INTRODUCTION
Brazil is a leader in the world market for production and export of raw coffee. It has advanced technologies for production and crop protection and is prepared to offer high harvest yields. However, developing technologies that reduce drying time and energy consumption requires a more sustainable solution, which makes drying one of the main bottlenecks in Brazilian coffee farming (^{Borém, 2013}).
Technology currently available for drying coffee only increases drying rates by increasing temperature or airflow. However, coffee mass temperatures above 40 °C cause thermal damage, depreciating drink quality (^{Isquierdo, 2013}).
Drying kinetics of agricultural products has great importance to select suitable temperatures and times required for an adequate drying process and to obtain a final product of higher quality (^{Avhad & Marchetti, 2016}).
An alternative to increase drying rates without exceeding maximum tolerable temperatures for coffee is drying airflows higher than those used commercially. It is necessary to have experimental tests that provide data for process simulation before they are used on a commercial scale.
Several models have been fitted to describe drying process of hygroscopic capillaryporous products. Among these models are Midilli, Page, Thompson, Verma, Henderson and Pabis, modified Henderson and Pabis, twoterm, twoterm exponential, Newton, Wang and Sing, and Valcam (^{Corrêa et al., 2014}; ^{Goneli et al., 2009}; ^{Isquierdo, 2013}; ^{Resende et al., 2009}; ^{Siqueira et al., 2013}).
This research aimed to study the drying kinetics in a thin layer of coffee (Coffea arabica L.), cultivar Topázio, to adjust different mathematical models to the experimental values as a function of processing type, temperature, and drying airflow, as well as checking for differences in total drying time with each studied airflow.
MATERIAL AND METHODS
This study was carried out in the Laboratory of Agricultural Products Processing, Department of Engineering, Federal University of Lavras (UFLA), Minas Gerais State, Brazil.
The experiment was conducted with manually harvested coffee (Coffea arabica L. cv. Topázio) fruits. Only ripe or “cherry” fruits were selected from UFLA's experimental field. After harvesting, fruits were subjected to hydraulic separation to remove fruits of a low specific mass (dry, immature, insectdamaged, and malformed), followed by manual selection to remove immature and overripe fruits. Then, part of the fruits was taken to dryers, consisting of “natural” portion or processed through dry route, while the other part was peeled and subjected to spontaneous fermentation in water to remove mucilage under ambient conditions for 20 hours, forming the portion of pulped coffee processed by wet route. After this period, parchment coffees were washed under running water until mucilage was removed entirely and, afterward, a pulped coffee lot was sent for drying.
Drying was carried out in mechanical fixedlayer dryers, which allow flow and temperature control of drying air with precision until coffee reaches 0.125±0.005 (db). Coffee fruits were weighed during the entire drying process for subsequent preparation of curves, drying times, and rates.
Each dryer consisted of four removable trays with perforated bottoms. Four circularsection tubes with a diameter of 0.125 m and a height of 0.17 m, located on a plenum for uniform airflow, were placed on each tray. After processing, this coffee was placed inside these tubes, with approximately 0.17 and 0.315 kg each sample, corresponding to a thin layer of 0.025 and 0.043 m of pulped and natural coffee, respectively.
At the beginning and end of drying process, coffee fruit and parchment coffee moisture contents were determined using standard oven method at 105±3 °C for 24 hours, according to the Rules for Seed Testing (^{Brasil, 2009}). Yet for processed dry coffee, moisture content was determined by the ISO 6673 standard method (^{International Organization for Standardization – ISO, 2003}). After obtaining mass and initial moisture content of coffee fruits and parchment coffee, drying was monitored by gravimetric method (loss of mass) until reaching a content of 0.125±0.005 (db), using a 0.01g analytical scale, according to the equation below:
Where:
U_{t} is the moisture content at time t (kg water kg^{−1} dry matter, db);
Ma_{i} is the initial water mass (kg);
Mt_{i} is the initial total mass (kg);
Mt_{t} is the total mass at time t (kg),
M_{ms} is the dry matter mass (kg).
Water evaporation speed was determined from the drying rate of the product, according to the following expression:
Where:
DR is the drying rate (g water kg^{−1} dry matter h^{−1});
U_{prev} is the moisture content in the previous time (g water kg^{−1} dry matter, db);
U_{c} is the current moisture content (g water kg^{−1} dry matter, db),
Δt is the time interval between weighings (h).
Drying system consisted of three fixedlayer dryers, which allowed controlling dryingairflow and temperature with precision, using an electronic panel.
Drying airspeed was measured using a paddle anemometer. It was regulated and kept constant for all treatments at 0.4, 1.0, 1.6, and 2.2 m s^{−1}, corresponding to flows of 24, 60, 96, and 132 m^{3} min^{−1} m^{−2}, respectively. Two temperatures were used for drying air (40 and 45 °C), which were monitored using mercury thermometers placed in the middle of coffee mass. Different drying conditions were obtained depending on combination among processing, temperature, and drying airflows.
Moisture ratio (MR) is essential for drying data analysis since it describes different thinlayer drying models. During drying, it was determined as in [eq. (3)], as a function of evaluated variables. Values of MR as a function of drying time for all tested conditions were fitted to models used to describe coffee drying kinetics, as shown in Table 1.
Model designation  Model  Equation 

Dois termos 

(6) 
Exponencial de dois termos 

(7) 
Henderson & Pabis modificado 

(8) 
Henderson & Pabis 

(9) 
Midilli 

(10) 
Newton 

(11) 
Page 

(12) 
Thompson 

(13) 
Verma 

(14) 
Wang e Sing 

(15) 
Valcam 

(16) 
Modelo Proposto 

(17) 
MR – moisture ratio;
t – drying time (h);
k, k_{0}, and k_{1} – drying constants;
a, b, c, d, and n – model coefficients.
Where:
MR is the moisture ratio;
U is the moisture content of the product at time t (decimal, db);
U_{e} is the equilibrium moisture content of the product (decimal, db), and
U_{i} is the initial moisture content of the product (decimal, db).
Hygroscopic equilibrium moisture content was calculated by eqs (4) and (5) for natural and pulped coffee (^{Afonso Júnior, 2001}), respectively.
Where:
Ue is the equilibrium moisture content of the product (decimal, db);
T is the drying air temperature (°C),
RH is the relative humidity of the drying air (decimal).
Mathematical models frequently used to represent the drying kinetics of agricultural products were fitted to the experimental data of coffee MR obtained for each type of processing and drying air condition (Table 1).
Nonlinear regression analyses were performed by the GaussNewton method using the software STATISTICA 7.0^{®} (Statsoft, Tulsa, USA) to adjust mathematical models. The best model was chosen based on statistical parameters, namely: standard deviation of estimates (SD), relative mean error (P), coefficient of determination (r^{2}), and trend of distribution of residues. The standard deviation of estimates and relative mean error were calculated by eqs (18) and (19), respectively.
Where:
SD is the standard deviation of estimates (decimal);
Y is the value observed experimentally;
DF is the degrees of freedom of the model;
P is the relative mean error (%), and
n is the number of observed data.
Drying time was evaluated in a completely randomized design, in a 2 x 4 factorial scheme for each coffee processing system. Treatments consisted of two temperatures and four drying airflows, with four repetitions. Data were subjected to analysis of variance (ANOVA), and means were compared by Tukey's test at 5% significance using the SISVAR^{®} software (^{Ferreira, 2011}).
RESULTS AND DISCUSSION
Table 2 shows the drying times, initial moisture content of coffee fruits and parchment coffee, final moisture content of processed natural and pulped coffee, and mean and maximum drying rates as a function of temperature and drying airflow.
Processing  Tem (°C) 
Airflow (m^{3} min^{−1} m^{−2}) 
Drying time (h)  Moisture content (db) 
Drying rate (g kg^{−1} h^{−1}) 


Initial  Final  Mean  Maximum  
NAT  40  24  73.20  2.19  0.125  39.84  209.25 
60  71.06  2.19  0.125  41.77  217.17  
96  67.92  2.19  0.125  42.44  223.33  
132  66.10  2.20  0.125  44.16  234.27  
45  24  47.93  1.93  0.125  43.78  222.09  
60  45.84  1.93  0.125  45.57  240.23  
96  44.08  1.96  0.125  47.57  239.78  
132  44.46  1.95  0.125  48.79  256.78  
CD  40  24  13.30  0.98  0.125  64.27  164.85 
60  12.84  0.99  0.125  69.91  177.63  
96  12.59  0.99  0.125  70.24  177.99  
132  12.13  0.99  0.125  76.45  178.19  
45  24  10.65  1.00  0.125  80.35  210.79  
60  10.44  1.01  0.125  81.24  211.08  
96  10.10  1.01  0.125  88.77  211.20  
132  10.15  1.01  0.125  88.27  221.00 
According to Table 1, an airflow of 24 m^{3} min^{−1} m^{−2} and increased temperatures (40–45 °C) reduced by 35 (73.20–47.93 hours) and 20% (13.30–10.65 hours) drying times for natural and pulped coffee, respectively. An increased airflow (24–132 m^{3} min^{−1} m^{−2}) for natural coffee provided reductions of 10 (73.20–66.10 hours) and 7% (47.93–44.46 hours) in drying time for temperatures of 40 and 45 °C, respectively. The same increase in airflow for pulped coffee provided reductions of 9 (13.30–12.13 hours) and 5% (10.65–10.15 hours) for temperatures of 40 and 45 °C, respectively.
^{Santos et al. (2016)} evaluated temperature influence on drying time in palm fruits and found that a temperature range between 50 and 70 °C decreased drying times from 720 to 540 minutes. ^{Camicia et al. (2015)} found a reduction in drying time for cowpeas from 10.4 to 2.1 hours for temperatures of 30 and 50 °C, respectively. These results are in agreement with those obtained in our study. ^{Siqueira et al. (2017)} observed that the higher the temperature, the greater the difference between partial vapor pressure of dry air and the product, removing water easily and quickly.
The following factors are attributed to a reduction in drying time due to an increase in temperature: increased temperatures reduce water viscosity and directly influence fluid resistance to flow, while a decreased viscosity facilitates diffusion of water molecules through product capillaries (^{Corrêa et al., 2010}; ^{Tohidi et al., 2017}; ^{Araújo et al., 2017}), in addition to providing an increase in water molecule vibration levels, which also contributes to increasing drying rates.
Figure 1 (a) and (b) show the drying rates as a function of moisture content in coffee fruits and parchment coffee submitted to complete drying in a dryer, respectively.
As shown in Figure 1 (a) and (b), decreased temperatures provide high drying rates for the same moisture content, and these different rates at different temperatures are high at the beginning of drying, and such differences decrease considerably as coffee fruits and parchment coffee get drier. Airflow effect for the same processing and temperature is more evident at the beginning of drying. As drying process progresses, water removal from coffee becomes more difficult due to a stronger connection between water and other bean constituents. Thus, drying rates for the four airflows and two temperatures tend to be similar or get closer at the end of the process.
Drying rates of pulped coffee become slightly steady for moisture contents from 0.7 to 0.4 (db). This behavior is related to a constant drying rate, as there is much free water in the surroundings of coffee beans before that interval, greatly increasing drying rates. However, the amount of water present in the product is much lower for the period after the abovementioned interval, thus reducing drying rates.
Overall, water withdrawal speed from fruits decreases as drying progresses. This is because differences in heat and mass transfer between product and drying air are not compensated, and fruit temperature tends to increase, reaching a value close to that of drying air due to a high need for energy for evaporation of water, which is more strongly bonded (^{Alves et al., 2013}; ^{Siqueira et al., 2016}, ^{2017}).
Table 3 shows the statistical parameters for the eleven models used to describe drying kinetics of natural and pulped coffee, and respective coefficients of determination (r^{2}), standard deviation of estimates (SD), and relative mean error (P). The mean initial moisture content was 2.07 and 1.00 kg water kg^{−1} dry matter (db) for natural and pulped coffee, respectively, after subjected to both temperatures and the four airflows.
Pulped coffee (40 °C)  

Model  Airflow (m^{3} min^{−1}m^{−2})  
24  60  96  132  
SD  P (%)  r^{2}(%)  SD  P (%)  r^{2}(%)  SD  P (%)  r^{2}(%)  SD  P (%)  r^{2}(%)  
6  0.03  29.57  99.47  0.04  48.03  98.67  0.04  50.66  98.74  0.03  12.10  99.48  
7  0.04  68.18  98.32  0.04  51.16  98.59  0.04  54.14  98.65  0.04  25.31  98.58  
8  0.02  23.36  99.71  0.08  46.47  94.04  0.09  38.27  95.03  0.02  4.57  99.79  
9  0.04  63.22  98.46  0.04  48.03  98.67  0.04  50.67  98.74  0.04  24.00  98.66  
10  0.02  19.61  99.68  0.02  15.29  99.69  0.02  15.94  99.70  0.02  6.61  99.74  
11  0.04  68.18  98.32  0.04  51.16  98.59  0.04  54.14  98.65  0.04  25.31  98.58  
12  0.03  29.01  99.33  0.03  23.33  99.35  0.03  23.93  99.41  0.03  12.97  99.31  
13  0.04  68.18  98.32  0.04  51.15  98.59  0.04  54.15  98.65  0.04  25.32  98.58  
14  0.03  31.43  99.40  0.02  23.88  99.44  0.04  54.14  98.65  0.03  12.72  99.41  
15  0.02  13.98  99.72  0.02  12.53  99.64  0.02  15.84  99.65  0.02  2.73  99.69  
16  0.01  6.78  99.87  0.01  4.43  99.85  0.01  5.71  99.87  0.01  3.21  99.84  
17  0.01  3.85  99.88  0.01  5.85  99.86  0.01  5.20  99.87  0.01  3.17  99.85  
Pulped coffee 45 °C  
6  0.03  37.23  99.38  0.02  23.48  99.60  0.02  30.35  99.60  0.02  38.94  99.53  
7  0.04  76.11  98.65  0.02  29.03  99.51  0.02  37.38  99.52  0.03  83.47  98.91  
8  0.12  128.02  90.73  0.04  56.92  98.95  0.02  36.60  99.68  0.15  205.23  84.59  
9  0.04  72.50  98.70  0.03  56.93  98.95  0.03  72.78  98.90  0.03  79.41  98.96  
10  0.02  29.24  99.57  0.02  21.58  99.66  0.02  26.21  99.67  0.02  32.76  99.64  
11  0.04  76.11  98.65  0.03  61.01  98.88  0.03  78.32  98.81  0.03  83.45  98.91  
12  0.03  38.50  99.23  0.02  24.27  99.49  0.02  30.12  99.51  0.03  41.11  99.40  
13  0.04  76.11  98.65  0.03  61.03  98.88  0.04  78.35  98.81  0.03  83.47  98.91  
14  0.04  76.10  98.65  0.02  27.14  99.68  0.04  78.35  98.81  0.02  32.38  99.69  
15  0.03  33.09  99.37  0.03  42.01  99.40  0.03  56.64  99.42  0.03  61.99  99.21  
16  0.02  7.99  99.79  0.01  12.12  99.85  0.01  16.85  99.85  0.01  12.18  99.84  
17  0.02  7.81  99.76  0.01  7.48  99.84  0.01  7.81  99.86  0.02  3.40  99.82  
Natural coffee 40 °C  
6  0.01  2.43  99.95  0.01  4.23  99.93  0.01  2.99  99.96  0.01  3.87  99.94  
7  0.02  18.00  99.42  0.04  34.88  97.21  0.02  19.60  99.47  0.02  23.40  99.26  
8  0.01  1.61  99.96  0.00  2.63  99.99  0.00  2.05  100.00  0.01  3.87  99.94  
9  0.03  24.46  98.63  0.03  25.85  98.66  0.03  26.55  98.67  0.03  29.56  98.46  
10  0.01  2.45  99.96  0.00  1.08  99.99  0.00  2.21  99.98  0.01  2.66  99.96  
11  0.04  32.92  97.28  0.04  34.88  97.21  0.04  34.80  97.44  0.04  38.02  97.07  
12  0.01  4.30  99.94  0.00  4.80  99.96  0.01  5.52  99.95  0.01  6.62  99.92  
13  0.01  4.14  99.92  0.01  3.59  99.90  0.01  3.12  99.95  0.01  3.17  99.93  
14  0.01  3.11  99.91  0.04  34.88  97.21  0.01  4.21  99.93  0.04  38.02  97.07  
15  0.12  87.40  78.66  0.12  98.53  76.07  0.12  101.93  76.40  0.13  114.05  72.19  
16  0.02  11.59  99.65  0.02  11.82  99.61  0.02  13.14  99.61  0.02  16.08  99.45  
17  0.01  2.04  99.96  0.01  2.54  99.93  0.01  1.60  99.98  0.01  2.69  99.96  
Natural coffee 45 °C  
6  0.01  1.78  99.96  0.01  2.06  99.96  0.01  2.22  99.95  0.01  2.22  99.94  
7  0.01  2.46  99.94  0.02  12.73  99.26  0.01  3.25  99.93  0.02  17.10  99.07  
8  0.01  1.78  99.96  0.01  2.06  99.96  0.00  1.48  99.99  0.00  0.86  100.00  
9  0.02  11.35  99.61  0.01  8.01  99.71  0.02  12.02  99.56  0.02  12.15  99.57  
10  0.00  1.04  99.98  0.00  1.24  99.98  0.00  1.07  99.98  0.00  0.83  99.98  
11  0.02  15.96  99.17  0.02  12.73  99.26  0.02  17.06  99.05  0.02  17.10  99.07  
12  0.00  2.84  99.97  0.00  1.45  99.98  0.00  2.91  99.97  0.01  3.88  99.95  
13  0.01  1.82  99.94  0.01  3.17  99.90  0.01  2.11  99.93  0.01  2.14  99.91  
14  0.01  2.53  99.94  0.01  2.59  99.95  0.01  3.17  99.93  0.01  4.07  99.90  
15  0.08  45.58  91.63  0.07  36.89  93.38  0.08  46.94  91.04  0.08  47.22  90.98  
16  0.01  3.10  99.96  0.01  2.42  99.96  0.01  3.37  99.95  0.01  2.55  99.95  
17  0.01  1.67  99.97  0.01  1.94  99.97  0.01  1.95  99.96  0.01  2.67  99.94 
The analysis of statistical parameters was performed separately for each type of processing due to high differences in drying kinetics of natural and pulped coffee.
The analysis of a single parameter is not a useful tool for evaluation of nonlinear models, requiring a joint analysis of parameters: coefficient of determination, standard deviation of estimate, and relative mean error. The ability of a model to accurately describe a particular physical process is inversely proportional to the standard deviation of estimates. Relative mean errors below 10% are recommended (^{Madamba et al., 1996}; ^{Mohapatra & Rao, 2005}).
Regarding the coefficients of determination (r^{2}) of pulped coffee, both Valcam (16) and Proposed Model (17) presented the highest values (above 99.76%). Natural processed coffee presented a coefficient of determination (r^{2}) higher than 97.07% for almost all models used, except for Wang and Sing model (15), which, according to ^{Madamba et al. (1996)}, is a value considered acceptable to describe drying phenomena.
Considering the criterion of relative mean errors (P) below 10% for acceptable fit, the results obtained for pulped coffee showed that only the Proposed Model (17) presented a satisfactory fit for dry coffee at 45 °C (P<7.81%), and the best value of relative mean error for dry coffee at 40 °C (P<5.85%). Additionally, the models twoterm (6), modified Henderson & Pabis (8), Midilli (10), Page (12), Thompson (13), and Proposed Model (17) had relative mean errors lower than 10% for natural coffee, and they can also be used in other applications.
All models used presented SD<0.05, except for the modified Henderson & Pabis (8) and Wang and Sing (15) models.
Regarding the behavior (or trend) of distribution of residuals for the studied models, the models Valcam (16) for pulped coffee, Midilli (10) for natural coffee, and Proposed Model (17) had a random distribution of residuals for all studied conditions.
Among the models used in this study to describe the drying process of pulped coffee and considering the analysis of coefficients of determination, relative mean errors, standard deviations of estimates, and trend of distribution of residuals, the Proposed Model (17) presented the best fit. The models showing the best fit for natural coffee were Midilli (10) and Proposed Model (17), also considering the same evaluation parameters.
The Proposed Model (17) was adopted to represent drying kinetics of natural and pulped coffees under the conditions considered in this study due to its satisfactory fit under all drying conditions and ease of use.
Table 4 shows the coefficients of the Proposed Model for natural and pulped coffee, fitted to the observed data of thinlayer drying kinetics under the conditions considered in this experiment.
Processing  Temperature (°C) 
Airflow (m^{3} min^{−1} m^{−2}) 
Model coefficient  

a  b  k_{0}  k_{1}  N  
Natural  40  24  33.3836  33.1341  15.5549  44.3614  0.0083 
60  46.0625  46.0433  0.3655  0.9937  0.3984  
96  33.8310  33.5280  18.1085  47.3185  0.0080  
132  60.2551  60.3382  1.7779  5.1655  0.0861  
45  24  0.1086  0.8896  0.7714  0.1474  0.0480  
60  0.7720  0.2166  1.1412  2.3307  0.0510  
96  0.1208  0.8770  0.4736  0.1119  0.0720  
132  0.0916  0.9066  0.2470  0.0402  0.1532  
Pulped  40  24  0.3742  0.6176  0.0863  0.4642  0.0885 
60  0.3402  0.6503  0.0370  0.3516  0.1082  
96  0.3101  0.6839  0.0036  0.2948  0.1138  
132  0.2371  0.7575  0.0316  0.1994  0.1340  
45  24  18.1339  17.6652  22.3481  52.5765  0.0072  
60  17.3364  16.6682  23.0004  52.5763  0.0075  
96  21.1488  20.5184  21.9210  52.5764  0.0081  
132  20.4160  19.8862  23.7046  52.5764  0.0076 
Figures 2 and 3 show the behavior of the moisture ratio observed and estimated by the Proposed Model (17) for natural and pulped coffee dried at 40 and 45 °C in a thin layer. The high agreement between the moisture ratios obtained experimentally and those estimated by the Proposed Model for all studied conditions confirms the satisfactory fit of this model to describe drying kinetics for each type of processing under the studied conditions.
Table 5 shows the splitting of drying treatment effects for each temperature and airflow on the drying times of pulped and natural coffee. A significant interaction was observed between temperatures and drying airflows only for pulped coffee. Therefore, we presented means of natural coffee treatments and their comparisons with means of temperature and airflow.
Processing  Temperature (°C) 
Airflow (m^{3} min^{−1} m^{−2}) 
Mean  

24  60  96  132  
CD  40  13.30aA  12.84aB  12.59aC  12.13aC  
45  10.65bA  10.44bAB  10.10bB  10.15bB  
NAT  40  73.20  71.06  67.92  66.10  69.57a 
45  47.93  45.84  44.08  44.46  45.58b  
Mean  60.57A  58.45AB  56.00BC  55.28C 
Means followed by different lowercase letters in the columns and uppercase letters in the rows differ from each other for each type of coffee by Tukey's test at 5% probability.
Regarding the airflows for both drying temperatures, a flow of 24 m^{3} min^{−1} m^{−2} had the longest drying times for pulped and natural coffee. But at 45 °C, no significant differences were observed when compared to a flow of 60 m^{3} min^{−1} m^{−2} for both pulped and natural coffee.
Significant differences were observed between temperatures for all airflows in CD processing. The two highest flows, however, did not differ from each other for a temperature of 40 °C, which was also seen for the three highest flows at 45 °C. In this sense, flows of 96 and 132 m^{3} min^{−1} m^{−2} are recommended to speed up drying process regardless of the air temperature.
CONCLUSIONS
The Proposed Model presented the best fit to natural and pulped coffee drying data at drying air temperatures of 40 and 45 °C and airflows from 24 to 132 m^{3} min^{−1} m^{−2}.
Temperature and airflow rises increase coffee drying rates and thereby reduce drying times.
The shortest drying times can be achieved at 45 °C and at 96 and 132 m^{3} min^{−1} m^{−2} regardless of the coffee processing type.