SOLAR ENERGY Revista Mexicana de Fısica S59 (1) 163–167 FEBRUARY 2013

Kinetics modeling of the drying of Opuntia ficus indicawith solar energy

R. Lopez Callejas, A. de Ita, M. Vaca Mier, A. Lizardi Ramos, J. Morales Gomez, H. Terres, and A. Lara ValdiviaDepartamento de Energıa, Universidad Autonoma Metropolitana-Azcapotzalco,

Av. San Pablo No. 180, Col. Reynosa-Tamaulipas Del. Azcapotzalco, Mexico, 02200, D.F. Mexico,e-mail: rlc@correo.azc.uam.mx

Received 30 de junio de 2011; accepted 25 de agosto de 2011

Opuntia ficus indica, commonly known as nopal, is an endemic cactus plant of America. In this work the drying of nopal cladodes, usinga solar dryer with natural convection was studied. The drying process was monitored daily from 9:00 to 18:00 hours, during the monthsof April, May, and June, 2007. The experiment took place with two kinds of nopal cladodes, one with thorns and one without 30 % of thecuticle that protects the cladodes on both sides. The nopal without thorns was dried in 46 hours in June, while in April it took 75 hours. Forthe complete product these drying times were 150 and 300 hours, respectively. The numerical model that best described the drying processwas the double logarithm.

Keywords: Drying curve; solar energy modeling;Opuntia ficus indica.

El Opuntia ficus indica, conocido comunmente como nopal, es un cactus endemico de America. En este trabajo se presentan los resultadosobtenidos del secado de pencas de nopal en un secado solar que opero en condiciones de conveccion natural. El proceso fue monitoreadodiariamente desde las 9:00 hasta las 18:00 horas, durante los meses de abril, mayo y junio de 2007. El experimento se realizo con dos clasesde pencas de nopal, con espinas, es decir, completo y la otra sin el 30 % de la cutıcula que lo protege en ambos lados. El nopal sin espinasse seco en 46 horas en junio mientras que en abril se realizo en 75 horas. Para el producto completo estos tiempos de secado fueron de 150 y300 horas respectivamente. El modelo numerico que mejor describe al proceso de secado fue el doble logarıtmico.

Descriptores: Curva de secado; modelado de energıa solar;Opuntia ficus indica.

PACS: 44.30.+v; 44.40.+a; 66.30.jj; 66.30.Xj

1. Introduction

Opuntia ficus indica, commonly known as nopal, is an en-demic cactus plant of America and there are 258 knownspecies, 114 of which can be found in Mexico; in 2009, 8,800tons were produced for human consumption in approximately10800 cultured ha [1].

Nopal, an ancestral food source, has high contents of in-soluble and soluble fibers and it also offers medicinal proper-ties [2,3]. It has 17 amino acids, 8 of which are essential; theinsoluble fibers create a satiety sensation and help to a properdigestion. Also, the proteins promote the mobilization of liq-uids [4,5]. Nopal increments the levels and sensitivity to in-sulin, helping to stabilize and regulate the amounts of sugarin blood [6]. Amino acids, fibers and antioxidants, such as A(beta-carotene) and C vitamins, prevent damages in the wallsof blood vessels, the formation grease plaque, and colon can-cer [7,8]. The exportation from Mexico of nopal in its freshform is a recent activity, and the quantities devoted to this in-ternational commerce are as low as 60 tons per year, that is0.06 % of the national production. This promissory activityis highly limited by the necessity of exporting the nopal withthorns, because the clean nopal quickly becomes oxidizedin the cut zones. This limitation can be easily overcomedthrough the drying of the product and further processing ofthe powder into medicines and cosmetics.

Drying has been used from immemorial times to pre-serve food products. Open-air drying is the most commonlyused method, especially in tropical and subtropical countries.However, several disadvantages are usually confronted [9]:

product damage caused by rodents, birds and insects; productdegradation due to direct exposure to sun light, rain, storms,and dew; contamination with particles and gases due to airpollution; possible cracking of the product and loss of ger-mination capacity; quality reduction during storage due toinefficient or no-uniform drying. Open-air drying is also acommon practice for nopal, taking between 35 to 40 days insummer time to attain complete drying of the product [10].Thus, alternative drying processes, such as those based onsolar energy may represent important savings and effectiveprofits, if these drying times can be cut off with the corre-sponding benefits in the product quality.

Several solar devices for food drying have been con-structed and evaluated; for instance, a cabin type dryer hasrecently been used to dry vegetables such as zucchini, greenpepper, beans and onion [11], at 46◦C, using up to 90 effec-tive sun hours for beans. Corn was also dried in a similardrier, requiring 75 hours of sun to dry 10 kg of product at42◦C [11]. The drying of pineapple has also been studied us-ing a combined biomass-solar system [12]. Such device usesthe alternate source of energy (biomass) to cover the nightperiods in order to have a continuous drying system. Theproduct temperature was kept constant at 65◦C, requiring 39hours for total drying.

In this work we studied the drying of nopal in naturalconvection, using a solar drier. We analyzed the influence ofsolar radiation, in the air temperature and mass flow to at-tain the desired dryness of the product (98 %). Two typesof nopal samples were studied: one with thorns and another

164 R. LOPEZ CALLEJAS, A. DE ITA, M. VACA MIER, A. LIZARDI RAMOS, J. MORALES GOMEZ, H. TERRES, AND A. LARA VALDIVIA

without thorns, which was denuded of approximately 30 %of the cuticle that protects both sides of the nopal.

2. Materials and methods

2.1. Equipment

The equipment used in this work is presented in Fig. 1. Thechimney-type solar collector operated in natural convection.The capture surface was 3 m wide and 5 m long. The porousmedium made from steel turnings scraps, was 0.20 m thick.The drying chamber dimensions were 0.60×0.60×1.00 m,with three trays for products, separated 0.15 m between them.Product samples were set in a de 0.45×0.45 cm tray crossedby hot air. It had a 0.005 m-thick crystal cover, separated0.06 m from the porous media. The trapping surface incli-nation was 40◦ with respect to the horizontal plane and wasoriented south-north to capture the maximum solar energy.

Air and product-surface temperatures within the dryingchamber were measured using 3 calibrated K-type thermo-couples with reading accuracy of± 0.1◦C, located at theentrance of the chamber and another 3, located at the exit.Relative humidity of the environment was determined usingan EA25 EXTECH digital hygro-thermometer, with a read-ing accuracy of± 0.1%, which was located outside the so-lar dryer. An AN200 EXTECH Thermo-anemometer, witha reading accuracy of± 0.01 m/s, was used to measure thevelocity of air, at the exit of the dryer’s chimney. The productmass was continuously quantified using a BL1505 SARTO-RIUS scale, with an accuracy of± 0.01 g, which was locatedon top of the drying chamber.

The total solar radiation was measured with a 8-48 EP-PLEY pyranometer with a reading accuracy of± 1 W/m2,located on top of the solar collector and therefore, with the

FIGURE 1. Diagram of the solar collector, a) capture area;b) porous medium; c) drying chamber; d) three trays for productdrying; e) data acquisition system.

same inclination. All these variables were registered usingthe Lab-view software in 10 minutes intervals.

2.2. Experimental procedure

Nopal samples were acquired form the largest production re-gion in Mexico, known as Milpa Alta. Nopal samples weretested in two fashions, one using the complete cladode andthe other without thorns and 30% less of its protective cuticle.Both tests were done simultaneously and with identical ther-mal conditions. We selected those between 45 and 60 daysold, which had an average mass of 180 g and had physicaldimensions of 0.15 m-wide, 0.25 m-long and 0.016 m-thick.Three sets of two complete cladodes and two without thornsand 30 % less cuticle samples (an approximate mass chargeof 2.16 kg) were deposited in the drying trays of the chamber(Fig. 1).

The daily measuring period was from 9:00 to 18:00 hours.The following hours the solar collector was totally coveredwith a canvas to prevent nightly heat loss. During this periodnopal was kept inside a sealed plastic bag within an isolateddeposit to preserve its humidity. The following morning ex-perimentation continued, taking care to maintain the sameconditions as in the previous day.

2.3. Drying kinetics of nopal

In the drying process of vegetable products it is importantto determine the model that describes such process, whichis obtained from experimental data [13-19]. Several modelsthat describe the moisture relationship (MR) of a product asa function of time have been developed. The moisture rela-tionship (MR) is defined as,

MR =M −Me

M0 −Me(1)

whereM is the moisture content at time t,M0 in the ini-tial andMe is the equilibrium moisture content, whose valuedepends on the environmental relative humidity. This hygro-scopic balance ofOpuntiacladodes is presented by Lahsasni

TABLE I. Mathematical models used to determine the moisturecontents of agricultural products during drying processes.

Model Equation

Page [13] MR = exp(-ktn)

Newton [14] MR = exp(-kt)

Modified Page [15] MR = exp(-(kt)n)

Henderson [16] MR = a exp(-kt)

Logarithmic [17] MR = a exp(-kt) + c

Two terms [17] MR = a exp(−k0t)+b exp(−K1t)

Verna [18] MR = a exp(-Kt) + (1- a) exp(-Kt)

Wang and Singh [19] MR = 1 + at+bt2

Rev. Mex. Fis. S59 (1) (2013) 163–167

KINETICS MODELING OF THE DRYING OF OPUNTIAFICUS INDICAWITH SOLAR ENERGY 165

FIGURE 2. Average solar radiation in May 2007.

et al., [20], and is useful to predict the contents of water in rel-ative to the humidity present in air. They presented the sorp-tion curves, necessary to determine the drying kinetics of theproduct, as well as the conditions of storage of the product.The most used numerical models are presented in Table I.The criteria used to select the most appropriate model wasthat the correlation coefficient r tended to the unit and thatthe square chi (χ2) tended to zero. In these equations the val-ues of constants vary for each product and each experimentalcondition.

3. Results and discussion

Solar collector was only used to warm up the air that was usedin the drying chamber. The average solar radiation curve asa function of time registered for the month of May, 2007 andits representative equation are presented in Fig. 2. The max-imum average radiation, 987.4 W/m2 was observed approxi-mately at 14:00 hours. The corresponding total energy overthe collector surface was 6.40 kW/m2 h. The maximal solarradiation, 1052.45 W/m2 was registered in the month of Juneand the minimal radiation, 887.45 W/m2, occurred in April.The energy over the collector values were 7.23 kW/m2 h and5.55 kW/m2 h, respectively, these are relevant data, since theyinfluence the observed temperature and the mass flow of air.

The average temperatures versus the time of the day arepresented in Fig. 3. The highest temperature at the entranceof the drying chamber was 66.3◦C; the temperature measuredat the product was 63.5◦C, and at the outlet of the chamber,58.4◦C. These values were registered at 14:00 hours and co-incided with the value of highest solar radiation. The environ-mental temperature at the time was 26.8◦C, which was alsothe highest value registered during the period of experimen-tation. The difference in temperature between the inlet andthe outlet of the chamber was not constant through the day,early in the morning the difference was a minimum of 1.4◦C.The highest gradient was registered around 15:00 hours, as

FIGURE 3. Average temperatures in the drying chamber and envi-ronment, May 2007.

FIGURE 4. Average mass flow in the drying chamber.

FIGURE 5. Moisture contents versus time for nopal without thorns.

Rev. Mex. Fis. S59 (1) (2013) 163–167

166 R. LOPEZ CALLEJAS, A. DE ITA, M. VACA MIER, A. LIZARDI RAMOS, J. MORALES GOMEZ, H. TERRES, AND A. LARA VALDIVIA

FIGURE 6. Moisture contents versus time for complete nopal.

FIGURE 7. Numerical model for the drying of nopal withoutthorns, May, 2007.

8.7◦C. The temperature at the outlet of the chamber at the endof experimentation was 32.2◦C.

The average mass flow of air registered at the dryingchamber is presented in Fig. 4. The larger value of massflow was 0.0312 kg/s and occurred in June, in May it was0.0276 kg/s and in April it was only 0.0228 kg/s. All of thesemeasures corresponded to a time close to 14:00 hours. Thisflow follows the drying chamber because of the convectivedraft chimney effect.

The results of the drying experiment of nopal withoutthorns, for which 30% of the cuticle was cut off as well, forApril, May, and June 2007, are presented in Fig. 5. The graphshows the moisture content versus drying time. At the begin-ning of the process it was 19 kg water/kg of dry mass (d. m.)and at the end it was approximately 0.135 kg water/kg d. m.The drying time was directly dependent on the solar radiationcaptured on the cover of the drier. The longest drying timewas registered for April as 75 hours and the shortest time wasobserved in June, as 46 hours. The time in May was 55 hours.

TABLE II. Numerical model of solar energy drying of nopal

MonthNopal Equation

thorns

April

withoutMR=0.594exp(-0.125t)+0.550 exp(-0.0.19t)

r = 0.998,χ2 = 0.00001

withMR=0.521exp(-0.016t)+0.521 exp(-0.016t)

r = 0.996,χ2 = 0.00001

May

withoutMR=0.364exp(-0.172t)+0.793 exp(-0.031t)

r = 0.995,χ2 = 0.00001

withMR=0.515exp(-0.018t)-0.515 exp(-0.018t)

r = 0.997,χ2 = 0.00001

June

withoutMR=0.504exp(-0.091t)+0.504 exp(-0.091t)

r = 0.997,χ2 = 0.00001

withMR=0.463exp(-0.073 t)-0. 544 exp(-0.027t)

r = 0.998,χ2 = 0.00001

For the complete product (Fig. 6) the drying times wereconsiderably longer: 300 hours of sun drying in April,225 hours in May, and 150 hours in June, which correspondedrespectively to 300 %, 310 %, and 226 % longer than for theproduct with the cuticle removed. This was undoubtedly dueto the protection exerted by the cuticle in the complete prod-uct. These results are direct consequence of the average solarradiation observed in the months evaluated. If its value ishigher, so are the temperatures and flow mass.

It is relevant to notice that this technology results at-tractive for the drying of the product without thorns (46 to75 hours) when comparing it to the open-air drying processthat takes from 35 to 40 days [10]. However, the process isless effective and almost comparable to the open-air dryingof the complete product.

Experimental data were fed to each of the numerical mod-els presented in Table I. The double logarithmic model de-scribed the best performance of the drying process, in agree-ment with the two imposed criteria. The graph of the numericmodel obtained for the month of May is presented in Fig. 7.The equations of the numerical model for the six experimentsperformed are presented in Table II, in all cases this modelwas the better result for the imposed conditions.

4. Conclusions

The hot air used in the drying of nopal was attained in a solardevice packed with a porous medium to increment the storageof energy. The physical variables necessary to energeticallyevaluate the drying process were monitored daily from 9:00to 18:00 hours, during the months of April, May, and June,2007. The maximum air temperature at the inlet of the dry-ing chamber was 69◦C in June and 60◦C in April. The nopalsamples were studied in two fashions: complete and without30 % of its protective cuticle and no thorns; this was rele-

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KINETICS MODELING OF THE DRYING OF OPUNTIAFICUS INDICAWITH SOLAR ENERGY 167

vant to the results, because for the second type of sample thedrying time diminished considerably.

The shortest drying times were observed in June, and thelongest, in April, due to the intensity of the solar radiationfalling over the surface of the collector. The nopal withoutthorns was dried in 46 hours in June, while in April it took 75hours. For the complete product these drying times were 150and 300 hours, respectively. The drying of the nopal withoutthorns (46 to 75 hours) can be competitively performed usingthis solar drying device, when comparing it to the open-airdrying process that takes from 35 to 40 days. Nevertheless,for the complete product the process is less effective and al-most comparable to the open-air drying method. The numer-ical model that best described the drying process with solarenergy was the double logarithmical model. The criteria usedto select the most appropriate model were that the correlation

coefficientr tended to the unit and that the square chi (χ2)tended to zero. These results could be used to design solardryers to process largest amount of products.

Nomenclature

a, b, c, n dimensionless drying constants in drying models

d.m. dry mass

k drying velocity constant in drying models (1/h)

MR moisture rate, (kg water/kg dm)

M wet mass in time t, (kg water/kg dm)

Me equilibrium mass, (kg water/kg dm)

M0 initial mass, (kg water/kg dm)

t time, (h)

1. Servicio de informacion y estadıstica agroalimentaria y pes-quera con informacion de las delegaciones de la SAGARPA enlos estados, http://www.sagarpa.gob.mx, (visited in december,2010).

2. V.K. Deshpande, A.M. Joshi,J. Power.47 (1994) 185-188.

3. A. C. Frati, H. Hernandez de la Riva, C. R. Ariza, and M. D.Torres,Arch. Inv. Med. (Mexico)14 (1983) 117-125.

4. E. Galati, M. Monforte, M. Tripodo, A. d’Aquino, M.Mondillo, J. Ethnopharmacol.76 (2001) 1-9.

5. E. Park, J. Kahng, S. Lee, K. Shin,Fitoterapia 72 288-290(2001).

6. S. Gurrieri, L. Miceli, M. Lanza, F. Tomaselli, P.R. Bonomo, E.Rizzarelli,J. Agric. Food Chem.48 (2000) 5424-5431.

7. M. Mailainine, A. Dufresne, D. Dupeyre, M. Mahrouz, and M.Vignon, Parenchyma cell cellulose from cladodes of Opuntiaficus indica extraction and characterization, 11th InternationalSymposium on Wood and Pulping Chemistry (ISWPC). (2001).Grenoble, France, 18-19.

8. O. Yaldyz, and C. Ertcklyn,Dry. Technol.19 (2001) 583-597.

9. A. Mujumdar,Handbook of Industrial Drying. 2nd ed. (MarcelDekker, New York, 2007).

10. R. Lopez, A. De Ita, and M. Vaca,Internacional Drying Sympo-sium. Budapest, Hungary.20-23(2006) 1682-1886. ISBN963-9483-59-1.

11. I. Simate,Dry. Technol.19 (2001) 1137-1155.

12. B. Bena and R. Fuller,Solar Energy72 (2002) 75-83.

13. Y. Agrawal, R. Singh,ASAE paper No: 3531. (St Joseph MI:ASAE, 1977).

14. J. O’Callahan, D. Menzies and P. Bailey,Journal of Agricul-tural Engineering Research16 (1971) 223-244.

15. D. Overhults, G. White, M. Hamilton and I Ross.,Transactionsof the ASAE16 (1973) 195-200.

16. P. Westerman, G. White, and I. Ross,Transactions of the ASAE16 (1973) 1136-1139.

17. S. Henderson,Transactions of the ASAE17 (1974) 1167-1168.

18. L. Verna, R. Bucklin, J. Enda and F. Wratten,Transactions ofthe ASAE28 (1985) 296-301.

19. C. Wang, R. Singh,A single layer drying equation for roughrice. ASAEPaper No: 3001. St. Joseph (MI): ASAE (1978).

20. S. Lahsasni, M. Kouhila, M. Mahrouz, and M. Fliyou,EnergyConversion and Management44 (2003) 923-936.

Rev. Mex. Fis. S59 (1) (2013) 163–167