Mathematical modeling and multivariate analysis applied earliest soybean harvest associated drying and storage conditions and influences on physicochemical grain quality

Anticipating the harvest period of soybean crops can impact on the post-harvest processes. This study aimed to evaluate early soybean harvest associated drying and storage conditions on the physicochemical soybean quality using of mathematical modeling and multivariate analysis. The soybeans were harvested with a moisture content of 18 and 23% (d.b.) and subjected to drying in a continuous dryer at 80, 100, and 120 °C. The drying kinetics and volumetric shrinkage modeling were evaluated. Posteriorly, the soybean was stored at different packages and temperatures for 8 months to evaluate the physicochemical properties. After standardizing the variables, the data were submitted to cluster analysis. For this, we use Euclidean distance and Ward's hierarchical method. Then defining the groups, we constructed a graph containing the dispersion of the values of the variables and their respective Pearson correlations for each group. The mathematical models proved suitable to describe the drying kinetics. Besides, the effective diffusivity obtained was 4.9 × 10–10 m2 s−1 promoting a volumetric shrinkage of the grains and influencing the reduction of physicochemical quality. It was observed that soybean harvested at 23% moisture, dried at 80 °C, and stored at a temperature below 23 °C maintained its oil content (25.89%), crude protein (35.69%), and lipid acidity (5.54 mL). In addition, it is to note that these correlations' magnitude was substantially more remarkable for the treatments allocated to the G2 group. Furthermore, the electrical conductivity was negatively correlated with all the physicochemical variables evaluated. Besides this, the correlation between crude protein and oil yield was positive and of high magnitude, regardless of the group formed. In conclusion, the early harvest of soybeans reduced losses in the field and increased the grain flow on the storage units. The low-temperature drying and the use of packaging technology close to environmental temperatures conserved the grain quality.

Drying conditions. The soybean was subjected to drying in a continuous dryer (Fig. 1), commercial convectional model dryer-KW-Khronos, capacity 60 t h −1 (Kepler Weber, Panambi, Brazil), at 80, 100, and 120 °C. We consider thin layer drying due to the high airflow (238 m 3 /h) that occupies a large part of the drying chamber and crosses a thin layer of grains in downward movement. The dryer has a specific point in the drying chamber for the passage of heated air, where measurements and sampling of the grains were carried out.
Three tests were performed for each initial moisture content grain harvested (18 and 23%) and drying air temperature (80, 100, and 120 °C) for three repetitions. During drying, soybean samples were collected at 15 min intervals to determine the moisture content and volumetric shrinkage. In total was collected 102 samples of 2 kg were at the exit of the drying chamber on the bucket elevator belt. Drying was carried out until the grains reached moisture contents of 11% (d.b.). At the end of the drying, a sample of each repetition (a total of 18 samples) was collected to determine the physicochemical grain quality.
The moisture contents were measured by the indirect method of electrical capacitance using the G650i model equipment (Gehaka, São Paulo, Brazil) calibrated by drying oven method TE-394/2-MP model (Tecnal, Piracicaba, SP, Brazil), with convective heated air at 105 ± 1 °C for 24 h and forced ventilation with air. Then, the sample was sent to a desiccator with silica for cooling, for 5 min. The moisture content was calculated by the initial and final difference of the sample weight using a digital balance, model B13200H (Shimadzu, Kyoto, Japan), in three replications 25 . We also measured the temperature and relative humidity of the ambient. The temperature and relative humidity were checked with studio monitors with the aid of a psychrometer, model PY-5080 (Instrufiber, São Paulo, Brazil).

Scientific Reports
| (2021) 11:23287 | https://doi.org/10.1038/s41598-021-02724-y www.nature.com/scientificreports/ The volume (V g ) of the fifty grains was determined at each sampling performed during the drying process with the aid of a caliper, according to the expression (1) 26 . The unitary volumetric shrinkage (Ψg) during the drying of the product was determined by the ratio between the final and initial volumes of the grain for each moisture content.
where a: major axis of the grain (mm), b: mean axis of the seed (mm), c: minor axis of the seed (mm).
The experimental unit shrinkage, expressed by the following mathematical models have been adjusted 26,27 :
For determining the ratios of moisture during drying under different conditions, the following expression was used (Eq. 19) 4,10,19,28 : where X e : equilibrium moisture content of the product (d.b.) In thin-layer drying of agricultural products, analysis of the dehydration process that takes place in the falling rate period is calculated using a simple diffusion model based on Fick's second law. Evaluation of the moisture diffusion mechanism in spherical bodies can be represented by the following Eq. (20) 27,28 : where X: moisture content (kg water /kg DS ), t: time (s), D: diffusivity (m 2 s −1 ), r: radius coordinate (m).
The method of slopes was used for the estimation of effective moisture diffusivity of soybean kernels at corresponding moisture content under different drying conditions. The uniform moisture content was assumed as the initial condition (Eq. 21). Due to the geometry, the asymmetry boundary condition was defined (Eq. 22). Finally, the second boundary condition was the neglect of external resistance (Eq. 23) 27,28 : A sphere with initial moisture content, which is subjected to the drying process in the open air, under constant conditions, can be described by Fick's theory, having the following analytical solution (Eq. 24) 29,30 : where R: sphere radius (m).
It is usual to consider the value of the diffusion coefficient constant or linearly. This relationship has been expressed by the Arrhenius model (Eq. 25) 20 : where A: constant (m 2 s −1 ), E: activation energy (kJ kmol −1 ), R: universal gas constant (8314 kJ kmol −1 K −1 ), T: absolute temperature (K).
Storage conditions. Soybeans harvested at different moisture content (18 and 23%) and dried at different temperatures (80, 100, and 120 °C) were stored in paper and plastic raffia-polyethylene bags at 15, 23, and 30 °C in climatic chambers for 0, 4, and 8 months. Three repetitions per treatment were performed. A total of 432 soybean samples were collected and submitted to physicochemical quality assessments.
Physicochemical quality of soybeans. The moisture content, oil content, acid index, and crude protein content (% d.b.) were determined according to AOAC 25

Statistical analysis.
To adjust the mathematical models of analysis of soybean drying, nonlinear regression was performed, through the Quasi-Newton method, using the computer program Statistica 7.0 ® . To check the degree of fit of each model, the significance of the regression coefficient by t-test was considered, adopting the 1 and 5% level of probability, the magnitude of the coefficient of determination (R 2 ), the mean relative error values (P), the average estimated error (SE), and verified the behavior of the distribution of residuals. The relative aver- where Y : experimentally observed value, Ŷ : value calculated by the model, n: number of experimental observations, GLR: degrees of freedom of the model. The data for physicochemical quality were analyzed by analysis of variance, Tukey's test at 1 and 5% probabilities, and linear regression. After standardizing the variables, the data were submitted to cluster analysis. For this, we use Euclidean distance and Ward's hierarchical method. After defining the groups, we constructed a graph containing the dispersion of the values of the variables and their respective Pearson correlations for each group. These analyzes were performed with the "ggfortify" and "GGally" packages from software R (Table S1).
Ethics declarations. The experimental research and field studies on plants and plant material were comply with local and national regulations. The study complied with institutional, national, and international guidelines and legislation.

Results and discussion
Drying kinetics and quality of soybeans on the drying. In the results obtained ( Fig. 2A), the drying curves at different temperatures describe a logical behavior and values. It was observed that the increase in the drying air temperature to lower the initial moisture content of the soybean reduced the drying time. However, at the end of the process, the grains reached the same moisture ratio. Soybeans with initial moisture contents of 23% (d.b.) and drying at 80 °C completed the drying process in a higher time of 2.6 h, while soybean with initial moisture contents of 18% (d.b.) subjected at 120 °C took 0.7 h to complete the process. The other conditions evaluated varied the drying time from 0.8 to 2.0 h. During the drying period, the ambient air temperature varied between 22 and 26 °C and the relative humidity between 50 and 65%. Regardless of the initial moisture contents, in the final third of drying with an air temperature above 100 °C there was an increase in the temperature of the grain mass to 45 °C, while in the drying at 80 °C and from the middle of the process, the soybean remained with a mass temperature between 36 and 38 °C.
The coefficients of the adjusted models analyzed during the drying of soybean are shown in Tables 1 and 3. The coefficients of determination R 2 indicated a satisfactory representation of the phenomenon under study (Tables 2  and 4). Among all tested models, Wang and Singh's model showed the lower values of the mean relative error (P), average estimated error (SE) ( Table 3), and distribution of residues for the temperature of the air drying 80, 100, and 120 °C (Tables 2 and 4). Thus, the experimental drying results fit satisfactorily with the estimated data ( Fig. 3A, B). It was observed that soybean with an initial moisture content of 23% (d.b.) had a better fit (Fig. 3A) for the estimated and experimental moisture ratio values in drying. This may have occurred due to the longer drying time and homogeneity, especially at temperatures of 80 and 100 °C.
These findings are consistent with that published recently [32][33][34] . The moisture remotion occurs fast in the first half of the process, afterwards, it is slower since the diffusion of the water in the grain's inner geometry is more difficult to happen. Even though the process parameters require an air temperature of 100 °C to obtain a faster drying, the literature recommends that the temperature should be lower, so as not to damage the structure of soybeans and accelerate degradation. It was found that the effects of initial moisture content and temperature on drying time were proportional, which means that both factors influenced the soybean quality.
The effective diffusion coefficient increased significantly and with a uniform variation, with the increase of the drying air temperature (Fig. 3C, D) for a linear adjustment 27,30,35,36 , being the higher values of diffusion obtained in the drying with initial moisture contents of 23% (d.b.). Thus, the diffusivity results reflected on soybean volumetric shrinkage, being that it was 23.20% for moisture content of 0.18 to 0.11 (d.b.) and 21.1% for moisture content of 0.23 to 0.11 (d.b.) (Fig. 2B, C). In this study, the Rahman model was the best set of data obtained volumetric shrinkage of soybeans, with a less pronounced trend of distribution of residuals (random distribution) ( Tables 5 and 6). These models had a higher coefficient of determination and lower estimates and average errors relative. Thus, the Rahman model was recommended to predict the phenomenon of shrinkage of the soybean.
The results obtained in this study confirm that drying has immediate effects on soybean quality (Tables 7 and  8). Drying at air temperatures above 100 °C negatively affects the physicochemical quality, mainly in soybeans harvested with 18% moisture (Tables 7 and 8 time zero). Similar results were observed by Mourad et al 37 and Wang et al 22 when evaluating the effect of temperature on the grain drying. It is observed that the grain cell has been compromised grain structure along with the different drying air temperatures, the higher the amount of ions leached at the drying temperature of 120 °C. The damage to the cell walls of grains causing high values of electrical conductivity affects the oil content and acidity. The increase in electrical conductivity may be implicated in the major damage caused by the drying air temperature on the soybean cellular structure during drying, causing them to lose physiological and nutritional quality 38,39 .
Comparing the evaluations of volumetric shrinkage ( Fig. 2A, B) and oil yield (Tables 7 and 8), it was found that a 5% reduction in the volume of the grains provided a 4.88% decrease in the oil yield extracted. The  (Tables 7 and 8), due to the effects of drying temperature and initial moisture content. According to the increase in drying temperature, a reduction in soybean oil extraction yield was observed. According to Timm et al 40 , the drying temperature from 30 to 90 °C can reduce the corn starch extraction yield by 10%. When drying was   Fig. 2A) there was a reduction of 20, 21, and 23% in the grain volume for temperatures of 80, 100, and 120 °C (Fig. 2B), respectively, while the oil content was 25.89%, 24.19%, 23.34%, respectively. Although the diffusion process was more intense in soybeans with an initial moisture content of 23% (d.b.) compared to 18% (d.b.), mainly for the drying at 120 °C, the effects on quality in oil yield, acid index, and crude protein were better. This fact is suggested by the anticipation of soybean harvest, minimizing the effects of natural drying on the plant. Thus, harvesting with 23% (d.b.) moisture content allows the drying of the beans more slowly at a temperature around 80 °C to obtain better quality (Tables 7 and 8). Harvesting soybeans with 18% moisture content, in addition to the adverse effects of the climate that the grains were subjected to, still needs to be subjected to faster drying at a higher temperature for more efficiency in the process.   The most significant effects of soybean quality reduction were observed in paper packaging and a temperature of 30 °C. According to Maciel et al 42 for a constant temperature, the equilibrium moisture hygroscopic content increases with the relative humidity. Although the temperature influences the hygroscopic equilibrium humidity, this influence is weak. This is because water is transferred from the air to the soybean when the relative humidity of the storage ambient air is higher than the equilibrium humidity 43 , being more intense when the soybeans are stored in high permeability packages (Tables 7 and 8).
The storage conditions at 15 and 23 °C in plastic bags were favorable for quality. The soybean storage in the temperature at 15 °C was favorable to the yield and the acidity index of the extracted oil, while the storage time was the main factor that altered the change in the acidity indexes. Mbofung et al 44 reported increases in the soybean acid value for all storage conditions; however, increases in temperature and air humidity led to further grain deterioration 45 . Investigations according to evaluate the quality of the soybean grains stored in different conditions at 25 °C, the physicochemical properties, such as ash (4.7%), protein (3.9%), lipids (21.9%), and carbohydrates (34.4%) were not altered. Oppositely, at 35 °C, a reduction in the tegument color (88% to 85%) was observed, in addition to an increase in free fatty acids (3.7% to 4.7%) and, consequently, the grains acidity content due to the hydrolytic degradation of fat components by the action of lipase, in which these fatty acids are liberated from the triacylglycerol structures 18 . Assessing the effects of drying and storage on soybean quality, some studies found that the increase in grain drying temperature from 75 to 105 °C associated with storage conditions of 25 °C and 50%, 20 °C and 60%, 30 °C and 40% relative humidity over six months reduced the oil extraction yield and increased the acid index 46,47 .  Tables 7 and 8 were observed regardless of storage and packaging conditions, a significant reduction in the percentage of crude protein in the grains on the 8 months of storage. In the evaluation of the quality of soybeans stored for 6 months in permeable paper bags and polyethylene plastic bags at 3, 10, and 23 °C. Coradi et al 46 found that the increased storage time reduced the quality of soybeans, regardless of storage conditions and packaging. In addition, the storage temperature of 23 °C was the most negatively altering the quality of soybeans. However, the storage in air temperature of 3 °C was most favorable for the quality of soybeans, although some quality results were similar, with storage at 10 °C.
As with other quality evaluations, it was observed that the crude protein content was higher in soybeans stored at lower temperatures. Lee & Cho 48 evaluated soybean storage for 2 years, at room temperature, and observed a reduction in protein levels from 43 to 38.30%, for 1 and 2 years, respectively. Kibar 49 and Rani et al 50 studied soybean storage at different moisture contents (12 and 16% d.b.) and temperatures (8,13,18,23, and 28 °C) and reported a reduction in crude protein content with increased moisture content and the temperature. Neethirajan et al 51 found similar results, with a significant reduction in the soybean protein content at a storage temperature of 30 °C and relative humidity of 88%. Although the storage conditions affected the crude protein content in the soybean, storage at lower temperatures allowed greater conservation 44 .   (11,18,25, and 32 °C) of soybeans on the functional properties of the protein isolate. Protein solubility reduced 18% with increasing temperature from 11 to 32 °C in soybean stored with 12% moisture. When the soybeans were stored with 15% moisture, the protein solubility reduced by 16% with increasing temperature from 11 to 32 °C. Furthermore, when soybeans were stored at the same temperature, for example, 25 °C, increasing moisture from 12 to 15% reduced protein solubility by 4%.

Multivariate analysis.
Cluster analysis showed the existence of four homogeneous groups for the variables evaluated (Fig. 4). G1 group gathered the largest number of treatments and stood out for the higher average of electrical conductivity and lower averages of acid oil and crude protein. The treatments allocated in this group belong to the higher storage times (4 and 8 months). G2 group allocated most treatments with zero storage time, which had the higher averages of oil yield and crude protein and intermediate values of electrical conductivity Table 5. Parameters estimated, coefficient of determination (R 2 ), estimated average (SE) and relative error (P) and distribution of residues of the mathematical models used to describe the shrinkage of soybeans grains to different drying air temperatures and an initial moisture content of the grains of 23% (d.b.).

Mathematical models
Estimation of parameters R 2 SE (decimal) P (%) Distribution of residuals www.nature.com/scientificreports/ and acid oil. G3 and G4 groups allocated treatments from all storage times, and it is not possible to associate the grouping pattern to a specific storage period. The treatments in the G3 group showed lower averages of electrical conductivity, in addition to intermediate values for the other variables. G4 group in turn brought together treatments with the higher averages of acid oil, in addition to intermediate values and with high variability for the other variables. The results indicated that there were effects of the association of the conditions of harvest, drying, and storage on the quality of the grains. It is important to highlight that storage time was the main study factor that impacted the groups formed 53 .
Similar results were observed by Ferreira et al 54 evaluated the effects of drying temperature (30,50,70,90, and 110 °C) and storage time (0 and 12 months) on physicochemical parameters in soybean. The authors reported that the increase in drying temperature resulted in a reduction in the quality of physical. In 12 months of storage, soybeans dried at 70, 90, and 110 °C showed higher (20, 65, and 14%, respectively) amounts of contamination than soybeans dried at 30 °C, accelerating the metabolism of grains, reducing antioxidant compounds such as isoflavones 54 , and reduces protein solubility and increases lipase activity and lipid acidity in soybeans 55 . Table 6. Parameters estimated, coefficient of determination (R 2 ), estimated average (SE) and relative error (P) and distribution of residues of the mathematical models used to describe the shrinkage of soybeans grains to different drying air temperatures and an initial moisture content of the grains of 18% (d.b.).

Mathematical models
Estimation of parameters R 2 SE (decimal) P (%) Distribution of residuals www.nature.com/scientificreports/ Regarding Pearson's correlations between the variables for each group, it is noted that the direction of the correlations was similar (Fig. 5). The electrical conductivity is negatively correlated and in low magnitude with all the physicochemical variables evaluated. However, it is to note that these correlations' magnitude was substantially more remarkable for the treatments allocated to the G2 group. These treatments also showed a positive and high magnitude correlation for acid oil and oil yield. Another correlation worth mentioning was that observed between crude protein and oil yield, which was positive and of high magnitude, regardless of the group formed.
Coradi et al 56 verified changes in the yield of protein and oil extracted in the grains in function from the presence of fermented, rotten, and burned soybeans caused by the high drying temperature and storage conditions. Ramos et al 55 found that the solubility of the protein isolates extracted from fermented, rotten, and burned soybeans are 17, 40, 59% lower compared to the protein isolate from not defective soybeans. The acidity of oil extracted from fermented, rotten, and burned soybeans is 969, 1350, 2248% higher than the acidity of oil extracted from not defective soybeans. Thus, the importance of optimizing the conditions for drying and storing soybeans is evident.

Conclusions
The low drying air temperatures decreased the effective diffusivity and the time of volumetric shrinkage. Although storage time was the main factor influencing grain quality, the early harvest at 23% moisture content, adopting drying systems with air temperatures of 80 °C, and storage in controlled environments with temperatures below 23 °C are favorable to conserve the physicochemical quality of the soybean.

Final considerations
The parameters obtained from soybean harvesting, drying, and storage make it possible to improve the management of the grain mass, to achieve better quality results. When applied at the farm level, it can enhance the production chain, improve transport and distribution logistics, reduce soybean losses, and add value to the marketing of soybeans. The results and conclusions obtained in this research are indicated for future investigations in soybean pre-processing and storage units, mainly at the farm level, to optimize harvest and post-harvest operations. For future research, it is suggested to carry out diagnoses on the different existing technologies of drying and storage, to propose a project that can more effectively implement the conclusive parameters of this study. Table 7. Quality of soybeans harvest at 23% (d.b.) moisture content subjected to drying at 80, 100 and 120 °C, stored in different environments and packaging for eight months. Means followed by the capital letter in the column for each time of storage and lower lines for each temperature of storage. do not differ at 1 and 5% probability. PL-polyethylene plastic bag. P-paper bag.