Experimental investigation on the carob extraction using arrhenius approach and response surface

Abstract

Environmental problems have increased the need for sustainable agricultural practices that conserve water and energy. Carob, an eco-friendly crop with multiple health benefits, holds the potential for economic evaluation. This study investigates the carob molasses extraction process, focusing on the influence of temperature and water quantity on the diffusion coefficient. The rheological behavior of carob molasses was analyzed experimentally, and a model was developed to optimize energy consumption during the extraction process. The impact of temperature on the mass transfer coefficient was examined using the Arrhenius approach, with the extraction conducted at a maximum of 50 °C to prevent caramelization. The activation energy for carob extraction was determined to be 5.475 kJ/mol, and a new equation is proposed for estimating the mass transfer coefficient.

Introduction

Carob (Ceratonia siliqua) is a versatile plant with various applications in food and health industries as a thickening agent, medicinal uses, nutritional benefits, and potential antioxidant properties. The carob seed is a thickening agent in the food industry and is also employed in medicine to address gastrointestinal (GI) disorders. Also, carob pulp has been utilized as a side product of the seed industry and can be made into a commercial product in kibbles or powder¹. Moreover, several compounds such as carbohydrates, minerals, polyphenols, flavonoids, proteins, and lipids are available in carob pods and leaves^2–4. In this respect, scientific publications on the carob have been published in recent years^5–7.

Solid fruits like carob cannot be effectively pressed to extract their juices. Therefore, an extraction method involving water is used instead⁸. This process involves soaking the solid fruits in water to leach out their soluble components, which are then concentrated to produce molasses. The quality of molasses produced from different fruits, including carob, can be influenced by various factors such as extraction temperature and the quantity of water used during the process. These parameters can affect the molasses’ flavor, consistency, and quality. However, traditional or conventional production methods may not always prioritize controlling these parameters precisely.

Şenay⁹ studied the optimal extraction and clarification conditions for producing liquid sugar from carob. The effects of parameters such as hydration ratio, temperature, particle size, mixing, pressing, etc., on yield were investigated during the extraction process. Various extraction tests were conducted to evaluate the impact of these parameters on yield. Although a light-colored sugar syrup was obtained at a temperature of 90 °C and a water ratio of 1:4 using classical clarification methods, a color darkening attributed to the high polyphenol content of carob was observed after the concentration process. Yoğurtçu and Kamışlı¹⁰ conducted research into the rheological properties of molasses samples derived from various sources, including mulberry, grape, rosehip, and carob juice. In their study, they employed the Arrhenius equation to elucidate the relationship between viscosity and temperature variations in the molasses samples. Consequently, the researchers calculated activation energy values ranging from 18.509 to 74.658 kJ/mol, which exhibited variability corresponding to the solid contents investigated in their analyses. They observed a direct correlation between the concentration of soluble solids in the molasses samples and the activation energy values, as predicted by the Arrhenius equation. Specifically, as the soluble solid concentration increased, the activation energy values demonstrated a proportional rise. Demirtaş¹¹ conducted a study on the production of carob gum from carob seeds, and the investigation of some physical and chemical properties of the obtained gum. The contents of moisture, protein, ash, foreign matter, acid-insoluble substances, and viscosity values of the produced gum were compared. The analyses revealed that there were no significant differences in the contents of ash, moisture, and protein, while notable differences were observed in the contents of foreign matter, acid-insoluble substances, and viscosity values. It was concluded that HCl was the most suitable chemical for gum production. Huang et al.¹² generated four distinct particle-sized samples utilizing superfine grinding and ordinary pulverization techniques. Throughout their experimental investigations, they observed a positive correlation between the particle size of sugar beet pulp (SBP) and the activation energy. Additionally, they noted that the particle size of SBP powder significantly influenced both the properties of extracted pectin and the efficiency of the extraction process. Tetik and Yüksel¹³ studied the optimization conditions of extraction of d-pinitol compound from carob pods with the ultrasonication method. Temperature, ultrasonic power, dilution rate, and time were taken into account as independent parameters. They suggested that ultrasound-assisted extraction could be used as an alternative to conventional extraction. Mulet et al.¹⁴ have investigated the extraction optimization of complex raw materials. They concluded that the size of carob kibbles and the amount of polyphenols left in the kibbles significantly affect the extraction time and temperature. Doymaz and Pala¹⁵ compared the drying behavior of treated and untreated corn kernels. Different mathematical models were suggested fitting the experimental data to predict the drying behavior of corn types and calculate the activation energies of corn kernels. The activation energies of untreated and treated corn kernels were calculated as 29.56 kJ/kg.mol and 30.56 kJ/kg.mol, respectively.

Notably, in Turkey, the production of molasses from carob stands as a longstanding tradition alongside other fruits like grape, mulberry, apple, and pear. In traditional production, temperature and water amount are decided according to the experiences of the people. For this reason, each process has a different energy consumption. In this study, the parameters of water quantity and temperature have been experimentally investigated. These are determinant parameters that directly affect the extraction yield. This study aims to examine the rheological behavior of carob molasses depending on temperature and water quantity. Besides, the effect of temperature on mass transfer was studied by the Arrhenius approach. Arrhenius equations are generally used to explain temperature relations in food and biological systems¹⁶. The experiments in this study were performed at various water temperatures (30 °C, 40 °C, 50 °C), water quantities (100 g, 200 g, 300 g), and also fixed holding time (60 min) and batch number (6). Since the difference between the fifth and sixth batches has decreased considerably, and in order not to increase energy consumption further, the batch number is fixed at 6. In addition, an experiment was conducted at 250 g and 45 °C to validate the resulting equation. Consequently, it is proposed an equation depending on the temperature to obtain the diffusion coefficient. In this way, the parameters in sugar extraction and molasses production processes from carob were optimized using less energy and resources.

Experimental setup

The carob fruits used in the experiment were purchased from a single, specific vendor in a single batch to ensure consistency in sugar content and avoid any variability between samples. Different parameters, such as water temperature, water quantity, holding time, batch number, etc., affect the extraction processing. Also, the grain size is another parameter. In order to increase the contact surface of the carob with water, the grain size was chosen as 5 mm × 5 mm. Being smaller makes the preparation phase more difficult and the pulp turns into powder at the end of the process. This is a disadvantage in the production of products such as animal feed from the desugared pulp. 50 g of carob were prepared for the experiments. The experiments were carried out in thermos bottles in order to prevent heat losses. The tare of the cups and the weight of the mixture were determined at each phase. After mass transfer processing, we get the syrups from each cup. All six cup syrups were completely dried in the oven at the end of the experiments. Batch processing is a production system in parts, which can be carried out instead of a continuous production system. A schematic diagram explaining the experiment phases and the batch system in this study is given in Fig. 1.

Fig. 1.

Schematic diagram of the experiment phases and 6-batch processing system.

Initially, each cup contains an equal amount of carob (50 g). The experimental conditions, including the temperature and the volume of water, are set to predefined levels, as in Table 1. For instance, the initial conditions were set as 100 g of water, a temperature of 30 °C, and a duration of 60 min. In the first step, 100 g of water at 30 °C is added to the first cup containing the carob. After a duration of 60 min, the syrup extracted from the first cup is transferred to the second cup. Subsequently, additional water is added to the second cup until the total volume reaches 100 g for the subsequent processing step. It is essential to maintain an equal liquid volume of 100 g in the first cup as well. Following this, the same procedural steps are repeated for the remaining cups after another 60 min. The process is repeated every 60 min for each batch. Upon completion of the batch processing, the syrup is dried in an oven. The preparation of carob and the resulting dried syrups for the six-batch system are illustrated in Fig. 2.

Table 1.

Test conditions.

Carob (g)	Water quantity (g)	Temperature (°C)	Time for a batch (s)	Batch number
50	100	30,40,50	60	6
50	200	30,40,50	60	6
50	300	30,40,50	60	6

Fig. 2.

The carob preparation and dried syrups for the 6-batch system^17,18.

The experiments that were conducted and the test conditions are shown in Table 1.

Conservation of mass and energy are fundamental laws of physics. Mass and energy balances are essential in analysing physical and chemical processes. The mass balances on the extraction are represented as shown below in Eq. (1).

1

• : The mass in the system after a small increment in time (g).

• : The mass in the system at the initial time (g).

• t: The time variable (s).

• : The mass flow rate into the system (g/s).

• : The mass flow rate out of the system (g/s).

The sugar mass fraction (SMF) is calculated as in Eq. (2).

2

• C: The concentration of solute in the solution (g/L).

• C_s: The maximum solute concentration in the solution (g/L).

• : Diffusion coefficient (s^− 1).

The Arrhenius equation describes the diffusion coefficient that varies with temperature. Arrhenius equation¹⁹ in Eq. (3) calculates activation energy () from experimental results.

3

• D₀: The pre-exponential factor or Arrhenius Constant (s^− 1).

• E_a: The activation energy of the reaction (J/mol).

• R: The universal gas constant (J/(mol. K)).

• T: The absolute temperature at which the reaction occurs (K).

Experimental data uncertainty can be calculated with the in Eq. (4). presented by Kline and McClintock²⁰. The error rates resulting from the structure of the glass thermometer, the temperature measurement of the test environment, and the laboratory oven are ± 0.25 °C, ± 0.25 °C, ± 0.5 °C, respectively. The rate of random errors that may occur naturally, such as opening the lid of the styrofoam vessel and fluctuating air in the room, is ± 0.6 °C. Also, the error rate of the analytical balance is ± 1 g. According to the Kline-McClintock method, the maximum absolute temperature error in the experiments was calculated as ± 0.857 °C.

4

Results and discussions

The temperature and water quantity values, which are the most critical parameters in carob extraction, can be seen in Table 1. According to these values, the amount of sugar was obtained, as shown in Fig. 3.

Fig. 3.

Amount of the sugar from carob extraction in the experiment.

It has been experimentally determined that 50 g of carob contain 28 g of sugar and soluble matter. SMF and diffusion coefficients were calculated from all experiments in Table 2. 1:2,1:4, and 1:6 represent the carob-water fraction (CWF). Moreover, the mixture with a ratio of 1:2 contains 50 g of carob and 100 g of water.

Table 2.

Experimental results.

CWF	Temperature (°C)	SMF	Diffusion coefficient (1/s)
1:2	30	0.33
1:2	40	0.347
1:2	50	0.359
1:4	30	0.44
1:4	40	0.459
1:4	50	0.494
1:6	30	0.463
1:6	40	0.52
1:6	50	0.54

Figure 4a explains the Arrhenius charts indicating the natural logarithm of diffusion coefficients of carob samples versus 1/absolute temperature. Figure 4b demonstrates the graphs of D values for different treatments, showing the influence of applied temperatures on the diffusion coefficient.

Fig. 4.

(a) Arrhenius charts (b) Graph of D values.

Diffusion coefficients tend to increase with increasing temperature and water quantity, as seen in Fig. 4. The curve equations for 1:2, 1:4, and 1:6 ratios are given in Table 3, respectively.

Table 3.

Equations depending on CWF.

CWF	Arrhenius equations	R 2	Eq. No
1:2		0.9957	(5)
1:4		0.9643	(6)
1:6		0.9338	(7)

Through the equations proposed above, the effect of temperature on sugar extraction for three different CWF can be calculated approximately. The equations were validated for different levels (250 g-45 °C) of the parameters in the experiment. The mass of sugar and soluble matter can be calculated as 84.52 g by interpolating the results obtained from Eqs. (6) and (7). Eventually, there is a 3.6% difference when the estimated data is compared with the experimental result.

Carob pulp, which remains as waste foodstuff, still has a lot of sugar because the water quantity is incapable if CWF is 1:2. When the CWF is in the range of 1:4 and 1:6, increasing the water quantity does not significantly change the SMF value, as shown in Table 2. Therefore, the mean of the other two curves is represented as a single curve. The equation of the mean curve, illustrated in Fig. 4a, is defined as follows.

8

As is known, the activation energy has a constant value on the sugar extraction process for all cases. Multiplying the slope value of the Mean Arrhenius curve with the universal gas constant (R_u) gives the activation energy. As a result, activation energy was determined as 5.475 kJ/mol in this process, which is compatible with the literature. The mean activation energy calculated in this study is very close to the value of 5.66 kJ/mol in the current literature for the continuous system²¹.

Besides, the amount of obtained sugar increases or decreases depending on the water quantity. The diffusion coefficient depends on water quantity. It can be calculated practically by using Table 4 or Fig. 5.

Table 4.

Arrhenius constants according to the water quantities.

Water quantity (g)	Arrhenius constant

Fig. 5.

Arrhenius constant curve.

The linear curve for the Arrhenius constants in Table 4 is shown in Fig. 5.

The equation of the curve in Fig. 5 is given as follows. Equations (9) and (10) represent the water quantity in grams.

9

The proposed equation calculates the Arrhenius constant for the water quantity between 100 and 300 g.

10

Thus, the one equation can calculate the diffusion coefficient more simply.

Response surfaces are commonly used in optimization^22,23, experimental design²⁴, and analysis²⁵ to understand the behavior of a system and to identify optimal conditions or parameter settings for achieving desired outcomes.

Figure 6a represents the response surface plot demonstrating the influence and interaction of the independent variables on the diffusion coefficient. The red-colored area represents the highest value of the diffusion coefficient, whereas the blue one represents the lowest diffusion coefficient. Also, the effect of parameters on the diffusion coefficient is shown as a contour plot in Fig. 6b. As shown in Fig. 6b, it is possible to achieve a relatively high diffusion coefficient using 240 g water and 50 °C temperature boundary conditions. According to Fig. 6b, working at a temperature of 45–46 °C and 250–260 g water quantity is appropriate to provide less resource and energy consumption and achieve a high diffusion coefficient.

Fig. 6.

(a) Response surface plot showing the effects of parameters on diffusion coefficients (b) Water Quantity-Temperature contour plot.

Conclusion

Due to the global drought threat, the significance of obtaining sugar from foodstuffs such as carob, which needs less water instead of sugar beet and sugarcane, is increasing daily. Since the sugar mass fraction depends on the extraction process, the extraction conditions to provide less energy and resource consumption are crucial.

In this study, the effect of temperature and water on the diffusion coefficient was investigated using the Arrhenius approach. Activation energy is determined as 5.475 kJ/mol using the equation. Thereby, the sugar mass fraction can be calculated without measuring the brix value with a refractometer on the sugar production processes.

During the experiments, the extraction process was conducted at a maximum of 50 °C, considering the caramelization effects on human health at high temperatures. The equation can calculate it more accurately between 30 and 50 °C.

An equation, , is proposed depending on the temperature to obtain the diffusion coefficient. Similarly to the findings of this investigation, it is feasible to conduct more effective extraction processes for various other fruit types.

Author contributions

Mehmet Berkant Özel, Ufuk Durmaz, Mustafa Özdemir, Orhan Yalçınkaya, Norah Alomayrah, Imed Boukhris, and M.S. Al-Buriahi wrote the main manuscript text and prepared the figures. All authors reviewed the manuscript.

Data availability

The authors declare that the data supporting the findings of this study are available within the paper.

Declarations

Competing interests

The authors declare no competing interests.