DRYING KINETICS OF PEELED COFFEE SUBMITTED TO DIFFERENT TEMPERATURES AND RELATIVE HUMIDITY OF THE AIR OF DRYING AFTER PARTIAL DRYING

1 PhD in Agricultural Engineering at Federal University of Lavras (UFLA), rodrigovicmoreira@hotmail.com 2 PhD Professor at Food Science Department of Federal University of Lavras (UFLA), jefferson@ufla.br 3 PhD Professor at Agricultural Engineering Department, Federal University of Lavras (UFLA), ednilton@deg.ufla.br 4 PhD Professor at Food Science Department of Federal University of Lavras (UFLA), roney.rocha@ufla.br

the dew point temperature and increase of the dry bulb temperature.

INTRODUCTION
Drying reduces risks with respiration, fermentation, oxidation and microorganisms development, directly influencing the final quality of the coffee drink. In addition, it is the stage of greatest energy demand, which results in high financial costs (BORÉM, 2008).
Therefore, the studies of drying kinetics have aroused the interest of several researchers, because, according to Resende et al. (2010), the mathematical simulation of drying is fundamental for the understanding of related processes. Thus, the use of some techniques, such as the adjustment of mathematical models, can bring some contributions CORRÊA et al., 2010b;ISQUIERDO et al., 2013;SIQUEIRA et al., 2013), as indicate the ideal time for changes in drying characteristics aiming at greater energy savings and shorter drying times.
Numerous models have been proposed to describe the rate of water reduction during thin layer drying of biological materials (ERBAY; ICIER, 2010). An equation describing the water reduction rate of a thin layer is necessary for thick layer drying simulation because simulation models are generally based on the assumption that the thick layer is composed of a series of thin layers (KASHANINEJAD et al., 2007). The adjustment of mathematical models for the drying of agricultural products provides information of fundamental importance for the development of processes and for the dimensioning of equipment. Using this information, it is possible to estimate the drying time and, consequently, the energy expenditure that will reflect on the processing cost VILELA;ARTUR, 2008).
There are three types of mathematical simulation models of the thin layer drying process, which aim to describe the drying kinetics of agricultural products. The semi-empirical and empirical models, which are generally based on conditions external to the product, such as temperature and relative humidity of the drying air; and the theoretical models, which normally consider not only external conditions, but also internal mechanisms of energy and mass transfer and their effects (BORÉM, 2008).
Most of the time, the empirical and semi-empirical models, due to their ease of use, have been shown as the best options to represent the drying process of agricultural products. However, their validity is restricted to the temperature, relative humidity and air velocity under which the experimental data were obtained (BROOKER et al., 1992;MOHAPATRA;RAO, 2005).
Depending on the conditions of the drying process, different models can be adjusted to adequately describe the drying kinetics of porous, hygroscopic hair products. The models of Midilli et al. (2002), Page, Logarithm, Henderson and Pabis, Modified Page, Two Terms, Exponential of Two Terms, Newton, Wang and Sing (AKPINAR, 2010;ANDRADE et al., 2006;CORRÊA et al., 2010b;ISQUIERDO et al., 2013;KAYACAN et al., 2018;SOUSA et al., 2011), among others, have been frequently adjusted to predict the drying process of agricultural products.
The objective of this study is, for peeled coffees, to evaluate the influence of different temperatures and relative humidity of the drying air on the drying kinetics after partial drying. This influence has not yet been studied or modeled. The knowledge and prediction of these conditions helps in making decisions regarding the equipment sizing and process variables that can result in lower costs and better quality of the final product.
The selective harvesting of coffee fruits was performed manually. After harvesting, the fruits were subjected to hydraulic separation to remove fruits of lower specific mass and to a new manual selection to remove remaining immature and overripe fruits.
Right after the manual selection, the coffee was wet processed, the peeled coffee portion was determined, with the exocarp and part of the mesocarp removed mechanically. The water content was 1.565 ± 0.065 db, determined according to the standard greenhouse method, 105 ± 3 ° C, for 24 hours, according to the Seed Analysis Rule (BRASIL, 2009).
Before the beginning of mechanical drying, the equivalent radius of the coffee grains was calculated, defined as the radius of a sphere with volume equivalent to the volume of the fruit. In order to calculate its volume, due to the greater uniformity of the grains, a sample of 25 grains was taken from each repetition, from all treatments, from which measures of length (a), width (b) and thickness (c) were taken using a digital caliper with 0.01 mm resolution, with the volume of coffee fruits (V) being calculated by Equation 1 (ISQUIERDO, 2011). (1) Where, V = grain volume, m 3 ; a = length, m; b = width, m; and c = thickness, m.
The drying system was composed of an air conditioning system coupled to a fixed layer dryer ( Figure 1). The air characteristics were controlled by a laboratory air conditioning system (SCAL), a model proposed by Fortes et al. (2006). This equipment allows the control of the flow, dry bulb temperature (T bd ), dew point temperature (T pd ) and the relative humidity (RH) of the drying air with precision. In order to obtain the lowest dew point temperatures and, consequently, the lowest relative humidity, before SCAL, the air was preconditioned by a refrigeration system composed of three air conditioning units.
The dryer consisted of four removable trays with a perforated bottom, of square section, with sides equal to 0.30 m and depth of 0.10 m, located on a plenum for uniform air flow. Air velocity was monitored using a paddle anemometer. The dew point temperature was measured inside the SCAL chamber and the drying air temperature was measured in the plenum, under the perforated bottom trays. The relative humidity of the drying air was measured by a psychrometer inserted inside the plenum (Assmann type psychrometer). The temperature of the coffee fruits was measured with mercury thermometers inserted in the center of the dough.
For the design of the coffee drying experiments, nine treatments in a 3x3 factorial scheme, with three dry bulb temperatures (40 °C; 40 °C -35 °C and 35 °C; T bd ) and three point temperature dew (2.6 °C; 10.8 °C and 16.2 °C; T pd ) were performed. Two more treatments were performed without dew point temperature control, with two dry bulb temperatures (40 °C and 35 °C). For each treatment, four repetitions were performed. Depending on the combinations between dry bulb temperature and dew point temperature, different relative humidity (RH) of the drying air were obtained (Table 1) The drying operation took place in two stages for treatments numbered from one to nine. The first stage started at the moment of the grain entering the dryer and its completion occurred when the product reached approximately 0.428 ± 0.01 db. During the first stage there was no control of T pd and consequently of the RH of the drying air. The second stage started after the product reached 0.428 ± 0.01 db, with T pd control and consequently of the UR. The T bd were changed in relation to the first stage, only for treatments four, five and six, remaining unchanged until the grain mass reached a water content of 0.123 ± 0.006 db.
After processing, 1.2 kg of wet peeled coffee were deposited in each tray, promoting the complete filling of its bottom (0.30 x 0.30 m), corresponding to a thin layer of approximately 0.015 m in height. Knowing the mass and the initial water content of the fruits, the drying of the product was monitored using the gravimetric method (Equation 2). The trays containing the samples were removed from the dryer and weighed on a semi-analytical scale with a resolution of 0.01 g, every fifteen minutes in the first hour of drying, thirty minutes in the second hour, every hour until approximately 0.428 ± 0.01 db and every two hours until the coffee grains reached a water content of 0.123 ± 0.006 db. After each treatment, the water content of the endosperm of the grains was determined by the drying oven method, 105 ± 1 ° C, for 16 hours (INTERNATIONAL ORGANIZATION FOR STANDARDIZATION -ISO, 1999). In order to minimize possible differences in temperature and air flow between the perforated bottom trays, a 90° rotation was made in the position of the trays at each weighing, as well as the turning of the grain mass.
(2) Where, Ut = water content at time t, kg of water.kg of dry matter -1 (db); m ai = initial water mass, kg; m ti = initial total mass, kg; m tt = total mass at time t, kg; and m ms = dry matter mass, kg.
For all treatments, the drying air speed was kept constant at 0.33 m s -1 , corresponding to the flow of 20 m³ min -1 m -2 . State points for the drying air from DRYING KINETICS OF PEELED COFFEE SUBMITTED TO DIFFERENT TEMPERATURES AND RELATIVE... the relationship between dry bulb temperatures (T bd ) and dew point temperatures (T pd ) were experimentally obtained and these conditions were adopted during the drying of the grains.
In the analysis of drying data, the moisture ratio (RU) is essential to describe different models of thin layer drying. The moisture ratio during drying, as a function of the variables evaluated, was determined by Equation 3. At each drying time, a water content was correlated with the initial water content and the equilibrium water content, for specific conditions of drying. Thus, in all conditions tested, the models were adjusted to the values of moisture ratio as a function of drying time to describe the drying kinetics of coffee grains (Table 2).
( 3) Where, RU = moisture ratio, dimensionless; U = water content of the product at time t, decimal (db); Ue = equilibrium water content of the product, decimal (db); and Ui = initial water content of the product, decimal, (db).
MOREIRA, R. V. et al. Table 2. Mathematical models used to predict the drying phenomenon
To adjust the mathematical models, non-linear regression analyses by the Gauss-Newton method were performed using the STATISTICA 5.0® software (Statsoft, Tulsa, USA). The choice of the best model was based on the following statistical parameters: standard deviation of the estimate (SE), average relative error (P), coefficient of determination (R 2 ) and trend in the residues distribution. The standard deviation of the estimate and the average relative error were calculated, respectively, by Equations 19 and 20.
Where, SE = standard deviation of the estimate, decimal; Y = value observed experimentally; = value calculated by the model; GLR = model degrees of freedom; P = average relative error, %; and n = number of observed data.
The effective diffusion coefficient for the drying conditions used in this study was calculated by adjusting the model based on the liquid diffusion theory (Equation 21) to the observed data, using non-linear regression, using the STATISTICA 5.0® software (Statsoft, Tulsa, USA). This equation (21) is the analytical solution for Fick's second law, considering the product's geometric shape as spherical, disregarding the volumetric contraction of the fruits and considering the contour condition of the water content known on the product surface (BROOKER et al., 1992).
Where, D eff = effective diffusion coefficient, m² s -1 ; R = equivalent radius of coffee fruits, m; n = number of terms; and t = time, s.

RESULTS AND DISCUSSION
The statistical parameters used for the comparison between the fourteen models used to describe the drying kinetics of peeled coffee grains (Table 2) are shown in Tables 3 and 4. The average initial water content was 1.565 ± 0.065 db, when subjected to dry bulb temperature and dew point temperature of the drying air used in this experiment, for the first and second part of drying. The values of the coefficients of determination (R²), standard deviation of the estimate (SE), average relative error (P) and trend of the distribution of residues are also presented. The choice of a model to represent the drying phenomenon of an agricultural product is based on the joint analysis of these parameters presented, as well as the behavior of the error distribution, and the analysis of a single parameter is not a good tool for the selection nonlinear models.
According to Kashaninejad et al. (2007) and Madamba et al. (1996), determination coefficients (R 2 ) greater than 95% indicate a satisfactory representation of the drying process. Draper and Smith (1998) state that the ability of a model to accurately describe a particular physical process is inversely proportional to the value of the standard deviation of the estimate (SE). Therefore, the lower the SE value, the better the model fits the experimental water content ratio data . For the average relative error (P) that indicates the deviation of the values observed in relation to the curve estimated by the model (KASHANINEJAD et al., 2007) values below 10% are suggested for the model recommendation (MOHAPATRA; RAO, 2005).
Analyzing the first part of the drying of the coffee grains (Table 3), it can be seen that the Diffusion Approximation, Modified Midilli and Page models reached the desired requirements for the three statistical parameters analyzed. Among the models that met the three requirements, the When more than one model satisfactorily represents the drying phenomenon, it becomes necessary to consider the complexity of each model, for its recommendation. The analysis of the distribution of error is another tool that has been constantly used in a complementary way to the statistical parameters in the choice of the model, because even though subjective, it provides a good indication of the model's adjustment to the experimental values. For Goneli et al. (2011), a model is considered random if the residual values are close to the horizontal range around zero and also do not form defined figures, indicating no bias in the results. If it presents a biased distribution, the model is considered inadequate to represent the phenomenon in question. Thus, among the models that met the statistical requirements, the Diffusion Approximation model was the only one that obtained a random error distribution.
When studying only the second part of drying (Table 4), we can note that all models used in this study meet the requirements of R 2 , P and SE. All models showed a coefficient of determination (R 2 ) greater than 99.15%. When considering the criterion of the average relative error (P < 10%) and the standard deviation of the estimate (SE) for an acceptable adjustment, all values are less than 6.75% and 0.0943 respectively. The Midilli and Modified Midilli models were the ones that resulted in the best adjustments, with the highest values of determination coefficient (R² ≥ 99.97%) and the lowest values of average relative error and standard deviation of the estimate (P ≤ 1.24% and SE ≤ 0.020). Regarding the trend of error distribution, the Midilli, Modified Midilli and Valcam models were the only ones to present randomness.
Among the models used in this experiment to describe the drying kinetics of the peeled coffee submitted to different combinations of T bd and T pd , the Diffusion Approximation was the one that presented the best adjustments for the first part of the drying, after a joint analysis of the coefficient of determination, average relative error, standard deviation of the estimate and trend of error distribution values. For the second part of the drying, the Midilli and Modified Midilli models were the ones that presented a more adequate fit. Therefore, the modified Midilli model is indicated due to its less complexity. Isquierdo et al. (2013), studying the effect of different dry bulb temperatures and dew point on the drying kinetics of natural coffee, also indicated the Modified Midilli model as the one that best describes the process. The same result was verified by Corrêa et al. (2010b), who obtained a satisfactory fit of the Modified Midilli model to describe the drying of coffee fruits. Goneli et al. (2009) and Alves (2013), studied the drying kinetics of peeled and natural coffee respectively, and concluded that the Midilli model was the most suitable for representing the process.
In addition to coffee in its different forms of processing, the Midilli model is also recommended to predict the drying phenomenon of other agricultural products, such as red beans (CORRÊA et al. 2007), adzuki beans (RESENDE et al., 2010 and jatropha grains (SIQUEIRA et al., 2012).
The comparison between observed and estimated values of the moisture ratio by the Diffusion Approximation and Modified Midilli models, for the first and second drying periods, respectively, is showed in Figures 2 and 3. We can observe, in these figures, a high agreement between the moisture ratio values observed experimentally and the values estimated by the Diffusion Approximation and Modified Midilli models for all studied conditions, which confirms the satisfactory fit of these models to describe the kinetics drying of coffee grains, under the studied conditions.
In Tables 5 and 6 are shown the coefficients of the Diffusion Approximation models, for the first part of the drying of the peeled coffee, and the coefficients of the Modified Midilli model for the second part of the drying of the peeled coffee, adjusted to the observed data of thin layer drying kinetics, under the conditions considered in this experiment.

Figure 2. Moisture ratio values (dimensionless) observed (x-axis) and estimated (y-axis) by the Diffusion
Approximation model for the first part of the drying of coffee grains    Average relative humidity of the drying air, obtained according to the ambient air conditions. * Ghazanfari et al. (2006) In Table 5 no trends in relation to the constant "k" and the coefficients "a" and "b" is observed. In Table 6 we can verify that the magnitude of the drying constant "k", which represents the effect of external drying conditions (GONELI et al., 2009) increased with the increase in the drying temperature (T bd ), which indicates that the rate of water reduction rises with increasing temperature. According to Babalis and Belessiotis (2004) and Madamba et al. (1996), Driscoll andBuckle (1996), the drying constant "k" is related to the effective diffusivity in the drying process for the decreasing period. Regarding the "n" and "a" coefficients of the Modified Midilli model, no definite trend in their values as a function of the temperature and relative humidity of the drying air was observed.
In Figures 4 and 5 are shown the behavior of the moisture ratio of the coffee grains, estimated by the Diffusion Approximation and Modified Midilli models for all studied conditions. A high agreement between the moisture ratio values observed experimentally and the values estimated by the models was observed, which confirms the satisfactory fit of these models to describe the kinetics for each studied condition.
In Figure 4 we can also observe that the start of drying, referring to the first minutes, occurred under a constant rate period, due to the high water content of the grains. After the first minutes, drying took place under a decreasing rate period. During this period, resistances to water and energy transfers are found essentially inside the grains, making the rate of surface evaporation higher than the rate of displacement of water from the interior to the product surface (BROOKER et al., 1992).
In the graph of the first part of drying (FIGURE 4), we can observe that the treatments that started drying with T bd of 40 °C obtained greater water loss in the first hours of drying. However, some treatments that after partial drying presented T bd of 35 °C (second part of drying), had total drying times higher than the times of some treatments that started and ended drying with T bd of 35 °C. This result can be observed for treatment 5 (first part T bd 40 °C -second part T bd 35 °C and T pd 10.8 °C), which despite starting the process with 40 °C T bd , obtained a total time of drying equal to treatment 7 (first part T bd 35 °C -second part T bd 35 °C and T pd 2.6 °C), which started the process with 35 °C T bd . The same result occurred for treatment 6 (first part T bd 40 °C -second part T bd 35 °C and T pd 16.2 °C), which obtained a total drying time greater than treatments 7 and equal to treatment 8 (first part T bd 35 °C -second part T bd 35 °C and T pd 10.8 °C). In these cases, the lower T pd , promotes higher rates of water reduction at the end of drying, when the removal of water becomes more difficult due to the internal mechanisms of the grains, making the process faster. Thus, for these conditions, the effect of T pd at the end of drying becomes greater when compared to the effect of T bd at the beginning of drying.
Analyzing Figure   (treatment 2, 17.5% RH), occurred similarly during the end of drying. However, around 0.24 moisture ratio, the treatment without T pd control (treatment 10) started to have lower rates of water reduction, probably due to greater oscillations in the RH of the drying air, resulting in a total drying time greater than the treatment with T pd of 10.8 °C (treatment 2). When we analyze the treatments 5 and 8, both submitted to T bd of 35 ° C and T pd of 10.8 °C (UR of 23.0%), plus its equivalent without T pd control (treatment 11; average RH monitored of 26.0%), we noticed that the oscillations between the water reduction rates were smaller during the final part, resulting in drying times practically equal.
The average values of the equivalent radius and the effective diffusion coefficients obtained for drying coffee grains, for the different combinations of dry bulb temperature and dew point temperature used in this experimente are shown in Table 7.
The results provided by the analysis of variance showed that the temperature of the drying air and the dew point temperature and, consequently, the relative humidity of the air had a significant effect both on the effective diffusivity coefficient of the first part of drying and on the coefficient of effective diffusivity of the second part of drying.
In Table 7 we can verify that for the first part of the drying of the peeled coffee grains, the effective diffusivity coefficient was higher for the treatments that started the process with higher T bd . Analyzing only the second part of the drying (after partial drying), the increase in the dry bulb temperature and the reduction in the dew point temperature of the drying air to the same dry bulb temperature, increased the effective diffusion coefficient. However, greater differences between the coefficients obtained by each T pd , were observed when using T bd of 40 °C. Furthermore, we can observe a linear increase in the diffusion coefficient due to the reduction in T pd , with values obtained in the range of 1.80 to 3.29 x10 -11 m 2 s -1 for T bd of 40 °C and from 1.69 to 2.14 x 10 -11 m 2 s -1 for T bd of 35 °C.
The pattern seen in the behavior of the diffusion coefficient is determined by some factors and explained by other authors. Corrêa et al. (2010a), state that the increase in temperature reduces the viscosity of water, directly influencing the resistance of the fluid to flow and facilitating the diffusion of water molecules in the product's capillaries. Another factor that can be attributed to this increase in the effective diffusion coefficient is that, with the increase in temperature, the level of vibration of water molecules increases, which also contributes to faster diffusion (GONELI et al., 2009). The effect of the dew point temperature, consequently of the relative humidity of the drying air on the diffusion coefficient can also be explained by the internal vapor diffusion mechanism, due to the higher partial vapor pressure gradient (BROOKER et al., 1992). The values obtained in this study show the same pattern as those obtained by Isquierdo et al. (2013), working with natural coffee, which also observed higher coefficient values for higher T bd and lower T pd , consequently lower relative humidity. Alves et al. (2013), working with low relative humidity and different drying air temperatures, obtained coefficients of 1.908 x 10 -11 m 2 s -1 for combination of T bd -T pd of 35 °C -2.6 °C; 2.456 x 10 -11 m 2 s -1 for T bd -T pd of 40 °C -2.6 °C and 3.721 x 10 -11 m 2 s -1 for combination of T bd -T pd of 45 °C -2.6 °C.
The values of the effective diffusion coefficient obtained in this experiment, are in agreement with the values found for agricultural products, which according to Madamba et al. (1996), range from 10 -11 to 10 -9 m² s -1 . Corrêa et al. (2010b) studied the drying kinetics of coffee fruits at temperatures of 35, 45 and 55 °C and obtained effective diffusion coefficients of 2.99 x 10 -11 , 2.39 x 10 -11 and 5.98 x 10 -11 m 2 s -1 respectively. The effective diffusivity of pigeon pea grains ranged from 2.1 x 10 -10 to 6.8 x 10 -10 m 2 s -1 , for the temperature range of 40 to 70 ° C, in a study performed by Silva et al. (2014). For Jatropha curcas, according to Siqueira et al. (2012), higher temperatures resulted in higher diffusion coefficients, ranging between 9.29 x 10 -10 and 41.48 x 10 -10 m 2 s -1 for grains and between 16.20 x 10 -10 and 68.11 x 10 -10 m 2 s -1 for fruits.

CONCLUSION
• In the conditions in which the present study was performed, we can conclude that the reduction of the dew point temperature and, consequently, of the relative humidity after the partial drying, increases the water reduction rate and reduces the drying time of the coffee grains.
DRYING KINETICS OF PEELED COFFEE SUBMITTED TO DIFFERENT TEMPERATURES AND RELATIVE... Table 7. Values of equivalent radius (R eq ) and effective diffusion coefficient (D eff ) of the peeled coffee grains, as a function of the combinations of dry bulb temperature (T bd ) and dew point temperature (T pd ) of the drying air, for first and second part of drying • Among the tested models, the Diffusion Approximation and Modified Midilli models were the ones that best fit the experimental data regarding the first and second drying stages of coffee grains (Coffea arabica L.), respectively. The effective diffusivity coefficient of coffee grains ranged from 0.81 x 10 -11 to 1.84 x 10 -11 m² s -1 during the first part of drying and from 1.49 x 10 -11 to 3.29 x 10 -11 m² s -1 during the second part of drying, increasing significantly with a reduction in the dew point temperature and an increase in the dry bulb temperature.