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Analysis of the heat and mass transfer during coffee batch roasting
Journal of Food Engineering 78 (2007) 1141–1148 www.elsevier.com/locate/jfoodeng
Analysis of the heat and mass transfer during coffee batch roasting J.A. Herna´ndez
a,*
, B. Heyd b, C. Irles c, B. Valdovinos b, G. Trystram
b
a
b
Research Center of Engineering and Applied Sciences (CIICAp), Autonomous University of Morelos State (UAEM), Av. Universidad No. 1001 Col. Chamilpa, CP 62210, Cuernavaca, Mor., Mexico Joint Research Unit Food Process Engineering (Cemagref, ENSIA, INAPG, INRA) ENSIA, 1 Avenue des Olympiades, 91744 Massy Cedex, France c National Institute of Perinatology, Montes Urales 800, Lomas, de Virreyes, CP 11000, Mexico DF Received 21 May 2005; accepted 19 December 2005 Available online 17 February 2006
Abstract In this paper, an experimental and theoretical analysis of the heat and mass transfer was carried out to evaluate the coffee bean’s temperature and moisture content during the roasting in batch system. Arabica coffee from Colombian origin was roasted using different air temperatures between 190 and 300 C, during 10 min. Bean’s temperature and weight loss have been measured on-line by robust sensors. The experimental results allowed better understanding of the phenomena that appears during roasting. For example, an evident increase of the bean’s temperature curve tendency is observed when this one exceeds the 250 C, it is probably due to the end of exothermic reactions and to the beginning of the bean burn. The experimental data of moisture shown a decrease of 10.5% d.b. to 0–7% d.b. A dynamic model is evaluated and analyzed to predict bean’s temperature and moisture content during roasting. The results (simulations and experimental kinetics) were in good agreement. This model can be used for on-line estimation and control of coffee roasting. 2006 Elsevier Ltd. All rights reserved. Keywords: Heat and mass transfer; Coffee roasting; On-line measures
1. Introduction In order to obtain a good cup of coffee, the step of roasting is very important to develop specific organoleptic properties (flavors, aromas and color), underlying the quality of the coffee. The amount of heat transferred to the bean is essential in the roasting process. The process can be divided into two phases. The first phase corresponds to the drying (bean’s temperature below 160 C) and the second phase is the roasting (bean’s temperature between 160 and 260 C). In this last phase, pyrolytic reactions start at 190 C causing oxidation, reduction, hydrolysis, polymerisation, decarboxilation and many other chemical changes, leading to the formation of substances essential to give among other, the sensory qualities of the coffee. These moisture loss and chemical reactions are accompanied by important changes *
Corresponding author. Tel.: +52 777 3 29 70 84; fax: +52 777 3 29 79
84. E-mail address: [email protected] (J.A. Herna´ndez). 0260-8774/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2005.12.041
(color, volume, mass, form, bean pop, pH, density, volatile components) and generate CO2, of which a part escapes and other part is retained in the cells of the beans. After this second phase, the beans must be rapidly cooled to stop the reactions (using water or air as cooling agent) and to prevent an excessive roast which alter the quality of the product (Illy & Viani, 1998; Nagaraju, Murthy, Ramalakshmi, & Srinivasa, 1997; Raemy, 1981; Raemy & Lambelet, 1982; Schwartzberg, 2002; Singh, Singh, Bhamidipati, Singh, & Barone, 1997; Sivetz & Desrosier, 1979). During the process, several parameters can be used as indicators to determine the degree of roasting (aroma, flavor, color, bean’s temperature, pH, chemical composition, bean pop, mass loss, gas composition and volume) (Dutra, Oliveira, Franca, Ferrez, & Afonso, 2001; Herna´ndez, 2002; Illy & Viani, 1998; Mendes, De Mendes, Aparecida, & da Silva, 2001; Schwartzberg, 2002). Nevertheless, in the industry, in order to obtain the optimal degree of roasting and to control the quality of the product, the roast master take up an essential position. In one hand, he interprets the
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algorithm is managed in bash (Bourne, 2002); Type K Thermocouples allowed to measure internal and external temperatures of the beans and to control the air temperature with a precision of ±0.5 C. One bean is drilled in order to insert a thermocouple 4 mm below the surface (internal temperature), and another thermocouple about 0.2 mm below the surface in order to measure the near surface temperature (see Fig. 1B). The beans are placed on a mesh to keep them on static suspension, where convection is the predominant mode of heat transfer. Beans weight is automatically measured using an electronic scale METTLER (SB16001) and controlled by the computer (see Fig. 1A). A program written in bash makes the weight acquisition each minute. Before each weight acquisition, the fan of the roaster is automatically stopped for 8 s to stabilize the measure.
physic measure (temperature and time of stay), and in the other hand, the organoleptic properties of the coffee beverage (color, aroma and flavor). However, these measures are obtained out-line. Automation is limited by the lack of captors allowing to follow the quality in real time, and by the process conditions (the mass of beans is always in agitation) which make instrumentation difficult (Herna´ndez, 2002; Schwartzberg, 2002). It is important to mention that the control of temperatures and duration, in industry, are only effective, if the quality of the raw material does not vary. Today, the chemical reactions are extensively studied by Illy and Viani (1998), nevertheless, coffee roasting is slightly studied as an unit operation. Indeed, in this operation, a specific instrumentation, working in real time and taking into account the variables of the product does not exist. Several variations are presented as a function of the raw material and of the process conditions. The aim of this work is to measure and analyze the bean temperature and moisture content during coffee roasting and to evaluate the model in the purpose of process control.
3. Results During coffee roasting, mass and temperature are measured on-line. The results will allow a better understanding of the process, and a validation of the mathematical model. Fig. 2 shows the evolution of the internal and external bean’s temperature and of the air temperature (C) during the roasting. These curves (Fig. 2) put in evidence the effect of the air temperature on the evolution of the bean’s temperature. The internal bean’s temperature has an exponential behavior described by Schwartzberg (2002) if bean’s temperature is below 250 C. An evident deviation with exponential kinetic is observed between 80 and 100 s of roasting (Fig. 2B) for experiments where the bean’s temperature become higher than 260 C. When the optimal bean’s temperature is surpassed, the exothermic reactions responsible of the aroma and flavor are reduced and the beans begin to be burn. This phenomenon is called over-roasting by Coste (1968), it can
2. Material and methods Colombia green coffee beans (Arabica) are roasted using hot air flow as heating medium. The experiments are carried out at constant air velocity of 4 m/s for constant air temperatures (190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290 and 300 C) during 10 min. The experiments are done with three replicates. Fig. 1 depicts the data acquisition and processing using a computer equipped with a temperature acquisition system (SCB7 thermocouple conditioner and Arcom PCAD12/16H A/D converter) and several software. The low level task (data acquisition and I/O port programming) are written in C (Lawyer, 2000; Photis, 1999), real time data processing are done with Octave (Eaton, 2001) and
Thermocouples carte ADC
Bean Coffee
carte SCB7
C captemp (write in bash)
R R
fichie (data)
R
octave
relais
balance
Temperatures
balance cafe.ensia.inra.fr
capmas (in bash)
fichie (data) octave
relais
C
Mass
A
B
Fig. 1. Scheme of experimental data used (temperatures and mass).
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Fig. 2. Evolution of bean’s temperatures for roasting at 190 and 300 C.
be responsible of the observed deviation. Consequently, this confirm that the bean’s temperature versus the time can be an indicator of the roast-degree during coffee roasting. It is important to mention that Schwartzberg (2002) stopped the process when the bean temperature reach 238 C, so he never observed this phenomenon. During roasting, weight loss is measured each minute. The results in Fig. 3, show that we obtained a good repeatability of the measures (two repetition at 300 and 190 C, and three at 250 C). After a short stage of latency, we observe a quasi linear behavior followed by a marked deceleration. Weight loss clearly depend on the air temperature of the roasting time. After 10 min of process the percentage of mass loss ranged from 3% to 12% depending on roasting temperature. Similar results are reported by severals authors (Da Porto, Nicoli, Severini, Sensidoni, & Lerici, 1991; Dutra et al., 2001; Pittia, Dalla, Pinnavaia, & Massini, 1996; Schwartzberg, 2002). This authors also reported weight loss differences due to types of roasting machines, duration, type of bean and air temperature. According to Guyot (1993) and Illy and Viani (1998), the moisture content is about 8–12% d.b. in green coffee
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4. Heat and mass transfer modelling The heat and mass transport mechanisms during batch roasting (roaster using hot air flow) are given by the equations proposed by Schwartzberg (2002): • Moisture loss, the diffusive water transport in the bean is given by dX 4:32 109 X 2 9889 ¼ exp ð1Þ dt T b þ 273:15 d 2p
14 12
and below 5% d.b. in roasted coffee. Furthermore, volatile components are formed during roasting, inducing also noticeable mass loss. Dutra et al. (2001) determined weight loss during the process for 300 g of green coffee using a direct heating. They found two different speeds for mass loss: the first period, between 0 and 7 min, shows a linear kinetic with a weak slope, this period corresponds to a moisture and volatiles losses, the second period from 7 to 12 min the weight loss follows a right line with a strong slope, and this corresponds to a loss of CO2 and organic components of the bean. Besides, they showed that loss of CO2 increases when the moisture content diminishes significantly. The evolution of the mass loss can therefore be a criterion of the roasting degree, but it is not a key criterion for us because weight is difficult to measure on-line in the industry.
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Time (s) Fig. 3. Experimentals kinetics of weight loss.
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X: moisture content (kgwater/kgdry matter); Tb: internal temperature of the bean (C). The water loss is governed by an Arrhenius type equation, proportional to X2; and dp: effective bean diameter. • Heat transfer, the rate of temperature rise of the beans is given by dT b GC pa ½T ae T as Qa!m þ Qm!b þ mbs Qr þ Lv dX dt ¼ dt mbs ð1 þ X ÞC pb ð2Þ
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where Tae and Tas are respectively the in-air and out-air temperature (C). G is the air mass-flow rate (kg/s). Cpa and Cpb are respectively the air and bean heat capacity (kJ/kg C). mbs is the dry weight of the bean kg dry coffee and Lv is the latent heat of vaporization of the bean moisture, Schwartzberg (2002) gives 2790 kJ/kg. In this balance Eq. (2), the heat transfer from hot air to bean GCpa[Tae Tas], the heat transfer from air to metal parts Qa!m, the heat transfer from metal parts to beans Qm!b, the heat production by roasting reactions Qrmbs and the heat necessary to moisture evaporation at the bean surface during the roasting Lv ðdX Þmbs are considered. Howdt ever, in this work, the contact area between coffee beans and metal part is negligible. It is also possible to assume that the heat transfer from hot air to metal is negligible because the temperature of the metal is equal to the air temperature. Under this two hypothesis, the model is simplified as follows: dT b GC pa ½T ae T as þ mbs Qr þ Lv dX dt ¼ ð3Þ mbs ð1 þ X ÞC pb dt To determine [Tae Tas] in Eq. (3), a balance of air temperature is considered by Schwartzberg (2002). Under the previous hypothesis, it is possible to write: aAab ½T ae T as ¼ ðT ae T b Þ 1 exp ð4Þ GC pa where a is the effective air-to-bean heat transfer coefficient (W/m2 C), Aab is the area (m2) across which air-to-bean heat transfer occurs. 4.1. Properties estimation To solve Eq. (2) by considering Eq. (4), it is necessary to know a, Cpb and Qr: • Effective air-to-bean heat transfer coefficient, a, was estimated by Eq. (5) reported by Schwartzberg (2002): a¼
he 1 þ 0:3 Bi
ð5Þ
where, he is the heat transfer coefficient at the air–bean surface calculated by the Ranz–Marshall correlation (Perry & Green, 1998) and Bi (Biot number) is used to correct the overall air–bean heat transfer coefficient for heat transfer resistance in the bean (Kreith, 1967). • Specific heat of the coffee bean, Cpb, the values used are obtained by Eq. (6) reported by Schwartzberg (2002): C pb ð1 þ X Þ ¼ 1:099 þ 0:0070T b þ 5:0X
ð6Þ
• Exothermic roasting reaction, Qr (rate of exothermic heat production), in kJ/(kg dry coffee) s, was calculated using Eq. (7) reported by Schwartzberg (2002) Ha H et H e Qr ¼ A exp ð7Þ Rg ðT b ðKÞÞ H et
where, Ha is the energy of activation, Rg is the perfectgas-law constant, A, in kJ/(kg dry coffee) s, is the Arrhenius equation prefactor times the amount of heat generated per unit amount of reaction. Schwartzberg (2002) obtained HRga ¼ 5500 K, A = 116,200 kJ/(kg dry coffee) s and Het = 232 kJ/kg. Measured bean properties: • Aab = 1.4 · 104 m2 equivalent sphere area. • mbs = 1.75 · 104 kg dry matter. • db = 6.6 mm equivalent sphere diameter. 4.2. Model solution To solve the system of Eqs. (1)–(7), we wrote a computer program in Octave (Eaton, 2001). This program works in the following way: at instant t = 0, we know: • the initial bean temperature Tb initial = 29 C, • the initial bean moisture X initial = 0.105 kg water/kg dry matter, • the in-air temperature Tae, measured on-line. These data allow to calculate in time t = 0: • the effective air-to-bean heat transfer coefficient a (Eq. (5)), • the out-air temperature Tas (Eq. (4)), • the rate of moisture loss dX (Eq. (1)), dt • the specific heat of the coffee bean Cpb(1 + X) (Eq. (6)), • the rate of exothermic heat production Qr (Eq. (7)). The set of differential equations was numerically integrated using fourth-order Runge–Kutta method written in Octave (Eaton, 2001). 4.3. Simulation of the heat and mass transfer An important characteristic of the model is that no parameter was adjusted to describe the bean’s temperature and moisture content. The program was written in order to estimate the bean’s temperature and moisture content versus time, for a hot air roaster with 25 g of green coffee in different constant air temperatures (Tae from 190 to 300 C). Fig. 4 shows agreement between experimental and simulated bean’s temperature for three roasting temperatures. This three kinetics are representatives for all the experiments. Below 250 C, the model fits very well the data. For hight bean’s temperature, the model do not predict the small deviation which we had already observed in the experimental part (Fig. 2B). The deviation can be explained by a beginning of an over-roasting, the exothermic reaction parameters (Eq. (7)) given by literature are not valid for this experimental domain. Consequently, the model cannot consider this perturbation. It could be possible to add an other factor to take this phenomena into account, but we
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and CO2; the model, which only considers water loss, should give higher results. It would be interesting to measure the water content of the beans during roasting, and to develop a more physical model considering water diffusivity in the bean and mass transfer coefficient between bean and air. But the perturbation of bean’s temperature model induced by the bad estimated water loss is negligible. Bean reach the roasting air temperature in less than 180 s, and the moisture content simulation become bad after 300 s of roasting, when the heat transfer is very low.
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4.4. Sensitivity analysis 50
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preferred to keep a robust model with no adjusted parameter. The moisture content simulation using Eq. (1) leads to acceptable results (Fig. 5) for the beginning of the kinetic. After 300 s the model significantly underestimates the water content. The weight loss include water, volatiles 0.105
X (g H2O/g Dry matter)
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As shown in the previous section, the model reproduced with good accuracy the experimental data (Tb and X). However, this model is developed for process control purpose, as a consequence it is important to test the robustness of the model for small perturbations of the process variables (Va, HR) or of the product characteristics (a, Aab, db, X, Cpb, Qr, mbs). A variation of air velocity, Va, from 2 to 6 m/s induces important changes on the Tb (see Fig. 6). This change can be explained, since the air velocity have an effect on the heat transfer coefficient calculated by Ranz–Marshall correlation (Perry & Green, 1998) he and the air mass-flow rate G. These two parameters are very important to predict the bean’s temperature and out-air temperature (see Eqs. (2) and (3)). Therefore, it is necessary to know the air velocity in an exact way. A variation of relative humidity, HR, from 20% to 80% (at ambient temperature) did not show an effect on the simulated bean’s temperature (data not shown), since when air is heated at 200 C, it become very dry (HR < 0.1%). Fig. 7 shows the effect of the bean’s size (db) on the bean’s temperature versus time. One can observe that the variations of db have a very important effect on the bean’s temperature Tb as mentioned by Schwartzberg (2002). When we consider a relatively small variation of bean’s dimensions (Aab), the prediction of the bean’s temperature vary appreciably (Fig. 8), thus this parameter Aab must be known with precision, because this value will reflect itself
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Fig. 6. Bean’s temperature versus time, (-): Va = 2, (): Va = 4 and (+): Va = 6 m/s.
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Fig. 7. Evolution of bean’s temperature versus time (line continuous) represents d = 4, (line discontinuous) is d = 5, (+) is d = 6 and (*) is d = 7 mm.
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-- Aab 0.03 m 2 - Aab 0.02 m2
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Time (s) Fig. 8. Variations of Aab in Eq. (2).
on the results of Tb. Besides, according to Eq. (4), the dimensions of the bean tends to be a very influential parameter on Tb, Tae and Tas. These dimensions can vary according to the batch of coffee to be roasted and during the course of the process Herna´ndez (2002). When a mixture of varieties (i.e. Arabica and Robusta) is roasted, these dimensions are delicate to determine in the batch and during the process, and by consequence a model to predict Aab is necessary inside the system of proposed equations.
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Fig. 9 presents the results of bean’s temperature versus time for different initial moisture contents X0. These curves show well that it exists a minor effect on the values of Tb. However, if initial moisture content is considered as null (X0 = 0), the simulated beans temperature increased quickly, it is normal, because the phase of drying does not take place. Therefore, the initial moisture is a very important factor that must be considered in the model bean’s temperature prediction, but the analysis of the initial moisture value X0, of 9%, 11% and 13% in d.b., have shown that the effect of this parameter on the kinetics of bean’s temperature is rather weak (see Fig. 9). Fig. 10 compares the two bean’s temperature kinetics, first using a constant Cpb (2.41 kJ/kg C) and the other a variable Cpb f(X, Tb) (Eq. (6)). Also, this figure shows the experimental data (indicated by *) of the bean’s temperature. It can be observed that the constant specific heat of the bean can also simulate the bean’s temperature but in a way less satisfactory than if one uses a variable Cpb for the bean’s temperature of roasting. Nevertheless to predict bean’s temperature over 260 C is better to use the constant Cpb but this it is not the case because carbonization begins. In addition, the dry weight of the beans mbs has also shown a change in the behavior of Tb versus t. To recapit-
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Fig. 9. Bean’s temperature versus time, line continuous is X0 = 9%, line discontinuous is X0 = 11%, + is X0 = 13% d.b.
J.A. Herna´ndez et al. / Journal of Food Engineering 78 (2007) 1141–1148 50 100 150 200 250 300 350
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Fig. 10. Bean’s temperature versus time, (line continuous) represent the variable specific heat of the bean (Eq. (6)) and (line discontinuous) is a constant Cpb = 2.41.
ulate this analysis of succinct sensitivity of the dynamic model, we showed that if the changes of operation variables and parameters linked with the product like: • the specific heat Cpb, • the mass of product m, • the air velocity Va. The model takes into account these parameters in order to predict the bean’s temperature in a satisfactory manner. For variables not controlled by the model as: • dimensions of the bean db (diameter) and Aab (surface of the bean), • initial moisture X0. It is necessary to measure the correct values in order to have a reliable model. Some variables, like relative humidity HR, does not influence the output of the model, under the studied conditions. 5. Conclusion The suggested model can be used in a satisfactory way to describe the behavior of the coffee bean’s temperature versus time, in an hot air roaster. This model showed a good agreement with all the experimental kinetics. It is necessary to note that no parameter were adjusted in this model. Furthermore, it can be used to determine how behavior can be affected by parameters variations which are not controlled in the course of roasting. If the parameters are known correctly (aAab, mbs, X, db, Cpb, Va and Tae), the model can be used directly, or with small modifications, for other roasting machines where the heat transfer takes place between air and metal and/or a heat transfer of metal towards the bean and the bean towards metal (i.e. Rotating-drum roaster, Rotating-bowl roaster, Scoop-wheel roaster and Swirling-bed roaster). Schwartzberg (2002) showed that bean’s temperature is a good criterion to evaluate coffee quality during roasting process. This temperature is diffi-
cult to measure on industrial roaster, but we showed that it is possible to calculate this temperature as a function of input temperature Tae. The model calculates the output air temperature Tcas at the same time, which is easy to measure on-line. If some perturbation appears, that it is not take into account by the model, the simulated bean’s temperature Tcb , will be wrong, this will appear on the difference between simulated and experimental temperature ð Tcae T ae Þ, allowing to adjust the model parameters online. Further studies will try to adapt this strategy to industrial roaster. Acknowledgment We thank to Prof. Henry G. Schwartzberg for his personal communication to this work. References Bourne, S. (2002). Bash (free software). In Bourne Again SHell. Available from http://www.gnu.org/software/bash/bash.html, consulted April 2005. Free Software Foundation. Coste, R. (1968). Le cafe´ier, G. P. Maisonneuve et Larose, 14 ed., 11, rue Victor-Cousin, Paris (Ve). Da Porto, C., Nicoli, M. C., Severini, C., Sensidoni, A., & Lerici, C. R. (1991). Study on physical and physico-chemical changes of coffee beans during roasting. Note 2. Italian Journal of Food Science, 3, 197–207. Dutra, E. R., Oliveira, L. S., Franca, A. S., Ferrez, V. P., & Afonso, R. J. (2001). A preliminary study on the feasibility of using the composition of coffee roasting exhaust gas for the determination of the degree of roast. Journal of Food Engineering, 47, 241–246. Eaton, J. W. (2001). Octave (free software). In GNU Octave. Available from http://www.octave.org/octave.html, consulted April 2005. University of Wisconsin. Guyot, G. (1993). Torre´faction: Mecanismes, transformation physiques et chimiques. In Journe´es du CAFE, CIRAD-CP a´ Montpellier, France. Herna´ndez, J. A. (2002). E´tude de la torre´faction: Mode´lisation et de´termination du degre´ de torre´faction du cafe´ en temps re´el. PhD Thesis in E´cole Nationale Supe´rieure des Industries Agricoles et Alimentaires, France. Illy, A., & Viani, R. (1998). Espresso coffee. San Diego, US: Academic press.
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Kreith, F. (1967). Transmission de la chaleur et thermodynamique. Masson et Cie e´diteurs, 120 Boulevard Saint Germain Paris VIe. pp. 129–137. Lawyer, S. D. (2000). Serial-HOWTO. In the Linux Serial HOWTO. Available from http://www.linuxdoc.org/HOWTO/Serial-HOWTO.html. Consulted January 2005. Mendes, L. C., De Mendes, H. C., Aparecida, M., & da Silva, A. P. (2001). Optimization of the roasting of robusta coffee (C. canephora conillo) using acceptability test and RSM. Food Quality and Preference, 12, 153–162. Nagaraju, V. D., Murthy, C. T., Ramalakshmi, K., & Srinivasa, R. P. N. (1997). Studies on roasting of coffee beans in a spouted bed. Journal of Food Engineering, 31, 263–270. Perry, R. H., & Green, D. W. (1998). Perry’s chemical engineers’ handbook. 0071344128. McGraw-Hill, pp. 5–24. Photis, G. (1999). Coffee-HOWTO.txt. In software coffee-HOWTO. Available from http://www.cl.cam.ac.uk/coffee/coffee.html, consulted January 2005, Cambridge University.
Pittia, P., Dalla, M., Pinnavaia, G., & Massini, R. (1996). Evoluzione di alcune caratteristiche fisiche del caffe` durante la torrefazione. Industrie Alimentari, 245–950. Raemy, A. (1981). Differential thermal analysis and heat flow calorimetry of coffee and chicory products. Thermochimica Acta, 43, 229– 236. Raemy, A., & Lambelet, P. (1982). A calorimetric study of self-heating in coffee and chicory. Journal of Food Technology, 17, 451–460. Schwartzberg, H. G. (2002). Modelling bean heating during batch roasting of coffee beans. In J. Welti-Chanes, G. Barbosa-Canovas, & J. M. Aguilera (Eds.), Engineering and food for the 21st century. London, New York, Boca Raton: CRC Press LLC. Singh, P., Singh, R., Bhamidipati, S., Singh, S., & Barone, P. (1997). Thermophysical properties of fresh and roasted coffee powders. Journal of Food Process Engineering, 20, 31–50. Sivetz, M., & Desrosier, N. W. (1979). Coffee technology. Westport: AVI Publishing Co., pp. 226–264.
Analysis of the heat and mass transfer during coffee batch roasting J.A. Herna´ndez
a,*
, B. Heyd b, C. Irles c, B. Valdovinos b, G. Trystram
b
a
b
Research Center of Engineering and Applied Sciences (CIICAp), Autonomous University of Morelos State (UAEM), Av. Universidad No. 1001 Col. Chamilpa, CP 62210, Cuernavaca, Mor., Mexico Joint Research Unit Food Process Engineering (Cemagref, ENSIA, INAPG, INRA) ENSIA, 1 Avenue des Olympiades, 91744 Massy Cedex, France c National Institute of Perinatology, Montes Urales 800, Lomas, de Virreyes, CP 11000, Mexico DF Received 21 May 2005; accepted 19 December 2005 Available online 17 February 2006
Abstract In this paper, an experimental and theoretical analysis of the heat and mass transfer was carried out to evaluate the coffee bean’s temperature and moisture content during the roasting in batch system. Arabica coffee from Colombian origin was roasted using different air temperatures between 190 and 300 C, during 10 min. Bean’s temperature and weight loss have been measured on-line by robust sensors. The experimental results allowed better understanding of the phenomena that appears during roasting. For example, an evident increase of the bean’s temperature curve tendency is observed when this one exceeds the 250 C, it is probably due to the end of exothermic reactions and to the beginning of the bean burn. The experimental data of moisture shown a decrease of 10.5% d.b. to 0–7% d.b. A dynamic model is evaluated and analyzed to predict bean’s temperature and moisture content during roasting. The results (simulations and experimental kinetics) were in good agreement. This model can be used for on-line estimation and control of coffee roasting. 2006 Elsevier Ltd. All rights reserved. Keywords: Heat and mass transfer; Coffee roasting; On-line measures
1. Introduction In order to obtain a good cup of coffee, the step of roasting is very important to develop specific organoleptic properties (flavors, aromas and color), underlying the quality of the coffee. The amount of heat transferred to the bean is essential in the roasting process. The process can be divided into two phases. The first phase corresponds to the drying (bean’s temperature below 160 C) and the second phase is the roasting (bean’s temperature between 160 and 260 C). In this last phase, pyrolytic reactions start at 190 C causing oxidation, reduction, hydrolysis, polymerisation, decarboxilation and many other chemical changes, leading to the formation of substances essential to give among other, the sensory qualities of the coffee. These moisture loss and chemical reactions are accompanied by important changes *
Corresponding author. Tel.: +52 777 3 29 70 84; fax: +52 777 3 29 79
84. E-mail address: [email protected] (J.A. Herna´ndez). 0260-8774/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2005.12.041
(color, volume, mass, form, bean pop, pH, density, volatile components) and generate CO2, of which a part escapes and other part is retained in the cells of the beans. After this second phase, the beans must be rapidly cooled to stop the reactions (using water or air as cooling agent) and to prevent an excessive roast which alter the quality of the product (Illy & Viani, 1998; Nagaraju, Murthy, Ramalakshmi, & Srinivasa, 1997; Raemy, 1981; Raemy & Lambelet, 1982; Schwartzberg, 2002; Singh, Singh, Bhamidipati, Singh, & Barone, 1997; Sivetz & Desrosier, 1979). During the process, several parameters can be used as indicators to determine the degree of roasting (aroma, flavor, color, bean’s temperature, pH, chemical composition, bean pop, mass loss, gas composition and volume) (Dutra, Oliveira, Franca, Ferrez, & Afonso, 2001; Herna´ndez, 2002; Illy & Viani, 1998; Mendes, De Mendes, Aparecida, & da Silva, 2001; Schwartzberg, 2002). Nevertheless, in the industry, in order to obtain the optimal degree of roasting and to control the quality of the product, the roast master take up an essential position. In one hand, he interprets the
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algorithm is managed in bash (Bourne, 2002); Type K Thermocouples allowed to measure internal and external temperatures of the beans and to control the air temperature with a precision of ±0.5 C. One bean is drilled in order to insert a thermocouple 4 mm below the surface (internal temperature), and another thermocouple about 0.2 mm below the surface in order to measure the near surface temperature (see Fig. 1B). The beans are placed on a mesh to keep them on static suspension, where convection is the predominant mode of heat transfer. Beans weight is automatically measured using an electronic scale METTLER (SB16001) and controlled by the computer (see Fig. 1A). A program written in bash makes the weight acquisition each minute. Before each weight acquisition, the fan of the roaster is automatically stopped for 8 s to stabilize the measure.
physic measure (temperature and time of stay), and in the other hand, the organoleptic properties of the coffee beverage (color, aroma and flavor). However, these measures are obtained out-line. Automation is limited by the lack of captors allowing to follow the quality in real time, and by the process conditions (the mass of beans is always in agitation) which make instrumentation difficult (Herna´ndez, 2002; Schwartzberg, 2002). It is important to mention that the control of temperatures and duration, in industry, are only effective, if the quality of the raw material does not vary. Today, the chemical reactions are extensively studied by Illy and Viani (1998), nevertheless, coffee roasting is slightly studied as an unit operation. Indeed, in this operation, a specific instrumentation, working in real time and taking into account the variables of the product does not exist. Several variations are presented as a function of the raw material and of the process conditions. The aim of this work is to measure and analyze the bean temperature and moisture content during coffee roasting and to evaluate the model in the purpose of process control.
3. Results During coffee roasting, mass and temperature are measured on-line. The results will allow a better understanding of the process, and a validation of the mathematical model. Fig. 2 shows the evolution of the internal and external bean’s temperature and of the air temperature (C) during the roasting. These curves (Fig. 2) put in evidence the effect of the air temperature on the evolution of the bean’s temperature. The internal bean’s temperature has an exponential behavior described by Schwartzberg (2002) if bean’s temperature is below 250 C. An evident deviation with exponential kinetic is observed between 80 and 100 s of roasting (Fig. 2B) for experiments where the bean’s temperature become higher than 260 C. When the optimal bean’s temperature is surpassed, the exothermic reactions responsible of the aroma and flavor are reduced and the beans begin to be burn. This phenomenon is called over-roasting by Coste (1968), it can
2. Material and methods Colombia green coffee beans (Arabica) are roasted using hot air flow as heating medium. The experiments are carried out at constant air velocity of 4 m/s for constant air temperatures (190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290 and 300 C) during 10 min. The experiments are done with three replicates. Fig. 1 depicts the data acquisition and processing using a computer equipped with a temperature acquisition system (SCB7 thermocouple conditioner and Arcom PCAD12/16H A/D converter) and several software. The low level task (data acquisition and I/O port programming) are written in C (Lawyer, 2000; Photis, 1999), real time data processing are done with Octave (Eaton, 2001) and
Thermocouples carte ADC
Bean Coffee
carte SCB7
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capmas (in bash)
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Fig. 1. Scheme of experimental data used (temperatures and mass).
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be responsible of the observed deviation. Consequently, this confirm that the bean’s temperature versus the time can be an indicator of the roast-degree during coffee roasting. It is important to mention that Schwartzberg (2002) stopped the process when the bean temperature reach 238 C, so he never observed this phenomenon. During roasting, weight loss is measured each minute. The results in Fig. 3, show that we obtained a good repeatability of the measures (two repetition at 300 and 190 C, and three at 250 C). After a short stage of latency, we observe a quasi linear behavior followed by a marked deceleration. Weight loss clearly depend on the air temperature of the roasting time. After 10 min of process the percentage of mass loss ranged from 3% to 12% depending on roasting temperature. Similar results are reported by severals authors (Da Porto, Nicoli, Severini, Sensidoni, & Lerici, 1991; Dutra et al., 2001; Pittia, Dalla, Pinnavaia, & Massini, 1996; Schwartzberg, 2002). This authors also reported weight loss differences due to types of roasting machines, duration, type of bean and air temperature. According to Guyot (1993) and Illy and Viani (1998), the moisture content is about 8–12% d.b. in green coffee
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4. Heat and mass transfer modelling The heat and mass transport mechanisms during batch roasting (roaster using hot air flow) are given by the equations proposed by Schwartzberg (2002): • Moisture loss, the diffusive water transport in the bean is given by dX 4:32 109 X 2 9889 ¼ exp ð1Þ dt T b þ 273:15 d 2p
14 12
and below 5% d.b. in roasted coffee. Furthermore, volatile components are formed during roasting, inducing also noticeable mass loss. Dutra et al. (2001) determined weight loss during the process for 300 g of green coffee using a direct heating. They found two different speeds for mass loss: the first period, between 0 and 7 min, shows a linear kinetic with a weak slope, this period corresponds to a moisture and volatiles losses, the second period from 7 to 12 min the weight loss follows a right line with a strong slope, and this corresponds to a loss of CO2 and organic components of the bean. Besides, they showed that loss of CO2 increases when the moisture content diminishes significantly. The evolution of the mass loss can therefore be a criterion of the roasting degree, but it is not a key criterion for us because weight is difficult to measure on-line in the industry.
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X: moisture content (kgwater/kgdry matter); Tb: internal temperature of the bean (C). The water loss is governed by an Arrhenius type equation, proportional to X2; and dp: effective bean diameter. • Heat transfer, the rate of temperature rise of the beans is given by dT b GC pa ½T ae T as Qa!m þ Qm!b þ mbs Qr þ Lv dX dt ¼ dt mbs ð1 þ X ÞC pb ð2Þ
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where Tae and Tas are respectively the in-air and out-air temperature (C). G is the air mass-flow rate (kg/s). Cpa and Cpb are respectively the air and bean heat capacity (kJ/kg C). mbs is the dry weight of the bean kg dry coffee and Lv is the latent heat of vaporization of the bean moisture, Schwartzberg (2002) gives 2790 kJ/kg. In this balance Eq. (2), the heat transfer from hot air to bean GCpa[Tae Tas], the heat transfer from air to metal parts Qa!m, the heat transfer from metal parts to beans Qm!b, the heat production by roasting reactions Qrmbs and the heat necessary to moisture evaporation at the bean surface during the roasting Lv ðdX Þmbs are considered. Howdt ever, in this work, the contact area between coffee beans and metal part is negligible. It is also possible to assume that the heat transfer from hot air to metal is negligible because the temperature of the metal is equal to the air temperature. Under this two hypothesis, the model is simplified as follows: dT b GC pa ½T ae T as þ mbs Qr þ Lv dX dt ¼ ð3Þ mbs ð1 þ X ÞC pb dt To determine [Tae Tas] in Eq. (3), a balance of air temperature is considered by Schwartzberg (2002). Under the previous hypothesis, it is possible to write: aAab ½T ae T as ¼ ðT ae T b Þ 1 exp ð4Þ GC pa where a is the effective air-to-bean heat transfer coefficient (W/m2 C), Aab is the area (m2) across which air-to-bean heat transfer occurs. 4.1. Properties estimation To solve Eq. (2) by considering Eq. (4), it is necessary to know a, Cpb and Qr: • Effective air-to-bean heat transfer coefficient, a, was estimated by Eq. (5) reported by Schwartzberg (2002): a¼
he 1 þ 0:3 Bi
ð5Þ
where, he is the heat transfer coefficient at the air–bean surface calculated by the Ranz–Marshall correlation (Perry & Green, 1998) and Bi (Biot number) is used to correct the overall air–bean heat transfer coefficient for heat transfer resistance in the bean (Kreith, 1967). • Specific heat of the coffee bean, Cpb, the values used are obtained by Eq. (6) reported by Schwartzberg (2002): C pb ð1 þ X Þ ¼ 1:099 þ 0:0070T b þ 5:0X
ð6Þ
• Exothermic roasting reaction, Qr (rate of exothermic heat production), in kJ/(kg dry coffee) s, was calculated using Eq. (7) reported by Schwartzberg (2002) Ha H et H e Qr ¼ A exp ð7Þ Rg ðT b ðKÞÞ H et
where, Ha is the energy of activation, Rg is the perfectgas-law constant, A, in kJ/(kg dry coffee) s, is the Arrhenius equation prefactor times the amount of heat generated per unit amount of reaction. Schwartzberg (2002) obtained HRga ¼ 5500 K, A = 116,200 kJ/(kg dry coffee) s and Het = 232 kJ/kg. Measured bean properties: • Aab = 1.4 · 104 m2 equivalent sphere area. • mbs = 1.75 · 104 kg dry matter. • db = 6.6 mm equivalent sphere diameter. 4.2. Model solution To solve the system of Eqs. (1)–(7), we wrote a computer program in Octave (Eaton, 2001). This program works in the following way: at instant t = 0, we know: • the initial bean temperature Tb initial = 29 C, • the initial bean moisture X initial = 0.105 kg water/kg dry matter, • the in-air temperature Tae, measured on-line. These data allow to calculate in time t = 0: • the effective air-to-bean heat transfer coefficient a (Eq. (5)), • the out-air temperature Tas (Eq. (4)), • the rate of moisture loss dX (Eq. (1)), dt • the specific heat of the coffee bean Cpb(1 + X) (Eq. (6)), • the rate of exothermic heat production Qr (Eq. (7)). The set of differential equations was numerically integrated using fourth-order Runge–Kutta method written in Octave (Eaton, 2001). 4.3. Simulation of the heat and mass transfer An important characteristic of the model is that no parameter was adjusted to describe the bean’s temperature and moisture content. The program was written in order to estimate the bean’s temperature and moisture content versus time, for a hot air roaster with 25 g of green coffee in different constant air temperatures (Tae from 190 to 300 C). Fig. 4 shows agreement between experimental and simulated bean’s temperature for three roasting temperatures. This three kinetics are representatives for all the experiments. Below 250 C, the model fits very well the data. For hight bean’s temperature, the model do not predict the small deviation which we had already observed in the experimental part (Fig. 2B). The deviation can be explained by a beginning of an over-roasting, the exothermic reaction parameters (Eq. (7)) given by literature are not valid for this experimental domain. Consequently, the model cannot consider this perturbation. It could be possible to add an other factor to take this phenomena into account, but we
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and CO2; the model, which only considers water loss, should give higher results. It would be interesting to measure the water content of the beans during roasting, and to develop a more physical model considering water diffusivity in the bean and mass transfer coefficient between bean and air. But the perturbation of bean’s temperature model induced by the bad estimated water loss is negligible. Bean reach the roasting air temperature in less than 180 s, and the moisture content simulation become bad after 300 s of roasting, when the heat transfer is very low.
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preferred to keep a robust model with no adjusted parameter. The moisture content simulation using Eq. (1) leads to acceptable results (Fig. 5) for the beginning of the kinetic. After 300 s the model significantly underestimates the water content. The weight loss include water, volatiles 0.105
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As shown in the previous section, the model reproduced with good accuracy the experimental data (Tb and X). However, this model is developed for process control purpose, as a consequence it is important to test the robustness of the model for small perturbations of the process variables (Va, HR) or of the product characteristics (a, Aab, db, X, Cpb, Qr, mbs). A variation of air velocity, Va, from 2 to 6 m/s induces important changes on the Tb (see Fig. 6). This change can be explained, since the air velocity have an effect on the heat transfer coefficient calculated by Ranz–Marshall correlation (Perry & Green, 1998) he and the air mass-flow rate G. These two parameters are very important to predict the bean’s temperature and out-air temperature (see Eqs. (2) and (3)). Therefore, it is necessary to know the air velocity in an exact way. A variation of relative humidity, HR, from 20% to 80% (at ambient temperature) did not show an effect on the simulated bean’s temperature (data not shown), since when air is heated at 200 C, it become very dry (HR < 0.1%). Fig. 7 shows the effect of the bean’s size (db) on the bean’s temperature versus time. One can observe that the variations of db have a very important effect on the bean’s temperature Tb as mentioned by Schwartzberg (2002). When we consider a relatively small variation of bean’s dimensions (Aab), the prediction of the bean’s temperature vary appreciably (Fig. 8), thus this parameter Aab must be known with precision, because this value will reflect itself
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Fig. 7. Evolution of bean’s temperature versus time (line continuous) represents d = 4, (line discontinuous) is d = 5, (+) is d = 6 and (*) is d = 7 mm.
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-- Aab 0.03 m 2 - Aab 0.02 m2
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on the results of Tb. Besides, according to Eq. (4), the dimensions of the bean tends to be a very influential parameter on Tb, Tae and Tas. These dimensions can vary according to the batch of coffee to be roasted and during the course of the process Herna´ndez (2002). When a mixture of varieties (i.e. Arabica and Robusta) is roasted, these dimensions are delicate to determine in the batch and during the process, and by consequence a model to predict Aab is necessary inside the system of proposed equations.
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Fig. 9 presents the results of bean’s temperature versus time for different initial moisture contents X0. These curves show well that it exists a minor effect on the values of Tb. However, if initial moisture content is considered as null (X0 = 0), the simulated beans temperature increased quickly, it is normal, because the phase of drying does not take place. Therefore, the initial moisture is a very important factor that must be considered in the model bean’s temperature prediction, but the analysis of the initial moisture value X0, of 9%, 11% and 13% in d.b., have shown that the effect of this parameter on the kinetics of bean’s temperature is rather weak (see Fig. 9). Fig. 10 compares the two bean’s temperature kinetics, first using a constant Cpb (2.41 kJ/kg C) and the other a variable Cpb f(X, Tb) (Eq. (6)). Also, this figure shows the experimental data (indicated by *) of the bean’s temperature. It can be observed that the constant specific heat of the bean can also simulate the bean’s temperature but in a way less satisfactory than if one uses a variable Cpb for the bean’s temperature of roasting. Nevertheless to predict bean’s temperature over 260 C is better to use the constant Cpb but this it is not the case because carbonization begins. In addition, the dry weight of the beans mbs has also shown a change in the behavior of Tb versus t. To recapit-
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Fig. 10. Bean’s temperature versus time, (line continuous) represent the variable specific heat of the bean (Eq. (6)) and (line discontinuous) is a constant Cpb = 2.41.
ulate this analysis of succinct sensitivity of the dynamic model, we showed that if the changes of operation variables and parameters linked with the product like: • the specific heat Cpb, • the mass of product m, • the air velocity Va. The model takes into account these parameters in order to predict the bean’s temperature in a satisfactory manner. For variables not controlled by the model as: • dimensions of the bean db (diameter) and Aab (surface of the bean), • initial moisture X0. It is necessary to measure the correct values in order to have a reliable model. Some variables, like relative humidity HR, does not influence the output of the model, under the studied conditions. 5. Conclusion The suggested model can be used in a satisfactory way to describe the behavior of the coffee bean’s temperature versus time, in an hot air roaster. This model showed a good agreement with all the experimental kinetics. It is necessary to note that no parameter were adjusted in this model. Furthermore, it can be used to determine how behavior can be affected by parameters variations which are not controlled in the course of roasting. If the parameters are known correctly (aAab, mbs, X, db, Cpb, Va and Tae), the model can be used directly, or with small modifications, for other roasting machines where the heat transfer takes place between air and metal and/or a heat transfer of metal towards the bean and the bean towards metal (i.e. Rotating-drum roaster, Rotating-bowl roaster, Scoop-wheel roaster and Swirling-bed roaster). Schwartzberg (2002) showed that bean’s temperature is a good criterion to evaluate coffee quality during roasting process. This temperature is diffi-
cult to measure on industrial roaster, but we showed that it is possible to calculate this temperature as a function of input temperature Tae. The model calculates the output air temperature Tcas at the same time, which is easy to measure on-line. If some perturbation appears, that it is not take into account by the model, the simulated bean’s temperature Tcb , will be wrong, this will appear on the difference between simulated and experimental temperature ð Tcae T ae Þ, allowing to adjust the model parameters online. Further studies will try to adapt this strategy to industrial roaster. Acknowledgment We thank to Prof. Henry G. Schwartzberg for his personal communication to this work. References Bourne, S. (2002). Bash (free software). In Bourne Again SHell. Available from http://www.gnu.org/software/bash/bash.html, consulted April 2005. Free Software Foundation. Coste, R. (1968). Le cafe´ier, G. P. Maisonneuve et Larose, 14 ed., 11, rue Victor-Cousin, Paris (Ve). Da Porto, C., Nicoli, M. C., Severini, C., Sensidoni, A., & Lerici, C. R. (1991). Study on physical and physico-chemical changes of coffee beans during roasting. Note 2. Italian Journal of Food Science, 3, 197–207. Dutra, E. R., Oliveira, L. S., Franca, A. S., Ferrez, V. P., & Afonso, R. J. (2001). A preliminary study on the feasibility of using the composition of coffee roasting exhaust gas for the determination of the degree of roast. Journal of Food Engineering, 47, 241–246. Eaton, J. W. (2001). Octave (free software). In GNU Octave. Available from http://www.octave.org/octave.html, consulted April 2005. University of Wisconsin. Guyot, G. (1993). Torre´faction: Mecanismes, transformation physiques et chimiques. In Journe´es du CAFE, CIRAD-CP a´ Montpellier, France. Herna´ndez, J. A. (2002). E´tude de la torre´faction: Mode´lisation et de´termination du degre´ de torre´faction du cafe´ en temps re´el. PhD Thesis in E´cole Nationale Supe´rieure des Industries Agricoles et Alimentaires, France. Illy, A., & Viani, R. (1998). Espresso coffee. San Diego, US: Academic press.
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Kreith, F. (1967). Transmission de la chaleur et thermodynamique. Masson et Cie e´diteurs, 120 Boulevard Saint Germain Paris VIe. pp. 129–137. Lawyer, S. D. (2000). Serial-HOWTO. In the Linux Serial HOWTO. Available from http://www.linuxdoc.org/HOWTO/Serial-HOWTO.html. Consulted January 2005. Mendes, L. C., De Mendes, H. C., Aparecida, M., & da Silva, A. P. (2001). Optimization of the roasting of robusta coffee (C. canephora conillo) using acceptability test and RSM. Food Quality and Preference, 12, 153–162. Nagaraju, V. D., Murthy, C. T., Ramalakshmi, K., & Srinivasa, R. P. N. (1997). Studies on roasting of coffee beans in a spouted bed. Journal of Food Engineering, 31, 263–270. Perry, R. H., & Green, D. W. (1998). Perry’s chemical engineers’ handbook. 0071344128. McGraw-Hill, pp. 5–24. Photis, G. (1999). Coffee-HOWTO.txt. In software coffee-HOWTO. Available from http://www.cl.cam.ac.uk/coffee/coffee.html, consulted January 2005, Cambridge University.
Pittia, P., Dalla, M., Pinnavaia, G., & Massini, R. (1996). Evoluzione di alcune caratteristiche fisiche del caffe` durante la torrefazione. Industrie Alimentari, 245–950. Raemy, A. (1981). Differential thermal analysis and heat flow calorimetry of coffee and chicory products. Thermochimica Acta, 43, 229– 236. Raemy, A., & Lambelet, P. (1982). A calorimetric study of self-heating in coffee and chicory. Journal of Food Technology, 17, 451–460. Schwartzberg, H. G. (2002). Modelling bean heating during batch roasting of coffee beans. In J. Welti-Chanes, G. Barbosa-Canovas, & J. M. Aguilera (Eds.), Engineering and food for the 21st century. London, New York, Boca Raton: CRC Press LLC. Singh, P., Singh, R., Bhamidipati, S., Singh, S., & Barone, P. (1997). Thermophysical properties of fresh and roasted coffee powders. Journal of Food Process Engineering, 20, 31–50. Sivetz, M., & Desrosier, N. W. (1979). Coffee technology. Westport: AVI Publishing Co., pp. 226–264.