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' «#1 fiQ‘m 1 3 "j “ ‘ ' ...111' ‘..-I “ ‘ 3" 1’3 nggffl" I? i ‘ M . “1.1 -“““"',' ,1 5‘ 1% sum. 3‘“ 333.3133”; 1'11). IS I“. *1... :11: 1111211111113'W “13:11.5. “-- “1‘ I 1 \‘1‘3‘1 " 3 Illlllllll lllllllll ll\lllllllllllllll 3 1293 104242114 FWW‘ Wei-:7 J ilfifiu Ii Y T ‘ Michigan State University This is to certify that the thesis entitled PHJCESS ANALYSIS OF A MULTISTAGE (DNCURRENT RICE DRYER presented by Larry Phillip Walker has been accepted towards fulfillment of the requirements for Ph . D. degree in Agi‘icmtural Engineering fizz/64%; Major professor /, gfiifi 5“"? d1 v' ufibkg, r" (9-3 a 99 Tl : _\ My a . l . K, ' v . WI 1 «M #9179: " ‘3‘de OVERDUE FINES: ‘ Q q p _ I“ ' . :7; . ‘ V 9-H” =< i) ,, ‘3 £ '1'" My / , "N évfiw ‘29 25¢ per du per {tan REFUNDS LIBRARY MTERIALS: Place in book return to move charge from circulation ncords Pmss ANALYSIS OF A MULTISI‘AGE CH‘ICURRENI‘ ' RICE DRYER BY Larry Phillip Walker A DISSERTATIOI Suhnitted to Michigan State University in partial fulfillment of the requirements for the degree of IDCIOR 0F PIIILOSDPHY Agricultural Engineering Department 1978 ABSTRACT PRCXIESS ANALYSIS OF A MULTISTAGE (INCURRENT RICE DRYER By Larry Phillip Walker Rice, like most cereal grains is usually harvested at a moisture content too high for safe storage. This generates a need for artificial drying. The drying process is complicated by the susceptibility of rice to checking and breaking during drying and subsequent milling . The current multipass procedure of drying and tampering rice in bins for 4 to 24 hours requires a large number of bins for wet storage and a substantial amount of material handling. Fran a logistical point of view, it is advantageous to canplete the drying process in one oper- ation, thus reducing the number of bins needed for wet storage, decreasing the handling of the rice, and improving the energy efficiency of the entire drying process. The purpose of this investigation was to evaluate the physical feasibility of drying rice in a multistage concurrent flow dryer to determine the operating characteristics of such a dryer. This objective was achieved by conducting a series of pilot scale experiments with a onestage concurrent flow dryer and by developing conputer mdels to sim- ulate anmlti—stage concurrent flow dryer. The results show that: (1) rice can be dried in a one-stage con- current flow dryer at temperatures as high as 121°C without any significant decrease in head yield, provided that the grain flow is 0.17 m3/hr and the air flow 2.27 mS/min; (2) under constant drying con- ditions higher initial moisture content results in a higher moisture removal rate and energy efficiency, and a lower grain temperature; (3) an increase in the initial grain temperature under constant drying conditions results in an increase in the moisture removal rate, higher grain temperatures , and higher energy efficiencies; (4) under constant drying conditions, an increase in the drying air temperature results in an increase in the moisture removal rate and maximum grain temperature , and a reduction in energy required to remove a poxmd of water if there is not a corresponding increase in grain flow; (5) both air flow and grain flow can be used to control grain temperatures and moisture gra— dients; (6) an increase in the bed depth results in an increase in the moisture removed, a lowering of head yield, and a more uniform final moisture distribution; (7) tempering does not significantly improve the drying rate of rice in a concurrent flow dryer because rice dried in a concurrent flow dryer has a fairly uniform final moisture distribution; (8) drying rice in a concurrent flow dryer generally results in accept- able head yield, because of the uniform moisture distribution. To Tina ii AW It has been a great privilege to work under the guidance of Dr. Fred W. Bakker—Arkema. Through his example I have become aware of my social and professional responsibilities. His friendship, counsel, and understanding will always be remembered. I would like to thank Dr. James V. Beek, Dr. Larry J. Connors, and Dr. Bill A. Stout for serving on my guidance committee. 'Iheir advice and encouragement were very helpful. I would also like to thank Dr..kmmxs£t Ehmfilton, Dr. Gerald L. Parks, Mr. Roland.Lartigue, and.Dr. Lloyd E. Lerew for their encourage— ment and.moral support. Special thanks goes to Mr; Dave Calderwood of ABS-USDA, Beaumont, Texas, for his technical assistance, and.Westelaken Agricultural Engineering, St. Marys, Ontario, Canada, for their financial support. I offer my gratitude to my parents, Joe and Christine Fowlkes, and my grandmother, Mrs. Emheus Jeffery. 'lheir love, encouragement, and moral support helped me through some of the diffith moments. Finally, I would like to thank.my wife, Tina, for her love and understanding during these last difficult months. Her warm smile made the task a little easier. iii TABLE OF CINTENI‘S LIST OF TABLES . LIS'I‘OFFIGURE‘S I. LISTOFSYMBOIS....... ..... INI‘RCXIJCI‘IQ‘I l-l General remarks ....... 1—2 History of U. S. rice market . . . 1-3 Traditional method of rice drying . II. III. IV. LITERATUREREVIEW. . . ...... 2-1 2—2 2-3 2-4 2-5 2-6 Constant vs. falling rate drying ..... Drying equation . . . . Moisture equilibrium content Deepbeddryermodels. Tampering . ....... . . ...... Cracking or checking of rice . . . . . MATHEMATICAL NUJELS . 3-1 3—2 3—3 3-4 Dryer model . . ....... . . Drying parameters . . . ..... 3—2 . 1 Latent heat of vaporization ........ 3-2.2 Diffusion coefficient . . . 3-2 . 3 Convective heat transfer coefficient 3-2.4 Convective mass transfer ..... Tampering model . . ............ Numerical solution of differential equations EXPERIMENTAL AND MDEL VALIDATICN . 4-1 4—2 Experimentat 1on ............. Extimat ion of convective heat and mass transfer coefficient ................ iv Page . viii V. RESULTANDANDDISCUSSICN...... .......... 67. 5-1 Effect of boundary condition ........... 67 5—2 Effect of initial moisture content . . ...... 77 5—3 Effect of initial grain temperature ..... 82 5—4 Effect of drying air temperature . . . ...... 82 5-5 Effect of air flow . . . .......... 87 5-6 Effect of grain flow ........... 90 5—7 Effect of bed depth ............. 95 5—8 Effect of ambient air temperature . . . . . 95 5-9 Effect of tampering ............. . . 97 5-10Numberofstages........... ...... 102 5-11 Grain quality . . . ............. .103 VI. SUMMARY AND CINCIUSIO‘I . . 109 VII. SUGGESTICNSHBFURI‘HERRESEAKH ....... . 113 VIII. REFERENCES ............... . 115 APPENDICES A. Comparison of diffusion equation and thin-layer equation ............... . . 120 B. Physical and thermal properties . . 123 C. Conversion factors . . . . ..... 124 D. Programs ..... . . 126 E . Input / output example . 140 Table 2—2 2—3 3-2 3-3 4-1 4-2 4—3 4-4 5—1 5—2 LIST OF TABLES Rough rice crop acreage, yield and production, by states, 1977 . . . . . . . Comparison of rough rice and shelled corn diffusion coefficients at different moisture and temperatures using equation (2-8) and equation (2-9), respectively . . . . . Equilibrium moisture contents at different tempera- tures and relative humidities Effect of tampering rice, then cooling by aeration in bins following dryer passes, upon the amount of moisture removed during the cooling period and the milling yield of the rice . . . . . . . . Summary of the concurrent flow dryer model equations . Physical and thermal properties of rice and the drying air needed to simulate rice drying Physical properties of rough rice Thermal properties of medium grain rough rice Summary of monitoring equipment Results of the Beaumont drying tests . Summary of East Lansing drying tests . Canparison of experimental and simulated values for concurrent flow dryer Standard operating conditions for drying simulations . Comparison of moisture content, grain temperature, and diffusion coefficient at different bed depths for the convective and EMC boundary conditions . The values were calculated from equation 2-11 . vi Page 57 61 69' 72 Table Page 5—3 Comparison of the effect of initial moisture content on the diffusion coefficient at different bed depths. The values were calculated from equationZ-ll..... ...... .........80 5-4 Summary of the results from three simulations with different initial moisture contents. Drying variables are listedinTable 5—1 . . . . . . . . . . 81 5-5 Sumary of the results obtained from three drying simulations using the standard operating conditions listed in Table 5-1 for a single stage dryer. The initial moisture content was varied as shown below. . 84 5—6 Comparison of the effect of initial grain temperature on the diffusion coefficient at different bed depths. The values were calculated from equation 2—-ll . . . . 84 5-7 Smmary of the results from three simulations with different inlet air temperatures. The drying variablesarelistedinTableSd . . . . . . . . . . 85 5-8 Summary of the results from three simulations with different air flows. The other drying variables arelistedinTableS—l...... 91 5-9 Summary of the results from three simulations with different grain flow rates. The drying variables arelistedinTableS—l............... 94 5-10 Effect of dryer length on the drying performance of a single stage concurrent flow dryer. The drying variablesarelistedinTable5—l . . . . . . . . . . 96 5-11 Effect of ambient air condition on the drying performance of a concurrent f low dryer . The other drying variables are listed in Table 5-1 . . . . . . 96 5—12 Effect of drying temperature and initial moisture content , and time on the ratio of surface moisture content to average moisture content . . . . . . . . . 99 5—13 Summary of four simulations of the second stage with four different tempering times. The temperature of the drying air is 65. 6°C. All other drying variables are listed inTable 5—1 . . . . . 100 5-14 Sumary of four simulations of the second stage with four different tempering times. The drying variables are listed in Table 5—1 . . . . . ...... 101 vii Table Page 5-15 Summary of four simulations of the second stage with four different tempering times. The terperature of the drying air is 176. 6°C and the air flow is 2. 83 m 3/min. The other drying variables are listed inTable5-1..... . ...... ..101 5-16 Recommended dryer settings for a multistage concurrentflowdryer.... .......104 viii LIST OF FIGURES Figure 1—1 Schematic of multistage concurrent flow dryer 2-1 Comparison of drying curves for long and short grain rice using equation (2—9) and equation (2—6) . 2-2 Effect of tempering time and temperature on head yield . 2—3 Effect of tempering time and temperature on total drying time 2-4 Air and rice flow pattern in L. S. U. mixing—type dryer 3-1 Cylindrical representation of a rice kernel with mass diffusion in radial direction only . 4-1 M. S. U. dryer before modifications 4-2 Modified M. S. U. concurrent flow grain dryer 5-1 Comparison of the drying rate profiles for the convect ive and EMC boundary condit1ons. The drying variables are listed in Table 5—1 . . 5-2 Comparison of moisture content profiles for the convective and EMC boundary conditions. The drying variables are listed in Table 5—1 . . . 5-3 Comparison of absolute humidity profiles for the com- vect ive and EMC boundary condit1ons. The drying variables are listed in Table 5-1 . 5-4 Comparison of grain temperature profiles for the convective and EMC boundary conditions. The drying variables are listed in Table 5-1 . . . ix Page 17 24 25 53 58 68 7O 73 Figure Page 5—5 Comparison of air temperature profiles for the convective and EMC boundary conditions . The drying variables are listed in Table 5-1 ..... . . 76 5-6 Effect of initial moisture content on the drying rate profiles. The drying variables are listed in Table 5—1 ............. . ....... 78 5—7 Effect of initial moisture content on the moisture content profiles. The drying variables are listed in Table 5-1 .................... . 79 5—8 Effect of initial grain temperature on the moisture content profile. The drying variables are listed inTables-l.... ............. ....83 5—9 Effect of drying air temperature on the moisture content profile. The drying variables are listed in Table 5-1 ..................... 85 5—10 Effect of airflow on the drying rate profile. The drying variables are listed in Table 5-1 ....... 88 5—11 Effect of airflow on the moisture content profile. The drying variables are listed in Table 5-1 . . . . . 89 5—12 Effect of grain flow on the moisture content profile. The drying variables are listed in Table 5—1 . . . . . 92 5—13 Effect of grain flow on the drying rate profile. The drying variables are listed in Table 5-1 ....... 93 5-14 Comparison of moisture distribution in a rice kernel after different telpering periods. The drying variables are listed in Table 5—1 ....... . . . 98 5—15 Broken kernels versus air temperature . . . . . . . . . 106 5—16 Percent loss of head rice versus saturation deficit of thedryingair..... ............ ...107 93% H U) NO ’69 mCD ”CU U 80 <0 .60 {3" 0 :53" 535‘ H: (IQ (DE 3 SI L" N (.1. K p. LIST OF SYMKLS Specific product surface area, mz/m3 Specific heat of air, KJ/Kg Specific heat of dry grain, KJ/Kg Specific heat of water vapor, KJ/Kg Specific heat of water, KJ/Kg Diffusion coefficient, onZ/hr Product diameter, m Air flow rate, Kg/hr m2 Grain flow rate, Kg/hr m2 Convective heat transfer coefficient KJ/m2 Convective mass transfer coefficient, en/hr Heat or evaporation, KJ/ Kg Humidity ratio, Kg/Kg Phenomenological coefficient Phenomenological coefficient length, m Average moisture content , % w.b. local moisture content, decimal d.b. Equilibrium moisture content, decimal d.b. Initial moisture content, % w.b. xi Symbol H :Ug’d <‘Umeg OSI Fifi-10) Final moisture content , % w.b. Surface moisture content, decimal d.b. Moisture reroved, % w.b. Vapor pressure, Kgf/cm2 Saturated vapor pressure, Kgf/cm2 Radius of rice, em Radius, cm Surface area of grain, m2 Air temperature, °C Entering air temperature, °C Wetbulb temperature , °C Absolute air temperature, °K Time, hours Volume, m3 Grain velocity, m/hr Phenomenlogical coefficient Phenomenlogical coefficient Phenomenlogical coefficient Phenomenlogical coefficient Non-dimensional time Variable bed depth, m Bed depth , m xii I . INTKDUCTIQ‘I , 1-1 General remarks Mankind's potential to evaluate and solve coiplex scientific and engineering problems expanded tremendously with the birth of the computer era. Queration research and system analysis are some of the problem solving methodologies that developed with the advent of the computer. Although these methodologies differ in some respect and have different meanings for different disciplines they all have the following objectives: (1) exact specification of the problem, (2) detailed analysis, and (3) development of a viable solution. Operation research, system and process analysis differ from classi- cal analysis in that they focus on the interact ion or interdependencies of components and not just the components themselves. They are based on the premise that the "wtole is more than the sum". Both, the terms system science and process analysis are used by engineers to refer to the scientific methodology described above. Process analysis seems to be the most appropriate for this rice drying investiga— tion because the term process denotes an actual series of operations or treatments of material in contrast to the more abstract term system. The rice drying process is a complex interaction between the grain and air. Like most processing problems, the analysis of rice drying entails: (l) mathematical specification of the problem for a given 2 physical situation, (2) detailed analysis to obtain mathematical models, (3) synthesis of discrepancies between theoretical and experimental results, and (4) development of procedures for obtaining viable solutions. Dryer manufacturers and design engineers are depending more and more on corputer models to evaluate preliminary designs and to gain better insights for making improvements in their current equipment. This is particularly important in light of the increased interest in grain quality and energy efficiency. Often the design parameters and operating characteristics of a process can be obtained from field experimentation. However, this approach is costly in time and money. Mathematical modeling and simulation are an economical means of experimentation. In addition, it provides a means to explore extreme ranges of operation which may seem impractical or be impossible to obtain in the field. Also, a set of alternative designs and operating policies can easily be generated when new factors or elements are introduced into the system. 1-2 History of U. S. rice market The birth of the U. S. rice industry can be traced back to 1685. From a bag of rice given to Dr. Henry “bodward, the Carolina Gold Variety was established (Pratt, 1960). Rice was primarily grown in the south- central states until 1890. The four Atlantic Coast states produced 96 percent of the domestic rice Sipply by 1856. This was reduced to 77 percent by 1879 and to 27 percent by 1899. Currently, less than 6 percent is grown in that region . 3 From 1884 to 1886 trial plantings of rice were made in the prairie section of southwest Louisiana (Adair, 1972). The plantings revealed that the crop was well adopted to this area. Production increased rapidly in southwest Louisiana and southeast Texas . Rice production in Arkansas did not become an important industry until 1904. Rice was grown on an experimental basis in California in 1909 and rapidly became established as a commercial crop by 1912. Table 1-1 indicates the rice growing area of the U. S. in 1977. Commercial varieties of rice grown in the U. S. are classified and marketed under three market classes, long grain, medium grain, and short grain. At present, long-grain rice is grown primarily in the southern states and practically all short-grain rice is produced in California. Medium—grain rice is grown in all U. 8. rice production areas (Adair, 1972). The average annual U . S . product ion for the five years ending in 1899 was 154,200 metric tons (Adair, 1972). The average for the five- year period ending in 1949 was over 1,600,000 metric tons. By 1969 the 5—year average was 4,071,000 metric tons, better than double that of 1949. Production in 1976 was approximately 5,610,000 metric tons (USDA, 1976). The dorest ic rice consumption can be divided into four main areas: (1) direct food use, (2) food processing use, (3) industrial use, and (4) feed and seed use. Currently 69 percent of the domestic rice ccnsurption is used for food, 23 percent for industrial use and 8 percent for seed (USDA, 1976). Domestic use for 1976/1977 is expected to be about 1.94 million metric tons (USDA, 1976). The U. S. is the number one rice exporter in the world. 4 Table 1-1. Rough rice crop acreage, yield and production, by states, 1977 . Area Yield Production State ha kg/ ha million metric tons Arkansas 322 , 541 5 , 267 l . 699 California 138 , 406 6 , 051 0 . 8377 Iouisiana 193 , 444 4 , 147 0 . 8022 Mississippi 42 , 088 4 , 875 0 . 2052 Missouri 5 , 261 5 , 896 0 . 0259 Texas 189 , 397 4 , 931 0 . 9765 United States 891 , 137 5 , 101 4 .467 Source: USDA (1977) 1-3 Traditional method of rice drying Rice is usually harvested at a moisture content too high for safe storage (Schmidt and Jebe, 1959). This generates a need for artificial drying prior to storage. Rice drying is complicated by the product's susceptibility to checking and breaking during drying and subsequent milling. Because rice is eaten whole its market value decreases as the proportion of broken grains in a sample increases . To prevent checking and breaking of the kernel, rice has tradi- tionally been dried in three to five stages or passes. In each stage the rice passes through the dryer and then is allowed to temper in a bin from 4 to 24 hours, to allow time for the moisture in the kernel to 5 redistribute. Most of the rice crop in the U. S. is dried at commercial drying installations or rice mills in continuous-flow dryers by this multipass or multistage method (Wasserman and Calderwood, 1972). There are a variety of gain dryer designs on the market. Basically, the designs fall into four categories: (1) the fixed bed dryer, (2) the crossflow dryer, (3) the concurrent flow dryer, and (4) the cascade type (Bakker-Arkema e_t__a_11. , 1974) . Of the four designs, the concurrent flow dryer seems to have the best operating characteristics for rice drying. It can be operated at a higher terperature than fixed beds, crossflow and cascade dryers resulting in a higher thermal efficiency without excessive gain damage. Uniform drying is also achieved in a concurrent flow dryer because there is no moisture gadient across the bed perpendi- cular to the direction of flow, as is the case for crossflow dryers (Brooker M. , 1974) . Thus, each kernel receives the same treatment in a concurrent flow dryer. The current multipass procedure of drying the rice and tempering in bins for 4 to 24 hours requires a large number of bins for wet storage and a substantial amount of material handling. From a logistical point of view, it would be desirable to complete the drying and tempering pro- cess in one operation, thus, reducing the number of bins needed for wet storage, decrease the handling of the rice and improve the energy effi- ciency of the entire operation. This objective can be achieved with a multistage-concurrent flow dryer. Figure 1—1 is a schematic of a mmltistagwncunent flow dryer. Each drying stage with the exception of the last one is followed by a terpering section. The final stage is followed by a mterflow cooler. Dryer Inlet Grain Dryer l Dryer Exhaust Tempering Section r Dryer Inlet j, D er Exhaust 57 TY Section FJ&___£E:_———_- Dryer Inlet . Dryer Exhaust Cooler Exhaust Dryer Cooler { { { { ler Inlet Figure 1-1. Schematic of multistage concurrent flow dryer. The concurrent flow dryer was selected for this study because of the characteristic noted earlier. The purpose of this study is to evaluate the feasibility and operating characteristics of a multi- stage—concurrent flow dryer. II . LITERATURE REVIEW In view of the enormous amount of literature on dryers and the drying process, it is not possible to corpletely cover the topic. Instead, the principal models and theories which have been advanced to describe the single layer and deep bed drying and the terpering processes will be examined. An understanding of these processes is essential for the mathematical specification of the rice drying problem and for assessing the impact of these two processes on the energy efficiency of the dryer and the checking or cracking of the rice. 2—1 Constant vs. falling rate drying In some biological products the moisture content is high enough to maintain a free water surface. The drying process under this condition is governed by heat and mass transfer between the water surface and the drying medium and is independent of the material (Allen, 1960). Drying under these conditions proceeds at a constant rate until the surface moisture is removed. The constant rate drying period is followed by a falling rate period. During the falling rate period moisture transfer at the surface of the kernel is greater than the moisture movement through the interior of the kernel. This results in a decreasing rate of moisture reloval. Rice and other cereal gains usually dry solely during the falling 8 9 rate period (Brooker et a1. , 1974). 2—2 Drying equation Essential to any dryer simulation is a single kernel or thin-layer drying equation that predicts moisture reloval rates as a function of the drying variables. A substantial portion of the gain drying literature is devoted to the development of thin-layer or single kernel drying equations. Empirical thin -1ayer equations are derived from experimental data of continuous drying. They constitute a lumped parameter representation of the drying process , and ignore the contributions of spatial variation in the kernel. Erpirical equations are accurate and dependable as long as the analysis is conducted within the range of the experimental observations. Several purely empirical drying equations have been developed for cereal gains . Henderson and Perry ( 1955) conducted a series of studies on the drying of agricultural products and observed that the drying rate during the falling rate period is approximately proportional to the difference between the moisture content of the product and the product equilibrium moisture content : — = a’(M - M ) (2—1) e = e-a t (2_2) 10 The constant 01’ is determined by the physical characteristics of the product. Equation (2-1) is the basis for many thin-layer drying equations. It is simple to evaluate and lends itself well to digital computaion. Allen (1960) developed an equation similar to equation (2—2) for corn and rice: M ~M -1 o e 1:'-0L*10g(M-Me) The value of 01* for rice is 0.067. Chancellor (1968) in his investigation of conduct ion-heat drying obtained the following empirical thin-layer equation for rice: M - M e = 0.0735 (e'Gt + l e‘4Gt + -1- e_96t) (2.4) M - M 4 9 0 e where G = 8.860 e‘6147°0/9abs Chancellor's equation is a good prediction of conduction drying but has not been verified for convective drying systere. Ramaro and Wratten (1969) developed a matheratical expression relating moisture reroval for rice to the drying parameters in the drying process. A series of experiments on rice drying was conducted in which the drying variables were formed into dimensionless parameters. The following equation was obtained: 11 MR = (73.109 - 59.319 Té/Tg) (37 167 - 0.068 Té/G) M. - M T - T (1 %( e W) (2_5) W 1.45 -1.108 1 - ram-7.963 (51%) (Rero'438 0%) W where Te = inlet air terperature, °C Tw = wet bulb terperature, °C 0 = gain terperature, °C Equation (2—5) has not been verified for air temperature to grain temper- ature, (Te/0) other than 1.0. Agawal and Singh (1977) conducted a thin-layer drying experiment on short grain rice. From their analysis of the experimental data the following thin-layer equation was obtained: M - Me Y ' 0 e where x = 0.02953 - 0.44565 rh + 0.01215 T y = 0.13365 + 1.93653 rh + 1.77431 rb2 + 0.009468 T Equation (2-6) was obtained from a limited number of initial moisture content from one initial moisture content, 24% w.b. 12 Wang and Singh (1978) conducted a series of thin-layer drying experiments with medium gain rough rice. Four different erpirical models were selected and fitted to the experimental observations. They concluded that all four models with several regession constants could be used as a thin—layer equation. They recommend that the following quadiatic equation be erployed because it required less corputational time in a corputer simulation: M-M e 2 M.-M 1 e 1+At+Bt where t=time,min -0.001303 x 00'4687 x rh'0'3187 {D II and 0 .03408 x -O. 3187 0.00006625 x O rh UJ II Appendix I contains a comparison of the equation of Wang (1978) and Husain ( 1973) . All of the empirical thin-layer equations examined so far require very little corputational time to evaluate drying rates. The primary disadvantage of the empirical thin-layer equations is that they are lurped parameter representations of the drying process, and thus ignore spatial variation in the moisture content of the kernel. This results in a model that predicts the same drying rate regardless of terpering 13 time or kernel moisture distribution. A more realistic model would be based on the physical mechanisms of moisture movement in a single rice kernel. A number of physical mechanisms have been proposed to describe mass transfer in capillary porous products. It is generally agreed that moisture movement within a gain kernel takes place by diffusion (Brooker gt_a;l_., 1974). Kumar (1973) has studied moisture moverent into a kernel of corn. It seems clear that moisture movement into a corn kernel occurs primarily through the base end of the tip cap. Still several researchers have successfully erployed radial diffusion models in their approximation of single kernel drying. Becker (1959) solved the spherical diffusion equation and corpared it with the experimental results of some wheat drying tests. The diffusion equation in spherical coordinates is, assuming a constant D: —-=D [— +— ——1 (2-7) Becker concluded that the spherical diffusion equation representation yields an acceptable approximation to the drying of wheat. Several researchers (Chu and Hustrulid, 1968; Hamdy and Barre, 1969; and Ingam, 1976) have successfully simulated single kernel drying of corn. Chu and Hustrulid (1968) obtained the following equation for the diffusion coefficient of a spherical corn kernel: 14 D(M) = 1.5134 Exp [(0.00045 Oabs - 0.05485)M - 75a;— S 2513.0] (2-8) Husain, Chen and Clayton (1973) developed a matherat ical model for rice drying based on simultaneous heat and mass transfer. The model is based on the assumption that radial mass diffusion is the predominant mechanism of moisture moverent in rice. system of equation: 3M _ 1 3 3M 7 ‘ r 5; (Dr Br 39 - E .3. E EM 7: r 3r (r 3r k at where a = thermal diffusivity, cmz/h w II The authors solved the following (2.9) (2—10) thermal conductivity, Kcal/h m °C The diffusion coefficient for rice was found to be: D(M) = g exp {mama} where g(0) = 94.8737 exp [”13914-9/Oabs] and = -u f(9) 4.90722 x 10 Gabs - 0.3788 (2-11) They concluded that the thermal gradients in the kernel could be neglected. 15 Table 2—1 is a comparison of the diffusion coefficient for rice and corn. Figure 2-1 is a corparison of drying curves for long gain and short gain rice using the equations of Agawal and Singh (1977) (equation (2—6)) and Husain, Chen and Clayton (1973) (equation (2-9)). Nishiyama ( 1975) solved the spherical diffusion equation (equation 2-6) for rice assuming a constant surface moisture content. He obtained the fol lowing solution: 00 2 M - M ‘n X e 6 Z 1 e _____ = ”'2 (2-12) MO Me E2 h = 1 n where X = kt + X0 = dimensionless time correct ion term Xo The correction term was chosen to correct for the discrepancies between the experimental and theoretical drying curves due to the assumption of a constant surface moisture content. Nishiyama’s (1975) approach has sore of the same drawbacks that are encountered with empirical thin—layer equations . The primary disadvantage is that the moisture distribution inside of the kernel is not evaluated. Radial diffusion equat ions (equations 2—9 and 2—10) provide considerable insight into the effects of spatial moisture variation on drying, teipering and cracking of rice. The major drawback in using these equations is the large amolmt of computational time needed to evaluate the drying rates . 16 $00: seasonal 00.8 05b 880C sores one .56 .5895 ”00.500 0050.0 0050.0 088.0 088.0 0600.0 $m80 088.0 m$80 «New «880 838.0 0600.0 808.0 580.0 008.0 RN80 8048.0 :48 0800.0 808.0 8000.0 0080.0 8000.0 «88.0 s880 028.0 8.00 808.0 028.0 $8.0 880.0 wmm80 a280 H280 880.0 80¢ 088.0 a280 088.0 380.0 >280 0080.0 0.280 808.0 when Eco moon 980 SE ECU 00E goo 03m Do 08 u a 0.0m u 2 0.2 u 2 0.0a n 2 00526989 0.8 e n 3828 050202 Eben . “3523808 88038 new??? .313 defiance one 3L3 aoflpmooo moan: $593953 one 0559.5: pogomwflo Hm mucosa Imooo oofimamfio 28 wood u .3 ounce ooHHobm one A80 wooed u .C swoon ”Room mo :03ng .HIN 39mm. Moisture Content - % d.b. 30 17 25 \ 20 15 10L Short Grain 2 3 4 Time- hrs Ul Ch Figure 2"1- Comparison of drying curves for long and short grain rice using equation (2-9) and equation (2-6) oorputed at a drying terperature of 50° C and a relative humidity of 25%. 18 2-3 Moisture equilibrium content The concept of the equilibrium moisture content is important in the analysis of the drying process. It serves as a boundary condition in several drying equations. Also, it is the minimum moisture content to which a gain can be dried under a given set of environmental condi— tions. The equilibrium moisture content (EMC) is dependent upon the humidity and teiperature of the surrounding air as well as on the species, variety, and maturity of the gain (Brooker £11., 1974). A number of equilibrium moisture content (EMC) models have been proposed. Henderson (1952) used Gibb ' 5 adsorption equation to derive the following semi-theoretical equation for the moisture equilibrium of biological products: 1 - (pV/pvs) = libip (-h Tabs Me) (2-12) The Henderson equation has been found to be inadequate for cereal gains (Brooker et al., 1974 and Thompson, 1967). Day and Nelson (1965) developed the following modified version of the Henderson equation for wheat: 1 - (Pv/va) = Exp <-i Mel‘) (2—13) where the parameters j and k’are terperature dependent. This model has proven adequate for wheat . 19 Henderson (1970) proposed the following EMC model for rice: 1 - rh = Exp (-a Men) (244) where equation (2-14) was evaluated at room temperature and therefore is not appropriate for predicting the equilibrium moisture content in dryers using tameratures significantly above ambient. Kachru and Matthes (1976) conducted a series of desorption exper- iments on a long gain variety called Starbonnett over a wide range of relative humidities (5—90%) and temperatures (526 °R - 560 °R). From these experiments the following empirical model was developed for predicting the equilibrium (dry basis): Me = 4.510 + 0.069 rh + 8.837 rh°°5-0.015 rh°'5 Tabs (2-15) Equation (2—6) fits the data very well over the range of humidities and tameratures qtoted earlier. In addition, there are no stability pro- blems when condensation occm's. T‘abulated in Table 2-2 are some of the values of the equilibrium moisture content of rice at different tempera- tures and relative humidities. 2—4 Deep bed dryer models In the previous section several thin-layer and single kernel drying models were examined. In this section model design to simulate the complete drying process will be examined. 20 Table 2-2. Equilibrium moisture contents of rice at different tempera- tures and relative humidities. Temperature Equilibriumanisture Content - %>d.b. °K °R rh=40%> rh=50% rh=60%> rh=70% rh=80% 280.0 504.0 15.35 16.99 18.54 20.02 21.45 300.0 540.0 11.93 13.17 14.36 15.51 16.62 320.0 576.0 8.52 9.35 10.18 10.99 11.79 340.0 612.0 5.10 5.53 5.99 6.47 6.96 360.0 648.0 1.69 1.72 1.81 1.95 2.13 Source: Kachru and Matthes (1976) Cbmputer simulation of deep bed grain drying is a recent development. Alttough sophisticated mathematical models based on heat and mass trans- fer were developed as early as 1955 (van Arsdell, 1955), it was not until the late 60's that deep bed computer solutions were obtained. Thompson (1967, 1968) developed a series of semi-empirical models of concurrent-cross— and counter-flow corn dryers. Thompsonksmodels require a thin-layer equation and therefore have the same disadvantage memt ioned earlier. Bakker—Arkema _e£__a_1_. (1970, 1971 , 1974) developed a series of theoretical fixed bed, concurrelt , crossflow and counter—current dryer models. The.mode1s were developed by evaluating enthalpy and mass balances on a differential volume with the following assumptions: 1. no appreciable vollmme shrinkage occurs during the drying process ; 21 no tamerature gradient exists within each gain particle; particle to particle conduction is negligible; the airflow and gain flow are plug-type; 8T/at and aH/at are negligible compared to aT/ax and aH/ax; the bin walls are adiabatic, with negligible heat capacity; qmmoww the heat capacities of moist airand gain are constant during short periods of time; 8. an accurate thin-layer drying equation and moisture equilibrium isotherm are known . The assumptions and balances result in the following system of equations for a concurrent-flow model: 3T .. hca __ = (T- a) (2-16) 8x GaCa + Ga CWH ; + _ %=GC 22cm (T‘O)':f% +Cg(:me)6a%g (2’17) P P P W P P P W -G AI! = .12 fl (2—18) x G 3x a '3'? = an appropriate thin-layer or single rice kernel drying equation. The MSU models (Bakker—Arkema 9:931. , 1974) are based on heat and mass transfer and are general enough to be used for different products , pro- vided that the physical properties of the products are known. Chan (1976) used the LBU fixed bed model to simulate the drying of rice in a bin. Several researchers (Evans £31., 1970; Lerew e_t_g._1_., 22 1972; Brook, 1977) have simulated drying of other agricultural products with the aid of other models developed by Bakker—Arkema et a1. (1974) . Spencer (1969) developed a model similar to Bakker-Arkema et a1. (1969). Spencer (1969) obtained the following system of equations: 3T _ 11(9 - T) __ .. .__.___... (2—19) ax GoCa 3p .1 = ____(l " E) 11"} ex P G Va 3t (2’20) 8M {- h(0-T)+h —P (1-3)} .3_0_= fgat G _ a {PG (1 - 6) (CG + cm M} (2 21) 3M _. ‘a‘t’ - f(e, M, M , t) (2-23) Since these equations are non-linear a numerical means of solving the problem is needed . Spencer's (1969) model of wheat drying predicts drying rates well at both high and low moisture contents. However, the theoretical tempera- ture curve deviates considerably from the experimental curve in the early period of the drying process. Baughmon, Hamdy and Barre (1973) and Ingram (1976) developed deep bed dryer models for wheat and corn similar to Bakker—Arkema 5213.1. (1969). Both models were based on intra-particle diffusion. (lily one of the dryer models mentioned so far have been applied to rice drying (Chan, 1976). None of the contimous flow dryer models has been applied to rice drying. 23 2-5 Tampering During the falling rate drying period an internal moisture gradient develops in the rice kernel . This moisture gadient causes cracking (Prasad _e_t_a_1., 1965; Schmidt and Jebe, 1959; Kunze and Ctoudhury, 1972). In the tempering process the moisture content in the kernel equalizes. Very little theoretical work has been done on the rice tempering process. Ibwever, it is generally accepted that moisture diffusion is the primary mechanism of tempering (Wasserman 31:411. , 1964). Several researchers have conducted experiments on tempering. Wasserman gt__a_l_. (1964) found that tempering shortens the total in-dryer time and helps prevent breakage of the rice during subsequent milling (see Figures 2-2 and 2—3) . From their experimental observations it was concluded that the rate of moisture migration increases with temperature. Sabbah 3131. (1972) studied the effect of tempering on cooling shelled corn. He concluded that change in average grain temperature and moisture content due to tempering was negligible and that the only change during tempering is in the moisture distribution in the kernel . Sabbah 91:31. (1972) also concluded that terpering had a limited effect on moisture reroval during cooling. Calder-wood and Webb (1971) conducted a series of tests in a L.S.U. mixing type rice dryer (Figure 2-4). They concluded that terpering rice for periods up to 12 hours at high temperature following the dryer pass did not significantly change the amount of moisture reroved during Subsequent cooling cycles. In addition, they concluded that tempering duration had no significant effect on the milling yield (Table 2-3). 24 62 L TEMPERED WITHOUT COOLING (105° F) O O / A 60 " r 0 .\° I . 58 " I t x o. ’ f K __, 55 _ I I TEMPERED AFTER COOLING (75°F) U I >- 54_ I ’l o I I g 52 -/ I I 50 L / -J I <1 2 48 4 L: I 46 l l l l I I I l o 4 8 :2 I6 20 24 28 32 TEMPERING TIME, HOURS Figure 2—2. Effect of tempering time and temperature on total head yield. Source : Wasserman and Ferrel (1964). 25 .40 \ \ x TEMPERED AFTER COOLING (75's) IIO \ TOTAL DRYING TIME, MINUTES IOO 90 80 \ /TEMPERED WITHOUT COOLING IIOS'FI o ‘ I? #— I6 20 24 28 32 TEMPERING TIME , HOURS‘ Figure 2-3. Effect of tempering time and temperature on total drying time. Source: Wassermen and Ferrel (1964).. Figure 2—4. Air and rice flow patterns in L. S. U. mixing— type dryer. - Source: Calderwood (1972) 27 Moisture Rice temperature removed, Milling yield"? Variety Tampering leaving dryer avg. per _ head rice time average max. cooling control treated change period* Hours °F °F Percent Percent Percent Percent Belle 0 111 112 1.0 52.6 48.7 -3.9 Patna 0 114 119 1 . 2 50. 6 48. 9 -1. 7 6 111 112 1.1 51.5 47.3 -4.2 6 115 117 0.5 49.4 49.2 -0.2 12 111 112 1.3 48.5 48.2 -0.3 12 114 117 0.8 49.7 46.0 -3.7 Nato 0 113 114 1.0 66. 4 67. 1 +0. 7 0 111 113 1.4 66.4 64.0 -0.9 6 111 115 1.2 65.4 64.0 -1.4 6 111 113 0.8 67.2 64.6 -2.6 12 111 112 1.4 65.3 64.0 -1.3 TP 49 0 113 113 1.0 65.0 61.9 -3.1 0 106 111 1.4 65.3 64.0 —1.3 6 112 115 1.3 64.3 62.0 —2.3 6 106 110 1.2 62.5 64.5 +2.0 12 112 114 1.0 64.1 60.2 -3.9 12 108 111 1.1 63.0 63.2 +0.2 Avg. all lots not tempered, 1.2 -2.0 Avg. all lots tempered 6 hours, 1.0 -2.3 Avg. all lots tempered 12 hours, 1.0 -l.8 * Moisture reroved, percent (dry basis) T Milling yields were obtained by project personnel. Table 2-3. Effect of tempering rice, and subsequent cooling by aeration in bins following dryer passes, upon the amount of moisture removed during the cooling period and the milling yield of the rice. Source: Calderwood and Webb (1971) . 28 Beeny and Ngin ( 1970) concluded that milling head yields increase with prolongation of terpering durations but only slightly after 5 hours. He also noted that the fuel consumption was reduced as tempering duration was increased. Beeny and Ngin's (1970) conclusion about the effect of tempering duration on head yields contradicts the observation of Calder- wood and Webb (1971) and confirms the observation of Wasserman 312.1. (1964). Brook (1977) concluded that tempering times beyond 1.25 hours had a negligible effect on the final moisture content and temperature of corn in a concurrent flow dryer. He attributes this to the uniformities of the average moisture content and terperature between kernels after drying in a concurrent flow dryer. Brook (1977) also noted that higher inlet temperatures resulted in a decrease in tempering time. Steffe, Singh, and Bakski (1978) investigated the effect of terpering time on moisture reroval and milling yields in the drying of high moisture medium gain rice. The dryer was constructed so that three rice samples could be dried simultaneously. The rice was dried in three identical bins (23.5 cm2 base, 18 cm deep) at 38°C and 50°C for periods of 20 and 35 minutes. Tampering time varied from 0 to 24 hours. They concluded that terperimg high moisture rice between drying resulted in an increase in moisture removed without a reduction in head yield. They also concluded tempering times of 3 hours are satisfactory and shorter times were ade— quate for maintaining grain quality. 2—6 (racking or checking of rice There have been many investigations of checking or cracking of rice and other cereal gains. Schmidt and Jebe (1959) found that approximately 57 percent of the total variability found in head rice losses could be attributed to variations in the saturation deficit of the drying air and 30 percent to the drying temperature. The saturation deficit is the difference between the saturated water vapor pressures at the dew point and the dry-bulb temperature of the drying air. It is interpreted as a measure of the drying rate. Caution must be used in applying Schmidt and Jebe's (1959) results to dryer configurations other than a fixed bed thin-layer dryer. Kunze and Hall (1965. 1967) observed that brown rice fissured readily from moisture adsorption effects without the presence of a temperature gadient. They determined that a temperature difference of 16.67°C between the rice and air did not produce fissures as long as the rice was maintained at a constant moisture content. They also observed that high moisture rice kernels fissured faster than low moisture kernels when exposed to the same vapor-pressure difference at a particular temperature. Kunze and Choudhury (1972) investigated the relation between moisture adsorption and tensile strength of rice. They observed that the rate of moisture adsorption and its penetration into the kernel depends on the initial condition of the kernel and the environment to which the kernel is subjected. For slow adsorption the rheological properties of a kernel are such that no fissuring occurs. At fast rates fissures occur rapidly . 3') Arora, Henderson and Burkhardt (1973) found the same temperature dependency on the fissuring of rice that Kunze (1972) had observed. They reported that a temperature larger than 43°C between the air and the rice kernel results in serious cracking. They recommended that the texperature of the drying air be kept below 53°C to avoid thermal stress that may cause cracking. Prasad, Mannapperuma and Wratten (1975) investigated the thermal and hydroscopic expansion of brown rice. They concluded that stresses due to moisture gadient are a major cause of cracking or checking whereas thermal stress constitutes a minimal source of damage. Kuntz (1977) observed that rice fissuring occurs after drying. He concluded that the fissuring was caused by: ( 1) the gain surface readsorbing moisture from the environment; (2) the gain surface adsorbing moisture from center of the kernel; (3) the grain surface moisture from both environment and center of the kernel. One of the most comprehensive studies on multipass drying of rice was conducted by Beeny and Ngin (1970). From a series of shallow bed drying tests they were able to assess the effects of the number of passes, number of hours of teIpering, and airflow rate through the gain on milling head yield, drying rate and fuel consumption. The results of their study can be summarized as follows: 1. The head yield increases with an increase in the number of passes through the dryer. 2. The drying time is greatly reduced as the number of passes is increased. 31 The head yield increases with prolongation of tempering period but only slightly after 5 hours; The fuel consumption is reduced as the length of tempering is increased. The dryer capacity increases with increased airflow. The head yields are lowered with increased airflow. III. MATHEMATICAL MDDEIS 3—1 Dryer model Each of the conCurrent flow grain dryer models (Thompson, 1967; Bakker—Arkena e]; _a_1_. , 1969; and Ingam,1976) examined in the literature is based on a system of four equations and four unknowns: 8T _ a; — f1(T,M,H,0) (3-1) H g; = 2(T2M9H26) (3.2) so _ 3,; - f3(T.M,H,G) (3-3) am _ 3; - fu(T,M,H,G) (3—4) where T = drying air terperature, °C M = moisture content, KgHzO/KgDry Matter H = humidity ratio, KgHgO/KgDry air 0 = gain telperature, °C 33 Thompson's model (Thompson, 1967 ) is partly expirical and can be generalized for crops other than corn if the proper thin-layer equation and EMC is provided. The Bakker—Arkera 933.1. (1969) model is based on heat and mass transfer and is general enough to be used for different products, provided the transfer properties are known. Spencer (1969), Handy fl. (1969) models are extensions of the work of Bakker-Arkema 933.1. (1969). In all of the models an appropriate equation for predicating moisture reroval from a product (equation 3-4) is needed. Empirical thin-layer equations are accurate and dependable as long as the analysis is conducted within the range of the experimental data. Because empirical thin-layer equations are lumped parameter representations of the drying process the influence of moisture distribution in the kernel is masked. A single kernel diffusion model that takes into account the effects of spatial variat ion in a gain kernel is a more appropriate model . In this investigation the moisture distribution and the rate of moisture removal is assumed to be governed by the following radial diffusion equation: (ole) ft £1! ll HIH cold) '53 | (3-5) where 11 is the local moisture content. Tb carplete the concurrent-flow dryer model the following equations developed by Bakker-Arkema et a1 . (1969) will be used: 3T_ -ha - - (T - 0) (3—6) 8x Gaca + GanI-I h G aCa + GanH GpCp + (3pr E a X G .— 3H = _ ___1g 8M (3-8) ’3} Ga “532 Equally as important as the formulating of the differential equation (equation 3-5, 3-6, 3-7 and 3—8) is the selection of the appropriate boundary conditions and initial conditions. Several researchers (Young and Whitaker, 1971; Chu and Hustrulid, 1968; and Brook, 1977) assured that the gain surface moisture content instantaneously reach the equilibrium moisture content : M(t,r = R) = Me (3—9) This bourdary condition is based on the assumption that hD approaches infinity. The other alternative would be to solve the diffusion equation with a convective boundary condition: 8M _ -D .5; S - hD (MS - Me) (3-10) In this section a model for each of these two boundary conditions will be tested. In a later chapter these two models will be compared to determine which one yields the best approximation . The boundary condit ions are T(x = 0) = T(inlet) (3-11) C(x = 0) = 0(in1et) (3-12) H(x = 0) = H(inlet) (3-13) M(x = 0,r) -- M(initiar) (3-14) g—DI/kx = 0,r) == 0 (3‘15) Equations (3—5 to 3-15) define the concurrent drying process. The next step is to develop a technique to solve this system of equations. Equations (3—6), (3—7), and (3-8) are first order-corpled—nonlinear ordinary differential equations. Equation ( 3-5) is a second order partial differential equation, An analytical solution does not exist fOr this system of equat ions . Thus, numerical techniques must be employed to solve the system of equations. Nurerical techniques for solving first order ordinary differential equations are well established (Henrici, 1964 and Hamming, 1971). Therefore, it is desirable to express equation (3—5) as a first order ordinary differential equation. This can be achier by approximating the spatial derivativeby a set of finite difference equation (Carver, 1976). Consider a cylindrical representation of a rice kernel with its radius divided into n equal increrent as shown in Figure 3—1 . The moisture content gadient can be obtained from the following forward and backward difference equations: M =M +314] Ar+132M| Ara +errorterm (3—16) 1+1 1 ar 1 2 '3'}? i / i. \ r \ /‘// \\‘ V /‘/\ /) +1 Figure 3-1. Cylindrical representation of a rice kernel with mass diffusion in radial direction only. 3M 1 32M 2 Mr-l-Mi-S—rliA +‘2’ 2 liAr (3'17) foriS‘O. From equations (3-16) and (3—17) the following solutions are obtained: 32M. M. + M. - 2M. 1 1+1 1—1 1 3r2 = 2 (3-18) Ar 3M1 _ M1+1 + Mi-l Tr - 2A1. (3—19) Substituting equation (3—17), (3—18) and r = iAr (3-20) into equation (3—5) yields: 314—1 = D[(21 + 1) Mi+l + (21 - 1) Mi-l - 41Mi] (3—21) at ZiAr2 Crank (1957) derived the following equation for the center node: 3M0 _ 4 3?- - F (3-22) (Mi _ MO) The moisture gadient at the surface of the kernel assuming a convective bomdary condition (Type 3) can be obtained by substituting equation (3—10) into the following backward difference equation: _ 3M 132M 2 Ms-l-Ms""8? SM+2WIS(Ar) +° ' 38 This yields, neglecting third and higher order terms: h = .2 1 32M 2 Ms-l Ms + D (Ms _ Me) Ar + 2 3r2 Ar S or 32M_2(Ms—1 - Ms) _ 2hD (Ms - Me) D 73? - ArT Ar (3-23) Substituting equations (3-23), (3—10) and (3-20) into equation (3—5) yields: 3M _ 2D 1 2 TI; 8‘52(Ms-1'Ms)'hD(E+E)(Ms‘Me) (3’24) If the assumption that the surface moisture content equals the equilibrium moisture content (equation 3—9) then the moisture gadient at the surface is: (21+1)M+(21-1)M —4iM = r e s-l s] 3_25 '37. D‘ 2iAr2 ( ) Tb make equations (3-21), (3-22), (3-24) and (3—25) compatible with equations (3-6), (3-7) and (3—8) they should be expressed as derivatives with respect to bed depth, x. This can be achieved by using the chain rule 8M__3M 3t_1 3M .. ' _ a; _ "at ”a; ‘ v; "5E (3 26) where V = gain velocity, m/hr which yields the following results: for i = 0 (3-27) (21 + 1) M1+1 + (21 -1) Mi_1 - 41 M11 i _ D 5;?" " V5 [ 21 Arz ’ (3‘28) 8M 2D hm 2 3; =V r (MS_1 -MS) -VE(%+F) (MS -Me) (Type 33.0) S (3-29) 01' 21+1)M +(2i-1)M —4iM 3M D ( -1 5; =V-GI 31M, 5 5} (spews) S (3-30) for i = 1, 2 , n It is important to remember that the moisture contents and gadients obtained from equations (3-27), (3—28), (3—29) and (3-30) are local or point values . They represent the values of the concentration at a point and are functions of the kernel radius, r. Because the entire model is a plug flow model (sometimes called maximum gadient) a cross sectional averaged value for the average moisture content and its derivatives is needed (Himmelblau and Bischoff, 1968) . The average moisture content and the average rate of change of the moisture content with respect to time are defined by the following equations : 3 - 1 IRBM 2113 (331 274th OEU’X) I'I‘ _) XE 40 and 1 R -— f M (r,x) 2nrar (3—32) H (x) = H32 0 There are several ways of evaluating equations (3-31) and (3—32). (be way is to approximate the local moisture content and its derivative as Lagrangian interpolation polynomials: 8 51;:- (r,x) = X 3% Li (r) ($33) i=0 i n M (r,x) = Z MiLi (r) (3-34) i=0 where r - rm L. (r) = m _ (3—35) 1 m=l ri ro mfi Equations (3—33) and (3—24) can now be substituted into equations (3—31) and (3—32) and integrated numerically. The disadvantage of this approach is that is requires excessive corputer time to evaluate the integal. An alternative technique involves the use of the moisture content and its derivative with respect to x at each node to define the following funct ions : 3M 3M. _ 1 i _ 2 1 41 and M (r,x) 2Hr = —2—— Mn (r,t) mAr (3-37) G N2 ARZ =_L 1 HR2 Equations (3—36) and (3—37) can be integrated using the trapesodial rule: _ m 3M Ar —(r,x)=Z (F +F)—- 3x 11:0 n+1 n 2 8M naMn _ l_ n+1 - i=0 N, ((n+1 Q + 3x > (3.38) " _ Ar M (”0 " i=0 (Gm-+1 + en) ‘2 n — .1. — z N2 ((n + 1) Mn+l + n Mn (3-39) n=0 Thus, equations (3-38) and (3-39) corplete the matheratical definition of the system. Table 3-1 is a summary of the equations which define the drying process. In the next section some of the parameters which enter into the model will be examined. 3-2 Drying parameters The evaluation of the physical and thermal properties of rice and the drying air is crucial for the successful simulation of a dryer. Specific heats, convective mass and heat transfer coefficient and latent heats of evaporation must be obtained. Table 3-2 contains a list of all Table 3-1. Surmary of the concurrent flow dryer model equations. 3T__ -ha ax ‘avac+GCH (T‘e) (3’6) aP h C 80 - ha (T 0) fg + V(T-0) 3H (3 7) _’ " G + G c M " + M "‘ ' 3x pCp p w GpCp GpCW a 8x G _ 3H _p_ 8M '55? " " G “SE (3'8) a 3M0 4 b?- = -A-r-2-V— (M1 - M0), for i-O (3-27) G , (21+1)M. +(21-1)M. -4iM. 31-i— = 2— [ 1+1 1-1 1] (3—28) ax VG 21Ar2 3M _ an hml Tags—VGA? (MS_1-MS)- VG’(R gh)(M 'Me) TYP93BC (3-29) or (21+1)M+(Zi-1)M -4iM $24. = 3— e 8’1 S Type 1 B c G 2iAr2 (3-30) N — 3 8M _ 1 Nh+__1_ 73—); (x) — 11:0 N2 ((n+ l) T—x +-—:—:—-) (3-38) _ N 1 M (x) = Z + nM ) (3-39) n E ((n + 1)Mn+1 n 43 Table 3-2. Physical and thermal properties of rice and the drying air needed to simulate rice drying. Parameter Symbol Units Diffusion Coefficient D cmZ/hr Heat Of Evaporation hf" kJ/kg Convective Heat Transfer h kJ/m2 0C Coefficient Convective Mass Transfer 11D cm/hr Specific Heat of Water CV kJ/kg °C Vapor Specific Heat of Liquid Cw kJ/kg°C Water Specific Heat of Dry Grain Cp kJ/kg°C Specific Heat Of Air Ca kJ/kg°C Equilbrium Moisture Content Me decimal - w.b. the physical and thermal properties of rice and dry air needed to simu- late the drying process. Appendix II contain a table with the rice property used, EMC equation, and drying rate equation. The specific heat of water and air can be obtained from any heat transfer book (Holman, 1976; Perry and Chilton, 1973; Threlkeld, 1970). Wratten et a1. (1969) evaluated some of the physical and thermal properties of rough rice. Tabulated in Table 3-3 are some of the indivi- dual gain and bulk physical properties for medium and long grain rough rice. Table 3—4 is a tabulation of the thermal properties of rough rice. 3-2.1 Latent heat of vaporization The latent heat of water in rice is the energy needed to evaporate water from the gain. There are no specific values or functions for the latent heat of water in rice. However, Gallaher (1951) derived a general expression for predicating the latent heat of water in cereal grains: hf = (1.0 + 23.0 Exp (—40.0 M) hv (340) g 3—2 . 2 Diffusion coefficient In the development of the radial diffusion model it is assumed that the diffusion coefficient is not a constant but a function of temperature and moisture content. This assumption is verified by the observation that higher temperature results in a more rapid moisture redistribution (Wasserman et al., 1964). Also Kunze and Hall's (1965, 45 .38: mm mm 5322 ”@638 mHo.o m.om HH.mHo wmm.H eo.mmma www.mfi me.o mom.o moc.H ma ooo.o m.sm HH.moo Nsm.H mm.ssma muH.mH mmH.o vo~.o owm.o 0H 0mm.o m.mm o~.wmm mum.a No.HsmH sam.wH HmH.o NoN.o mum.o ea owm.o o.om. eo.mmm ewm.H um.momfi emm.wH HmH.o mm~.o wom.o NH Aom-uo::ocoofimv camsm woos mmo.o H.mm mm.weo mme.o mNm.H Nw.Han msH.mH Ho~.o mam.o wan.o ma omo.o o.mm mo.mmo omm.H vo.vmma oo~.n~ mmH.o Nam.o mma.o 0H wfio.o m.om oo.w~o mmm.a oo.umma mHB.OH omH.o Nam.o was.o ea mmm.o m.mm m~.mmm Noe.o vsm.H em.emma mmo.0H omH.o Nam.o omu.o NH mesoummv cfimsm ssfiooz muconmaomv w E.:O\mx Eu E\wx QOOH x so Eu so w apw>mpu .om xofl>mau moshuv so .so psoucou cameocom xpmeMOQ xufimoom wou< couscoom xpflmcoo osoao> mmochfish suofiz sumsoq oaoumfioz mowpsoaouo xfiom mowuuoooum cacao stow>flocH .ooap swoop mo mOHusoQOHa Hwowmxnd .mIm capes Table 3-4. Thermal properties Of medium grain rough rice. Moisture Content Specific Heat Conductivity Diffusivity % kJ/kg'OC W/m °CA mz/hr x 10’4 12 1.599 0.102 3.7904 14 1.696 0.105 3.5953 16 1.796 0.108 3.4188 18 1.892 0.111 3.2516 20 1.993 0.112 3.0844 Source: Wratten gt a_1_. (1969). 47 1967 ) observation that high moisture rice fissures faster than low moisture rice. Assuming a constant diffusion coefficient over a signi- ficant moisture range will lead to serious error. The effect of the kernel moisture content and temperature on the diffusion coefficient, D, has been determined for rice by Husain, Chen and Clayton (1973) in the 37 to 100°C terperature range and the 5 to 50% d.b. moisture content range. The following empirical relation for the diffusion coefficient was developed: D(M) = 2(6) EXP (f(5)fi) (2-11) The function g(6) and f(5) are defined in the literature review. 3-2.3 Convective heat transfer coefficient The convective heat transfer coefficient between a flowing fluid and particle in a packed bed has been examined by several researchers. Gamson et a1. (1943) and Wilke and Hougen (1945) developed the following equations for the convective heat transfer coefficient in a packed bed for turbulent and laminar flow: DG"°"” Cp’2/3 h = 1.064 c G [L] [—10—] , Re 2 450 (3—41) 0 P u k DG -0.l+1 CU -2/3 h = 1.95 c G [—13—] [—13—] , Re < 40 (3.42) c p u k where 48 The cylinder diameter, Dc for rice was determined from the relation: (72;) , = (g) . (343) cylinder rice Clifford (1972) and Brook (1977) used equations (3—41) and (3-42) in simulation of the drying of corn in a concurrent-flow dryer; Chan (1976) used the two equations to simulate rice drying. Equations (3—41) and (3—42) will be used in this investigation. 3—2.4 Convective mass transfer Very little work has been conducted on the convective mass transfer coefficient of packed beds of cereal gains. However, a geat deal has been done on mass transfer in packed beds in general (Barker, 1965). Wilke and Hougen (1945) noted that the Colburn j—factor for mass transfer jD and the j factor for heat transfer, jh, were approximately equal in a packed bed. This observation was supported by Mche, Wilhelm and Barker's (1965) review. Clifford (1972) used this approximation and derived the following equation for the convective mass transfer coefficient: hD = 8111 (3'44) Clifford (1972) determined the value of 81 for corn using thin-layer data. 49 In the next chapter a method for obtaining B; for rice using experimental observations will be developed. Appendix III contains a set of conversion factors to go from metric to english unit. 3-3 Terperimg model As stated earlier very little theoretical work has been done on the tempering process. However, it is generally agreed that radial diffusion is the primary mechanism. Thus equation (3—5) with the following assumption completely defines the process: _QM 3r surface = O (3.45) 3% = 0 (3—46) g; = 0 (3-47) gil- = 0 (3-48) M(r,0) = M(r, Z) (349) where X is the bed depth of the dryer. The first assumption, equation (3—45) is based on the fact that no moisture is lost from the kernel during the terpering process. Equation (3—46) is based on the assumpt ion that the product terperature changes very little over a short period (2-4 tours). Equations (3-47) and (3-48) are based on the assumption that terpering takes place in a steady state environment . Equation (3—49) is based on the assumption that the final moisture distribution out of the dryer is the initial moisture distri- bution for the tempering stage. For the tempering model equation (3-5) is solved using the same numerical technique developed for the dryer model. The right side of equation (3-5) is approximated by a finite difference equation which results in the following equation for the inner rodes: 3M 53:0 = 753v— (M1 - M0), for i = 0 (3—27) G 3M. . . . 1 _ D (21 + 1) M.+1 + (21 - l) M. l - 41 M. (3—28) ‘33.— " v— 1 1- 1 G ZiAr2 for i — l, 2 ... n Equation (3-45) is used as a boundary condition to obtain the following equation for the surface node: (Ms-1 ‘ Ms) (3-50) surface Ar2 __3_M 3x o<|§ Equat ions (3—27) , (3—28) and (3-50) completely define the tempering process. The diffusion coefficient is the same one used in the dryer model (equation 2-9) . 51 3-4 Numerical solution of differential equations The matheratical formulation of many engineering problems leads to relations which cannot be evaluated analytically. Such is the case in the analysis of a multi—stage rice dryer. Both the dryer model and the cooling models are systems of first order nonlinear ordinary differential equations for which there are no explicit solutions. However, there are several powerful numerical techniques for solving these systems of equations (Henrici, 1964; Hamming, 1971). One such program contains both the Adams—Moulton and the Runge-Kutta methods. The Runge—Kutta metrod is used as a starting method for the Adams- Moulton method. A computer program developed by Lasunan (1964) was used to solve the system of equations for the drying and tempering model. Appendix IV contains a Fortran computer code for the EMC and convective models . Appendix V contains the input. and output format for the models . IV. EWERIMENTATICN AND MEL VALIDATIQ‘I The experimental results reported in this chapter are important for two reasons. First, the experimental results are needed to estimate parameters in the model and secondly, to establish whether or not the models are a valid representation of the concurrent-counterflcw drying process . 4-1 Experimentation In the summer of 1976 a series of rice drying experiments was conducted at the Texas A. M. Experiment Station, Beautont, Texas. The Michigan State University experimental concurrent flow dryer was erected on a site at the Experiment Station. The dryer was made of round steel sections bolted together. Rice was manually fed into a bucket elevator and entered into the dryer via a mechanical airlock. The rice was distributed by a mechanical gain spreader powered by a heavy motor and gear boxes. The gain flow was regulated by a perforated circular drying and cooling unloading mechanism. Both the drying and cooling unloading mechanisms and the cooler air lock were powered by the same motor. A gear box at the base of the dryer was used to match the dryer and cooler gain flow rate. The dryer bed depth was 1.52 meters and the cooler bed depth 0.60 meter. Figure 4-1 is a drawing of the Michigan State University concurrent flow dryer used in 52 53 Figure 4.1 MSU dryer before modifications. legend: Cooling fan Counter-current cooling sect ion Air exhaust Concurrent drying section Bucket elevator Mechanical air lock Grain storage hopper Mechanical gain spreading device Burner 10. Dryer fan <1"- Grain flow « Drying air flow (t: Cooling air flow mooqmcnI-bwbcI—I 55 the Beaumnt drying test. The airflow was measured with a Meriam Flow Meter (Model 50 1132-4P) and a Meriam Manometer (Model 406D10WM-6). Temperatures of the drying air and in the bed were measured with copper-constantan thermocouples and recorded on a Honeywell multi-point recorder. Moisture contents were measured with a Motoroo moisture meter which was checked by using a Brown-Duvel moisture tester (Calderwood, 1972) . The grain flow rate was determined by measuring the amount of gain discharged from the dryer in a given period of time. Tabulated in Table 4-1 is a sumary of the monitoring equipment and their accuracy . Several tests were conducted with the long grain rice variety, Labelle. During the tests several problems were encountered. The dryer had many air leaks which effected the accuracy of the temperature and air flow measurements. The gain flow could not be kept at a constant rate. In addition, the cooler and dryer grain flows were not matched properly, resulting in a bottle neck at the entrance to the cooler. Because of these difficulties only three of the tests were successful . Tabulated in Table 4—2 are the results from the three tests. As a result of some of the mechanical and logistical problems encountered during the Beaumont drying tests, the M. S. U. concurrent flow dryer was modified. The modification involved the separation of the dryer and cooler, the addition of a garner bin to prevent air losses through the gain entry point and a complete redesign of the gain dis- charge mechanism. Figure 4-2 is a diagram of the modified concurrent flow dryer. A more corplete explanation of the modifications can be found in Kline (1977). 56 Table 4—1. Summary of monitoring equipment. Instruments Description -- Accuracy l . Manometer 2. laminar Flow Elexents 3 . Recorder 4 . Recorder 5 . Recorder 6 . Moisture Tester 7 . Moisture Tester 8 . Drying Oven Meriam Model 4OGDIOWM—6 Accuracy 1- 0.02-inch water Meriam Model 50 m2-4p. Accuracy :1: 0 . 05 of calibration curve Honeywell twenty-four Channel Model Electronik 15 Accuracy :1: 0.75 °F Texas Instrument two—channel Model P 502 W6A Accuracy 1 2 F, linearity i 0.3 °F Esterline Angus twenty channel Model 2020 D Accuracy 1 0.5 °F Steinlite Model 400G Accuracy 1; 0.5% moisture content wet basis ' Motomco Model No. 915 Accuracy 1- 0.5% Blue M Electric Company Model 0V510 Mercury in steel thermometer used Accuracy 1 2.5 °F 57 Table 4-2. Results of the Beaumont drying tests. Variables Test Nurber 5 6 7 Bed Depth - m 1.524 1.524 1.524 Initial Ave. M.C. - ’bmb. 17.56 22.53 18.36 02 0.038 0.049 0.006 Initial Grain Temp. - °C 23.3 33.8 32.7 Initial Head Yield - % 64.00 60.00 60.00 Pass 1 Ambient Air Tarp. - °C 33.0 35.19 35.33 Relative Humidity - % 52.00 41.67 45.60 Drying Air Temp. - °C 121.1 118.2 11.7.5 Grain Flow Rate -kg/hr 78.94 85.31 101.34 Air Flow Rate - m3/s 0.033 0.033 0.033 Final Ave. M.C. - %w.b. 13.94 17.88 15.66 Final Grain Temp. - °C 42.2 40.0 41.6 Tampering Time - hr 2.5 1.42 -- Pass 2 Ambient Air Tarp. - °C 34.3 34.3 35.3 Relative Humidity — % 46.0 40.50 53.80 Drying Air Temp. - °C 121.12 121.12 119.45 Grain Flow Rate - kg/hr 278.63 77.20 117.19 Air Flow Rate - m3/s 0.033 0.033 0.033 Final Ave. M.C. - %w.b. 13.12 14.78 14.00 Final Grain Temp. - °C 41.7 42.2 41.6 Tampering Time - hr - 1.17 -- Pass 3 Arbient Air Temp. - °C 28.70 33.12 Relative Humidity - % 66.83 57.60 Drying Air Temp. - °C 118.70 119.67 Grain Flow Rate - kg/hr 88.58 106.56 Air Flow Rate - Ina/S 0.033 0.033 Final Ave. M.C. - %w.b. 12.69 12.72 Final Grain Tarp. - °C 42.23 41.67 Final Head Yield - % 66.00 51.00 58.00 Figure 4—2. Legend: 58 Mbdified MSU Concurrent Flow Grain Dryer (DmxlmmtwaT-J Bucket elevator Grain storage hopper Natural grain airlock Heating air and grain boundary area Concurrent drying section Dryer exhaust Burner Grain flow rate metering auger D. C. shunt wound variable speed motor Cooler exhaust Cooling section Cooling air entrance Cooler base Cooling section discharge auger Grain flow Drying air <3::1 Cboling air hc 1.064 CpG[ k ] u , u 350 (3—41) U Cu-z/a G]-o.51 DG he: 1.95 ch [—13—] [—13— ' , 4;; <_350 (3-42) 61 Table 4—3. Surnary of East Lansing drying tests. Variables Test Number 1 2 3 4 Bed Depth - m 0.9144 0.9144 0.9144 0.9144 Initial Ave. M.C. - %w.b. 17.51 16.85 16.81 17.13 02 0 . 1387 0 .4705 0 . 1612 0 . 5202 Initial Grain Tarp. - °C 23.7 24.1 19.3 12.2 02 0.12 0.21 1.30 3.95 Initial Head Yield - % 61.9 62.4 62.6 60.3 Pass 1 Ambient Air Temp. — °C 25.4 26.0 29.0 25.5 Ambient Wet Bulb Temp - °C 17.2 20.0 23.3 21.1 Drying Air Tarp. - °C 93.3 93.3 121.1 121.1 Grain Flow Rate - kg/hr 106.24 101.46 158.74 131.16 Air Flow Rate - m3/s 0.0408 0.0409 0.0312 0.0298 Final Ave. M.C. -- %w.b. 15.23 14.79 15.57 15.72 02 0.0974 0.5641 0.2558 0.1283 Final Grain Tarp. - °C 32.6 33.7 36.6 35.6 02 0.41 0.14 0.38 0.79 Head Yield - % 63.1 61.6 60.00 61.0 Tampering Time - hr — 2.0 -- 2.0 Pass 2 Ambient Air Tarp. - °C 23.4 28.3 29.7 25.0 Ambient Wet Bulb Tarp - °C 16.4 21.1 23.0 20.5 Drying Air Tarp. - °C 93.3 93.3 121.1 121.1 Grain Flow Rate — kg/hr 108.8 110.5 158.7 135.8 Air Flow Rate - m3/s 0.0408 0.0409 0.0312 0.0298 Final Ave. M.C. - %w.b. 13.2 13.0 14.0 13.6 02 0 . 1913 0 . 1661 0 . 8483 0 .4387 Final Grain Tarp. - °C 35.4 37.8 39.8 39.1 02 0.3022 0.0000 0.3810 0.8439 Head Yield - % 60.7 60.7 61.2 59.7 Table 4-3 (continued) 62 Cooler Bed Depth Ambient Air Tarp. - °C Ambient Wet Bulb - °C Grain Flow Rate — kg/hr ' Air Flow Rate — m /s Final Ave. M.C. - %w.b. 0 Final Czlrain Tarp. - °C 0 Final Head Yield - % 29.4 25.0 22.8 20.5 158.7 135.9 0.00834 0.00958 13.79 13.35 0.0935 0.2765 34.1 31.2 0.1921 0.2142 61.2 60.0 63 Fbr most gain drying systems the latter equation is used. However, preliminary analysis indicated that equation (3-42) does not adequately simulate the temperature profile in a concurrent flow dryer. This can be attributed to the discrepancy between the reported and the actual surface area of rough rice. Morita and Singh (1977) reported the average surface area of short gain rice to be approximately 0.475 omz . Wratten et a1. (1969) reported a surface area for skort grain rice of 0. 392 an2 . The discrepancy between the two can be attributed to the difference in the technique used. Wratten 2131; (1969) sliced a rice gain into fifteen sections. The major and minor axes were measured by use of a pre-calibrated microscope. Once the major and axes were determined, the following formula was used to determine the perimeter (P) of each section: (4-1) Morita and Singh (1977) used electron microscope scans to determine the surface area of rough rice. They observed that the surface of rough rice consists of many small ridges which have to be considered in the deter- mination of the surface area. They determined the average density of the ridges per urit basic area of hull. The total surface area was calcu— lated from the dimension of the ridges, the surface area of the ridges , the average density of the ridges, and the average total basic area of the hull. T‘o correct for this discrepancy, the following modification is made to equation (3—42): C 11 ..2/3 D G -o.51 hC = 80 {1.95 CpG [-E-] [l] }, DDG < 350 (4.2) where Bo is a corrective parameter to be estimated. In addition to estimating Bo the convective mass transfer coefficient, 11D, must be estimated. As stated earlier, the mass transfer coefficient should be proportional to the heat transfer coefficient: hm = 81 h (3—44) where h is equal to the left hand side of equation (3—42). Both 80 and 81 can be estimated from the experimental results tabulated in Tables 4-2 and 4-3. Tb obtain the best values of so and B; for a concurrent flow dryer, a multivariable unconstrained search alogirthn (Kuester and Mize, 1973), developed by Nelder and Mead (1964), was used to minimize the following objective function: 0.)?- s=100 Z (‘M _ 8X!) S1111 exp- Mam)2 + z (0 The weightirg factor of 100 was used so that a 01% error in moisture content counted as much as a 1°F error in temperature. The objective function was evaluted over five runs - all four of the East Lansing drying tests (Table 4-3) and number 6 of the Beauront drying tests (Table 4—2). Test number 6 of the Beaumont drying tests was used because it was the only test conducted at a high initial moisture content (22.5% w.b.). The best values for Bo and 81 were fourd to be 0.07105 and 0.002065, respectively. This indicates that the value used for the surface area is too large. Substituting 80 and 81 into equations (4—1) and equation (3-44), respectively, yields: Cu-2/3 DG-O.51 DG hC = 0.13855 ch [—fi— [-fi- , J:— < 350 (4-3) and C 11 -2/3 D G -o 51 D “m = 0.00403 ch 413—- —§- . _rf s 350 (4-4) 11 Tabulated in Table 4-4 is a comparison of the experimental and simulated values . 66 Table 4-4. Corparison of experimental and simulated values for concurrent flow dryer. Test No. 1 2 3 4 6 Grain Flow Rate, 106.24 101.46 158.74 131.16 85.31 kg/hr Air Flow Rate, 0.0408 0.0409 0.0312 0.0298 0.0330 m3/min Inlet Conditions: T, °C 93.33 93.33 121.11 121.11 118.56 M, %W.b. 17.51 16.85 16.81 17.13 22.53 0, °C 23.73 24.12 19.39 12.22 33.89 H, Kg/Kg 0.009 0.0125 0.0150 0.0130 0.0120 Experimental Exit Conditions: 0, °C 32.62 33.78 36.67 35.67 40.00 M, %w.b. 15.23 14.79 15.57 15.72 17.88 Simulated Exit Conditions: EM} B.C. 0, °C 32.61 34.39 31.83 29.56 27.78 M, ¢704th. 15.72 15.08 15.88 16.23 18.93 Convective Mass B.C. 0, °C 35.11 36.89 31.83 29.44 27.78 M, %w.b. 15.87 15.23 16.04 16.35 19.15 V. RESULTS AND DISCUSSION 5-1 Effect of boundary condition From Table 4—4 it seems that the EMC boundary condition yields the best approximation . However , the difference between the residuals of the EMC (Type 1 B. C.) and the convective (Type 3 B. C.) models is not significant enough to warrant a reject ion of the convective model . The discrepancy between the values predicted by the experimental values can be attributed to the relatively large convergence parameter used. The convergence parameter had to be large to keep the computational time down to practical levels. Despite this restriction, both models predicted the moisture contents to within 0.5% w.b. of the experimental values. Also, the final gain tarperatures predicted by both models are within 5% of the experimental values. The convective and EMC models exhibit very different transient be- havior. Figure 5—1 is a comparison of the drying rates BM/BX as a function of bed depth, X, for the two models. Both simulations were run using the standard conditions listed in Table 5—1. The use of an EMC boundary condition results in a larger area under the curve than the convective model indicating more moisture raroved as shown in Figure 5—2 . The shapes of the two drying curves in Figure 5—1 are also dissimilar. The drying rate curve of the convective model very rapidly reaches a 67 68 .Tm 838. 5 35m: 93 mmfifiaare memes 2:. _ 5902 QB 98 9300280 05 no.“ adduced one." uses one .«0 8339.00 .70 0.83m gems. I x . Itwo 0mm 63 . owe 0 s. w 0.. ....IO w>F0w>z8 I J . mace pfioooo 00N0.0 003.0 00m. .0 00?. .0 Table 5—1. Standard operating conditions for drying simulations. Number of Stages Number of Tampering Sections Environmental Conditions: Ambient Tarperature Absolute Humidity Grain Status: Initial Moisture Content Initial Grain Temperature Stage 1. : Inlet Air Temperature Airflow Rate Grain Flow Rate Bed Depth Length of Tampering Sect ion Stage 2: Inlet Air Tarperature Airflow Rate Bed Depth 25.6°C 0.009 kg/kg 20.0% w.b. 23.9°C 121.1°c 2.27 m3/min 130.0 kg/hr 0.91 m 4.6 m 121. 1°C 2.27 m3/min 0.91 m AVERAGE MOISTURE CONTENT-d.b.-DECIMAL 70 0.25 A CONVECTIVE 0 EMC 0.24 - 0.23 '- 0.22 - 0.2! r- 0.20 l l L l _l 0.0 0.2 0.4 0.6 08 LG BED DEPTH ,X . METERS 0'0 OTI 0T2 of: 034 TIME ,I -hn Figure 5-2. Comparison of moisture content profiles for the convective and EMC boundary conditions. The drying variables are listed in Table 5—1. 71 maximum and gadually decreases with bed depth (Figure 5—1). The explanation for this is that the surface moisture is very rapidly raroved after which the term, D 3% S = hD (MS - Me) (340) becomes very small, and the rate of moisture diffusion from the center to the rice surface becores the limiting factor. ()1 the other hand, the EMC model reaches its maximum later than the convective model, and the magnitude of the maximum is larger. Also, the curve decreases very rapidly . The explanation for this is that during the initial drying period, the rate of the moisture migration to the surface is approximately equal to the rate of moisture reroved. By the time the grain reaches about 10 on into the bed, the rate of moisture diffusion to the surface can no longer keep pace with the rate of moisture raroved at the surface. Tabulated in Table 5—2 are the values of the diffusion coefficient at different positions in the bed for the two models. Equation 2-11 was used to calculate the values in Table 5—2. The rate of change of the absolute humidity with respect to bed depth is directly proportional to the rate of change of the gain moisture content, 8M/3x [Equation (3—8)] . Because the rate of change of the moisture content aM/BX is larger for the EMC model, the rate of change of the absolute humidity, BH/BX, is larger for the EMC model than for the con- vective model . Figure 5-3 shows how the absolute humidity changes with bed depth for both the convective and EMC models. 72 Table 5—2. Corparison of moisture content , gain tarperature, and diffusion coefficient at different bed depths for the convective and EMC boundary conditions . The values were calculated from equation 2-11 . Convective B. C. EMC B C Bed M - C Grain Diffusion M - C Grain Diffusion Depth (1 - b Tarp Coeff. d - b Temp Coeff. M dec. °C cmZ/hr dec. °C cm2/hr 0.021 0.2481 32.7 0.0011 0.2484 32.7 0.0011 0.034 0.2468 36.2 0.0015 0.2466 35.8 0.0014 0.064 0.2444 40.4 0.0020 0.2423 38.6 0.0017 0.095 0.2423 42.2 0.0023 0.2381 39.2 0.0017 0.125 0.2404 42.9 0.0024 0.2346 39.0 0.0016 0.155 0.2387 42.9 0.0023 0.2318 38.6 0.0015 0.186 0.2370 42.6 0.0022 0.2296 38.0 0.0014 0.213 0.2355 42.2 0.0021 0.2278 37.4 0.0013 0.244 0.2342 41.6 0.0020 0.2264 37.0 0.0012 0.274 0.2329 41.1 0.0019 0.2252 36.6 0.0012 0.305 0.2315 40.5 0.0017 0.2241 36.3 0.0011 73 :70 033. 5 oOpmHH 0.3 mcHocHHw> MES 05. 6:033:00 Season 9sz e5 25858 mfi no.“ 8:53 383.5 3388 3. 82898 .mA 252 ,. .80 \' mmwhuzI x . Ihdwo cum 0N0 . . . _ . . . 0.2 w OI II0 u>:.0m>200 I J l ’ l m00.0 00.0.0 Om _0.0 00~0.0 00N0.0 00m0.0 0mm0.0 'vaoao- H‘ AllOlWflH almosev 74 The grain temperature profile is also influenced by the choice of the boundary conditions. Figure 5-4 shows how the grain tenperature changes with bed depth for both the convective and EMC models. The con- vective model predicts higher grain temperatures than the EMC model. An examination of equation (3—7) will provide sane insight into the response: 39 = ha (T - G) _ hfg + CV (T- 9) G 3H (3_7) x GaCa+GaCV Gp Cp+Gp Cw aBX Because the EMCmodel predicts more moisture renoved that the convective model evaporat ive cooling would be higher for the convective model . Therefore, lower grain temperatures are predicted by the EMC model. Figure 5-5 shows how the air temperature changes in the bed. Both models have very similar air temperature profiles. Initially. the EMC model predicts higher air temperatures than predicted by the convective model. However, very soon the situation reverses. This also can be attributed to the higherevaporative cooling that is predicted by the EMC model. Throughout the remainder of this chapter, the EMC model will be used to evaluate the response of the dryer to changes in the drying parameter. The EMC model was selected because it yields the best approximation of the drying process. However, this is not simply a rejection of the convec- tive model. Unless otherwise stated, the operating conditions listed in Table 5—1 will be used as the standard conditions. All of the simulated results presented in the following sections will be based on the standard condi- tions. 75 .Tu. 033. 5 8pm: 0.8 mofiaflg 338 0.0. 0:03:58 553 02m can 0350280 05 no.“ 03595 055309.00 5.95 Ho :omfiumEBO .vlm 0.33m 95th n x . thawo 0mm 0¢0 . ONO 0 — q . a W a _ . mN 1 0n 1 mm 1 0v 1 we . 0.2 w 0510 u>Fow>28 I 1 On oo-o‘aanivaadwal NIVBS 76 .Tm 038. :0 8%: 9a.. $33.5, 05.50 9:. $83028 gases BE 0:“ 03000280 0:0 00.0 0000.00.00 0.8020980 03 .00 800.898 .mnm 050mg mmwhwz .. x .Ihnwo 0mm 0¢0 ONO 0 W . . u q _ a 0 .. ON 1 0o. .. 00 I 00 v. o s. m 05:0 . . . .. 00. w>§om>zoo I .0 LON. ‘ o.-‘J. aunlvaadwal aw 77 5—2 Effect of initial moisture content Under field conditions, the moisture content of rice my vary from batch to batch. This can have a significant effect on the performance of a dryer. Figure 5—6 shows how the initial moisture content effects the drying rate, aM/Bx. Note how the maximum drying rate increases with increasing initial moisture content. The increase in moisture removal rate results in lower moisture contents as shown in Figure 5—7. The rapid increase in BM/Bx with increasing initial moisture content is due to an increase in the diffusion coefficient. Equation 2—11 shows that the diffusion coefficient increases exponentially with moisture content. Tabulated in Table 5—3 are the values for the diffusion co— efficients at the different bed positions for three initial moisture content values. In addition to increasing points removed, increasing the initial moisture content results in a reduction in the maximum and final grain temperatures (Table 5—4). One explanation for this is that more energy is utilized to vaporize the additional easily diffused moisture, and therefore, the amount of energy available for heating the grain is reduced. Eventually, the lower grain temperature begins to effect the rate of moisture diffusion and the rate of drying as can be observed in Figure 5—6. Because more moisture is removed at a higher initial moisture content for the same amount of energy , the energy efficiency is higher at the higher initial moisture contents (Table 5—3). Thus, an increase in the initial moisture content will lead to lower grain temperatures, higher energy efficiency and more moisture removed. In a later section. the effect of initial moisture content on head yield will be discussed. 78 0.2000 {- EMC B.C. I OJBOO _ ' M“ 22.0% w.b. M8 20.0% w.b. M8l8.0% w.b. O.I600 - I / \ 0.:400 - / \ #1 \\ g . , R I \ O.IZOO , \\ I I, \\ I \ O.IOOO P- ‘ fi.\\ ‘\ . .....- \‘x / 0.0600 - \ l-d.b.-m -| Ian dX ff, I I IV- 0.0400 - x Z “ A I 4 .3 0.0200 - ' 9 _- 0g 1 l I l 1 1 J J 0 0.20 040 BED DEPTH , X 'METERS Figure 5—6. Effect of initial moisture content on the drying rate profiles. The drying variables are listed in Table 5-1. A 28.2. ‘/o d.b. O28 a 25.0 ‘I. d.b. 0 2|.9 96 db .4 <1 2 g 0.26- ‘3: $3 : E u 0.24 >- p. Z 0 O m 5 a ,__ 0.22 2’2 0 a m 2 0.20— a: u 2 0J8 _l L 1 l 1 0.0 0. 2 0.4 0.6 0.8 I . 0 BED DEPTH, x - METERS I r I I I 0.0 0.! 0.2 0.3 0.4 TIMEJ -hrs Figure 5—7. Effect of initial moisture content on the moisture content profiles. The drying variables are listed in Table 5—1. Table 5—3. Comparison of the effect of initial moisture content on the diffusion coefficient at different bed depths. 'The values were calcu- lated from Equation 2—11. 0. Diffusion Coefficient Bed Depth “DZ/hr meter 18% w.b. 20% w.b. 22% w.b. 0.000 0.0004 0.0005 0.0007 0.095 0.0015 0.0017 0.0019 0. 155 0. 0014 0. 0015 0. 0016 0.311 0.0011 0.0011 0.0012 0.491 0.0009 0.0010 0.0010 0.616 0.0008 0.0009 0.0009 0.765 0.0008 0.0008 0.0008 0.914 0.0007 0.0008 0.0007 81 Em m.m as: v.2. mime 82 a; 0.2 Tom 9:. 3: new m.m m.m0 0.wm m.mv mew m.m m.00 s.mm m.mm o.om 0mm m.m m.00 >.em n.0v st m.m m.m0 m.wm n.0m o.mm one 3280 as e 23 e o. o. om: 3280 n3 e as .0. o. o. as 0 0880000 @983 E 0 vas 8603000. B>20m o: o fie 02 08cm 358 o o .0080 3:08 0800 e o 0300.: m 030w H 0wm0m .Tm 038. 5 8%: 0.8 80005, 80g 00:00:00 0.500008 000005.” 0:000:00 c003 0:033:50 00.50 50.0.0 0010000 020 .00 gm .1 0H3 82 5—3 Effect of initial grain temperature The effect of initial grain temperature on the moisture content dis- tribution within the bed is shown in Figure 5—8. An increase in the initial grain temperature results in an increase in the amount of moisture removed and higher grain temperatures as shown in Table 5-3. The increase in the moisture removed can be attributed to an increase in the grain temperature. Increasing the grain temperature results in higher values for the diffusion coefficient (Table 5—6) and more moisture migration to the surface. In addition to increasing moisture reroval rate and grain temperature, increasing the initial grain temperature results in higher energy eff i— ciency as shown in Table 5—5. The explanation for this is that more moisture is removed due to higher grain temperatures, while the energy used to heat the air remains constant. Thus, the overall effects of increasing the initial grain temperature are an increase in moisture reroved, higher grain temperature, and higher energy efficiency. 5—4 Effect of drying air temperature Increasing the drying air temperature significantly increases the amount of moisture removed as shown in Figure 5—9. There seems to be two factors responsible for this. First , part of the additional energy goes to increasing the temperature of the product, as shown in Table 5—7. As the product temperature increases, so does the diffusion coefficient and the rate of moisture migration to the surface. In addition, at higher temperatures, less energy is needed to rerove the moisture from the surface of the grain. AVERAGE MOISTURE CONTENT-d.b. , % 83 25.0 . A-Ias-c o- 23.9 °c o- 32.2 'c 24.0 23.0 22.0 - , . 2|.0 ' 20.0 . ' a . l _. 0.0 0.2 04 0.6 03 LC BED 059114,): mavens I T r I I 00 on 0.2 0.3 0.4 TIME. I -hn Figure 5-8. Effect of initial grain temperature on the moisture content profile. The drying vari- able are listed in Table 5—1. Table 5—5. Summary of the results obtained from three drying simulations using the standard operating conditions listed in Table 5—1 for a single stage dryer. The initial moisture content was varied as shown below. Initial Initial Maximum Final Final Points H20 Energy Moisture Grain Grain Grain Moisture Beloved Eff iciency Content Temp Temp Temp Content % wb °C °C °C % wb % wb Kg Kcal/Kg H20 18.0 18.3 35.9 30.8 18.2 1.8 3.6 1070 20.0 26.7 39.8 33.0 17.7 2.3 4.4 859 22.0 32.2 42.2 34.8 17.4 2.6 5.7 757 Table 5-6. Comparison of the effect of initial grain temperature on the diffusion coefficient at different bed depths. The values were calculated from Equation 2—ll. Diffusion Coefficient Bed Depth cmz/hr Meter 18. 3°C 26. 7°C 32.2°C 0.000 0.0003 0.0007 0.0011 0.159 0.0012 0.0015 0.0017 0.308 0.0010 0.0011 0.0013 0.463 0.0008 0.0010 0.0011 0.613 0.0008 0.0009 0.0010 0.765 0.0007 0.0008 0.0009 0.917 0.0007 0.0008 0.0009 AVERAGE MOISTURE CONTENT 'd.b., DECIMAL 0.25 . A 1' - 93.3’0 __ a T- I2I.l 2:: 0'24 . 0 T- I488 0.23 r- 022 ~ ° ' . l I 0 I 0.21 "" . ° 0 0.20 I 1 I 1 1 _l 0.0 0.2 0.4 0.6 0.8 ' 1.0 BED DEPTH,X-METERS I—' I I T l 0.0 0.1 0.2 0.3 0.4 TIME , I -I'Irs Figure 5-9. Effect of drying air temperature on the moisture content profile. The drying variables are . listed in Table 5—1. mow 0d 0.3 adv 0.3 :0 ed m.: bdm Emv 0.03 mum m.m 0.00 Ewm 0.00 mum Nd 0.: 5mm Ndm .730 new 0.0 8.00 Emm 0.0m now 5.0 0.00 mdm fimm m.m® om: 00:80 :3 .0. be 0. o. 0.. can 3:80: ea .0. e3 e o. oo o.v «8:003 .0 0m 00>0E0m 88. 23.00000 0 0 m 00:60.00 02 808 050.0. 300cm 00500 02 .00 o 0.00:0 00:00am Hafih 0G 0 03. 00m m owe0m 0 00000 .Tm. 033. .0 80: 0.8 0280.82, 05.06 0:9 000500000000 .0000 000:0 000000.000 £003 0:035:50 00.50 50.00 03:00.: 0:0 00 g . him 0H3 87 The effect of drying air temperature on the energy efficiency of the dryer is tabulated in Table 5-5. According to the simulated results, the energy efficiency of the dryer decreases with increasing hot air temperature, and keeping the other drying variable fixed. The reason for this is that as the air temperature is increased, more energy is exhausted and the relative humidity of the air is lower; therefore, the full drying potential of the air is not used. The results indicate that operating at higher air temperature and lower airflow or higher grain flow rates would result in better efficiencies. In assessing the impact of the drying air temperature on the cracking of rice, factors such as air and grain flow and initial moisture content must be considered along with the drying rate and maximum grain temperature. Fran the field work conducted during this investigation, it can be con- cluded that rice can be safely dried at a drying air temperature of 121°C and airflow of 0.17 mB/hr. A more complete discussion on the effect of air temperature on cracking will be presented in a later chapter. Besides increasing the moisture removed and maximum grain temperature in the first stage, increasing the drying air temperature does signifi- cant ly increases the maximum grain temperature even more in the succeeding drying stage, as shown in Table 5-7. This will result in additional moisture removal and an increase in the risk of cracking. 5—5 Effect of air flow Airflow has a significant effect on the drying of rice as shown in Figures 5—10 and 5—11. This can be attributed to a significant increase in the total energy supplied. The increase in the total energy supplied 0.2000 - EMC B.C. . 0—0 2.3 mglmin 5.-..43 1.7 /min o'8m_ O—--O 2.0 m /min I O.I600 - - O.I4OO " 0 1200 - I” \~ . 16 I” ‘\ u ’ \ . I ‘3 I \ ‘3 0.1000 ,’ \ k I 2 X “ A. \ b v . o \ [cf \ \\ OO ' ‘ 0.08 ./ \ ‘ ' . \ \. \ I 0.0600 ‘°\ \ \ 0.0400- \°\ \. . \o‘. 0.0200 - ‘O~.Q;~ °~‘8 o 1 1 1 l 1 1 1 J 0 0.20 090 BED DEPTH ,X ' METERS Figure 5-10. Effect of airflow on the drying rate profile. The drying variables are listed in Table 5—1. AVERAGE MOISTURE CONTENT 'dh, DECIMAL 0.25 . 0.24 0.23 0.22 T Figure 5—11. Effect of airflow on the moisture content profile. The drying variables are listed in Table 5-1. 0.2 0.I A L? m3/ml.1 2.0 m3! min 0 2.3 m3! min D 1 J 0.4 0.6 BED DEPTH.X ' METERS I 1 I 1 0.2 0.3 TIME. ! 'hn 90 results in an increase in the grain temperature (Table 5—8) and therefore, an increase in the diffusion of moisture. In addition, energy efficiency of the dryer decreases with an increase in airflow. This can be attri— buted to the fact that more energy is exhausted without a significant increase in the humidity; thus, the full drying potential of the air is not used. The simulated results tabulated in Table 5—8 indicate that increasing the air flow rate does not cause a large enough increase in the grain temperature or points removed to cause a significant reduction in head yield. However, it cannot be stated conclusively that higher airflows coupled with higher drying temperatures and lower grain flows will not cause significant cracking. Airflow, along with grain flow and drying air temperatures, can be used to control grain temperatures and mois- ture gradients. 5—6 Effect of grainflow Grainf low strongly effects the rate of moisture removed as shown in Figures 5—12 and 5—13. The reason for this is that as the grain velocity is increased, the retention time of the product in the dryer is shortened and the temperature of the product is decreased, as shown in Table 5—9. This can be attributed to the fact that as the grain flow is increased, more grain has to be dried with the same amount of energy resulting in a reduction in grain temperatures and the amount of moisture removed. It was stated earlier that grain flow and airflow could be used to control grain temperature and moisture gradients. Fran a logistical point of View, it is easier to use grain flow. It is much simpler to change the speed of a discharge auger than to change the pully on a fan 91 000 0.0 0.00 0.00 0.00 000 0.0 0.00 0.00 0.00 00.0 000 0.0. 0.00 0.00 0.00 000 0.0 0.0: 0.00 0.00 00.0 000 0.0 0.00 0.00 0.00 000 0.0 0.00 0.00 0.00 00.0 cm: 0.5 080 as 0. 03 .0. o. o. 000 00:5. 03 0. 03 0. o. o. seine 0880000 09800 0: x02 0:000:00 8>800 2 x0: 000:0 00:08 005.0 00 0 000:0 0058 00:00 00 0 so: .02 N 000000 0 0.0000 .70 030.0 :0 030: 0.3 00300.5 0:05 00:00 02.0. 0300,0000 0:000:00 :00? 080000250 00.50 .500 0000000 0:0 .00 5:50 .010 0000.0. 92 .1 0.25 4 E. g A 0J8 03m 5‘ . D 0.23 03/ m P 0.24 - ‘ ' o 0.28 03/»: E E . z I 8 . g 0.23 0 - . . a ' - - . 92 u o 0 I z . . g 0.22 - ‘ °\-o 4 a: w I 5 . L 0.2l l 1 l 1 4 n 0.0 0.2 0.4 0.6 0.8 I.O BED DEPTH , X ' METERS Figure 5-12. Effect of gain flow on the moisture content profile. The drying variables are listed in Table 5—1. 93 0.2000» EMC 8.0 . 0—-0' 0.18 n13/hr bun-A 0.2303/10- OJBW" O—-—O 0.28 111 [hr I O.IGOO- I 0.1400- /A I / \\ 0.1200-. I ~ '. ’1’ ”x T ” \\ :3 I’ x . 0.1000 ,’ ‘0‘ . 3: A\\ \ ' \ \ 0.0800 // ‘ “ \, . \. \ ooeoo- \°\ )\ ' ' \ \K \\ . 00400- \.\§ ' .\\ I \o‘.‘\A\‘ I \O\.‘A.‘ - . 002000 ‘00.$;?:6 O 1 1 1 J 1 1 1 J 0 0.20 040 BED DEPTH ,X ’ METERS Figure 5-13. Effect of grain flow on the drying rate profile. The drying variables are listed in Table 5—1. wmm 0.4 0.6a 9mm 0&0» 3% m4 v.wH mém HSm de 000 0.0 0.00 0.00 0.00 000 0.0 0.00 0.00 0.00 00.0 000 0.0 0.00 0.00 0.00 000 0.0 0.00 0.00 0.00 00.0 N 0 N o 0 0 0000080 03 .0 03 0 0.. 0.. 0 0 00:80 03 0 03 .0 0.. 0.. 0:02 00000000000 0.9800 0: 0 .8... 00000000000 09080 02 fie 3000 000000 000000 00000 0 0 000000 000000 00:00 00 0 00000 0 00000 0 00000 .010 0000.0. :0 000000 0.0.... 00000000., 0:05 003. 0000.0 300.0 50.0.0.0 000000000 :00...» 0000000000000 00.0000 80.0.0 00000000 050 .00 55m .0100 00000.0. 95 and thus, the horsepower requirement of a fan. In addition, the response . dM . . of the drymg rate (a). to changes in grain flow is greater than that to changes in airflow. 5.7 Effect of bed depth Increasing the length of a concurrent flow dryer results in a lower final grain temperature and moisture content as shown in Table 5-10. However, it has no effect on the maximum grain temperature. Because more moisture is removed as the length is increased, the energy efficiency will increase to a limited degree. Eventually, a point will be reached were the energy required to move the air will negate any additional energy saving from increasing length. In addition to lowering the final grain temperature and moisture con- tent, increasing the bed depth results in a more uniform moisture distri— bution. The explanation for this is that during the latter portion of the drying process, the rate of moisture removed from the surface is smaller than the rate of diffusion fram the center of the kernel to the surface of the kernel. This results in tempering of the rice. 5—8 Effect of ambient air temperature and humidity Ambient air temperature and humidity have a marginal effect on high temperature drying of rice as shown in Table 5—11. The reason for this is that during the drying process, the rice kernel will approach equilibrium. The equilibrium moisture content is a function of the air temperature and humidity, as given by (Equation (2—15). When the Table 5—10. Effect of dryer stage concurrent flow dryer. % . length on the drying perfonmance of a single The drying variables are listed in Table 5—1. Maximum Final Final Points [-120 Energy Bed Grain Grain Moisture Removed Efficiency Depth Temp Temp Content Removed Meters °C °C % wb % wb Kg Kcal/Kg H20 0.91 38.5 32.1 17.9 2.1 4.16 911 1.22 38.5 31.2 17.8 2.2 4.41 870 1.52 38.5 29.7 17.6 2.4 4.76 8.19 Table 5—11. Effect of ambient air condition on the drying performance of a concurrent flow dryer. Table 5--1. The other drying variables are listed in Ambient Relative Absolute Final Final Energy Air Humidity Humidity Grain Moisture Efficiency IEmp Thug) Content °C %z lb/lb °C %>wb Kcal/Kg H20 12.8 95.0 0.009 33.1 17.7 995 23.9 50.0 0.009 32.8 17.8 889 35.0 25.0 0.009 32.4 17.9 785 23.9 60.0 0.012 32.3 17.9 938 29.0 50.0 0.012 32.7 17.9 882 35.0 40.0 0.012 32.0 18.0 827 23.9 80.0 0.015 32.5 17.9 945 35.0 50.0 0.015 32.1 18.0 834 97 air is heated to high temperatures (93.3°C or higher), the relative humid- ity becomes very small and the EMC approaches zero regardless of the initial relative humidity of the air. hence, the drying rate is essen- tially constant regardless of the ambient humidity. 59 Effect of tempering The moisture distribution in a rice kernel is shown in Figure 5—14 for different tempering periods. As the tempering time is increased, the moisture distribution becomes more uniform. The tempering time required to obtain a uniform distribution is a function of the grain temperature and moisture content as shown in Table 5—12. At high grain temperatures and moisture contents, moisture diffusion through the kernel occurs rapidly. Therefore, rice at high temperatures and moisture content tempers faster than rice at lower temperature and moisture content. Tabulated in Tables 5—13, 5—14, and 5—15 is a summary of the results from a series of simulations. The results indicate that tempering had very little effect on the maximum and final grain temperature, and on the moisture removed in the second stage. In addition, tempering had only a marginal effect on the energy efficiency of the dryer. This can be attri- buted to the uniform moisture distribution in the kernel after drying in a concurrent flow dryer as shown in Table 5-12. Even at a drying temperature of 176.7°C and no tempering the surface moisture content, Ms is within 82% of the average moisture content of the kernel . Brook (1977) obtained similar results in his investigation of concurrent flow corn drying; he attributed this to the uniformity of the moisture content and temperature profile within the kernel after drying in .Tn fins. 3 68m: 98 833.52, ”355 35.3393 M5595» ”E98320 .893 Hmfimx 00H.” a 5 cog—52pm? 8339: m0 83.8950 .Slm 83E mt. 00.. 00.0 00 .0 Ch .0 8.0 On. 0 0¢.0 0nd 0N0 0. .0 0 m . . . a . u q u . 0N..O J 09.0 W m S m. m m 3 0 N a N .1 W nommd . P m _ .z cod all... . m. .... 3... Clio -83 o 3.. 50.0 91.5.0 W». s: 0 I towno .o.m DEM 8o; 02d aaad aaad aaad aaad aaad aaad aaad add 084 02d aaad aaad aaad aaad aaad aaad aaad and 8d; aaad oaad aaad aaad aaad aaad aaad maad odd aaa.o aaa.o oaa.a aaa.o aaa.a aaa.o aaa.o aaa.a aaa.o oa.a Sad aaad aaad aaad Haad oaad Sad aaad aaad 8d aaa.o aao.o aaa.o aaa.o aaa.o Haa.o aaa.o aaa.d aaa.o am.H add Fad aaad Ead mead mead Sad aaad aaad 8A avad waad sad add mead Bad aaad mead «mad dad aHa.o HHa.o aaa.o aoa.o maa.o aaa.o aas.o afia.o oaa.o oo.o a.aaH H.HaH a.aa a.aaH H.Hafi a.aa H.asH H.2afi a.ma a: o. .... o. a. o. a. 95a. .93 adda u 2 dd osoda u 2 .93 eon: u 2 $28an e\m2 #23200 @55ng mmapga 8. 28:00 manages moamhsw do 03.2 23 so 2i can .2880 8338. 332a Ea mépammazmu v.35 do 88% .aTa 28a. 100 Table 5.13. Summary of four simulations of the second stage with four different temering times. The temperature of the drying air is 65.6°C. All other drying variables are listed in Table 5—1. Maximum Final Final Points Energy Tampering Grain Grain Moisture Removed Efficiency Time Temp Temp Content hr °C °C % w.b. % w.b. Kcal/Kg H20 0.00 31.8 27.8 17.83 1.0 823 0.67 31.6 27.4 17.80 1.1 796 1.34 31.5 27.3 17.79 1.1 785 2.00 31.5 27.3 17.78 1.1 779 101 Table 5—14. Summary of four simulations of the second stage with four different tempering times. The drying variables are listed in Table 5—1. Tampering Maximum Final Final Points Energy Time Grain Grain Moisture Removed Efficiency Temp Temp Content hr °C °C % w.b. % w.b. Kcal/Kg 0.00 46.2 38.8 15.6 2.2 912 0.67 45.7 38.3 15.6 2.2 888 1.34 45.6 38.2 15.5 2.3 880 2.00 45.5 38.1 15.5 2.3 875 Table 5-15. Summary of four simulations of the second stage with four different tempering times.3 The temperature of the drying air is 176.€°C and the air flow is 2.83 m /min. The other drying variables are listed in Table 5—1. ' Tampering Maximum Final Final Points Energy Time Grain Grain Moisture Removed Efficiency Temp Temp Content hr °C °C ‘70 w.b. % w.b. Kcal/Kg 0.00 60.1 49.0 13.4 4.3 950 0.67 59.1 48.4 13.3 4.4 933 1.34 58.8 48.2 13.3 4.4 928 2.00 57.8 47.3 13.2 4.5 911 102 a concurrent flow dryer. The results obtained by Oaldermod and Webb (1971) and the results from the author drying test support the simulated results. Although tempering does not significantly improve the drying perfor- mance of a concurrent flow dryer, it does reduce the moisture gradient in the kernel as shown in Figure 5—14. This reduction in the moisture gradient should result in an improvement in the head yield. In a later section, the problem of predicting the impact of tampering on head yield will be discussed. 5—10 Number of stages Throughout most of this investigation the primary emphasis has been on one and two-stage dryers with the standard operating condi- tions listed in Table 5—1. The main reason for this is that most of the rice used in the experiments was in the moisture content range of 17 to 20.0% w.b. The dryer settings in Table 5—1 are quite adequate for this initial moisture content. However, for very moist rice in the initial moisture content range between 20—24% w.b. , a different set of dryer settings or dryer design is needed. Om alternative is to raise the drying air terperature to 150°C or higher. This may result in a final moisture content of approximately l4.0—l4.5%. Increasing the air terperature to 150°C or higher might cause significant cracking at the low grain flow rates. The drying experiments have proven that rice can be dried safely at 121.1°C. However, at that temperature, the head yield is very sensitive to the grain flow and the sensitivity would increase with an increase in the drying air terperature. 103 The best alternative is to choose a threehstage dryer, using for example, the dryer settings listed in Table 5—16. A three-stage dryer has greater flexibility. If the moisture content of the rice being harvested is around 22% w.b. the operator can use the dryer settings in Table 5—16 for a three-stage dryer. This will insure him that the final moisture content is low enough for safe storage. If the rice harvested is lower in moisture content, aromd 18 or 20% w.b. , an oper- ator has the option of using a three- or two-stage dryer as shown in Table 5—16. In summry, a three—stage dryer provides the operator with more flexibility in selecting drying air terperature and better quality control than one— and two-stage dryers. 5—ll Grain quality It is very difficult to predict the amount of cracking that occurs during the drying of rice. Arora e_t _ai. (1973) conducted a series of experiments on rice and observed a strong correlation between the drying air temperature and head loss (Figure 5—15). If the same correlation is used for the concurrent flow dryer the values predicted (40% broken kernels by weight at 121°C) far exceed the maximum value obtained from the field (10% broken kernels by total weight at 121°C). Part of this may be attributed to the difference in drying technique. In the study conducted by Arora, rice was dried in a thin layer at a constant temper- ature from 22 to 13% w.b. in which the grain temperature equals the air temperature. In the concurrent dryer, the grain is constantly passing by the hot inlet air entrance without reaching the inlet air terperature . Also, the residence time at the maximum temperature is very short, on the order of a couple minutes. mam m.mm 9% mg: mg“ Rd m.mm N 104 aoaH H.aa a.aa a.aH a.H aa.a Ha.o a.aoH H o aH saw a.am a.aa a.aH a.H Ha.a a.aa a dam a.om a.aa a.sH a.H Ha.a aH.o a.aoH H dew a.aa o.oa a.aH a.H aa.a a.aa a 0 ca mam a.aa H.aa a.aH a.H sa.a Ha.o m.aa a vHa a.aa a.aa a.aH a.H aa.a a.aoH H «aw a.ma a.aa a.v m.H Ha.a a.aa a aaa a.aa a.oa a.aH a.H He.a aH.o a.soH a aHa a.sa o.sa a.aH a.H Ha.a H.HaH H mam a.va H.aa H.aH a.H Ha.a a.aa a o.aa baa o.aa a.aa o.sH m.H Ha.a Ha.o a.aoH a dds a.aa v.aa H.aH a.H Ha.a H.HaH H can @580: o. co dd a 2 55% 55“.: do as a 959 95:. “Em ”Eco 959 33:00 88333 :35 £ch 85532 spasm: Sam 32: :2 dz 9538: madam Hana Snags Ham: scams. £ch 8H5 mafia H33: 38?: 303 ”59:50:00 oWapmeHsfi .a How mwfippom .85 @3380 .oHIm 38am. 105 A similar problem is encountered if the correlation of Schmidt and Jebe (1959) (Figure 5—16) is used. They observed a correlation between the saturated deficit of the drying air and head yield. If this corre- lation is used for the concurrent flow dryer the predicted value (35% at 121°C) also far exceeds the value obtained in the field (10% at 121°C). The saturated deficit is only a measure of the drying potential of the air and therefore, cannot be used to assess the effect of the initial moisture content, maximum grain temperature and moisture gradient. Figure 5—14 is a plot of the moisture distribution in a rice kernel after tampering for different time periods. The distribution serves as the initial condition for the second stage. As stated earlier, there is no significant difference in the grain temperature and final moisture content leaving the second stage as shown in Table 5-14. But there is a significant difference in the moisture distribution and gradients within the kernels, because the initial distribution entering the second stage is different. A similiar problem is encountered if a head yield- temperature correlation is used to assess the effect of initial moisture content on head yield. The results in Table 54 indicate that the maximum and final grain temperatures decrease with an increase in the initial moisture content. The Arora gt 31. correlation predictes a decrease in head yield loss for an increase in moisture content. However, this contradicts the obser- vation of Kunze and Hall (1965. 1967) and Mannapperuma and Wratten (1975). Therefore, any model that does not consider the moisture gradient inside the kernel cannot be used to predict the effect of drying temperature, initial moisture content. and tampering on head yield. 106 40- [-0 :1: CD H L11 3 >* m3o~ a ‘< E... Z Li] 0 m (:1 O-n .20‘ (I) ...] LL] 2 E Z § 0 -1 mm an L4,. . . . H 40 50 60 70 80 TEMPERATUREOF DRYING AIR - °C Figure 5—15. Broken kernels versus air tarperature. Source: Arora, Henderson and Burkhardt (1973) 107 0.: Hana: Saw as #0258 “meadow ..Haa mgg map Mo 9358 :oHpahsuam mama? 8H: 6.8: 00 $3 ”Emoaom $013153 .3 9.5 .6 5:8 8:228 ON. 0.0. 0d 0. m 0. c , O.N .oHln charm o d a m 8- a. 3 U. o_- m 5 a o .u.. H 9 o. W m ON a m... an m M. U .D 0 v 108 More research has to be conducted on moisture movement from the grain to the environment before an adequate model can be developed for predicting head losses. Until better models are developed, the dryer designer will have to rely on field tests to determine the effect of drying air temperature, initial moisture content and tampering on head yield losses. From the experiments conducted by this author, it can be concluded that rice can be safely dried at temperatures as high as 121.1°C provided that the other drying variables are within the range listed in Table 5—16. IV. SUMMARY AND mNCLUSION Two computer models of multistage concurrent flow drying were developed and verified by limited pilot scale, field experiments with a long grain rice variety called "Iabelle." Both models are based on radial moisture diffusion. One model employes a convective type boundary condition to describe moisture transfer at the grain surface. The other model uses an EMC boundary condition. Although this investigation was conducted with one rice variety, the results obtained can be extra- polated to other varieties, because the radii, r, of the other varieties are approximately the same, and the drying rate is proportional to 1 /r2. Both models yield acceptable approximations to the drying process. However, the results are obtained by traveling two different paths. The magnitude and position of the maximum rate of change of the moisture content, aM/BX and the maximum rate of change of the grain temperature ae/ax are different for the two models. This is of little significance if the models are only being used to predict the amount of moisture raroved and the final grain temperature. However, if the models are also used to predict the maximum stresses due to the moisture gradients, then the models will predict different quality changes for the same drying condition . For this investigation the EMC model was used to obtain the oper- ating characteristics of a multistage dryer. The EMC model was selected because it predicts the final moisture content more accurately, which is important for the determination of the timber of passes needed to dry rice to 14.5% w.b. f109 110 The following conclusions were drawn fram the dryer simulations and field experiments: 1. Under constant drying conditions, an increase in the initial mois- ture content results in an increase in the moisture reroval rate and the energy efficiency of the dryer and a reduction in the maximum and final grain temperature. 2. An increase in the initial grain temperature under constant drying condit ions results in an increase in the moisture raroval rates, higher grain temperatures , and higher energy efficiencies . 3. Under constant drying conditions, an increase in the drying air temperature results in an increase in the moisture raroved and the max- imum grain temperature. Also, for the standard drying conditions used in this investigation (Table 5-1) the energy efficiency of the dryer de- creased with an increase in the drying air temperature. However, an increase in air temperature coupled with a higher grain flow or lower air flow would result in better energy efficiencies. 4. The field experiments have shown that rice can be dried at air temperatures as high as 121.1°C provided that the air flow is 2.27 m3/min, and the grain flow is 0.17 m3/hr. It may be possible to dry rice at 150°C with higher grain flow. However,more field work will have to be conducted to prove the feasibility of operating at 150°C. 5. Both airflow and grainflow can be used to control grain temperature and moisture gradient . However, this is best achieved by using grainf low. 6. An increase in the bed depth results in an increase in the moisture raroved, a lowering of the final grain temperature, and a more uniform moisture distribution. In addition, an increase in bed depth results in an increase in static pressure and horsepower requirements. 111 7. Ambient air temperature has no effect on the moisture removal rate, the maximum grain temperature, nor the final grain temperature. However, it does have a significant effect on the energy required to raise the air to the desired drying temperature. 8. Absolute humidity has a marginal effect on the moisture removal rate, the maximum and final grain temperature, and energy efficiency. The moisture reroval rate and the energy efficiency of the dryer decrease with an increase in absolute humidity, but only slightly. 9. Tampering does not significantly improve the drying rate of rice in a concurrent flow dryer. The reason for this is that rice dried in a concurrent flow dryer has a fairly uniform final moisture distribution. For the standard conditions listed in Table 5-1, the maximum difference between the surface and center moisture content is 6.3% w.b. However, the final difference is 4.6% w.b. , a reduction of 27%. Also, the final surface moisture content out of the first stage is within 85% of the average moisture content of the kernel . At 176. 7 °C drying air temperature and an initial moisture content of 22% w.b. , the maximum difference is 9.4% w.b. and the final difference is 6.5%w.b,. a reduction of 31%. For this simulation the surface moisture content is within 82% of the final average moisture content. Because the drying rate is proportional to 1/r2 the moisture distribution would have a lesser effect on the drying of rice (radius: r = 0.098 cm) than on corn (radius: r = 0.296011). Therefore, tampering would have a greater effect on corn drying than on rice drying. 10. Rice can be dried in a three stage dryer to a desired moisture con- tent of 14.5% w.b. However, this may not be the optimum number of stages. To determine the _be;s_t_ number of stages and operating conditions , an optimization study needs to be conducted. The success of this would 112 depend on the development of a model to predict head yield as a function of temperature, time, and moisture gradient. Without such a model it is difficult to determine the benefits derived from increasing the number of stages and lowering drying temperatures. 11. As stated earlier the concurrent flow drying of rice results in a fairly uniform kernel moisture distribution. The moisture gradient reaches a maidmum in the first 5 minutes of drying and then decreases with time and bed depth. This feature of a concurrent flow dryer should result in better grain quality. This conclusion is based on observations of Kunze (1977). He concluded that rice cracking and fissures are caused by: (l) the grain surface readsorbing moisture from the environment; (2) the grain surface adsorbing moisture from the center of the kernel; (3) the grain surface adsorbing moisture from both the environment and fromlthe center of the kernel, following drying. Because concurrent drying of rice results in a fairly uniform final moisture distribution, the moisture movement from the center of the kernel and the surrounding environment is reduced. This should result in better grain quality. This conclusion is also supported by the good head yields obtained during the field trials. More research must be done before a model can be developed to pre- dict head losses. Grain temperatures and saturation deficit alone cannot be used to predict head losses . 113 VI . SUGGESTIONS FOR FURTHER RESEARCH As a result of this investigation, the following recommendations are made: 1 . The Convective Mass Transfer Coefficient The relation derived in this study for the convective mass transfer coefficient can be improved considerably if more experimental data is obtained . 2. Multistage Concurrent Flow Dryer A deronstration model of a multistage concurrent f low rice dryer should be constructed and tested in the field to gain further insight into the operating characteristics. 3. gitimizat ion An optimization study needs to be conducted to determine the optimum number of stages, the bed depth, drying tarperature, and other drying variables. 4 . Head Yield Recent work by Kunze (1977) has shown that rice fissures and cracking are caused by the grain surface adsorbing moisture from the environment , the center of the kernel, or both. Therefore, any model design to predict head losses must be a function of the moisture distri- but ion in the kernel and not just the grain temperature or the saturation deficit of the drying air. More research needs to be conducted on mois- ture movement f ran the grain to the environment and from the environment 114 to the grain from both the environment and from the center of the kernel. Therefore, a head yield model must be based on the moisture distribution and gradient to successfully predict head loss. REFERENCES REFERENCES Adair, C. Roy, 1972. Production and utilization of rice. Chapter 1, pp. 1-15. In: D. F. Houston, Ed., Rice Chemistry and Technology. American Association of Cereal Chemists, Inc., St. Paul, Minne— sota. 517 p. Agrawal, Y. C., and R. P. Singh, 1977. Thin-layer drying studies on short—grain rough rice. ASAE Paper No. 77-3531. Am. Soc. Agr. Eng. , St. Joseph, Michigan. Ahmadnia-Sokhansanj, A. , 1977. Quality of soft wheat dried in a con- current—countercurrent dryer. Unpublished M. S. Thesis. Michigan State University, East Lansing, Michigan. Allen, J. R. , 1960. Application of grain drying theory to the drying of maize and rice. J. Agr. Eng. Res. 5:363~-386. Arora, V. K. , S. M. Henderson and T. H. Burkhardt, 1972. Rice drying cracking versus thermal and mechanical properties. Trans. ASAE 16:320-323, 327. Bakker-Arkema, F. W., W. G. Bickert and R. J. Patterson, 1967. Simul- taneous heat and mass transfer during the cooling of a deep bed of biological products under varying inlet air conditions. J. Agr. Eng. Res. 12:297. Bakker-Arkema, F. W., T. W. Evans and D. M. Farmer, 1969. Simulation and multiple-zone grain drying. ASAE Paper No. 69—835. Bakker-Arkema, F. W. , T. W. Evans and L. E. Lerew, 1970. Michigan State Grain Drying Models. ASAE Paper No. 70—832. Am. Soc. Agr. Eng. , St. Joseph, Michigan. Bakker—Arkema, F. W., R. J. Patterson and L. E. Lerew, 1971. Multiple— zone drying in stationary and moving bed dryers. ASAE Paper No. 71—302. Bakker-Arkema, F. W., L. E. lerew, S. F. DeBoer and M. G. Roth, 1974. Grain Dryer Simulation. Research Report 224. Agr. Exp. Sta., Michigan State University, East Lansing, Iichigan. Barker, J. J ., 1965. Heat transfer in packed beds. Ind. Eng. Chem. 57(4):43—51. Baugrman, G. R., M. Y. Hamdy and H. J. Barre, 1973. Experimental study and simulation of concurrent-flow dryers. Trans. ASAE 16:894-896. Becker, H. A. , 1959. A study of diffusion in solids of arbitrary shape, with application to the drying of the wheat kernel. Journal of Applied Polymer Science, 1(2):212-226. 115 116 Beeny, J. M. and C. S. Ngin, 1970. Multipass drying on paddy (rice) in the humid tropics. J. Agr. Eng. Res. 15:364—374. Brook, R. C., 1977. Design of multistage grain dryers. Unpublished Ph. D. Thesis, Michigan State University, East Lansing, Michigan. Brooker, D. B., F. W. Bakker—Arkema and C. W. Hall, 1944. Drying of Cereal Grains. AVI, Inc., Westport, Connecticut. 265 p. Calderwood, D. L. and B. D. Webb, 1971. Effect of the method of dryer operation on performance and on the milling and cooking character— istics of rice. Trans. ASAE 14:142—146. Carver, M. B., 1976. The choice of algorithms in automated method of lines solution of partial differential equations. In: Numerical Method for Differial Wstans. Edited by L. lapidus and W. E. Schiesser . Academic Press , New York. Chan, N. K., 1976. Simulation of batch drying of rice. Unpublished M. S. Thesis. Michigan State University, East Lansing, Michigan. Chancellor, W. J ., 1968. Characteristic of conducted—heat drying and their comparison with those of other drying methods. Trans. ASAE 11:863-867. Chu, S. T. and A. Hustrulid, 1968. Numerical solution of the diffusion equation. Trans. ASAE 112705-710, 715. Clifford, W. H. , 1972. Simulation and open-loop control of a concurrent dryer. Unpublished Ph. D. Thesis, Michigan State University, East Lansing, Michigan. Crank, J ., 1957. The Mathematics of Diffusion. Claredon Press, Oxford, England. Day, D. L. and G. L. Nelson, 1965. Desorption isotherms for wheat. Trans. ASAE 8:293-297. Evans, W. E. , 1970. Simulation of counter-flow drying. Unpublished M. S. Thesis. Michigan State University, East Lansing, Michigan. Gallaher, G. L. , 1951. A method of determining the latent heat of agri- cultural crops. Agric. Engnr. 32:34. Gamson, B. W., G. Thodos and O. A. Hougen, 1943. Heat mass and momentum transfer in the flow of gases through granular solids. Trans. Am. Inst. Chem. Engrs., 39:7-35. Hamdy, M. Y and H. J. Barre, 1969. Evaluating film coefficient in single— kernel drying. Trans. ASAE 12:205-208. Hamming, R. W. , 1971. Introduction to Applied Numerical Analysis. McGraw Hill, New York. 331 p. 117 Henderson, S. M. , 1952. A basic concept of equilibrium moisture. Agri- culture Engineering 33:29-32, January 1952. Henderson, S. M. and R. L. Perry, 1955. Agricultural Process Engineering. John Wiley 8: Son, Inc. , New York. Henderson, S. M. , 1970. Equilibrium moisture content of small grain hysteresis. Trans. ASAE 13:762-764. Henrici, P., 1964. Elements of Numerical Analysis. John Wiley 8: Sons, Inc., New York. 336 p. Himmelblau, D. M. and K. B. Bischoff, 1968. Process Analysis and Simu— lation: Deterministic Systers. John Wiley 8; Sons, Inc. , New York. 348 p. ‘ Holman, J. P., 1976. Heat Transfer. Fourth edition. McGraw—Hill, New York. 530 p. Husain, A., C. S. Chen and J. T. Clayton, 1973. Simultaneous heat and mass diffusion in biological materials. J. Agr. Eng. Res. 18:343- 354. Ingram, G. W. , 1976. Deep bed dryer simulation with intra—particle moisture diffusion. J. Agr. Eng. Res. 21:263-272. Kachru, R. P. and R. K. Matthes, 1976. The behavior of rough rice in sorption. J. Agr. Eng. Res. 21:405-416. Kline, D. R. , 1977. Design of a pilot—scale concurrent flow grain dryer. Unpublished Ph. D. Thesis, Michigan State University, East Lansing, Michigan. Kuester, J. L. and J. H. Mize, 1973. Optimization Techniques with Fortran. McGraw-Hill, New York. 500 p. Kumar, M., 1973. Moisture distribution between whole corn, endosperm and germ by various method of conditioning. J. Fd. Technol. 8:407- 403. Kuntz, O. R. and C. W. Hall, 1965. Relative humidity changes that cause brown rice to crack. Trans. ASAE 8:396-399, 453. Kuntz, O. R. and C. W. Hall, 1967. Moisture absorption characteristic of brown rice. Trans. ASAE 102448-450, 453. Kuntz, O. R. , (1977). Fissuring of the rice grain after heated air drying. ASAE Paper #77-3511. Am. Soc. Agr. Eng., St. Joseph, Michigan. Kunze, O. R. and Choudhury, MSU, 1972. Moisture adsorption related to the tensile strength of rice. Cereal Chemistry 49:684-696. Lastman, G. J. , 1964. Solution of first—order differential equations by Runge—Kutta or Adams-Moulton method. Coop ID: D2 OI‘EX RKAMSUB. 118 Lerew, L. E., F. W. Bakker—Arkema and R. C. Brook, 1972. Simulation of a commercial crossflow dryer: the Hart-Carter model. ASAE Paper No. 72-829. Am. Soc. Agr. Eng., St. Joseph, Michigan. McCune, L. K. and R. H. Wilhelm, 1949. Mass and momentum transfer in solid liquid system-fixed and fluidized beds. Ind. Eng. Chem. 41: 1124—1134. Morita, T. and R. P. Singh, 1977. Physical and thermal properties of short-grain rouge rice. ASAE Paper No. 77-3510. Nelder, J. A. and R. Mead, 1964. A simplex method for function mini- mization. Computer J. 7:155-162. Nishiyama, Yoshio, and Akira Hosokawa, 1975. Method of calculation for grain intermittent drying (in Japanese). J. Society Agr. Machinery Japan, 37(2), 209—216. Perry, R. H. and C. H. Chilton, 1973. Chemical Engineers Handbook. Fifth edition. McGraw—Hill, New York. Prasad, S., J. D. Mannapperuma and F. T. Wratten, 1975. Thermal and hygroscopic expansion of brown rice. Paper presented at Southwest Region ASAE Meeting. April 3—4, 1975. Pratt, P. M., 1960. Rice Domestic Consumption in the United States. University of Texas, Austin. Ramarao, V. V., F. T. Wratten and M. D. Faulkner, 1969. Development of a generalized prediction equation for drying rice in a continuous flow intermittent type dryer. Paper presented at Southwest Region ASAE Meeting. March 27—28, 1969. Sabbah, M. A., G. H. Foster, C. G. Haugh and R. M. Peart, 1972. Effect of tampering after drying on cooling shelled corn. Trans. ASAE 15:763-765. Schmidt, J. L. and E. H. Jebe, 1959. The effect of artificial drying on the yield of head rice and the germination of rice. Trans. ASAE 2:26—29, 31. Spencer, H. B., 1969. A mathematical simulation of grain drying. J. Agr. Eng. Res. 14:226-235. Stefe, J. F. , R. P. Singh and A. S. Bakshi, 1978. Influence of ten- pering time on rice milling yields and moisture removal. ASAE Paper No. 78-3055. Am. Soc. Agr. Eng., St. Joseph, Michigan. Thorpson, T. L., 1967. Predicated performances and optimal designs of convection grain dryers. Unpublished Ph. D. Thesis. Purdue Uni— versity, West Lafayette, Indiana. Thompson, T. L., R. M. Peart and G. H. Foster, 1968. Mathematical simu— lation of corn drying a new model. Trans. ASAE 11:582-586. 119 Threlkeld, J. L. , 1970. Thermal Environmental Engineering. Second edi- tion. Prentice-Hall, Inc., Englewood Cliffs, New Jersey. Van Arsdel, W. B. , 1955. Simultaneous heat and mass transfer in a non isothermal system. Am. Inst. Chem. Eng. Symposium Series No. 16, 1955. U. S. Department of Agriculture, 1976. Rice situation. Economic Re search Service, Rs—. Washington, 113 (Rs-28, 1976). U. S. Department of Agriculture, 1977. Rice situation. Economic Research Service, Rs-30. Washington, III. (October, 1977). ' ' ' ‘ tion for Wang, C. Y. and R. P. Singh, 1978. A Single layer drying equa rough rice. ASAE Paper No. 78—3001. Am. Soc. Agr. Eng., St. Joseph, Michigan. Wasserman, T., R. E. Ferrel, D. F. Houston, E. Breitwieser and G. S. Smith, 1964. Tampering western rice. Rice Jour. 67:16. Wasserman, T. and D. L. Calderwood, 1972. Rough rice drying. Chapter 5, pp 140—165. In: D. F. Houston, Ed, Rice Chemistry and Technology. American Association of Cereal Chemists, Inc., St. Paul, Minnesota. 517 p. Wilke, C. R. and O. A. Hougen, 1945. Mass transfer in the flow of gases through granular solids extended to low modified reynolds numbers. Trans. Am. Inst. Chem. Engrs., 41:445—451. Wratten, F. T., W. D. Poole, J. L. Chesness, S. Bal and V. Ramarao, 1968. Physical and thermal properties of rough rice. Trans. ASAE 12:801- 803. Young, J. H. and T. B. Whitaker, 1971. Numerical analysis of vapor diffusion in a porous composite sphere with concentric shells. Trans. ASAE 14:1051—1057. APPENDICES APPENDIX A CDMPARISON OF DIFFUSION EQUATION AND THIN—LAYER EQUATION APPENDIX A Wang, C. Y. , and Singh, R. P. (1978) conducted a series of thin- layer drying experiments. The eiperimental data were fitted to four equations using nonlinear regression analysis. The results of the regression analysis for the four models are shown in Table A—1. Table A—2 is a comparison of Wang and Singh (1978) equations and Husian gt 31; (1973) equation (Equation 2—9). The corparisons are based on an air tarperature of 50°C and a relative humidity of 25%. Equa- tions A and B predict higher moisture content than Equation (2—9) as shown in Figure (A—2). Equation C agrees with Equation (2—9) for the first two hours, but deviates considerably after two hours. Equation D corpares favorable with Equation (2-9) for the first hour, but becomes unstable. 120 121 Table A-1. Regression analysis results for the four model. Empirical Thin-Layer Equations M" Me 6 l -n2 m2 D 0 (A) “—M -M = ‘3 "'2' EXP 1,2 1 e m n = 1 n where D= 1.6377 Exp — __glm abs R = 0.18 cm M - M (B) M __ M - a Exp ("be) 1 e where a = 0.96 - 0.00008826 Ta + 0.02324 rh b = 0.002814 + 0.0001267 T - 0.003620 rh M - Mg Y (C) M.-—M = Exp(-X0) 1 e where X = 0.01579 + 0.001746 TA - 0.01413 rh Y = 0.6545 + 0.002425 Ta - 0.07867 rh Mi- Me 2 (D) m— = 1 + A0 + B0 1 e where A = -0.001308 x TO'4687 x rh‘o'3187 B = 0.00006625 x T '03408 x rh‘°°4842 Source: Wang and Singh (1978). 122 Table A-2. Comparison of Equation (2—9) and Equation A, B, C and D of Table Arl. The comparisons are based on an air temperature of 50°C and a relative humidity of 25%. Moisture Content % d.b. Time Husian Wang, C. Y. and Singh, R. P. (1978) hr. ( 1973: Equations Eq. 2—9) A B C D 0.0 26.0 26.0 26.0 26.0 26.0 0.17 23.0 23.4 24.5 23.4 23.6 0.42 20.0 22.1 23.5 21.1 21.2 1.0 17.0 20.3 21.3 17.3 21.3 2.0 14.0 18.3 18.2 13.4 - 3.0 13.0 16.8 15.7 11.0 - 4.0 12.0 15.7 13.6 9.4 - 5.0 10.5 14.7 12.0 8.3 —- 6.0 10.0 13.9 10.7 7.5 —- APPENDIX B PHYSICAL AND 'IHERMAL PROPERTIES 123 Table A-3. Summary of physical and thermal properties. Source a = 98.8 m Chan (1976) cat = 1.3020 x 10‘3 KJ/ Holman (1976) cp = 3.4004 x 10"3 Wratten gt 11; (1969) cV = 2.4211 x 10‘3 - Holman (1976) CW = 0.0054 Holman (1976) D(M) = g(0) Exp {f(0) - M} D = g(0) = 9.48787 Exp {-13914.9/0abs} Husian g5 g1_. -4 (1973) f(0) — 4.90722 x 10 eabs - 0.3788 . - -2 D G 0.41 c u /3 _ 1.064 cps {1- %— Re > 450 Gamson gt 9.1_- (1943) h = D G ‘0.51 C U _2/3 1.95 C G —P— —P—— Re < 40 Wethe and Hougen P U K (1945) Cpu -2/3 0pc 0.51 9&6 hD = 0.0043 ope "K" “K" n < 350 Derived hfg = (1.0 + 23.0 Exp {-40.0 1Tb) hv Gallaher (1951) _ 0.5 0.5 Me — 4.510 + 0.069 rh + 8.837 rh - 0.015 rh Tabs Kachrer and Matthes (1973) r = 0.09756* an Husian e_t _ai; (1973) 17.45 kg Wratten gt _a_1_. (1969) D II APPENDIX C (INVERSION FACIDRS :9 O O p I LI- 5' mzzzt-‘m CUEJOUUQQJQUUUSO<06 of: "U <‘U f m: 03' U) <1 Multiply ftz/ft3 Btu/1b Btu/ lb Btu/1b Btu/1b ftz/hr ft Ib/hr ft2 1b/hr ft2 Btu/ hr ft2 ft/hr Btu/lb lb/lb ft % w.b. Decimal d.b. Decimal d.b. % w.b. % w.b. Deciml d.b. % w.b. _§L_ 3.28 2.3236 2.3236 2.3236 2.3236 929.0 0.3048 4.8827 4.8827 11. 3455 30.48 2.3236 0 . 0703 0. 0703 To Obtain mz/ms KJ/Kg KJ/Kg KJ/Kg KJ/Kg cm /hr Kg/hr m2 Kg/hr m2 KJ/Kg Kg/Kg m % w.b. Decimal d.b. Decimal d.b. % w.b. % w.b. Decimal d.b. % w.b. Kgf/cm2 Kgf/cm2 H 86 (DI-3 v--] 01 H abs d (1* (1* INI MultiElZ ft ft ft °F °F °F °F ft ft/hr 30.48 30.48 0 CO .0929 . 02832 . 3648 .3048 °C °C °C °K APPENDIX D PRLXERANB 126 00000000000000000000000000000OOOOMOOWOOOOOCOWDWODW00““on“”MWUNNNOWWNMWWMNWWWWNNWW U123A5§7090123N5678901Z3NSG789012 “5 7890123 5 78 01 A5 0 A 1111111.11122222222223333333333.4.4.9“ 9 Q“ A ““5 555555 5556666666 6667777 7777770880886 8539 E 0 1 E L H P X H . v. .. m . 9 H T . 6 T 0 N 9, N 1 R o ...» m m G 0 1| NE 89 N H .1Y :. U1. 0 F RR 5 S( C C ED R "a 9 3 Q. 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OOUOOOOOON G HJN I L U N3 5 330315 F ES HN1HHN1NNEA o HHTHHHNHHHT R..OOOOOO.§OO. ... ....DSCOUO.DO...UCOOHOOOOODIA P....O.......................C.....CCvCCCCCCDD ......o....o..0...I..O.....O0.0..¢ O ......O....U..“D..C..O......O..... .0.........n.. ...”..M......O....O ........... ...... .. ............ ccccccccccccc ccccccccccccccccccccc \l \l )1. 0' 0' E 0 E J J J J O G P H 6 1| 1‘0 1| \1 1| 0 A H B X A H MT H 1 H m T E H N 0 .N T N H C D S T A .1 Mn 01 SJ 7.. F0 P H E I N N T H X 0H N T 35 B H B 9 1T 9 0 ‘1 P 550 90 '0 10 905 10‘ 95 12051525352051/53 22101112122222021 1 1 1 1 1 N1 00 TTT TTTTT TX TOOK/TTT T I‘T NNNJNJNDNJNNUN:DNOUZNNDNDJNDTHNU TIIAIAIAIAIIAIOAzaz IIAIA‘IANHIA RRRERERERERRERHERNAORREREFREOPRE PPPRPRPRPRPPRPXRPEHDPPRPRIPRCBPR O . . . 0 . ...... C “"" INPUT INFORMATIJN C c 1. 127 0000 0000000000123“567090.123445676901234456789012344567890123445676901234N56739nnd2>34wfimw7BWWOI 123h56vl L.-L.11.L?2222222223333333333“AAAAAAABI v 94 999999 T. ...... LLL LLL LLLLLL LLL LL L.LL. L.L.L L..L. L .0...L.0L.L.L4 1 A 44 4 4 444 14 4444 444 4 4444441444 444 4 44444444 44414444 44 4 44.414 44 4 N I I O T ) F 0 2 . \III R = 9 \a U 5 I E o P S XX T T N H N XX ) N 9. A E 0 xx 2 E T N 9 T I XX 9 H . A 9 1 T XX 6 T H Y = T I XX F R 9 G s N 0 XX 9 7 A R R E E N XX 9 9 P E E Y I 0 XX : 9 M) 1‘ c xx 9’ B . W W . m xx I) I R 9 9 9 A T XX 95 H GE N N X I N XX .08 NY E E 2 9 E XX FL T IR N N / X I XX 91‘ N RD 0 0 O 5 B \a XXTX E E. H H ... I H 9 XX. 10 c E 9 X X I A T XXE E R NX 9 9 .E O F XXC. V E II N N L on T XXN=0 P G 9 T E B s A Q XXA H N5 5 L A N (9 s XXHTE 9 FA N P ) E 0 ) 9.. _ XXRNR T) 9 E H o R I 9 -T R XXOE NoEX L E ... I T ... FF H )XXFNR EFR1 X T s I Q / I XXREE T U 9 I I S E 0 0‘1 98 U TXXERT N T. H H E D N IO P/ B FXXPIA)0 OLE P P G 0 TS NH XX UHZCPUG B 8 A .b c AE EF 9 9XXRQ 9 HnbA 9 9 T N RLTTC ETLXXEEFBEEIT) B B S I L 32 T9 AXXYROFRTRS. H H R A HAIR 9 ATVXXR 9U 615 A ,0 A V. E T UI IE RFRXXDYTXTNATU 5 T 0.9 T N P N HR. AT .LXX GN1$I LT 25 9 49 9 A H E AE A NTXXLR IA 9UA 2 N O N H E N SVGTR OHNXXAE .ORUHT 9903 I CT I T N 3 AE LTIXXTNH..HG 9 5 JT H T H H 0 AGTLH PP XXOEA SF ( 0 ) 9 0 9 m S R NSNO ET (T BLL 90N HOG J 0 N) Dru )N 0 I I TI. IL hr. 4 l LLLAAH I R6) 4! 9 E T .4. IP 6) JI T R 2 I I V Ev. ......u I PxX AA/II. NA P)5 L 9 G J J HH )5 (H R A ETH 9 9 N LRX9P ADTxXXTTUTT40R T2 P I A ( ( TE 20 LT) E H NAU X X E)N00XI REU!X000TNNXIG 3. H 6 0 H H (T 9A P(P N I EHT 1 1 90191QA 5809.1TTBII1T. 0T E ST... 0 .90 S))D)R J RN T J HRH E R B 9 9 9999999 9.999999999A9 E5 T 7H9 1 91 NJJEJP 9 U9|I._E<~ EUE T E 999 0.9.. 7.09.0.9 9990.099999OL. 0 9 9N0 9 954.. 00 10 9((BI‘T9000CRB 9N9nn0 TCT 9 A N950500010 101x00 X XXX000XXXXX0 0 75p 955E0I ..OH = E: :E1HH .. H8738 9NP1P 9793 : NNHE N EE709900. I. I. F5. 0 I .3 555. O . 55555. D INQZZU 9ENHX)UNTU ..NHHHD12100T41u-01211N0 AUNRO U:111121((( ] 1E 1NON X:NN NNJIFTP : :CBYEE ..ECR: NEEATNO TTT TTTTTTTT TTTTTTTTTTTTST REFFREOEAO(((00(OOIFLPBRRRTAIHFFRRRTEA0(0NNAA0TRRRRRROOOJ 00000000 00000000000020 PRIIPRCDCOYYYCOYCOTCXEDPPPNCTTIIPPPNTC9YCEEHHCBPPPPPPFFF.)FFFFFFFF)FFFFFFFFFFFF/F 050 505 05050 05 0905050505 0 5 0 .9 0 0 001 1223314445 567755990011 2 2 1 1 A 5 111 11111111 111111112222 2 128 000000000000000000000000000000000000000000000000000000000000000000000000000000000 230567090123“5678901234567090123k567090123“567890123b567890123A5578901239567 9012 7777777706008008809999999999000000000011111111112222222222333333 333AAQAAAAA A555 111111111111111111111111111122222222222222222222222222222222222222222222222222222 R NL E EE m D E o N "D 94.1) H s I I H A“ X N A T T0 0 66 9 A R N R9 YRH L 99 m m m. N F 11 U E 1“ H R R T TA T T T I E 9 A N 38 N A A 0 T N IPR E 9 E I Y SEE R NH N T T N 9N T G U AA 0 EN U I X 0 R RUYR C KK C VE P S T 2 E E N RR 9 3 IT H E U 9 T a E R0 0 A F TN 0 I 0 CE F A C XX 6 N T CO C T P R 9 VCDE EE 9 C 0 EC R G B 05 . 8 LR A TT 6 C 6 0 V D E 9 U H IN E UU N 9 T E NE N P L 5 NA N 9 TH F O 0 X T Y OR A O E O G NINCH O 22 C F m A M CU R V N T I N EA DD 9 N L T R P G I T E URIJR N 5 0 D U R ES H 9 ES C L 06 O N CG 9 H A TI I D 0 S E X EAR I DO 0 9” T I U0 8 N H m G S 9 P T II C T 0 S Y PH L A X . H EER P A 9 29 6 H 9 I AC G P 9 L PP A 1P ( E E OH 0 S E T N B TNGA9 w 00 N (0 X B Z CU N N H A TN I 9 NH 00 O 2H 0 I I 9 A 0 X U R 8 AI E I CC C FR H 0 L DR 0 I 9 0 SI E H K 5 9 N9 T T A NBT6 R T H E P A TCHRE 99 3 0H 0 I AIN/ H I E R H T AL E JJD N 3C 9 R T LIT I D H Y E 9 SNU - H 9 CE 0 9 9 \l E I RIHN T N X 3 RE TT N R9 T 555 C TV 0 Y N HU9I F 0 9 9 I ELEE 99U L9 2C 6 R I IQTH C C 0 EP F9 H K9 R NN E2 19 D C D BEB9 O H E OC 9 N FKL O AAS EVN (P 0 X DT L HT T F 9 S YH 9 N A F HHH 550 1C R D F NN DAN 092T U H3 m AL 5 TTA A-C F9 P T 0 AI ONTI H 010 RE T H 55R KH9 NA I TO H TATT 0 E0 H S G: T CAT 9 AU AAC CF1 03 T 2 9 S H 9 FT 9 L 510H T UT NH I H RE LLO ACN 09H 2 1T N RT HTTF 9 A F AOTF N EE R IRN9 GSA .. P40 9AT 0 90 0 N CH (15 9) P) C A O. L U P OUT .. 0C RSAAZ 06 I TI LE A99 CNN 909 T 99 .H C HUE R A B 8 TH/ L/PN( 6‘ T ET FIBH10 .II RiGA S XX 9T NT PSDN U U RXT LY/IYHCX I L( R0089. .TA 9 L9TG N 00 XI 0P CTR EKUQSTS A/N DTS/IA009 0 NF IISDZ. A9R Q 0E19 O 11 “N CH NNCFEHR HNT lRSEH/HHB N I( AFVS A CNS 2? AHoH C 9 9 99 E ILR IIORFAA uIS DPEHATXD 9 50 A F/VTC 9 I 90E EXR 99 99 ET ATLEIKT AN IRRAKS 9 9.0 EH N TEN... SHT 1HTPHTE9 EAVAP 00 0X NN HUU HUBCDRSI 5H0 RPPNRENN5 5 T1TBNNI0 RCFA08 1RR ORIG I901T CSC O9 92 I9 0 TC ’0 Gill/T000 9T20UDIIH9 ECC600 7(E0H9N/TER11U .9. (TT(( TR CC R CH I / III9000U19PHTHT0N V 9:5330CVIPLIANHP33PAACP TT1TT UP 3 NE NNTNNNNNNSST9:1P(:HR===:I0 NR9T.0 9HATBEFGIXH HGGHG AAIAA 0T IN U U OOUOOOOOONN:0T=NY00:TTTTH9 0E00A900E0A:V :R=TTTO:=:: HH9HH R3 5 F HHIHHHNHHEET:INI:N3N1395R01CF5450T :3RLGL:PHNNN31239 RRXRRDBD R0 HHTHHHHHHHHTLXT 0E I1111= : s 4. H99 .. ..E E: LG ECI NNNN OOZOONU9 OOHOOODOOIITREA HH H((((HPC AFFCOCH VPAF HFRR 0000 FF9FFESN GC CC9CCCCCCDDFPIP XX RYYYYRSI GCIHGHX GGCA XIPP CCCC 9 999 99.99999999999099 9 . 9 99 99 9 9 .9A ......9499999909. . . 99 3.. 9 9 9. 60......000009090 O O .9 Q. 9 O 00 05 .. .u............... . . .. .. . . 3A 52 9. 9 9.9.9.9...99999 . 9 9. .9 9 .2 22 22 CCCCCCCCCCCCCCCCCCCCC C C CC 1 2 CC C C1 129 00000000000000 0000 00000000000 000 000000000 000000000000 0000 00000000 000000000000 39567090123956759012395678901239567890123“567%90123056789flnfluHfimflflflfluauflfifi783NMM” 555 5566666666667777777777006088808099999999 90000000000 22 222582222222222222222222222222222222222222222223333333333333333333333333333333333 s N P 0 I E T G T E 5 fl 3 A I 0 T T T T U G T R N K F I 0 R u H X U u ... w u N P T N E T U0 2 R O U T N E 00 1 2 R 5 S NL ( T H 9 E E VI 0 U G 9 F F 9 N .99 N 6 U I NO 8 B I o P 9 O N F 9 K E H 9 LG 9 I N R A 9 O 9 N T 9 O E T 1 C 5 TT A 9 I T 0 R 9' SN 1 0 '0 A Y 1 7 L T T H 1EN ( T A N B 0 9.. F 0 9.9 R (TI V9 E s 9 9 9 C 7 9 YNC 9 H N V N 9 N 2 2 9 90E T H E C o a 0 o 9|" 0 9.908 N R N D R I g T I TY5Y 6 93 I 9 E N H E T E L TP 5(1( 0 07E0 T R T E 0 P N U 9 9 AE 15(5 9 61RT E P 3 B C 8 E L 9.9 Sol ABV-BT) T ICU H 1 I 9 o 9 F NS YA ..ASDT 9.. 9109.90 0 999 s R 99 G S 9Q. I E = = x = 135) 9... \l 956 N N V. A O a U c 9 0.99 T XXAX‘l‘Ia 9| 301 o A 0 9 N N R E E 9 NX 5TAAHAYY(2 Y IIOE I H T N A T E z 9 9 0E 14HHTH==T( ( (0H5 T S 2 I N 0 T H 9 I 1 T CN (1OHOTXX:Y TH Y9 E I N 9 1 O I . P R L 9 N Y(XOXDAAX= TR 91 9H 0 0 1 9 I. I T N 8 I A 6 E 0E ..YTTTTHHAX 3B T‘HT N I 90 V9 T P I 9 6 X A IT. TTNK X=XXXXHHHA 10 T95 C T P009 I R T 5 6 XAXE TTE TAA AXAAAATTH (A I9UF C A 011E C 0 ( 9 5 6 XAHA9 I29P 2 T HAHHHHXDD YH 1T0087 L H9 H N S 9 ( U XAHHHN T NIICCIN THHHTTTTXU 9: (IN 99 T U RTOI TC 8 T I ARQANTTHA 0 I(90 (00 XTDDODXXTT TT Y7EE669I C 99TT T TC 9A N 9 EETHDDXDF 1 TIL TIT TT 9 9 9 AAXX T3 99\ 9 N 9 9 9x L 991. E 2 3 9 I 3 9T TXX 9XE 9 099 9T XXTTTTHHAA 111F050689E ALT909 2. 9T 1R H 1 NA0X99X99 1 TT3FUTPB AACCGGHHHH 1(=(#NNTT9 CE2TGTTE11 T EIP10 99h ANC9XXAXP = 190T1RU HH9999TTHH (YHAIU GUAF V12T55H9NTT0T FX09F V03 F/TXAAHAH I T10 5105 TTTTTTDDDDHYTRHTLFNNTI RLG(IIIII3(8739 9E0“ 059 EYIAHHHH9 9 C F R(13I(SHB99TTTT9999R(0T5H IEEL PAIY(9((T T22(2 X L E 93P OG9HHTTHP I I Fm AY(N0YBAUT0377TTTT .. 9 9DFF 9LHRG TNT 9 TRYYE : ..((Y( 2F ”9‘ A6H RRTCUDDS 99 9 N 0 AT(TIH(AKSGGZZZZGGGGE(11SCI9XXPA BI50(E9:: TYY:Y (IF E CI9 IEE999999 9 1 CA 0090GSPRM P RH99((((9999TA99V( 9...L 0F1 I92TT11::T: 0 0.H (P6 AN967090B000 : 9 ’0 9 90 9’ AA KAK ATTYYYYTTTTUHE.9.9 NTTTTF 9 l9 TRIIZNNTTCTE 1N T E9 SQCEER0000191709 I P9900:0PLVTICVCLKAB((((0099PBGGA9CN525 1LEY(2P399 9CCICU1(CCITUA979::PAAHQA33331 510:=X:CLGSCEGELR11$SSS3322HD99G EI111T:RK:=1H CCOCII(IN9TENXINCH90Y0H .0 :::XXAX:AH EHHHA ((BBBB((((OHHH=PHR(((ETPAER(TTII5I((X(ICAHIEXI=F:=52TTTTTTTTTTC0 55KAANACC .. LBC .. CCLYYAAAAYYYTCQRRTSS: YTYSI: HNEYNN((L.(XX3XTIH3NIET:2 «NGRHNNNNNNNNNNIQ NNAHHHHN GL 5 L(((((((((( ..((H.. ((( XL IT:(IDD DCCHDN..R ( NI:AUEU(IIIIIIIII: OOHHTTHO FA F AFFFFFFFFFF HFFFP FFF ER TABFRHHOHHTTHOCO F OAPFANTFRRRRRRRRRCO CCTCDDDC NC H CIIIIIIIIII RIICS III IP ENNIPXXDXDODDCIF I CEHEEEBIPPPPPPPPPID 9 U 9 9 9 0 9 9 9 O 9 9 9 9 "9 995 u 99 679899 99 91 9 9 99 99 9 9 99 91 9 99 99 9 99 9 9 0 099 9 6 9 99 99 9 99 9 9 0 5 599 9 6 C CCHCC C CC C C 1 A 5CC C 6 13) 80°000000000ooanoooooosgoogoooogoooogouooooaoooooooogooooooooooooooooooooo 9567690123Q56789012399567690123 “567890 123 B567690123 “567890 123 “567690123 “567890 123“ 333333kk644h4«a#55555555556666666666777777777786685866889999999999000000000011111 333333333333333333333333 333333333333 3333 3333333333333333 333333333 99949» “#9499399 9*.“ 99.59% 9% 2 790 F tuQAH I I I 0 SEE 0 o 1 1. IHR 0 C O c A RH \9 E E 6 L6 H I EUR 9 I. H 1 F AF N I NXE N I X I 9 N9 2 D 0 OUT N 9 1 T IN )X L E P1A 0 I m X F CI 26 M L EIH F H U 0 I BI I 0 R 9H 9 X )9 G T 0 3 .l B FA C 0 071 T X .9 .9 9 9 N N 9 I 9A O C R m H HFZ Id. 9 9 9 9 U 9 I 9 99 99v! I H 6 995 )I U 9 9 6 9 9 9 s D I F 0 UH F FHI E HFI 9 .l FI F U N 99 6 9 HF 9 58.! 8 TF0 B X F 99 F F 0 F 0 X F0 6 C L QXDN 1F. 9 0 I XF 0 0 0 S C L L 0 95 F L A S3HE .l I 7 I T F 1 9 H E 9 3 E E H N 9 E H L20 0 2F 0 9 9G H H T. H V A F N N ol .1 9 II R. .1 EXR N 9 9X R O 9 2.9» ..l 0| P 9| I G N R R 0 I “A B 1 C HR6E 6997 9 X 90 P P E P T 9 0 E E 9 I E H 9 9 E IHBP. N F L ...-99 X 5 7. E E D E A 6 c K K \9 U GR ’6 0 R3" A DNA 9 6 9 F 9 D D D V N 9 I A A T IFI EXHF C 2A.... 55 9 9 92 T I 0 0 F F 9.9 I Y IN 9 9 3 9 T5ZH HFO m 9 T X 9 I I A I R C F 0 0 X A REZE SI 95 TSX7 H H... I X F 26 A A 9 A E 9 N 0 0 CC C EFCI AB6199C FZH 0 0 I 9F 9 9 9 9 0 5 0 E S 99 9| K AGR U F5 HAPXNI 01.9 0N9: H F 2 9 9 9 X 9 N c D E H D C FE LQI A HH7 9H XX 9 9 \l D 9 Q». X X a X E 50 9 \l O 0 R 9 0 9 P ASFB Y3EL0H99500 9 92 9 9 = 3 3 3 .l FC 99 \9 N 0 9 99 L 9 Uol VII IRXTAF 919.119.: XXI, 9 X F I I 2 I A H 9 Z 1 N 9 I B 3SF5 RTY QDSHH CFHIIZ 30 91X 6 9 9 2 2 9 2 L 9.9 1 N T 0 9| 9 O’DHFR 9 RQIZE CUU 9 93x33 9 XP 9 9 9 9 U PN '9 19 S E 6 X N EOUHZEW DbBIXCoRNN899 99599 9 1H 9 9 F 9 3 00 2 Y R N h 0 0 FIC1 I nu FLAQE5E3II7F E9 (“9 I 9E F F 9 F L HC F 9 I I 9 \9 H RIOFI OCAIS O HHDFI 9 UFO EgFE 2 “cl 9 9 C 9 A R 9 N 9.9 F o \l 99 0 F9 RIBIFLAI L9 3U 9N3 IXZRH 9 9H I 9 9 9 9 C 93 0 1 1 1 9 ICCLG9 U R9 AZXHHIU 9EBZH9 IZXI 1 7N) : NN 3 N T. .l 1 1 99 99 TFPE 9ICYNZH 95H8 906R N UTIZI 9 FI9 .. = s 0 CO 9 99 A A 99 99 99 Z Z UIAP CSLRI I6E388CFU IB 9 9999 9 9A 9 9 I C I. N 0 I. Y Y 1 9 PBVSYHPADUBCF XLFN SSALFoI 9X90 9 X XRYI 9 9 X 0 v 9 Z 9 F 9 3 9| 9 9 I NL T99 C TFE9 I5I EFSTR/ X21X h. lGFX X A X N 02 1 9 V N V 1 H 0 1 9‘ IIRO I 9 889 URIHB“ OEUGU 9S3 9 93 9 9 9 A A H A G 9N 1 R 0 R 9| R0 9 = 0 UEISNEYL vl HHUL 9N RP .IP 99 Z 9 9 2H 9H H H I P0 1 99 E C E v9 301 J H LII3NORR 9NSI9§HH00HPNEBHI9 R 99 R 9 X X s R 8 F 1 D 9 0 9 U 91 9 X ABA 9EIUA FEITXHSFIT IV E HHAH H 5 1X X 0 X E E 9 9 N 9 99 9 A00 .9 9 N H60I5N...E. «SF 53Xzol53 .JHIJT‘ .. f. 9 F1 90 0 I 0 0 X A1 0 1 E .9 ... 0 H: H J 99 0 9 F ASITORA HX3 ANIYH1 P 9 9P) 9 9X2I I H I L CN )C N I 1 T 6 :EE 9 1 Is MnRZEH CEB I5F1UF9I5H 1THEXXE9 X XAcaH T T H N H A 9O 2 9 9.9 A 9.99.9 A “(IIH .- I 9 TE Parke... P YPPH O.ILARUINI DSZDXB 2H 0 D D D U A H AC 0R Y. L 99V: L +993XE 19 I 1719 ET PL R VuTEng TElIE 99 9 99 D 9 99 F9 9 9 9 F R SI 2L 9 U A.- U 9911.1H 0 9- 073TT0 EHEBPIDEXFSTSNXZT.X 99 2 9H9 2 9 9 9) 9) 9) 9) R G 9 IT. (LH \9 C 1) C 11(0X H CO DI AAPCROFNDWHT? 9HA E0 985XT 9X0T 9X9 X9 X9 X9 X9 E 0 P YN YDA 91 L (2 L 1(Y0) X IH AC6HHAIPLS 5HRZ6 H 17H21F519 F 61 1 91 91 91 9 0 R I III 99 A Y9! A (Y) 90 l. 9X AF VR FN 9 9LXBN 99T1HIFA 9 99 F 9 99 F 9F 99! 99' 99! II P 9 2‘5 H09! 11 C 9v- 0 v9 9 90 9 9 1 9 9 9.9 CY E9 RACCE3XH8IE3ZCU9 9 9 9 99 X 9 99 09 F9 F9 F9 F E B L FN AIS 9.9 H99 (H1 91 5 12:3 IARIRFHIIRHHVIOZFISIZ 9BX00XX0AX X0 09 09 09 09 N U R0 KRE .. ( A9 AR 97 9 EODIDEICIUDOP/AT IZXZI II7I59 9 529 93 19 H9 99 99 99 9 I 5 PC RGT HE (C HCELT “Uh“ AU! AU SI LTN(/6((G(/FB((((((9()((T(X(X(X(X T II III 1(U SD 80595 N A NIT IKTOT TIEITCTITATZXLTTTTTTXT9TTPT171T1I1 U NN)NNN1N9N 0: 0H9E9 TITTUIIAAYLLAHA9AULAAHFAALA 9A AAAAAADATAAEA 9A 9A 9A 9 0 000000 9 HI H) HEHHH7 NTNNBNTHER UETHBEQNRHHNNH:N6R9HHNHNN44¢HH0NZHZNZHZ R NH11HHU1AT CT R:RXR1 INII INRHD CHAR 9HEIGR22RR RFIDRRRRRRTRIRR R 9R 9R 9R 908 HHCHHH: .. N :1 .. E99119: RORR R00 06 OXXOOHOTAEOOOOOODOlOOTOSOSOSOSNU OOHOOOHOHO C1 HHFFFN PCPP PCF9 9 9 9 9 9 FF9 9 9 9 F66FFZFF VFFFFFFR F9 FFAFFFFFFFFES CC CCCADAC DY RXIIII 999999 99999 99 1 999 9 .9 9 9 9 9 99999 9 999 99 3 9 9 9 9 9 3 9 9 9 O 1 9 9 9 9 9 9 9 9 9 9 0 949 0 1 22 0. 500051 2 36 7 6 9 0 9 9 ”9 9 9 9 9 9 O 0 00 1 1 1 1 1709990 5 00 0 C ..U 1 9 9 9 9 9 9 9 9 9 9* 993 3 3 3 3 3333B. .9 B. A“ 99 :9 9» L. CCCCC 100° CBC 131 a -0 ‘ CONF1‘K)'Y(K01) 0 CONFZCKT‘YIK-i) - CONFB’YIKDT 2 E R.GT.0)GO To 1“ C..... 5.1.,50 TO I“ g::::: DERIVATIVE FOR MOISTURE AT SURFACE OF KERNEL Y(26)=DC’(CONF1(10)‘KME o CONFZC10)'Y(9) - CONFB‘YTIOT) c..... g::::: DERIVATIVE OF AVERAGE MOISTURE CONTENT E 1 9 1° (R(N*1)‘Y(17+N) o H(N)'Y(16¢N)) COO... E g::::: DERIVATIVE FOR AIR HUMIDITY - DH/DX Y(29)=-COND‘Y(28) C""’ DERIVATIVE FOR GRAIN TEMPERATURE - OTHETA/DX (ODD) V O V O ( ~H)€O N Z< . 0 N E U A 0-0 uh. I!