C up to constant weight (24 h). Total protein was determined by the Kjeldahl method. Protein was calculated using the general factor of 6.25 (El-Shurafa et al., 1982). Fat content was determined by using the Soxhlet method, using hexane as a solvent. Ash content was measured

Fig. 1 – Schematic representation of the solar dryer. (1) Solar collector, (2) circulation fan, (3) fan, (4) air flow direction, (5) control box, (6) auxiliary heating system, (7) shelves, (8) drying cabinet, (9) recycling air, (10) control foot (11 exit of air), (12) humidity probes, and (13) thermocouples.

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trays and flowed upwards through samples. The air temperature can vary with the magnitude of the solar radiation. The auxiliary heater was so used to control the air temperature. The amounts of solar radiation were measured by using Kip & Zonem-Solarmeter. Temperature measurement recordings at different positions in the solar dryer were made by Cr-Alumel thermocouples (0.2 mm diameter) connected to a data-logger enabling ±0.1 ◦ C accuracy and the outlet temperatures were measured with thermometer. The relative humidity was measured by capacitance sensors. These values were determined by probes Humicolor having ±2% accuracy. The drying experiments were conducted during the period of July 2005 in Marrakech (Morocco). Experiments started at 8:30 a.m. and continued till 5:00 p.m. During the experiment, daily solar radiation value varied from 200 to 950 W/m2 , ambient temperature ranged from 32 to 36 ◦ C. Each variety of Tunisian olive leaves was dried at three air temperatures (40, 50 and 60 ◦ C), a fixed drying air flow of 0.0556 m3 /s and an ambient relative humidity varying from 29 to 32%. The mass loss of the product during the drying experiments was measured by a digital weighing apparatus (±0.001 g). During each drying experiment (duration = 165 min), the weight of the product on the tray was measured by removing it from the drying cabinet for approximately 15–20 s. These measurements were performed every 10 min at the beginning of the drying experiment and then every 30 min at the end. The initial and dried moisture contents of the leaves were measured by drying samples 24 h in an oven at 105 ± 1 ◦ C.

2.5.

Mathematical treatment

The Van Meel transformation (Van Meel, 1958) is applied for describing drying kinetics and determining the characteristic drying curves. Lopez et al. (2000) and Kouhila et al. (2002) used simply the initial moisture (X0 ) and the equilibrium (Xeq ) moisture contents to normalize the moisture content obtained at any drying time (Xt ). The moisture ratio (MR) of the olive leaves obtained at any time of solar drying experiment is calculated as following: MR =

Xt − Xeq X0 − Xeq

where Xeq is determined from the desorption isotherms of olive leaves (Boudhrioua et al., 2006) and Xt was deduced from product weight and initial moisture content and dry matter content of the leaves. The dimensionless drying rate (f) was also determined for each drying experiment as following: f =

−(dMR/dt) (−(dMR/dt))0

where (−dMR/dt)0 is the initial drying rate. The drying rate was calculated by deriving a sliding polynomial of second order fitted over five points. The experimental variations of moisture ratios versus drying time (MR = f(t)) of each olive leaves variety were described by using Newton, Page and Henderson and Pabis models (Table 1) chosen from the most used equations in literature to describe the thin layer drying kinetics of agricultural products (Lahsasni et al., 2004; Ait Mohamed et al., 2005). The corresponding experimental characteristic drying curves given by plotting the drying rates (f) as a function of moisture ratios were also described by the mathematical correlation giving the best fit of experimental data. Marquardt–Levenberg

Table 1 – Mathematical models applied to the drying curves Model name

Model expression

Newton Page Henderson and Pabis

MR = exp(−kt) MR = exp(−ktn ) MR = a exp(−kt)

Parameters k k, n a, k

non-linear optimization method, using the computer program “Curve Expert 3.1” was used to determine the parameters of the used equations. The parameters of each model were determined by minimizing the difference between calculated and experimental data. The adequacies of the models were evaluated by using two statistical parameters: the standard error (S) and the correlation coefficient (r). These parameters are defined as following:

 S=

nexp .data (Expi i=1

− Cali )

2

(1)

nexp .data − nparam

  nexp .data 2  (Expi − Cali )  r= 1 −  i=1   nexp .data i=1

Expi − Expi

2

(2)

where “Cal” is the value of the moisture ratio or of the drying rate (f) calculated by using the tested model, “Exp” is the experimental value of the moisture ratio or of the drying rate, nparam is the number of parameters of the particular model and nexp.data is the number of experimental points.

2.6. Determination of apparent moisture diffusivity and activation energy Analytical solution of Fick’s equation for an infinite slab (Eq. (3)) was used in order to estimate apparent moisture diffusivity (Crank, 1979; Boudhrioua, 2004) of the olive leaves from the drying kinetics. ln(MR) = ln

8

2

−

2 Dapp t (e/2)

2

(3)

This equation was applied assuming one-dimensional moisture movement without volume change; a constant diffusivity, uniform moisture distribution and negligible external resistance (Boudhrioua et al., 2003a). In Eq. (3) MR is the moisture ratio, Dapp is the apparent moisture diffusivity (m2 /s), t is the drying time (s) and e is the olive leaf thickness (m). The apparent moisture diffusivity could be related to temperature by a simple Arrhenius equation (Lopez et al., 2000) as given below:

E

a

Dapp = D0 exp −

RT

(4)

where Dapp is the apparent diffusivity (m2 /s), D0 is the constant equivalent to the diffusivity at infinitely high temperature (m2 /s) Ea is the activation energy (kJ/mol), R is the universal gas constant (8.314 × 10−3 kJ/mol K) and T is the absolute temperature (K). Eq. (4) was linearized as following: ln(Dapp ) = ln(D0 ) −

Ea RT

(5)

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Table 2 – Global chemical composition of the fresh olive leaves Variety

Content (% wet basis) Moisture

Chemlali Chemchali Chetoui Zarrazi

55.99 55.40 52.72 50.96

± ± ± ±

2.42 2.18 3.27 1.17

Protein 9.84 7.41 9.35 9.46

± ± ± ±

Fat

0.08 0.07 0.04 0.17

3.11 3.58 3.87 3.21

± ± ± ±

0.26 0.00 0.53 0.41

Ash

Carbohydrates

± ± ± ±

22.59 23.79 26.01 29.77

8.47 9.82 8.05 6.60

0.14 0.09 0.36 0.22

The activation energy, Ea , is determined from the slope of ln (Dapp ) versus 1/T.

3.

Results and discussion

3.1.

Global chemical composition of the leaves

The mean values of the chemical components of the four olive leaves varieties were presented in Table 2. Mean values of different components were expressed as the mean ± standard deviation of repeatability. Fresh olive leaves are intermediate moisture products: the moisture content (wet basis) varied from 51% (Chemlali) to 56% (Zarrazi). Protein and fat contents of the leaves varied, respectively, from 7.41% (Chemchali) to 9.84% (Chemlali) and from 3.10% (Chemlali) to 3.90% (Chetoui). Ash content varied from 6.60% (Zarrazi) to 9.80% (Chemchali). Accordingly, carbohydrate content varied from 22.6% (Chemlali) to 29.80% (Zarrazi). According to this result, the olive leaves of different varieties seem to have similar global chemical composition and could be considered as a rich natural source of valuable nutriments (carbohydrate, ash and protein) that could be used for animal feed and food industry applications.

3.2.

Preliminary

The moisture contents of fresh and stored (10 days at 5 ◦ C) olive leaves of Chemlali, Chemchali, Chetoui and Zarrazi varieties are given in Table 3. The variability of the average moisture content measurements calculated by using three repetitions varies between 1 and 3%. The moisture contents of the leaves remain relatively constant after storage in plastic bags at 5 ◦ C for 1–10 days (variation about 1–3%). Consequently, it could be assumed that the storage of the leaves at 5 ◦ C during this period has no significant effect on their moisture contents. Fig. 2 shows the variation of the average moisture ratio of Zarrazi olive leaves versus drying time (t) performed at 50 ◦ C and obtained for three repetitions. The corresponding standard deviation varies from 0.01 to 0.06. The repeatability of drying experiments was thus judged acceptable.

Table 3 – Moisture contents (kg/kg d.b.) of fresh and stored (at 5 ◦ C) olive leaves Variety

Chemlali Chemchali Chetoui Zarrazi

1.272 1.242 1.115 1.039

3.3. Temperature and olive leaves varieties effects on drying kinetics The moisture contents of fresh olive leaves decrease considerably (from 46.5 to 98.5%) by solar air drying during 165 min. The initial moisture content of Chemlali olive leaves decreases by a factor of 98.5% after 165 min of solar drying at 60 ◦ C (Table 4). Fig. 3a and b shows, respectively, the variations of the moisture ratios versus drying time (Fig. 3a) and of the drying rates (f) versus moisture ratios (Fig. 3b) of Chemlali olive leaves obtained at 40, 50 and 60 ◦ C. Whatever the drying temperature, it could be noticed that there is only the presence of the falling drying rate period corresponding to phase 2 in the characteristic drying curves (absence of phase 0 and phase 1). The same observations were made for the solar drying curves of the other varieties (Chemchali, Chetoui and Zarrazi). These results indicate that diffusion is the most likely physical mechanism governing moisture movement in olive leaves (Lahsasni et al., 2004; Togrul and Pehlivan, 2002; Yaldiz and Ertekin, 2001; Yaldiz et al., 2001; Midilli and Kucuk, 2003).

Table 4 – Moisture contents (kg/kg d.b.) of fresh and dried olive leaves Variety

Olive leaves At harvesting

Fig. 2 – Experimental Chemlali olive leaves moisture ratios versus drying time. Three repetitions obtained at an air temperature of 50 ◦ C, an ambient relative humidity of 32% and a drying air flow rate of 0.0556 m3 /s.

Fresh leaves

After 10 days at 5 C 1.169 1.296 1.059 0.991

Dried leaves during 165 min ◦

◦

Chemlali Chemchali Chetoui Zarrazi

1.169 1.296 1.059 0.991

40 C

50 ◦ C

0.152 0.452 0.218 0.556

0.059 0.059 0.146 0.194

60 ◦ C 0.019 0.045 0.026 0.024

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Fig. 3 – Experimental Chemlali olive leaves drying rates versus moisture ratios (Fig. 3a) and corresponding moisture ratios versus drying time (Fig. 3b): experimental drying curves obtained at 40, 50 and 60 ◦ C, ambient relative humidity and a drying air flow rate of 0.0556 m3 /s.

Fig. 3a and b shows that the drying rates increased with the increase of air temperature. In fact, a higher drying air temperature produces a higher drying rate of the leaves and accelerates the moisture migration. Air temperature is known to be the main parameter influencing air drying of agricultural products. These evolutions of drying curves are characteristic of drying kinetics of biological products and are also observed by other authors (Lahsasni et al., 2004; Ait Mohamed et al., 2005). Figs. 4 and 5 show, respectively, the variation of the moisture ratios versus drying time (Fig. 4) and the dimensionless drying rate versus moisture ratio (Fig. 5) of the four varieties of olive leaves obtained at 40, 50 and 60 ◦ C. It could be noted that the drying curves of the four varieties obtained at the same solar drying condition did not superpose. At the beginning of drying, Zarrazi olive leaves seem to have the lowest drying rate. The difference between the drying curves of the four varieties decreased with increasing air temperature. The difference between drying kinetics of the leaves could be attributed to their different initial moisture contents and the morphological variability among the leaves of different varieties. A mathematical treatment was performed to find the best model describing the moisture variations of olive leaves during drying (drying curve equations, DCEs). These drying curve equations were treated separately to determine the corresponding characteristic drying curve of each olive leaves variety.

3.4.

equation) variations of moisture ratios versus time of Chemlali, Chemchali, Chetoui and Zarrazi olive leaves obtained at 40, 50 and 60 ◦ C is illustrated in Fig. 6a–c. These curves show the adequacy between calculated and experimental drying curves. The temperature dependency of Page parameters obtained for each olive leaf varieties was determined (Table 6). The Page model could thus be retained to determine the drying curve equation of the olive leaves between 40 and 60 ◦ C.

Mathematical treatment of experimental data

3.4.1. Fitting of the variations of moisture ratios versus drying time The experimental variations of moisture ratios versus drying time of the four studied olive leaf varieties obtained at 40, 50 and 60 ◦ C were fitted to the third thin layer drying models shown in Table 1 in order to determine the appropriate drying curve equation. The drying models coefficients and the respective values of the correlations coefficients (r) and the standard errors (S) are shown in Table 5. The Page model is found to be the appropriate equation to describe the thin layer drying curves of olive leaves for the studied solar drying conditions (Table 4). In fact, this model shows the highest values of “r” and the smallest values of “S” for the four varieties and all examined air conditions. The corresponding correlations coefficients (r) and standard deviation (S) values vary, respectively, from 0.98 to 0.99 and 0.035 to 0.422. A comparison between the experimental and calculated (Page

Fig. 4 – Experimental Chemlali, Chemchali, Zarrazi and Chetoui olive leaves moisture ratios versus drying time: experimental drying curves obtained at 40, 50 and 60 ◦ C, ambient relative humidity and a drying air flow rate of 0.0556 m3 /s.

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Table 5 – Results of models used to describe the thin layer drying kinetics k

a

n

r

S

Chemlali Newton model

40 ◦ C 50 ◦ C 60 ◦ C

0.015 0.0246 0.088

– – –

– – –

0.960 0.950 0.989

0.196 0.340 0.400

Page model

40 ◦ C 50 ◦ C 60 ◦ C

0.0563 0.083 0.112

– – –

0.723 0.745 0.943

0.992 0.985 0.990

0.088 0.210 0.422

Henderson and Pabis model

40 ◦ C 50 ◦ C 60 ◦ C

0.0125 0.0213 0.0845

0.759 0.706 0.792

– – –

0.988 0.973 0.990

0.107 0.286 0.417

Newton model

40 ◦ C 50 ◦ C 60 ◦ C

0.0072 0.0133 0.057

– – –

– – –

0.977 0.930 0.960

0.072 0.206 0.550

Page model

40 ◦ C 50 ◦ C 60 ◦ C

0.0195 0.0646 0.182

– – –

0.79 0.667 0.743

0.995 0.992 0.994

0.035 0.071 0.238

Henderson and Pabis model

40 ◦ C 50 ◦ C 60 ◦ C

0.0064 0.0106 0.0486

0.918 0.752 0.492

0.989 0.970 0.985

0.053 0.122 0.384

Newton model

40 ◦ C 50 ◦ C 60 ◦ C

0.018 0.0162 0.0445

– – –

– – –

0.989 0.950 0.857

0.129 0.225 0.926

Page model

40 ◦ C 50 ◦ C 60 ◦ C

0.0369 0.0697 0.3154

– – –

0.85 0.693 0.5868

0.996 0.997 0.985

0.083 0.053 0.330

Henderson and Pabis model

40 ◦ C 50 ◦ C 60 ◦ C

0.0164 0.0132 0.0326

0.840 0.726 0.284

– – –

0.989 0.987 0.957

0.129 0.120 0.552

Newton model

40 ◦ C 50 ◦ C 60 ◦ C

0.0089 0.0216 0.0376

– – –

– – –

0.840 0.969 0.923

0.190 0.252 0.526

Page model

40 ◦ C 50 ◦ C 60 ◦ C

0.0717 0.0546 0.147

– – –

0.5618 0.8054 0.699

0.993 0.982 0.973

0.045 0.205 0.343

Henderson and Pabis model

40 ◦ C 50 ◦ C 60 ◦ C

0.00637 0.01885 0.031

0.7584 0.742 0.583

– – –

0.968 0.985 0.952

0.094 0.187 0.451

Zarrazi

Chetoui

Chemchali

Table 6 – Page parameters dependency upon temperature k

n

Chemlali

a b c

1.00E−05 0.0016 −0.0275

0.0009 −0.077 2.395

Zarrazi

a b c

0.0004 −0.028 0.5621

0.001 −0.1019 3.272

Chetoui

a b c

0.1065 −0.2866 0.217

0.0254 −0.2332 1.0578

Chemchali

a b c

0.0548 −0.1814 0.1983

−0.175 0.7686 −0.0318

Here k and n show polynomial variations (aT2 + bT + c) versus temperature.

3.4.2.

Determination of the characteristic drying equations

The variations of the experimental dimensionless drying rates versus experimental moisture ratios obtained at 40, 50 and 60 ◦ C for different olive leaf varieties were fitted by using different mathematical correlations. Polynomial equations (order 3) were found to fit the best the experimental data. The polynomial equations obtained for the four olive leaf varieties and the respective correlation coefficients and standard deviations values are given in Table 7. The dimensionless drying rates versus moisture ratios obtained for each olive leaves variety fall into a tight band indicating that the effect of air temperature on these curves could be described by a single equation in the examined solar drying conditions. Fig. 7 shows a comparison between experimental and calculated values of the drying rates versus moisture ratio obtained for Chemlali olive leaves.

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Fig. 5 – Experimental Chemlali, Chemchali, Zarrazi and Chetoui olive leaves drying rates versus moisture ratios: experimental drying curves obtained at 40, 50 and 60 ◦ C, ambient relative humidity and a drying air flow rate of 0.0556 m3 /s.

3.4.3.

Apparent moisture diffusivity and activation energy

The values of apparent moisture diffusivity, Dapp of olive leaves obtained at 40, 50 and 60 ◦ C for the four varieties are recapitulated in Table 8. The values of the activation energy deduced from the linearized Arrhenius relationships are also added in the same table. Apparent moisture diffusivity of the leaves varies from 2.95 × 10−10 to 3.60 × 10−9 m2 /s. The values seem to depend on the olive leaves variety, for example at 40 ◦ C, values of Dapp of Chemlali and Zarrazi olive leaves are, respectively, equal to 5.70 × 10−10 and 2.95 × 10−10 m2 /s. The effect of temperature on apparent moisture diffusivity is considerable. In fact for Zarrazi olive leaves, for example,

Fig. 6 – Comparison between the variations of experimental and calculated (Page model) moisture ratios versus drying time of olive leaves.

the value of Dapp is increased by a factor of ≈10 when temperature of the thin layer dryer increased from 40 to 60 ◦ C. The effect of temperature on apparent moisture diffusivity is largely documented in literature (Andrieu et al., 1988; Lopez et al., 2000; Boudhrioua et al., 2003a, 2003b). Many authors have also reported the dependence of apparent moisture diffusivity upon the composition, the structure and the variety of the product (Andrieu et al., 1988; Zogzas and Maroulis, 1996; Zogzas et al., 1996; Lopez et al., 2000; Boudhrioua et al., 2003a,

Table 7 – The polynomial equations of the characteristic drying equations Variety Chemlali Zarrazi Chetoui Chemchali

CDE f = −0.006 + 1.108 MR − 1.105 MR + 1.214 MR3 f = 0.008 + 0.719 MR − 0.917 MR2 + 1.042 MR3 f = 0.01 + 0.358 MR − 1.242 MR2 –0.505 MR3 f = −0.017 + 0.278 MR − 0.046 MR2 + 0.976 MR3 2

r

S

0.98

0.05

0.92

0.08

0.96

0.08

0.97

0.05

Fig. 7 – Variation of the dimensionless drying rate versus moisture ratio of Chemlali olive leaves, Dots: experimental data, line: calculated value by using the polynomial equation (Table 7).

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Table 8 – Apparent moisture diffusivities at activation energy determined for the olive leaves Variety

D (m2 /s)

Ea (kJ/mol) ◦

Chemlali Chemchali Chetoui Zarrazi

79.20 74.24 52.15 83.60

◦

◦

40 C

50 C

60 C

5.70 × 10−10 3.00 × 10−10 4.95 × 10−10 2.95 × 10−10

1.05 × 10−9 7.20 × 10−10 6.30 × 10−10 5.40 × 10−10

3.60 × 10−9 1.66 × 10−9 1.66 × 10−9 2.05 × 10−9

183

Acknowledgements This study was supported by CMPMT for a Tunisian–Moroccan project (Ref. 04/MT/17) on Solar Drying and Quality of Medicinal and Aromatic Plants. The authors would like to thank Mme KAMMOUN Naziha, researcher from the Olive Institute of Sfax (Tunisia), who guaranteed us a regular supply of olive leaves.

references

Fig. 8 – Arrhenius type relationship between apparent moisture diffusivity of Chemchali olive leaves and reciprocal of absolute temperature, Dots: calculated data from Fick’s diffusion equation, line: linearized Arrhenius equation.

2003b, 2005). The values of Dapp of olive leaves are in the general range 10−9 –10−12 m2 /s for drying of agricultural and food products. The plot depicting the relationship between ln (Dapp ) and 1/T was found to be a straight line in the range of investigated temperatures, indicating Arrhenius dependence (Fig. 8). The values of activation energy vary from 52.15 kJ/mol (Chetoui) to 83.60 kJ/mol (Zarrazi).

4.

Conclusion

The drying kinetics of four varieties of Tunisian olive leaves (Chemlali, Chemchali, Zarrazi and Chetoui) have been studied by using an indirect convective solar dryer. Experiments are conducted at three air temperatures (40, 50 and 60 ◦ C), ambient relative humidity (29–32%) and at a drying air flow rate of 0.0556 m3 /s. Drying curves of different olive leaf varieties show only the falling drying rate period. Temperature is shown to have a considerable effect on the variation of moisture ratios versus drying time. The Page model gave the best agreement with the experimental variations of olive leaves moisture ratios versus drying time for the four varieties and the examined solar drying conditions. The characteristic drying curve of each olive leaves variety was established. Apparent moisture diffusivities of the leaves were determined by using the analytical solution of Fick’s equation. They vary from 2.95 × 10−10 to 3.60 × 10−9 m2 /s. The values depend on the olive leaves variety and considerably on temperature. The values of activation energy of the olive leaves vary from 52.15 to 83.60 kJ/mol.

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