Kinetics and mathematical model of sugarcane bagasse drying in laboratory scale rotary dryer

Abstract

Keywords: Bagasse; Drying; Mathematical Models; Moisture Ratio; Rotary Dryer

Introduction

Sugar as a sweetener is one of the basic human needs. The need for sugar will increase along with the increase in population, welfare and mobility/physical activity. Sugar is beneficial in providing the body with energy in a short time. Sugar is widely used in the food industry (Singh et al., 2020). The plants can produce sweeteners such as sugar cane, stevia, yacon, coconut, maple, dates, corn and cassava. Sugar cane is the most widely used plant to produce sweeteners. The most widely used natural sweetener is made from sugar cane. North Sumatra, with a population of around 14,800,000 people in 2020, is one of the provinces in Indonesia as a sugar producer. The amount of sugar produced is about 144,323 tons per year, but it is still insufficient to cover the demand. Sugar cane plantations in North Sumatra are located in the Langkat district and Binjai City. There is one sugar factory in the Langkat Regency area, Indonesia. The area of ​​sugar cane plantations owned by the people and the state and sugar production in Indonesia are shown in Table 1. While making sugar cane, bagasse will be produced as waste used as fuel in the boiler. The moisture content of this bagasse is about 50%. It is still too high used as fuel. On the other side, the exhaust gas in the boiler chimney has a temperature of 150 – 200 °C [2], [3]. Utilizing exhaust gas temperatures that are still high enough to dry bagasse will be very useful for saving energy in sugar factories. Sugarcane bagasse used in the boiler is about 50% of that produced by the sugarcane mill. The rest can be used for various other purposes. Sugarcane bagasse can be used as fuel in boilers, particle boards, paper, furfural, and feedstock [4]. For some of the uses above, it is better to dry the bagasse before using it. Other uses still in the research stage include making bioethanol, carbon, and coagulant. Drying is an attempt to reduce the moisture to improve the material’s quality. The drying of bagasse is intended to increase the calorific value (as fuel in the boiler), reduce the growth of fungi (as animal feed), prevent decay (in making particle board), and shorten storage (in making pulp). Drying is an attempt to reduce the moisture content in a material to upgrade the material’s quality. The drying of bagasse is done to increase the calorific value (as fuel in the boiler), reduce the growth of fungi (as animal feed), prevent decay (in making particle board), and shorten storage (in making pulp) (Table 1) [1].

Bagasse dryers that have been studied use microwaves, vertical fluidized beds, cyclones, tube dryers and polyhouses. Simanjuntak and Widyawati, 2020 [5] dried bagasse utilizing a microwave to determine the effect of the power used. Meanwhile, [6] used a fluidized bed vertical dryer to dry sugarcane bagasse. The study examines the impact of the cyclone shape and operating parameters on determining the residence time and changes in particle moisture ratio. Wheatly et al., 2020 [7] examined optimizing the dimensions of industrial-scale rotary dryer tubes. Other research on bagasse is mainly directed at its function as bioenergy [8], [9], [10] and biomaterial [11] and [12]. Biomass dryers widely used on industrial scale are sun drying, flash/pneumatic dryers, and rotary dryers [13]. The disadvantage of sun drying is that it depends on the weather. Flash/pneumatic dryers use hot air flowing at 25 m/s. Thus, this dryer requires a lot of hot air, so it is more wasteful regarding heat consumption. According to Delele et al., 2014 [14], the advantages of rotary dryers are suitable for products of various sizes and shapes. In addition, it can be used in low to high-humidity environments and is suitable for sticky and difficult-to-flow materials. Rotary dryers are also widely used for extensive materials drying (> 10 mm) or materials that do not pose a problem during the handling process [15]. The weakness is the high capital and maintenance costs. It cannot be used for brittle materials. Commonly dried materials are biomass, animal feed, by-products, waste, granules, herbs, and vegetables. The industry has widely utilized rotary dryers for fertilizers, seaweed, cement, and minerals such as lead and zinc. Besides that, this dryer type is also used to dry various agricultural products such as rice, corn, coffee beans, and peanuts [4]. Drying in a rotary dryer takes place in a rotary drum. This tool consists of a cylindrical shell that rotates at a certain speed and is supported by bearings. The feed is entered from one side and exits from the other side. Hot air can flow in the same direction or opposite to the feed flow. This hot air can directly or indirectly contact the dried material. The drying process can take place in a continuous or batch system. Considering some of the above things, further study into drying bagasse in a rotary drying is quite interesting. Researchers use statistical analysis to obtain a drying kinetic model. Many studies have been conducted to

Table 1. The total area of sugarcane plantations and sugar production in North Sumatera Year 2017

determine the drying kinetic model that occurs. To get the model is preceded by statistical analysis. This tool obtains correlation coefficients, RMSE, Chi-square and several other parameters. The moisture ratio is obtained from the moisture content. Then, those data are input into the statistical equations. The most appropriate kinetic model must meet requirements such as how the value of the statistical parameters. Drying kinetics describe the mechanism of microscopic and macroscopic heat and mass transfer as long as the drying process, the type of dryer, the drying conditions, and the characteristics of the material influence it. Studying the kinetics of drying is useful for choosing the proper drying method and controlling the drying process. It is important for process engineering and optimization [16]. Shah dan Joshi, 2010 [17] researched the modeling bagasse drying kinetics using a microwave. The most appropriate kinetic model is the Midilli model. Szadzińska and Mierzwa, 2021 [18] researched the drying kinetics of white mushrooms. This study stated that Page and Weibull’s mathematical model is the best applied to microwave drying. Kadam, 2015 [19] suggested that the drying models of Wang and Singh is the most suitable for convective drying of brown seaweed. Selvi, 2020 [20] stated that using an infrared dryer, the Midili-Kucuk and Verma drying kinetics model is most suitable for drying linden leaves. Khaloahmadi et al., 2023 [21] stated that the drying model of logarithmic was the most suitable for drying homemade food waste on a cabinet dryer. Meanwhile, the two-term drying model is the best for drying rubber sheets using sunlight [22]. In addition, there are other studies regarding the kinetics of drying biomass, such as taxus chinensis [23], municipal sewage sludge [24], and acacia wood [25]. From the existing literature, research on drying sugarcane bagasse using a rotary dryer is primarily about moisture content and drying rate. A’yuni et al. 2024 [26] reported that the Page, Newton, and Logarithmic models were the most suitable for drying rice in a rotary dryer. Also, they noted that the more samples were dried, the more efficient the energy consumption would be. Drying was done at 56.4 °C and the energy efficiency was 15.64%. Moisture effective diffusion explains how quickly moisture diffuses into the surrounding air per unit area and time. This speed will be influenced by various factors such as differences in temperature, surface air pressure with the environment, differences in water content, air speed used and others. Simanjuntak dan Widyawati, 2022 [27] dry bagasse in a microwave and the most suitable model is the rational model. The study also reported Deff of 1.044 x 10-7 to 2.009 x 10-7 m2/s, the specific energy consumption of 2.1 - 3.1 kWh/ kg and the activation energy of 4.789 W/gr. Research on drying kinetics and effective moisture diffusion with variations in mass and temperature is still difficult to find. It is very likely to cause errors in every data collection in research. The errors in research can be errors in the tool or data collection and data analysis. These two things are

substantively different. Akan and Unal, 2021 [28] reported various data errors in oil-heated convection drying systems. The data errors include measuring sample thickness, thermocouple temperature, wind speed, mass and relative humidity. The most significant error was the temperature measurement; the study’s total error was 4.8%. Error analysis is used to explain how accurate the data predictions made are compared to the existing data. If the predicted data is getting closer to the existing data, the error that occurs is very small and can be ignored. If the error is significant, the prediction is wrong and needs to be corrected. However, error analysis carried out in drying research is still rarely found in the open literature. In addition, determining the drying stage, which includes constant rate, first and second stage falling rate is also difficult to find in open literature. This gap is an opportunity to be discussed further in this study. This literature gap is an opportunity to find interesting topics for further research. This study uses a laboratory-scale rotary dryer based on several previous researchers’ proposed equations to determine the bagasse drying kinetics model mathematics.

Experimental Setup

This study obtained the sample from sugar factories located around the city of Medan. The sample was chopped to around 3 cm. The mass of the experimental sample was 100, 125, and 150 gr [17]. The sample is put in the basket, which rotates at 3 rpm according to the dryer’s capabilities. It was measured by a Lutron DT1236L photo-contact tachometer with an accuracy of 0.05% and a detecting distance of 5-200 cm. Sai, 2013 [15] uses a rotational speed of 5 - 15 rpm, while Chia and Chog, 2015 [29] use 1-3 rpm. The temperatures used are 140, 160, 180, and 200 °C, referring to the boiler exhaust gas temperature. The temperature is set by a knob on the dryer and measured again by a mercury thermometer with a range of 0-250 °C. Singh et al., 2018 [30] state that the exhaust gas temperature can reach 300 °C, while Wheatly et al., 2020 [7] mention 140 -155 °C temperatures. The flue gas actual temperature in many boilers is 180 – 200 °C [31]. The rotary dryer is modified from a commercial electric oven Oxone Type OX 8330 with a volume of 30 ltr. The oven already has a rotating shaft with 3 rpm. The basket is made from wire mesh so that the hot air can freely heat the sample, which is placed inside while rotating. Two heaters are placed at the bottom and top of the sample so the heat is evener. The operator can adjust the temperature by the button. The experimental setup is shown in Figure 1. During the drying process, the sample mass was weighed every 2 minutes with the basket and then put back into the dryer as soon as possible. Weighing was stopped

after the sample mass was constant. The mass balance used is SF-400C which has an accuracy of 0.01 gr. Formulations There are quite a lot of studies on Statistical analysis to obtain drying kinetics that have been done. Ismail et al. 2016 [32] did it on drying nectarines using the sun, hot air, microwave and infrared drying techniques; Doymaz and Kipcak, 2019 [33] and Halig et al., 2023 [34] also did it. The moisture ratio is the ratio of humidity, which is a dimensionless number representing the moisture content in the dried material. The moisture ratio is needed to obtain a mathematical drying kinetics model. The value of the moisture ratio that remains in the dried material for each sample mass measurement is calculated using equation (1).

(1) Where MR is the moisture ratio, Mb is the moisture content as wet basis, Mi is the moisture content in the initial condition, and Meq is the moisture content on the equilibrium condition. For Meq is too small, the equation (1) can be expressed as: (2) The MR values of each experiment were regressed using CurveExpert software to get the correlation coefficient (R2) value. The correlation coefficient shows the relationship between the measurement and predictions based on the

k = constant, t = time, y = constant, a = constant, b = constant, g = constant, k1 = constant 1, k2 = constant 2, g = constant, α = Weibull model scale parameter, β = shape parameter

equations obtained. The value of the R2 closest to 1 is the best equation model due to the slightest deviation from the experiment data. This study calculated the moisture ratio from 7 model equations, as shown in Table 2. Other researchers often use these equations to obtain a mathematical drying kinetics model. The R2 is calculated based on equation (3): (3) Where MRPred is the moisture ratio predicted, MREx is the moisture ratio experimental, and ( ) is the average moisture ratio predicted. The next step is calculating the Root Mean Square Error (RMSE) and Chi-Square (χ2) values ​​for each experiment using MS Excel. Then, the most appropriate drying kinetics model is obtained. RMSE is the magnitude of the error rate prediction. The prediction data will be accurate when the RMSE is closest to 0. The RMSE value is calculated according to equation (4). (4) The reduced chi-square (χ2) was used in the fit test. The square root was the standard error of the regression. The equation with the smallest chi-square value is the best. Chisquare (χ2) was calculated according to equation (5) (5) Where χ2 is the reduced chi-square, n is the number of positive integer parameters and N is the number of observations. The assumptions used in this chi-square test are that both variables are categorical, observations are independent, cells in the contingency table are mutually exclusive, and the number of data is more than 5. This study

calculated the moisture ratio from 7 equation models, as shown in Table 3. An assessment was carried out using CurveExpert Professional 2.3.0 software to see the correlation coefficient (R2) values. After that, further analysis was carried out on the three best equations. Then, a statistical analysis was conducted to obtain the best Root Mean Square Error (RMSE) and Chi-Square (χ2) values. Equation (6) shows the value of the moisture ratio as a result of modifying the Fick equation for rectangular, cylindrical, and round materials. (6) Where n is the positive number, Deff is the effective moisture diffusion and L is the half-length of a sample. The above equation can also be applied to objects like plates such as bagasse, assuming a uniform moisture ratio. For drying over a sufficiently long period, equation (6) can be written as equation (7): (7) Equations 6 and 7 are used to obtain the value of the effective diffusion (Deff ). Moisture effective diffusion (Deff ) describes the moisture movement rate from the inside of the material to the surface area. Graphically, the coefficient of effective diffusion is the slope of the curve, which can also be obtained by plotting the ln MR value and drying time [39] and [40]. The Deff value is calculated using the following equation: (8) The error in each experiment is also calculated in this study. This error is calculated to see the difference in results obtained between the equation model and the experimental results. A slight difference indicates that the equation

obtained is good. The error that occurs is calculated from equation 9 [41]. (9)

Results And Discussion

The equilibrium moisture content in the experiment is obtained when there is a significant change in the sample’s mass. The investigation was carried out by varying the drying temperature of bagasse, namely 140, 160, 180, and 200 °C, with the longest time being 46 minutes. The moisture ratio is calculated based on equation 2 for each mass sample. The results of experiments for different sample masses are shown in Figures 2, 3, and 4. There are three stages in drying: constant rate, first-stage falling rate and second-stage falling rate. In this study, constant drying cannot be seen because this stage usually lasts very briefly.

From the beginning, the drying that occurs is the first stage falling rate followed by the second stage. At a temperature of 140°C for a mass of 100 gr, the first stage falling rate ends at around minute 20 (Fig. 2). While at 200 °C drying and a mass of 100 gr, the first stage falling rate ends at around minute 12th. After that, the second stage of falling rate occurs until drying is complete or reaches equilibrium. Figures 2, 3 and 4 also show the change in the drying stage from the first-stage falling rate to the second-stage falling rate. The change is faster when the temperature is higher and the mass is smaller. In the first stage falling rate, the drying rate will be controlled by the rate of moisture diffusion from the inside to the object’s surface. In the second stage falling rate, the drying rate is controlled by the moisture concentration gradient between the inside and the object’s surface [42]. This condition is seen in all Figures 2, 3, and 4 even though it is at different times and in different moisture content. For drying 150 gr and temperature 200 °C (Fig. 4.), this change occurs around the 22nd minute.

Figure 2. Moisture ratio for 100 gr sample mass at various temperatures.

Figure 3. Moisture ratio for 125 gr sample mass at various temperatures.

Figure 4. Moisture ratio for 150 gr sample mass at various temperatures.

The three figures show an exponential trend of decreasing moisture ratio. The results showed that the lightest sample mass and the highest temperature required 22 minutes. This sample was the fastest in reaching equilibrium moisture content. The moisture content is decreased rapidly in the first 20 minutes. The graph shows that constant rate drying and falling rate dominate the drying process and last until the end of drying. This condition is the same as in previous studies conducted by Akpinar, 2010 [43] and Simanjuntak et al., 2019 [44]. Figure 2 shows that the moisture ratio approaches zero for temperatures 140, 160, 180, and 200 °C after 36, 28, 24, and 24 minutes of drying, respectively. For temperatures 160 and 180 °C, insignificant differences occur until the 10th minute and then widen until the end of drying. Figure 3 shows that a temperature of 200 °C dries faster than a lower temperature. Temperatures of 160 and 180 °C did not significantly differ in moisture ratio from the beginning to the end of drying. For a temperature of 200 °C, the moisture ratio approaches zero after the sample is dried for 35 minutes. Meanwhile, a temperature of 200 °C will approach zero after 28 minutes. Figure 4 shows that for temperatures of 140 and 160 °C, the moisture ratio approaching zero takes 38 minutes. For temperatures of 180 and 200 °C, it takes 36 minutes. Temperatures of 140 and 160 °C do not significantly differ in moisture ratio, as do the temperatures of 180 and 200 °C. Figures 2, 3 and 4 show that increasing the sample mass will increase the drying time, especially at lower temperatures. For a temperature of 140 °C, an additional mass of 50 grams or 50% will affect drying time from 22 to 38 minutes or around 58%. It is shown that adding heat is in line with the speed of evaporation of the water mass in the sample. In constant-rate drying, there is sufficient moisture in the material so that the diffusion rate is controlled by the moisture diffusion from the inside to the surface. In the falling rate section, the drying rate will be affected by the diffusion rate to the surface and in this condition, the amount of

moisture is low. In all drying conditions, it can be seen that the highest temperature and the least mass will experience the fastest drying. It occurs because the material absorbs more energy to evaporate the moisture of the material. The statistical parameters like constant, R2, RMSE, and 2 (χ ) values are shown in Tables 3, 4, and 5. These values ​​are important to determine which equation model best suits the experiments carried out in this research. The most suitable equation model is the one that has the R2 value closest to 1 and the smallest RMSE and chi-square values. The R2 value is calculated according to equation 3, and then the R-value is found. The results of statistical analysis in those tables show that the Wang and Singh equation model is the most suitable for this study. The coefficient of correlation R was obtained from 0.9987 - 0.9998 or 0.9974 - 0.9996 for R2 values. The RMSE value is calculated according to equation

4. It is obtained that the smallest RMSE value is 0.00307

in Wang and Singh’s drying model for the 160 °C experiment and 150 gr sample mass. This value indicates a slight deviation from the prediction, represented by the equation model and the observation results. These results are also consistent with research conducted by Nurafifah et al. [45]. The chi-square value (χ2) is calculated based on equation 5. The chi-square value (χ2) results from a test that measures how the model compares to the observed data. Wang and Singh’s model shows the smallest value of χ2 the most of all types of experiments conducted. Overall, the value of χ2 ranges from 0.00001 – 0.01290. The small values indicate slight deviations between predictions and experiments. Of all the experiments conducted, the Wang and Singh equation model was the best because the correlation coefficient value was the closest to 1. Then followed by the Logarithmic equation model and Modified Page. Wang and Singh’s Model as the best-fit model was also found by [46] on carrot drying by using a tunnel dryer and [47] on tincalconite drying by using a microwave.

Table 3. The results of statistical analysis at different temperatures for a mass of 100 gr Temperature (°C) Model 140

a = -2.983 E+03; k1 = 1.000 E+00; b = 2.984 E+03; k2 = 1.001 E+00

a = 2.821 E +03; k1 = 1.007 E +00; b = -2.819 E +03; k2 = 1.007 E +00

a = 8.894 E +00; = 1.000 E +00 k = 1.013 E +00; g = 8.839 E +01

Table 4. The result of statistical analysis at different temperatures for a mass of 125 gr Temperature (°C) Model

Effective moisture diffusion Deff is important for drying. It shows the amount of moisture that moves through a unit of surface area in a unit of time. The Deff value will be influenced by temperature. Higher temperatures will increase the difference in moisture in the air and the material’s surface. In addition, it also causes vapor pressure on the surface of the material. High surface vapor pressure will make moisture more easily diffused into the air. Effective moisture diffusion

Deff calculated in this equation is an average value or linearized from the data that occurs during drying. Effective moisture diffusion (Deff ) is calculated based on equation 8. Its value can be obtained by linearizing the value of the moisture ratio. In this study, Deff was obtained from experiments at a temperature of 200 °C with varying masses. The linear relationship between the bagasse drying time and ln (MR) is shown in Figure 5. The effective

Table 5. The result of statistical analysis at different temperatures for a mass of 150 gr Temperature (°C) Model 140

Figure 5. The relationship between drying time and Ln (MR) at T = 200°C.

diffusion values of Deff for each sample mass of 100, 125, and 150 gr for a sample mass of 200 °C were 2.72 x 10-5, 2.60 x 10-5, and 1.93 x 10-5 m2/s. This means that lighter samples will dry more quickly than heavier samples. A significant moisture diffusion effective (Deff ) value indicates that moisture leaves the material more quickly and vice versa. The moisture diffusion effective (Deff ) value for the 100 gr sample is lower than the others. Bagasse has higher porosity, so moisture diffuses more easily into dry air. The high temperature of the drying air causes moisture to diffuse into the air much more quickly. This value is not much different from the highly porous material reported by Tong dan Lung, 1990 [48] in bread drying. This study reported a Deff value of 2.5 × 10−5 to 5.5 × 10−3 cm2/s in drying at 20 - 100 °C

temperatures. In addition, Kupzack et al., 2018 [49] stated that the effective moisture diffusion in the paper was 2 x 10-6 m2/s measured at a temperature of 24 °C. Paper is also a porous medium and sugar cane fiber can be used as pulp. A comparison of the moisture ratio between the experiment and the Wang and Singh model for temperatures of 140 and 200 °C is shown in Figures 6 a, b, c and d. Differences can be seen according to data collection from time to time. Generally, there are no significant differences between the types of experiments that were carried out. The average error values ​​that occur can also be seen in Table 6. It shows that the Wang and Singh model is not much different from the experiments carried out.

c d Figure 6. Validity experiment and Wang and Singh model on the temperature of (a). 140 °C, (b). 160 °C, (c). 180 °C and (d). 200 °C.

Error analysis compares experiments and predictions based on the kinetic model used. It will be reflected in RMSE (Root Mean Square Error), where the calculation is based on equation 4. It can also be calculated using equation 9, as researchers did [42]. The error obtained for this method is shown in Table 7, for the most significant error is obtained when the Moisture ratio becomes smaller. It is normal, considering that slight differences in numbers will significantly influence the value received. The value is still low on average. The error values obtained were 4.14, 4.00, and 2.25% for masses of 100, 125, and 150 gr, respectively, for experiments with a temperature of 200 °C. These values ​​are quite small, as are the RMSE values. Generally, the error value is below 5%, which means it is an extremely good fit. The most significant error was obtained in experiments with a temperature of 180 °C. The error values ​​above 10% (poor agreement) were obtained in experiments with masses of 100 and 125 gr. Errors in MR calculations are shown in Table 7.

Conclusion

This research was carried out to obtain a drying kinetic model for bagasse, moisture effective diffusion, drying stage and error calculation. The samples were dried in a rotary dryer with 3 rpm and temperatures of 140, 160, 180, and 200 °C. The sample masses are 100, 125, and 150 gr with lengths of 3 cm. The sample’s moisture content decreased significantly

after drying for 35 minutes for all experiments. This research shows that the most suitable drying model is the Wang and Singh model due to the highest correlation coefficient. This model also has low Root Mean Square Error and chi-square (χ2) values. In this model, the R2 value is 0.9974 – 0.099969, the RMSE value is 0.00640 – 0.06770. The chi-square value is 0.00005 – 0.07250. The constant drying rate cannot be known because this phase lasts very briefly. The first and second falling rate stages are quite clear and are influenced by the temperature and mass of the sample. The effective moisture diffusion is evaluated at the highest drying air temperature of 200 °C. The Deff values of 100, 125, and 150 gr sample masses are 2.72 x 10-5, 2.60 x 10-5 and 1.93 x 10-5 m2/s, respectively. The error between the experimental and the Wang and Singh model was mainly below 5% except at a temperature of 180 °C for sample masses of 100 and 125 gr.

Nomenclature

MR moisture ratio Mb moisture content on a wet basis, % Mi initial moisture content, % Meq equilibrium moisture content, % R2 the correlation coefficient MRPred the (dimensionless) predicted moisture ratio MREx experimental (dimensionality) moisture ratio average predicted moisture ratio k constant T time, min y constant a constant b constant g constant k1 constant k2 constant RMSE root mean square error N number of observations n number of parameters that are positive integers. L the half-length of material, m Deff the moisture effective diffusion, m2/s Greek symbols α Weibull model scale β shape parameter 2 χ chi-square

data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

Statement On The Use Of Artificial Intelligence

Artificial intelligence was not used in the preparation of the article.

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