This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright Author's personal copy Journal of Food Engineering 107 (2011) 253–261 Contents lists available at ScienceDirect Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng Estimating the theoretical energy required to dry rice Maria A. Billiris a, Terry J. Siebenmorgen a,⇑, Andy Mauromoustakos b a b Department of Food Science, University of Arkansas, Fayetteville, AR 72704, USA Agricultural Statistics Lab., University of Arkansas, Fayetteville, AR 72701, USA a r t i c l e i n f o Article history: Received 2 March 2011 Received in revised form 9 June 2011 Accepted 11 June 2011 Available online 23 June 2011 Keywords: Heat of desorption Desorption isotherms Clausius–Clapeyron equation a b s t r a c t The total heat of desorption of rice (Qt) was determined for several rice types as a function of moisture content (MC), and kernel temperature, using a semi-theoretical approach in which desorption isotherms were used in conjunction with the Clausius–Clapeyron equation. Qt decreased exponentially as MC increased, decreasing sharply for MCs above 15% and approaching the latent heat of vaporization of free water at MCs around 20%. Qt of parboiled rice at 12.5% MC was significantly less than that of nonparboiled lots. Qt of medium-grain ‘‘Jupiter’’ was significantly greater than that of long-grains at 12.5% MC. Equations that predict the energy required to dry a unit mass of rice from an initial MC to a final MC were derived. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction In order to maximize field yield and quality, rice is typically harvested at MCs greater than the level deemed safe for long-term storage, which is often taken to be around 13% (Howell and Cogburn, 2004). To preserve its quality, rice should be thus dried to this safe level (Siebenmorgen and Meullenet, 2004). Verma (1994) stated that the United States consumes 15 million barrels of crude oil per year for drying grains, making grain drying operations a major source of energy consumption. Kasmaprapruet et al. (2009) reported that drying was the most energy-consumptive unit operation in rice processing, accounting for 55% of the total energy consumed for production and processing of rice. The energy required to dry grains under ideal conditions varies from 2500 to 2670 kJ/kg water depending on the drying temperature (T) (Fluck and Baird, 1980). However, Gunasekaran and Thompson (1986) stated that drying of crops actually requires from 3000 to 8000 kJ/kg water. Therefore, the efficiency of a drying process depends on how drying is performed. Considering the ongoing interest in reducing energy requirements and the importance of the rice crop in the United States and globally, it is timely to investigate means of improving rice drying efficiency. The first step in quantifying the performance of a rice drying process is to calculate the theoretical energy required to remove water from rice. The energy required for drying foodstuffs mainly comprises the thermal energy required to remove water from the food material; the mechanical energy required for conveyance or airflow is less significant. Depending on the initial MC (MCi) of the material and the desired final MC level (MCf), the removal of ⇑ Corresponding author. Tel.: +1 479 575 2841; fax: +1 479 575 6936. E-mail address: tsiebenm@uark.edu (T.J. Siebenmorgen). 0260-8774/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2011.06.015 water from foodstuffs may require more energy than that required to vaporize free water (latent heat of vaporization, hfg) (Okos et al., 1992; Rizvi, 2005). Cenkowski et al. (1992) explained that when the MC of a material is below 12% dry basis (d.b.), the increase in intra-particle resistance to moisture migration increases the energy required to remove water. Okos et al. (1992) stated that the energy required to remove water from foods increases as the binding-force between water and the food increases. Rizvi (2005) indicated that, in general, the energy requirement for drying food materials has two main components: the energy required to evaporate free water and the energy required to remove water that is associated with the food matrix. The entire amount of energy required to remove water from a food material has been referred to as the isosteric heat of sorption (Iglesias and Chirife, 1976), the heat of sorption (Tsami et al., 1990) and the isosteric heat of desorption (Kechaou and Maalej, 1999). Herein, this quantity will be referred to as the total heat of desorption (Qt). The difference between Qt and hfg, which has been referred to as the net isosteric heat of sorption (Iglesias and Chirife, 1976; Tsami et al., 1990), will be called the net heat of desorption (Qn). Aviara et al. (2004), Kechaou and Maalej (1999) and McMinn and Magee (2003) indicated that Qn represents the energy beyond hfg required to remove a unit mass of water from a foodstuff due to water–solid bonds. The strength of water–solid bonds in foodstuffs varies with MC, generally increasing as MC decreases (Okos et al., 1992). Consequently, Qn would be expected to increase as drying progresses. Researchers have confirmed this expectation (Aviara et al., 2004; Cenkowski et al., 1992; Mulet et al., 1999; Toğrul and Arslan, 2006; Tsami et al., 1990; Zuritz and Singh, 1985). Cenkowski et al. (1992) found that the energy required to remove water from grain is close to hfg for MCs above 20% (d.b.). However, Johnson and Dale (1954) reported that energy requirements to Author's personal copy 254 M.A. Billiris et al. / Journal of Food Engineering 107 (2011) 253–261 remove water from wheat and shelled corn at MCs above 14% (d.b.) are close to hfg. Since Qn is the theoretical minimum energy above hfg required to remove a unit mass of water from a particular food (Rizvi, 2005), it is important to establish the relationship between Qn and MC in order to quantify the theoretical energy requirements for drying rice. In addition, it is possible that the relationship between Qn and MC changes depending on kernel properties, including kernel temperature (Truong et al., 2005). Therefore, it is also relevant to investigate energy requirements of different rice types, cultivars and T levels. Thus, Qt should be determined as a function of MC and T for a given rice type/cultivar. Actual energy requirements for a specific dryer can be compared to this ideal situation, and thus efficiencies for different commercial dryers can be calculated. Little research has assessed theoretical energy requirements for drying rice, particularly for different rice types and current cultivars. Iguaz and Vírseda (2007) estimated Qn values at different MC levels for medium-grain rough rice; Toğrul and Arslan (2006) and Zuritz and Singh (1985) estimated Qt values at different MC levels for long-grain and medium-grain rough rice, respectively. Researchers have used the Clausius–Clapeyron equation, in combination with sorption isotherm data, to calculate heats of desorption for diverse foodstuffs (Aviara and Ajibola, 2002; Aviara et al., 2004; Chen, 2006; Iglesias and Chirife, 1976; Iguaz and Vírseda, 2007; Kechaou and Maalej, 1999; Mulet et al., 1999; Tolaba et al., 2004; Toğrul and Arslan, 2006; Tsami et al., 1990). The fact that sorption isotherms of foodstuffs demonstrate hysteresis is an indication of irreversibility, which has posed doubts on the reliability of the Clausius–Clapeyron equation for determining Qn and Qt (Iglesias and Chirife, 1976; McLaughlin and Magee, 1998). However, Iglesias and Chirife (1976), after analyzing works performed by other researchers who compared the Clausius–Clapeyron approach to calorimetric heats, concluded that the heats of irreversible processes are small enough to be neglected when calculating energy requirements for drying foodstuffs. Mulet et al. (1999) obtained good agreement between calorimetric heat measurements using a thermogravimetric analyzer (TGA) in combination with a differential scanning calorimeter (DSC) and those obtained from the Clausius–Clapeyron method for potato starch and cauliflower. Consequently, the application of the Clausius–Clapeyron method was deemed appropriate for estimating energy requirements for drying rice. The objectives of this study were (1) to calculate Qn and Qt values at various MCs and Ts for different types of rice using equilibrium moisture content (EMC) data and the Clausius–Clapeyron equation, (2) to mathematically model Qt as a function of MC and T for the rice types under study, (3) to develop an equation that predicts the theoretical energy required to dry rice from varying MCi to a desired MCf. 2.2. Heat of desorption calculation Qt was calculated using the form of the Clausius–Clapeyron equation developed by Othmer (1940): lnðpv Þ ¼  Qt lnðps Þ þ c hfg  ð1Þ where pv is water vapor pressure in the rice kernel associated with a particular T, ps is vapor pressure of pure water associated with a particular T, Qt is the total heat of desorption (kJ/kg water), hfg is the latent heat of vaporization of pure water at a given T (kJ/kg water), c is an integration constant. Qt/hfg was calculated from the slope of the regression line relating ln(pv) to ln(ps) at different Ts for a specific MC; the slope of the line equals Qt/hfg for a specific MC. The pv values were calculated from ERH data using the following relationship: ERH ¼ pv ps ð2Þ ERH is equilibrium relative humidity in a decimal form. It is critical to select an appropriate equation to predict ERH using T and MC as inputs in order to calculate Qt. Research indicates that the modified Chung–Pfost equation (Chung and Pfost, 1967; Pfost et al., 1976) best describes rice isotherm data (Basunia and Abe, 1999; Ondier et al., 2011):  ERH ¼ exp  A expðB  MCÞ T þC  ð3Þ where A, B and C are constants, MC is expressed in a d.b. decimal form, T is temperature (°C) and ERH is equilibrium relative humidity expressed in a decimal form. The values of the constants A, B and C were obtained from Ondier et al. (2010, 2011), depending on the temperature range and cultivar. Zuritz and Singh (1985) reported that among the isotherm equations at that time, only the Chung– Pfost equation was appropriate for heat of desorption calculations, because it was the only equation in compliance with the necessary mathematical restriction that the heat of desorption decreases with an increase in temperature. Thus, pv values were calculated using Eqs. (2) and (3) and ps values from the psychometric relationships in ASAE (1998). Linear regressions of ln(pv) vs. ln(ps) were developed for selected MCs. Qt/hfg was estimated from the slope of each curve for a given MC. The ratio Qt/hfg was assumed to be constant in the temperature range over which the data were collected. Thus, Qt for a given MC and T combination was calculated using a consistent Qt/hfg ratio for a given MC level: however, to account for varying T levels, hfg was varied to correspond to the desired T level using Perry and Chilton (1973). The net heat of desorption Qn was then calculated using Eq. (4). Q t ¼ Q n þ hfg ð4Þ 2.3. Heat of desorption prediction 2. Materials and methods 2.1. Sorption isotherms EMC data were obtained from two previous studies. Elevatedtemperature desorption isotherms (60, 70, 80 and 90 °C) for long-grain ‘‘Cybonnett’’ rough rice were obtained from Ondier et al. (2010). In addition, rough rice sorption isotherms at low temperatures (10, 20, 30, 45 and 60 °C) for long-grains ‘‘Wells’’ and ‘‘CL XL730’’, medium-grain ‘‘Jupiter’’ and a long-grain parboiled rice of unknown cultivar were obtained from Ondier et al. (2011). The data from both studies were used to calculate Qt and Qn at selected MCs and Ts. In order to mathematically express Qt as a function of MC and T for the different types of rice, Qt, MC and T data were used to statistically determine the constants of the relationship used by Truong et al. (2005): Q t ¼ A1 þ B1  T þ ðA2 þ B2  TÞ expðA3  MCÞ ð5Þ where A1, A2, A3, B1 and B2 are constants of the equation estimated iteratively by fitting the non-linear model. Qt is in J/kg water, MC is in dry basis, decimal and T is in K. Truong et al. (2005) successfully used this model to describe Qt data for a mixture of maltodextrin–sucrose. Non-linear least squares regression analyses were performed on the data to obtain Author's personal copy 255 M.A. Billiris et al. / Journal of Food Engineering 107 (2011) 253–261 Table 1 Equilibrium relative humidities (%) of long-grain ‘‘Cybonnett’’ rough rice at the indicated moisture contents and temperatures calculated using the modified Chung– Pfost equation (Ondier et al., 2010). Temperature, °C Moisture content, % w.b. 8 60 70 80 90 26 37 46 53 10 49 60 67 72 12 70 77 82 84 14 84 88 91 92 16 92 94 95 96 18 96 97 98 98 20 98 99 99 99 22 99 99 99 99 the constants for Eq. (5). Root mean square error (RMSE) and standard error of the coefficients (SE) were used to assess the fit and precision of the estimates. 2.4. Energy requirements per unit mass of rice and per unit mass of water removed Qt data was used to develop an equation that predicts the theoretical energy required per unit mass dry matter of rice (QTrice) to dry rice from a given MCi to a MCf when drying at a given T, similar in approach to Tsami et al. (1990). To calculate QTrice, an integration of Eq. (5) was performed: Q Trice ¼ Z MCf Q t dMC ð6Þ MCi where QTrice is the energy required to dry rice from MCi to MCf per unit dry mass of rice at a given T. Thus, T was considered constant throughout the integration. Substituting Eq. (5) into Eq. (6) and integrating: Q Trice ¼ Z Table 2 Net heat of desorption (Qn), total heats of desorption (Qt) and standard errors (SE) of Qn and Qt, calculated from linear regressions using the Clausius–Clapeyron equation at the selected moisture content levels for long-grain ‘‘Cybonnett’’ rough rice at 60 °C. The value of hfg was 2359 kJ/kg water. MCf ðA1 þ B1  T þ ðA2 þ B2  TÞ expðA3  MCÞÞdMC MCi ¼ A1 ½MCf  MCi  þ B1  T  ½MCf  MCi  þ  ðexpðA3  MCf Þ  expðA3  MCi ÞÞ ðA2 þ B2  TÞ A3 ð7Þ Moisture content, % w.b. Qn, kJ/kg water Qt, kJ/kg water SE, kJ/kg water 8 10 12 14 16 18 20 22 1381 743 359 180 81 42 18 0 3741 3102 2718 2539 2440 2401 2377 2359 166 106 57 29 9 9 10 0 Table 3 Estimated constants of Eq. (5) and associated root mean square errors (RMSEs) for long-grains ‘‘Wells’’, ‘‘CL XL730’’ and ‘‘Cybonnett’’, medium-grain ‘‘Jupiter’’, parboiled rice and for a general model describing all non-parboiled, long-grain rice cultivars. Cultivar ‘‘Jupiter’’ ‘‘Wells’’ ‘‘Cybonnett’’ ‘‘CL XL730’’ General Parboiled Parameter RMSE A1 A2 A3 B1 B2 3,150,878 3,150,927 3,200,035 3,150,916 3,189,745 3,151,394 12,725,771 11,509,211 19,950,786 10,117,409 9,742,417 8,107,920 23.2 23.4 27.1 22.7 24.2 23.0 2377 2377 2521 2377 2496 2377 9601 8683 15,719 7632 – 6117 0.22 0.23 1.15 0.23 4.0 0.72 By using Eq. (7), expressions for each type of rice were obtained, whereby energy requirements for drying a unit mass of rice dry matter were obtained for given MCi, MCf and T inputs. The value of QTrice (J/kg dry matter rice) is negative but the absolute value was reported. To express the energy requirements to dry rice from an MCi to an MCf on a per unit mass of water removed basis, QTrice from Eq. (7) was divided by Dmevap the mass of water removed in the drying process per unit rice dry matter, which can be expressed as: Fig. 1. Natural logarithm of water vapor pressure in the rice kernel vs. the natural logarithm of vapor pressure of pure water, for long-grain ‘‘Cybonnett’’ rough rice at four moisture content levels (w.b.) and temperatures ranging from 60 to 90 °C. The slope of each moisture content level regression line equals the total heat of desorption/latent heat of evaporation of pure water (Qt/hfg) quotient, per Eq. (1). Author's personal copy 256 M.A. Billiris et al. / Journal of Food Engineering 107 (2011) 253–261 Fig. 2. Total heat of desorption (Qt) as a function of moisture content (% wet basis) for medium-grain ‘‘Jupiter’’, at 45 °C and those reported for a medium-grain rice at 40 °C by Zuritz and Singh (1985). Table 4 Predicted values and confidence intervals for the total heat of desorption (Qt) as obtained from Eq. (5) at 12.5% moisture content and 60 °C and for the rice types indicated. Rice type Qt, kJ/kg water 95% Confidence interval, kJ/kg water Medium-grain ‘‘Jupiter’’ 2705 2704–2707 Long-grain ‘‘Wells’’ Long-grain ‘‘Cybonnett’’ Long-grain ‘‘CL XL730’’ 2665 2665 2656 2664–2666 2659–2672 2655–2657 Long-grain non-parboiled (general) 2669 2656–2671 Long-grain parboiled 2590 2587–2593 Dmevap ¼ MCi  MCf same trends were observed for all rice types. Values of Qn for long-grain ‘‘Cybonnett’’ at 60 °C are tallied in Table 2. The standard error of Qn is equal to the SE of Qt because the difference between these two values is a constant (hfg). Iguaz and Vírseda (2007) reported for medium-grain rough rice, Qn values from 139 to 1021 kJ/kg water for MCs ranging from 19% to 0.04% and Ts from 40 to 80 °C. The Qn values obtained in this study are greater than those of Iguaz and Vírseda (2007) at low MCs and are lower than those of Iguaz and Vírseda (2007) at high MCs. 3.1. Total heat of desorption prediction ð8Þ It is emphasized that QTrice can thus be expressed as drying energy required per unit mass of rice dry matter, Eq. (7), or energy per unit mass of water removed by dividing Eq. (7) by Dmevap (Eq. (8)). All statistical analyses were performed using JMP 8.0.1 software (SAS Institute, Inc.). 3. Results and discussion Table 1 shows the predicted ERH values, at temperatures ranging from 60 to 90 °C, calculated from Eq. (3), for selected MCs for long-grain ‘‘Cybonnett’’ rough rice (Ondier et al., 2010). For each MC value, linear regressions of ln(pv) vs. ln(ps) were performed using Eq. (1); Fig. 1 shows the corresponding linear regressions obtained for the MC levels of 8%, 10%, 12% and 18%. Qt was calculated from the slope of each line. The same procedure was used for estimating Qt when using EMC data collected at Ts ranging from 10 to 60 °C for the four lots listed previously (data not shown). Qn was calculated through Eq. (4). The slope of the ln(pv) vs. ln(ps) line approaches unity as MC increases (Fig. 1). Consequently, Qt approaches hfg as MC increases. This can also be interpreted to indicate that the energy required to dry rice, in terms of energy per unit moisture removed, increases as drying progresses. The Heats of desorption obtained from Eq. (1), along with corresponding MCs and Ts, were used to determine the parameters of Eq. (5) for each type of rice. Because of great differences among the SEs of Qt across MCs (Table 2), non-linear regressions were performed using the weighting feature of JMP (SAS Institute, Inc.), in which the SEs were weighted by using the reciprocal of SE (1/ SE). RMSE and equation constants obtained for Eq. (5) are shown in Table 3. Eq. (5) describes the experimental data well based on the low RMSE values for every rice type (Table 3). Additionally, the model consistently converged with little iteration to the estimates of the parameters, which is an indication of goodness of fit. When Iguaz and Vírseda (2007) modeled heat of desorption data, using the modified Guggenheim Anderson De Boer (GAB) isotherm equation (Anderson, 1946; De Boer, 1953; Guggenheim, 1966; Jayas and Mazza, 1993) to predict ERH, they found that the Kechaou and Maalej model (Kechaou and Maalej, 1999) was appropriate in describing Qn vs. MC data. Heat of desorption data for rice reported by Zuritz and Singh (1985), who used the Chung–Pfost equation to predict ERH, showed an exponential trend (Fig. 2), which is in agreement with the results obtained in this study. However, it is noted that Zuritz and Singh (1985) did not test any model to describe heat of desorption vs. MC. Discrepancies in findings can be explained by Souza et al. (2006), in that regardless of the crop, Qn, and thus Qt, behavior varies, depending on the equation that is used to predict ERH from sorption isotherm data. Rice was among the crops studied by Souza et al. (2006) who observed that when the modified Chung–Pfost equation was used to predict ERH, the heat of desorption curve followed an Author's personal copy 257 M.A. Billiris et al. / Journal of Food Engineering 107 (2011) 253–261 Fig. 3. Total heat of desorption (Qt) at different moisture content levels for long-grain ‘‘CL XL730’’, long-grain ‘‘Wells’’, medium-grain ‘‘Jupiter’’ and parboiled rice at 60 °C. The value of hfg is indicated and was 2359 kJ/kg water. Table 5 Equations based on Eq. (7) and Table 3 to predict the energy required to dry rice from an MCi to a desired MCf (QTrice) in J/kg dry matter, for the indicated rice types.a Equation Medium-grain/non-parboiled Q Trice ¼ ð3; 150; 878  2377TÞðMCf  MCi Þ þ e23:2MCf  e23:2MCi 23:2   Q Trice ¼ ð3; 189; 745  2496TÞðMCf  MCi Þ þ e24:2MCf  e24:2MCi ð9;742;417Þ 24:2   Q Trice ¼ ð3; 151; 394  2377TÞðMCf  MCi Þ þ e23:0MCf  e23:0MCi ð8;107;9206117TÞ 23:0 Long-grain/non-parboiled Long-grain/parboiled a b Temp. range,b °C Rice type   ð12;725;7719601TÞ 10–60 10–90 10–60 MCi and MCf are inputs on a dry basis. Temperature range over which EMC data were collected. Fig. 4. Total energy required to dry rice (QTrice) to 12.5%, 13.5% and 14.5% w.b. moisture content, expressed on a per unit mass of wet or dry matter of rice, as a function of the initial moisture content of the rice for long-grain, non-parboiled rice at 60 °C. exponential trend. In the case of other ERH equations, such as the modified Henderson equation (Thompson et al., 1968), the Qn curve was linear. To assess differences in drying energy requirements among rice cultivars, a final, target MC of 12.5% was chosen based on the fact that 12.5% is a typical, desired final MC in the rice industry. Since Qt Author's personal copy 258 M.A. Billiris et al. / Journal of Food Engineering 107 (2011) 253–261 Fig. 5. Energy required to dry rice (QTrice) to 12.5%, 13.5% and 14.5% w.b. moisture content, expressed on a per unit mass of water removed, basis as a function of the initial moisture content of rice for long-grain non-parboiled rice at 60 °C. Fig. 6. Energy required to dry rice (QTrice) to 12.5% w.b. moisture content, expressed on a per unit mass of water removed, basis as a function of the initial moisture content of the rice for long-grain non-parboiled, long-grain parboiled and medium-grain non-parboiled rice at 60 °C. increases as MC decreases, Qt is greatest at the end of drying and consequently it was relevant to evaluate if the differences in energy requirements among rice types were significant at this MC level. In addition, a T of 60 °C was selected to compare energy requirements among rice cultivars. Table 4 shows Qt values predicted using Eq. (5), and the 95% confidence intervals (CIs) obtained for each predicted Qt value for the different rice types. The Qt predicted for medium-grain ‘‘Jupiter’’ was significantly greater than the other rice types since the CI of ‘‘Jupiter’’ does not overlap with the other CIs; thus, the energy required to remove a unit mass of water from medium-grain rough rice with 12.5% MC at 60 °C is estimated to be significantly greater than that required for the other rice types (Table 4). Long-grain parboiled rice required significantly less energy to remove a unit mass of water from rough rice with 12.5% MC at 60 °C than that required for non-parboiled rice. The Qt CIs of long-grains ‘‘Wells’’ and ‘‘Cybonnett’’ do overlap. This indicated that the difference in Qt between these two cultivars at 12.5% MC and 60 °C was not necessarily significant. While Qt values for long-grain ‘‘CLXL 730’’ were significantly lower than those of long-grains Wells and ‘‘Cybonnet’’, the general level was similar among long-grains. As the differences in Qt between ‘‘Wells’’ and ‘‘Cybonnett’’ were not significant and as Qt of ‘‘CL XL730’’ was similar to those of ‘‘Wells’’ and ‘‘Cybonnett’’, one general model for long-grain, Author's personal copy M.A. Billiris et al. / Journal of Food Engineering 107 (2011) 253–261 259 Fig. 7. Energy required to dry rice (QTrice) to 12.5% w.b. moisture content expressed on a per unit mass of water removed basis as a function of the initial moisture content of the rice for long-grain non-parboiled rice. non-parboiled rice was developed. The predicted range of Qt for general, long-grain cultivars at 12.5% MC and 60 °C is shown in Table 4, while the RMSE for this general model is shown in Table 3. It is noted that the term B2 was not significant when fitting the general model. A possible explanation for this could be that the effect of cultivar on Qt was greater than that of T in affecting the exponential term of Eq. (5). Therefore, when considering all the cultivars separately, the B2 coefficient was significant but when all long-grain cultivars were used to develop the general model, the B2 coefficient was not significant. 3.2. Total heat of desorption results The values of Qt and their corresponding SE for long-grain ‘‘Cybonnett’’ are shown in Table 2. The total heat of desorption increases exponentially as MC decreases for all rice types (Fig. 3). There was a sharp increase in Qt for MCs below 15% and Qt approached hfg at MCs around 20%. The increase in Qt as MC decreases indicates that water is increasingly bound to the rice matrix as MC decreases. This is of interest to the rice industry as rice is dried within the range in which Qt increases considerably. Qt varied for long-grain ‘‘Wells’’ from 2371 to 3488, for long-grain ‘‘CL XL730’’ from 2371 to 3413, for medium-grain ‘‘Jupiter’’ from 2372 to 3624 and for parboiled rice from 2368 to 3194 kJ/kg water, for MCs from 8% to 22% at 60 °C. Zuritz and Singh (1985) reported Qt values for medium-grain rough rice from 2438 to 4015 kJ/kg water, for MCs from 4.8% to 23%, at 40 °C. Based on the trends shown in Fig. 3, parboiled rice requires less energy to be dried than non-parboiled rice lots at MCs below 15%. A possible explanation for this would be that during the parboiling process, part of the hull typically cracks, reducing the resistance to moisture transfer. Another possibility is that since starch gelatinizes during the parboiling process, the change in starch structure could increase the diffusivity of the endosperm, producing less resistance to moisture flow. Fig. 3 also shows the general effect of kernel dimensions and shape on the energy requirements to dry rice. Boyce (1965) referred to an unspecified study stating that kernels with similar dimensions would have similar energy requirements. Fig. 3 shows that the energy requirements for long-grain, pureline ‘‘Wells’’ and for long-grain, hybrid CLXL730 are equivalent, reinforcing the Boyce (1965) statement. Nevertheless, more cultivars should be studied to confirm this hypothesis. Another observation regarding kernel dimensions is shown in Fig. 3 in that the energy requirements for drying the medium-grain cultivar are slightly greater than that of the long-grains for MCs below 15%. Since medium-grain kernels are thicker, wider and shorter than long-grains, moisture has to migrate through a longer pathway, producing an internal resistance that is greater in medium-grain than long-grain rice. Therefore, the energy required to remove water from medium-grain rice would be expected to be greater than that of long-grain rice. Cnossen et al. (2002) found that the effect of drying air conditions on the drying rate of a medium-grain cultivar was less significant than for a long-grain, presumably due to the fact that internal resistance to moisture transport is greater in the first case. The Qt-results obtained for medium-grain ‘‘Jupiter’’ at 45 °C in this study and those for a medium-grain rice at 40 °C reported by Zuritz and Singh (1985) are shown in Fig. 2. The results are in general agreement, although a slight difference exists at the lowest MC level reported by Zuritz and Singh (1985). 3.3. Energy requirements to dry rice from an MCi to an MCf Based on Eq. (7), mathematical expressions that predict the energy required to dry rice from an MCi to a desired MCf (QTrice) at a given drying T were developed. These equations were developed using the appropriate A1, A2, A3, B1 and B2 values from Table 3. The resulting equations are shown in Table 5. Eq. (7) can be adjusted to predict energy requirements to dry rice from an MCi to an MCf on a per unit mass of water removed basis by dividing by the mass of water removed (Eq. (8)). Fig. 4 shows the variation of QTrice (drying energy required per unit mass wet rice and per unit dry matter) with MCi for longgrain, non-parboiled rice for three MCf levels at 60 °C. QTrice per unit mass wet rice was obtained by dividing QTrice (Eq. (7)) by the amount of wet rice corresponding to a unit mass dry matter at the MCi. The trends indicated in Fig. 4 are practically linear. Author's personal copy 260 M.A. Billiris et al. / Journal of Food Engineering 107 (2011) 253–261 An explanation for this would be that the linear terms of the equations shown in Table 5, representing the energy required to vaporize free water, are considerably greater than the exponential terms and therefore, the linear terms contribute considerably more to QTrice. Nevertheless, in order to obtain accurate theoretical energy requirements, including both terms in the equation is necessary because as MC decreases, the contribution of Table 5 exponential term becomes more important. For instance, the exponential term is 4.2% of the QTrice value when drying from 22% to 12.5% MC at 60 °C but is 10.0% of QTrice when drying from 14% to 12.5% at 60 °C for long-grain, non-parboiled rice. A conventional way of quantifying drying energy requirements in the grains industry is to express energy requirements on a per unit mass of water removed. Fig. 5 shows the energy required to dry rice from an MCi to a desired MCf of 12.5%, 13.5% and 14.5% on a per unit mass of water removed at 60 °C. QTrice decreased exponentially as MCi increases, when expressed on a per unit mass of water removed. In addition, QTrice increases as MCf decreases. Both of these observations reflect the increasing importance of Qn at the lower MC levels. Therefore, the energy required to remove a unit mass of water from rice should not be considered constant across MCi. Fig. 6 shows that QTrice decreases exponentially as MCi increases for the different rice types, when expressed on a per unit mass of water removed. Further, Fig. 6 confirms the findings discussed in Table 4 in that medium-grain rice required more energy than longgrains and that non-parboiled rice requires more energy than parboiled rice, when expressed on a per unit mass of water removed. The effect of temperature on energy requirements to dry rice from MCi to 12.5% is shown in Fig. 7. The energy required to dry rice from MCi to 12.5% decreases as drying T increases. For instance, the energy required to dry rice from 20% to 12.5% at 40 °C was of 2517 kJ/kg water removed, at 60 °C was of 2467 kJ/kg water removed and at 80 °C was of 2417 kJ/kg water removed (Fig. 7). 4. Conclusions The net heat of desorption (Qn) and total heat of desorption (Qt) decreased exponentially as MC increased for all types of rice in the range of 10–90 °C and 8–22% MC. Mathematical models were developed to predict the Qt (the amount of energy required to remove a unit mass of water from rice with a specific MC) for rough rice of long-grains ‘‘Wells’’, ‘‘Cybonnett’’ and ‘‘CLXL730’’, mediumgrain ‘‘Jupiter’’ and long-grain, parboiled rice. The Qt of parboiled rice at 12.5% MC and 60 °C was significantly less than that of non-parboiled lots, and the net heat of desorption of medium-grain rough rice was significantly greater than that of long-grains at 12.5% MC and 60 °C. Equations that predict the energy required to dry a unit mass of rice from an MCi to a desired MCf at a given T were obtained for long-grain non-parboiled, medium-grain non-parboiled, and parboiled rice. 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