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Modeling of olive cake thin-layer drying process Article in Journal of Food Engineering · June 2005 DOI: 10.1016/j.jfoodeng.2004.06.023
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Journal of Food Engineering 68 (2005) 455–461 www.elsevier.com/locate/jfoodeng
Modelling of olive cake thin-layer drying process Nalan A. Akgun, Ibrahim Doymaz
*
Department of Chemical Engineering, Yildiz Technical University, Davut Cad No 127, Esenler-Istanbul 34210, Turkey Received 23 January 2004; accepted 29 June 2004
Abstract Olive cake is a sub-product of the mechanical olive oil extraction industry, which consists of pit and pulp of the olive fruit, olive oil and vegetable water. It has been using for direct combustion in bakeries and olive oil mills due to its energy content. However, the initial moisture content of olive cake is approximately 44.78% ± 0.5 (wet basis), and this has to be reduced to about 5% to recover its energy content. Therefore, the characterization of the thin layer drying kinetics was investigated at a wide range of drying temperatures (50–110 C), a constant sample thickness and air velocity of 1.2 ± 0.03 m/s at a laboratory scale dryer. Various mathematical models simulated drying curves of olive cake. The logarithmic model was found to give better predictions than the others. In addition, the temperature dependence of the effective diffusivity coefficient was expressed by an Arrhenius type relationship. The effective diffusivity varied between 0.3 and 1.1 · 108 m2/s with an activation energy of 17.97 kJ/mol. 2004 Elsevier Ltd. All rights reserved. Keywords: Olive oil; Olive cake; Drying kinetics; Modelling; Nonlinear regression
1. Introduction Spain, Greece, Italy, Tunisia and Turkey are important olive oil producers in Mediterranean basin, which represents 97% of olive oil production in the world (Lo´pez-Villalta, 1998). Recently, as the strong correlation was observed between olive oil production and environmental pollution, researchers became concerned with two basic issues, namely, the wastes obtained after extracting of oil from olive fruit, aqueous sludge and olive cake. Aqueous sludge, which equals to about 45–54% of total wastes, consists of vegetation water and solid, and is extremely hazardous to the environment due to its high phenolic content. It is treated by using different methods such as chemical, biochemical and electrochemical treatments, supercritical extraction and separation processes based membrane (Israilides, Vlyssides, Mourafeti, & *
Corresponding author. Tel.: +90 212 449 1732; fax: +90 212 449 1895. E-mail address:
[email protected] (I. Doymaz). 0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.06.023
Karvouni, 1997; Rivas, Gimeno, Portela, de la Ossa, & Beltron, 2001; Vitolo, Petarca, & Bresci, 1999). The olive cake, which is also considered a major pollutant, constitutes more than 80% by weight of the olives consumed and depends on olive varieties and the extraction process. Generally, olive cake is utilized as a fuel due to its high energy content, and as a raw material for soap making due to its high-quality variable oil content of about 5–8%. However, these application areas require drying of the olive cake from a moisture content of 20–45% to approximately 5–6%. The literature contains several studies on drying of olive cake for soap making, animal feed or high quality fertilizer (Arjona, Garcı´a, & Ollero, 1999; Freire, Figueiredo, & Ferra˜o, 1999; Freire, Figueiredo, & Ferra˜o, 2001; Gogus & Maskan, 2001; Krokida, Maroulis, & Kremalis, 2002). In Turkey, there are around 90,000 olive trees. Although the size of the olive industry is very difficult to establish and oil-grade olive production changes according to periodicity of olives fruits, production annually was estimated to be around 106 tones (DIE,
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Nomenclature a, b, c, k, y constants in models Deff effective diffusivity, m2/s D0 pre-exponential factor of the Arrhenius equation, m2/s dp particle size, lm Ea activation energy, kJ/mol L half-thickness of the slab, m MR dimensionless moisture ratio M moisture content, kg moisture/kg dry matter Me equilibrium moisture content, kg moisture/kg dry matter M0 initial moisture content, kg moisture/kg dry matter
2002). However, there are about 3500 olive oil mills, operated seasonally from November to March. The basic problems in production of olive oil are related to traditional extraction processes and to the existence of mills with small capacity. Consequently, the olive cake has approximately 10–12% oil content before solvent extraction, and is used as a fuel in the bakeries in these districts. It can be seen that direct combustion is the easiest and the most attractive way of utilization. Before combustion, sun drying has been traditionally carried out, followed by compress into briquettes, although sun drying requires a large area and a long time. Nevertheless, controlled drying at high temperature is a better alternative by using waste heat from the olive oil mill. Consequently, knowledge of moisture content in the olive cake is important for process design and conditions. Moreover, mathematical models would also be desirable for describing the drying mechanism. Thin layer drying models have found wide application among mathematical models and these kinds of models have three categories. While theoretical thin layer models take into account internal resistance to moisture transfer, semi-theoretical and empirical models consider external resistance to moisture transfer between product and heated air. Some parameters are related to the properties of the sample such as thickness, shape, particle size, and drying air temperature and relative humidity. Nevertheless, modelling of such a drying process is a complex task, because olive cake exhibits macroscopic non-homogeneity, consisting of pieces of pit and pulp with different size, shape and ratios. Therefore, description of a model and the repeatability of the drying curves are important. In this study, attention is focused on drying and modelling of olive cake over a wide temperature range by using mathematical models. In addition, the effective diffusivities and activation energy were calculated.
N R r2 T t z
number of observations universal gas constant, kJ/mol K coefficient of determination temperature, C or K drying time, min number of constants
Subscripts exp experimental pre predicted
2. Material and methods 2.1. Material Fresh extracted olive cake samples were obtained from an olive oil mill in Aydin district, which is located in the southwest of Turkey, in March 2003. The samples exhibited macroscopic non-homogeneity due to the granular structure. Particle size (dp) distribution can be classified in three granularities with typical dimensions, e.g. dp > 1000 lm (80.3 ± 2% by weight), between 1000 and 560 lm (14.9 ± 1.7% by weight) and between 560 and 200 lm (4.3 ± 0.4% by weight). Moreover, olive cake had an initial moisture content of 44.78% ± 0.5 (wet basis), determined by drying in an oven at 105 C for 4 h, the tests being performed in triplicate. 2.2. Experimental set-up Drying experiments were performed in the cabinet dryer, described previously by Doymaz, Gorel, and Akgun (2004). The dryer mainly consists of a centrifugal fan to supply the air, an electrical heater, an air filter and a proportional temperature controller. The air velocity was measured with a TESTO 440 vane probe anemometer (Lutron, Taiwan). The samples were dried in a square basket of 30 cm width (height of 11 cm), and moisture loss was recorded during drying by a specially developed weighing unit. This weighing unit consisted of a balance, hanger rod, digital indicator, and load cell (Revere Transducers Europe, Holland). 2.3. Experimental procedure After the dryer reached steady-state conditions for the set points (at least 30 min), the olive cake samples were distributed uniformly into the basket as a thin layer. Drying experiments were performed at 50, 60,
N.A. Akgun, I. Doymaz / Journal of Food Engineering 68 (2005) 455–461
70, 80, 90, 100 and 110 C, sample thickness/load of 0.8 cm/250 ± 0.2 g, and constant air velocity of 1.2 ± 0.03 m/s. Moisture loss was recorded at 10 min intervals. The experiments were continued till the moisture content of the sample was reduced to 5% (w/w). Three replications of each experiment were done. The dried samples were cooled at the laboratory conditions after each drying experiment, and packed in low-density polyethylene bags, which were heat sealed, and kept to use in further experiments.
3. Results and discussion 3.1. Analysis of the drying curves The changing of the moisture ratio versus drying time for olive cake samples at various temperatures is given in Fig. 1. It can be seen that moisture ratio decreases continuously with drying time, and no constant drying rate period exists. This observation is in agreement with previous literature studies on drying of olive cake (Gogus & Maskan, 2001; Kadi & Hamlat, 2002). The rate of moisture loss was high initially. However, twothirds of the time may be spent removing the last one1.0 50˚C 60˚C 70˚C 80˚C 90˚C 100˚C 110˚C
Moisture ratio
0.8
0.6
457
third of the moisture content due to the slow diffusion process. Moreover, the rate of moisture loss was greater at higher temperatures, and the total drying time was reduced substantially with the increase in air temperature. 3.2. Modelling of drying curves It is vital to model the falling rate period effectively. Therefore, in this study, a wide range of the thin layer drying models was examined to describe the drying curves of olive cake at different temperatures. The selected mathematical models, namely, the Lewis, the Page, the Modified Page, the Henderson and Pabis, the Logarithmic, the Approximation of diffusion and the Wang and Singh, are identified in the Table 1. In these models, MR is the dimensionless moisture ratio = (M Me)/(M0 Me), where M is the moisture content of the product at each moment, M0 is the initial moisture content of the product and Me is the equilibrium moisture content. The values of Me, are relatively small compared to M or M0. Thus, MR = (M Me)/ (M0 Me) can be reduced to MR = M/M0 (Thakor, Sokhansanj, Sosulski, & Yannacopoulos, 1999). Nonlinear regression was used to obtain each constant of the selected mathematical models. Moreover, the criteria such as coefficient of determination (r2), reduced chi-square (v2), root mean square error (RMSE) and residuals of graphs were calculated to evaluate the fitting of a model to experimental data. The highest values of r2, lowest values of v2, RMSE, and residuals which are the closest to zero, were chosen for goodness of fit. These parameters can be calculated as below (Akpinar, Bicer & Yildiz, 2003; Rosello´, Can˜ellas, Simal, & Berna, 1992)
0.4 2
v ¼
PN
i¼1 ðMRexp;i
0.2
MRpre;i Þ N z
2
"
N 1 X RMSE ¼ ðMRpre;i MRexp;i Þ2 N i¼1
0.0 0
50
100 150 Drying time (min)
200
ð1Þ #1=2 ð2Þ
250
Fig. 1. Thin-layer drying curves of olive cake at different temperatures.
Residuals ¼
N X ðMRexp;i MRpre;i Þ i¼1
Table 1 Thin layer drying curve models considered Model name
Model
References
Lewis Page Modified Page Henderson and Pabis Logarithmic Approximation of diffusion Wang and Singh
MR = exp(kt) MR = exp(kty) MR = exp(kt)y MR = a exp(kt) MR = a exp(kt) + c MR = a exp(kt) + (1a) exp(kbt) MR = 1 + at + bt2
Bruce (1985) Page (1949) Overhults et al. (1973) Henderson and Pabis (1961) Togrul and Pehlivan (2002) Yaldiz et al. (2001) Wang and Singh (1978)
ð3Þ
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N.A. Akgun, I. Doymaz / Journal of Food Engineering 68 (2005) 455–461
where MRexp,i and MRpre,i are the experimental and predicted moisture ratios, respectively. N is the number of observations and z is the number of constants. The results of the statistical computations are summarized in Table 2. In all cases, r2 values were greater than 0.97, indicating a good fit. Fig. 2 shows the comparison of mathematical models considered for a drying temperature of 50 C, and simi-
lar results were obtained at all temperatures. It can be seen that drying curves of all models tended to under or over estimate the experimental data at different stages of drying. For instance, the Henderson and Pabis model, which is a semi-theoretical thin layer drying model, was tending to a good fit for low temperatures, while the model was tending to underestimate for higher temperatures during the first 1 h of drying. The Lewis model
Table 2 Statistical results obtained from different thin-layer drying models Model
T (C)
Residuals
r2
v2
RMSE 4
Lewis
50 60 70 80 90 100 110
0.0035 0.0167 0.0242 0.0278 0.0104 0.0443 0.0133
0.9906 0.9880 0.9934 0.9882 0.9783 0.9856 0.9916
7.620 · 10 9.890 · 104 5.620 · 104 1.031 · 103 2.090 · 103 1.293 · 103 8.630 · 104
0.1139 0.1215 0.0841 0.0921 0.1292 0.0918 0.0701
Page
50 60 70 80 90 100 110
0.0334 0.0583 0.0516 0.0529 0.0352 0.0585 0.0224
0.9981 0.9951 0.9978 0.9939 0.9966 0.9882 0.9977
1.660 · 104 4.260 · 104 1.970 · 104 5.780 · 104 3.650 · 104 1.169 · 103 2.710 · 104
0.0448 0.0738 0.0452 0.0699 0.0486 0.0882 0.0337
Modified Page
50 60 70 80 90 100 110
0.0547 0.0756 0.0478 0.0608 0.0450 0.0640 0.0242
0.9985 0.9956 0.9979 0.9941 0.9968 0.9884 0.9978
1.280 · 104 3.800 · 104 1.910 · 104 5.580 · 104 3.360 · 104 1.155 · 103 2.620 · 104
0.0406 0.0762 0.0445 0.0698 0.0461 0.0876 0.0353
Henderson and Pabis
50 60 70 80 90 100 110
0.0974 0.0954 0.0681 0.0677 0.0753 0.0529 0.0448
0.9934 0.9901 0.9945 0.9892 0.9831 0.9856 0.9927
5.630 · 104 8.590 · 104 5.050 · 104 1.021 · 103 1.792 · 103 1.429 · 103 8.530 · 103
0.0935 0.1084 0.0786 0.0924 0.1143 0.0942 0.0673
Logarithmic
50 60 70 80 90 100 110
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.9993 0.9992 0.9997 0.9992 0.9998 0.9964 0.9998
6.195 · 105 7.536 · 105 2.536 · 105 8.036 · 105 2.725 · 105 4.100 · 104 2.061 · 105
0.0303 0.0296 0.0166 0.0249 0.0129 0.0446 0.0092
Wang and Singh
50 60 70 80 90 100 110
0.0330 0.0549 0.0550 0.0561 0.0011 0.0738 0.0210
0.9987 0.9977 0.9979 0.9967 0.9999 0.9914 0.9985
1.089 · 104 1.900 · 104 1.920 · 104 3.090 · 104 6.470 · 106 8.590 · 104 1.755 · 104
0.0404 0.0460 0.0459 0.0498 0.0072 0.0641 0.0298
Approximation of diffusion
50 60 70 80 90 100 110
0.0383 0.0623 0.0397 0.0546 0.0407 0.0610 0.0215
0.9988 0.9963 0.9985 0.9950 0.9968 0.9898 0.9981
1.010 · 104 3.430 · 104 1.490 · 104 5.160 · 104 3.770 · 104 1.140 · 103 2.560 · 104
0.0360 0.0694 0.0381 0.0638 0.0456 0.0821 0.0319
N.A. Akgun, I. Doymaz / Journal of Food Engineering 68 (2005) 455–461 1.0
1.0 Experimental Wang and Singh Page Lewis Modified Page Logarithmic Henderson and Pabis App.diffusion
0.6
0.8
Predicted values
0.8
Moisture ratio
459
0.4
0.2
0.6 50˚C 60˚C 70˚C 80˚C 90˚C 100˚C 110˚C
0.4
0.2
0.0 0
50
100 150 Drying time (min)
200
250
Fig. 2. Comparison of the selected models fitted for olive cake dried at 50 C.
is a special case of the Henderson and Pabis model and tended to overestimate in the early stages and underestimate in the later stages of the drying for all temperatures. The Page model, which was developed by Page (1949), produced a good enough fit except for drying at 50 C. The Page model, which was modified by Overhults, White, Hamilton, and Ross (1973), described drying of olive cake much better than the original one. The approximation of the diffusion model tended to underestimate in the latter stages while the model was tending to a good fit in the initial stages for all temperatures. Although the Wang and Singh model shows better results, the logarithmic model was the best descriptive model as shown in Table 2. Generally r2, v2 and RMSE values were varied between 0.9964–0.9998, 2.061 · 105–4.1 · 104 and 0.0092–0.0446, respectively. The residuals of this model also were found to be zero at all temperatures. Fig. 3 includes the comparison of predicted and experimental moisture ratio values for the logarithmic model. The data was generally banded around a straight line of 45. Consequently, it can be said that the logarithmic model could adequately describe the drying of olive cake.
0.0 0.0
0.2
0.4 0.6 Experimental values
0.8
1.0
Fig. 3. Experimentally determined and predicted moisture ratio values at different temperatures for the logarithmic model.
1 8 X 1 ð2n þ 1Þ2 p2 Deff t MR ¼ 2 exp p n¼0 ð2n þ 1Þ2 4L2
! ð4Þ
where, Deff is the effective diffusivity (m2/s); L is the halfthickness of slab (m). The linear solution of the equation is obtained by using a simple approach that assumes that only the first term in the series equation is significant (Tutuncu & Labuza, 1996). Then, Eq. (5) is obtained by taking the natural logarithm of both sides. It shows that the time to reach given moisture content will be directly proportional to the square of the half-thickness and inversely proportional to Deff ln MR ¼ ln
8 p2 Deff t p2 4L2
ð5Þ
Diffusivities are typically determined by plotting experimental drying data in terms of ln(MR) versus time in Eq. (5), and the plot gives a straight line with a slope of Slope ¼
p2 Deff 4L2
ð6Þ
3.3. Determination of effective diffusivities The results obtained have shown that internal mass transfer resistance due to presence of a falling rate-drying period controls drying time. Therefore, experimental results can be interpreted by using FickÕs diffusion equation. The solution of this equation developed by Crank (1975), and the form of Eq. (4) can be applicable for particles with slab geometry by assuming uniform initial moisture distribution:
Values of Deff for different temperatures are presented in Table 3. The effective diffusivities of dried samples at 50–110 C varied in the range of 0.3–1.1 · 108 m2/s. As expected, the values of Deff increased greatly with increasing temperature. Additionally, these values are comparable to 2–4.2 · 1010 m2/s for drying garlic slices in temperature range of 50–90 C (Madamba, Driscoll, & Buckle, 1996), drying of corn 0.948 · 1010– 1.768 · 1010 m2/s in temperature range of 55–70 C
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Table 3 Values of effective diffusion coefficients obtained for olive cake at different temperatures Temperature (C)
Effective diffusion coefficient (m2/s)
50 60 70 80 90 100 110
3.382 · 109 4.846 · 109 6.252 · 109 7.146 · 109 7.887 · 109 8.818 · 109 1.134 · 108
(Doymaz & Pala, 2003) and drying of vegetable wastes 6.03 · 109–3.15 · 108 m2/s in temperature range of 50–150 C (Lopez, Iguaz, Esnoz, & Virseda, 2000).
shows the effect of temperature on Deff of olive cake with the following coefficients: 2162:3 6 Deff ¼ 3:128 10 exp ð8Þ T The activation energy can be found to be 17.97 kJ/ mol by using Eq. (8). This value is higher than that corresponding to vegetable waste drying (19.82 kJ/mol) (Lopez et al., 2000) but lower than the value obtained for garlic (54.9 kJ/mol) (Madamba et al., 1996) and for corn (29.56 kJ/mol) (Doymaz & Pala, 2003).
4. Conclusions 3.4. Activation energy The temperature dependence of the effective diffusivity may be represented by an Arrhenius relationship (Madamba et al., 1996; Sanjuan, Lozano, GarciaPascal, & Mulet, 2003). Deff
Ea ¼ D0 exp RT
ð7Þ
where D0 is the pre-exponential factor of the Arrhenius equation (m2/s), Ea is the activation energy (kJ/mol), R is the universal gas constant (kJ/mol K), and T is the absolute temperature (K). The natural logarithm of Deff as a function of the reciprocal of absolute temperature was plotted in Fig. 4. The results show a linear relationship due to the Arrhenius type dependence. Eq. (8)
Olive cake investigated in this study belongs to the Aydin district, western of Turkey. It consists of pits, pulp and skin, and it has initial moisture of 44.78 ± 0.5%. In this study, attention was also focused on modelling of experimental thin layer drying kinetics. The drying time was decreased by using higher drying temperatures. The logarithmic model fitted better to the drying curves than the others. Effective diffusivity values varied from 0.3 · 108 to 1.1 · 108 m2/s. The temperature dependence of the effective diffusivity was described by an Arrhenius type equation. The activation energy was found to be 17.97 kJ/mol.
Acknowledgements Authors gratefully acknowledge the financial support of Yildiz Technical University Organization of Scientific Research Project (project no: BAPK-23-07-01-06), and _ ¨ BITAK TU (project no: 103M031).
-18 -18.2
References
-18.4 -18.6
ln Deff
2
R = 0.9746 -18.8 -19 -19.2 -19.4 -19.6 0.0025 0.0026 0.0027 0.0028 0.0029 0.003 0.0031 0.0032 1/T (1/K)
Fig. 4. Arrhenius-type relationship between effective diffusivity and temperature.
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