1 Introduction

Today, some local plants are dried by traditional methods that are widely used in the food industry. For example, the basil plant can be dried under appropriate conditions without losing food and vitamins. Since the drying process causes changes in the appearance, composition, and quality of basil, the drying method applied and the effective parameters should be optimized.

Research examining the drying kinetics of basil leaves was studied in tunnel and tray dryers at temperatures of 55, 60, and 65 °C. Basil leaves have been found to dry faster in the tray dryer than in the tunnel dryer. The effective diffusion coefficient of basil leaves was calculated between 2.65 and 5.69·10−10 m2/s. The activation energy for the samples dried in both types of dryers was found to be between 33.21 and 9.03 kJ/mol [1].

In an article evaluating the effect of drying on the structural integrity of basil (Ocimum basilicum L.), drying in an oven at 45 °C, in the air at room temperature, and freeze-drying was compared. The total amount of volatile components of fresh basil leaves decreased significantly during oven drying and freeze-drying. When the flavor quality has been evaluated among the basil leaves dried with different methods, it was understood that the dried samples most similar to the fresh herb were those that were air-dried at ambient temperature [2].

In the study evaluating the effect of the drying method on aroma compounds of basil (Ocimum basilicum L.), convective, vacuum microwave, and combinations have been tried. While the drying kinetics is defined by a two-term exponential model in the convective dryer, it changes linearly up to a critical point and exponentially above this point in the vacuum microwave. To obtain high-quality dried basil, convective pre-drying (40 °C) and post-drying with vacuum microwave (360 W) were determined as the best option (nearly 250 min) [3].

In another research, the necessary optimizations for the protection of the color, aroma, and microbial safety of dried basil have been evaluated. Newly improved drying techniques are discussed to minimize both the valuable compounds and the energy cost of the basil plant. It has been seen that the most economical dryers are the systems improved using solar energy. Studies on the drying of basil and other herbs have been extensively compared in the literature [4, 5].

In the article, the drying behavior of purple basil leaves in the sun, freeze, convective, and microwave oven was investigated, the effects of drying time, speed, and kinetic parameters were investigated. The energy efficiency of different dryers was compared, and a higher drying rate was obtained in microwave drying compared to other methods. When the drying kinetics of basil were examined, it was determined that Henderson and Pabis models were effective in freeze-drying, logarithmic in the sun, Page model in convective and microwave ovens. The effective diffusion coefficient values of purple basil leaves were calculated between 1.62·10−9 and 7.09·10−8 m2/s [6].

In a study using artificial neural networks and fuzzy logic methods, the drying behavior of basil seed mucilage in an infrared dryer was modeled. The variation of moisture content with drying time has been evaluated depending on the radiation power, mucilage thickness, and surface distance. By using experimental data, it has been determined that artificial neural networks and fuzzy logic simulations gave successful results according to statistical analysis results [7].

Energy savings have been achieved by optimizing processes with the development of new dryers and modification of existing systems [8]. With the advanced exergy analysis, inefficiencies in the energy system were determined quantitatively and qualitatively [9]. To evaluate the performance of the energy system from a thermodynamic and economic point of view, its real potential for improvements and system parameters should be used effectively [10].

In another study investigating the drying kinetics, the mass transfer equation was solved analytically by considering concentration-dependent shrinkage and dehumidification at a constant rate [11]. Besides, in another research conducted by drying foods, the priority is that they do not lose their freshness, color, and vitamin value. Therefore, air temperature, velocity, and system parameters need to be optimized well [12].

In an article that dried basil leaves at 45, 55, and 65 °C air temperatures using different drying methods, the effective diffusion coefficient was calculated between 4.54·10−10 and 1.08·10−9 m2/s. The activation energy was found to be between 38.54 and 20.32 kJ/mol with the help of the Arrhenius relation [6]. In another research, basil leaves were dried using different techniques at 55, 60, and 65 °C air temperatures, and the drying kinetic models were compared with the help of statistical approaches. It has been determined that basil leaves dry faster in the tray dryer. The logarithmic equation of the kinetic model compatible with the experimental data was obtained at the highest R2 values. The effective diffusion coefficient calculated for basil leaves was found to be between 2.65·10−10 and 5.69·10−10 m2/s. The activation energy calculated using the Arrhenius relationship was found to be between 33.21 and 9.03 kJ/mol [13].

In this research, fresh purple basil leaves grown in Arapgir region were collected and prepared for drying. The new improved PID-controlled drying system and conventional tray dryer were used in the drying process. The parameters affecting the drying kinetics under isothermal and non-isothermal conditions have been investigated. The results obtained in experimental studies have been modeled with theoretical equations. Based on energy efficiency, the drying systems were compared by performing an exergy analysis.

2 Materials and methods

2.1 Materials

Arapgir purple basil was procured in the field located at the north 38° 55′ 24.5″ latitude and east 38° 32′ 51.2″ longitude coordinates in the Arapgir district of Malatya province. The basil leaves collected in Arapgir region shown in Fig. 1 were cleaned and prepared for drying. The drying process was carried out in a tray dryer system (Fig. 2) according to the experimental conditions in Table 1.

Fig. 1
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Image of Arapgir basil (Ocimum basilicum L.) leaves growing in Eastern Anatolia Region

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Fig. 2
figure 2

Forced convection insulated tray drier: Inflow air (1), air flow control (2), temperature controller (3), heater fun (4), temperature measurement system (5), first region (6), porous metal trays (7), digital mass scale (8), second region (9), and outflow air (10)

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Table 1 RSM study plan designed for the tray dryer experiment system
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2.2 Methods used in experimental study

The drying kinetics of Arapgir basil were investigated in a laboratory environment at 1.5, 2.25, and 3.0 m/s constant air velocities and 25 °C, 35 °C, and 45 °C temperatures in a laboratory environment. Characteristic drying curves were determined in the constant drying speed region under experimental conditions. The enthalpy change was calculated taking into account the inlet and outlet temperatures of the air and the losses in the system. It was determined that there was a constant drying region in the system at approximately 5 to 120 min. It was observed that the enthalpy changes in the drying system decreased after 120 min in the region where drying decreased.

In the PID-controlled drying system in Fig. 3, experimental studies were conducted from 20 to 70 °C at a heating rate of 0.15 and 0.20 °C/min.

Fig. 3
figure 3

PID-controlled isothermal and non-isothermal drying system: Electrical source (1), potentiometer (2), mass scale (3), temperature controller (4), and insulated drying the system (5)

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2.3 Mathematical modeling of drying kinetics

2.3.1 Convectional drying system

In the mass of the basil leaf (MT), αt is defined as the conversion rate at any time, the mass of the sample (Mt) at any time, and (t) time. It is the drying rate (Dr) and drying area (As) at any given time. The (i) and (f) symbols used in the model equations represent the initial and final time, respectively.

$${\alpha }_{t}=\left(\frac{{M}_{t}-{M}_{f}}{{M}_{i}-{M}_{f}}\right)$$
(1)
$${D}_{r}=-\frac{{M}_{T}}{{A}_{s}}\frac{d\alpha }{dt}$$
(2)
$${D}_{r}=-\frac{{M}_{T}}{{A}_{s}({\alpha }_{t})}\frac{\left({\alpha }_{t}-{\alpha }_{t-1}\right)}{({t}_{t}-{t}_{t-1})}$$
(3)

Moisture content was determined as a function of time and drying rate with the average derivative approach [14]. Shrinkage is the volume reduction that occurs during the drying process of the food, and it can generally be up to 85–90% of the initial volume (β = 0.942 and δ = 0.058) [15].

$$\frac{V}{{V}_{i}}=\beta \left(\frac{\alpha }{{\alpha }_{i}}\right)+\delta$$
(4)
$${A}_{s}\left({\alpha }_{t}\right)=\left(\varphi {l}^{2}+\phi {w}^{2}\right){e}^{({\alpha }_{t}-1)}+\xi$$
(5)

Area changes according to time were calculated according to the surface area model developed for the basil leaves. Correlation coefficients were calculated according to the transformation ratio of the leaf with its length (l) and width (w). Shrinkage coefficients (R2 = 0.9982) were found for the length (\(\varphi\)) and width (\(\phi\)) of the leaf. Besides, the species correction coefficient (\(\xi\)) was added to Eq. 5, since the leaves of various vegetative species show different characteristics [16, 17].

2.3.2 Non-isothermal drying kinetics

Non-isothermal drying kinetics model equations are solved according to the Coats-Redfern method [19, 20]. The activation energy (E), Arrhenius constant (A), and R2 values were calculated with the help of the models in Eq. 8 and Table 2.

Table 2 The non-isothermal drying kinetics models used for Arapgir basil [18]
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$$\frac{da}{dt}=k(T)f(\alpha )$$
(6)
$$k\left(T\right)=Aexp(-\frac{E}{RT})$$
(7)
$$ln\frac{g(\alpha )}{{T}^{2}}=ln\frac{AR}{E\delta }-\frac{E}{RT}$$
(8)

Activation energy and other correlation coefficients were calculated according to the Coats-Redfern method with the drying kinetic equations (Eqs. 6, 7, and 8) using the conversion rate which were specified in Eq. 1. In Table 2, drying kinetic models commonly used in the literature for non-isothermal conditions are given.

2.4 Exergy analysis

Dehumidification, enthalpy change, maximum enthalpy value, time, and energy amount during drying are very important for drying thermodynamics. In the drying process, exergy analysis is carried out according to the second law of thermodynamics, in which the quality of energy is important as well as the quantity and this process takes place in a direction that reduces the energy quality [21, 22].

According to the principle of conservation of energy in a system, the total amount of energy entering and leaving is in equilibrium. Equation 9 is written for the energy balance in the drying system according to this principle. Here, \(\dot{\mathcal{Q}}\) is the heat energy input, \(\dot{m}\) is the mass flow, and h is the enthalpy.

$$\dot{\mathcal{Q}}=\sum {\dot{m}}_{out}{h}_{out}-\sum {\dot{m}}_{in}{h}_{in}$$
(9)

Equation 10 is obtained if the forces entering and leaving the system are constant.

$$\dot{\mathcal{Q}}=\dot{m}\left({h}_{out}-{h}_{in}\right)=\dot{m}\Delta h$$
(10)

Cp is the specific heat, T is the temperature, λ is the latent heat of evaporation, and w is the humidity. The enthalpy of the drying air is calculated as follows: Eq. 11

$$h={C}_{p,air}{T}_{air}+\lambda w$$
(11)

The second law of thermodynamics states that some losses can occur in a system due to irreversibility. In the drying process in this study, input, output, and losses in the system for exergy analysis were calculated. The energy is given to the system in a steady-state; the energy coming out of the system and other losses have been determined.

Equation 12 can be used to calculate exergy inputs and outputs at inlet and outlet temperatures, respectively, where Eα is exergy and ∞ indicates the ambient condition. Also, the exergy loss during the process is determined using the following expression.

$${E}_{\alpha }={C}_{p,air}\left[\left({T}_{g}-{T}_{\infty }\right)-{T}_{\infty }\mathrm{ln}(\frac{{T}_{g}}{{T}_{\infty }})\right]$$
(12)
$$\sum {E}_{\alpha ,loss}=\sum {E}_{\alpha ,in}-\sum {E}_{\alpha ,out}$$
(13)
$$\sum {E}_{\alpha ,loss}=\sum {E}_{\alpha ,in}-\sum {E}_{\alpha ,out}$$
(14)

Exergy efficiency (ηα) is defined by the characteristics of the air entering and leaving the system [23, 24].

3 Results and discussion

3.1 Activation energy results and correlation coefficients

The results in Table 3 were found using the models in Table 2 according to the Coats-Redfern method. While examining the drying kinetics of Arapgir basil, the models common in the literature have been preferred [18].

Table 3 Drying correlation coefficients of Arapgir basil for two experiments
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For the model equations in Table 4, statistical analysis was performed, and correlation coefficients, R2 values, and error function were calculated, and the results in Table 5 with Table 6 were found.

Table 4 Kinetic models used in non-linear regression analysis of the for the basil [6]
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Table 5 Drying kinetics and statistical analysis for Arapgir basil leaves
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Table 6 Correlation coefficients and statistical analysis for Arapgir basil leaves
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3.2 Results of statistical analysis

In this section, a statistical comparison has been made with experimental data to investigate the reliability of theoretical equations. By calculating the error functions, the closeness of the most suitable models to the real experimental results was determined. As can be seen in Tables 5 and 6, the models with calculated correlation coefficients have found the most suitable models for high R2 values and low error functions. In the statistical error analysis examined here, root mean square error (RMSE), chi-square (χ2), and sum of squared error (SSE) were performed [25,26,27].

Statistical analyses were performed to determine the most suitable models in the non-isothermal experimental studies conducted in the PID controlled system. When the results obtained in the non-isothermal drying were examined in Table 3, it was seen that the R2 values of models 2, 3, 6, 8, 13, and 14 were higher. In the model equations, activation energies in the constant drying region were found between 1 and 10 kJ/mol. In addition, it has been determined that the increase in temperature also increases the activation energy.

The drying process with the convection system was carried out at different temperatures (25 °C, 35 °C, and 45 °C) and different airflow rates (1.5 m/s, 2.25 m/s, and 3.0 m/s). It is seen in Fig. 4 that the drying time was maximum at both low air flow rate and low temperature.

Fig. 4
figure 4

Drying curves of the basil leaves at different temperatures of air at 1.5 m/s

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As seen in Figs. 5 and 6, the drying time decreased as the temperature increased with the flow rate of air. In the drying process, the leaves of the basil vegetable can be dried as much as the equilibrium moisture amount carried by air at a certain temperature.

Fig. 5
figure 5

Drying curves of the basil leaves at different temperatures of air at 2.25 m/s

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Fig. 6
figure 6

Drying curves of the basil leaves at different temperatures of air at 3.0 m/s

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Under natural conditions, Arapgir basil leaves lose 80% of their mass at room temperature in about a week. As seen in Fig. 7, the evaporation rate of moisture in the first 4-day period with natural convection can be expressed by a decreasing curve equation. In the following days, the evaporation rate of moisture slowed down and reached the equilibrium humidity of the air.

Fig. 7
figure 7

Drying Arapgir basil under the natural conditions with the help of sunlight at nearly 25 °C

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As seen in Fig. 8, the evaporation rate of moisture in the basil leaf is directly proportional to both the temperature and the flow rate of the air. The drying process with forced convection takes place much faster than natural convection. The parameters affecting the evaporation rate can be listed as the surface area of the leaf, the humidity of the air, the flow rate, and the temperature of the air.

Fig. 8
figure 8

The rate of moisture evaporation over time at different flow rates and different temperatures of Arapgir basil leaves per unit area

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3.3 Evaluation of drying kinetics with RSM

In this study, an experimental design was made with statistical regression according to RSM method, and optimum conditions were determined according to response functions. In experimental design, it is necessary to determine the effective parameters to find optimum results with a small number of experiments. The response functions of these parameters in the process are evaluated statistically in a fast and reliable way, and a solution is reached. According to the RSM method, the most appropriate results are obtained in the most economical, short time, and with maximum efficiency by consuming less energy. Similar RSM design and experimental optimizations have been used in studies on drying kinetics of plant leaves. Comparisons were made by evaluating the experimental and theoretical model results obtained with a statistical approach [28,29,30,31].

In Fig. 9, the effect of airflow rate and temperature on the drying time is given according to the results of RSM. In Table 7, statistical analysis values of the most suitable models are given. With the approach obtained in natural logarithmic Eq. 15, the closest results to the experimental values were modeled (Fig. 10).

Fig. 9
figure 9

RSM model of the drying time of Arapgir basil, which depends on airflow rate and temperature

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Table 7 The most suitable models determined according to the RSM work plan and their statistical analysis
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$$ln(t)=-0.000471\cdot {T}^{2}-0.008760\cdot {v}^{2}-0.004212\cdot T\cdot v+0.268564\cdot T+1.19984\cdot v-32.12951$$
(15)
Fig. 10
figure 10

Linear and regional distribution of experimental data according to the model according to the RSM statistical analysis

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4 Conclusion

It is known that drying foods at high temperatures reduce their nutritional value. For this reason, the drying process was not carried out with convection and a PID-controlled system at high temperatures. Energy efficiencies in different processes were compared by performing an exergy analysis in the drying process. It has been observed that the energy consumed and lost especially in the convectional drying system (tray dryer) is very high. In the experiments conducted in the PID system, the lowest efficiency was found in the isothermal process.

The shrinkage behavior of Arapgir basil during drying has been determined according to the new improved model. It has been observed that the equation developed depending on the leaf width, length, and conversion ratio is compatible with both the experimental data and the models in the literature. Here, it is understood that the transformation rate directly affects the area and mass of the leaf.

Accordingly, the most suitable system in exergy efficiency has been determined as the non-isothermal system. Maximum energy loss and minimum exergy efficiency in the convection drying process were found at 45 °C temperature and 3.0 m/s airflow. Exergy efficiencies were calculated to be approximately 4% in convection, 26% in isothermal, and 32% in non-isothermal drying. The exergy efficiency of the system is very low as there is a lot of energy loss in convectional systems such as tray dryers. Especially in systems where energy losses are minimum, there is maximum exergy efficiency.