Fuzzy and Conventional Modeling of Open Sun Drying Kinetics for Roasted Green Wheat

Abstract

Roasted green wheat is a high-value product made by roasting green (under-mature) wheat. Due to its high initial moisture content, drying is needed to avoid fast deterioration. Open sun drying of this product is by far the most common practice due to its simplicity, effectiveness, and low cost. The assumption of open sun drying adequacy to prevent deterioration was tested in this study. The drying data were fitted into eight common thin-layer drying models. Goodness of fit for each model was evaluated using coefficient of determination (R²) and root mean square error. The two-term exponential model was found to best describe open sun drying of roasted green wheat with R², and root mean square error values of 0.988 and 0.038, respectively. A fuzzy model of open sun drying for roasted green wheat was also developed and compared with conventional modeling. The results showed a much better performance of fuzzy model compared to conventional models with a much lower value of root mean square error (1.2 × 10⁻⁶). The effective diffusivity was also evaluated for roasted green wheat kernels and found to be 1.7 × 10⁻¹¹ m²/s, which was in agreement with published data. The results showed that open sun drying for 5.5 h was effective and adequate to reduce moisture content to a safe level and to prevent deterioration of this product. These findings will provide valuable information for the design of a commercial roasted green wheat solar drying system.

Keywords:

• Roasted green wheat
• Frikeh
• Effective diffusivity
• Fuzzy modeling

INTRODUCTION

Roasting of green (under-mature) wheat is a common practice in Middle Eastern countries and throughout parts of the world, such as Turkey and Australia. In Middle Eastern countries, the product is commonly known as frikeh (also known as frekeh or freekah). Roasting provides the green wheat with a distinctive, favorable, smoked flavor. Yearly production of this food staple in the Middle East region is between 200 and 300 thousand tons.[1] Nutritional composition of roasted green wheat shows that it has superior nutritional value compared to rice and wheat, where it contains 77% carbohydrates, 12.7% protein, 16.5% dietary fiber, high amounts of potassium, magnesium, and calcium, and small amounts of vitamin A, B1, B2, C, and E.[2]

Drying of agricultural commodities is one of the oldest preservation methods. Drying is used to extend shelf life and reduce volume and weight of agricultural commodities. This leads to minimum handling, transportation, and packaging costs.[3] Sun drying has been used to dry a variety of crops in tropical and subtropical regions throughout the world. Although it has some disadvantages, such as uncontrolled rate of drying, inferiority in product quality, and dependence on climatic and weather variations, it has the advantages of being an inexhaustible, environment friendly, and cheap source of energy.[4]

Mathematical modeling of thin layer drying has been used to predict the performance of drying systems, and in the design of artificial food dryers under deep-bed drying conditions. There have been many studies on thin layer drying of field grains, including barley,[5] rice,[6] and wheat.7–10 Several studies have been reported on using solar and artificial drying to dry agricultural commodities.11–13 Conventional mathematical modeling of non-linear systems, however, has some limitations including the need for good starting points for parameter estimates, which are difficult to get sometimes, and the difficulty to converge to an absolute minimum. To date, relatively little attention has been devoted to the modeling of drying kinetics using intelligent techniques, such as fuzzy or neural fuzzy approaches. All of the previously discussed regression-based models are aimed at obtaining conventional solutions that simply model the data with the best possible accuracy, without paying much attention to the capability of these models to predict new measurements. Therefore, fuzzy modeling (FM) was used in this work to model drying kinetics and compared the results with those from conventional models.[14]

Roasted green wheat production provides an economic advantage for local farmers, since it is commonly sold at a price that is three times as high as ripe wheat. The amount of production, however, is limited by two main factors: the first is the dependence of this industry on traditional, non-mechanized methods, and secondly, the need for efficient drying of the product to reduce moisture from about 45% to less than 12% (w.b.) in less than 1 day to avoid spoilage. Sun drying of this product remains the most acceptable practice since it is gentle, simple, effective, and the least expensive. A good understanding of sun drying behavior, therefore, would help improve production efficiency and minimize crop spoilage. Thus, the objective of this research is to model sun drying kinetics using conventional and fuzzy modeling (FM) and to check the adequacy of this drying practice.

MATERIALS AND METHODS

Roasted Green Wheat Preparation

Roasted green wheat was prepared according to the traditional procedure from under-mature durum wheat (variety Hourani) on May 5, 2008 at a nearby wheat field in Northern Jordan. According to the traditional method, wheat sheaves were cut and collected in the morning and allowed to dry for 3 h in an open place. After drying, sheaves were placed on clean pieces of metal sheets and burned by dried remains of barley straw. Sheaves were turned frequently with a pitch fork to expose the green leaves and glumes to direct fire. Burning stopped after 15 min when the glumes were charred and the tips of some of the grains were slightly blackened. The spikes were then left to cool in the open atmosphere. Two hours later, the heads were threshed by feeding them into a threshing machine that was brought to the site. Five kilograms of roasted green wheat were filled in polyethylene plastic bags directly after threshing and stored in a refrigerator at 4°C to preserve quality until use.

Moisture Content

Moisture content was measured according to ASAE standards,[15] as follows: triplicates of 10-g samples were obtained using a Boerner grain divider (Kartar Scientific Industries, Haryana, India). The samples were oven dried at 103°C for 72 h, then transferred into a desiccator with a desiccant and allowed to cool down. The sample weights were then recorded using a digital balance to ±0.005 g (Denver Instruments, Bohemia, NY, USA). Average moisture content was obtained and found to be 43.2% (w.b.).

Open Sun Drying

At 10:00 a.m. of the following day after roasting green wheat, three plastic trays each containing 300 g of roasted green wheat at 43.2% moisture content were spread in a single layer at a thickness of 0.4 ± 0.01 cm and placed in an open sun field. The weight of roasted green wheat was recorded for each tray every half-hour using a digital balance to ±0.01 g. The drying was completed after 5.5 h when the weight of the samples became approximately constant as they dropped below 10% m.c. required for safe storage.

Theoretical Considerations

Newton's law of cooling in heat transfer was originally used to model the mass transfer of water in thin layer drying as follows: [16]

(1)

where MR is a dimensionless moisture ratio; M is the moisture content at time t and M_o and M_e , the initial and equilibrium moisture contents, respectively, on a dry basis; and k is the drying constant. Page[17] suggested improving the Lewis model by adding an exponent n, such that:

(2)

Other models were also developed and tested by researchers. The most applicable models with their corresponding authors are listed in Table 1. Some of these are recently used for accurate determination of moisture content with time during thin layer drying.[18]

Table 1  Conventional mathematical models for crop drying given by different authors

Model equation	Name	References
	Geometric	Chandra and Singh[29]
	Lewis	Lui and Bakker-Arkema[30]
	Page	Agarwal and Singh[31]
	Henderson and Pabis	Chhinman[32]
	Wang and Singh	Wang and Singh[33]
	Logistic	Chandra and Singh[29]
	Two-term exponential	Henderson[34]
MR: moisture ratio; k: drying coefficient specific to each model; k 1 and k 2: drying coefficients on two-term exponential equation; t: time; a, a 0, a 1, a 2: coefficients specific to each model; n: exponent specific to each model.

Mathematical Modeling the Effective Moisture Diffusivity

Analytical solution of one-dimensional Fick's law for spherical objects with constant moisture diffusivity was used to calculate the effective diffusivity as follows:[19]

(3)

where D_eff is the effective diffusivity in (m²/s) and r is the radius of the roasted green wheat kernel in m, obtained from the effective mean diameter (the average of width and thickness of the kernel). For long drying times, n can be set to 1, and Eq. (3) can be simplified into a straight line as follows:[20]

(4)

The slope of the relationship between ln (MR) and drying time (t) can be used to calculate D_eff .

Fuzzy Modeling

The input variable of this model was the drying time, while the output was moisture ratio (normalized moisture). The drying time was classified into seven trapezoidal membership functions as shown in Fig. 1. The fuzzy model was generated using a subtractive method and trained using a hybrid technique.[14]

Figure 1 The seven trapezoidal membership functions for fuzzy model. (Color figure available online.)

Statistical Analysis and Non-Linear Regression

To estimate model coefficients and the goodness of fit statistics, SAS non-linear least square regression was used.[21] The adequacy of each model was measured using three criteria: Root mean square error (RMSE) and coefficient of determination (R ²) as follows:

(5)

where MR_exp,i is the ith experimentally observed moisture ratio, MR_pre,i is the ith predicted moisture ratio, N is the number of observations, and n is the number of constants in the thin layer drying model. A good model will normally have a combination of the highest R ² and the lowest RMSE.

RESULTS AND DISCUSSION

Analysis of Sun Drying Curve

The variation of ambient temperature during sun drying of roasted green wheat under natural convection during the experiment and in a typical day at the first week of May is shown in Fig. 2. During the drying experiment, the ambient temperature varied between 26 and 32°C. The highest temperatures were recorded between 11:00 a.m. and 3:00 p.m. The equilibrium moisture content of M_e  = 0.08 in the normalized moisture equation MR = (M − M_e )/(M_o  − M_e ), was obtained from equilibrium moisture content charts for durum wheat at 30°C and RH = 20%.[15] This assumption was made since about two-thirds of the drying period took place at relative humidity (RH) and temperatures of 16% and 30 to 32°C. This value of equilibrium moisture content would be more appropriate than a value of zero as shown in Fig. 3. [13] The drying curve was obtained by plotting the moisture ratio (MR) against the drying time in hours when M_e  = 0 and M_e  = 0.08. Figure 3 shows that assumption of zero equilibrium moisture content was not acceptable; therefore, M_e  = 0.08 was used instead. The drying rate curve was also obtained by plotting drying rate against drying time as shown in Fig. 4. The results show that roasted green wheat samples were dried to a moisture ratio of 0.002, which corresponds to a moisture content of 12.3% (w.b.). The final moisture content was selected to assure safe storage. The drying rate curve showed that all drying took place during the falling rate region and there was no constant rate drying region. Drying rate during the first half hour was very low, which might be due to the sensible heating of the roasted green wheat kernels to reach the ambient temperature before drying starts effectively. The falling rate drying indicates that drying was controlled by diffusion of the moisture from the interior to the surface of the roasted green wheat kernel.[22] Results were in agreement with Sun and Woods[5] for barley, and Sun and Woods[7] for wheat.

Figure 2 Variation of ambient temperature with time during the day of experiment and in a typical day in the first week of May. (Color figure available online.)

Figure 3 Variation of moisture ratio with drying time during open sun drying of roasted green wheat. (Color figure available online.)

Figure 4 Variation of drying rate with time for roasted green wheat. (Color figure available online.)

Thin Layer Drying Models and Fuzzy Modeling

The drying data were fitted with seven known conventional thin-layer drying models, including Lewis, Page, Henderson and Papis, Logistic, Two-term exponential, Geometric, and Wange and Singh models. Table 2 shows that R ² varied between 0.85 for the Geometric model and 0.988 for the Two-term exponential model, while RMSE varied between 0.11 for the Geometric model and 0.038 for the Two-term exponential model. Based on the findings above, the Two-term exponential model was selected to model the sun drying of roasted green wheat (although other models, such as Page, Wang and Singh, and the Logistic models, performed well also). A plot of experimental moisture ratio and the Two-term exponential model predicted MR is shown in Fig. 5. The figure shows a close agreement between the experimental and predicted values. Better results were obtained using fuzzy modeling with RMSE = 1.2 × 10⁻⁶ and R² = 0.999. In addition, better agreement between experimental and predicted values was observed when using fuzzy model to predict moisture ratio for roasted green wheat as shown in Fig. 6.

Table 2  Thin-layer model fitting results for roasted green wheat

Model name	Model coefficients	R ^2	RMSE
Geometric	a = 0.63, n = 0.76	0.85	0.110
Lewis	k = 0.41	0.94	0.082
Page	k = 0.24, n = 1.53	0.984	0.038
Henderson and Papis	a = 1.11, k = 0.45	0.958	0.070
Wang and Singh	a 1 = −0.29, a 2 = 0.019	0.981	0.047
Logistic	a 0 = 1.34, a = 0.31, k = −0.84	0.987	0.039
Two-term exponential	a = 2.07, k = 0.66	0.988	0.038

Figure 5 Comparison between experimental and predicted moisture ratio for roasted green wheat sun drying using two–terms exponential model. (Color figure available online.)

Figure 6 Comparison between experimental and predicted moisture ratio for roasted green wheat sun drying using fuzzy modeling. (Color figure available online.)

Effective Diffusivity

Effective diffusivity was obtained by plotting the relationship between ln (MR) and drying time (t) in hours. The slope of the relationship was used to calculate D_eff. . The effective mean diameter of roasted green wheat kernels, measured using a digital caliper, was 4.74 ± 0.11 mm. Effective diffusivity was estimated to be 1.726 × 10⁻¹¹ m²/s after correcting for ellipsoidal shape of wheat kernel by multiplying by a factor of 0.86 according to findings reported by Gastón et al.[10] They reported that effective diffusivity for wheat ranged between 3.336 and 7.772 × 10⁻¹¹ m²/s. Jaros et al.,[23] however, reported a diffusivity range between 1 and 2.4 ×10⁻¹⁰ m²/s for wheat kernels. Table 3 shows the effective diffusivity of some common crops. The present study results were in agreement with those reported by Madamba et al.[24] It can be noted also that effective diffusivity is located within the general range of 10⁻⁰⁹ to 10⁻¹¹ m²/s for food materials.

Table 3  Comparison of moisture diffusivity of roasted green wheat with wheat and other grains

Crop	M.C.*(% w.b.)	Deff ** (m^2/s)	Reference
Roasted green wheat	43	1.7 × 10^−11	This study
Wheat	5–17	1.7 × 10^−10	Jaros et al.[23]
Wheat	—	5.1 × 10^−11	Gastón et al.[10]
White beans	11–38	1.1 × 10^−11	Adu and Otten[25]
Rough rice	—	2.3 × 10^−11	Zuritz and Singh[26]
Sorghum	—	2.8 × 10^−11	Suarez et al.[27]
Soybean	—	8.7 × 10^−11	Kitic and Viollaz[28]
*Wet based moisture content.
**Effective diffusivity.

CONCLUSIONS

Drying roasted green wheat from 43 to 13% under sun drying conditions was accomplished in 5.5 h. Among the conventional thin layer drying models, the two-term exponential model was found to best fit the roasted green wheat sun drying data. Fuzzy modeling, however, provided better modeling capabilities compared to conventional models. All drying of roasted green wheat under sun drying conditions was in the falling rate period. Effective diffusivity of roasted green wheat was found to be 1.73 × 10⁻¹¹ m²/s, which was comparable to other agricultural crops.

NOMENCLATURE

a, a 0, a 1, a 2, k, k 1, k 2	=	Constants in models
Deff	=	Effective diffusivity (m2/s)
M	=	Moisture content at time t (% w.b.)
Me	=	Equilibrium moisture content (% w.b.)
Mo	=	Initial moisture content (% w.b.)
M/Mo	=	Moisture ratio when Me is assumed to be zero.
MRexp, I	=	ith experimentally observed moisture ratio
MRpre, I	=	ith experimentally predicted moisture ratio
N	=	Number of observations
n	=	Constant, positive integer
R 2	=	Determination of coefficient
R	=	Radius (m)
t	=	Drying time (h)
z	=	Number of constants