LIBRARY Michigan State University This is to certify that the dissertation entitled MODELLING OF THE FEED-PELLET COOLING PROCESS presented by Joao Domingos Biagi has been accepted towards fulfillment of the requirements for Eh D, degnmin.AgrinulIuraJ Engineering Major professor Date 12/ 12/1986 nun.-- AL 5: A ' r1 In, v y - . o-‘m1 MSU LlBRARlES m RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. MODELLING OF THE FEED-FELLIT COOLING PROCESS Joao Doningoa Biagi A DISSERIAIION Submitted to Michigan State University in partial fulfillment of the require-ants for the degree of DOCTOR OF PHILOGOPHY ' in Agricultural Engineering Depart-ant of Agricultural Engineering 1988 3’KJI , JK/ ~ ABSTRACT MODELLING OF THE FEED-PELLET COOLING PROCESS By Joao Domingos Biagi The commercial feed industry ranks among the top 25 industries in the United States. It is projected that 107.5 million metric tons of feed will be pelleted in the 0.8. in 1985-86. Pelleting is a process of conditioning, compacting, and extruding small feed particles into larger particles. Following the pelleting process, cooling and drying of the pellets are necessary to remove excess heat and moisture resulting from steam conditioning and frictional heating. Thin-layer drying of individual pellets was investigated. Experimental drying tests were conducted at 15.6 to 43.3 C, 40 to 703 relative humidity, and 18.1 to 19.1% DB initial moisture content. The thin-layer data was used to determine the equilibrium moisture content equation and diffusion coefficient equation of pelleted feed with a pellet diameter of 4.76 .- and density of 673 kg/m3. Joao Domingos Biagi The horizontal-belt cooling of pellets was evaluated experimentally and theoretically in the same temperature, relative humidty, and moisture content range. Two deep-bed simulation models were developed and tested; both models are solvable on PC-sise microcomputers. The simulated results are in good agreement with the experimental data. The effect of the cooling conditions, including the cooling air temperature, humidity and velocity, on the pellet temperature and moisture content in a horizontal-belt pellet cooler was analysed. The cooling air temperature and velocity have a marked effect on both these values; the relative humidity only has an effect on the pellet moisture content. Likewise, the effect of several pellet properties, including the pellet diameter, conductivity, and specific heat, on the pellet temperature and moisture in a horizontal-belt pellet cooler bed was investigated. The pellet diameter and specific heat are the main pellet properties affecting the cooling rate and drying behavior of a horizontal-belt pellet cooler. Appmd/fl ’ Major Pro essor MAP/7, Approved 0W Department Chairman Dedicated to my parents Domingos and Alcinda and to my wife Cintia iv ACKNOWLEDGEMENTS A special thanks to Dr. Fred W. Bakker-Arkema, major professor and chairperson of my committee. His words of encouragement and belief in my abilities will always be remembered and appreciated. The author is grateful to Dr. James Beck, Professor of Mechanical Engineering, Dr. Lawrence Copeland, Professor of Crop and Soil Sciences, and Dr. Roger Brook, Assistant Professor of Agricultural Engineering for serving on his guidance committee. In particular to Dr. James Beck for helping with the statistical analysis. I would like to acknowledge the financial support of the Conselho Nacional de Desenvolvimento Cientifico (CNPq) and the Universidade Estadual de Campinas (UNICAMP). Thanks are due to several MSU students, especially Carlos Lescano, Abbas Eltigani, and Dirk Maier for helping with various aspects of this study, and also to Dr. Steve Sargent for helping with the editing of this work. To my parents Domingos and Alcinda, my sisters Neusa, Vilma, and Neide, my brothers-in-law Rubens and Nilto, my nephews Evandro, Enrico, Eduardo, and Rubens, and my nieces Giovanna, Natasha, and Erika, I extend warmest thanks and appreciation for their love, assistance and encouragement throughout my life, which has served as an impetus for my desire to always succeed. A sincere appreciation to my sister Neuza for making all the arrangements in Brazil that made it possible for me to stay in the USA while doing my graduate studies. The understanding and moral support of the author’s wife’s parents Cassio and Giselda, brother Joao Luis, sister Lia, and uncle Marcelo are sincerely appreciated. To my wife Cintia for her patience, encouragement, and sacrifices endured throughout the years of my graduate studies during which this work was completed and her love makes it meaningful. vi TABLES OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS Chapter 1. INTRODUCTION 2. OBJECTIVES 3. LITERATURE REVIEW “0.103 UN“ 3.4 3.5 3.6 Feed Mills . The Pelleting Process Cooling of Pellets . 3.3.1 Vertical Crossflow Coolers 3.3.2 Horizontal Belt Coolers . 3.3.2.1 Single-Deck Horizontal Coolers 3.3.2.1 Dual-Deck Horizontal Coolers . 3.3.2.3 Multi-Deck Horizontal Coolers 3 Cooler Comparison . . . . .4 Counterflow Coolers le Particle Drying Equations .1 Theoretical Equations Semi- -Theoretical Equations .3 Empirical Equations uwmuumwu .1 Equilibrium Moisture Content (EMC) 3.5.1.1 Nellist Equation . . 3.5.1.2 Modified Henderson Equation 3.5.1.3 Chung- Pfost Equation . . .2 Diffusion Coefficient .3 Heat and Mass Transfer Coefficients . .4 Thermal Conductivity and Specific Heat .5 Latent Heat of Vaporization . . .6 Air and Water Vapor Properties lity of Pellets .1 Nutritional Quality of Pellets .2 Physical Quality of Pellets “0390303wa QQO 0101010101 vii Page ix . xiii .xviii re '4 w 7. 8. 3. 7 Deep-Bed Models and Simulation . 3.7.1 Algebraic or Heat and Mass Balances (HMB) Models . 3. 7. 2 Partial Differential Equation (PDE) Models 3. 7. 3 Psychrometrics . 3.8 Statistics . . 3.9 Summary . MODEL DEVELOPMENT 4.1 Model 81 - Heat and Mass Balances (HMB) Model . 4. 2 Model #2 - Partial Differential Equations (PDE) Model . . 4. 3 Pellet Properties . 4. 4 Psychrometric Chart Model . EXPERIMENTAL PROCEDURES 5.1 Pellets 5. 2 Equipment . 5. 3 Single- Layer Tests 5. 4 Fixed- Bed Tests 5.5 Instrumentation . RESULTS AND DISCUSSION . 6.1 Thin- -Layer Drying Tests . 6.1.1 Equilibrium Moisture Content and Diffusion Coefficient . . . . . . . . 6.2 Deep-Bed Cooling Tests . 6.2.1 Comparison of Experimental and Simulated Deep- -Bed Data . . . . . 6. 3 Effects of Model Parameter Values . 6. 4 Effects of Air Temperature, Relative Humidity, Air Velocity, Pellets Initial Temperature and Moisture Content, and Pellet Diameter SUlliARY AND CONCLUSIONS SUGGESTIONS FOR FUTURE RESEARCH LIST OF REFERENCES APPENDICES Experimental Results . . Psychrometric Chart Medel and Output Sample . Heat and Mass Balances Model and Output Sample . Partial Diffferential Equations Model and Output Sample . . . BMDPAR Subroutine: EMC and D Estimation . 5" PPS”? viii Page 60 61 65 66 68 70 70 72 79 61 82 82 83 85 88 91 91 94 104 119 132 147 164 166 167 175 175 189 195 201 211 LIST OF TABLES Production Share of Different Agricultural Sectors in Developed and Developing Countries. . . . . . . . World Production and Consumption of Feed Grains (corn, barley, soybeans, oats, rye, and millet). Connected Motor Horsepower for Various Processes in a Feed Mill with a Capacity of 10- -20 tons/h. . . . . . Pelleting System Connected Motor Horsepower for a Plant with a Capacity of 10-20 tons/h. . . . . . . . Effects of Fines and Steam Addition on the Capacity of a 100 HP Pellet Mill. . . Cooling Air Requirements for Various Pellet Diameters. . . . . . . . Minimum Retention Time in a Cooler for various Pellet Diameters. . . . Effect of Cooling Time on Pellet Durability. . . . . . ‘. . Effect of Air Velocity, Bed Depth, Residence Time on Pellet Temperature During the Cooling Pellets in a Stationary Bed. Pelleting Moisture Loss. EMC (X DB) of Pelleted Rations Measured at Various Temperature and Relative Humidity. Pelletability Chart. Screens Sizes for Pellet Durability Tests. ix Page 12 14 20 23 24 25 26 27 47 58 59 .1a .1b Experimental Single-Layer Drying Conditions for 4.76 mm Diameter Pellets. . . Experimental Cooling Test of a 30.48 cm Fixed-Bed of Pellets of 4.76 mm Diameter. Experimental and Predicted Pellet Moisture Content (EBB) as a Function of Temperature, Relative Humidity and Time. Experimental Data Obtained in Thin-Layer Pellet Drying Tests. . . . . . . . . Experimental and Predicted Pellet Moisture Content (ZDB) as a Function of Temperature, Relative Humidity and Time. Experimental Data Obtained in Thin- -Layer Pellet Drying Tests. . . . Constants and Statistical Data Obtained by Regression Analysis of the Equilibrium Moisture Content Data in Tables 6.1a and 6.1b. . . . . . . . . Observed and Predicted Values of the Equilibrium Moisture Content (XDB) of Feed Pellets. . . Predicted Pellet Moisture Content (XDB) using a Constant Diffusion Coefficient = 1.66E-06 m2/h. . . . . . . . Experimental Values of the Air Temperatures (C) Between the Pellets in a Deep-Bed Cooling Test. Cooling Air Temperature 26.7 C, RH 55%, Air Velocity .5 m/s. Test #3. Experimental Values of the Air Temperatures (C) Between the Pellets in a Deep-Bed Cooling Test. Cooling Air Temperature 26.7 C, RH 55%, Air Velocity .1 m/s. Test #4. Experimental Values of Moisture Content (XDB) within a Fixed-Bed of Pellets Cooled at Two Airflow Rates. Air Temperature 26.7 C, RH 55%. . . . . . . . . Input Parameter Values to the Simulation Models of a Fixed-Bed Pellet Cooler. Standard Input Parameter Values Used in the PDE Model of a Fixed-Bed Pellet Cooler. Page 86 88 92 93 96 98 103 105 108 108 119 132 .10 .10 Input Values to the Simulation PDE Model of a Fixed-Bed of Pellet Cooler. . . Experimental Values of the Between the Pellets (C) Cooling Test. Cooling Air C, RH 55%, Air Velocity .5 Experimental Values of the Between the Pellets (C) Cooling Test. Cooling Air C, RH 55%, Air Velocity .1 Experimental Values of the Between the Pellets (C) Cooling Test. Cooling Air C, RH 55%, Air Velocity .5 Experimental Values of the Between the Pellets (C) Cooling Test. Cooling Air C, RH 55%, Air Velocity .1 Experimental Values of the Between the Pellets (C) Cooling Test. Cooling Air C, RH 70%, Air Velocity .5 Experimental Values of the Between the Pellets (C) Cooling Test. Cooling Air C, RH 70%, Air Velocity .1 Experimental Values of the Between the Pellets (C) Cooling Test. Cooling Air C, RH 70%, Air Velocity .5 Experimental Values of the Between the Pellets (C) Cooling Test. Cooling Air C, RH 70%, Air Velocity .1 Experimental Values of the Between the Pellets (C) Cooling Test. Cooling Air C, RH 70%, Air Velocity .5 Experimental Values of the Between the Pellets (C) Cooling Test. Cooling Air C, RH 70%, Air Velocity .1 xi Air Temperatures in a Deep-Bed Temperature 21-1 m/s. Air Temperatures in a Deep-Bed Temperature 21.1 m/s. Air Temperatures in a Deep-Bed Temperature 32.2 m/s. Air Temperatures in a Deep-Bed Temperature 32.2 m/s. Air Temperatures in a Deep-Bed Temperature 17.7 m/s. Air Temperatures in a Deep-Bed Temperature 17.7 m/s. Air Temperatures in a Deep-Bed Temperature 21.1 m/s. Air Temperatures in a Deep-Bed Temperature 21.1 m/s. Air Temperatures in a Deep-Bed Temperature 26.7 m/s. Air Temperatures in a Deep-Bed Temperature 26.7 m/s. Page 147 175 176 177 178 179 180 181 182 183 184 .11 .12 .13 .14 .15 .16 .17 .18 Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 21.1 C, RH 55%, Air Velocity .1 m/s. Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 21.1 C, RH 55%, Air Velocity .5 m/s. Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow Rates. Air Temperature 21.1 C, RH 55%. Tests 1 and 2. . . Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow Rates. Air Temperature 32.2 C, RH 55%. Tests 5 and 6. . . . Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow Rates. Air Temperature 17.7 C, RH 70%. Tests 7 and 8. . . . . Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow Rates. Air Temperature 21.1 C, RH 70%. Tests 9 and 10. . . . Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow Rates- Air Temperature 26.7 C, RH 70%. Tests 11 and 12. . . Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow Rates. Air Temperature 21.1 C, RH 55%. Tests 13 and 14. . . xii Page 185 186 187 187 187 188 188 188 3.7 3.8 3.9 3.10 LIST OF FIGURES Feed Mill Process Flow Diagram. Pelleting Process Flow Diagram. Components of a Pellet Mill. Boiler Requirements Based on Pellet Production and Moisture Addition. . Schematic of Operation of Ring-Type Die Roller. . . . . . . . . Graph Showing Average Air Temperature vs Average Pellet Moisture. Graph Showing Average Finished Feed Moisture Over a 3-year Period. . . Vertical Crossflow Cooler. Single-Deck Horizontal Cooler Dual-Deck Horizontal Cooler Flow Diagram of the HMB Stationary-Bed Pellet Cooling Model. . . . . . Flow Diagram of the PDE Stationary-Bed Pellet Cooling Model. . . . . . Fixed-Bed Cooling Arrangement. xiii Page 11 13 16 18 21 28 28 30 33 36 71 80 84 .10 .11 .12 .13 .14 Observed and Predicted Equilibrium Moisture Content. Relative Humidity 55%. . Residuals of Equilibrium Moisture Content for Chung-Pfost EMC Equation. . . . Determined and Predicted Diffusion Coefficients as a Function of Temperature. Effect of Cooling Time on the Observed Temperatures of a Fixed- -Bed of Pellets. Cooling Air Temperature 26. 7 C. Effect of Cooling Time on the Observed Moisture Content of a Fixed-Bed of Pellets after 20,15,10 min. of Cooling. Cooling Air Temperature 26.7 C. . . . . . Effect of Cooling Air Temperatures on the Observed Temperatures at the Top of a Fixed-Bed of Pellets. . . . . Effect of Cooling Air Temperature on the Observed Moisture Content of a Fixed-Bed of Pellets after 20 min. of Cooling. . Effect of Air Velocity on the Observed Temperatures at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Effect of Air Velocity on the Observed Moisture Content of a Fixed-Bed of Pellets after 15 min. of Cooling. Cooling Air Temperature 26.7 C. . . . . . Effect of Air Velocity on the Observed Temperatures at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 32.2 C. Effect of Air Velocity on the Observed Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 32.2 C. . Effect of Relative Humidity on the Observed Temperatures at the Top of a Fixed-Bed of Pelltes. Cooling Air Temperature 26.7. Effect of Relative Humidity on the Observed Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . Observed and Simulated Moisture Content using 3 Different EMC Equations after 20 min. of Cooling. . xiv Page 97 99 101 106 109 111 112 113 114 115 116 117 118 120 .15 .16 .17 .18 .19 .20 .21 .22 .23 .24 .25 .26 .27 Observed and Simulated Temperatures at the Bottom and Top Layers of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Observed and Simulated Moisture Content of a Fixed-Bed of Pellets after 20 min. of Cooling. Cooling Air Temperature 26.7 C. Observed and Simulated Temperatures at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C, RH 55%. . . Observed and Simulated Moisture Content of a Fixed-Bed of Pellets after 15 min. of Cooling. Cooling Air Temperature 26.7 C, RH 55%. . . . . . . . . . Observed and Simulated Temperatures at the Top Layer of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C, RH 70%. Observed and Simulated Moisture Content of a Fixed-Bed of Pellets after 20 min. of Cooling. Cooling Air Temperature 26.7 C, RH 70%. . . . . . . . . . Observed and Simulated Temperatures at the Top Layer of a Fixed-Bed of Pellets. Cooling Air Temperature 17.7 C. . Observed and Simulated Moisture Content of a Fixed-Bed of Pellets after 20 min. of Cooling. Cooling Air Temperature 17.7 C. Effect of Pellet Density on the Simulated Temperatures at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Effect of Pellet Density on the Simulated Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . Effect of Heat Transfer Coefficient on the Simulated Temperatures at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . . . . . Effect of Heat Transfer Coefficient on the Simulated Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Effect of Mass Transfer Coefficient on the Simulated Temperatures at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . . . . . Page 122 123 125 126 127 128 129 130 ' 133 134 136 137 138 .28 .29 .30 .31 .32 .33 .34 .35 .36 .37 .38 .39 .40 Effect of Mass Transfer Coefficient on the Simulated. Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Effect of Specific Heat on the Simulated Temperatures at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Effect of Specific Heat on the Simulated Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . Effect of Thermal Conductivity on the Simulated Temperature at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . . . . Effect of Thermal Conductivity on the Simulated Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Effect of Bed Porosity on the Simulated Temperature at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Effect of Bed Porosity on the Simulated Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . Effect of Cooling Air Temperature on the Simulated Temperatures at the Top of a Fixed-Bed of Pellets. . . . . Effect of Cooling Air Temperature on the Simulated Moisture Content of a Fixed-Bed of Pellets. . . . . . . . Effect of Relative Humidity on the Simulated Temperature at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . . . . Effect of Relative Humidity on the Simulated Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Effect of Air Velocity on the Simulated Temperature at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Effect of Air Velocity on the Simulated Moisture Content of a Fixed Bed of Pellets. Cooling Air Temperature 26. 7 C. xvi Page 139 140 141 143 144 145 146 148 149 150 151 153 154 .41 .42 .43 .44 .45 .46 .47 .48 Effect of Initial Pellet Temperature on the Simulated Temperature at the Top of a Fixed-Bed of Pellets. . . . . Effect of Initial Pellet Temperature on the Simulated Moisture Content of a Fixed-Bed of Pellets. . . . . . . Effect of Initial Pellet Moisture Content on the Simulated Temperature at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . . . . . Effect of Initial Pellet Moisture Content on the Simulated Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . . . . Effect of Pellet Diameter on the Simulated Temperature at the Top of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. Effect of Peller Diameter on the Simulated Moisture Content of a Fixed-Bed of Pellets. Cooling Air Temperature 26.7 C. . . Simulated Temperature and Moisture Content Gradients within a Pellet. Pellet Diameter 4.76 mm. . . . . . . . . Simulated Temperature and Moisture Content Gradients within a Pellet. Pellet Diameter 6.35 mm. . . . . . . . . xvii Page 155 156 157 158 159 160 162 163 ggsgggggba OO‘WU > rzarflqnfli h gzfiifagtflvfiflfllflfimte HHiafi D 0 0‘ fl iglid LIST OF SYMBOLS constant constant constant constant specific heat, J/kg K constant diffusion coeffcient, m2/h dry basis pellet diameter, m pellet dry matter, kg pellet radial increment, m time increment, h cooler depth increment, m pellet density, kg/m3 equilibrium moisture content decimal,dry basis dry weight flow rate, kg/h .2 humidity ratio, decimal convective heat transfer coefficient, N/m2 E mass transfer coefficient, m/h latent heat of vaporization for water in product kJ/ks index index thermal conductivity, W/m K local pellet moisture content, decimal,dry basis average pellet moisture content, decimal, dry basis mean relative deviation modulus, dimensionless pellet radius, m relative humidity, decimal Reynolds number = (G Di/P), dimensionless pellet radial coordinate, m pellets specific surface area, mz/m3 Schmidt number = (P/Di dp), dimensionless air temperature, C absolute temperature, K time,h bed coordinate, m wet basis xviii Subscripts a air abs absolute e equilibrium f final 0 initial p pellet s surface t time t+Dt time plus time increment v water vapor w water liquid Greek W 3.141592654 3 local pellet temperature, C 9 average pellet temperature, C 3 thermal diffusivity, w m2/J * bed porosity, decimal u viscosty, kg/h m xix 1 - INTRODUCTION Feed pelleting can be defined as the agglomeration of small feed particles into larger pellets by means of a mechanical process in combination with moisture, heat and pressure. The nature of the feed pelleting process requires the removal of excess heat and moisture resulting from steam conditioning and frictional heat during the pelleting phase. This is most economically accomplished by drawing atmospheric air through a uniform bed of pellets, evaporating the excess moisture and at the same time reducing the temperature. Cooling and drying in this manner' can be accomplished in a wide range of temperatures and relative humidities without requiring artificial conditioning of the cooling air. The pelleting process has a relatively short history, beginning in 1929 with the conception and design of equipment using the die- and -roller principle (Robinson, 1977). For many years, pelleting was classified as an art, because the process was governed more by feeling than by the use of instrumentation and controls (Falk, 1985). More recently, the feed industry has become a science due to technology being developed in this field. 2 The commercial feed industry in the 0.8., which ranks among the top 25 industries, currently is composed of about 400 companies, with about 3,000 primary feed manufacturing plants serving 10,000 secondary manufacturing plants (Anderson, 1985).» The formula feed industry is divided by the United States Department of Agriculture in the following categories: (1) Feed-milling - usually a stationary mill operation at a single location together with a mobile mill based at that location. (2) Primary feed manufacturing - the processing and mixing of individual feed ingredients, sometimes with addition of a premix at a rate less than 100 pounds/ton of finished feed. (3) Secondary feed manufacturing - the processing and mixing of one or more ingredients with formula feed supplements. Supplements are usually used at a rate of 300 .pounds or more per ton of finished feed, depending on the protein content of the supplement and percentage of protein desired in the finished feed. (4) Custom grinding and mixing - grinding customer-owned feed ingredients and usually mixing supplements with them. Mainly, this is a service provided to farmers feeding their own animals. Feed costs represent 60% to 60% of the total production cost of livestock production (Olentine, 1985). It is essential for the livestock or poultry producer to 3 maximize the use of the feed. To accomplish this, feed is pelleted to prevent spillage and waste, to enhance consumption, and to improve the feed efficiency and the handling characteristics. It is estimated that approximately 90% to 95% of the feed produced in Holland and 65% in the United States is pelleted (Olentine, 1985; Perry, 1984). There are a number of models presently available for the classification of the status of a nation’s economy. Most divide the world into developed and developing countries. Developing usually connotes the fact that a country has not reached the economic development of western industrialised countries. Whatever the status of a developing nation, one of the key areas of growth that is evaluated is the upgrading of agriculture, in particular of the livestock and poultry industries, and thus also the feed industry. The importance of developing countries in agriculture is shown in Table 1.1. In 1970 the share of the total agriculture output was 64% for the developed countries and 36% for the developing countries. It is projected that in the year 2000 the developing nations will produce 62% of the total agricultural output, while the developed countries will produce 38% (Olentine, 1985). Feed production will follow the same trend. The problems incurred by feed manufactures vary from country to country. Culture and religion, governmental policies, transportation, handling and storage are among the factors that need to be evaluated when the feed formula industries are analyzed. Table 1.1 - Production Share of Different Agricultural Sectors in Developed and Developing Countries. 1970 2000 (M (%) Share of total agriculture output Developed 64 38 Developing 36 62 Grain consumption Developed 45 33 Developing 55 67 Animal Products Developed 64 42 Developing 36 58 From Olentine (1985) With the rapid rise in the speed of transportation and the methods of communications, the feed industry has become a world business. The ingredient prices are being determined by world demand rather than local or regional demand as has been the case in the past. South. America, including Brazil (the author’s birth place), increased between 1972 and 1982 the per capita food production and increased its share of global exports by 16% (Samuelson, 1986). The feed industry increased accordingly. Table 1.2 shows the world production and consumption of feed grains. The U.S. share of the world production of feed grains has decreased from 32% in 1981 to a projected 29.5,; in 1986, while the 0.8. consumption has remained at about 22% since 1981 (Feedstuffs, 1985). Table 1.2 - world Production and Consumption of Feed Grains (corn, barley, soybeans, oats, rye, and millet). Country or 1981-82 1982-83 1983-84 1985-86 Region Projected Production millions of metric tons. Canada. 26.0 26.5 21.0 21.9 Eastern Europe 64.5 71.8 67.1 74.3 US 246.8 250.7 137.1 237.1 USSR 72.0 86.0 99.0 86.0 western Europe 87.8 93.6 84.8 103.4 Total Non US 522.1 528.0 548.0 565.7 world Total 768.8 778.8 685.1 802.9 Consumption US 154.8 167.9 147.9 165.5 USSR 98.5 98.3 110.5 112.0 world Total 738.6 753.0 758.7 782.7 End of Stocks Total Non US 44.7 41.3 33.4 39.4 US 68.2 97.5 31.7 45.8 world Total 113.0 138.7 65.8 85.2 From Feedstuffs (1985) Brazil is a developing country with a steady increase in agricultural production in the past ten years. It needs new technologies to support its growth. The pellet cooling techniques, described in this study, should aid in the development of a successful feed pellet manufacturing industry in Brazil. The effective cooling of the pellets immediatelly after leaving the pellet-mill is very important; it has a considerable effect on the quality of the pelleted feed. It is essential that the moisture content is controlled to ensure acceptable shelf-life and reduce the risk of mould. Since the cooling and drying in the feed pelleting process have not been investigated in depth (Trickett, 1982), a comprehensive study of these two subjects from a engineering point of view will contribute to a better understanding of the pelleting process. 2 - OBJECTIVES The main objective of this study is to analyze the cooling and drying of pellets in a horizontal-belt pellet cooler. An experimental investigation had to be conducted of single-layer drying and stationary deep-bed cooling of pellets to verify the simulation models of the horizontal- belt cooling process. The specific objectives of this investigation of the cooling of feed pellets in a horizontal-belt cooler are: 1. To determine the drying and cooling rate of a single-layer of pellets under various environmental conditions. 2. To determine the equilibrium moisture content and diffusion coefficient' of feed. pellets under various environmental conditions. 3. To determine the drying and cooling rate of a stationary deep-bed of pellets under various environmental conditions. 4. To develop two microcomputer-based simulation models for the cooling and drying of a horizontal-belt pellet cooler. 5. To investigate the effects of air velocity, air temperature, and air relative humidity on the pellet cooling and drying rate of a horizontal-belt pellet cooler. 6. To investigate the sensitivity of several pellet and bed parameters on the pellet cooling and drying rate of a horizontal-belt pellet cooler. 3 - LITERATURE REVIEW The literature review will focus on the factors that affect the cooling process of pellets, and on the development of a computer model of the cooling of pellets in a deep-bed cooler. The review is subdivided in eight major sections: (1) feed mills, (2) pelleting process, (3) cooling of pellets, (4) single particle drying equations, (5) pellet properties, (6) quality of pellets, (7) deep-bed models and simulation, and (8) statistics. 3.1 - Feed Mills The term "feed processing" refers to any treatment that a feedstuff or part of a feedstuff undergoes prior to the consumption by animals. The processing may be one step or a series of steps, and may include cooking, mechanical extraction, dehydration, grinding, and pelleting. According to Robinson (1971) and Perry (1984), in the United States approximately 60% of the non-forage feeds are processed in feed mills. 10 A feed mill process flow diagram is shown in Figure 3.1, illustrating the different mill processes and the flow of material from plant entry to exit (Balding, 1985). The receiving is the first process of the plant and includes the actual receiving of the materials, scheduling of ingredients, quality control analysis and material handling. The second process is the processing which consists of the grinding, rolling and flaking operations, and the movement of the materials to and from the processing equipment. The third is the mixing process, including the movement of both sacked and bulk ingredients from storage to the mixing center, proportioning these ingredients, and mixing, conveying, scalping, and blending them. The fourth is the pelleting process which includes conditioning, compacting, extruding, and cooling/drying. The final two processes are packaging, consisting of weighing, bagging, and loading of the finished, packaged products on railcars and trucks. A list of the equipment in a typical feed mill is given in Figure 3.1. Table 3.1 lists the connected horsepower values for the various processes of a 10-20 ton/h capacity feed manufacturing plant. The processing and pelleting processes account for 70% of the total horsepower required in a feed mill plant. Wm MW 1. imam-m WW 2. Tmmm lfmumm Conveyor imam Hopper indium CW imam 1m lmlbvlht mammal-inn Control 10.th 1140mm Scale 12.?ch imam/Cleaner 11.060!!va ILWCMW 11W 17. “Welshman. m4 10.6m 1!. Surname 20.8mm 21.6w 21mm nfwnheedOlsM 2c. ”mama 21“.“!ch 20.80am 21. unionism?“ mace. ans-renmmw Ila Ilia-rem WM" WWW Mun-ulna mm Fig. 3.1 - Feed 11 ,. 1‘ (J—e (‘3 +4 , ‘ 9 1 J) A L/ l .4— : 3 Z d 1 !_J/ "L." l ’7'“: a o r". l / g» \ 1"- (.17) «at; \9 Q?) EULK ‘4 boNs V...“ \3/ wt) [my 1 mill process flow diagram (Balding, 1985). 12 Table 3.1 - Connected Motor Horsepower for Various Processes in a Feed Hill with a Capacity of 10-20 tons/h. m 90W Receiving 80 Processing Griding 160 Cracking 25 Steam Roling 129 Total Processing 375 Mixing Batch 120 Continuous 59 Total Mixing 170 Pelleting 300 Packaging 30 Bulk Loading 39 Mat 265 Pro. HcEllhiney (1985) 3.2 - The Pelleting Process A typical flow diagram of the pelleting process is shown in Figure 3.2. Feed lash from an overhead bin flows into the feed conditioner where steam and binders are added. The conditioned lash flows into the pelleting hill in which the pellets are formed. The hot pellets pass to the cooler where they are cooled by ambient air. Fines carried by the cooling air are separated in a cyclone and returned to the feed lash to be reprocessed. The cool pellets are passed through the crunbler, if crumbled pellets are required. After the crunbler the pellets pass over a screen in a rote-shaker to remove the fines and overs. The pellets COLLECTORI t “A ‘ ROIO- SHAKER 4. ...." ""a'iiaili Fig. 3.2 - Pelleting process flow diagram (Falk, 1985). 14 flow into bins for conditioning, while the fines and overs are returned to the pellet mill to be reprocessed (Falk, 1985). Table 3.2 lists the connected horsepower for the various electric motors used in a 10-20 ton/h pelleting system. The pellet mill uses 66% of the energy, while the cooling/drying systemw including the cooler/dryer, the cooler fan, and the airlock. accounts for 17% of the energy consumption of the pelleting process. Therefore, only an improvement in the pellet mill can significantly reduce the final cost of the pelleted feed. Table 3.2 - Pelleting System Connected Motor Horsepower for a Plant with a Capacity of 10-20 tons/h. Driven Unit Motor HP Feed Conveyor 1.00 Mash Conditioner 7.50 Pellet Mill 200.00 Centri-Feeder 3.00 Cooler (Horizontal Belt) 1.00 Cooler Fan 50.00 Airlock 0.75 Crumble Rolls 20.00 Bucket Elevator 5.00 Shaker 3.00 Distributor 0.25 Pellet Coater with Pump 6.00 Conveyor 2.00 Distributor __ 9.25 Total Connected Motor HP 300.00 From.McEllhiney (1985) 15 Figure 3.3 shows the major components of a pellet mill: the variable feeder. the conditioning chamber, the die and roller assembly, the speed reducer, and the motor. Pellet mills are available in a wide range of capacities, varying from 20 HP (14.9 kW) to 700 HP (522 kW) (Talk, 1985). The inside diameter of the pellet-die varies from 30.5 cm (12 in.) to 81.3 cm (32 in.). The working area of the pellet die ranges from 582 c-2 (90 in.2) to 5.190 cm? (804 in.2). The pellet-mill capacity varies with the physical characteristics of the material being pelleted. It also depends on the number of time different formulas are pelleted, and on the number of die-changes per day. The average pellet-mill capacity is 68 Kg/HP-h (150 lb/HP-h) (Pfost, 1970). Some products pellet readily while others require the addition of binders or lubricants to produce a stable pellet. Moisture content, density, and particle size contribute to the condition of the finished pellet. Other factors affecting the pelletability are: pellet-mill die-design, die-speed, and the mash flowrate. The actual pelleting process consists of conditioning, compacting, extruding, cooling/drying, and conditioning. The pelleting process transforms finely divided materials into larger particles with a greater bulk density and improved flow characteristics. The feeder is generally of the screw type, and is equipped with a speed-control device. In normal operations the screw-speed is over 100 rpm (Balk. 1985). The purpose of 16 ® ® r (ll/f” ”a ’5 ‘ A; @343“l r1 - Fig. 3.3 - Components of a pellet mill (Robinson, 1971). Variable feeder Conditioning chamber Die and roller assembly Speed reduction device Motor mmbwrow I Base 17 the feeder is to provide a uniform flow of feed to the mdxing and pelleting operations. Conditioning is an important step to improve the feed value, pellet durability, and power requirements of the pellet mill. The conditioning occurs in a mixer before the pellet mill. and is accomplished by the addition of steam, fat, or molasses to the mash. The flow-through.mixer with either fixed or adjustable paddles, is equipped with steam manifolds and liquid injection ports. The mixer-shaft speed varies from. 90 to 500 rpm depending on the material being pelleted. Steam used in conditionig process should be of a specific quality and have a constant pressure. Usually, high pressure steam ranging from 80 to 150 psig is introduced to the mixer through a steam harness designed to remove moisture and to ensure the required pressure. The addition of a conditioner ensures the pelleting of the mash, increases die-life, and reduces the power requirements (Robinson, 1971). Figure 3.4 describes the boiler requirements of a pellet mill based on the percentage of moisture added to the pellet mash by the steam. This amount is usually less than 82 and varies with the type of feed pelleted (McEllhiney. 1985). The conditioning process of the meal results in an increase in the moisture content of the meal. About 1! moisture is added in the steam conditioning process for every 11 C (20 F) increase in temperature. In the case of dairy pellets, the addition of 83 of molasses adds 2% of W100 mm 18 'ELLEY PRODUCNON RATE TONI PER "OUR o u 6 3 3 3 8 3 0' 01 1500 mosmocoz 2M Ol 2500 an cm as Human: sm-aunnau union 9m ”1‘” oasva au-ansurnoo 0H '1 3500 091 071 “I 4500 0“ at Fig. 3.4 - Boiler requirements based on pellet production and moisture addition (McEllhiney, 1985). 19 moisture. In general, the moisture content of the pellets leaving a pellet mill varies from 15X to 18.52 (HB) (Atkinson, 1981b). Table 3.3 shows the effects of fines and steam addition on the pellet-mill capacity (McBain, 1968). The results are the average of 100 tests on two typical high-corn content formulas and one natural 32% high-protein formula. The data shows that low pressure steam results in the highest capacity and quality for the high-corn formulations, whereas high-pressure steam is best for the high-protein formulation. At the higher pressure, less moisture is added by the steam. Compaction of the feed mash is accomplished in the pellet mill by the action of rollers upon a perforated die face. The first pellet mill using steel dies and rollers was build on the principle of a flat steel die with four rollers running on the upper surfaces. The ring-type die and roller pellet mill was developed in the mid 1930’s; it has become the most popular pellet mill in the pelleting industry (Robinson, 1971). Figure 3.5 shows a drawing of a ring-type die and roller pellet mill. The die-speed of a pellet mill normally ranges from 100 rpm to 400 rpm. The rotation of the rollers and die develops the force necessary to extrude the material through the die holes. The extruded product is cut off by knives adjustable in length to the desired pellet length. 20 Table 3.3 - Effects of Fines and Steam Addition on the Capacity of a 100 HP Pellet Mill. Steam Meal Condition. Moisture Fines Over Pellet Pressure Temp. Meal Moist. Added 816 Screen Mill Cap. (P810) (P) (S W3) (M (3) (Tana/h) Test 91 Formula: Pig Grower (70$ Corn) Dry Meal Bound Moisture: 10.8 MWB Die 3/16” x 2” 50 190 12.8 2.0 9.7 8.5 20 190 14.0 3.2 4.3 7.0 14 202 18.3 5.5 2.3 8.5 Test 62 Formula: Chick Grower (65X Corn) Dry Meal Bound Moisture: 11.9 SHB Die 5/32“ x 1 3/4" 75 180 13.4 1.5 7.5 7.0 40 190 14.1 2.2 8.2 7.5 16 195 18.6 4.7 2.5 10.0 Test 83 Formula: 32% Steer Fattner Dry Meal Bound Moisture: 12.0 SWB Die 1/4” x 1 1/2” 75 155 13.1 1.1 1.3 5.5 55 160 14.0 2.0 1.2 6.5 40 140 14.0 2.0 1 8 5.0 18 140 15.3 3.3 2.3 4.0 From McBain (1968) The commercially available die-sizes for cylindrical pellets range in diameter from 0.24 cm (3/32 in.) to 3.5 cm (1 3/8 in.). The pellet lengths are 1.5 to 3.0 times the diameter. For some of the large pellets sizes, square and oval shapes are available (Robinson, 1971). Die-thickness is determined by the quality and production rate desired for the product being pelleted. A thick die normally produces a better quality product, but also reduces the production rate compared to that of the thinner dies. Products which are difficult to pellet, such Fig. 3.5 - Schematic of operation of ring-type die and roller pellet mill (Robinson, 1971). 1 - Feed material 2 — Compacted and extruded feed 3 - Knives 22 as fiber and urea, are normally produced in thin dies, while grain products ~are most frequently pelleted in thick dies. The usual die-thickness varies between 3.2 cm (1 1/4 in.) and 12.7 cm (5 in.) (Falk, 1985). The pellets leave the die at an elevated temperature between 85 C (150 F) and 93 C (200 F) because of the combined effects of the steam injected into the meal during the conditioning process and of the temperature rise resulting from the friction in the die (Atkinson, 1981a). 3.3 - Cooling of Pellets After a feed has been pelleted, it is necessary to remove the excess heat and moisture to ensure safe long-term storage. The cooling and drying process is acomplished by moving ambient air through a bed of the warm, moist pellets. The process objectives of a pellet cooler are (Trickett, 1982): (1) to reduce the temperature to just above the ambient air temperature; (2) to reduce the moisture content of the pellets to 12-14X DB; (3) to cool at a controlled rate to prevent overdyring of the pellet surfaces, and ensure pellet durability; (4) to operate effectively under a wide range of climatic conditions; and (5) to operate efficiently with the minimum usage of power. Factors affecting cooler performance include (Whiteley, 1983): (1) cooler design (vertical, horizontal, crossflow, or counterflow); (2) air flow rate, air inlet 23 temperature, air inlet relative humidity; and (3) pellet flow rate, pellet size, pellet inlet temperature, and pellet initial moisture content. Regardless of the inlet relative humidity of the cooling air, the relative humidity is decreased due to the heating of the air by the warm pellets. However, the absolute humidity of the air increases. Thus, the cooler removes moisture along with excess heat from the pellets. Pellets are usually dried to 12% to 14X (DB) moisture content and to within 2 to 8 C (5 to 15 F) above the ambient temperature (Atkinson, 1981b; Falk, 1985). The approximate cooling air requirement for various pellet diameters is listed in Table 3.4; the required retention time in the cooler of pellets of different diameter is shown in Table 3.5. Large diameter pellets require higher air flows and larger cooling times than smaller pellets because a larger path has to be traversed by. the heat and moisture, in migrating from the inside to the outside, in large than in small diameter pellets (Falk,1985). Table 3.4 - Cooling Air Requirements for Various Pellet Diameters. Pellet Diameter CFM/Ton/Hours Lin-) 10/64 to 12/64 800 1/4 900 3/8 1000 1/2 to 3/4 1100 Zl§_to 1 1209 From Falk (1985) 24 Table 3.5 - Minimum Retention Time in a Cooler for Various Pellet Diameters. Pellet Diameter Retention Time (in.1 (min) 10/64 to 12/64 5 to 6 1/4 6 to 8 3/8 7 to 8 1/2 8 to 10 3/4 12 718 15 From Falk (1985) Pfost and Young (1973) investigated the effect of colloidal binders on the pellet durability and on the pellet energy requirement. This last quantity is also called the pelleting efficiency, and measured in lb/Kwh. Factors studied included the amount of steam or binding agent added, the granulation of the pelleted grain, and the cooling time. Table 3.6 shows the effect of cooling time on pellet durability. The percentage of fines refers to the damage of the pellets occurring in the handling system. Long cooling times resulted in fewer fines than short cooling times. At the low steam level, which corresponds to 30 F temperature rise and 1.4% moisture added to the mash, 24% fines was produced at an efficiency of 125 lb of pellets/Kwh. At the high steam level, corresponding to 90 F temperature rise and an addition of 3.9% in moisture to the mash, 10% fines was produced at an efficiency of 250 lb of pellets/Kwh. The use of betonite as a binding agent increased the durability but did not affect the pelleting efficiency. 25 Table 3.6 - Effect of Cooling Time on Pellet Durability. Cooling Time Moisture Content (% VB) % Fines (min) Before Cooling After Cooling 5 14.4 11.4 10.5 10 14.3 11.8 8.5 15 14.5 10.8 8.6 From Pfost and Young (1973) Whiteley (1983) studied the effects of air flow, residence time, bed depth, product size, and air inlet humidity, on the cooling and drying of .95 cm (3/8 in.) diameter pellets initially at 65 C (150 F) and 15% (HB) moisture content; cooling took place in a vertical and a single deck horizontal cooler. Table 3.7 shows some of the results. A high air flow rate cools the pellets faster; a long cooling time results in a cooler product. Also, a deeper bed improves the drying, and a smaller diameter pellet improves the cooling and removes more moisture content; and, the relative humidity of the cooling air has little effect on the moisture loss. Improper cooling and drying can result in: (1) poor pellet quality, (2) pellet breakdown, (3) spoilage, (4) heating and spontaneous combustion in large volume storage, (5) caking in bags or bins, and (6) monetary loss from excess moisture removal (Robinson, 1983). 26 Table 3.7 - Iffect of Air Velocity, Bed Depth, Residence Time on Pellet Temperature During the Cooling of Pellets in a Stationary Bed. Air Velocity Bed new?“ Temperature (0) Above Ambient (ft/min) (in.) After Cooling Period (min) 5 10 20 30 2 17.5 7.0 3.0 1.0 4 23.5 12.5 5.0 2.0 40 6 27.0 17.0 8.0 3.0 8 28.0 20.0 10.0 4.5 10 29.0 22.0 11.5 6.0 2 13.0 5.0 1.0 1.0 4 18.5 8.0 3.0 1.0 60 6 22.5 12.0 4.5 1.5 8 25.5 16.0 6.5 2.0 10 26.5 17.0 8.5 3.0 2 8.0 4.0 1.0 1.0 4 14.0 6.0 2.0 1.5 80 6 17.5 8.0 3.0 1.5 8 21.0 11.5 4.0 2.0 10 23.5 14.0 5.0 2.5 2 8.0 3.0 1.5 - 4 12.0 5.0 2.0 - 120 6 16.5 7.0 2 5 - 8 20.0 9.5 3.5 - 10 21.0 12.0 4 0 - 3 Bed depth measured in direction of air flow From.Whiteley (1983) Pelleting is a cause of shrink in feed manufacturing operations. A part of the shrink is the result of moisture loss between the mash-feed inlet and the pellet outlet. Table ~3.8 shows the results of typical cooling tests conducted by Rolfe (1982), as cited by MoEllhiney (1985a). Wolfe (1982) considered the level of shrink occuring in the feed manufacturing process to be directly affected by the cooling air temperature. The water-holding capability of the cooling air doubles for every 11 C (20 F) rise in 27 temperature. Thus, pellets can be cooled in a pellet cooler even on high relative humidity days. Figure 3.6 illustrates the effect of the average moisture content on the pellet temperature during a 12-month period. Table 3.8 - Pelleting Moisture Loss. 1191M) Dairy w/ Dairy w/ Moefimummw Feed Inlet 12.80 13.30 Cond. Chamber with Molasses 1. Steam" 16.37 16.81 Die Discharge 16.67 16.81 Cooler Discharge 12.62 12.70 Moisture Loss 0.18 0.60 Value of Loss Based on d 1 012111211 4.1M *Molasses added at conditioner From Wolfe, cited by McEllhiney (1985a) Figure 3.7 shows the average moisture content of pellets over a 3-year period. The moisture content of the pellets is lower during the warmer months when the ambient temperature is high (McEllhiney, 1985a). Dust particles exiting a pellet cooler are normally large and therefore easy to collect. To avoid breakage of the dust particles into smaller sizes and reduce fan impellor wear, the air system fans is located on the negative pressure side of the collector (MCEllhiney, 1985). Pellet cooling takes place in a crossflow, horizontal belt, or .counterflow cooler. In the following sections each of these cooler-types will be discussed in detail. 28 Av. hep. Av. Polio! 7 Moist" '1. IN ‘ '- 12.3 ” J /.‘l\ " '2.’ H/ \1 Arm-go Mm .0 ‘ / \ Ann” 7min l ".1 10< ./ ::_~(///’ ‘\\\ :110 60 -l ' \ \ r- ".7 \ ° ‘/ sol ‘ \\\\ LIL. \ /3\ . / I. < / \ __.n / \n’ "\ » ".7 U’ ‘\ ./ ‘ a. d 3 P "e‘ \ ‘/‘ 20 4 \n/ _ ".5 I 1 In 2 :3 i 1 1 i 5 a} 1 Fig. 3.6 - Graph showing average air temperature vs average moisture content of cooled pellets (McEllhiney, 1985a). IJ'I. .. .l "I" "AI ‘. .4 hw‘ “ m 4 - ~ .4 \\,' cl "‘ v v v v v v v ‘7 Vi r I I M A M l l A S 0 W 0 Fig. 3.7 - Graph showing average finished feed moisture content over a 3-year period (McEllhiney, 1985a). 29 3.3.1. Vertical Crossflow Coolers Figure 3.8 is a schematic of a vertical crossflow cooler. The supply hopper has a level—sensing device (1) which spreads the pellets over the width of the cooling column (2). The air is drawn through the screen-walled columns into a central plenum (3). The discharge drive gate motor (4) powers the discharge control mechanism (5) which is usually of the star-wheeled or vibratory type. The fan drive motor (7) centrifugal fan assembly draws the air through the pellets and discharges it into a cyclone for removal of the fines. The cooler must a have uniform air flow through the pellet columns and an uniform pellet flow. Cooling requires a high air volume and, therefore, has a high power requirement (Trickett, 1982). Typical dimensions of a vertical cooler are: 140 cm (55 in.) to 152 cm (60 in.) wide, 198 cm (78 in.) to 518 cm (204 in.) 'high, with the thickness of the cooling columns varying from 23 cm (9 in.) to 25.4 cm (10 in.). The cooler capacity depends on the equipment dimensions, the air flow rate and the pellet size, and ranges from 3.5 to 22 tons per hour. A vertical cooler to cool and dry 8 to 13 tons of pellets per hour, requires a 40 HP fan and a pellet-flow control-gate powered by 1/4 HP variable speed motor (Robinson, 1970). 30 ‘0' nigh @ @ . O‘" .c‘-‘- .‘CO .. / P. 00"... _ Fig. 3.8 - Vertical crossflow cooler (Robinson, 1971). - Hopper and level sensing device - Cooling column - Plenum chamber Discharge gate drive motor Discharge augers Centrifugal fan Fan drive motor mebwmi—o 31 Atkinson (1981) emphasized that the main problem with vertical coolers is that they need to be full to operate, and that the retention time is inversely proportional to the production rate. Thus, for a specific capacity of small versus large pellets, the retention time should be larger for the larger pellets. If, for instance, a cooler is designed to cool .95 cm (3/8 in.) diameter pellets in 20 minutes at a rate of 10 tons/h, .24 cm (3/32 in.) diameter pellets will be cooled at 5 tons/h remaining in the cooler for 40 minutes. Because of the small diameter and greater surface area, a period of 5 to 10 minutes would have been adequate for the smaller pellets; in 40 minutes excessive dehydration would occur. This problem may be solved by adding in the cooler a discharge mechanism which regulates the rate of discharge to correspond to the rate of pellets delivered to the cooler. Trickett (1982) stated that the use of vertical coolers in hot humid climates is likely to lower product quality and shelf life. 3.3.2 - Horizontal Belt Coolers In a horizontal cooler the pellets are carried on a moving perforated metal belt through the cooler while air is drawn through the layer(s) of pellets on the belt. Single, . double, and triple belt coolers are used in the pellet mill industry. The capacity of a belt cooler depends on the length, 32 width and depth of the bed(s). The width, usually four to seven feet, is limited by the requirement to spread the incoming pellet-flow evenly over the bed to ensure uniform cooling. In order to limit the length of a cooler, dual or triple passing is employed (Atkinson, 1981). The pellets are delivered from the pellet mill to the cooler feeding device which spreads the incoming pellet flow evenly over the cooling belt and also controls the speed of the cooling belt. Therefore, the retention time will be different for each pellet type, thereby avoiding overdrying (Atkinson, 1981b; Robinson, 1983). When pelleting high molasses, high fat, or urea pellets, a horizontal cooler should be used (MoBain, 1968). In these cases, the weight of the pellets in the vertical cooler can cause caking of the pellets prior to the discharge and can lead to screen clogging. 3.3.2.1 - Single Deck HorizontalCoolers In a single-deck horizontal cooler the cooling air passes only through one layer of pellets as in the vertical coolers. Figure 3.9 is a schematic of a single-deck horizontal cooler. A bed of pellets 5 cm (2 in.) to 30.5 cm (12_ in.) is evenly spread on a perforated belt (2) by the oscillating feeder .(1). A level sensing device is incorporated in the design to start and stop the belt, thus maintaining a constant thickness of the cooling bed 33 Fig 3.9 - Single deck horizontal cooler (Robinson, 1970). 1 - Oscillating feeder 2 - Product carrying belts 3 - Air chamber 4~- Air inlets 5 - Cooling belt drive 34 regardless of the production rate. Air flows through the pellets by means of a centrifugal fan, drawing air from the space below the cooling belt (4) to the plenum chamber (3). As in the vertical cooler, the cooling fan discharges the air into a cyclone for removal of the fines which are subsequently reprocessed. The typical dimensions of a single-belt horizontal cooler are: .9m (3 ft) to 2.4 m (8 ft) wide, 3 m (10 ft) to 16.8 m (55 ft) long with a pellet bed adjustable to 5 cm (2 in.) to 30.5 cm (12 in.). The capacity varies from 2 to 60 tons/h, depending on pellet size and type of feed (Robinson, 1983). The single-deck horizontal cooler requires about 1,000 CFM of air per ton/hour of pellets. Thus, a unit rated at 10 tons/h needs a fan and dust separation equipment capable of handling about 10,000 CFM. When less air is required, to pass through the pellet bed due to a lower output, a lower temperature drop and/or a lower moisture decrease, a bypass valve is opened to prevent all the air from flowing through the cooler. This construction allows some air to be passed to the dust collector to avoid the possibility of condensation (Atkinson, 1981b). 3.3.2.2 - Dual-Deck Horizontal Coolers The dual-deck horizontal cooler is usually constructed in a single enclosure with one air source. Figure 3.10 is an illustration of a dual-deck horizontal 35 cooler. The operation and components are the same as for the single-deck horizontal cooler, except that the dual-deck models have two carrying belts. A dual-deck cooler is more efficient than a vertical and a single-deck horizontal cooler because the cooling air passes twice through the pellets. It cools pellets with approximatelly half the air volume of the single-deck cooler (500 CFM per ton/hour); however, the static pressure will be slightly higher (Trickett, 1982). Absorption of moisture of the exhaust air is higher in the dual-belt cooler than in the single-belt cooler because of the higher absolute humidity of the exhaust air. 3.3.2.3 - Multi-Deck Horizontal Coolers A multi-deck horizontal cooler can be made in four, five or six deck versions (Trickett, 1982). It is the most efficient of the horizontal belt coolers in terms of cooling and drying. A four-deck horizontal cooler operates at one quarter of the air volume of a single-deck cooler, thus at 250 CFM per ton/hour of pellets. The average temperature of the exhaust air in a multi-deck cooler is much.higher than in a single-deck cooler, about 56 C (132 F); this greatly increases the moisture carrying capacity of the exhaust air. The multi-pass cooler is the only existing pellet-cooler design that can successfully cope with the full range of climatic conditions encountered at many pellet mill locations (Trickett,1982). 36 Fig. 3.10 - Dual-deck horizontal cooler (Robinson, 1971). - Feeding device Perforated carrying belts Plenum chamber Air inlets Belt drive motor mmbwmv—o I Discharge 37 3.3.3 - Cooler Comparison Robinson (1983) compared vertical and horizontal coolers: WW: Advantages - lower first cost; relatively maintenance free; require less floor space. Disavantages - require more headspace; capacities limited unless multiple units are provided; tend to choke, bridge and channel with pellets of certain types of feed; no control on retention time as cooler must be full to properly function; the column thickness is nonadjustable; the output is a function of the pelleting rate. WW: Advantages - basically unlimited in size; retention time is easily adjustable by varying bed-thickness; no bridging or channeling; require mimimum.headspace. Disavantages - high first cost; high maintenance cost. Space limitation in the feed mill is a major criterion in selecting a cooler. Low ceiling-height and adequate floor-space favor a horizontal cooler (MoBain, 1968). Atkinson (1981b) stated that the use of horizontal coolers in the feed mill industry is increasing. 38 3.3.4 - Counterflow Coolers A counterflow pellet cooler has been advertised by the Geelen Company (Geelen, the Netherlands) in the German journal die Muhle and Mischfuttertechnik (May,l986). The counterflow cooler is manufactured in three models in capacities of 2.75 to 33 tons/h at bed depths from 25 cm (10 in.) to 147 cm (58 in.). The air volume is about 244 cubic meter per minute/ton or 800 CFM/ton. The advantages of counterflow cooling according to the Geelen Company are:(1) the counterflow cooler saves up to 50% in energy compared to other cooler types, (2) requires less maintenance, (3) controls the cooling time more precisely, (4) requires less power, and (5) can be installed quickly into an existing pellet line. No research has been. reported on the topic'of- counterflow pellet cooling. 3.4 - Single Particle Drying Equations In thin-layer drying experiments the drying behavior~ of a thin-layer of moist material exposed to constant external conditions - air at constant temperature, humidity, and flow rate - is observed over a period of time. Sherwood (1936) observed that the drying process takes place in two or more distinct periods. First, in very 39 wet materials, there is a period during which evaporation occurs at a constant rate; this is followed by one or more periods in which evaporation continuously falls (Parry, 1985). A comprehensive analysis of the constant-rate period, the falling-rate period(s), and the theories proposed for the transport of moisture in biological materials, is presented in Brooker et al. (1974), Fortes and Okos (1980), and Parry (1985). The mathematical models proposed for describing the falling-rate drying period of biological materials, including pellets, may be divided into three categories: 1 - theoretical equations 2 - semi-theoretical equations 3 - empirical equations. 3.4.1 - Theoretical Equations Simplifying assumptions made for Luikov’s capillary-porous products drying model lead to the following equation in rectangular co-ordinates (Brooker et al., 1974 and Parry, 1985): SH 8 SH ---- = ---- (D ----) (3.1) St 8r 8r where D is the diffusion coefficient, and M is the moisture content. 40 If a constant diffusion coefficient is assumed, equation (3.1) may be written as: 8M 52M c H! ---—-- : D ( ---- + ------ ) (3-2) St 8r2 r 8r where: c is zero for a slab, unity for a cylinder, and two for a sphere. In order to solve equation (3.2), an appropriate geometric shape must be assumed for the representation of the individual product particles (e.g. rectangular, cylindrical, or spherical). Solutions to equation (3.2) for various solid shapes have been used as drying equations for solid biological materials to provide estimates of the average moisture ratio (MR) as a function of time (Crank, 1975). The MR is defined as: m=m.,-u.)/(uo-H.) (3.3) where: Mt: the average moisture content at time t = the average (initial) moisture content at time = 0 Me: equilibrium moisture content (EMC). The initial and boundary conditions usually assumed in solving equation (3.3) are of the form (Brooker et al., 1974): M(r,0) M(in) (3.4) a, (3.5) M(r°,t) In this study, pellets of cylindrical shape are used. Thus, with c = 1, equation (3.2) becomes: -_-- a n ( ..... + --— -—--) (3.6) For conditions (3.4) and (3.5) and assuming negligible end effects, the average moisture ratio of the pellets is given by (Crank, 1975): m 4 Uni MR = 2 --- OXP(' "“ D t) (3'7) 11:1 an? R1 where: an are the positive roots of the Bessel function of order zero, Jo(u§) = 0 D diffusion coefficient (m /h) R radius (m) t time (hour) Equation (3.7) is used in this study to predict the thin-layer drying curve for pellets; it allows calculation of the moisture content after time t as a function of diffusivity (D) and pellet diameter. A convective type boundary condition given by Brooker et al. (1974) can replace equation (3.5): 8M - D -;;- = hd (M8 - EMC) at r = R (3.8) where: D = diffusion coefficient (m2/h) convective mass transfer coefficient (kg/h m2 ) = moisture content at pellet surface (dec, DB) EMC = equilibrium moisture content (dec, DB). The temperature gradients inside a pellet can be calculated by solving the heat conduction equation for constant thermal diffusivity without heat sources. The unsteady-state differential equation is (Rohsenow and Choi, 42 1961): 56 826 1 86 ---- = a c ----- + ------- ) (3.9) St 82r r 8r where pellet temperature (C) thermal diffusivity = k/ *Cg thermal conductivity W C 9 a k d = pellet density (kg/m ) o: = pellet specific beat (J/kg o). Equation (3.9) is solved in this study assuming a boundary condition of the third kind which implies that the surfaces under consideration dissipate heat by convection according to Newton’s law of cooling, i.e. heat transfer is proportional to temperature difference. Thus, the boundary condition has the form (Ozisik, 1980): 89 - k ---- = h (68 - T) at r = R (3.10) 8r where: k thermal conductivity (W/h C) h = convective heat transfer coefficient (W/mi-C) 93 = pellet surface temperature (C) T = air temperature (C). The initial condition is given by: 9(r,0) = 9(in) (3.11) 3.4.2 - Semi-Theoretical Single Particle Equations The solution to the diffusion equation (3.2) in spherical coordinates, with conditions (3.4) and (3.5), is (Crank, 1975): 43 6 m 1 D n3 n: t MR = --- 2 ---- exp( - ---------- ) (3.12) "2 n=1 112 RI Instead of an infinite number of terms, only the first term of Eqn. 3.12 is often used, resulting in the expression (Brooker et al., 1974): 6 D n2 t 6 MR = --- exp(- -------- ) = --- exp(-kt) (3.13) n2 R n2 Alves (1985), Chhinnam (1984), Pabis and Henderson (1961), Sharaf-Eldeen (1979), Steffe and Singh (1980), and Young and Whitaker (1971) employed equation (3.13) in the study of drying grain and other agricultural products. A second semi-theoretical expression often used is Newton’s law of cooling; thus, for dehydration (Parry, 1985): 5M ---_ = - k (u — no) (3.14) St Integrating equation (3.14) and using equations (3.4) and (3.5), results in (Brooker et al., 1974): MR = exp( - kt) (3.15) Equations (3.13) and (3.15) are both called the drying equations; k, the drying constant, has units of hr‘l or sec'l. 44 3.4.3 - Empirical Equations Brook and Foster (1981), Brooker et al. (1974), and Parry (1985) compiled a number of empirical drying equations for biological products. Thompson (1967) proposed for shelled corn in the temperature range of 140 to 300 F the following equation: t = A*In(MR) + Bxlnuin)2 (3.16) where: A = - 1.86178 + 0.00448*6 B = 427.3640 x exp(-0.03301se) product temperature (F). Sabbah (1968) proposed for corn in the temperature range of 36 to 70 F: MR = exp(- k#(t-664)) (3.17) where: k = exp(- xtty) x and y are 9 and relative humidity dependent. Nellist and O’Callaghan (1971) determined a two-term exponential equation for the drying of ryegrass seeds: M = Me + A*exp(-k1t) + Btexp(-kat) (3.18) where A, B, K1, and K2 are product constants. Morey and Li (1984) investigated the effects of the thin-layer equation on deep bed drying prediction. The deep bed drying model developed by Bakker-Arkema et al. (1974) was used to evaluate the thin-layer equations proposed by Li and Morey (1984), Misra and Brooker (1980), Thompson (1967), and Sharaf-Eldeen et al. (1979). They concluded that the drying rate predicted with all these equations is slower 45 than the measured results, that the Li and Morey (1984) equation predict-faster drying than the other equations, and that the thin-layer equation significantly affects the results derived from deep bed models. Bruce (1985) obtained a set of thin-layer drying curves for barley at drying air temperatures from 50 to 150 C. Two empirical equations and a diffusion type equation with a time-varying boundary condition were fitted to the data. He concluded that: (1) the moisture loss data are described well by the diffusion model if the grain temperature rather than the air temperature is used to calculate the diffusivity; (2) the two empirical models do not describe the drying curves as well as the diffusion model; and (3) the diffusion model allows intra-kernel moisture movement calculation unlike the empirical models. Thin-layer models are required for calculation of the drying rate of the individual particles in the deep-bed cooling/drying models (the subject of section 3.7). 3.5 - Pellet Properties 3.5.1 - Equilibrium Moisture Content (EMC) The equilibrium moisture content (EMC) determines the moisture content to which a biological material is dried or wetted in a certain environment. Knowledge of the EMC is essential for simulating the cooling/drying of a bed of feed 46 pellets. Berry and Dickerson (1973), Boquet et al. (1978), Hall and Rodriguez-Arias (1958), Headley (1969), and Nellist (1976) have determined the EMC for feedstuffs. Empirical and semi-empirical equilibrium moisture equations have been proposed by Becker and Sallans (1956), Chung and Pfost (1967), Henderson (1952), Pfost et al. (1976), Rellist (1976), Smith (1947), and Thompson (1967). Parry (1985) reviewed the EMC models. Boquet et al. (1978) and Chirife and Iglesias (1978) compiled the origin, range of applicability, and use of 23 equations reported in the literature for fitting the water sorption isotherms of foods. Brook and Foster (1981) presented a tabulation of grain property values, EMC data, and EMC models available in the literature. Variations in the EMC reported for one grain at the same temperature and humidity are common (Brooker et al., 1974). The variations may be caused by the difference in the EMC determination methods or the chemical composition of the grain samples. Errors in moisture content measurement or difficulties encountered in maintaining and measuring temperature and humidity while the sample equilibrates may cause experimental errors in the EMC determination. EMC values for desorption are different from those for absorption due to chemical or physical changes which take place upon drying to a low moisture content (Bakker-Arkema et al., 1978). 47 Desorption values are generally higher than adsorption. The difference between adsorption and desorption isotherms is called hysteresis. Several theories have been proposed to explain hysteresis. Chung and Pfost (1967) suggested that hysteresis is due mainly to molecular shrinkage in the absorbent. Ngoddy and Bakker-Arkema (1970) and Labuza (1968) used the ”ink-bottle" theory to explain the hysteresis effect. Headley (1969) determined the EMC, using the static EMC method, of several pelleted feeds and feedstuffs. including cattle ration, high-urea cattle supplement, and high-urea cattle supplement coated with animal fat. All pellets were 3/18 in. in diameter. The temperature varied from 10 to 32 C (50 to 90 F) and the relative humidity ranged from 20 to 90%. Table 3.9 shows the results for the three pelleted rations. Table 3.9 - EMC (%DB) of Pelleted Rations Measured at Various Temperatures and Relative Humidities. Temperature L F) 19 50 Relative Humidity (%) ”“‘“‘!‘Q 58 75 82. 35 55 76 80 32 51 16 Feeds 11.2 17.8 20.9 21.8 10.0 15.9 17.9 21.5 8.1 15.7 17.0 12.0 19.5 21.2 22.2 10.4 15.7 16.3 21.4 9. 9 15.9 17.2 17 6 8. 8 14.3 14.2 1 2 3 10.1 13.9 14.8 16.4 8.7 13.6 14.9 * Cattle Ration High Urea Cattle Supplement High Urea Cattle Supplement (surface coated) From.Headley (1969) 1 2 3 48 Headley (1969) compared the results of the pelleted rations with EMC data for corn and milo available in the literature. Except for the data for high-urea cattle supplement (surface coated), the results indicate that the EMC of pelleted rations is higher than of corn and milo. Berry and Dickerson (1973) investigated the effects of particle size on EMC of laying mesh and laying mash pellets. They concluded that at relative humidities up to 70% the pellets equilibrate at about .5% higher in moisture content than the mash. According to Headley (1969), the reason why only limited EMC data for pellets is available, is due to the variation in the quantities of the different materials used in formulating livestock feeds. Though empirical or semi-empirical models of EMC for various agricultural and food products have been developed,, similar models for pelleted feeds are not known. In this study three models - the Nellist (1976), the Modified Henderson (1952), and the Chung and Pfost (1987) equations - are used to analyze the experimental pellet EMC data. The models were chosen because they have been widely used, are simple, have a limited number of parameters, and are temperature dependent. 49 3.5.1.1 - Mellist Equation Smith (1947) used the Langmuir and the BET equations to model the EMC data for high polymers: Me = Hb - a“Ilium-RH) (3.19) maximum bound moisture content (decimal, DB) relative humidity (decimal) equilibrium moisture content (decimal, DB) product constant. where: :3 Nellist (1976), investigating the EMC of ryegrass, proposed a modified version of the Smith EMC equation (3.19): Mo = a - b#1n(1-RH) - c*ln(6) (3.20) where: a,b,c are product constants 9 = product temperature (C). 3.5.1.2 f Modified Henderson Equation Henderson (1952) proposed a semi-empirical model to predict the EMC of biological products. Using Gibb’s adsorption equation the following equation was derived: 1 — RR = exp(-axeab,*(u,)b) (3.21) where: M, = equilibrium moisture content (% DB) 0 = absolute product temperature (K) a and b are product constants. Henderson's equation in its original form was found to be inadequate for cereal grains (Brooker et al., 1974). The modified form of the Henderson’s equation was proposed 50 by Thompson (1967): 1 - RR = exp(at(6+b)*(M°)°) (3.22) 2 product temperature (C) where: 0 a,b,c are product constants. 3.5.1.3 - Chung and Pfost Equation Chung and Pfost (1967) developed an EMC equation based on the potential theory: Me = a - b*1n(-(°+c)*1n(nfl)) (3.23) where: a,b,c are product constants 0 = product temperature (C) Me = equilibrium moisture content (decimal, DB). 3.5.2 - Diffusion Coefficient The diffusion coefficient is a measure of the moisture flow in a biological product. It is a function of the product temperature and moisture content (Crank, 1975). The units of the diffusion coefficient are usually given in terms of length2 per time (12/t). The relationship between the diffusion coefficient and the product temperature is usually of the Arrhenius type (Brooker et al., 1974): D = atexp(-b/Oab5) (3.24) where: o = diffusion coefficient (lengch/ti-e) eabs = product temperature (K) a and b are product constants. 51 Thus, as the product temperature increases, the diffusion coefficient increases. Diffusivity is measured by collecting drying data of a particular biological product with respect to time. It is frequently assumed that the diffusion coefficient of grain products is not affected by moisture content (Brooker et al., 1974). For feed pellets the same assumption is made in this study. 3.5.3 - Heat and Mass Transfer Coefficients The values of h and hd, the convective heat and mass transfer coefficients, are functions of the particle Reynold’s number. Baker (1965) conducted an extensive literature review of the available theoretical and empirical relationships for the heat and mass transfer coefficients. The following equations were considered by Bakker-Arkema et al. (1967) to be the most satisfactory and are used for pellets in this study: h = .992 Ga ca Re--34 (3-25) hd = 15.5 Ga Re-l Sc‘2/3 (1 - ()1-2 (3.26) where: h = convective heat transfer coefficient (BTU/h-ft2-F) hd = convective mass transfer coefficient (lb H20/ft2-h) Ga = air flow rate (lb/h-ftl) Ca = specific heat of the air (BTU/lb-F) ( = porosity of the deep bed Re = Reynolds number = Ga Di/P Sc = Schmidts number = P/D dp Di = particle diameter (ft) absolute viscosity (lb/ft-h). 52 3.5-4 - Thermal Conductivity and Specific Heat Fortes and Okos (1982) investigating the drying of extruded corn at 30-70 C (76-158 F) and 8 to 36% DB, developed the following equations for the thermal conductivity and specific heat of this product: For the thermal conductivity: k = .1133 - 2.936 u2 + 25.44 M3 - 36.71 34 (3.27) and for the specific heat: Cp = 4180 (.343 + M) / (1 + M) (3.28) where: E ii? thermal conductivity (W/m-K) specific heat (J/kg-K) moisture content (decimal, DB). It is assumed that the k and CD values for feed pellets are the same as for extruded corn. 3.5.5 - Latent Heat of Vaporization Spencer (1971), simulating drying of wheat in a deep-bed, developed the following equation for the latent heat of vaporization as a function of the grain temperature and moisture content: hf; = (1065 - .55(e - 520)) (1 + 23 exp(-4 e n)) (3.29) 53 where: hr: = latent heat of vaporization (BTU/lb) 9 = product temperature (R) M = moisture content (decimal, DB). It is assumed in this study that the hfg for feed pellets is the same as for wheat. 3.5.6 - Air and Water Vapor Properties The values of the density of air, and the specific heat of air, vapor, and water were obtained from thermodynamic tables (Threlkeld, 1962). 3.6 - Pellet Quality 3.6.1 - Nutritional Quality of Pellets The nutritional value of pellets is affected by different factors including the equipment utilized, the conditions employed during the pelleting process, the nutritional value of the ration, and the animal itself. Crampton (1956) observed that some animals have a tendency to select the coarse materials in a feed mixture from the fines. When small quantities of purified nutrients are added as supplement to a pelleted mixture, pellets should not disintegrate easily. Calet (1965) reviewed the pelleting of poultry feed end its relative value versus mash and grain, and concluded 54 that pellets reduce wastage, improve feed conversion, improve feed digestibility, and increase the retention of nutrients. Slinger (1972) and Pepper et al. (1960) studied the effects of pellet use in the diets of chickens and turkeys, and concluded that significantly less concentrate was consumed with pellets than with mash, although more weight was gained with the pellets. Jensen et al. (1962) investigated the pelleting of wheat bran and noted an increase in feed intake of chickens; this led to an increase in weight gain and a decrease in the feed/gain ratio. They pointed out that the improvement was probably due to an increase in the bulk density of the feed, resulting in less time and energy expended for eating. Kling et al. (1985) investigated the effect of pelleting the feed of chickens on egg production and size, and concluded that neither the egg-production nor egg-size was affected by the physical form of the feed. Olsen and Slinger (1968) and Saunders et al. (1969) found that most of the feed intake improvement in rats from steam pelleting wheat bran and shorts is due to the increased availability of the contents of the aleurone layer. Perry (1984) investigated the effect of pelleting a swine diet containing corn, soybeans, and barley. The pelleted diet produced a 14% faster and 15% more efficient gain than the same unpelleted diet. Ensminger (1985) stated that in diets containing a 55 low level of crude fiber, there is no advantage in pelleting feed for beef cattle and swine. However, with more fibrous feeds, especially barley, there is a decided advantage in pelleting feed for swine. Rinehart (1981) reviewed the effect of pelleting on feed value, and observed that the nutritional value of pelleting is due to the mechanical pressure and heat production of the process rather than to the form of the ration. He also noted that pelleting increases the feed intake of animals, and improves the feed conversion. Nutrient destruction and decreased nutrient availability were mentioned as potential disavantages. Slinger (1972) observed that during the formulation of least-cost rations the nutritional value of the pelleted feed and not the mash feed should be considered. In determining nutrient requirements, the pelleted feed should be used. Cassard and Juergenson (1963) listed the advantages and disavantages of the pelleting compared to the grinding of grains. The advantages are: larger, feed intake (especially with high roughage rations), increased gain, increased feed efficiency, no sorting of the ration by the animals, easier mechanical feeding, reduced labor requirement, reduced waste, easier handling, reduced storage space,, greater net energy availablity, and reduced dust production. Disavantages are: the cost of grinding and .pelleting, the reduced rumination in cattle sometimes .leading’ to digestive troubles, and the cost of handling 56 bulky ingredients to the mill for pelleting. 3.6.2 - Physical Quality of Pellets The physical quality of pellets from the producers' point of view concerns the hardness, the lack of fines, and the ability to withstand physical deterioration during handling and feeding operations (Slinger, 1972). The ingredient characteristics which affect the physical quality of the pellets include the fat-, fiber-, and protein-contents, and the texture of the mix (McBain, 1968). The fat content may refer to natural fat, which is already a feed ingredient, or to added fat; adding 1% fat to a feed mixture has a greater effect on pellet quality than the 1% fat already present in the mixture. Fiber is considered a natural binder; a high-fiber feed produces high quality pellets but results in a low production rate. Feeds with a high protein content have a relatively high bulk density because they plasticize as the mix passes through the die during pelleting. Bulk density is a major factor in pellet production. For example, a 100 HP mill pelleting 100% dehydrated alfalfa at 272 Kg/m3 (17 lb/cft), can pellet 4 to 5 tons/h; the same mill pelleting 100% solvent extracted cottonseed meal at 560 Kg/m3 (35 lb/cft) to 640 Kg/m3 (40 lb/cft) can pellet 16 to 17 tons/h. Also, pelleting materials with high density require less power for the pellet mill than pelleting of low density materials (McBain, 1968). 57 The texture (or granulation) includes three general categories: coarse, medium, and fine grinds. ASAE Standard=R248.1 (1984b) defines coarse as the remaining material, after screening, on the 3/8, 4, and 8-mesh screens; that on 14 and 28-mesh screens as medium, and that on 48 and 100-mesh screens and in the pan as fine. Medium and fine grinds generally result in a higher pellet-mill capacity and an improved feed compared to that made from a coarse grind. The reasons are a greater surface area for aborption of moisture from the steam, and a higher starting bulk density provided by the medium and fine grinds. Table 3.10 lists the common ingredients used in pelleted feeds (Falk, 1985). The chart can be used to rate the pelletability of single ingredients. Also, it is possible to determine the characteristics of a feed formula based on the percentage of the ingredients used. A composite rating provides an approximate capacity rating for a feed formula. The physical quality of a certain type of pellet will change when the content of the ingredients changes. The fat, fiber, and protein contents provide a key to the pellet quality. The column "abrasiveness" gives an indication of how an ingredient will affect die life. Pellet durability tests are important to determine the pellet quality and are used to designate pellet resistance to breakage. The equipment utilized to obtain the IPOllet durability is, described in ASAE Standard:8269.3 (1984b). Table 3.10 - Pelletability Chart (Falk, 1985). 58 Weigh: Percent Percent Percem Peiiei- Abresivenese Moisesee W per cu. 11. Protein F91 Fiber ability Degree fleeson mm were W 12-19 20 3 0 20 Mad High LGC 40% .8181 33 10 2 8 Med Med HGC 0881 Pulp 18-20 8 .8 20 Law Med WHP Blood Mad 3540 80 1 1 Mod Low Brewers Grain 18 24 8 18 Low Med W8! 9% Wit 31 32 8 0 Low High CHEM cm Pulp 20 5 2.5 15 Law Med we? Cocoon Med 20 8 11 Low High CHEM 33% Corn 40 8.4 3.8 2.8 Mod Low H00 18% Corn Cob 8 Mod 38 7 3 8 V Low V High HAY Corn Giuhn Food 28 21 1.8 8 Mad LOU W0? 7% Corn Gluten Med 30 82 4 4 Med Low W8? Corn 011 and :15 15.5 1 11.5 111911 Low HGC Cottonseed Md 901v 38-40 41 1.8 13 High Low H00 18% Cottonseed Mad Exp 38—40 38 4 18 Med Med H0O Distiiisrs Grain 18 28 8 12.8 Low Mod VI” 8% Distillers Sohlhiss 27 8 3 Med Med VllP Fish H 38 68 8 1.8 Mad Mad CHEM Horniny-Vsiiom 28 10 2.8 3.7 Low Low VIBP 22% thCun 1w45 11 25 25 ans Hun 13c Kuwnuecmm 10 2 7 low imp loo Lmeuduaucui 27 32 35 5 Huh new Mac 9% Linseed Mssi 90111 33 34 2.0 8 High Mod CHEM 7% Meet Scrap 41 88 9 2.8 High Low Milo Maize 40-48 11 2.8 2.8 High High 1.00 lflhHueCM» 1o 2 7 low Huh Lac Moisssss Oars-guano 30 13 3.8 12 Med Merl H06 20% 0d Halls 8 18.8 8 38.8 V Low Hifli NAT 0. Screening 8-12 3.8 1 34 V Low Hid! NAV Hmmnwauswv 40 50 5 7 Huh law we! Rice 8m 21 14 .8 18.8 Low High CHEM site mm 45—54 11 1o 4 Med 111911 CHEM Soyssssns Meal up. 40 42 3 8 8 High Low VIIP 10% W Mssi 80111 40 48 8 High Low W8! 8% Wheat-Grey Shorts 18 18 3.8 8.8 Med Low WIP Wheat-Hod Dog 28 1 8 3.8 3 Med Low W W Shorts 18 18 3.8 8 Mod Lew W wwnuaaa 26 15 35 5 Huh law was m 31 14 2 1 Mod Low wsr W 11-18 14 3.8 11 Low Low \VIP 18% Whey-Dried 38 12 .8 0 Low High CHEM lone Med 48 m 48 Ursa 40 Abbrev1ations: CHEM - Chemical reaction plast1c1ty LGC - Low grown crops HGC - High grown crops NAT - Naturally abra51ve WBP - Washed by-product 59 In a pellet durability test a 500 g (1.1 lb) sample/ of whole pellets is placed in tumbling box (30x30x7.5 cm). After tumbling for 10 minutes at 50 rpm, the sample is raoved, sieved, and the percentage of whole pellets is determined. The pellet durability is defined by: Mass of Pellets After Tumbling Durability = ------------------------------- (100) (3.30) Mass of Pellets Before Tumbling The percentage of fines is determined by screening the pellets on a wire sieve with openings slightly smaller than the nominal pellet diameter. Table 3.11 shows the recommended sieves for pellets of various diameters. Table 3.11 - Screens Sizes for Pellet Durability Tests. Diameter of Pellets Required Screen Size (mm) (in.) Size (mm) (in.) 2.4 0.094 No. 10 2.0 0.079 3.2 0.125 No. 7 2.8 0.111 4.8 0.188 No. 5 4.0 0.157 5.2 0.203 No. 4 4.8 0.187 6.4 0.250 No. 3.5 5.7 0.223 12.7 0.500 7/18 11.1 0.438 From ASAE Standard:8269.3 (1984b) Normally, pellets are tested imediately after cooling. If tested at a later time, the time will be indicated by a subscript. For example, if the pellet durability tested 95 four hours after cooling, then the 60 durability is expressed as (95)4. If pellets are tested before cooling, there will be a significant weight-loss caused by water vaporization; the durability will be decreased by the loss of moisture. The loss of moisture must be evaluated by determining the moisture content before and after tumbling, and compensating for the final mass accordingly. When this procedure is followed, the durability is expressed as (95)-1 (Falk, 1985). The pellet durability index of pellets stored under equilibrium relative humidities ranging from.22% to 92% and temperatures from 10 C (50 F) to 33.2 C (90 F) was investigated by (Headley, 1969). The relative humidity range from 55% to 75% resulted in better pellet durabilities than those obtained at higher or lower relative humidites. 3.7 - Deep Bed Models and Simulation Deep bed models are generally divided into three types: (1) logarithmic, (2) heat and mass balance (HMB), and (3) partial differential equation (PDE) models (Parry, 1985). The first two models are of an empirical or semi-empirical nature, and require little computer time. However, the product temperature and moisture profiles are predicted inaccurately (Bakker-Arkema, 1984; Sharp, 1982). Therefore, both logarithmic and heat mass balance models are 61 limited in their range of applicability (Parry,1985). The HMB model is used in this thesis because it is suitable for PC-size computers. 3.7.1 - Algebraic or Heat and Mass Balances (HMB) Model Thompson et al. (1968) first proposed a deep-bed drying model for grain based on heat and mass balances. The model first calculates an equilibrium drying temperature based on the sensible heat balance between air and grain; subsequently, the equilibrium moisture content and the drying rate of the grain are estimated using this temperature. The equations proposed by Thompson et al. (1968) are presented in this section. The drying air temperature is the equilibrium temperature of the drying air and the grain. It is calculated by performing a heat balance on each layer and has the form: (1.005+1.884 Ho) To + Op 00 Te = ----------------------------- (3.31) 1.005+1.884 Ho + Cp where: Te = equilibrium air temperature, K To = initial air temperature, K Ho = initial air humidity ratio, Kg/Kg Cp = specific heat of product, KJ/Eg E 00 = initial product temperature, K. 62 The final moisture content is calcualted by using a single-layer drying equation (Eqn. 3.7), and the equilibrium moisture content equation (Eqn. 3.22). The final air and grain temperatures are assumed to be equal and are determined by: (1.005+1.884H0)Te - DH(2467.4 +hfg+273.16-Te) + CpTe Tf: ----------------------------------------------------- 1.005 + 1.884 Hf + Cp (3.32) where: Tf = final product temperature, K To = equation (3.31) hf‘ = latent heat of vaporization, KJ/Kg Hf = final air humidity ratio, Kg/Kg and (Mo - Mk) Dm DH 2 Hf - Ho = --------------- (3.33) 100 Ga t where: . Mo = initial product moisture content, % DB Mf = final product moisture content, % DB Dm = product dry matter in each layer, Kg Ga = air mass flow rate, Kg/ min t = time step for simulation, min. Noomhorn and Verma (1986) used the Thompson et al. (1968) model to evaluate the influence of two generalized single-layer equations on the drying rate of a fixed-bed of rice. They concluded that both equations underpredicted the moisture content; the rice temperatures were higher than the observed values, and the largest difference was observed at the top layers. 63 3.7.2 - Partial Differential Equation (PDE) Models The development of stable computational techniques and the increasing power of modern computing have encouraged researchers to implement drying and cooling models of the PDE type. These models are formulated according to the standard laws of heat and mass transfer, and are of a more fundamental nature than the algebraic (HMB) models. In the development of the deep-bed drying model for stationary bed the following assumptions are made: (1) particle to particle conduction is negligible, (2) there are no temperature or mass gradients in the y- and z-directions,(3) the heat capacities of moist air and of grain are constant during short periods of time, (4) the airflow is plug type, (5) 6T/St and SH/St are negligible compared ‘to 5T/5x and SH/Sx, and (6) accurate thin-layer drying and moisture equilibrium equations are known (Bakker-Arkema et al., 1967; Brooker et al., 1974; Sharp, 1982). The PDE models of the drying, cooling, and heating of a deep-bed of biological products such as feed pellets consist of four to six differential equations, depending on the assumptions made in the analysis. For a stationary bed of pellets in which the airflow is of the plugflow type the following simulation has been proposed (Brooker et al., 1974): 64 68 5M -_-- = - -92- -_-_ (3.34)‘ 5x Ga 8t 6T - h SA __-- z ............... (T - e) (3.35) 8x Ga(Ca + CV 3) 59 h SA (T - a) hfs + cv(T - 6) 53 ---- = --------------------------------- c,--—- 5t dp(Cp + C" H) (Cp + C" H) 5! (3.36) SM ---- = single pellet drying equation (3-37) 5t For a bed of depth L, the appropriate initial and boundary conditions are, respectively: M(r,0) M1(x), 9(x,0) 61(x) 0 < x < L (3.38) H(0,t) H1(t), T(0,t) T1(t) t > o (3.39) Equations (3.36) and (3.37) compute the average product temperature and moisture content values, respectively. In the solution of the model (Eqns. 3.34 - 3.39) the deep-bed is divided into layers. Each layer is assumed to be of uniform moisture content and temperature; the inlet conditions for a layer are the outlet conditions of the previous layer. Numerical techniques are applied to solve 65 the set of differential equations for each layer. Carnahan et al. (1969) .and Ozisik (1980) describe the numerical methods for solving such systems of differential equations. Bakker-Arkema (1984) and Brooker et al. (1974) presented the PDE models for the basic grain cooler/dryer configurations of the fixed bed, crossflow, concurrent flow, and counterflow. Parry (1985) and Sharp (1982) reviewed the deep bed models which have been employed in the simulation of heat and mass transfer in biological products. Bakker-Arkema et al. (1984) used a counterflow model to analyze the cooling of grain; the simulation model accurately described the counterflow cooling process. The airflow rate and cooling air temperature significantly affected the exit grain temperature but not the exit grain moisture content; the relative humidity of the cooling air neither affected the exit grain temperature nor the exit grain moisture content. 3.7.3 - Psychrometrics The topic of psychrometrics is important to the understanding drying and cooling of bilogical products. Professional organizations, such as ASAE (1984a) and ASHRAE (1977), have published psychrometric charts, tables, and . equations. A Since charts and tables are not suitable for the applications of computer-aided design and simulation, a 66 standard computer model of the psychrometric chart is needed. Brooker (1967) and WilheLm (1976) have compiled thermodynamic and empirical equations which describe the psychrometric chart. The equations have been programmed as a computer subroutine for use in grain drying simulation programs (Brooker et al., 1974). Bakker-Arkema et al. (1974) published a package of psychrometric subprograms in SI units. Chau (1980) proposed new empirical psychrometrics equations for the saturation temperature given the saturation vapor pressure and the wet-bulb temperature, or the dew-point temperature and dry-bulb temperature. 3.9 - Statistics The statistical package Bio-Medical Data Processing (BMDP) program BMDPAR (Dixon, 1981) estimates the parameters of a nonlinear function by a least squares technique using a pseudo Gauss-Newton algorithm. The program is suitable for functions not linear in the parameters; it does not use the derivative of the function. The information provided by BMDPAR. includes the total number of data points, the number of data points in the, analysis, the standard deviation, the mean, the minimum and maximum of each variable, and the residual sum squares for each iteration. The program calculates a linear function equal to the given function, using an improved set of 67 parameters. This process is repeated until convergence, or the specified number of iterarions, is reached. The following results are printed out: the best set of parameters encountered, the estimated mean square error, the estimated asymptotic correlation matrix, the estimated standard deviation for each parameter, and the estimated and observed value at each data point. If required, the program draws simple graphs of the predicted values and the residuals. When the predicted values, obtained by a prediction equation using the estimates of the parameters, are compared with the observed values, and result in the smallest residual sum of squares, the estimate of the parameters is said to be the best set of parameters. The criterion used to evaluate goodness of fit is the average of the relative percent difference between the experimental and predicted values. For instance, for the. case of the EMC data points, the mean relative deviation modulus (P) is defined by the following equation (Lomauro et al., 1985): 100 n iEMCi - EMCPil P = ----- E ---------------- (3.40) n i=1 DICi Where EMC 2 equilibrium moisture content at observation EMC 1: predicted equilibrium moisture content at observation n = number of observations. The value of P is minimized when the error sum of squares is minimized in the selection of the equation parameters. The P value is an indication of the goodness of fit. A P value of less than or equal to 5 is considered to be a good fit (Lomauro et al., 1985). 3.10 - Summary The review of literature has emphasized the cooling process of feed pellets. The following are the principal findings relevant to the current study: - The pellets should leave the cooler within 5 C (10 F) of the ambient temperature and should be stable at that temperature. - The pellets should be at a moisture level such that at average ambient temperature and humidity they remain at a constant weight. - The pellet moisture content should be suficiently low to avoid mold growth. - The retention time in a pellet cooler is a function of pellet size, initial temperature and moisture content; the amount of heat to be removed is a function of formulation, steam addition and die friction; and, the ability of the air to cool and dry is a function of the flow rate, temperature and relative humidity. - Space limitation is one of main points to be considered when selecting a pellet cooler; horizontal 69 coolers are high in initial cost but need limited vertical space; also, they are flexible since the retention time is easily adjustable. - No simulation models are available in the literature for the cooling of feed-pellets. - The equilibrium, moisture content and the single pellet drying/cooling equations are required for the solution of the simulation models for pellet coolers. 4 — MODEL DEVELOPMENT The following sections present the development of two pellet cooling simulation models. 4.1 - Model 81 - Heat and Mass Balance (HMB) Model The development of this model is based on the approach followed by Thompson et al. (1968). The deep-bed of pellets is assumed to consist of a series of thin-layers positioned normal to the direction of the air flow. No heat transfer is assumed to occur through the cooler walls. The cooling air passes through a thin-layer of pellets in a specific cooling-time interval. The average pellet temperature is assumed to be equal to the temperature of the air surrounding the pellet. The thin-layer cooling/drying equation and the moisture equilibrium equation are known. The relationships used in the development of this model are: (1) equation (3.31) for the equilibrium air temperature, (2) equation (3.7) for the drying rate, (3) equation (4.1) for the absolute humidity ratio, and (4) equation (3.32) for the pellet temperature. The flow diagram of the heat and mass balance stationary bed pellet cooling model is shown in Figure 4.1. 70 71 Input data read data l Set initial conditions H(X.0) = Mi 6(mm = Oi T(x,0) = 0i H(x,0) 2 Hi RH(X.O) = fo('l'(1.0). H(x,0) l Time loop ' I For t = Dt to total time Position (depth) loop I For x = 0 to bed l EMC 2 fc(0(x,t), RH(x,t)) DC = fc(9(x,t)) M(x,t) = Eqn. (3.7) H(x,t) = Eqn. (4.1) Te = Eqn. (3.31) 0(x,t) = Eqn. (3.32) M(x,t) = fc('l‘(1.t). H(X.t)) 1 IF time for __X_._ Print: 0,Mc,EMC, print out 7 RH,H N L¢+4 {gNext x Lfi—i {NeIL t] L Enfl 4.1 - Flow diagram of the HMB stationary-bed pellet cooling model. 72 4.2 - Model 82 - Partial Differential Equations (PDE) Model The equations used in PDE stationary-bed pellet cooling model to simulate the cooling of a fixed bed of pellets are: equations (3.34) through (3.37) with initial and boundary conditions (3.38) and (3.39). To determine the moisture content and temperature gradients inside the pellets, equations (3.6) and (3.9) with initial conditions (3.4) and (3.11) and boundary conditions (3.10) and (3.11), respectively, are employed. Since the set of equations can not be solved analytically due to non-linearity, numerical techniques are used to obtain the solution of the set of equations. In order to compute the air temperature (T), absolute humdity (H), pellet temperature (9), and average pellet moisture content (M) at each Dx location at time t+Dt within the cooler, the equations (3.34) to (3.37) are written in finite-difference form using forward-difference formulae. Thus, dp Dx Hx+1,t “ 3x,t = - ------- (Hg,t+1 - H&,t) (4.1) Ga Dt - h SA Dx Ti+l,t * Tx,t = --------------- (Tx,t - 9x,t) (4.2) Ga(Ca + Cv H) 73 h SA (Tx,t‘ex,t) hfg+CV(Tx,t‘ex,t) 9x,t+1 ‘ ex,t = ““““““““““““““““““““““ dp(Cs + Cw fix,t) dp(Cp + CH fix,t) Ga "“ (31+1,t ‘ Hx,t) (4'3) Dx Mi,t+1 2 Equation (3.7) (4.4) To determine the internal moisture content and temperature gradients at each Dx location within the cooler, the pellet is divided into n concentric shells. The moisture content and temperature are calculated at n+1 points from the center (r = 0) to the surface (r = R). Given the pellet moisture content and temperature at time t and the equilibrium moisture content and air temperature at t+Dt, the model subsequently computes the values of moisture content and temperature at each internal node at time t+Dt. Numerical techniques are also used to solve equations (3.6) and (3.9). Since the equations are similar in form, only the finite-difference form of equation (3.6) is discussed. Applying the forward-difference formula to the left-hand side term, and the central-difference formula to both terms on the right-hand side of equation (3.6), gives: 74 H1-1,g_:_231.i i H1+1,g + 1 H1+1.) - Hi-1,J (Dr)2 r 2 Dr _E. _§112:1-:.!1;2_ (, 5, Setting r = N Dr and a = D Dt/(Dr)2, and solving equation (4.5) for Hi,j+lv gives: 1 l Hi,J+1 = a(1 - ----)M1-1,j + (l-2a)M1’J + a(1+--*-)M1+1’J 2N 2N (4.6) Setting b = 1 - 1/2N and c = 1 + 1/2N, Eqn. 4.6 becomes: M1.J+1 = ab M1_1’j + (1-2a) M1,: + ac M1+1.j (4.7) Equation (3.6) is not valid at the center of the pellet because r equals zero. This implies that the (1/r)(6M/5r) term cannot be determined. However, by l’Hopital’s rule (Thomas,1969), at r = 0 the center of a pellet: 1 an 523 lim ( --- ----) = ----- r70 r 5r Era The moisture-diffusion equation at the location r=0 takes the form: 2 -—--- : ------- (4-8) At i = 0, equation (4.7) becomes: Hon-1+1 = ab H.1’j + (1’28) "0.3 + ac ”1,3 (4.9) 75 Equation~ (4.9) has a fictitious moisture content M-1’J which can be eliminated by using equation (4.8). Applying the central-difference formula at the left-hand side and the forward-difference formula at the right-hand side, and solving for M_1,J at i = 0, results in: 1 1 - 4a "-1.1 = ‘g;‘ “6.1+: ' “';;“‘ "0.1 - "1.3 <4-10) where a = D Dt/(Dr)2. Substituting equation (4.10) into (4.9) and solving for M0,J+1, the moisture content at the center of the pellet becomes: 1 + 2N - 4a 4a -------------- Ho,j + -------- M1,) (4-11) 1 + ZR 1 + 2“ uo,.1+1 where N = R / Dr. At r = R.(i=N), the surface of the pellet, equation (4.7) becomes: Mfi'3+1 = ab Mh_1,3 + (1-2a) MN,j + ac MN+1,3 (4.12) Equation (4.12) has a fictitious moisture content HN+1,j- which can be eliminated by using the convective boundary condition at r = R: 5M D —--- +hdfls :thHc (3-8) 8r 76 The central-difference formula gives: Hum ‘ M1-1.1 D ----------------- + hd "1,3 = hd EMC (4-13) 2 Dr At i = N and solving for MN+1,j‘ 2 hd Dr 2 hd Dr 59+1.: = Hn-1.1 - ----5---- 56.1 + ----- 5—-- EMC <4-14> Substituting Equation (4.14) into (4.12) and rearranging, results in: 2ac hd Dr 2ac hd Dr HN,J+1 = 28 ”N-l,j + (l-Za- ----B ----- ) HN,j + ----5 ----- EMC (4.15) Let d = (2ac hd Dr) / D. Thus, “N,J+1 = 28 HN-l,j + (1-2a- d) HN,j + d EMC (4.16) The final finite-difference equations for calculation of the moisture content inside a pellet are: At r = 0 (i=0), the center of the pellet: 1 + 2N - 4a 4a Ham = ------------- so.) + -------- 111,, (4.11) For r = Dr to r = R - Dr (i = 1 to N - 1): Hi,.1+1 = 81> 141-1,.) + (l-Za) 151,3 + no 111““, (4.7) 77 At r = R (i = N), the surface of the pellet: bu,3,1 = 2a uh_1,3 + (1-2a-d) up,3 + d EMC (4.16) where: a = D Dt / (or)2 b = 1 - 1/29, c = 1 + 1/29, d = (2ac hd Dr)/ D D = diffusion coefficient, uZ/h hd = mass transfer coefficient, m/h. The initial condition is: M(r,o) = MJ 0 IA '1 IA w (4.17) Following the same procedure as for moisture content, the finite-difference temperature equations inside a pellet can be written. At r = 0 (i=0), the center of the pellet: 9°,J+1 = ------------ 90,5 + -------- 91,3 (4-13) For r = Dr to r = R - Dr (1 = 1 to N - 1): 61’J+1 ab 91-1,) + (l-Za) 91.3 + no 91+1,J (4-19) At r = R (i = N), the surface of the pellet: 93,J+1 - 2a 93-1.3 + (1-2a-d) 9N,j + d Tair (4.20) The initial condition is: e(i.o) = 91 p o s R (4.21) IA ’1 ‘where: a = a Dt / (Dr)2 and a = x / dp cp 78 b = 1 - 1/2N, c = 1 + 1/2N, d = (2ac h Dr)/ K h = heat transfer coefficient, W/mz-K a = thermal diffusivity, W/mz-J E = thermal conductivity, W/m-K dp = pellet density, kg/m3 Cp = specific heat, J/kg-K. At all time steps and locations within the fixed bed the average moisture content and temperature inside the pellets are computed by the following formula: 8 A0. .1 + ;:fi‘r..i A... = ----------------- (4.22) where: Aave = average moisture content or temperature ’3 = moisture content or temperature at each node within the pellet N number of nodes. In the above calculations, once the a (thermal diffusivity), D (diffusion coefficient), and Dr are fixed,’ the size of the time step is limited by the following stability criterion (Ozisik, 1980): D Dt/(Dr)2 - (4.23) o A u H A 01 A 0‘ u nt/(nr)2 - (4.24) O A u ii The three differential equations (4.1),(4.2),(4.3), and the thin-layer drying equation (3.7), along with the moisture content gradient equations (4.7), (4.11), (4.16), (4.17), (4.22), (4.23) and the temperature gradient equations (4.18) to (4.22), and (4.24) constitute the PDE 79 simulation model for the horizontal-belt pellet cooler. The flow diagram. of PDE pellet cooling model is presented in Figure 4.2. 4.3 - Pellet Properties The pellet properties necessary in the the pellet cooling models are given by; Equilibrium moisture content (EMC) Eqns. 3.20,22,23 Diffusion coefficient (D) Eqn. 3.24 Heat transfer coefficient (h) Eqn. 3.25 Mass transfer coefficient (hd) Eqn. 3.26 Thermal conductivity (K) Eqn. 3.27 Specific heat (Cp) Eqn. 3.28 Latent heat of vaporization (hfg) Eqn. 3.29 Pellet bulk density (at 90:20.5 %DB) 673 kg/m3 Surface area (SA) = 2/R where: R = pellet radius. The fixed-bed cooling simulation model programs are written in IBM BASICA which runs on IBM PCs and other IBM compatible microcomputers. The programs are compiled with a MICROSOFT BASIC compiler. Each cooling test simulation is performed with a bed depth of 30.48 cm (1 ft). The HMB and PDE computer programs are presented in Appendices C and D each with a sample run. 80 start ‘_f—‘ Input data read data 1 Set initial conditions M(x,0) = Mi 0(x,0) = Oi H(x,0) = Hi = fc(Ti,RHi) T(x,0) = 16(°(1.0).H(X.0)) = Eqn. (4.1) RH(x,0) = fc(T(x,0), H(x,0) l _a.. Time loop For t = Dt to total time 1 Position (depth) loop I For x = 0 to bed i EMC = fc(0(x,t), RH(x,t)) DC = fc(0(x,t)) M(x,t) = Eqn. (3.7) M(r,J) = Eqns. 4.7,11,16,17,22 H(x,t) Eqn. (4.1) 0(x,t) Eqn. (4.3) 0(r,j) = Eqns. 4.18 to 4.22 T(X.t) = Eqn. (4.2) RB(‘rt) = fC(T(X,t), H(xrt)) l + IF tile for Y I Print: T,9c,9s,9,Mc,M8, print out M.EHC.RH:H N “*7 Next x “‘y' Next t End IFig. 4.2 - Flow diagram of the PDE stationary-bed pellet cooling model. 81 4.4 - Psychrometric Chart Model The psychrometric model developed in this study for use on the IBM-AT is written in BASICA. It is based on a combination of theoretical and empirical equations presented by Brooker et al. (1974), Chen (1980), and Wilhelm (1976). The model accepts as input, in English or SI units, the following combination of dry air-water vapor mixture properties: (1) dry-bulb temperature and relative humidity, (2) dry-bulb temperature and absolute humdity, (3) dry-bulb temperature and wet-bulb temperature, (4) dry-bulb temperature and dew-point temperature, (5) wet-bulb temperature and relative humidity, (6) dew-point temperature and relative humdity, and (7) dew-point temperature and enthalpy. The psychrometric model was developed for use as a subroutine in the drying and cooling simulation models of biological materials. The PSYCHART program is presented in the Appendix B. 5 - EXPERIMENTAL PROCEDURES The research reported in this study was carried out at the processing laboratory in the Agricultural Engineering Department at Michigan State University. 5.1 - Pellets The pellets used in this study were obtained from Purina Mills, Lansing, Michigan. The pellet type was Milk Generator 8 1000 (B) 16%, with a diameter of 4.76 mm (3/16 in.). The following ingredients are contained according to the company in the pellets: grain products, processed grain by-products, plant protein products, molasses products, vitamins, and minerals. Purina was unwilling to supply the exact composition of the pellets. The analysis of the pellets indicates that the pellets have at least 16% of protein, 2% of crude fat, and no more than 7.5% of crude fiber. The moisture content of the warm pellets ranged from (18.1 % to 20.7% DB., the temperature after rhe pellet-mill from 60 C (140 F) to 80 C (176 F). 82 83 5.2 - Equipment Figure 5.1 is the schematic of the equipment used in the deep-bed cooling and drying tests. The cooling and drying chamber is constructed of sheet metal. It measures 50.8 cm (20 in.) hight and 20.32 cm (8 in.) in diameter, and has a volume of .02 m3 (.6 ft3); it is insulated with 2.5 cm (1 in.) of fiber-glass to minimize the effect of temperature fluctuation in the surroundings. At 10.16 cm (4 in.) from the bottom, the chamber is fitted with a wire mesh to hold the bed of pellets. The bed-depth of the cooler is 30.48 cm (12 in.). A series of 4 mm diameter holes were drilled in the cooler wall for the thermocouples probes; an additional set of holes of 2.5 cm (1 in.) diameter enable withdrawal of small samples for moisture determination. The .22 cubic meter (eight cubic foot) plenum chamber is constructed of plywood. An Aminco-Aire* air conditioning unit, model 4-5460, was used to deliver air to the drying and cooling chamber. The unit is able to condition a maximum of 8.5 cubic meters per minute (300 CFM); it is designed to condition chambers of less than 1.1 cubic meters (40 cubic feet). About 2.8 cubic meter (100 CFM) of air were required 4 Trade names are used solely to provide specific information. Mention of a trade name does not constitute an endorsement by the Agricultural Engineering Department of the Michigan State University of the product nor to the exclusion of other products not mentioned. 84 air {—— x0 + 0 0 Air + o Conditioning 0 Cooler Unit + o o +--—-{»-—-s Mesh Bottom . air--—9 x Damper Airflow Control 0 Dry-bulb temperature probe x Net-bulb temperature probe + Moisture content probe Fig. 5.1 - Fixed-bed cooling experimentation. 85 in the experiments. The air is conditioned by the Aminco-Aire in two stages. In the first stage, in which the air is washed by a spray of water droplets, the required dew-point temperature is obtained. In the second stage, the air is heated or cooled to the desired dry-bulb temperature. The solid state controls on the Aminco-Aire unit maintain the dry-bulb temperature and relative humidity of the air to within 1 .5 C and t 1%, respectively. The Aminco-Aire unit is connected with a 10.16 cm (4 in.) diameter flexible plastic hose to the plenum chamber of the dryer or cooler. The top of the cooler is connected with a similar plastic hose to the inlet port of the air-conditioning unit. The hoses are insulated with 1.2 cm (.5 in.) of fiber-glass. 5.3 - Single-Layer Tests The single-layer drying tests were conducted using the Aminco-Aire unit at an airflow of .5 m/s (100 CFM) (Bruce, 1985). The experimental single-layer drying conditions are summarized in Table 5.1. When the Aminco-Aire conditions had reached the desired air temperature and relative humidity, a single-layer of pellets of approximately 200 g was placed on a wire-mesh tray in the drying chamber. The moisture content was determined before and after each specified drying time.. The values of the moisture content (as a function of drying time, temperature, and relative humidity) formed the input to the BMDPAR program of the statistical package HMDP (Dixon, 1981). BMDPAR performed the non-linear regression analysis for the estimation of the equilibrium moisture content and diffusion coefficient of the feed pellets. Table 5.1 - Experimental Single-Layer Drying Conditions for 4.76 mm Diameter Pellets. Test Drying R.H. Air Drying Initial 8 Air Temp. Flow Time Mois.Cont. (C) (5) (III!) (Him) (%DB) 1 15.6 55 .5 1,2,5,10,60 19.1 2 15.6 70 .5 1,2,5,10,60 18.7 3 21.1 40 .5 1,2,5,10,60 18.6 4 21.1 55 .5 1,2,5,10,60 18.1 5 21.1 70 .5 1,2,5,10,60 18.5 6 26.7 40 .5 1,2,5,10,60 18.6 7 26.7 55 .5 1,2,5,10,60 18.2 8 26.7 70 .5 1,2,5,10,60 18.6 9 32.2 40 .5 1,2,5,10,60 18.6 10 32.2 55 .5 1,2,5,10,60 18.5 11 32.2 70 .5 1,2,5,10,60 18.7 12 37.8 40 .5 1,2,5,10,60 18.6 13 37.8 55 .5 1,2,5,10,60 19.1 14 37.8 70 .5 1,2,5,10,60 18.6 15 43.3 40 .5 1,10,60 18.6 16 43.3 55 .5 1,2,5,10,60 19.1 17 43.3 70 .5 10,60 18.6 87 5.4 - Fixed-Bed Tests The parameters required for the evaluation of the fixed-bed pellet cooling process are: (1) the pellet inlet moisture content (2) the pellet inlet temperature, (3) the pellet diameter, (4) the pellet density, (5) the cooling air temperature and relative humidity, (6) the air flow, (7) the cooling time, and (8) the bed depth. The warm pellets were transported from the commercial pellet mill to the MSU laboratory in an insulated box. About 25 Kg (55 lb.) were used to conduct each test. The hot pellets were poured into the cooler by free-fall from about 30 cm (1 ft) hight. Thus, the condition of the pellets is similar to that encountered in commercial horizontal belt coolers. Therefore, the fixed-bed of pellets represents a working section of a cooler with an elapsed time corresponding to the passage time over the length of the cooler belt. Air velocities of .1 and .5 m/s were tested. the values represent the lower and upper limit of the commercial pellet coolers. It was assumed that the moisture content and temperature of the pellets were initially uniform throughout the cooler. The test condition desired in the cooling chamber was maintained for at least one hour before the start of a test. The dry-bulb and wet-bulb temperatures were 88 continuously monitored; they varied by less than i .5 C. Table 5.2 is a summary of the experimental cooling test conditions during the fixed-bed cooling tests. Only the tests for which a complete set of data was collected are used in the evaluation. Table 5.2 - Experimental Cooling Test Conditions of a 30.48 cm Fixed-Bed of Pellets of 4.76 mm diameter. Test Cooling R.H. Air Cooling Initial Initial 8 Air Temp. Flow Time Mois.Cont. Pel.Temp. (C) (%) (I/B) (14111.) (%DB) (0) 1 21.1 55 .5 10,15,20 20.7 71.6 2 21.1 55 .1 15 20.7 65.6 3 26.7 55 .5 10,15,20 20.5 62.8 4 26.7 55 .1 15 20.5 58.5 5 32.2 55 .5 10,15,20 19.1 72.7 6 32.2 55 .1 15,20 19.1 67.2 7 17.7 70 .5 10,15,20 19.6 69.4 8 17.7 70 .1 15,20 19.6 61.7 9 21.1 70 .5 10,15,20 19.8 71.1 10 21.1 70 .1 15,20 19.8 63.3 11 26.7 70 .5 10,15,20 20.5 65.6 12 26.7 70 .1 15 20.5 60.0 13 21.1 55 .1 10,15,20 18.1 69.3 14 21.1 55 .5 15 18.1 63.4 5.5 - Instrumentation The following parameters required measurement for the performance evaluation of a pellet cooler: (1) air velocity, (2) air temperature, (3) relative humidity, (4) pellet temperature, (5) initial and final moisture contents, and (6) pellet densities. The air flow across the pellets was controlled by a manually adjustable damper located in the duct to the plenum chamber. It was measured by a Weathertronics hot-wire anemometer model 2440, with an accuracy of 2.05 m/s. Temperature: The temperatures (dry- and wet-bulb) were measured with copper constantan Ithermocouples and recorded every minute with a Ramp/Processor (Kaye Instruments) data logger. A total of 11 thermocouples monitored the temperatures of the inlet air (dry- and wet-bulb),the exhaust air (dry and wet-bulb), and at seven selected points between the pellets within the cooler. The accuracy of the temperature measurement is 2.5 C. The relative humidity was controlled automatically by the air conditioning unit and measured by dry- and wet-bulb copper constantan thermocouples located at the inlet of the cooler. The accuracy of the relative humidity measurements is i 1%. 90 mm The initial moisture content was obtained by sampling the warm pellets. After the cooling was completed four samples were collected at the locations indicated in Figure 5.1. The moisture content of the pellets was determined by drying triplicate samples for 24 hours in an air oven at 103 C according to ASAE Standards (1984b). The samples were cooled in a desiccator before reweighing. The accuracy of the moisture content measurement is 3.2%. Ballet 22.4115 ties}. The pellet bulk density was obtained by weighing a container of known volume filled with pellets. A scale with an accuracy of $.03 Kg was used to weigh the container. The individual pellet density was determined by the ratio weight/volume of a single pellets. A PAV digital caliper with an accuracy of t.001 mm was used to measure the pellet lenght and diameter. The pellet weight was measured with a analytical scale with an accuracy of 3.001 g. 6 - RESULTS AND DISCUSSION In this chapter the experimental results of the thin-layer drying and of the fixed-bed cooling tests are presented. Also, the experimental and simulated results of the deep-bed cooling tests are compared. Subsequently, the simulation models are used to predict the pellet temperature and the pellet cooling rate under different conditions. 6.1 - Thin-Layer Drying Tests The drying experimental data of 18% to 19% DB moisture content milk pellets obtained during thin-layer drying at constant temperature and relative humidity are shown in Table 6.1a and Table 6.1b. The air velocity during the experiments was .5 m/s. The drying air temperature ranged from 15.8 to 43.3 C (60 to 110 F), the relative humidity between 40 and 70%. 91 92 Table 6.1a - Experimental and Predicted Pellet Moisture Content (%DB) as a Function of Temperature, Relative Humidity and Time. Experimental Data Obtained in Thin-Layer Pellet Drying Tests. Temperature (C) Time 15.6 21.1 26.7 (min) Obs . Pred. 1‘ Obs . Pred. Obs. Pred . Relative Humidity = 40% 0.0 - 18.6 18.6 18.6 18.6 18.6 1.0 17.9 18.0 17.8 18.0 17.7 2.0 - 17.6 17.8 17.5 17.7 17.3 5.0 - 17.1 17.2 16.8 17.2 16.6 10.0 - 16.6 16.5 16.2 16. 3 15.9 60.0 - 14.6 13.5 13.9 12. 8 13.3 180.0 - 13.9 - 13.2 - 12.6 Relative Humidity 2 55% 0.0 19.2 19.2 18.1 18.1 18.2 18.2 1 0 18.7 18.7 17.9 17.6 17.5 17.6 2.0 18. 5 18.5 17.6 17.5 17.5 17.4 5.0 18. 3 18.1 17.4 17.1 17.1 16.9 10.0 17. 7 17.7 17.2 16.7 16. 6 16.5 60.0 16.5 16.2 15.8 15.4 14. 9 14.8 180.0 - 15.7 - 15.0 14.4 Relative Humidity 2 70% 0.0 18.7 18.7 18. 5 18. 5 18.6 18.6 1.0 18.4 18.6 18. 4 18.3 18.2 18.3 2.0 18.4 18.5 18.4 18.2 18.0 18.2 5.0 18.2 18.5 18.3 18.1 17.9 17.9 10.0 17.9 18.4 18.1 17.9 17.7 17.7 60.0 16.9 18.0 16.6 17.3 16.4 16.8 180.0 - 17.9 - 17.2 - 16.5 Milk pellet 16% protein; diameter 4.76 mm. (3/16 in.) Assumed that equilibrium has been reached after 60 minutes. Airflow rate = .5 Pellet density Pellet bulk density (at MC = m/s 945 Kg/m3 20.5 %DB) * Predicted values obtained using Eqns. and (6.6). = 673 Kg/m3 (6.1). (6.2). (8.5) 93 Table 6.1b - Experimental and Predicted Pellet Moisture Content (EDD) as a Function of Temperature, Relative Humidity and Time. Experimental Data Obtained in Thin-Layer Pellet Drying Tests. Temperature (C) Time 32.2 37.8 43.3 (min) Obs. Pred.‘ Obs. Pred. Obs. Pred. Relative Humidity = 40% 0.0 18.6 18.6 18.6 18.6 18 6 18.6 1.0 18.2 17.6 18.2 17.5 17.8 17.4 2.0 17.7 17.2 17.7 17.1 - 16.9 5.0 16.8 16.4 16.7 16.2 - 16.1 10.0 15.7 15.6 15.6 15.4 14.7 15.1 60.0 11.7 12.8 11.4 12.3 10.3 11.9 180.0 - 12.0 - 11.5 - 11.1 Relative Humidity = 55% 0.0 18.5 18.5 19.1 19.1 19.1 19.1 1.0 17.8 17.7 18.7 18.2 18.4 18.1 2.0 17.5 17.5 18.4 17.8 18.2 17.7 5.0 17.5 16.9 17.6 17.2 17.3 17.0 10.0 16.6 16.4 16.7 16.5 16.2 16.2 60 0 14.5 14.4 13.8 13.9 12.7 13.5 180.0 - 13.8 - 13.4 - 12.9 Relative Humidity = 702 0.0 18.7 18.7 18.6 18.6 18.5 18.5 1.0 18.6 18.3 18.5 18.1 - 17.9 2.0 18.5 18.1 18.4 17.9 - 17.7 5.0 17.8 17.8 17.5 17.6 - 17.3 10.0 17.4 17.5 17.2 17.2 17.8 16.9 60.0 16.0 16.3 15.9 15.8 15.7 15.4 180.0 - 16.0 - 15.5 - 15.1 Milk pellet 16% protein; diameter 4.76 mm. (3/16 in.) Assumed that equilibrium has been reached after 60 minutes. Airflow rate = Pellet density Pellet bulk density (at MC = 20.5 %DB) = 673 Kg/m3 * Predicted values obtained using Eqns. and (6.6). 5 m/s 945 K8/m3 (6.1). (6.2). (3.5) 94 8.1.1 - Equilibrium Moisture Content and Diffusion Coefficient The program BMDPAR, contained in the HMDP statistical software package of Dixon (1981), was used in the statistical analysis to fit a nonlinear model to the experimental thin-layer drying data shown in Tables 6.1a and 6.1b,and to estimate the constants in the EMC and D equations. In the first step, the data is fitted to Equation (3.7) (in which it is assumed that hd = m). using three exponentials terms to estimate the values of the equilibrium moisture content (EMC) and the diffusion coefficient (D) at the same time (Byler, 1983). Assuming that ha = m Equation (3.7) can be then written in the following form: Mt = EMC + (Mi-EMC)#(A*exp(-k1*D*t) + (Btexp(-k2*D*t) + (Ctexp(-k3*D*t)) (6.1) where: Mt 2 Moisture content at time t (decimal DB) Mi = Initial moisture content (decimal DB) EMC = Equilibrium.moisture content (decimal DB) D = Diffusion coefficient (ma/h) t = Time (hour) A = 4/(u1)2 B = 4/(a2)2 c = 4/(u3)3 k1 = («uz/m k2 = (ma/w 13 = (aaflm “n = Roots of the Bessel function of zero order given by Churchill and Brown (1978) al 2.405 a2 = 5.52 «3 = 8.654 95 A subroutine EMCD, presented in Appendix E, was written in FORTRAN using Equation 6.1 with EMC and D as parameters to be estimated for each combination of temperature and relative humidity (five points, the moisture contents at time zero were excluded) listed in Tables 6.1a and 6.1b. The results showed that the EMC and D are highly correlated, (correlation coefficient = .9997). Therefore, it is impossible to estimate EMC and D simultaneously and accurately (Beck, 1986). Hence, one parameter has to be fixed to estimate the other. It was assumed that equilibrium has been reached after 60 minutes of drying time. Thus, the observed values of the moisture content (decimal) in Tables 6.1a and 6.1b at 60 minutes (17 points) can be employed as EMC data in the BMDPAR program for the estimation of the parameters in the Mellist (Eqn.3.20), Henderson (Eqn. 3.22), and Chung-Pfost (Eqn. 3.23) EMC equations. The parameter values, with the asymptotic standard deviation, the residual sum of squares and the mean relative deviation modulus (P) are presented in Table 6.2. The goodness of fit of the equations can be evaluated from: (1) the mean relative deviation modulus (P) (defined by Equation 3.40). A P value of less than or equal to 5 means that the equation is a good fit (Lomauro, 1985); the equation with the smallest P value is considered the best fit. All three EMC equations gave P values less than 5; thus the equations can be considered a good fit. (2) the residual sum of squares (2R2). The equation with the 98 smallets value of 282 is considered the best fit. The Chung-Pfost EMC- equation resulted in the smallest P and residual sum of squares values. Table 6.2 - Constants and Statistical Data Obtained by Regression Analysis of the Equilibrium Meisture Content Datam'mK in Tables 6.1a and 6.1b. EMC Constants Asymptotic St Pi 2R2a Kantian: Dexiat ion a .191 .017 Mellist b .055 .005 3.40 5.906E-04 c .028 .004 a 6.66 5.03 Henderson b 22.12 10.82 3.44 5.750E-04 c 3.11 .32 a .277 .017 Chung-Pfost b .042 .003 3.13 4.898E-04 c 13.3 7.82r I P = Mean relative deviation modulus *1 2R2 2 Residual sum of squares *1! EMC is assumed to be the moisture content reached after 60 minutes of drying. The observed and predicted values of the EMC in the three equations are presented in Table 6.3. Figure 6.1 shows the observed and predicted values at 552 relative humidity; there is acceptable agreement between the two sets of values. The predicted EMC values are also in good agreement with the experimental data shown in Table 3.9 obtained by Headley (1969). For example, at 21.1 C and 55% relative humidity, Headley’s values range from 13.6 to 15.9 XDB compared to the predicted EMC value of 15.0 XDB from the Chung-Pfost equation. Equilibrium Moisture Content (%DB) 97 20.0 Pellet diameter = 4.76 mm. J v—v Predicted by Chung-Pfost Eqn. H Predicted by Henderson Eqn. ‘ H Predicted by Nellist Eqn. 50 :3 Observed 10.0 15.0 26.0 25.0 36.0 35.0 46.0 45.0 50.0 Temperature (C) Fig. 6.1 Observed and predicted e uilibrium moisture content. Relative hum: Ity 55%. Table 6.3 - Observed and Predicted Values of the Equilibrium IMoisture Content (%DB) of Feed Pellets. Temp. Observed Predicted by Equations (C) Nellist Henderson Chung-Pfost Relative Humidity = 40% 21.1 13.5 13.4 13.0 13.2 26.7 12.8 12.7 12.5 12.6 32.2 11.7 12.2 12.1 12.0 37.8 11.4 11.7 11.7 11.5 43.3 10.3 11.4 11.4 11.1 Relative Humidity = 55% 15.6 16.5 15.8 15.7 15.7 21.1 15.8 15.0 15.1 15.0 26.7 14.9 14.3 14.5 14.4 32.2 14.5 13.8 14.0 13.8 37.8 13.8 13.3 13.8 13.3 43.3 12.7 12.9 13.2 12.9 Relative Humidity = 702 15.8 16.9 18.0 18.0 17.9 21.1 16.6 17.2 17.2 17.2 26.7 16.4 16.5 16.5 16.5 32.2 16.0 16.0 16.0 16.0 37.8 15.9 15.6 15.5 15.5 43.3 15.7 15.2 15.0 15.1 The plots of the residuals of the three EMC equations were examined. Figure 6.2 shows the residuals of the Chung-Pfost Equation plotted against the predicted equilibrium. moisture content. Instead of being randomly distributed around the y-axis, the residuals form a systematic pattern, which implies that the parameters in the equation are correlated (Beck and Arnold, 1977). The other two-EMC equations showed similar pattern. 99 0.015 0.010- 0.005% 0.0004 Residual -.0101 “'0'5 I I I I I I I I I 0.10 0.11 0.12 0.13 0.14 0.15 0.15 0.17 0.18 0.19 0.20 Predicted Equilibrium Moisture Content (dec. DB) Fig. 6.2 Residuals of equilibrium moisture content for Chung-Pfost EMC equation. 100 With the experimental EMC values known (see the 60 minutes data in Tables 6.1a and 6.1b), the D values can be determined at each of the six temperatures (it is assumed that D is only a function of temperature). Equation (6.1) is used for time > 2 minutes, and the following equation is employed for time 1 2 minutes (Crank, 1975): Mt 4 D t 1/2 D t 1 D t 3/2 ---- = ———- ( ----- ) - ----- — ----- ( ----- ) + . (6 2) us nl/Z R1 R2 mill2 1:2 where:Mt = moisture content at time t (decimal DB) Mm = moisture content after infinite time (dec DB) D = diffusion coefficient (mZ/h) R = pellet radius (m) t = time (hour) Figure 6.3 shows the values of D (with asymptotic standard deviation varying from 2.00E-07 to 2.65E-07) found with Equations (6.1) and (6.2). These D values was. subsequently employed to determine the parameters a and b in the Arrhenius equation (3.24); the results were: a = 1.015E-05 and b = 547, with asymptotic standard deviations of .1E-06 and 301, respectively. The analysis of the residuals showed that the parameters are correlated. (Figure 6.3 shows the five individual D values determined with the BMDPAR program along with the values predicted by the Arrhenius equation. The high value of D at 26.7 C appears to be due to experimental error). Diffusion Coefficient (mZ/Hr) E-06 2.20 101 Pellet diameter - 4.76 mm D - 1.015E-05 EXP(-547/(T+273.15)) 2.00-J D 1.80s El 0 D 1.60j 1.404 e—e Predicted 1 20 a Obeewed 15.0 26.0 26.0 36.0 35% 46.0 46.0 Temperature (C) Fig. 6.3 Determined and predicted diffusion coefficients as a function of temperature. 102 The resulting equations for the EMC of feed pellets are Nellist Equation (Eqn. 3.20): EMC = .191 - .055*1n(1-RH) - .028*ln(6) (6.3) Henderson Equation (Eqn. 3.22): sac = (-1n(1-RH)/(6.88*(9 + 22.12)))(1/3-11) (6.4) Chung-Pfost Equation (Eqn. 3.23): EMC = .277 - .042*1n(-(e + 13.3)*1n(RH)) (6.5) The resulting equation for the diffusion coefficient is (Eqn. 3.24): D = 1.015E-O5*EXP(-547/(6 + 273.15)) (6.6) assuming that Equation (3.6) in cylindical form is used in the temperature range 15.6 to 43.3 C. In Equations (6.3) to (6.6): 6 Average pellet temperature (C) and RH Relative humidity (decimal). The use of equations 6.3 to 8.6 is limited to the temperature range of 15.6 C to 43.3 C, the relative humidity range from 40% to 70%, for pellets with a density of 673 kg/m3 and a chemical analysis as given on page 82. The analysis of the residuals shows that the parameters in the EMC and D equations are correlated. This seems to imply that the pellets did not reach equilibrium after 60 minutes of drying. This is confirmed in Tables 6.1a and‘ 6.1b (compare the predicted values at 60 minutes of drying with the predicted values at 180 minutes of drying). In the opinion of the author, the correlation of the 103 parameters in the EMC and D equations does not introduce a serious error in the analysis. Finally, close analysis of the results shows that in the 15.6 to 43.3 C range the variation in D is so small that use of an average value of D may suffice. This is confirmed by comparing the data in Table 6.4, obtained with a constant D in Equation (6.1), with that in Tables 6.1a and 6.1b. Table 6.4 - Predicted Pellet Moisture Content (x03) using a constant Diffusinon Coefficient = 1.66E-06 mzlh. Time Temperature (C) (min) 15o6 21.1 26.7 3gp; 37.8 4.33 Relative Humidity = 40% 0.0 18.6 18.6 18.6 18.6 18.6 18.6 1.0 17.8 17.7 17.6 17.6 17.5 17.4 2.0 17.6 17.4 17.3 17.2 17.1 17.0 5.0 17.1 16.8 16.6 16.4 16.3 16.1 10.0 16.5 16.2 15.9 15.6 15.4 15.2 60.0 14.5 13.8 13.3 12.8 12.4 12.0 180.0 13.9 13.2 12.6 12.1 11.5 11.1 Relative Humidity = 55% 0.0 19.2 18.1 18.2 18.5 19.1 19.1 1.0 18.6 17.6 17.6 17.7 18.2 18.1 2.0 18.5 17.4 17.4 17.5 17.8 17.8 5.0 18.1 17.1 16.9 16.9 17.2 17.1 10.0 17.6 16.7 16.5 16.4 16.5 16.3 60.0 16.2 15.4 14.8 14.4 14.1 13.6 180.0 15.7 15.0 14.4 13.8 13.4 12.9 Relative Humidity = 70% 0.0 18.7 18.5 18.6 18.7 18.6 18.5 1.0 18.6 18.3 18.3 18.3 18.1 17.9 2.0 18.5 18.2 18.2 18.1 17.9 17.7 5.0 18.4 18.1 17.9 17.8 17.6 17.4 10.0 18.3 17.9 17.7 17.5 17.2 16.9 60.0 18.0 17.3 16.8 16.3 15.9 15.5 lflflsfl. 17.9, 17L2 16o5 IQLQ 15.5 15.1 104 6.2 - Deep-Bed Cooling Tests The objective of these experiments was to study the effect of cooling air temperature, relative humidity, and velocity on the pellet temperature and moisture content during the fixed-bed cooling process. A major problem encountered in the study of pellet cooling is the extreme variation in the additives used in formulating a livestock feed. The frequent change in price and availability of the different ingredients greatly affects the formulation of a feed. This change influences the amount of steam and liquid added to the mash during the pelleting process. This in turn results in different temperatures and moisture contents of the pellets. The change in formulation also affects the pellet properties such as the diffusion and mass transfer coefficients, the density, the thermal conductivity, the specific heat, etc. Tables 6.5 and 6.6 show typical temperature data of deep-bed pellet cooling tests. The results correspond to the conditions of test numbers 3 and 4 shown in Table 5.2. The results of the other tests are presented in Appendix A. In test number 3 (Table 6.4) the pellets cooled from 63 C to an average temperature of 24.6 C after 20 minutes at an air velocity of .5 m/s. (The average temperature is defined as the sum of the thermocouple readings divided by the number of thermocouples within the bed of pellets after 20 minutes of cooling). to evaporative cooling, 105 The data of Table 6.5 is plated in Figure 6.4. Due the pellet temperatures at the centre and top of the bed after 11 minutes cooling time are lower than the cooling air temperature. Table 6.5 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 26.7 C, RH 55%, Air Velocity .5 m/s. Test #3. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 81.7 62.6 63.8 63.4 63.4 82.9 63.2 1 32.6 43.9 47.8 50.7 52.8 53.9 55.2 2 31.4 37.7 41.8 44.0 45.8 47.0 48.2 3 30.1 33.6 37.4 39.4 40.7 42.1 43.1 4 28.9 30.9 34.1 36.1 37.3 38.6 39.4 5 28.1 28.9 31.4 33.4 34.7 35.8 36.7 6 27.6 27.7 29.4 31.2 32.4 33.4 34.3 7 27.5 26.9 28.0 29.4 30.6 31.6 32.4 8 27.4 26.4 26.9 28.1 29.1 30.0 30.8 9 27.3 26.1 26.1 27.1 27.9 28.7 29.5 10 27.3 25.9 25.6 26.2 26.9 27.7 28.3 11 27.3 25.8 25.2 25.6 26.1 26.7 27.3 12 27.3 25.8 25.0 25.1 25.4 26.0 26.6 13 27.3 25.8 24.8 24.7 24.9 25.4 25.9 14 27.3 25.7 24.7 24.3 24.5 24.8 25.3 15 27.2 25.8 24.7 24.2 24.2 24.6 24.9 16 27.2 25.8 24.6 24.1 23.9 24.2 24.5 17 27.3 25.9 24.6 23.9 23.8 23.9 24.2 18 27.3 25.9 24.6 23.8 23.7 23.7 23.9 19 27.3 25.9 24.6 23.8 23.6 23.6 23.7 20 27.3 25.9 24.7 23.9 23.4 23.4 23.5 Initial moisture content = Pellet diameter = 4.76 mm, Pellet density 945 Eg/m3 Pellet bulk density 20.5 %DB 673 Kg/m3, Bed depth = 30.48 cm Temperature (C) 106 65.0 Relative humidity = 55% Air velocity - .5 m/s Bed depth 8 30.48 cm Pellet diameter - 4.76 mm Initial Moisture Content - 20.5 %08 H 30.48 cm H 15.24 cm 15.0 H B°"°.'" ' T I ' T I I ' I f I ' 1 '—I r I ' I 0 2 4 5 8 10 12 14 15 18 Cooling Time (Min.) Fig. 6.4 Effect Of coolin time on the Observed temperatures of a. fixed ed of pellets at three bed depths. Cooling Oll" temperature 26.7 C. 107 Table 6.6 shows the results of test 4. The pellets in this test were cooled at an airflow rate of .1 m/s from 58.5 C to an average temperature 27 C in 15 minutes. The moisture contents in a bed of pellets after cooling are presented in Table 6.7 for tests 3 and 4. (The average moisture content is the sum of the moisture content measured in four different positions within the bed divided by four). In test number 3, pellets were dried from an initial moisture content of 20.5 X dry basis to an average moisture content of 17.3 XDB after 20 minutes cooling with air velocity of .5 m/s. There was no change in the average moisture content at .1 m/s (test 4). These results show a deviation from the expected trend. In the cooling and drying of pellets the heat necessary to evaporate liquid is supplied by the pellets, which is not the case in conventional drying where the heat comes from the airstream. Therefore, the initial heat content of the product limits the amount of moisture which can be removed. It was expected that rapid cooling, high air velocity, would reduce moisture content less than low air rates. Figure 6.5 shows the moisture content within a stationary bed of pellets after three cooling periods at a cooling air temperature of 26.7 C and an air velocity .5 m/s. Longer cooler times results in lower moisture contents. 108 Table 6.6 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 26.7 C, RH 55%, Air Velocity .1 m/s. Test 4. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 56.7 58.6 56.9 58.6 58.7 61.6 58.7 1 31.3 44.8 48.1 52.7 54.9 56.1 56.5 2 29.8 39.1 42.2 47.1 50.6 53.3 55.1 3 29.0 35.8 38.6 42.7 46.2 49.5 51.6 4 28.3 33.4 35.9 39.4 42.5 45.8 48.1 5 27.8 31.7 33.9 36.9 39.6 42.7 44.9 6 27.4 30.2 32.3 35.0 37.4 40.3 42.4 7 27.2 29.2 30.9 33.3 35.4 38.1 40.1 8 26.9 28.1 29.7 31.9 33.8 38.2 38.1 9 26.7 27.3 28.8 30.7 32.4 34.6 36.3 10 26.7 26.7 28.0 29.7 31.2 33.3 34.9 11 26.4 26.2 27.2 28.8 30.2 32.1 33.6 12 26.4 25.8 26.7 28.1 29.3 31.1 32.4 13 26.4 25.4 26.1 27.4 28.5 30.1 31.5 14 26.3 25.2 25.8 26.9 27.9 29.3 30.6 15 26.3 25.0 25.5 26.5 27.3 28.7 29.9 Initial moisture content 2 20.5 XDH Pellet diameter = 4.78 mm, Pellet density = Pellet bulk density = 945 Kg/m3 673 Kg/m3, Bed depth = 30.48 cm Table 6.7 - Experimental Values of Moisture Content (EBB) within a Fixed-Bed of Pellets Cooled at Two Airflow Rates. Air Temperature 26.7 C, RH 55x. Air Velocity = .5 ml; 11 ml; Cooler Cooling Time (min) M1 10 15 29 15 Bottom 18.3 17.7 17.2 18.3 10.16 17.7 17.5 17.3 18.1 20.32 17.7 17.5 17.4 18.2 30.48 17.9 17.7 17.5 18.5 Average 17.9 17.6 17.3 18.3 Initial moisture content 20.5 %DB Moisture Content (2 DB) 109 19.0 Relative humidity = 55% Air velocity - .5 m/s Initial moisture content = 20.5 %08 Pellet diameter = 4.76 mm Initial pellet temp. - 63.0 C 18.0-i N c» p 17.01 H 20 min. H 15 min. :éj W e—e 10 min. 16.0 . T l 0.00 10.16 ‘7 Y Y r Y 20:32 Cooler Depth (cm) Fig. 6.5 Effect Of cooling time on the Observed moisture content of a fixed bed of pellets after 20,15,10 mm. of cooling. Cooling Oll’ temp.26.7 C. 30.48 110 Figure 6.6 shows the effect of cooling air temperature on the observed pellet temperature at the top of a fixed-bed. As expected, a lower cooling air temperature results in a cooler pellet temperature. The effects of cooling air temperature on the moisture content within the bed after 20 minutes cooling is depicted in Figure 6.7. Higher temperatures allow the pellets to approach the ambient conditions more rapidly, but results in lower pellet moisture contents. Figures 6.8 to 6.11 depict the effect of air velocity on temperature and moisture content of a fixed bed of pellets for two different cooling air temperatures, 26.7 and 32.2 C. The lower airflow produced the warmer pellets, although the pellets had a higher moisture content. The differences between the values for temperature and moisture content for different airflows were smaller for the higher (32.2 C) cooling air temperature. The effects of relative humidity on temperature at the top of a fixed-bed of pellets and on the moisture content within the bed are presented in Figures 6.12 and 6.13. The pellet temperatures were somewhat higher, about 5 C, for the 70% relative humidities. However, the moisture content at the bottom of the bed was 2% higher which is significant (see Figure 6.13). Since, the temperatures were high at the top of the bed, the moisture content was lower for the 702 relative humidity test. Temperature (C) 111 55.0-i 45.04 35.0~ 250. 15.0 0 Relative humidity =- 55% Air velocity = .5 m/s Bed depth - 30.48 cm Pellet diameter x 4.76 mm H Cooling air temp.- 33.3 C e—e Cooling air temp.- 26.7 C e—e Cooling air temL- 21.1 C f I I I ' I ' r 2 4 6 8 r T V T V f r 14 I 12 1'0 Cooling Time (Min.) Fig. 6.6 Effect Of cooling air temperatures on the observed tem erotures at the top of a fixe bed of pellets. Moisture Content (2'. DB) 112 19.0 Relative humidity = 55 57: Air velocity— = .5 m/s Pellet diameter - 4. 76m 18.0-i Bed depth =- 30. 48 cm CL 3 C" 3 17.01 \9 e .49 16 O-i A A 15.0-i H Cooling air temp. - 32.2 C; Initial MC - 19.1 %08 H Cooling air temp. - 26. 7 C; Initial MC - 20. 5 %DB 14 O H Cooling air temp. - 21.1 C; initial MC - 20. 7 %DH 0.00 10.16 20. r32 30.48 Cooler Depth (cm) Fig. 6. 7 Effect Of coolin air temperature on the observed moisture con ent of a fixed bed Of pellets after 20 min. of cooling. Temperature (C) 70.0 * 113 Relative humidity a 55% Bed depth - 50.48 cm so 0 Pellet diameter a 4.76 mm ' .. Initial moisture content - 20.5 xoe 50.0: 40.0“ s‘ : :50.O« = t - = . H Air velocity - .1 m/e ' 20.0 “1‘" Y°'°°‘,‘Y 's” '"fi' , . . . . f r - . ' 0 3 5 9 12 15 Cooling Time (Min.) Fig. 6. 8 Effect Of air velocit on the Observed temperatures at the top of a med bed of pellets. Cooling air temperature 26. 7 C. Moisture Content (2'. DB) 114 20.0 Relative humidity = 55% Initial moisture content - 20.5 7508 Pellet diameter = 4.76 mm 19.0~ 18.0~ W 17.0“ H Air velocity - .1 m/s 16 0 e—e Air velocity - .5 ma 0.00 10T16 2032 ' V 30.48 Cooler Depth (cm) Fig. 6.9 Effect Of air velocity on the Observed moisture content Of a fixed bed of pellets after 15 min. Of cooling. Cooling air temp. 26.7 C. Temperature (C) 75.0 115 515.0« 25.0 e—e Air velocity - .1 m/s Relative humidity = 55% Bed depth - 30.48 cm Pellet diameter = 4.76 mm lnitial moisture content - 19.1 208 0 H Air velocity - .5 m/s ' I ' I I I ' 2 4 6 7 8 I ' I I ' ' 10 12 14 16 18 20 Cooling Time (Min.) Fig. 6.10 Effect Of air velocity on the Observed temperaturesoot the top of a fixed bed of pellets. COOIIng on temperature 32.2 C. Moisture Content (2 DB) 116 18.0 Cooling time = 20 minutes Relative humidity = 55% Initial moisture content - 19.1 2508 Pellet diameter = 4.76 mm 17.0-i 16.0w: 3/'//_T 15’01 H Air velocity = .1 m/s 140 e—e Airvelocij-fi m/s r 0.00 10.16 if 20:32 ' ' ' 30.45 Cooler Depth (cm) Fig. 6.11 Effect Of air velocity on the Observed moisture content of a fixed bed of gellets. CoolIng on temperature 32.2 . Temperature (C) 75.0 , 65.0 " 55.0~ 45.0« 35.0% 25.0~ 15.0 0 117 Air velocity = .5 m/s Bed depth - 30.48 cm Pellet diameter =- 4.76 mm -‘ Initial moisture content a 20.5 %09 n g! “ 'd n M U H II II II ‘ H Relative humidity - 702 H Relative humidity - 55% . I ' I I I . T 2 4 6 a'I'O r I T 1 12 14 16 18 20 Cooling Time (Min.) Fig. 6.12 Effect Of relative humidity on the observed temperatures at the top of a fixed bed of pellets. Cooling air temperature 26.7 C. Moisture Content (7. DB) 118 20.0 Cooling time = 20 min. Pellet diameter - 4.76 mm Initial moisture content = 20.5 208 Air velocity 3 .5 m/s 19.01 18.0-< IL 17.01 [p l Ir e—e Relative humidity .- 70% 16 O H Relative humidity - 55% r 0.00 10.16 ' V f V r 2032 30.46 Cooler Depth (cm) Fig. 6.13 Effect Of relative humidity on the Observed moisture content Of a fixed bed Of pellets. CoolIng on temperature 26.7 C. 119 6.2.1 - Comparison of Experimental and Simulated Deep-Bed Data The deep-bed pellet cooling heat and mass balance (HMB) and partial differential equations (PDE) models discussed in chapter 4 were used to simulate the cooling of pellets. The experimental conditions given in Table 5.2, and the model parameters shown in Table 6.8, formed the inputs to the simulation models of the fixed-bed cooler. The experimental and simulated results are compared in Figures 6.14 to 6.22. Table 6.8 - Input Parameter Values to the Simulation Models of a Fixed-Bed Pellet Cooler. Bed depth (cm) 30.48 Bed porosity .44 Pellet bulk density (at MC=20.5 %DB) (Kg/m3) 673 Heat transfer coefficient (W/MZ K) Eqn. 3.25 Mass transfer coefficient (M/Hr) Eqn. 3.26 Pellet specific heat (J/Kg K) Eqn. 3.28 Pellet thermal conductivity (W/M K) Eqn. 3.27 Equilibrium.moisture content (dec. DB) Eqn. 6.5 Diffusion goefficient (M2/Hr) Eqn- 6.6 The PDE model requires between three to five minutes execution time on the IBM-AT micro-computer to simulate one minute of cooling time. The HMB model requires only 10 to 15 seconds to simulate this period of cooling. First, the equilibrium moisture content Equations (6.3), (6.4), and (6.5) were used in the PDE model to evaluate the effect of the EMC‘ equation on the pellet moisture content. The results are shown in Figure 6.14 Moisture Content (7. DB) 120 20.0 180D: H _¥ . D U do 16.0-i initial pellet temp. = 6.3.0 C Cooling air temperature = 21.1 C 1 Relative humidity == 55% Air velocity - .5 m/s Initial moisture content = 20.5 208 140* Pellet diameter =- 4.76 mm d H Simulated EMC Eqn. 6.3 H Simulated EMC Eqn. 6.4 e—e Simulated EMC Egn. 6.5 0 Observed 12-0 I I f r I 1 I I . T I 0.00 5.08 10.16 15.24 20.32 25.40 30.48 Cooler Depth (cm) Fig. 6.14 Observed and simulated moisture content usmg three different EMC e uotions after 20 minutes 0 cooling. 121 together with the experimental values. The three equations predicted practically the same moisture content within the fixed-bed after 20 minutes of cooling. When compared with the observed data, the predicted results are in reasonably good agreement. They experimental and predicted values are about the same at the bottom of the cooler, and slightly different at the other bed locations. Although all three EMC equations predict the moisture content well, the Chung-Pfost equation (Eqn. 6.5) is used in all subsequent simulations conducted in this study, because it had the smallest mean relative deviation modulus (P) (see Table 6.2). Figures 6.15 and 6.22 compare the experimental and the simulated values from the HMB and PDE models. Only the values at the bottom and top of the cooler are shown because these are the critical locations of the bed. Both models predict the temperatures at the bottom very well at the airflow of .5 m/s (see Figure 6.15). At the top, the HMB model shows better agreement with the experimental data than the PDE model for the first 9 minutes of cooling but after that overpredicts the temperatures. The opposite happens with PDE model which overpredicts the temperatures in the first 10 minutes but is in a good agreement with the experimental data during the last 10 minutes of cooling. The observed and simulated moisture contents are . shown in Figure 6.16 for the coaling conditions of Figure 6.15. Both models give results fairly close to the experimental data, although the PDE model better predicts Temperature (C) 70.0 * 122 Relative humidity =- 55% Air velocity - .5 m/s Initial Moist. Content - 20.5 %08 Pellet diameter - 4.76 mm ‘—_—_—_-——-——__—_ . - +—+ Simulated top - HMB model e—e Simulate bottom — HMB model e—e Simulated top - PDE model H a o Simulated bottom - PDE model Observed top Observed bottom , e I V I V '— f r TV 1' i— f 1 f 2 4 6 8 1'0 1'2 14 116 18 20 Cooling Time (Min.) Fig. 6.15 Observed and simulated temperatures at the bottom and top layers of a fixed bed of pellets. CoolIng aIr temperature - 26.7 C. Moisture Content (‘73 DB) 20.0 19.0 123 Relative humidity = 55% Pellet diameter - 4.76 mm .. Initial moisture content - 20.5 208 Air velocity - .5 m/s :t 18.0-I 0 i O 17.0 16.0-1 H Simulated HMB model a—e Simulated PDE model 15.0 °.°°’°"1°“ . r - i , . i . 0.00 10.16 20.32 30.48 Cooler Depth (cm) Fig. 6.16 Observed and simulated moisture content Of a fixed bed of pellets after 20 min. of coolIng. Cooling air temperature 26.7 C. 124 the pellet moiture content. Figures '6.17 and 6.18 show the pellet temperature and moisture content, respectively, during the process of pellet cooling at .1 m/s. For the low air flow the HMB model better simulates the temperatures. The moisture content, (see Figure 6.18) is predicted well by the PDE model at the bottom of the bed, but is underpredicted by the PDE model and overpredicted by the HMB model at the other bed locations. Still, the difference between observed and simulated moisture content is within 10%. Figures 6.19 and 6.20 show the pellet temperature and moisture, respectively, for cooling test 11 in Table 5.2. The trends are the sameas in Figures 6.15 and 6.16, except that both models slightly underpredict the temperatures during the last 10 minutes of cooling time. The moisture content values are better simulated by the PDE model. The final moisture content of the pellets was high at the bottom of the cooler for this test because of the high relative humidity (70%). Thus, the bottom-layer pellets equilibrated to a relatively high moisture content. Since the pellet temperature at the top of the cooler is higher for higher relative humidities, the pellets tend to equilibrate at a lower moisture content. Figures 6.21 and 6.22 represent the experimental and simulated values of temperature and moisture content for test 7. The profile of the temperature curves are similar as in Figure 6.15; the moisture content at the bottom is higher than the moisture content at the top of the cooler. Temperature (C) 125 75.0 . 65 06 Initial moist. content - 20.5 %08 ' Pellet diameter a 4.76 mm Air velocity - .1 m/s Relative humidity - 55% . \; 55.0~ . - g . D 2 ‘ J . § ‘ D ' : ~ 450- - CI ‘ = = . D c : q 4 e D ‘ C - D I 35.0.. - - I I ‘ - m . '- 3 I_I , 25.0~ . o—e Simulated PDE model e—e Simulated HMB model 15.0 °.°b’.°"'°“, . .1 . . , . - r . - 0 3 6 9 12 15 Cooling Time (min.) Fig. 6.17 The Observed and simulated temperatures at the top of .a fixed bed of gellets. CoolIng on temperature 2 .7 C.. Moisture Content (7. DB) 20.0 126 19.0-4 18.0 17.0-I 16.0-I 15.0 ° 9b’°"1°d e—e Simulated PDE model e—e Simulated l-NB model Air velocity = .1 m/s Pellet diameter - 4.76 mm Initial moist. content = 20.5 7308 Relative humidity - 55% 0.00 T 20132 ' ' ' 30.46 Cooler Depth (cm) I 10.16 Fig. 6.18 Observed and simulated moisture content of a .fixed bed Of pellets after 15 min. Of coolIng. CoolIng on temperature 26.7 C. Temperature (C) 75.0 127 65.0 55.0.. 45.0‘ Initial moist. content - 20.5 %08 Pellet diameter - 4.76 mm Air velocity - .5 m/s Relative humidity - 70% e—e Simulated PDE model ‘ H Simulated HMB model a Observed v I Y r a T V 12 14 16 18 20 Cooling Time (min.) ' I T 2 4 6 8 10 Fig. 6.19 Observed and simulated temperatures at the top layer of a fixed bed of ellets. Cooling air temperature =- 6.7 C. Moisture Content (7. DB) 128 20.0 E 19.0~ 18.0 " [:1 Cl 113 17.0-4 Air velocity - .5 m/s Relative humidity = 70% Pellet diameter - 4.76 mm 15.0-4 Initial-moisture content a 20.5 208 e—e Simulated PDE model e—e Simulated HMB model 15.0 ° 9"?" - , f . , . - . 0.00 10.16 20.32 30.48 Cooler Depth (cm) Fig. 6.20 Observed and simulated moisture content of a fixed bed Of pellets after 20 min. of cooling. Cooling air temperature 26.7 C. Temperature (C) 129 Relative humidity == 70% Air velocity - .5 m/s Bed depth - 30.48 cm Pellet diameter - 4.76 mm Initial moisture content - 19.6 208 10'0‘ H Simulated PDE model 4 H Simulated HMB model 0 Observed 00 I I I I I I I I I I I I I I I I I T I O 2 4 6 8 1O 12 14 16 18 20 Cooling Time (Min.) Fig. 6.21 Observed and simulated temperatures at the tOp layer of a fixed bed of ellets. Cooling air temperature - 1 .7 C. Moisture Content (7. DB) 130 20.0 Air velocity = .5 m/s Pellet diameter = 4.76 mm Initial moisture content - 20.5 308 1904 Relative humidity =3 70% 16.0-* D dP o—o Simulated PDE model H Simulated HMB model Is.o°.°b°°":°d., - 0.00 10.16 20.32 30.48 Cooler Depth (cm) Fig. 6.22 Observed and simulated moisture content of a .fixed bed of pellets after 20 min. of cooling. Cooling air temperature 17.7 C. 131 Based on Figures 6.15 - 6.22, it is concluded that the agreement between the experimental data and the values simulated by the HMB and PDE models is acceptable. The HMB model better predictes the pellet temperature at low air flow rates and during the first 10 minutes of cooling, but does not simulate the moisture content as good as the PDE model. The computer time plays an important role When selecting a simulation model. The HMB model can be used for a quick simulation of deep-bed pellet cooling and for an evaluation of the influence of selected parameters on the cooling process such as the cooling air temperature and humidity, the pellet temperature and moisture content, and the air flow rate. Although the PDE model requires longer computer time, it is more fundamental in nature (i.e. it contains fewer simplifications) and the results appear to be more accurate. Therefore, it will be used in the next section to evaluate the effect of the pellet thermal conductivity, specific heat, density, heat and mass transfer coefficients on the pellet cooling process. 132 6.3 - Effect of Model Parameter Values In this section the effect of several model parameters (shown in Table 6.9) on the pellet temperature and moisture content will be analysed. Table 6.9 - Standard Input Parameter Values Used in the PDE Model of a Fixed-Bed Pellet Cooler. Cooling air temperature (C) 26.? Relative humidity (X) 55.0 Air velocity (m/s) .5 Initial pellet temperature (C) 63.5 Initial pellet moisture content (X DB) 20.5 Pellet diameter (mm) 4.76 Bed depth (am) 30.46 Pellet bulk density (at MC=20.5 %DB) (kg/m3) 673 Heat transfer coefficient (W/mz K) Eqn. 3.25 Mass transfer coefficient (H/h) Eqn. 3.26 Pellet specific heat (J/kg K) Eqn. 3.28 Pellet thermal conductivity (W/m K) Eqn. 3.27 Equilibrium moistture content (3 DB) Eqn. 6.5 Diffusion coefficient (m2/h) Eqn. 6.6 Bed porosity (degimall 11$ The effects of the values of the parameters in Table 6.9 on the temperatures and moisture contents in a deep-bed of pellets is illustrated in Figures 6.23 - 6.34. Figures 6.23 and 6.24 show the effect of pellet density on temperature and moisture content. Two pellet bulk density values are compared: 673 and 801 Kg/m3, assuming that D is not a function of pellet density. The pellet temperature is higher for the higher pellet density while the pellet moisture content is lower. Temperature (C) 133 Relative humidity = 55% Bed depth - 30.48 cm Pellet diameter = 4.76 mm Air velocity - .5 m/s Initial moisture content - 20.5 208 H Density - 673 Kq/m3 a—e Density - 801 Kg/m3 . , . , . , . - T I T— I ' I 2 4 6 a 10 12 14 16 18 20 Cooling Time (Min.) Fig.6.23 Effect of pellet density on the simulated temperatures at t e top of fixed bed of pellets. Cooling air temperature =-= 26.7 C. Moisture Content (7. DB) 134 20.0 Cooling time = 20 min. Pellet diameter - 4.76 mm 19 0‘ Initial moisture content a 20.5 7.08 ' Air velocity = .5 m/s Initial pellet temp. - 63.0 C 18.0. [/K/ it 17.0.. 16.04 H Density = 673 Kg/m3 H Density - 801 Kg/mIS 15.0 . T . , . 1 . , r 0.00 10.16 20.32 30.48 Cooler Depth (cm) Fig. 6.24 Effect of pellet density on the simulated moisture content of a fixed bed of pellets. Cooling air temperature 26.7 C. 135 Three values for the heat transfer coefficient 80, 106, and 120 H/m2 K, are compared. The value of 106 W/m2 K was calculated by Equation (3.25) under the conditions of Table 6.9. Figure 6.25 shows that the heat transfer coefficient has a marked influence on the rate at wich the pellet temperature approaches equilibrium. For h = 80 W/m2 K, the pellet temperature is 40 C after 10 minutes cooling while for h = 120 W/mz K it is about 20 C at the top of the cooler. The heat transfer coefficient not only affects the pellet temperature but also affects the predicted moisture content (see Figure 6.26), because the moisture diffusivity is a function of the pellet temperature. For h = 80 W/mz K, the computed moisture content at the top of the cooler is 16.5 %DB, while for h = 120 W/m2 K this value is 18.4 %DB. Figures 6.2? and 6.28 show the influence of the mass transfer coefficient on the pellet temperature and moisture, respectively. The .0126 H/Hr value is computed by Equation (3.26) for the conditions given in Table 6.6. For the three values of the mass transfer coefficient (.009, .0126, and .025 m/h) used, the difference in the pellet temperature is not large. A lower value in the mass transfer coefficient results in a slightly higher pellet moisture content at the air inlet side of the cooler (see Figure 6.28). Figures 6.29 and 6.30 illustrate the effect of the specific heat on the pellet temperature and moisture content. Two fixed values of the specific heat 1700 and 2100 J/Kg K, and a specific heat value varying with the pellet Temperature (C) 136 80.0 70 0 Initial moist.content = 20.5 203 ' 'i Bed depth - 30.48 cm Pellet diameter = 4.76 mm Air velocity = .5 m/s 60.0~ Relative humidity - 55% 50.0- 40.0~ 30.0d 20.0-I 100‘ e—e Heat transfer coef. - 120 W/MZ K < H Heat transfer coef. - 106 W/MZ K H Heat transfer coef. - 80 W/MZ K 0.0 v 1 r I f I I T f‘f I I I I I I I I O 2 4 6 8 10 12 14 16 18 Cooling Time (Min.) Fig. 6.25 Effect of heat transfer coefficient on the sumulated temperatures at the top of a fixed bed of pellets. Cooling Oll’ temperature 26.7 C. 20 Moisture Content (2 DB) 137 20.0 CoolIng tIme = 20 mln. Pellet diameter a 4.76 mm Initial moisture content - 20.5 %08 19 0+ Initial pellet temp. - 63.0 C ' Relative humidity - 55% Air velocity - .5 m/s 44> —A 17.0-1 16.0-I e—e Heat transfer coef. - 120 W/MZ K H Heat transfer coef. - 106 W/MZ K 15 O m—e Heat transfer coef. - 80 W/M2 K fl 0.00 10:16 20252 . 30.48 Cooler Depth (cm) Fig. 6.26 Effect of heat transfer coefficient on the simulated moisture content of a fixed bed of pellets. Cooling Cllf' temperature 26.7 C. Temperature (C) 138 lnitial moist.content = 20.5 208 Bed depth a 30.48 cm Pellet diameter = 4.76 mm Air velocity =3 .5 m/s Relative humidity - 55% e—e Mass transfer coef. - .0250 M/l-lr H Mass transfer coef. - .0126 M/l-lr H Mass transfer coef. - .0090 M/l-lr 15.0 I I I I I I I I I T I I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 20 Cooling Time (Min.) Fig. 6.27 Effect of mass transfer coefficient. on the simulated temperatures at the top of a fixed bed of pellets. Cooling aIr temperature 26.7 C. Moisture Content (7. DB) 139 20.0 Cooling time = 20 min. Pellet diameter - 4.76 mm 19 0. Initial moisture content a 20.48 %DB ' lnital pellet temp. = 63.0 C Relative humidity - 55% Air velocity = .5 m/s 18.0- Pi 17.0-1 16.0-I e—e Mass transfer coef. - .0250 M/Hr H Mass transfer coef. - .0126 M/Hr 15 0 H Mass transfer coef. - .0090 M/Hr 0.00 10:16 ' 2052 V 30.48 Cooler Depth (cm) Fig. 6.28 Effect of mass transfer coefficient on the simulated moisture content of a fixed bed of pellets. Cooling Olf’ temperature 26.7 C. Temperature (C) 140 ‘ e—o Specific heat - 2100 J/Kg K Initial moist.content = 20.5 208 Bed depth - 30.48 cm Pellet diameter = 4.76 mm Air velocity = .5 m/s Relative humidity - 55% H Specific heat - Eqn. 3.28 H Specific heat - 1700 J/Kg K I I I I I I I I r 2 4 6 a 1'0 I I I I I I 1'2 ' 14 16 1a 20 Cooling Time (Min.) Fig. 6.29 Effect of specific heat on the simulated temperaturesct the top of a fixed bed of pellets. Cooling air temperature 26.7 C. Moisture Content (‘2'. DB) 141 20.0 CoolIng tIme = 20 mln. Pellet diameter = 4.76 mm Initial moisture content - 20.5 206 19 0‘ Initial pellet temp. = 63.0 C ' Relative humidity =- 55% Air velocity - .5 m/s 170‘ . N 16.0~ o—o Specific heat - 2100 J/Kg K H Specific heat - Eqn. 3.28 15 0 H Specific heat - 1700 J/Kg K 0.00 10T16 1 fl 20:32 ' 30.48 Cooler Depth (cm) Fig. 6.30 Effect of specific heat on the simulated moisture content of a fixed bed of Cpellets. Cooling Oll' temperature 26.7 . 142 moisture content (Equation 3.28), are compared. A small value of the* specific heat results in lower pellet temperature and high moisture content. The effect of the thermal conductivity on the pellet temperature and moisture content is shown in Figures 6.31 and 6.32. Two fixed values (.10 and .17 “In K), and a thermal conductivity value varying with the pellet moisture content (Equation 3.27), were used. The changes in the thermal conductivity neither affects the pellet temperature nor the moisture content significantly. Figures 6.33 and 6.34 show the effects of the bed porosity (.35, .44, and .50) on the pellet temperature and moisture content. In this range of bed porosities, the values of pellet temperature are practically the same; for the moisture content, a lower value of bed porosity results in a slightly lower moisture content. From the analysis in this section it is evident that the parameters that most affect the pellet temperature and moisture content are the pellet density, the heat and mass transfer coefficients, and the specific heat. The exact values of these parameters are not known; the values used in the PDE model are educated guesses. This illustrates the need for fundamental data for pelleted feeds. Temperature (C) 143 75.0 Initial moist.content = 20.5 208 Bed depth - 30.48 cm 55-0 Pellet diameter =- 4.76 mm Air velocity = .5 m/s Relative humidity - 55% 55.0-I J 45.0-1 35.0d 25.0-4 ‘ e—e Thermal conductivity - .17 W/M K H Thermal conductivity =- Eqn. 3.27 15 0 H Thermal conductivity - .10 W/M K ~ I I I I I I I I I I I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 Cooling Time (Min.) Fig. 6.31 Effect of thermal conductivityon the simulated temperaturesat the top of a fixed bed of pellets. Cooling Oll” temperature 26.7 C. Moisture Content (73 08) 20.0 144 19.04 18.0-1 17.0-I 16.0-1 / 15.0 Cooling time = 20 min. Pellet diameter - 4.76 mm Initial moisture content a 20.5 7506 Initial pellet temp. - 63.0 C Relative humidity - 55% Air velocity = .5 m/s e—e Thermal conductivity - .17 W/M K H Thermal conductivity - Eqn. 3.27 m—e Thermal conductivity - .10 W/M K +—-——+ T 0.00 10.16 V —Y V V 20132 Cooler Depth (cm) Fig. 6.32 Effect of thermal conductivity on the Simulated m01s_ture content of a fixed bed of pellets. Cooling Oll‘ temperature 26.7 C. 30.48 Temperature (C) 75. 145 0 Initial moist.content 8 20.5 208 Bed depth - 30.48 cm Pellet diameter a 4.76 mm Air velocity - .5 m/s Relative humidity - 55% ‘ e—e Porosity - .50 H Porosity - .44 m—a Porosity - .35 ' T 0 2 4 6 8 1'0 1'2 1'4 16 1a Cooling Time (Min.) Fig. 6.33 Effect of bed porosity on the simulated temperatures at the top of fixed bed of pellets. Cooling air temperature 26.7 C. Moisture Content (73 DB) 146 20.0 Cooling time = 20 min. Relative humidity . 55% Air velocity = .5 m/s Pellet diameter - 4.76 mm 19 0‘ Initial moisture content = 20.5 %DB ' Initial pellet temp. - 63. 0C 18.0j f 17.0~ 16.0-I e—e Porosity - .50 H Porosity - .44 G—O ' I- . 1 5' O jPorosity 35 a V 0.00 10:16 20252 Cooler Depth (cm) 30.48 Fig. 6.34 Effect of bed porosity on the simulated moisture content of a fixed bed of Cooling air temperature 26.7 . ellets. 147 6.4 - Effects of Air Temperature, Relative Bumidty, Air Velocity, Pellet Initial Moisture Content and Temperature, and Pellet Diameter Table 6.10 shows the range of the inputs to the PDE model. The parameter values shown in Table 6.8 were used in this analysis. Table 6.10 - Input Values to the Simulation PDE Model of a Fixed-Bed of Pellets Cooler. Cooling air temperature (C) 21.1, 26.7, 32.2 Relative humidity (X) 40, 55, 70 Air velocity (m/s) .5, .75 Initial pellet temperature (C) 48.9, 62.7, 71.1 Initial pellet moisture content (% DB) 16.3, 20.5 Pellet diameter (mm) 4.76, 6.35 MW: 1 30. 46 Figures 6.35 and 6.36 ilustrate the effect of the cooling air temperature on the pellet temperature and moisture content. A lower inlet air temperature results in faster cooling and a lower final temperature of the pellets, and in a higher moisture content. The effect of relative humidity is shown in Figures 6.37 and 6.38. The higher relative humidities result in slightly higher pellet temperatures, but greatly affect the moisture content. For example, at the bottom of the cooler after 20 minutes of cooling, the moisture content is 16.5% DB at 402 relative humidity and 16.5% DB at 70%. At the top the difference in moisture content is about 1% and 22 at the bottom of the bed. The difference is smaller at the top of Temperature (C) 148 75.0 65.0 55.0-1 45.0- 35.04 25.0n ‘ H Cooling air temp.- 26.7 C 15.0 0 Relatlve humldlty = 55% Air velocity = .5 m/s Bed depth - 30.48 cm Pellet diameter = 4.76 mm Initial moisture content 8 20.5 %DB I '1 '4 It I: '4' V I1 I. I l l I I e—e Cooling air temp.- 32.2 C a '1 H II II II II II I o—e Cooling air temp.- 21.1 C I I I If I I I 2 4 6 6 1'0 Cooling Time (Min.) f I 7 T F I 12 . 1'4 . 16 1a 20 Fig. 6.35 Effect of cooling air temperature on the simulated temperatures at the top of a fixed bed of pellets. Moisture Content (2 DB) 149 20.0 Cooling time = 20 min. Pellet diameter - 4.76 mm 19 0‘ Initial moisture content = 20.5 208 ' Air velocity 8 .5 m/s Initial pellet temp. - 65.5 C 180$— iir n :4 17.0 16.0-I e—e Cooling air temp. - 32.2 C H Cooling air temp. - 26.7 C 15 0 a—e CoolinLair temp. - 21.1 C . . . . , . , . e . 0.00 10.16 20.32 30.48 Cooler Depth (cm) Fig. 6.36 Effect of cooling air tem erature on the simulated moisture con ent of a fixed bed of pellets. Temperature (C) 75.0 150 65.0 55.0- 45.04 35.04 25.0~ ‘ H Relative humidity - 55% Initial moist.content =3 20.5 208 Bed depth - 30.48 cm Pellet diameter a 4.76 mm Air velocity =- .5 m/s e—e Relative humidity - 70% 15.0 0 H Relative humidity - 40% ' I V T Y 1 fir T f Y 2 4 6 8 1'0 {2% 14 16 18 20 Cooling Time (Min.) Fig. 6.37 Effect of relative humidit. on the simulated temperatures at the top of 1xed bed of pellets. Cooling air temperature 26.7 C. Moisture Content (73 DB) 151 20.0 Initlal pellet temp. = 63.0 C Cooling time = 20 min. Pellet diameter - 4.76 mm 19 0— Initial moisture content a 20.48 %DB ' Air velocity 8 .5 m/s <6— 9 A 17.0n 16.0- o—e Relative humidity - 70% H Relative humidity - 55% 15 O B—O Relative humidity- 40% // r 0.00 10.16 V I 20.32 30.48 Cooler Depth (cm) Fig. 6.38 Effect of relative humidity on the sumulated moisture content of a fixed bed of pellets. Cooling 01r temperature 26.7 C. 152 the cooler than at the bottom because the air is heated by the pellets as it passes through the bed thereby increasing its drying potential. Figures 6.39 and 6.40 show the effect of the air velocity on pellet temperature and moisture content. As expected, the higher air flow results in more rapid cooling. However, the faster cooling results in less pellet drying in 20 minutes. The inlet pellet temperature effect is illustrated in Figures 6.41 and 6.42. Only during the first 10 minutes there is a difference in the pellet temperatures. After 10 minutes the pellet temperatures at the top of the bed have reached about the same temperature. The moisture content of the pellets is lower for the higher initial pellet temperature due to the dependence of pellet diffusivity on the pellet temperature. Figures 6.43 and 6.44 show the effect of the initial pellet moisture content after 20 minutes cooling. The pellet temperature is not greatly affected in this range of initial moisture content. After 20 minutes of cooling the pellets with an initial moisture content of 20.5% DB at the bottom of the cooler had lost two percentage points while the pellets with 16.3% DB had lost only 1%. The diameter of the pellets significantly affects the cooling rate as illustrated in Figures 6.45 and 6.46. As expected, the smaller diameter pellets cool faster than the larger ones. The moisture content of the small pellets is lower at the bottom of the cooler where the temperature of Temperature (C) 75.0 153 65.0 55.04 45.04 35.04 25.04 h ‘ - ‘ - ‘ ‘ H M ‘ H Air velocity - .75 m/s 15.0 a—e Air velocity - .5 m/s ' T fi T ' T ' U '1 Initial molsture content = 20.5 208 Relative humidity 1: 55% Bed depth - 30.48 cm Pellet diameter a 6.35 mm M M M 0 Y Y I I I I I 2 4 5 8 10 12 14 Cooling Time (Min.) Fig. 6.39 Effect of air velocity on the simulated temperatures at the top of fixed bed of pellets. Cooling air temperature 26.7 C. Moisture Content (7. DB) 154 20.0 CoolIng tIme = 20 mln. Pellet diameter a 6.35 mm Initial moisture content - 20.48 %DB Relative humidity I 55% 19 0 Initial pellet temp. - 63.0 C 18.04 17.04 H Air velocity - .75 m/s 16 O H Air velocity - .5 ml: 20.32 . 30.48 Cooler Depth (cm) 0.00 10:16 Fig.6.40 Effect of air velocity on the simulated moisture content of a fixed bed of ellets. Cooling Oll‘ temperature 26.7 . Temperature (C) 155 75.0 4 I.‘ :1 Initial moist.content I- 20.5 208 5 Bed depth - 30.48 cm 5 0‘ k. Pellet diameter a 4.76 mm ' Air velocity - .5 m/s 4 a Relative humidity - 55% 55.04 n I: 3 a 45.04 ° 3 9\ 35.04 ° .~ _ -\. * 1\\. :\-\ 25.04 ‘\;§2:~-._,___ __ a-— . e—e Initial pellet temp. - 46.9 C - - H Initial pellet temp. - 62.7 C H Initial pellet temp. - 71.1 C 15-0 I I I I I I I 17 I I I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 20 Cooling Time (Min.) Fig. 6.41 Effect of initial pellet temperature on the simulated temperatures at the top of a fixed bed of pellets. Cooling air temperature 26.7 C. Moisture Content (75 DB) 156 20.0 CoolIng tIme = 20 mln. Pellet diameter = 4.76 mm Initial moisture content - 20.5 %08 19 04 Air velocity = .5 m/s ' Relative humidity - 55% 17.04 16.0-I e—e Initial pellet temp. - 48.9 C H Initial pellet temp. = 62.7 C 15 O H Initial pellet temp. - 71.1 C 0.00 10:16 ' ' 20i32 ' 30.46 Cooler Depth (cm) Fig. 6.42 Effect of intial pellet temperature on the simulated moisture content of a fixed bed of pellets. Cooling air temperature 26.7 C. Temperature (C) 157 75.0 4 Pellet diameter = 4.76 mm Bed depth - 30.48 cm 55-0‘ Relative humidty =- 55% Air velocity =3 .5 m/s 55.04 1 45.04 d 35.04 25.04 ‘ e—e Initial moist.content - 16.3 %06 H Initial moist.content - 20.5 %09 15.0 v I T I I I I 77' I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 Cooling Time (Min.) Fig.6.43 Effect of initial pellet moisture content on the simulated tem eratures at the to fixed bed of pellets. ofa ooling air temp. 2 .7 C. Moisture Content (2 DB) 158 20.0 Cooling time = 20 min. . Pellet diameter I 4.76 mm 1901 Initial pellet temp. I 63.0 C Air velocity I .5 m/s Relative humidity - 55% 18.0"1 a j 17.0-I 16.04 wag—‘3 : 4P H Initial moisture content I 20.48 %09 H Initial moisture content - 16.3 %DB 14.0 . . . , v f r . . 0.00 10.16 20.32 30.48 Cooler Depth (cm) Fig. 6.44 Effect of initial pellet moisture content on the simulated moisture content of a fixed bed of pellets. Cooling 01r temp. 26.7 C. Temperature (C) 75.0 159 65.04 55.04 45.04 35.04 25.04 5‘ 5‘ v I.‘ 5‘ '4 ‘ H Diameter I 6.35 mm H Diameter I 4.76 mm Initial moist.content = 20.5 208 Bed depth - 30.48 cm Relative humidty = 55% Air velocity I .5 m/s '4 '1 h II II II 15.0 0 V Y ' T r 2 4 03-4 T j I 8 10 T 12 14 16 16 Cooling Time (Min.) Fig. 6.45 Effect of pellet diameter on the S1mulated tem erotures at the top of a fixed bed of pellets. ooling air temperature 26.7 C. 20 Moisture Content (73 DB) 20.0 160 19.0 18.0q 17.0-1 16.0-1 15.0 Mai/j H Pellet diameter - 6.35 mm H Pellet diameter - 4.76 mm Cooling time = 20 mln. Relative Humidity = 55% Initial moisture content - 20.5 %08 Air velocity = .5 m/s lnitiol pellet temp. - 63.0 C V? f 0.00 10.16 1 Y 20:32 Cooler Depth (cm) Fig. 6.46 Effect a simulated moisture f pellet diameter on the content of a fixed bed of pellets. Cooling air temperature 26.7 C. 30.48 161 the small pellets equilibrates faster with the cooling air. At the top the larger diameter pellets have a low moisture content because they are about 20 C warmer than the small ones. Figures 6.4? and 6.46 illustrate the temperature and moisture content gradients within a 4.76 mm and 6.35 mm diameter pellet, respectively. The figures show that the temperature gradients inside the pellets are negligible. The pellet temperatures at the top of the bed are lower than at the bottom due to evaporative cooling (see also Figure 6.15). The moisture content gradients within the pellets at the bottom of the bed are significant due to the higher temperatures and lower relative humidities at the bottom. Figure 6.48 shows that for the larger pellets (6.35 mm diameter) there is a significant moisture content gradient inside the pellets at the bottom and at the top of the bed during the cooling process. As shown in Figure 6.45, larger pellets cool slower than smaller pellets and have a higher temperature; this results in dryer pellets with a higher moisture content gradient at the top of the bed. From the analysis in this section, it can conclude that the cooling air temperature and velocity, and the pellet diameter are the parameters that have a significant effect on the pellet temperature and moisture content; also that the relative humidity has a significant effect only on the pellet moisture content. Thus, these parameters should be measured accurately when performing a deep-bed cooling test. Temperature (C) 162 40.0 22.0 35.04 -20.D + 30.0 . 18.0 25.0-4 \ 16.0 E ‘3 S E} 3 Cooling time =- 20 min. 20-0“ Air temperature - 26.7 C "4'0 Relative humidity - 55% Initial moisture content - 20.5 7:08 lnitial pellet temp. = 63.0 C 15.0-1 Alr velocity - .5 m/s -12.0 H Pellet temp. at top H MC top 10 0 o—e Pellet temp. at bottom H MC bottom . I T T T 0.0 0.5 1.0 1.4 1.9 2.4 Pellet radius, centre to surface (mm) Fig. 6.47 Simulated temperature and moisture content gradients Wlthll‘l a pellet. Pellet diameter 4.76 mm. (30%) tuatuog aJmsiom Temperature (C) 163 50.0 22.0 45,0 "—U‘M ~20.0 40.0-1 ~18.D 35.0— ~16.D 300‘ e e e c e e = ”'0 25'0—7 Cooling time - 20 min. Air temperature - 26.7 C Relative humidity = 55% M2-0 20-0“ Initial moisture content - 20.5 %08 Initial pellet temp. 7 63.0 C Air velocity - .5 m s 15.0-4 10.0 a—e Pellet temp. at top H MC top 10 0 o—e Pellet temp. at bottom H MC bottom ' l T l l l l 0.0 0.5 0.9 1.4 1.8 2.3 2.7 3.2 Pellet radius, centre to surface (mm) Fig. 6.48 Simulated temperature and moisture content gradients Within a pellet. Pellet diameter 6.35 mm. (80%) lUGlUOO 91111810111 7 - SUMMARY AND CONCLUSIONS The summary and conclusions of this study of deep-bed cooling of pellets are: 1. Thin-layer drying tests of feed pellets were conducted at 15.6 to 43.3 C (60 to 110 F), 40 to 70% relative humidity, and 16.1 to 19.1% DB moisture content. 2. The Chung-Pfost equilibrium. moisture content equation for pellets best represents the equilibrium moisture content data. 3. An Arrhenius-type equation adequately describes the effect of temperature on the diffusion coefficient of feed pellets. 4. The heat and mass balance (HMB) and the partial differential (PDE) models for the cooling of pellets in a horizontal-belt cooler are both in acceptable agreement with the experimental data. 5. The PD! model requires between three to five minutes execution time on the IBM-AT, about ten times as long as the HUB model, to simulate one minute of cooling, but is more accurate than the HBH model. 164 10. 165 The cooling- air temperature and velocity significantly affect the final pellet temperature and moisture content in a horizontal-belt pellet cooler. The relative humidity only slightly affects the pellet temperature but significantly influences the pellet moisture content in a horizontal-belt pellet cooler. The pellet diameter greatly affects the cooling and drying rate of feed pellets in a horizontal-belt pellet cooler. The sensitivity analysis of the horizontal-belt pellet cooler model shows that the initial pellet moisture content has a minor influence on the final pellet temperature; however, the initial pellet temperature has a significant influence on the final pellet moisture content. The heat transfer coefficient, the specific heat, and density are the pellet properties significantly affecting the final pellet temperature and moisture content in a horizontal-belt pellet cooler. 8 - SUGGESTIONS FOR FUTURE RESEARCH Additional research remains to be carried out in the following areas: 1. To develop the equilibrium moisture content for different feed-pellet types. 2. To evaluate the dependence of pellet moisture content and density on the feed-pellet diffusion coefficient. 3. To determine the heat and mass transfer coefficients, the specific heat, and the thermal conductivity of different types of feed-pellets. . 4. To investigate the horizontal-belt cooling of different pellet types. 5. 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Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 71.4 71.5 72.3 71.8 71.6 72.8 72.6 1 29.6 47.0 52.0 54.3 57.6 60.4 82.4 2 28.8 38.5 43.7 45.5 48.3 50.6 52.1 3 26.9 33.8 38.6 40.4 42.7 44.6 45.9 4 25.4 30.6 34.7 36.8 39.0 40.6 41.6 5 24.3 28.1 31.8 33.7 35.8 37.4 38.6 6 23.6 26.1 29.2 31.1 33.2 34.6 35.8 7 23.2 24.6 27.1 28.9 30.9 32.3 33.4 8 22.6 23.4 25.6 27.2 29.1 30.5 31.6 9 22.4 22.6 24.2 25.6 27.4 28.7 29.8 10 22.0 21.8 23.1 24.2 25.6 27.1 28.2 11 21.7 21.3 22.2 23.2 24.6 25.9 26.9 12 21.6 21.0 21.6 22.3 23.6 24.8 25.8 13 21.4 20.7 21.0 21.6 22.7 23.6 24.7 14 21.2 20.4 20.6 21.1 22.0 22.9 23.8 15 21.2 20.2 20.2 20.6 21.3 22.2 23.1 16 21.2 20.2 20.1 20.3 20.9 21.6 22.4 17 21.2 20.1 19.9 20.1 20.5 21.1 21.8 18 21.1 20.1 19.7 19.8 20.2 20.7 21.3 19 21.1 20.1 19.7 19.7 19.9 20.3 20.9 20 21.1 20.1 19.7 19.6 19.8 20.2 20.6 Initial moisture content 2 20.7 %DB Pellet diameter = 4.76 mm, Pellet density = 945 Kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth = 30.48 cm 175 176 Test 2 Table A.2 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 21.1 C, RH 55$, Air Velocity .1 m/s. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 62.2 62.8 62.5 63.2 63.4 63.9 63.7 1 28.1 51.2 54.2 58.6 60.3 62.3 64.0 2 25.7 41.7 45.1 49.6 53.5 56.1 58.4 3 25.9 36.5 39.9 43.6 47.3 50.2 52.3 4 25.5 33.4 36.4 39.6 42.8 45.3 47.6 5 24.8 31.3 34.1 36.8 39.6 41.9 43.7 6 24.0 29.5 32.2 34.5 37.0 39.1 40.6 7 23.4 28.0 30.5 32.6 34.9 36.7 38.1 8 23.0 26.7 29.1 31.1 33.2 34.8 36.1 9 22.7 25.6 27.8 29.8 31.7 33.2 34.4 10 22.3 24.6 26.6 28.5 30.2 31.6 32.8 11 22.1 23.7 25.6 27.4 29.1 30.3 31.4 12 21.9 23.1 24.8 26.5 28.0 29.3 30.3 13 21.7 22.5 24.1 25.7 27.1 28.2 29.2 14 21.6 22.0 23.3 24.9 26.3 27.3 28.2 15 21.5 21.6 22.8 24.2 25.4 26.4 27.3 Initial moisture content = 20.7 %DB Pellet diameter = 4.76 mm, Pellet density = 945 kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth = 30.48 cm 177 Test 5 Table A.3 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 32.2 C, RH 55%, Air Velocity .5 m/s. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 D 71.2 73.7 73.3 72.4 71.6 73.4 73.3 1 36.8 51.3 54.8 56.4 59.1 62.1 64.0 2 34.9 42.6 46.2 47.0 49.4 52.3 53.9 3 33.9 38.0 41.2 42.7 43.9 46.3 47.8 4 33.2 35.4 38.1 39.6 40.5 42.4 43.7 5 32.9 33.6 35.7 37.1 37.6 39.6 40.6 6 32.8 32.6 33.9 35.2 35.9 37.4 38.3 7 32.7 32.0 32.8 33.9 34.6 35.7 36.6 8 32.6 31.4 32.0 32.8 33.3 34.3 35.1 9 32.8 31.3 31.5 32.1 32.4 33.3 33.9 10 32.8 31 2 31.1 31.4 31.8 32.5 33.1 11 32.9 31.2 30.8 31.1 31.3 31.9 32.4 12 33.0 31.1 30.7 30.8 30.9 31.3 31.7 13 33.0 31.2 30.6 30.5 30.6 30.9 31.3 14 33.0 31.2 30.5 30.3 30.3 30.6 30.9 15 33.0 31.3 30.5 30.3 30.2 30.4 30.6 16 33.0 31.3 30.4 30.1 30.0 30.2 30.4 17 33.1 31.4 30.4 30.1 30.0 30.1 30.2 18 33.1 31.4 30.4 30.0 29.9 29.8 30.0 19 33.2 31.4 30.4 29.9 29.7 29.7 29.9 20 33 0 31.4 30.5 29.9 29.7 29.6 29.7 Initial moisture content = 19.1 %DB Pellet diameter = 4.76 mm, Pellet density = 945 Kg/m3 Pellet bulk density = 673Kg/m3, Bed depth = 30.48 cm 178 Test 6 Table A.4 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 32.2 C, RH 552, Air Velocity .1 m/s. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 65.3 65.3 67.5 67.8 67.9 68.4 68.2 1 36.7 50.8 56.2 60.5 63.2 65.4 67.1 2 34.5 42.7 47.4 50.9 54.8 57.6 59.9 3 33.8 38.7 42.7 45.3 48.7 51.4 53.7 4 33.6 36.2 39.7 41.9 44.6 47.0 49.2 5 33.3 34.7 37.4 39.3 41.5 43.6 45.6 6 33.2 33.6 35.8 37.3 39.2 40.9 42.8 7 33.1 32.7 34.5 35.8 37.3 39.0 40.6 8 32.9 32.1 33.4 34.7 35.9 37.4 38.8 9 32.8 31.7 32.7 33.7 34.7 36.2 37.4 10 32.8 31.3 32.1 33.0 33.8 35.0 36.2 11 32.7 31.1 31.5 32.3 33.1 34.2 35.2 12 32.6 30.9 31.1 31.8 32.4 33.4 34.4 13 32.6\ 30.7 30.7 31.3 31.9 32.7 33.6 14 32.5 30.5 30.3 30.9 31.4 32.1 32.8 15 32.7 30.5 30.1 30.4 30.8 31.8 32.2 16 32.8 30.6 30.0 30.3 30.7 31.3 31.9 17 32.8 30.5 29.8 30.1 30.4 30.9 31.4 18 32.9 30.5 29.6 29.6 30.1 30.6 31.1 19 32.9 30.5 29.6 29.7 29.9 30.4 30.8 20 32.8 30.5 29.4 29.4 29.7 30.1 30.5 Initial moisture content 2 19.1 XDB Pellet diameter = 4.76 mm, Pellet density = 945 Kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth = 30.48 cm 179 Test 7 Table A.5 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 17.7 C, RH 70%, Air Velocity .5 m/s. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 D 67.6 70.0 70.5 69.4 66.5 70.2 70.9 1 23.2 44.5 50.6 52.6 55.3 57.1 59.2 2 23.8 35.3 41.9 44.9 47.1 48.6 50.3 3 22.6 30.2 36.0 39.6 41.6 42.9 44.3 4 21.4 27.1 31.9 35.5 37.6 39.1 40.3 5 20.3 24.8 28.6 32.1 34.5 36.0 37.3 6 19.7 23.1 26.4 29.5 31.6 33.3 34.7 7 19.3 21.5 24.3 27.2 29.3 31.0 32.3 8 19.0 20.3 22.7 25.2 27.2 28.9 30.3 9 18.7 19.4 21.4 23.6 25.5 27.2 28.7 10 18.4 18.7 20.2 22.2 23.8 25.6 27.0 11 18.2 18.2 19.3 21.0 22.4 24.1 25.6 12 18 1 17.7 18.6 20.0 21.3 22.7 24.2 13 17 9 17.4 18.1 19.2 20.4 21.7 23.1 14 17 8 17.2 17.7 18.6 19.5 20.7 22.1 15 17 6 16.9 17.2 17.9 18.8 19.8 21.1 16 17 4 16.8 16.9 17.5 18.2 19.1 20.2 17 17 3 16.6 16.7 17.1 17.7 18.5 19.5 18 17 2 16.6 16.6 16.9 17.3 18.1 18.9 19 17 2 16.4 16.3 16.6 17.0 17.6 18.4 20 17 1 16.3 16.3 16.4 16.7 17.3 17.9 Initial moisture content 2 19.6 XDB Pellet diameter = 4.76 mm, Pellet density = 945 Kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth = 30 180 Test 8 Table A.6 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 17.7 C, RH 70%, Air Velocity .1 m/s. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 60.3 61.2 60.0 61.6 62.4 62.4 62.6 1 23.9 45.3 50.1 53.3 56.4 58.3 59.3 2 22.4 36.6 42.9 45.8 49.1 51.5 52.5 3 22.4 31.9 38.6 41.4 44.2 46.4 47.6 4 21.9 28.8 35.1 38.1 40.5 42.4 43.7 5 21.2 26.7 32.4 35.4 37.6 39.4 40.6 6 20.4 25.1 30.1 33.2 35.3 36.9 38.2 7 19.8 23.7 28.2 31.3 33.4 34.9 36.2 8 19.4 22.5 26.6 29.6 31.6 33.1 34.4 9 19.1 21.5 25.2 28.1 30.1 31.6 32.8 10 18.7 20.6 24.1 26.8 28.8 30.3 31.4 11 18.5 20.0 22.9 25.6 27.5 28.9 30.1 12 18.2 19.3 21.9 24.5 26.3 27.7 28.9 13 18.1 18.8 21.1 23.4 25.3 26.7 27.8 14 17.9 18.4 20.3 22.6 24.3 25.8 26.9 15 17.8 18.0 19.7 21.7 23.4 24.8 26.0 16 17.7 17.7 19.1 21.1 22.6 23.9 25.1 17 17.5 17.4 18.7 20.3 21.6 23.1 24.3 18 17.4 17.2 18.2 19.8 21.2 22.4 23.5 19 17.2 17.0 17.9 19.3 20.6 21.8 22.9 20 17.1 16.7 17.5 18.8 20.1 21 2 22.2 Initial moisture content 2 19.6 XDB Pellet diameter = 4.76 mm, Pellet density = 945 Kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth: 30. 48m 181 Test 9 Table A.7 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 21.1 C, RH 70%, Air Velocity .5 m/s. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 61.1 62.4 64.4 63.9 62.1 64.6 64.6 1 26.7 46.8 50.4 51.9 54.4 56.4 57.9 2 24.5 37.4 42.8 44.5 46.8 48.3 49.6 3 23.9 32.1 37.8 40.1 41.6 42.8 43.9 4 23.5 28.8 33.8 36.4 38.1 39.1 40.1 5 23.3 27.1 30.9 33.6 35.3 36.4 37.3 6 23.2 26.1 29.1 31.6 33.3 34.2 35.2 7 23.0 25.3 27.7 29.6 31.4 32.4 33.3 8 22.9 24.8 26.7 28.5 29.9 31.0 31.8 9 22.8 24.3 26.1 27.4 28.8 29.7 30.6 10 22 8 24.1 25.6 26.8 28.0 28.8 29.6 11 22.8 23.9 25.2 26.3 27.3 28.0 28.8 12 22.7 23.7 24.6 25.8 26.7 27.3 28.0 13 22.7 23.5 24.5 25.4 26.2 26.7 27.4 14 22.6 23.4 24.3 25.2 25.9 26.4 27.1 15 22.6 23.3 24.2 24.9 25.6 26.1 26.6 16 22.6 23.3 24.0 24.7 25.3 25.8 26.3 17 22.6 23.2 23.9 24.6 25.2 25.5 26.0 18 22.6 23.1 23.8 24.4 25.0 25.3 25.8 19 22.5 23.1 23.7 24.3 24.8 25.1 25.6 20 22 6 23.0 23.6 24.2 24.7 25.1 25.4 Initial moisture content = 19.8 XDB Pellet diameter = 4.76 mm, Pellet density = 945 Kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth = 30.48 cm 182 Test 10 Table A.8 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 21.1 C, RH 70%, Air Velocity .1 m/s. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 58.5 58.7 58.4 58.4 58.6 59.9 59.1 1 26.9 46.4 50.8 53.2 55.8 57.1 58.3 2 24.9 38.9 43.7 46.4 49.9 52.1 54.1 3 24.4 34.2 39.1 41.7 44.8 47.1 48.9 4 24.3 31.3 35.8 38.4 41.0 43.1 44.8 5 24.1 29.5 33.5 36.0 38.3 40.2 41.8 6 24.1 28.2 31.7 34.0 36.1 37.8 39.3 7 23.9 27.4 30.3 32.5 34.3 35.7 37.5 8 23.7 26.7 29.2 31.3 32.8 34.1 35.5 9 23.7 26.2 28.4 30.3 31.7 32.9 34.2 10 23.6 25.8 27.7 29.3 30.6 31.7 32.9 11 23.6 25.6 27.3 28.7 29.8 30.8 31.9 12 23.5 25.3 26.8 28.1 29.1 30.0 30.9 13 23.4 25.1 26.5 27.7 28.6 29.3 30.3 14 23.3 24.8 26.1 27.3 28.0 28.7 29.6 15 23.3 24.7 25.9 26.9 27.6 28.2 29.0 16 23.3 24.4 25.7 26.6 27.2 27.8 28.5 17 23.3 24.4 25.5 26.3 26.9 27.4 28.2 18 23.2 24.3 25.3 26.1 26.7 27.2 27.7 19 23.2 24.2 25.1 25.9 26.4 26.9 27.4 20 23 2 24.1 24.9 25.8 26.2 26.6 27.1 Initial moisture content = 19.8 %DB Pellet diameter = 4.76 mmn Pellet density = 945 Kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth: 30. 48a 183 Test 11 Table A.9 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 26.7 C, RH 70%, Air Velocity .5 m/s. Cooling Cooler Depth (cm) (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 64.8 67.1 66.4 65.2 65.1 65.5 64.4 1 30.4 46.2 50.9 55.1 57.9 60.2 62.1 2 28.8 38.1 42.6 45.9 47.8 51.8 53.3 3 28.1 33.9 38.2 40.7 42.0 45.6 46.9 4 27.6 31.8 35.3 37.7 38.6 41.3 42.7 5 27.2 30.6 33.4 35.4 36.2 38.3 39.4 6 26.9 29.7 32.1 33.8 34.4 36.1 37.1 7 26.7 29.1 31.2 32.7 33.3 34.6 35.4 8 26.7 28.8 30.5 31.8 32.3 33.3 34.0 9 26.6 28.4 29.9 31.2 31.6 32.3 32.9 10 26.6 28 1 29.6 30.7 31.1 31.6 32.1 11 26.6 27.9 29.3 30.3 30.7 31.1 31.5 12 26.5 27.8 29.1 30.0 30.3 30.7 31.1 13 26.6 27.6 28.8 29.7 30.1 30.3 30.6 14 26.6 27.5 28.9 29.5 29.8 30.0 30.3 15 26.6 27.4 28.4 29.3 29.6 29.8 30.0 16 26.6 27.3 28.3 29.2 29.4 29.6 29.8 17 26.6 27.3 28.2 28.9 29.3 29.4 29.6 18 26.6 27.2 28.2 28.8 29.2 29.3 29.4 19 26.6 27.2 28.2 28.8 29.2 29.3 29.4 20 26 6 27.1 27.9 28.6 28.9 29.1 29.2 Initial moisture content 2 20.5 %DB Pellet diameter = 4.76 mm, Pellet density = 945 Kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth 2 30.48 cm 184 Test 12 Table A.10 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 26.7 C, RH 70%, Air Velocity .1 m/s. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 D 58.3 59.7 59.7 59.5 60.6 61.5 61.4 1 31.4 47.4 53.3 56.6 58.1 59.5 61.4 2 29.1 39.7 45.3 49.4 52.3 54.8 57.9 3 28.5 35.8 40.3 44.1 47.1 49.8 53.4 4 28.1 33.7 37.2 40.4 43.1 45.7 49.4 5 27.8 32.3 35.1 37.7 40.1 42.4 45.8 6 27.5 31.4 33.6 35.7 37.8 39.7 42.8 7 27.2 30.7 32.6 34.2 35.9 37.7 40.6 8 27.3 30.2 31.9 33.2 34.7 36.1 38.6 9 27.1 29.8 31.3 32.4 33.6 34.7 36.9 10 27.3 29.6 30.8 31.7 32.7 33.8 35.7 11 27.3 29.3 30.5 31.2 31.9 32.9 34.5 12 27.3 29.2 30.2 30.9 31.4 32.2 33.6 13 27.2 28.9 30.0 30.5 31.1 31.7 32.9 14 27.0 28.7 29.7 30.3 30.7 31.3 32.3 15 26.8 28.4 29.5 30.0 30.3 30.9 31.7 Initial moisture content = 20.5 XDB Pellet diameter = 4.76 mm, Pellet density = 945 Kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth: 30. 48a 185 Test 13 Table A.11 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 21.1 C, RH 55%, Air Velocity .1 m/s. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 68.7 69.8 68.5 69.2 68.7 68.8 71.4 1 29.4 52.6 64.3 65.2 67.9 68.2 69.2 2 26.1 42.5 55.2 62.4 63.8 65.3 67.8 3 25.7 36.9 47.8 55.9 57.9 60.2 63.8 4 25.4 33.8 42.4 50.4 52.8 55.3 59.3 5 24.8 31.7 38.2 45.4 47.9 50.7 54.7 6 24.3 30.2 35.2 41.6 44.1 46.8 50.9 7 23.7 29.0 32.9 38.5 40.7 43.4 47.3 8 23.2 28.0 31.3 36.1 38.2 40.8 44.4 9 22.7 27.0 30.0 34.0 36.0 38.5 41.7 10 22.3 26.0 28.8 32.4 34.1 36.4 39.4 11 21.9 25.1 27.7 31.0 32.6 34.7 37.4 12 21.7 24.3 26.8 29-8 31.2 33.3 35.7 13 21.4 23.6 26.0 28.7 29.9 31.9 34.2 14 21.2 22.9 25.2 27.7 28.9 30.7 32.8 15 21.2 22.5 24.5 26.9 28.0 29.7 31.8 16 21.1 22.1 23.9 26.1 27.1 28.7 30.7 17 20.9 21.7 23.4 25.4 26.3 27.8 29.6 18 21.1 21.3 22.8 24.8 25.6 27.3 28.8 19 21.1 21.1 22.4 24.2 24.9 26.3 28.0 20 21.1 20.8 22.1 23.7 24.3 25.7 27.2 Initial moisture content 2 18.1 XDB Pellet diameter = 4.76 mm, Pellet density = 945 Kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth 2 30.48 cm 186 Test 14 Table A.12 - Experimental Values of the Air Temperatures Between the Pellets (C) in a Deep-Bed Cooling Test. Cooling Air Temperature 21.1 C, RH 55%, Air Velocity .5 m/s. Cooling Cooler Depth (cm) Time (min) 0.00 5.08 10.16 15.24 20.32 25.40 30.48 0 62.2 63.3 63.3 63.7 63.6 63.5 63.8 1 27.6 45.3 52.8 58.4 62.3 60.8 62.6 2 27.1 36.7 42.0 47.4 53.2 52.9 54.7 3 26.3 33.2 36.9 40.8 45.6 46.1 47.7 4 24.8 30.5 33.5 36.4 39.9 40.9 42.2 5 24.0 28.4 31.1 33.4 36.2 37.3 38.4 6 23.4 26.5 29.1 31.1 33.5 34.5 35.6 7 22.9 25.1 27.4 29.3 31.3 32.4 33.3 8 22.4 23.8 25.9 27.6 29.4 30.4 31.3 9 22.2 22.8 24.7 26.3 27.8 28.7 29.6 10 21.9 22.1 23.7 25.2 26.5 27.4 28.2 11 21.6 21.5 22.8 24.3 25.4 26.3 27.0 12 21.4 20.9 22.1 23.3 24.5 25.2 25.9 13 21.3 20.6 21.5 22.7 23.7 24.3 24.9 14 21.3 20.3 21.2 22.2 23.0 23.6 24.3 15 20.9 20.1 20.6 21.6 22.3 22.9 23.4 Initial moisture content : 18.1 XDB Pellet diameter = 4.76 mm, Pellet density = 945 Kg/m3 Pellet bulk density = 673 Kg/m3, Bed depth = 30.48 cm 187 Table A.13 - Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow rates. Air Temperature 21.1 C, RH 55%. Tests 1 and 2. Air Velocity = .5.g[s .1 gig Cooler Cooling Time (min) _.._Depth_icml 10 15 120 15 Bottom 18.5 18.3 17.8 18.2 10.16 17.4 17.4 17.0 17.6 20.32 17.2 17.1 17.0 17.9 30.48 16.3 17.2 16.9 17.8 Average 17-6 17-5 17.2 17L9 Initial moisture content 2 20.7 %DB Table A.14 - Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow rates. Air Temperature 32.2 C, RH 55%. Tests 5 and 6. _Air_!elacitz_a_i§uals .laaés____. Cooler Cooling Time (min) Depth (99) 10 15 20 15 i_20 Bottom 16.2 15.9 15.4 16.2 15.8 10.16 16.3 16.0 15.8 16.4 16.0 20.32 16.3 16.1 15.9 16.7 16.0 30.48 16.3 16.1 16.0 17.1 16.2 _._Axerase 16.3 16.0 1518 16-6 16.0 Initial moisture content = 19.1 XDB Table A.15 - Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow rates. Air Temperature 17.7 C, RH 70%. Tests 7 and 8. sAir_!elagitz_i_i§Ja45 .1 ate Cooler Cooling Time (min) ___.Dsnihiigm1 ID 15 20 29 Bottom 18.6 18.1 17.4 18.0 10.16 17.5 17.1 16.9 17.5 20.32 16.8 16.4 16.1 17.2 30.48 16.8 16.6 15.9 17.4 -____Axerase 1714 1710 16.6 17.5 Initial moisture content 2 19.6 %DB 188 Table A.16 - Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow rates. Air Temperature 21.1 C, RH 70%. Tests 9 and 10. Air Velocity = .5 gig .1151s Cooler Cooling Time (min) _.Denth_lcn1 10 15 20 15 29 Bottom 19.0 18.9 18.9 18.7 18.7 10.16 17.8 18.0 17.9 17.7 17.5 20.32 17.3 17.2 17.2 17.6 17.2 30.48 17.1 16.9 16.9 18.1 17.3 Averflzo 11.8 1718 1717 1810 17.7 Initial moisture content = 19.8 XDB Table A.17 - Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow rates. Air Temperature 26.7 C, RH 70X. Tests 11 and 12. Air Velocity = .5 mls 11 ml; Cooler Cooling Time (min) ___.Denth_icai 10 15 .20 15 Bottom 18.9 19.1 19.2 18.8 10.16 18.0 17.7 17.7 18.0 20.32 17.8 17.6 17.5 17.9 30.48 17.6 17.4 17.3 18.3 Average 1811 17.9 17.9 18.3 Initial moisture content = 20.5 XDB Table A.18 - Experimental Values of Moisture Content (%DB) within a Fixed-Bed of Pellets Cooled at Two Airflow rates. Air Temperature 21.1 C, RH 55:. Tests 13 and 14. .Air.!elgsitz_a.ilun45 -igaés Cooler Cooling Time (min) _.__Dnnth_icml 10 15 20 15 Bottom 16.0 15.7 15.6 15.9 10.16 15.2 15.1 14.8 15.1 20.32 15.6 15.2 14.9 15.0 30.48 15.9 15.7. 15.3 15.4 ____.Axerase 1517 15.4 1512 1514 Initial moisture content = 18.1 %DB APPENDIX B PSYCMTRIC CHART EDDEL AND SAMPLE OUTPUT 100 102 104 106 108 110 112 114 116 118 120 I22 124 126 128 130 132 134 136 138 140 142 I44 146 148 150 152 154 156 158 160 162 164 166 168 170 172 174 176 178 180 182 184 186 188 PSYCHROHETRIC CHART MODEL CLS REH PSYCHROHETRIC CHART HODEL REH REH JOAO D. BIASI - SPRING/86 - HSU - E.LANSING REH PRINT TAB(51 ' ' STRIN63159,'§“1 LOCATE 2,12 PRINT 'FROH THO GIVEN INDEPENDENT PROPERTIES OF THE HOIST AIR THIS" LOCATE 3,12 PRINT 'PSYCHROHETIRC CHART HODEL COHPUTES THE REHAININS PROPERTIES" LOCATE 4,12 PRINT “OF A STATE POINT. THE INPUTS HAY BE IN ENGLISH OR SI UNITS." PRINT TABtSl ' ' STRINB$(59,'§'1 PRINT: PRINT PRINT SPC(18) “ YOU HAVE SEVEN CHOICES FOR INPUTS: ' PRINTIPRINT PRINT SPC(18) PRINT SPC(18) PRINT SPCllO) PRINT SPCtIO) 1) DRY BULB TEHP. AND RELATIVE HUHIOITv " 2) DRY BULB TEHP. AND ABSOLUTE HUHIDITv . 3) ORv BULB TEHP. AND NET BULB TEHP. ' 4) DRY BULB TEHP. AND DEN POINT TEHP.- PRINT SPCilB) 5) NET BULB TEHP. AND RELATIVE HUHIDITY PRINT SPCilB) 6) DEN POINT TEHP. AND RELATIVE HUHIOITv - PRINT SPC(16) - 7) DEN POINT TEHP. AND ENTHALPY - LOCATE 19,23: INPUT - ENTER A NUHBER FROM 1 TO 7 - -, I IF II>-1) AND II<=71 SOTO 150 ELSE LOCATE 9,1: SOTO 129 LOCATE 21,25:INPUT -ENSLISH OR SI UNITS 1 E or 91 ) 7 ',U4 IF (us=-E-) OR (us-'9") 6010 156 IF (us=~SI-) OR (Utl'si') SOTO 190 ELSE SOTO 150 TSa'i F )~:A93=~ (LB H20/LB DRY AIR) ':E4-' (BTU/LB DRY AIR) " SOTO 192 Ts--1 c )-aABs=- (K6 H20/KB DRv AIR) “:Es-- (KJ/KB DRY AIR) " LOOATE 23,9 1P 1:1 SOTO 17o ELSE IF 1:2 SOTO 174 ELSE IF 1:3 SOTO 179 IF 1:: SOTO 194 ELSE IF 1:5 SOTO 190 ELSE IF 1:9 BOTO 194 IF I=7 SOTO 199 PRINT ”DRY BULB TEHP. "T3”,RELATIVE HUHIDITv (z) "IIINPUT D9,RH IF RH>1oo THEN PRINT - RH > 100 ”IBDTO 17OIELSE SOTO 200 PRINT “DRY BULB TEHP."T1~,A9S. HUHIDITY ~AB:;:INPUT DB,HA SOTO 200 PRINT ”DRY BULB TEHP. "Ts",NET BULB TEHP. ”TS” “;:INPUT D9,NB IF DB < NB THEN PRINT - OB < N9 -: SOTO 179 6010 200 PRINT -DRv BULB TEHP. "Ts",DEN POINT TEHP. “TS“ ';:INPUT D9,DP 1F DB < OP THEN PRINT - DB < DP -: SOTO 194 SOTO 200 189 I90 192 194 196 198 200 202 204 206 208 210 212 214 216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276 278 280 282 284 286 288 290 292 294 296 298 190 PRINT “NET BULB TEMP. “T4“,RELATIVE HUMIDITY (X) 'IIINPUT HB,RHI IF RHI>100 THEN PRINT ' RH > 100 'ISOTO I901ELSE SOTO 200 PRINT 'DEH POINT TEMP.'T4',RELATIVE HUMIDITY (Z) 'ISINPUT DP,RH IF RH>100 THEN PRINT ' RH > 100 'ISOTO I941ELSE SOTO 200 PRINT 'DEN POINT TEMP.'T$',ENTHALPY ”ESIIINPUT DP,H RH = RH / 100: RHI I RHI / 100 IF (USI'E') OR (U4="e") SOTO 206 DB=DBII.S+32: NB=HBII.S+321 DPIDP41.S+32: NIH/2.326 REM PRINT FORMATS FISI' 440444.44 ':F24=' 400.44044 "1F34="44440.4444 ” F44I'444444.404 ”:FSSI' 044444.444 ' PSI“ LB/SO IN ‘IAH4I' LB M/LB D.AIR “:EN$=' BTU/LB D.AIR " vss=' FT3/LB D.AIR 'IAHIta ' KSM/KS D.AIR'1ENI$=' KJ/KS D.AIR' v51! = ' M3/KS D.AIR': P14 I ' KPa' REM MAIN PROGRAM IF I I 5 SOTO 260 ELSE IF (II6) OR (I=7) SOTO 236 T I DB + 459.691 SOSUB 496 PSD I PS: IF I=7 THEN RH I PDP/PSD: SOTO 254 IF I24 THEN TIDP+459.69:SOSUB 4961PDPIPSIRHIPDP/PSDIPVIPSISOTO 254 IF I I 3 SOTO 260 IF II2 THEN PVIHA*14.696/1.6219+HA):RHIPV/PSDISOTO 234 PV=PSD I RHIIF I=5 THEN PV I P80 4 RHI SOSUB 526: DP : A A PV‘B + CILOStPV) + D T I DP + 459.69: SOSUB 496 PDP I PS: IF I=7 THEN PV=PDP1 SOTO 290 IF I< >6 SOTO 252 ELSE PSD=PDPIRHIPVIPDP DELT I 10: DB I DP T I DB+4S9.69: SOSUB 496: PSDA I PS XP=PSD-PSDA:IF XP>0 THEN DBIDB+DELTISOTO 244 IF (DELT<.OOOOI) OR (XP=0) SOTO 252 IF XP<0 THEN DB=DB-DELT:DELT=DELT/2:DBIDB+DELTISOTO 244 IF I I 3 SOTO 294 ELSE IF I I 5 SOTO 290 DT I DB - DP SOSUB 544 NBIDP+(BIIDT*3+B2*DT“2+B3IDT)iEXPI(BQ!DT+BS)*DP086) T I NB + 459.691 SOSUB 496 P08 I PS IF I I 7 SOTO 294 IF I < > 5 SOTO 27B DELT I 101 DB = NS TIDB+459.69:SOSUB 4961PSD=PSIT=DBISOSUB SOSISOTO 284 XPIRHA-RHIIIF XP>0 THEN DBIDB+DELTTSOTO 270 IF (DELT<.00001) OR (XPIO) SOTO 232 IF XP<0 THEN DB=DB-DELT:DELT=DELTIZIDBIDB+DELTISOTO 270 IF I I 4 SOTO 290 IF I < ) 3 SOTO 288 T=N84 SOSUB SOB BPI.24OS I (PMS-14.696)/(.62194IHFS) PVIPHB+BPI(DB-HB)1RH=PVIPSDIIF IIS THEN RHAIRHISOTO 272 IF II2 SOTO 294 HAI.62I9B I (PV/(I4.696-PV)) IF II3 SOTO 234 ELSE IF I=7 SOTO 308 SVI153.3SI(DB+459.69)1/11444114.696-PV)l IF II7 SOTO 318 IF DP>32 SOTO 304 300 302 304 306 309 310 312 314 316 319 320 322 324 326 329 330 332 334 336 339 340 342 344 346 349 350 332 354 356 339 360 362 364 366 369 370 372 374 376 379 390 392 394 396 399 390 392 394 396 399 400 402 404 406 409 191 H=.24054DB+HA41.4494109+459.69)-.0137741DP+459.69)+962.3629) SOTO 319 HI.24OSIDB+HA4(.44S!(DB+459.69)-.OI7B3§1DP+459.69)+864.7168) SOTO 319 IF DP)I 32 SOTO 314 DBI(H-HAI(106S.304024-.01377I(DP+459.69)))/(.2405+HA!.44S) SOTO 222 DB=(H-HAIIIO70.657920-.01783IIDP+459.69))l/(.2405+HA4.44S) SOTO 222 REM TRANSFORMS ENSLISH UNITS TO SI UNITS DBIItDB-32l/1.S:NBII(HB-32)II.BIDPII(DP-32)/I.S RH=RH410011P 1:3 THEN RHIRH14100 PSDIIPSDIb.B947571PHBIIPNBI6.S94757:PDPI=PDP46.8947S7 SVI . SV 4 .0624281 HI . H 4 2.326 CLSIPRINTIPRINT SPCll9l; PRINT "RESULTS FROM THE PSYCHROMETRIS CHART HODEL' PRINT SPCII9) 'INPUTS . -; IF I I 1 THEN PRINT ' DRY BULB TEMP. AND RELATIVE HUHIDITY'I IF I I 2 THEN PRINT ' DRY BULB TEMP. AND ABSOLUTE HUMIDITY“ IF I 8 3 THEN PRINT ' DRY BULB TEMP. AND NET BULB TEMP.‘ IF I = 4 THEN PRINT ' DRY BULB TEMP. AND DEN POINT TEMP.‘I IF I I 5 THEN PRINT ' NET BULB TEMP. AND RELATIVE HUMIDITY" IF I I 6 THEN PRINT “DEN POINT TEMP. AND RELATIVE HUMIDITY" IF I = 7 THEN PRINT ' DEN POINT TEMP. AND ENTHALPY ' PRINT: PRINT PRINT SPCIzs) - ENSLISH UNITS ~ SPCIIBI ' SI UNITS . PRINT PRINT SPC(3) ~ DRY BULB TEMP. “;:PRINT USINS P14;DB; PRINT - F';IPRINT SPCIIB) USINS F14;DBI;:PRINT - C' PRINT SPCI3) - NET BULB TEMP. ";:PRINT USINS F143HBI PRINT ~ F'IIPRINT SPCtIB) USINS P14;NBI;IPRINT - C' PRINT SPC(3) ~ DEN POINT TEMP. "IIPRINT USINS F1410P; PRINT . P-;:PRINT SPCIIB) USINS FISIDPlgzPRINT ' C' PRINT SPC(3) ~ RELATIVE HUMIDITY “IIPRINT USINS P14;RH; PRINT - z-;:PRINT SPCIIB) USINS P1:;RH;:PRINT - 2' PRINT SPC(3) - ABSOLUTE HUMIDITY "IIPRINT USINS F24; HA; PRINT AHtgzPRINT SPCIS) USINS P24;HA;1PRINT AHIS PRINT SPC13) " ENTHALPv -;:PRINT USINS P44;H; PRINT ENSIIPRINT SPE(7) USINS P44;HI;1PRINT EN14 PRINT SPCI3) ~ AIR SPECIFIC VOL. ~;:PRINT USINS P14;SV, PRINT V5431PRINT SPC(6) USINS P54;SVI;:PRINT V914 PRINT PRINT SPCI3) ~ SATURATION VAPOR PRESSURES - PRINT PRINT SPC(4) " AT DRY BULB TEMP. "IIPRINT USINS P34;PSO; PRINT P4,:PRINT SPClIIl USINS P34;PSDI;:PRINT P14 PRINT SPCI4) . AT NET BULB TEMP. ";IPRINT USINS P34;PNB; PRINT P4;1PRINT SPCIII) USINS F34;PNBI;IPRINT P14 PRINT SPC(4) - AT DEN POINT TEMP.“;:PRINT USINS P34;PDP; PRINT P4,:PRINT SPClII) USINS F343PDPITIPRINT P14 REM LOCATE 22,2 INPUT 'DO YOU NANT THE RESULTS PRINTED OUT? (v or N) ",PRs IF PRss-N- OR PRs=-n- SOTO 494 IF PRSI'Y' OR PRSI'y' SOTO 410 ELSE SOTO 402 410 412 414 416 419 420 422 424 426 429 430 432 434 436 439 440 442 444 446 449 450 452 454 456 459 460 462 464 466 469 470 472 474 476 479 490 492 494 496 499 490 492 494 496 499 500 502 504 506 509 510 512 514 516 519 192 LPRINTILPRINTILPRINT SPC(19l; LPRINT LPRINT IF I I IF IF IF IF IF IF ”HP-CHM [a LPRINT: LPRINT LPRINT: LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT REM LOCATE INPUT 'DO YOU NANT TO INPUT NEN DATA? IF NDSI'N' “RESULTS FROM THE PSYCHROMETRIC CHART MODEL" SPC119) 'INPUTS . '1 1 THEN LPRINT ~ DRY BULB TEHP. AND RELATIVE HUMIDITY' 2 THEN LPRINT - DRv BULB TEMP. AND ABSOLUTE HUMIDITY' 3 THEN LPRINT - DRY BULB TEMP. AND NET BULB TEMP." 4 THEN LPRINT - DRY BULB TEMP. AND DEN POINT TEMP.“ 5 THEN LPRINT " NET BULB TEMP. AND RELATIVE HUMIDITY" 6 THEN LPRINT 'DEN POINT TEMP. AND RELATIVE HUMIDITY“ 7 THEN LPRINT ~ DEN POINT TEHP. AND ENTHALPv - LPRINT SPC125) LPRINT SPC(3) - DRY - F';ILPRINT SPC(3) - NET - F'IILPRINT SPC(3) - DEN - P-;1LPRINT SPClIS) USINS SPCI3) - RELATIVE HUMIDITY - z-;:LPRINT SPCtIB) USINS FISIRHIILPRINT - :- SPC13) - ABSOLUTE HUMIDITY ';:LPR1NT USINS F243HA; AH4;:LPRINT SPCIS) USINS F24;HA;:LPRINT AHIS SPC(3) - ENTHALPY ';:LPRINT USINS P443H; EN:;:LPRINT SPC(7) USINS F44;HI;ILPRINT EN14 SPC(3) - AIR SPECIFIC VOL. ';:LPRINT USINS FISISV; VSt;:LPRINT SPCI6) USINS F14;SVI;:LPRINT VSIs ” ENSLISH UNITS ' SPClIB) ' SI UNITS ” BULB TEMP. SPCIIB) USINS BULB TEMP. SPCtlBl USINS POINT TEMP. ”IILPRINT USINS FltgbBIIILPRINT ';1LPRINT USINS F14INBIIILPRINT ';:LPRINT USINS FI4IDPIIILPRINT ' C' ';ILPRINT USINS F14;RH; FISIDB; MCI FtthB; MCI F14;DPI SPCI3) ' SATURATION VAPOR PRESSURES ' SPC14) - AT DRY BULB TEHP. 'IILPRINT USINS F34;PSD; PSIILPRINT SPC(11) USINS E44;PSOI;:LPRINT P14 SPCI4) - AT NET BULB TEMP. “IILPRINT USINS P34;PN9; P3,:LPRINT SPClII) USINS E34;PNBI;:LPRINT P14 SPC(4) ~ AT DEN POINT TEMP.';:LPRINT USINS P34;PDP; P4;ILPRINT SPCIII) USINS P34;PDPI;:LPRINT P14 23,2 (Y or N) “,ND4 OR NDSI'n' SOTO 492 IF NDSI'Y' OR ND!=“y'SOTO 100 ELSE SOTO 484 END REM REM SUBROUTINE SATURATION VAPOR PRESSURE IF T > 491.69 SOTO 504 PSIEXP123.39240-(11286.6489O/T)-.460574LOS(T)) BOTO 506 PS=EXP(54.63290-(12301.6880/T)-5.1692344LOSIT)) RETURN REM SUBROUTINE LATENT HEAT OF VAPORIZATION IF (T)32) AND (T<150) THEN SOTO 518 IF T)150 SOTO 522 HFS=1220.8440-.0507704T SOTO 524 HFSI1075.89650-.5698341T-32) 520 522 524 526 528 530 532 534 536 538 540 542 544 546 548 550 552 554 556 558 560 562 564 566 568 570 572 574 576 578 580 582 584 586 588 590 592 594 596 598 600 I93 SOTO 524 HFSI(1354673.2I4I-.91252755880(T+459.69)‘2)“.5 RETURN REM SUBROUTINE CONSTANTS OF DEN POINT TEMP. ESUATION IF (PS>.0886) AND (PS B 32 SOTO 580 DBAi-l.I756E-04IDP‘3-.0032646§DP‘2-.19195iDP+45.35 IF (DB>'DBA) AND (08(180) THEN SOTO 562 IF (DB>180) AND (DB<300) THEN SOTO 568 IF D8 ) 300 SOTO 574 8189.04803E-07:B2=-.0033017383I.8312313848-2.3949E-05 85=-S.08793E-03:86'I.130519 SOTO 600 81'5.54717E-06382=-3.I4334E-03383'.84224TB4=5.93269E-06 853-S.630321E-034B6=I.082753 SOTO 600 81'2.32489E-06:82i-2.04027E-03:B3=.746559:B4=6.24943E-06 8588834.849TB6=I.074474 SOTO 600 8188.64159E-07:82=-.0011678:B3=.615543:B4=.392047 85=-.0082495:B6=l.070437 SOTO 600 IF (DB>180) AND (DB<300) THEN SOTO 590 IF DB > 300 THEN SOTO 596 BI=7.37013E-061823-3.53885E-03383=.827522:B4=3.89627E-06 85'-2.6OII3E-03:B6=1.404192 SOTO 600 8182.49546E-06:B2=-2.04326E-03383=.707415:B4=1.88247E-06 853-2.00086E-03:8631.442215 SOTO 600 BI=8.44289E-07:B2=-1.10977E-03:B3=.572561:B4=S.97368E-07 85t-I.53339E-03:B6=I.475598 RETURN 194 RESULTS. FROM THE PSYCHRDMETRIC CHART MODEL INPUTS I DRY BULB TEMP. AND RELATIVE HUMIDITY ENSLISH UNITS SI UNITS DRY BULB TEMP. 75.00 F 23.89 C NET BULB TEMP. 67.93 F 19.96 C DEN POINT TEMP. 64.54 F 18.08 C RELATIVE HUMIDITY 70.00 X 70.00 X ABSOLUTE HUMIDITY 0.01298 LB M/LB D.AIR 0.01298 KSM/KS D.AIR ENTHALPY 32.252 BTU/LB D.AIR 75.018 KJ/KS D.AIR AIR SPECIFIC VOL. 13.76 FT3/LB D.AIR 0.86 M3/KS D.AIR SATURATION VAPOR PRESSURES AT DRY BULB TEMP. 0.4292 LB/SO IN 2.960 KPI AT NET BULB TEMP. 0.3379 LB/SO IN 2.3296 KPI AT DEN POINT TEMP. 0.3003 LB/SD IN 2.0708 KPI RESULTS FROM THE PSYCHROMETRIC CHART MODEL INPUTS I NET BULB TEMP. AND RELATIVE HUMIDITY ENSLISH UNITS SI UNITS DRY BULB TEMP. 77.29 F 25.16 C NET BULB TEMP. 70.00 F 21.11 C DEN POINT TEMP. 66.72 F 19.29 C RELATIVE HUMIDITY 70.00 X 70.00 I ABSOLUTE HUMIDITY 0.01403 LB M/LB D.AIR 0.01403 KSM/KS D.AIR ENTHALPY 33.963 BTU/LB D.AIR 78.997 KJ/KS D.AIR AIR SPECIFIC VOL. 13.84 FT3/LB D.AIR 0.86 M3/KS D.AIR SATURATION VAPOR PRESSURES AT DRY BULB TEMP. 0.4631 LB/SD IN 3.193 KPI AT NET BULB TEMP. 0.3626 LB/SO IN 2.5003 KP. AT DEN POINT TEMP. 0.3240 LB/SD IN 2.2339 KPI APPENDIX C HEATANDHASSWMDIL ANDSAHPLKOU'I'PUT 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 160 162 164 166 168 170 172 174 176 178 180 182 184 186 188 190 192 HEAT AND MASS BALANCE MODEL FOR STATIONARY-BED PELLET COOLER CLS REM MODEL 01 - HEAT AND MASS BALANCE (HMB) REM COOLING OF A FIXED BED OF PELLETS REM PROGRAM: PELLETI REM REM THIS PROGRAM COMPUTES PELLET MOISTURE CONTENTS AND TEMPERATURES, REM ABSOLUTE AND RELATIVE HUMIDITIES NITHIN A FIXED BED OF PELLETS. REM BASED ON THOMPSON (1967) APPROACH. AIR AND PELLET TEMPERATURES REM ARE ASSUMED TO BE EQUAL. REM REM JOAO BIABI - SUMMER/B6 - MSU - EAST LANSINS REM DIM H(361),RH(361),EMCDI361),TPT(361,2),TA(361) DIM LA(S),AAIS),B(S),AR(5),MC(361,21 REM INPUT BLOCK CLSTLOCATE 3,101PRINT ‘ INPUT VALUES”1PRINT INPUT ' Air Temperature (F) I ' TAI ! INPUT ' Relative Hueidity (X) = “, RHI INPUT “ Air Flow Rate (CFM/FT2) = ', CFM INPUT ' Pellet Teeperature (F) a ', TPI INPUT ' Initial Moisture Content (ZNB) = ', MCIN INPUT ' Pellet Diameter (ln.) = ", DIAI INPUT ' Cooling Tine (Min) = ', TI PRINT REM DIAMETER IN FOOT and RADIUS IN METER DIAI=.1875:DIAF=DIAII123R=IDIAII21*.0254 REM COOLER DEPTH (FT); AREA (FT2) BED=13AREA'1 REM CONSTANTS OF MOIST.CONTENT E8N..ROOTS BESSEL FC. KL=31FOR I=1 TO KLI READ LA(I) AAII)=LA(I)!LA(I):8II)=4/AA(I)1AR(I)*-AA(I)/(RiR):NEXT I DATA 2.405,5.52,8.654 REM COOLINS TIME (HOUR) TI=TI/60 REM PELLET DENSITY (LB/FT3); (KS/M3) PDEE‘42:PDEM=PDEE*16.0185 RHC i .98 REM DT=HOUR3 TC=N OF ITERATIONS DT-1/60: TC=TI/DT REM REM RH-DECIMALgMCBDECIMAL DRY BASIS RHI'RHI/100:MCID=MCIN/(100-MCIN1 REM COMPUTE INLET ABS.HUMIDITY AND SPEC.VOLUME IJ=1:DB=TAI:RH=RHI:SOSUB 3583HIIHUTSVI=SV REM COMPUTE AIR FLON (LB/Hr) SAI(CFM*60)/(AREA*SVI) REM COMPUTE DEPTH INCREMENT 195 194 196 198 200 202 204 206 208 210 212 214 216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276 278 280 282 284 286 288 290 292 294 296 298 300 302 196 IF CFM<=30 THEN xA=760 ELSE XA=510 xTaINT(XA:RHC THEN RH(X+I)=RHC NEXT 1 MCAVE-SMC/XITPA=((STA/X1-491.69)/1.8 FOR x=0 TO XT:MC(X,0)-MC(X,I):TPTIX,0)=TPT(X,I):NEXT x REM SOSUB 466 IF PTI=CPRI THEN CPRI=0:SOSU9 570 NEXT N REM LOCATE 23,5 INPUT - DO YOU NANT TO INPUT NEN DATA? (Y or N) ",NDS IF ND$='N' OR NO4='n' SOTO 354 IF ND$='Y“ OR Nos-"y- SOTO 130 ELSE SOTO 346 END REM REM SUBROUTINE PSYCHART(DB,NB,DP,RH,HU,PV,SV,HFB) IF DB > 212 SOTO 366 A0892.297780:848.222688301C4812.8874341DN-9.4150020 SOTO 368 A4=44.117024:BN=.29492254:C4=21.777374:O4=55.997034 IF DB > 190 SOTO 376 914:7.37013E-06:924--3.53995E-03:934:.9275224:944:3.996279-06 954s-2.60113E-06: 964-1.4041914 SOTO 390 . 914:2.49546E-o6xB2os-2.043269-03:B34=.707415N:B44-1.99247E-06 8548-2.00086E-03x86.81.4422154 T=DB+459.69 I PStEXP(54.63294-(12301.6880/T)-5.1692349LOB(T)) IF IJ=2 THEN PV=HU§I4.696/(.621+HU):RH=PV/PSISOTO 399 PVIPB'RH DP-AOFPV~94+C4:LOSIPV)+O4 DTO-DB-DP NB=DP+(BIO*DTD‘3+B20!DTD‘2+B34!DTD)*EXP((B4AlDTD+BSI)!DP‘864) IF IJ - 2 SOTO 399 HU'.6219§(PV/(14.696-PV)) 9V=153.3544(OB+459.69)1/(144:114.696-PV1) SOTO 416 T=DB , IF (T>321 AND (T<150) THEN SOTO 410 ELSE IF T>150 SOTO 414 HF881220.844|-.0507744T BOTO 416 HEB-1075.99654-.569934:(T-321 SOTO 416 414 416 419 420 422 424 426 429 430 432 434 436 439 440 442 444 446 449 450 452 454 456 459 460 462 464 466 468 470 472 474 476 479 490 492 494 496 499 490 492 494 496 499 500 502 504 506 509 510 512 514 516 519 520 522 198 HFS'I1354673.2148-.91252755878*(T+459.69102)“.5 RETURN REM SUBROUTINES PRINT - SCREEN REM PRINT:PRINT PRINT TABIIDI ~ INITIAL CONDITIONS ': PRINT PRINT TAB(5) - AIR TEMPERATURE (F) = u; PRINT USINS F183TAI,(TAI-32)/1.B;1PRINT - C" PRINT TABI51 ' RELATIVE HUMIDITY (Z) = I; PRINT USINS F13;RHI*100 PRINT TABI6) 'PELLET TEMPERATURE (F) = ';:PRINT USINS FIs;TPI; PRINT USINS F14;1TPI-321/1.9;: PRINT ~ C' PRINT TABI6) “MOISTURE CONTENT (1 NB) . ';:PRINT USINS F14;HCIN; PRINT USINS Flt;MCID*IOO;:PRINT - 208' PRINT TAB(5) - PELLET DIAMETER (In.) a -; PRINT USINS F24;DIAI::PRINT U9IN9 F13;DIAI*25.4;IPRINT ' MM' PRINT TABIb) ”AIR FLON (CFH/FT21 a '::PRINT USINS F1$;CFM; PRINT USINS FIS:VA;:PRINT - M/S' PRINT TABIS) " COOLER DEPTH (FT) - ~; PRINT USINS F14:9EO,BEO:30.49:: PRINT - CM' PRINT TAB(6) ”DELTA x (In.) = ';:PRINT USINS F13;DELX*12; PRINT USINS F1::DELX:30.4S:: PRINT - CM - PRINT TAB(6) ”DELTA t (Min.) . "g: PRINT USINS F13;DT*60 PRINT RETURN REM CLSILOCATE 1,2:PRINT PRINT TABI6) “TIME (Min.) ' "TTPRINT USINS F3$|L*60 PRINTTPRINT TAB(5) ' BED DEPTH cn'; FOR Y=0 TO (12*BED) STEP (2*BED)1PRINT USINS F1$;Y*2.54; NEXT YTPRINTTPRINT: PRINT TABIS) 7 E8. TEMP. C '; KT=491.69 FOR Y=0 TO XT STEP XPRTPRINT USINS F1$;(TA(Y)-KT)/1.8;:NEXT Y PRINT: PRINT TABI5) ' PEL.TEMP. C '3 FOR Y=0 TO XT STEP XPRTPRINT USINS F1$;(TPT(Y,0)-KT)/1.8; NEXT YTPRINTIPRINT TAB(5) ' M.C. ZDB '; FOR Y=0 TO XT STEP XPRTPRINT USINS F13;MC(Y,0)*100;INEXT Y PRINT TAB(5) ' M.C. 1N8 ';:FOR Y=0 TO XT STEP XPR N=MC(Y,0):PRINT USINS F13;(N/(1+N))*100;TNEXT Y IF L = 0 SOTO 504 PRINTTPRINT TAB(5) ' EO.MC. ZDB "3 FOR Y=0 TO XT STEP XPRTPRINT USINS F14;EMCD(Y)*100;:NEXT Y PRINTTPRINT TABI5) ' REL. HUMID. '3 FOR Y-O TO XT STEP XPRIPRINT USINS F1$;RH(Y)*100;:NEXT Y PRINT PRINT TAB(5) ' ABS. HUMID. '3 FOR Y=0 TO XT STEP XPRTPRINT USINS F23|H(Y);INEXT YTPRINT PRINTTPRINT TAB(11) 'AVE. TEMP. (C) = "ITPRINT USINS F1$;TPA; PRINT ' AVE. MC. (%DB) 3 'gTPRINT USINS F18;MCAVE*100 RETURN REM SUBROUTINES PRINT 3 PRINTER LPRINT LPRINT TA8(10) ” INITIAL CONDITIONS “:LPRINT LPRINT TAB(5) ' AIR TEMPERATURE (F) = ' ; LPRINT USINS FI$;TAI,(TAI-32)/1.B;:LPRINT . C" 524 526 528 530 532 534 536 538 540 542 544 546 548 550 552 554 556 558 560 562 564 566 568 570 572 574 576 578 580 582 584 586 588 590 592 594 596 598 600 602 604 606 608 610 612 614 616 199 LPRINT TAB(5) ' RELATIVE HUMIDITY (z) = -, LPRINT USINS F14;RH14100 LPRINT TAB(5) - PELLET TEMPERATURE (F) LPRINT USINS F1:;TPI,(TPI-32)/1.9;:LPRINT ' LPRINT TAB(5) - MOISTURE CONTENT (2 NB) LPRINT USINS F1$;MCIN; LPRINT USINS F14;HCIO:100;:LPRINT " 109" LPRINT TAB(5) - PELLET DIAMETER (In.) = -: LPRINT USINS F24;DIAI::LPRINT USINS FI$;DIAI*25.4; LPRINT - MM" LPRINT TAB(6) -AIR FLON (CFH/FT2) . "; Cl! “1 LPRINT USINS F14;CFH: LPRINT USINS F1:;VA;:LPRINT - M/S" LPRINT TAB(5) ' COOLER DEPTH (FT) = 4; LPRINT USINS FIS;BED,BED§30.48;:LPRINT " CM" LPRINT TAB(5) - DELTA x (In.) = -; LPRINT USINS FIS;DELX*12; LPRINT USINS FIS;DELX*30.4B;1 LPRINT ~ CM " LPRINT TAB(5) - DELTA t (Min.) = "; LPRINT USINS F14;OT:60 LPRINT RETURN REM LPRINT:LPRINT TAB(6) "TIME (Min.) = ";:LPRINT USINS FI$;L*60 LPRINT: LPRINT TAB(5) - BED DEPTH cm“; FOR Y=0 TO (12*BED) STEP (249EO):LPRINT USINS F1$TYl2.54g NEXT Y LPRINT:LPRINT:LPRINT TAB(5) ' PEL.TEMP. C '; FOR Y=0 TO XT STEP XPR:LPRINT USINS Fl$;(TPT(Y,0)-KT)/I.8; NEXT Y:LPRINT LPRINT TAB(5) - M.C. XOB ': FOR Y=0 TO XT STEP XPR:LPRINT USINS FI$;MC(Y,O)*100;:NEXT Y LPRINT TAB(5) ' M.C. XNB ”;1FOR Y=0 TO XT STEP XPR N=HC(Y,0):LPRINT USINS F1$;(N/(1+N)):100;:NEXT Y IF L = o SOTO 604 LPRINT: LPRINT TAB(5) - EO.MC. %DB "; FOR Y=0 TO IT STEP XPR:LPRINT USINS Flt;EMCD(Y)*IOOIINEXT Y LPRINT: LPRINT TAB(5) " REL. HUMID. '; FOR Y=0 TO XT STEP XPR:LPRINT USINS F14;RH(Y)4100;:NEXT Y LPRINT LPRINT TAB(5) " ABS. HUMID. ”;:FOR Y=0 TO XT STEP XPR: LPRINT USINS - .4444-; H(Y);1NEXT Y:LPRINT LPRINT:LPRINT TAB(II) ”AVE. TEMP. (C) . "::LPRINT USINS F14;TPA; LPRINT - AVE. MC. (208) = ';ILPRINT USINS FIt;MCAVE*IOO LPRINT TAB(IO) STRINB$(S4,"§') LPRINT:LPRINT RETURN 200 HMB MODEL OUTPUT SAMPLE INITIAL CONDITIONS AIR TEMPERATURE (F) RELATIVE HUMIDITY (X) PELLET TEMPERATURE (F) MOISTURE CONTENT (1 NB) PELLET DIAMETER (In.) AIR FLON (CFM/FT2) COOLER DEPTH (FT) DELTA N (In.) DELTA t (M1n.) 80.00 26.67 C 55.00 150.00 65.56 C 17.00 20.48 XDB .1875 4.76 MM 100.00 0.51 M/S 1.00 30.48 CH 0.25 0.63 CM 1.00 TIME (Min.) I 0.00 BED DEPTH CI 0.00 5.08 10.16 15.24 20.32 25.40 30.48 PEL.TEMP. C 46.11 65.56 65.56 65.56 65.56 65.56 65.56 M.C. XDB 20.48 20.48 20.48 20.48 20.48 20.48 20.48 M.C. 2NB 17.00 17.00 17.00 17.00 17.00 17.00 17.00 ABS. HUMID. .0120 .0120 .0120 .0120 .0120 .0120 .0120 AVE. TEMP. (C) I 65.16 AVE. MC. (%DB) I 20.48 444559444444454OOOOODOOOOOOOOOOOOOSOOOODODOODAODOOOOOB TIME (Min.) I 20.00 BED DEPTH CI 0.00 5.08 10.16 15.24 20.32 25.40 30.48 PEL.TEMP. C 26.58 26.53 26.48 26.44 26.47 26.55 26.61 M.C. 208 16.87 17.16 17.49 17.85 18.16 18.24 18.09 M.C. 1NB 14.44 14.65 14.88 15.14 15.37 15.43 15.32 E8.MC. ZDB 14.09 14.61 15.18 15.82 16.38 16.52 16.26 REL. HUMID. 55.00 58.64 62.46 66.46 69.77 70.61 69.16 ABS. HUMID. .0120 .0128 .0136 .0144 .0152 .0153 .0150 AVE. TEMP. (C) I 26.51 AVE. MC. (%DB) I 17.73 COOSaSD44Oa454ODOOODOOOOOOOODOOOODOOOONOOOOOO545445944 APPENDIX D PARTIAL DIFFERENTIAL EQUATIONS 10D!!- AND SAHPLE OUTPUT 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 160 162 I64 166 168 170 172 174 176 178 180 182 184 186 188 190 PARTIAL DIFFERENTIAL EOUATIONS MODEL FOR STATIONARY-BED PELLET COOLER CLS REM MODEL 42 - PARTIAL DIFFERENTIAL EOUATIONS (PDE) REA COOLINS OF A FIXED BED OF FELLETS 9.4 PROSRAH: PELLET2 REM REH THIS MODEL COMPUTES AIR TEMPERATURES, RELATIVE HUMIDITY,ABSOLUTE REM HUMIDITY, PELLET MOISTURE CONTENTS AND TEMPERATURES OF A FIXED REM BED OF PELLETS. ALSO DETERMINES MOISTURE CONTENT AND TEMPERATURE REM SRADIENTS NITHIN A PELLET AT EACH ON LOCATION INSIDE THE BED. REM REM JOAO BIASI - SUMMER/86 - MSU - EAST LANSINS REM DIM T(15,65),TA(201),TC(201,2),TS(201),TAV(201),MT(15,65),MS(201) DIM MC(201,2),H(201),RH(201),EMCD(201),TPT(201,2),MAV(201,2) DIM LA(5),AA(5),B(5),AR(5),HCES(201) DIM TS(15), HCS(15) REM INPUT BLOCK CLS:LOCATE 3,5: PRINT ' POE HOOEL: INPUT VALUES“: PRINT INPUT ' Air Temperature (F) = ', TAI INPUT ' Relative Hueidity (X) = ', RHI INPUT ' Air Flow Rate (CFM/FTZ) = ', CFM INPUT “ Pellet Teeperature (F) I ', TPI INPUT ' Initial Moisture Content (1N8) = ', MCIN INPUT ' Pellet Diameter (In.) a ', DIAI INPUT ' Cooling Tine (Min) = ', TI PRINT REM DIAMETER IN FOOT, RADIUS IN METER DIAF=DIAII12IR=(DIAI/2)5.0254‘ REM CONSTANTS OF MOIST.CONTENT EON..ROOTS BESSEL FC. KL=3IFOR III TO KL: READ LA(I) AAII)=LA(I)*LA(I)18(I)I4/AA(I)TAR(I)I-AA(I)/(R*R)TNEXT I DATA 2.405,5.52,8.654 REM AIR AND VAPOR CONSTTANTS CNIIICA=.24051CV=.44STVII.0443IAIRD=.063415 REM SPECIFIC SURFACE AREA (FT2/FT3) SAI48/DIAI REM PELLET DENSITY (LB/FT3); (KS/M3) PDEEI42:PDEM=PDEE516.0185 REM AIR VELOCITY (M/S) VAIICFM§.304S)/60 REM BEDIFEET; AREAI FT2; POROSITY BED=IIAREAIIIPO=.44 REM DELXIFT; I LAYERS/FOOT; PRINTINS COUNT. DELXI.02081XT=INT(BED/DELX):XPR=(XT)/6 REM TI AND DT = HOUR TIITI/6OIDTI.5/60 201 202 192 REM CONSTANTS OF SUBROUTINE FINITE DIFF.FORMULAS 194 REM DELR-HETER:DELT=SECONDS 196 OELR-.0005:DELT=.5:TIHE=15 199 IF CFH>50 THEN KTI=18 ELSE KTIIIS 200 TTM IKTI/(DT460) 202 TT=TIMEIDELT 204 H-INT(R/DELR)+1 206 B=1-1/(2!M):CI1+1/(2!M) 209 REM RHIIDECIMAL; MC=DECIMAL DRY BASIS 21o RHI-RHI/100:HCID=HCIN/(Ioo-HCIN) 212 RHCI.98 214 REM COMPUTE INLET ABSOLUTE HUMIDITY AND SPEC.VOLUME 216 IJ=1:DB=TAI:RH=RHI:SOSUB 644:HI=HU:SVI=SV 219 REM COMPUTE AIR FLON (LB/Hr), REYNOLDS'A, SCHHIDT'A 220 6A=(CFM!60)/(AREA*SVI) 222 REN=(6A*DIAF)/Vl 224 SCN=VI/(AIRDSDIAF) 226 REM HEAT TRANSFER COEFF. (BTU/Hr FT2 F) 229 HT=CAIGAI.992I(REN)“(-.34) 23o HTH=5.677 4 HT 232 REM MASS TRANSF. COEFF. (LB/Hr FT2) 234 HM=6A415.54(REN)‘(-1)i(SCN)“(-2/3)4(1-PO)“1.2 236 REM MASS TRANSF. COEFF. (M/Hr) 239 HMIHM4(4.8823/PDEM) 240 REM CONSTANTS OF AIR,PELLET TEMP. AND ABS.HUM. EONS. 242 IF CFM>SO THEN BI2.41 ELSE 921.25 244 C1=PDEE40ELX/(BAIDT)ICZ=DT/(PDEE46) 246 C3=(HTGSA!DELX)/BAI C4=HTPSAI C5-SA/DELX 249 REM PRINTINS FORMATS 250 F14=' 444.44-:F2s=- .4444':F3s=- 44.44 - 252 REH PRINT INITIAL CONDITIONS 254 CLS: LOCATE 5,2 256 PRINT 258 PRINTIPRINT TAB(11) 'INITIAL CONDITIONS 'TPRINT 260 PRINT TAB(6) 'AIR TEMPERATURE (F) I ' ; 262 PRINT USINS F14;TAI,(TAI-32)/1.9;:PRINT " C" 264 PRINT TAB(6) ”RELATIVE HUMIDITY (X) a -; 266 PRINT USINS F14:RHI:100 269 PRINT TAB(6) “PELLET TEMPERATURE (F) -: 270 PRINT USINS FltITPI,(TPI-32)/1.B;:PRINT " C“ 272 PRINT TAB(6) ”MOISTURE CONTENT (1 DB) . ': 274 PRINT USINS F13;MCID*100;1PR1NT USINS F14;HCIN; 276 PRINT - INB' 279 PRINT TAB(6) “PELLET DIAMETER (In.) . '3 290 PRINT USINS F24;DIAI::PRINT USINS F13;DIAI*2$.4; 292 PRINT - an“ 294 PRINT TAB(6) ”AIR FLON (CFM/FT2) = "g 296 PRINT USINS F14;CFH;:PRINT USINS F14;VA;:PRINT ' M/S . 299 PRINT TAB(6) “HEAT T.COEF. (BTU/FTzHr F): ': 290 PRINT USINS F14:HT,HTH::PRINT - (N/M2 K)” 292 PRINT TAB(6) 'COOLER DEPTH (FT) = ": 294 PRINT USINS F13;BED,BED*30.4B;:PRINT ' CM' 296 DI”DELX*12382=DELX*50.48 298 PRINT TAB(6) 'DELTA X (In.) I '3 300 PRINT USINS FlinITTPRINT USINS F1$ID2;IPRINT " CM' 203 302 PRINT TAB(6) 'DELTA t (Min.) = '3 304 PRINT USINS F1$3DT560 306 PRINT 308 LPRINT: LPRINT: LPRINT 310 LPRINT TAB(10) ' INITIAL CONDITIONS 'TLPRINT 312 LPRINT TAB(6) “AIR TEMPERATURE (F) I “ 3 314 LPRINT USINS F183TAI,(TAI-32)/1.834LPRINT ' C' 316 LPRINT TAB(6) ”RELATIVE HUMIDITY (Z) I ”3 318 LPRINT USINS F133RH14100 320 LPRINT TAB(6) 'PELLET TEMPERATURE (F) I '3 322 LPRINT USINS F133TPI,(TPI-32)/1.S3ILPRINT ' C' 324 LPRINT TAB(6) ”MOISTURE CONTENT (2 DB) I '3 326 LPRINT USINS F153HCID§10038LPRINT USINS F1$3MCIN3 328 LPRINT ' ZNB” 330 LPRINT TAB(6) 'PELLET DIAMETER (In.) I '3 332 LPRINT USINS F233DIAI3TLPRINT USINS F1$3DIAIi25.43 334 LPRINT ' In" 336 LPRINT TAB(6) 'AIR FLON (CFM/FT2) I '3 338 LPRINT USINS F183CFM3ILPRINT USINS F1$3VA3ILPRINT ' M/S ' 340 LPRINT TAB(6) ”HEAT T.COEF. (BTU/FT2 HrF)I "3 342 LPRINT USINS F133HT,HTM3:LPRINT ' (N/M2 K) ' 344 LPRINT TAB(6) "MASS T.COEF. (M/Hr) I "3 346 LPRINT USINS F2$3HM 348 LPRINT TAB(6) ”COOLER DEPTH (FT) = "3 350 LPRINT USINS F1$3BED,BED*30.483TLPRINT ' CM' 352 LPRINT TAB(6) “DELTA x (In.) . "3 354 LPRINT USINS F14;D1;:LPRINT USINS F14;O2;:LPRINT ~ CM' 356 LPRINT TAB(6) "DELTA t (Min.) a ~; 359 LPRINT USINS F153DTS60 360 LPRINT 362 REM 364 REM AIR TEMPERATURE AT TIME=03INITIALIZE ARRAY POSITIONS 366 TA(0)=TAI:RH(0)=RHI:TPT(0,0)=(TAI+TPI)/2 369 TC(0,0)=TPT(0,0):TS(0)-TPT(0,0):TAV(0)=TPT(0,0) 370 FOR X=0 TO XT:TC(X+1,0)=TPI:TPT(X+1,0)=TPI:NC(X,0)=HCID 372 HAV(x,0)=HCIO:TS(X+1)=TPI:TAV(X+1)=TPI:H(X)=HI 374 TA(X+1)=TA(X)-(C3/(CA+CV4H(X)))4(TA(X)-TS(X)) 376 NEXT 1 379 CLS: LOCATE 1,2 390 PRINT:PRINT TAB(6) “TIME (Min.) = 0.00”1PRINT 392 PRINT TAB(5) - BED DEPTH Ce'3 394 FOR XIO TO (12*BED) STEP (2*BED):PRINT USINS F1$3X*2.543 396 NEXT X:PRINT:PRINT 399 PRINT TAB(6) "AIR TEMP. '3:FOR X=0 TO XT STEP XPR 390 PRINT USINS F14;(TA(X)-32)/1.9;:NEXT X:PRINT 392 PRINT TAB(6) ”PELLET TEMP.”3:FOR X=0 TO XT STEP XPR 394 PRINT USINS F133(TC(X,0)-32)/1.831NEXT X:PRINT 396 PRINT TAB(5) " MOIS.CONT. '; 399 FOR X=0 TD XT STEP XPR:PRINT USINS F133MC(X,0)4100;:NEXT X 400 PRINT:PRINT TAB(5) " ABS. HUMID. '; 402 FOR X=0 TO XT STEP XPR:PRINT USINS F24;H(X);:NEXT X:PRINT 404 REM PRINT: PRINT TAB(10) STRIN6$(53,'!'): PRINT 406 LPRINT:LPRINT TAB(6) I'TIME (Min.) I 0.00'3LPRINT 408 LPRINT TAB(5) ' BED DEPTH CI'3 410 FOR X=0 TO (12*BED) STEP (2*BEDllLPRINT USINS F1$3X*2.543 412 414 416 419 420 422 424 426 429 430 432 434 436 439 440 442 444 446 449 450 452 454 456 459 460 462 464 466 469 470 472 474 476 479 490 492 494 496 499 490 492 494 496 499 500 502 504 506 509 510 512 514 516 519 520 204 NEXT X:LPRINT:LPRINT LPRINT TAB(6) 'AIR TEMP. '3IFOR x-o TO XT STEP XPR LPRINT USINS F14;(TA(X)-32)/1.9;:NEXT X:LPRINT LPRINT TAB(6) 'PELLET TEMP.'3:FOR X=0 TO XT STEP XPR LPRINT USINS F14;(TC(X,0)-32)/1.9;:NEXT X:LPRINT LPRINT TAB(5) - MOIS.CONT. '3 FOR X=0 TO XT STEP XPR:LPRINT USINS F14;NC(X,0)4100;:NEXT x LPRINT:LPRINT TAB(5) ~ ABS. HUMID. "; FOR X=0 TO XT STEP XPR:LPRINT USINS F24:H(X);:NEXT X:LPRINT LPRINT:LPRINT TAB(10) STRINS$(53,"!")1 LPRINT REM CPRI=OIPTII1/(DT460) REM TIME LOOP FOR L . DT To TI STEP DT CPRI=CPRI+1:SHC=0: STA=0 LOCATE 22,5 PRINT - ELAPSED TIME - '34PRINT USINS “44.44“; Li603 PRINT - ain.1'3:PRINT - COHPUTINS CONDITIONS AT ' REM DEPTH LOOP FOR X . 0 TO XT LOCATE 22,56 PRINT USINS ' 44.44";((X430.4949ED)/XT):: PRINT - ce.“ REM EOUILIBRIUH MOISTURE CONTENT EOUATIONS TPC=(TAV(X)-32)I(5/9) REM NELLIST EOUATION REM EMCD(X)=.191-.055!LOB(1-RH(X))-.02B*LOG(TPC) REM HENDERSON EOUATION REM EMCD(X)I(-LOB(1-RH(X))/(6.66*(TPC+22.12)))“(l/3.11) REM CHUNS-PFOST EOUATION EMCD(X)=.277-.0424LOB(-(TPC+13.3)*LOB(RH(X))) REM DIFFUSION COEFFICIENT EOUATION DIC=1.015E-054EXP(-547/(TPC+273.15)) REM MOISTURE CONTENT DIFFERENTIAL EON. SUHN=0:FOR I . 1 TO KL SUMCIB(I)4EXP(AR(I)!DIC4L) SUNHaSUNH+SUHC:NEXT I MCEO(X)=EMCD(X)+(MCID-EMCD(X))ISUMM REM MOISTURE CONTENT — FINITE-OIFF. FORMULAS HCT-HC(X,0):ENC=EHCO(X) AM-(DIC*DT)/(DELRIDELR) SOSUB 609 HC(X,1)-NT(0,NI-1):NS(X)=NT(H,NI):HAV(X,1)=HAVE SMCISMC+MAV(X,I) REM ABSOLUTE HUMIDITY EOUATION H(X+1)-H(X)-C14(NC(X,1)-NC(X,0)) REM PELLET TEMPERATURE EOUATIONS PIMAV(X,0) KI.1133-2.936*(P*P)+25.44i(PiPIP)-38.71§(P4P*P*P) CP=4190o(.343+P)/(1+P):CPEsCP/4196;69 AI(KlDELT)/(PDEMSCP!(DELR*DELR)) REM TPKsTPT(x,0)+459.69 HFSI(1056.5-.55*(TPK-520))i(1+23*EXP(-4ITPK*P)) DTEMPITA(X)-TS(X)IAUXICPE+CN*PIAUX1IHFS+CVIDTEMP DHTIH(X+1)-H(X) 522 524 526 528 530 532 534 536 538 540 542 544 546 548 550 552 554 556 558 560 562 564 566 568 570 572 574 576 578 580 582 584 586 588 590 592 594 596 598 600 602 604 606 608 610 612 614 616 618 620 622 624 626 628 630 205 TPT(X,1)ITPT(X,0)+024(((C44DTEMP)-(AUX1!C5)4DHT)IAUX) REM TACITA(X)1TP=TPT(X,O)IBOSUB 572 TC(X,1)IT(0,N-1)1TS(X)=T(M,N):TAV(X)ITAVE REM AIR TEMPERATURE EOUATION TAIX+1)-TA(X)-(C3/(CA+CV.H(X))1:(TA(X)-TS(X)) STA=STA+TPT(X,1) REM RELATIVE HUMIDITY IJ=2:OB=TA(X+1):HU=H(X+1):SDSUB 644:RH(X+1)=RH IF RH>RHC THEN RH(X+1)=RHC NEXT 1 NCAVEsSNC/X:TPA:((STA/X)-32)/1.9 FOR X=0 TO XT:MC(X,0)IMC(X,1)1TC(X,O)=TC(X,1) TPT(X,0)ITPT(X,1)IMAV(X,0)IMAV(X,1):NEXT X REM SOSUB 704 IF PTIICPRI THEN CPRI-0:SOSUB 776 NEXT L LPRINT:LPRINT LOCATE 23,5 INPUT 'DO YOU NANT TO INPUT NEN DATA? (Y DR N) ',ND4 IF NOs=-N- OR NDSI'n' SOTO 569 IF ND4=-Y" DR NDss-y- SOTO 134 ELSE SOTO 560 END REM SUBROUTINE FINITE DIFFERENCE FORMULAS REM SUBROUTINE PELLET TEMPERATURES FOR J=0 TO N:T(J,0)=TP:NEXT J DI(2§AIHTMICIDELR)/K T1=(1+2iM-44A)/(1+2*M):T2=4iA/(1+2!M)4T3=A*B T4=1-2iAITS=A4C:T6=2IAIT7=1-2*A-D FDR N=0 TD TT SUM . 0 FOR J=1 TO M T(0,N+1)=T14T(O,N)+T2*T(1,N) T(J,N*1)=T3IT(J-1,N)+T4!T(J,N)+T54T(J+1,N) T(H,N+1)-T64T(N-1,N)+T7:T(H,N)+D4TAC SUM=SUM+T(J,N+1) NEXT J TAVE=(SUN+T(0,N+I))/J NEXT N IF X)0 SOTO 606 FOR I9-0 TO N: TS(IS)=T(IS,N):NEXT IS RETURN REM SUBROUTINE PELLET MOISTURE CONTENT FOR J-o TO H:NT(J,0)=HCT:NEXT a DI(2IAM*HM4C!DELR)/DIC M1I(1+24M-4*AM)/(1+2*M)1M2=4IAM/(1+2!M):M3IAMIB M4=1-2!AM4M5=AM§CIM6I2§AMIM7=1-24AM-D FOR NI=0 TO TTM SUM . 0 FOR I=1 TO M MT(0,NI+1)=M1*MT(O,NI)+M24MT(1,NI) MTIJ,NI+1)=M3§MT(J-1,NI)+M4IMT(J,NI)+M5!MT(J+1,NI) MT(M,NI+1)IM6§MT(M-1,NI)+M7*MT(M,NI)+D*EMC SUHaSUH+HT(J,NI+1) 206 632 NEXT J 634 MAVEI(SUM+MT(0,NI+1))/J 636 NEXT NI ' 638 IF X)0 SOTO 642 640 FOR ISIO TO M: MCS(IS)=MT(IS,NI):NEXT IS 642 RETURN 644 REM SUBROUTINE PSYCHART(DB,NB,DP,RH,HU,PV,SV,HFS) 646 IF DB>212 SOTO 652 648 A4392.297788:BBI.22268838:CII12.887434:D889.4150024 650 SOTO 654 652 A4344.117028:BO=.2949225I:C8821.777374:D4=55.987038 654 IF DB>180 SOTO 662 656 814I7.37013E-06:B2lI-3.53885E-03:B3NI.8275228:B44=3.89627E-06 658 B5II-2.60113E-06:B68I1.4041910 660 SOTO 666 662 814I2.49546E-06:B2NI-2.04326E-03:B38=.707415NIB4BI1.88247E-06 664 855=-2.00086E-03:86481.4422155 666 T=DB+459.69 668 PSIEXP(54.63298-(12301.6884/T)-5.1692354LOS(T)) 670 IF IJ=2 THEN PV=HU*14.696/(.621+HU):RH=PV/PS:SOTO 674 672 PVIPSiRH 674 DP=A45PVABI+CN|LOS(PV) +05 676 DTD=DB-DP 678 NBIDPP(B14*DTD‘3+824*DTD‘2+B3N*DTD)*EXP((844*DTD+B58)|DP0864) 680 IF IJ=2 SOTO 684 682 HUI.6219I(PV/(14.696-PV)) 684 SV=(53.35I*(DB+459.69))/(144*(14.696-PV)) 686 SOTO 702 688 TIDB 690 IF (T)32) AND (T<150) THEN SOTO 696 ELSE IF T>150 SOTO 700 692 HFSII220.8448-.0507754T 694 SOTO 702 696 HFS=1075.89654-.56983A*(T-32) 698 SOTO 702 700 HFS=(1354673.2144-.9125275587!*(T+459.69)‘2)“.5 702 RETURN 704 REM SUBROUTINE PRINT I SCREEN 706 CLS: LOCATE 1,2 708 PRINT:PRINT TAB(6) 'TIME (Min.) I "34PRINT USINS F3$3Li60 710 PRINT TAB(5) ' BED DEPTH ce'3 712 FOR YI0 TO (12*BED) STEP (2*BED):PRINT USINS F1$3Yi2.543 714 NEXT Y:PRINT:PRINT: PRINT TAB(5) ' AIR TEMP. C '3 716 FOR YIO TO XT STEP XPR:PRINT USINS F133(TA(Y)-32)/1.83:NEXT Y 718 PRINT:PRINT TAB(5) ' PELLET TEMPERATURES (C)' 720 PRINT TAB(5) ' AT CENTER '3 722 FOR Y=0 TO XT STEP XPR:PRINT USINS F183(TC(Y,0)-32)/1.83:NEXT Y 724 PRINT: PRINT TAB(5) ' AT SURFACE '3 726 FOR Y=0 TO XT STEP XPRTPRINT USINS F1$3(TS(Y)-32)/1.833NEXT Y 728 PRINT: PRINT TAB(5) ' AVERASE '3 730 FOR Y=0 TO XT STEP XPRIPRINT USINS F133(TAV(Y)-32)/1.83INEXT Y 732 PRINT:PRINT TAB(5) ' TEMP. EON. '3 734 FOR Y=0 TO XT STEP XPR: PRINT USINS F133(TPT(Y,0)-32)/1.83:NEXT Y 736 PRINT:PRINT TAB(5) ' PELLET MOISTURE CONTENTS (1 DB)' 738 PRINT TAB(5) ' AT CENTER '3 740 FOR YIO TO XT STEP XPRIPRINT USINS F1$3MC(Y,0)*1003INEXT YIPRINT 742 744 746 748 750 752 754 756 758 760 762 764 766 768 770 772 774 776 778 780 782 784 786 788 790 792 794 796 798 800 802 804 806 808 810 812 814 816 818 820 822 824 826 828 830 832 834 836 838 840 842 844 846 848 850 207 PRINT TAB(5) ' AT SURFACE '3 FOR Y I 0 TO XT STEP XPR: PRINT USINS F1$3 MS(Y)*1003: NEXT Y PRINT: PRINT TAB(5) ' AVERAGE 08. '3 FOR YIO TD XT STEP XPR:PRINT USINS F1$3MAV(Y,0)i1003:NEXT YIPRINT PRINT TAB(5) ' AVERASE ZNB '3 FOR Y=0 TO IT STEP XPR:NIMAV(Y,0):PRINT USINS F1$3(N*100)/(1+N)3 NEXT YIPRINTI PRINT TAB(5) ' MC.D. EON. '3 FOR YIO TO XT STEP XPR:PRINT USINS F133MCEO(Y)41003:NEXT Y PRINT:PRINT TAB(5) ' EO.MO.CONT. '3 FOR Y=0 TO XT STEP XPR:PRINT USINS F1$3EMCD(Y)41003:NEXT Y PRINT:PRINT TAB(5) ' REL. HUMID. '3 FOR Y=0 TO XT STEP XPR:PRINT USINS F153RH(Y)§1003:NEXT Y PRINT:PRINT TAB(5) ' ABS. HUMID. '3 FOR YIO TO IT STEP XPR:PRINT USINS F283H(Y)3:NEXT Y:PRINT PRINT:PRINT TAB(7) 'AVE.PEL.TEMP. (C) '3:PRINT USINS F1$3TPA3 PRINT ' AVE.MC. (%DB) I '31PRINT USINS F1$3MCAVE5100 RETURN REM SUBROUTINE PRINT = PRINTER LPRINT:LPRINT TAB(5) ' TIME (Min.) I '3:LPRINT USINS F183LI60 LPRINT: LPRINT TAB(5) ' BED DEPTH ce'3 FOR YIO TO (IZIBED) STEP (2IBED):LPRINT USINS F133Y§2.543 NEXT Y:LPRINTTLPRINT: LPRINT TAB(5) ' AIR TEMP. C '3 FOR Y=0 TO XT STEP XPR:LPRINT USINS F133 (TA(Y)-32)/1.831NEXT Y LPRINT:LPRINT TAB(5) ' PELLET TEMPERATURES (C)' LPRINT TAB(5) ' AT CENTER '3 FOR YIO TO XT STEP XPR:LPRINT USINS F133(TC(Y,0)-32)/1.83:NEXT Y LPRINT:LPRINT TAB(5) ' AT SURFACE '3 FOR Y=0 TO XT STEP XPR:LPRINT USINS F1$3(TS(Y)-32)/1.83:NEXT Y LPRINT: LPRINT TAB(5) ' AVERASE '3 FOR Y=0 TO XT STEP XPR:LPRINT USINS F133(TAV(Y)-32)/1.83:NEXT Y LPRINT:LPRINT TAB(5) ' TEMP. EON. '3 FOR Y=0 TO XT STEP XPR:LPRINT USINS F15;(TPT(Y,0)-32)/1.83:NEXT Y LPRINT:LPRINT TAB(5) ' PELLET MOISTURE CONTENTS (1 DB)' LPRINT TAB(5) ' AT CENTER '3 FOR Y=0 TO XT STEP XPR:LPRINT USING F133MC(Y,0)§1003:NEXT Y LPRINT:LPRINT TAB(5) ' AT SURFACE "3 FOR Y=0 TO XT STEP XPR:LPRINT USING F1$3MS(Y)51003:NEXT Y LPRINT: LPRINT TAB(5) ' AVERASE "3 FOR Y=0 TO XT STEP XPR:LPRINT USINS F1$3MAV(Y,0)*1003:NEXT Y LPRINT:LPRINT TAB(5) " AVERASE 1N8 "3 FOR Y=0 TO XT STEP XPR:N=MAV(Y,O):LPRINT USINS F133(NI100)/(1+N)3 NEXT Y:LPRINT: LPRINT TAB(5) ' MC.D. EON. "3 FOR YIO TO XT STEP XPR:LPRINT USING F153MCEO(Y)*1003:NEXT Y LPRINT: LPRINT TAB(5) ” EO.MO.CONT. '3 FOR Y=0 TO XT STEP XPR:LPRINT USINS F183EMCD(Y)91003:NEXT Y LPRINT:LPRINT: LPRINT TAB(5) “ REL. HUMID. ”3 FOR Y=0 TO XT STEP XPR:LPRINT USINS F183RH(Y)§1003:NEXT Y LPRINT:LPRINT TAB(5) " ABS. HUMID. '3:FOR YIO TO XT STEP XPR: LPRINT USINS F233H(Y)3:NEXT Y:LPRINT LPRINT:LPRINT TAB(7) “AVE.PEL.TEMP. (C) "33LPRINT USINS F183TPA3 LPRINT ' AVE.MC. (ZDB) = '3:LPRINT USINS F1t3MCAVE9100 LPRINT TAB(6) "MOISTURE CONT. INSIDE A PELLET AT THE BOTTOM LAYER" LPRINT TAB(4) ' '3ILPRINT USINS F1$3MCS(0)§1003 FOR OI1 TO MILPRINT USINS F183MCS(O)*1003:NEXT OILPRINT LPRINT TAB(6) 'MOISTURE CONT. INSIDE A PELLET AT THE TOP LAYER' 852 854 856 858 860 862 864 866 868 870 872 208 LPRINT TAB(4) - '31LPRINT USINS F14;HT(0,NI-I):100; FDR 9:1 TO M:LPRINT USINS F14;HT(O,NI-1)4100;:NEXT 9:LPRINT LPRINT TAB(6) 'TEMPERATURE INSIDE A PELLET AT THE BOTTOM LAYER' LPRINT TAB(5); FOR o-o TD MILPRINT USINS F14;(TS(O)-32)/1.9;:NEXT D LPRINT TAB(6) 'TEMPERATURE INSIDE A PELLET AT THE TOP LAYER“ LPRINT TAB(5); FOR O=o TO M:LPRINT USINS F14;(T(D,N)-32)/1.9;:NEXT O LPRINT TAB(10) STRING$(54,'I') LPRINT:LPRINT RETURN 209 PDE MODEL OUTPUT SAMPLE INITIAL CONDITIONS AIR TEMPERATURE RELATIVE HUMIDITY (I) PELLET TEMPERATURE (F) MOISTURE CONTENT (1 DB) PELLET DIAMETER (In.) AIR FLON (CFM/FT2) HEAT T.COEF. (BTU/FT2 HrF) MASS T.COEF. (MIHr) COOLER DEPTH (FT) DELTA N (In.) DELTA t (M1n.) (F) TIME (M1n.) I 0.00 BED DEPTH CI 0.00 80.00 55.00 150.00 20.48 .1875 100.00 18.68 .0126 1.00 0.25 0.50 26.67 65.56 17.00 4.76 0.51 106.04 30.48 0.63 C C 1N8 ee M/S (N/M2 K) CM CM AIR TEMP. PELLET TEMP. MOIS.CONT. ABS. HUMID. 26.67 46.11 20.48 .0120 5.08 65.56 65.56 20.48 .0120 10.16 65.56 65.56 20.48 .0120 15.24 65.56 65.56 20.48 .0120 20.32 65.56 65.56 20.48 .0120 25.40 65.56 65.56 20.48 .0120 30.48 65.56 65.56 20.48 .0120 O{HID1555559559085558955550855ODOOODOOODOODOOOONOOOODIO 210 TIME (M1n.) I 20.00 BED DEPTH CI 0.00 5.08 10.16 15.24 20.32 AIR TEMP. C 26.67 25.54 24.73 24.16 23.78 PELLET TEMPERATURES (C) AT CENTER 26.18 25.19 24.49 24.00 23.67 AT SURFACE 26.49 25.42 24.64 24.10 23.74 AVERASE 26.32 25.30 24.56 24.05 23.70 TEMP. EON. 26.14 25.17 24.47 23.99 23.66 PELLET MOISTURE CONTENTS (5 DB) AT CENTER 19.12 18.69 18.49 18.33 18.19 AT SURFACE 14.49 15.37 16.11 16.69 17.12 AVERASE 17.49 17.53 17.65 17.75 17.82 AVERASE XNB 14.88 14.91 15.00 15.08 15.12 MC.D. EON. 16.89 17.46 17.92 18.29 18.56 EO.MO.CONT. 14.12 15.11 15.92 16.56 17.04 REL. HUMID. 55.00 61.10 65.74 69.19 71.60 ABS. HUMID. .0120 .0125 .0128 .0130 .0132 AVE.PEL.TEMP. (C) 24.24 AVE.MC. (%DB) I MOISTURE CONT. INSIDE A PELLET AT THE TOP LAYER 17.97 17.96 17.93 17.86 17.76 17.63 TEMPERATURE INSIDE A PELLET AT THE TOP LAYER 23.31 23.32 23.32 23.33 23.34 23.34 25.40 23.52 23.45 23.50 23.47 23.45 18.07 17.43 17.85 15.14 18.75 17.38 73.21 .0133 17.71 30.48 23.36 23.31 23.34 23.33 23.32 17.97 17.63 17.85 15.15 18.88 17.60 74.24 .0133 INNS.55II55!llINDODDICIOIONNOOIODIONOIDDNNINCSNNNONII8 APPENDIX E BMDPAR SUBROUTINE: HBO and D ESTIIIATION 1008 1108 1208 1308 1408 1508 1608 1708 1808 1908 2008 2108 2208 2308 2408 250I 2608 270I 2808 2908 3008 310I 3208 330I 3408 350= 3608 3708 390: 390: 400: 410: 420: 430= 440: BMDPAR SUBROUTINE: EMC and D ESTIMATION / PROBLEM / INPUT I VARIABLE / TRANSFORM / RESRESS / PARAMETER / FUN / PLOT / SAVE / END TITLE IS 'PELLETS:EMC AND D'. VARIABLES = 4. UNIT . 55. FORMAT IS '(F4.1,1X,F4.1,1X,F4.1,1X,F4.1)'. NAMES - XMT,XM,T,TI. TI = TI/6o. DEPENDENT = XMT. PARAMETERS = 2. PRINT = XHT,TI. ITERATIDNS . 100. CONVERSE = .0001. HALVINS = 20. INITIAL = 10.,000001. MAXIMUM = 100,10. NAMES 8 EMC,D. ALP182.405i§24ALP2I5.52*i28ALP388.654!|2. ALP4II1.792*528ALP5I14.931*G2SALP6818.071II2. ALP7=21.22II2SALP8824.355*23ALP9827.49II2. ALP10I30.63**2. AI4/ALP1$884/ALP24C84/ALP3SE84/ALP4SS=4/ALP5. OI4/ALP6$PI4IALP7$OI4IALPSSR84/ALP9SSI4/ALP10. DIA 8 .1875. RMS I ((DIA/2)*.0254)**2. Cl=-ALP1IRMSSC2I-ALP2/RMS$C3=-ALP3IRMS. C4I-ALP4/RMSSC58-ALP5/RMS$C6I-ALP6/RMS. C78-ALP7/RMS$C8=-ALP8/RMS$C9=-ALP9/RMS. C10=-ALP10lRMS. FIEMC+(XM-EMC)*(A*EXP(C1*D*T)+(BIEXP(C2!D*T)+ (CIEXP(C3§D*T)). VARIABLE IS XMT. RESIDUAL. SIZE = 20, 12. CODE = T3B. UNIT . 9. NEN. 211