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' 'E‘Sl S MICHIGAN STATE UN vensm LIBRARIES \ llllllllllllllllll llllll \l l ill 3 1293 00909 6565 I This is to certify that the dissertation entitled The Development Of A Fixed Bed Drying Model For Wood Chips Under Forced Air At Ambient Condition presented by Yonggang Feng has been accepted towards fulfillment of the requirements for Ph.D. degree in Forestry ajor professor Date January IQ, 1992 MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 .,____- ._.. »___ -___i.. ——____ ___ ______ LIBRARY Hickman State Unlvcnity J l PLACE IN RETURN BOX to remove this checkout from your record. To AVOID FINES return on or before date due. MSU Is An Affirmative ActiorVEqual Opportunity Institution czwmmpma-pd THE DEVELOPMENT OF A FIXED-BED DRYING NODEL TOR 'OOD OBITS UNDER TOROBD AIR AT AMBIENT CONDITIONS by Yonggang Feng A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of- DOCTOR OF PHILOSOPHY Department of Forestry 1991 rapi been sour of ' nois fuel bade Prov Prac Sign rang sin-j Chan empl 0rde gap 7397 ABSTRACT TEE DEVELOPMENT OF A FIXED BED DRYING MODEL TOR NOOD CHIPS UNDER FORCED AIR AT AMBIENT CONDITIONS by Yonggang Feng The application of wood energy in industry has been developed rapidly since the 19703, and a considerable amount of research has been conducted to improve combustion and fuel handling. The major source of wood fuel in the industry is fresh cut.wood chips because of the convenience in processing them. However, their high moisture content greatly reduces the net heating value of this wood fuel, as well as its combustion efficiency. The objective of this study was to develop a fixed bed drying model for wood chips under forced air and at ambient conditions to provide the basic engineering information required for designing a practical wood chip dryer. Some physical properties of wood chips related to fixed bed drying were evaluated as the basic information in the drying simulation. These properties included (1) the moisture content range of wood chips, (2) wood chip size distribution, (3) bulk shrinkage during drying, and (4) airflow resistance in the wood chip bed. A thin layer drying experiment was performed in a conditioning chamber to develop a thin layer drying model. Then, this model was employed in a semi-theoretical grain drying fixed bed model in order to simulate a fixed bed dryer. The controlled factors incluc size. 1 experi condit expeti and Ito the Ho nonlin determ comput upiri inform. distril Values A “(has the MN tile. IOdel l time t] BI IOdel, dasign d1Ting included air temperature, air relative humidity, and wood chip size. An empirical fixed bed drying model was developed through the experiment with a small fixed-bed drying system mounted in a conditioning chamber. Pour factors were controlled in the experiment: air temperature, air relative humidity, airflow rate, and wood chip size. One variable, the original moisture content of the wood chips, was not controlled. The final model, including a nonlinear equation and a multiple polynomial equation was determined by using regression routines in a SAS program. A computer program called "CHIP DRY” executing the simulation of the empirical model was written in FORTRAN to provide the following information for the drying process in a dryer: moisture content distribution, average moisture contents, average net heating values, bulk shrinkage, and airflow resistance. A testing experiment was performed in a fixed bed dryer 14 inches in diameter and 48 inches high to test the feasibility of the models for larger scale dryers and over long periods of drying time. The results of the experiment indicated that the empirical model provided more accurate simulation and used much less computer time than the semi-theoretical model. Because of the accurate and rapid simulation of the empirical model, this information can serve as the basis for optimum dryer design which, in turn, will provide the best method for wood chip drying. To my parents and my wife for their love and support iv Henr tech COM WittI gradI Fore: dEVe] suPpc ”mm ACKNOWLEDGMENTS The author wishes to express his deepest appreciation to Dr. Henry A. Huber, advisor and friend, for his understanding, technical support, helpful criticisms, and patience. The author would like to thank the other members of the committee, Dr. Alan Sliker, Dr. David Nicholls, Dr. Karen Potter- Witter, and Dr. Kalinath Mukherjee, for their valuable guidance. A very special appreciation goes to the faculty, staff, and graduate students of the Michigan State University, Department of Forestry, Forest Products Laboratory, for their cooperation in developing the experimental equipment and their good suggestions. Finally, I thank my wife, Li, for her understanding and support.during the study, and my parents for their encouragement to complete this work. L18? C LIEII LIST I 1. I81 11. Q III, TABLE OP CONTENTS LI 8! or run” 0 O O O O O O O O O O O O O O O O O O O O O O x L1 8! or ’1 am. 0 O O O O O O O O O O O O O O O O O O O O O x i 1 L18! 0’ among 0 O O O O O O O O O O O O O O O O O O O O O xv CHAPTER I O IMODUCTIOI e o e e e e e e e e e e e e e e e e e e e e e 1 1 e 1 W e e e e e e e e e e e e e e e e e e e e 1 1.1.1 The Importance of Wood Energy . . . . . . . . 1 1.1.2 The Heating Value of Wood . . . . . . . . . . 5 1.1.3 Wood Energy Facilities in Industry . . . . . 11 1-2 H99d_Qhine_and_8elatsd_fitudiea - - - - - - - . - - - 12 1.2.1 Wood Chips in Industries . . . . . . 12 1.2.2 Production and Storage of Wood Chips . . . . 13 1.2.3 Studies on Wood Chips . . . . . . . . . . . . 14 1.3 . . . . . 15 1.3.1 Agriculture Products . . . . . . . . . . . . 15 1 O 3 O 2 “00d Partiales O O O O O O O O O O O O O O O 16 II. 18 18 19 19 20 III. reverent 2309329133 or noon cares RELATED ro tires are DRYING . . . . . . . . . . . . . . 21 3 1 Qrisinal_u2isture.§2ntent_2f_flesd_£hins - - - - . . 21 3 2 fl99d_Qhin_Size_and_§urfaselyglums_3atig . - - - - - 22 3.2.1 Study Methods on Wood Chip Size and Surface/Volume Ratio . . . . . . . . 23 3.2.1.1 Largest Cross Section Area of a Wood Chip 0 O O O I I O O O O O 27 3.2.1.2 Surface/Volume Ratio of a Wood Chip . 27 3.2. 2 Results of the Study on Largest Cross Section Area and Surface/Volume Ratio . . . . . . . . 28 vi 3.4 IV. Om 4.1 Inc. 0. you 4.4 3.3 3.4 3.2.3 Discussion on Largest Cross Section and Surface/Volume Ratio . . . . . . . 3.3.1 Study Methods . . . . 3.3.2 Results of Bulk Shrinkage Test . . 3.3.3 Discussion on the Bulk Shrinkage of Chips . . . . . . . . . . . . . 3.4.1 Study Methods . . . . . . . . . . 3. 4. 2 Results . . . . . . . . . . 3.4.3 Discussion on Airflow Resistance ....'§.... .....g'.... IV. DEVELOPMENT OR A TEIN LAYER DRYING MODEL AND MODIFICATIONS TO THE GRAIN DRYING MODEL 4.1 O O O O O O O I C O O O O O O O 0 4.1.1 Wood Drying Principle . . . . . . . . . . . 4.1.2 Thin Layer Drying Equation . . . . . . . . L 1. 3 Semi-theoretical Fixed Bed Drying Model . . L 2 Experimgn;_ngsign . . . . . . . . . . . . . . . . 4.3 4.4 4.3.1 Sample preparation for Thin Layer Wood Chip Drying Experiment . . . . . . . . . . . . . 4.3.2 Equipment . . . . . . . 4.3.3 Measurement of the Thin Layer Wood Chip Drying Experiment . . . . WW Erecting); 4.3.4 Development of a Thin Layer Wood Chip Drying ”Ode 1 C O O O O O O O O O O O O 0 4.3.4.1 Determining Drying Constants . . . . . 4.3.4.2 Determining the Relationship Between Drying Constant and Drying Conditions . . . . . 4.3.5 Modification of the Grain Drying Model . . 4.4.1 Thin Layer Drying Equations . . . . . . . . 4. 4.2 Drying Constant Equation . . 4. 4.3 Discussions on Thin Layer Wood Chip Drying Experiment . . . . . . 4.4.2.1 Air Temperature as Related to the Drying Constant . . . . . . . . 4.4.2.2 Relative Humidity as Related to the Drying Constant . . . . . . . . . 4. 4.2. 3 Wood Chip Size as Related to the Drying Constant . . . 4. 4.L 4 Temperature and Relative Humidity as Related to the Drying Constant . . . 4.4.2.5 Relative Humidity and Wood Chip Size as Related to the Drying Constant . 4.4.4 Semi-theoretical Fixed Bed Wood Chip Drying “Ode 1 O O O O O O O O O O O O O O O O I O 0 vii 56 56 57 59 61 61 69 69 70 71 71 72 V. 03‘ DR} VII. vIII V. DEVELOPMENT OP EMPIRICAL TIRED BED DRYING MODEL USING THE REGRESSION METHOD . . . . . . . 51W -. “WW” 5. L 1 Experiment Design . . . . . . . 5.2. 2 Equipment Used in the Fixed Bed Wood Chip Drying Experiment . . . . . . . 5.2.3 Measurement of the Fixed Bed Wood Chip Drying Experiment . . . . . . . . . . . . . . . . . 5.3 We flgggl . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Determining Depth Constant and Time Constant in the Fixed Bed Wood Chip Drying Model . . . 5.3. 2 Determining the Models to Explain k1 and RD . 5 3. 3 Development of a Computer Program from theD Empirical Fixed Bed Wood Chip Drying Model . 5.4mm“ 5.4.1 Determining k and k for Each Experimental Condition using Nonlinear Regressions . . . . 5.4.2 The Development of the Models for kx and kt 5.4.L 1 Analysis of Variance of k and kt . 5.4.2.2 Regression Analysis of kt and k3. 5-5 DE1E12RmEnS_Q1_§h§__£HIE_DBX__£QmPn§£I_EIQSIAE - - - VI. MODEL TESTING EXPERIMENT . . suinW 62W merino; 6.2.1 Experimental Design of Model Testing Experiment . . . . . . . 6. 2. 2 Equipment Used in the Large Scale Model Testing Experiment . . . . . 6. 2. 3 Measurement of the Large Scale Model Testing Experiment . . 63W W V: I . cayenne I one C O O O O O I O O O O O O O O O O O O O 0 VIII. SUGGESTIONS FOR ADDITIONAL RESEARCH . . . . . . . . . . viii 73 77 77 78 83 85 85 87 90 91 91 92 94 98 101 101 101 101 102 105 105 107 107 108 109 110 111 IEPEHD APPENI IPPENI IPPKHI APPENI lPPENl LIST 1 APPENDIX A APPENDIX B APPENDIX C THE INDEPENDENT VARIABLES (OMC, T, RH, v, e e e APPENDIX D APPENDIX E APPENDIX E COMPARISON OP THE RESULTS IN THE TESTING EXPERIMENT AND THE RESULTS OP EMPIRICAL MODEL SIMULATION LIST OP REPERENCE . ix LISTING OP THE COMPUTER PROGRAM "CHIP DRY" RESULTS OP LARGE SCALE TESTING EXPERIMENT AND DRYING MODEL SIMULATIONS DRYING CONSTANTS OBTAINED IN THIN LAYER DRYING EXPERIMENT DEPTH CONSTANTS AND TIME CONSTANTS OBTAINED IN TIRED BED DRYING EXPERIMENT RELATIONSHIP BETWEEN THE CONSTANTS (Rx and Mt) AND SS, AND 113 118 122 130 136 139 142 Table 1.1 1.2 3.1 3.2 3.3 3.4 3.5 3.5 Table 3.3 3.4 3.5 LIST OF TABLES Chemical composition and HHV of 7 species of North American Woods (Tillman, 1987). . . . . The influence of moisture on fuel value and combustion efficiency (Tillman, 1987). . . . Analysis data of the three dimensional measurement on three different sized red pine chips 0 O O O O O O O O O O O O O O O O O O O Largest cross section area and surface/volume of three different sized red pine chips. . . Largest cross section area distribution. . . Surface/volume ratio distribution . . . . . . Nonlinear regression data on bulk shrinkage taSte O O O O O O 0 O O O O O O O O O 0 O O 0 Nonlinear regression on airflow resistance in wood chip bed with airflow rate. . . . . . . Thin layer experimental design for wood chip drying. . . . . . . . . . . . . . . . . . . . Analysis of variance of the drying constant k in the thin layer wood chip drying experiment.. . . . . . . . . . . . . . . . . Parameter estimates of the drying constant equation after the multiple regression analysis. . . . . . . . . . . . . . . . . . . Experimental design for the empirical fixed bed wood chip drying model. . . . . . . . . . Analysis of variance of depth constant kx. . Analysis of variance of time constant kt. . . X 29 29 30 30 36 42 55 66 67 77 93 93 5.4 5.5 6.1 A1 Bl £1 £2 £3 A1 Bl E1 EZ E3 Example of the input data of the "CHIP DRY" computer program for the simulation of a wood chip dryer. . . . . . . . . . . . . . . . . . Example of the results of the wood chip dryer simulation computed by the computer program "CHIP DRY". . . . . . . . . . . . . . . . . Experimental conditions for model testing experiment. . . . . . . . . . . . . . . . . . Drying constants obtained by performing the nonlinear regressions for 192 testings. . . . The time constant kx and depth constant kt obtained by performing nonlinear regressions under different experimental conditions. . . Comparison of the results of testing experiment and the simulation results of the empirical drying model and the semi- theoretical drying model. Fixed bed wood chip drying condition: OMc- 133%, T-68°F, RH-73t, SZ-O.46 in2 , V882 cfm/ft2 . . . . . . . . . . Comparison of the results of testing experiment and the simulation results of the empirical drying model and the semi- theoretical drying'model. Fixed bed wood chip drying condition:2 OMC- 130. 7%, T-70'F, RH-7ot, 32-0. 30 in2 , V-82 cfm/ft2 . . . . . . Comparison of the results of testing experiment and the simulation results of the empirical drying model and the semi- theoretical drying’model. Fixed bed wood chip drying condition: onc- 137L T-70°F, RH-86L 82-0. 46 in2 , V=99 cfm/ft2 . . . . . . . . . . xi 100 100 102 113 118 132 133 134 Figure 1.1 1.2 1.3 3.1 302 3.3 30‘ 3.5 4.1 Figure LIST OP FIGURES Energy reserves in the 0.8.: About 300 quads are in standing forests with an annual production of 7 to 8 quads. About 200 quads are in Oil, about 300 quads in gas, and about 4,000 quads in coal. (Drawing from Department of Energy). . . . . . . . . . . . . . . . . . Influence of moisture content on the heating value of wood (Tillman, 1987). . . . . . . . Time required for natural convective drying of aspen and red maple chunks and chips (Sturos,J.B., Coyer,L.A. and Arola,R.A. 1983). . . . . . . . . . . . . . . . . - . . A four-level screen used for size sorting wood chips in the laboratory. The size of the screen openings are 1", 3/4", 8", and k". . . A typical wood chip shape and its three dimensions labeled as L (length), W (width), and 2 (thickness). . . . . . . . . . . . . Distribution and probability of largest cross section area of wood chips compared toITable 3.3. O O O O O O O O O O O O I O O O O O O 0 Distribution and probability of surface/volume ratio of wood chips compared to Table 3.4. . Nonlinear regressions on. pooled experiment data for (1) wood chips of sz-1 and 52-2 sizes and (2) all chip size samples. . . . . Airflow resistance of wood chip bed and airflow rate plotted from Table 3.6. . . . . Two drying steps for biomass material: constant drying rate and falling drying rate (Brooker, 1974). . . . . . . . . . . . . . xii Page 10 25 26 31 32 37 43 48 402 C1 1’1 C1 F1 Thin layer wood chip drying experiment performed in a controlled temperature and relative humidity conditioning chamber. . . . Representative drying curves in the thin layer wood chip drying experiment of 4 chip sizes at air temperature 96.8°F and air relative humidity 55%. . . . . . . . . . . . . . . . . A representative regression line related to the thin layer drying experiment for wood chip sample 82-1 at the experimental condition of temperature 96.8°F and relative humidity 5500*O O O O O O O O O O O O O O O O O O O O The drying constants change with air temperature, air relative humidity, and wood chip size in the thin layer wood chip drying experiment. . . . . . . . . . . . . . . . . . Fixed bed grain drying curves (Hukill, 1954)O O O O O O O O O O O O O O O O O O O O The fixed bed wood chip drying experiment was performed in three dryers mounted in a conditioning chamber. . . . . . . . . . . . . The structure of the dryer and the moisture samples in the fixed bed wood chip drying experiment. . . . . . . . . . . . . . . . . . Representative drying curves of the fixed bed wood chip drying experiment. . . . . . . . . A typical, representative fixed bed wood chip drying surface. . . . . . . . . . . . . . . The drying surfaces plotted for different kx and kt O O O O O O O O O O O O O O O O O O O O Fixed bed dryer used in the large scale model testing experiment. . . . . . . . . . . . . . The relationship between the constants (k." and ) and the independent variables is presented w th three dimension graphs for the fixed bed drying experiment. . . . . . . . . . . . . . (a) Results of large scale testing experiment and (b) results of empirical fixed bed drying model simulation, experiment condition: onc- 133:, T-68°F, 23-73:, sz-o.46 1n2, v-ez xiii 58 60 62 68 75 79 81 84 86 89 104 122 F2 P3 ctm/ ttz O O O O O O O O O O O O O O O O O O O O O O 135 (a) Results of large scale testing experiment and (b) results of empirical fixed bed drying model simulation, experiment condition: onc- 133t, Ti68°F, RH=73%, sz=o.46 1n2, v-ez cfm/ft2 . . . . . . . . . . . . . . . . . . . (a) Results of large scale testing experiment and (b) results of empirical fixed bed drying model simulation, experiment condition: one- 1333, Tt68°F, RH=73%, sz-o.46 in’, V882 cfm/ft . . . . . . . . . . . . . . . . . . . xiv . 136 . 137 BV 1! LIST OE SYMBOLS constant particle temperature, °F product density, lb/bu specific volume of air, ft3/lb particle surface area per unit bed volume, ftz/ft3 single particle surface area constant bulk volume coefficient fraction of wood consisting of holocellulose shape coordinate constant in airflow resistance formula specific heat of dry air, Btu/1b/°F largest cross section area, in2 cubic foot per minute specific heat of dry grain kernels, Btu/lb/°F specific heat of water vapor, Btu/lb/°F specific heat of liquid water, Btu/lb/°F depth factor equilibrium moisture content, % airflow resistance, inch ago airflow velocity, ft/min hI in ii Refit. OMC 0V OMC OV airflow rate, lb/hr/ft2 convective heat transfer coefficient, Btu/ft2/°F/hr heat of evaporation, Btu/lb higher heating value, Btu/lb drying constant, hr'1 phenomenological coefficient time constant depth constant length, mm moisture content, percent moisture ratio net heating value, Btu/lb original moisture content, percent original bulk volume, in3 vapor pressure, psi airflow resistance, inch H20 airflow rate, CFM particle coordinate determination of regression relative humidity, % surface area, in2 surface/volume ratio, in"1 wood chip size, in2 time, hour temperature, °F air temperature, °F xvi 0-1 I<3<§8< N temperature of the air leaving grain mass, °F volume, in3 air humidity ratio, lb/lb bulk volume, in3 depth value in the wood chip bed, in time unit thickness, mm xvii 1.1 ! increa Wood £0551; Value noist‘ Order induS Simul Years Btu). 1977) Suppl State INTRODUCTION 1-1 W Wood fuel, as a renewable energy source, has received increasing attention during recent years. Supplied as freshly cut wood chips for industrial energy supply, wood fuel, compared to fossil fuel, has a higher moisture content and a lower net heating value. Since drying is the method commonly used to reduce the moisture content of wood, it is possible to do so economically in order to increase the combustion efficiency of wood fuel boilers in industry. The objective of this study is to develop a model to simulate the wood chip drying process in a fixed bed dryer. 1.1.1 The Importance of Wood Energy Wood as a source of energy has a long history. One hundred years ago, 75 percent of the four quad ( 1 quad - 1,000,000 million Btu) energy supply in the United States came from wood fuel (Zerbe, 1977). Industrial development changed the distribution of energy supplies. Although the total energy consumption in the United States was about 75 quads in 1976, but consumption of wood energy drop; to th such such this energ used 1989) Food. (Hall Carbc energ energ (Iliad: in t) is 3I gas 1 2 dropped to 1.1 quads (Tillman, 1978). An important factor leading to this decline was the development of the coal and.oil industries. Since the energy crisis in 1973, renewable energy resources, such as wood, have been.examined as supplement to traditional fuels such as coal, oil, and natural gas. Research and development in this area has developed quickly since then. Today, biomass provides four to five percent of the total energy supply in the United States, 10 percent of this energy is used in the form of electricity (National Wood Energy Association, 1989). Fourteen percent of the world's total energy supply is from wood. This accounts for about 50 percent of all wood harvested (Hall, 1987, Cheremisinoff, 1970). Under sunlight, trees convert carbon dioxide and water to carbohydrates and oxygen in.a process called photosynthesis. Wood energy is generated in this process. The renewable amount of energy from forests in the United States per year is seven to eight quads (Koch, 1989). Forests are the largest solar energy reserve in the world. In the United States, the energy stored in forests is 300 quads. This is about equal to the United States' natural gas reserves and more than its oil reserves (Figure 1.1). Because of the ease of obtaining.wood fuel, including wood waste, forest product industries, such as the pulp and paper industry, lumber and furniture industries, have played an important role in the development of wood energy. In 1983, 1.5 quads of energy were produced by forest products industries in the United States (Koch, 1983) . The energy contribution from biomass is predict 1978) . Tl rapidlj practiI Demons Prograu SPOHSOI 3 predicted to be three to eight quads in the year 2000 (Del Gobbo, 1978). This brief review indicates wood energy use is increasing rapidly. Research and studies in this area have mainly focused on practical applications, such as the Michigan Wood Energy Demonstration Project sponsored by Michigan Energy Conservation Program (MECP) . The studies relating to this dissertation are also sponsored by MECP . pig“: 4000-1 see- ____. —- mane m ”7 I“! "-1 L— we: °~ .... m w WV Figure 1.1 Energy reserves in the 0.8.: About 300 quads are in standing forests with an annual production of 7 to 8 quads. About 200 quads are in Oil, about 300 quads in gas, and about 4,000 quads in coal. (Drawing from Department of Energy.) 1. th. 5P pe 43 re he fr CE 5P Ta '5 1.1.2 The Heating Value of Hood Wood is a complex organic material. It is composed mainly of three components: cellulose, lignin, and hemicellulose. Different species have different chemical compositions. In general, however, the proportion of cellulose, lignin, and hemicellulose are 43 percent, 22 percent, and 35 percent, respectively, in hardwood, and 43 percent, 29 percent, and 28 percent, respectively in softwood (Tillman, 1978). The heat released from a unit of material during the combustion is defined as higher heating value (HHV) . The relationship between the chemical composition and the higher heating value can be explained by following formula (Tillman,1978) W: Cx7527 + (1 - C) X11479 where HHV is the higher heating value (Btu/lb) , C is the fraction of wood consisting of holocellulose, the combination of cellulose and hemicelluloses. The chemical composition and higher heating values for some species of North American woods are listed in Table 1.1: Table 1.1 Chemical composition and HHV of 7 species of North American Woods (Tillman, 1978). Tree species Cellulose Lignin Hemicellulose HHV % % % suuub Beech 45.2 22.1 32.7 8455 White birch 44.5 18.9 36.6 8334 Red maple 44.8 24.0 31.2 8400 White cedar 48.9 30.7 20.4 8400 Eastern hemlock 45.2 32.5 22.3 8885 Jack pine 45.0 . 28.6 26.4 8930 White spruce 48.5 27.1 21.4 8890 he; 6 The data in Table 1.1 shows that the differences in higher heating value between different species are small. The pollution level of wood combustion is generally lower than that of fossil fuels. In some circumstances, such as with wood products companies, wood fuel has additional advantages including lower cost, local availability, and.easier waste cleanup. 1However, some disadvantages of wood fuel include its relatively low density, its chemical and biological instability, and its low net heating value, which is associated with its high moisture content. The moisture content of wood varies by species, normally from 31-249 percent (dry basis) (Hoadley, 1980). At higher moisture contents, a considerable amount of the heat generated in combustion is used to evaporate water. The moisture content (MC) of the fuel directly influences the net heating value. Net heating value (NHV) equals to the heat released from the combustion of the material subtract the heat of water evaporation. Tillman (1978) represented the relationship between the net heating value and the moisture content in the following equation, also plotted in Figure 1.2 (Tillman, 1978) NHV=HHVX [1-0.0114XMC] where NHV is net heating value (Btu/ lb) , HHV is higher heating value (Btu/lb) , and MC is moisture content of fuel, total weight basis (percent) . Both net heating value and combustion efficiency are related to the moisture content of wood fuel (Table 1.2) . Table 1.2 The influence of moisture on fuel value and combustion efficiency (Tillman, 1987). Moisture Net heating Combustion Content Value ‘ Efficiency (*l (Eta/1b) H) 0.0 8800 81 16.7 7125 78 28.6 5390 75 37.5 5040 72 44.4 4345 70 50.0 3785 68 54.5 3333 66 58.3 2950 63 61.5 2630 60 64.3 2350 57 66.7 2110 55 Although many methods have been used to dry wood fuel, air drying has been the most common. For example, letting trees die in the winter 10 to 12 weeks before felling can decrease the moisture content of the wood from six to 70 percent, total weight basis (Rogers, 1981). MCMinn experimented by cutting trees and letting them air dry for four weeks. Some of the trees were cut into bolts and some left lying with stems and crowns intact for further transpiration. The result indicated a recovered energy gain of about six to nine percent for stacked bolts and 14 percent for intact trees (McMinn, 1985). Stacking firewood outside is another example of air drying. The drying speed for the methods mentioned above varied with the species and the size of the wood bolts. Stu/ID Moisture cemenllo: received. 93) Figure 1.2 Influence of moisture content on the heating value of wood (Tillman, 1987). 9 Because the air spaces in a wood chip pile are smaller than those in a firewood stack, the airflow resistance is much higher in the wood chip pile. Under natural air convection, the smaller the size of wood particles, the slower the drying speed. Figure 1.3 illustrates the drying processes of wood chips and wood chunks under natural air convection (Sturos, 1983). If the wood fuel is in particle form, proper air drying requires that the particles be large enough to let air convection occur in the accumulation. In addition to increasing the net heating value, drying wood chips reduces the weight of the fuel and prevents deterioration and self-heating during storage (Springer, 1979). Therefore, finding an efficient way to reduce the moisture content of wood chips is important to the development of efficient wood energy production. 10 O'OSSUNUNSSU vvr .I A I I 4 I I ' II ‘4 AVG. HMWS‘ CONTENT!‘ OF ”I W.) eoIISISSSSS' I VIII YIN! IX 10' HOURS) Figure 1.3 Time required for natural convective drying of aspen and red maple chunks and chips (Sturos,J.B., Coyer,L.A. and Arola,R.A. 1983) . 11 1.1.3 Wood Energy Facilities in Industry Most wood energy ‘used. today is produced through direct combustion rather than through gasification or liquification. The energy produced for industrial purposes is thermal energy or electrical energy. There are several types of furnaces especially designed for using wood fuel. The most commonly used types are Dutch ovens, spreader-stoker boilers, fuel cell boilers, and inclined grate boilers. Dutch ovens are the oldest type of furnace used to burn wood. Spreader-stoker boilers are the most commonly used, with a capacity of 25,000 to 500,000 lb/hr of steam. Fuel cell boilers are a two-stage systemwwith.a capacity of 10,000 to 30,000 lb/hr of steam (Cheremisinoff, 1980). Suspension-fired boilers and fluidized bed incinerators are two types of energy systems developed during recent decades. Suspension-fired boilers are used with.wood fuel having a moisture content as low as 20 percent and performed at fairly high thermal efficiency. Fluidized bed incinerators, such as rubbish incinerators, are used to burn massive amounts of biomass fuel at a moisture content of around-50 percent. Wood chips are the ideal fuel, both in terms of combustion efficiency and ease of handling, for most of the furnaces (except the suspension burners) used in the industry today. 12 1.2 W 1.2.1 Iced Chips in Industries The use of wood energy by industry has increased during recent decades. A review of developments in wood chip applications since 1970 indicate that wood chip production will continue to increase. Today, wood energy facilities are usually designed to burn chip- sized or smaller materials (Koch, 1989). It is much easier to handle small particle fuel, such as wood chips, than firewood blocks. Wood chips can be delivered by trucks from the chipping area to the user's storage yard. Wood chip users include pulp and paper mills, particle board companies, and power stations. Formerly, most wood products manufacturers used logs as their raw materials and now the wood chips are the most commonly used material. Since the 19703, four factors have been instrumental in leading to the rapid development of wood chip use: ( 1) the growth in wood chip demand and local shortages, (2) the development of wood energy, (3) the low cost of raw materials, and (4) the availability of whole tree chipping equipment (FAO, 1975). Based on recent trends in the development of wood products and wood energy, it is predicted that the worldwide demand for wood will be about 141,000 million ft3 in the year 2000, as compared to 88,300 million ft’ in 1975 (no, 1990). Because the net heating value of wood can be increased by 13 drying, a suitable method to dry wood chips for energy gain is expected to be found. As the first step, the research discussed in this dissertation focused on the development of a fixed bed wood chip drying model for green wood chips. 1.2.2 Production and Storage of Iced Chips in Industry Wood chips are produced mainly by field chipping whole tree chips in harvesting areas. Some chips are saw mill residuals. The moisture content of green wood is 31 to 249 percent, depending on the tree species, the position in the tree, and the season of harvesting (Hoadley, 1980). Data from an 18 megawatt wood fuel power station in Michigan indicated that the average moisture content of randomly sampled green wood chips was 41.8 percent (total. weight basis) for' hardwood, 50.6 percent for softwood, and 46.5 percent for the combination of hardwood and softwood (Nicholle, 1991). In general, wood chips are stored outdoors in large storage piles, a simple and inexpensive method. A conveyor and a bulldozer are normally used to construct the piles in a storage yard. The jpiles are formed.with a mixture of different-sized chips. Because of'the high air flow resistance in the wood chip piles, the drying caused by air convection is very slow. The driving force of the airflow in the pile comes mainly from the gravity difference between warm air inside the pile and cold air outside it (Kubler, 11982). The temperature increase inside the piles is caused by the l4 respiration of living ray parenchyma cells and by direct chemical oxidation (Feist, 1973). Self-heating in the wood chip piles is obvious during the first two months of storage. 1.2.3 Studies on Wood Chips During the last 20 years, most of the research on wood fuel storage focused on variations in moisture content and temperature of wood fuel storage piles. In 1976 White, et. al., built three piles containing mixed hardwood bark, pine bark, and mixed hardwood and pine sawdust. In this study, be measured internal temperature, moisture content, acidity, and the heating value during five months of outdoor storage. White also evaluated the effects of pile geometry, :residue types, and methods of stacking'on.the fuel potential of the residues. The results of this study indicated that the steep pile sides increased internal drying and that an inexpensive drying :method could be found by constructing the storage piles properly (White, 1978). In the late summer of 1978, White, et. al., constructed Ianother three wood fuel piles. Three fuels (hardwood whole tree chips, bark, and sawdust) were stored in piles 10-, 15- and 20-feet liigh. After one year of storage, the average moisture content of ‘the chips, bark, and sawdust increased by 84, 108, and 191 percent (dry basis), respectively, over the original moisture content. The temperature in the piles increased rapidly during the first week to 15 a high of 113°F for the whole tree chips and 163.4'F for the bark and sawdust (White, 1983). Sturos developed two exploratory drying experiments to see whether chunks, with their much larger inter-particle voids, dry more rapidly than chips (Sturos, 1983). In one experiment, he used natural convective ambient air to dry chunks and chips and found that chips dried slower than chunks. In another experiment, he used forced ambient air to dry chunks and chips and found that chips dried faster than chunks. Studies so far on wood chip drying have been very limited, as have actual applications, though the potential for more widespread application exists. Many companies, power stations for example, have large amounts of waste heat left as a byproduct of their production. The total thermal efficiency of a wood energy system would be increased by predrying wood chips with this waste heat. Therefore, a suitable method of using waste heat or ambient air to economically dry green wood chips is likely to be found. 1-3 WW1 1.3.1 Agriculture Products The development of simulation models for drying biomass started from.drying agricultural products, such as corn, soybeans, and potatoes. In general, two types of models were developed: empirical models and semi-theoretical models. Drying curves were 16 developed through experiments on grain drying (Hukill, 1947) . Those results can be viewed as the earliest drying model. Along with the _development of computer applications, differential equations related to the heat and mass transfer in the drying process can be solved using a numerical method. Therefore a semi- theoretical model was developed by solving the differential equations numerically to simulate the fixed bed drying process. Both types of models were employed in the designs of drying equipment for agricultural products. A fixed bed grain drying model (Fixed Bed Dryer Model) was developed for the stationary deep-bed drying of all cereal grains. This model was based on the theoretical calculations on energy and mass balance in grain drying (Brooker, 1974). In this study, a standard finite difference method was used to solve the differential equations of the model. 1 . 3 . 2 Wood Particles Comparing wood chips with grains, the wood chips have higher moisture content and less regular shape and weight. In addition, different wood species have different physical and chemical properties and the drying properties of wood also changes with the species. Malter performed an experiment with a drying tube to study the drying process of small wood particles. He developed an empirical drying model and compared it to a theoretical model and found that 17 the theoretical model predicted the drying for smaller particles better than did for larger particles (Malter, 1983). Recently, Schneider developed a forced-air drying model for particulate wood fuel. This model was developed based on the assumption that air leaving the wood fuel bed was saturated with water. The volume of the air required for drying wood fuel was evaluated knowing the amount of moisture to be evaporated and the moisture holding capacity of the drying air. The model was designed to predict the drying time and the cost of drying (Schneider, 1990). However, no experiments have been done to develop a wood chip drying model that explains the moisture distribution of the wood chip bed during the drying process. Because of the complexity of wood chip properties, several factors that influence the drying process must be considered, such as bulk shrinkage, chip size distribution, and surface/volume ratio. Very limited studies on these properties have been found in the literature. CHAPTER II OBJECTIVES The objective of this study is to develop a fixed bed drying model for wood chip drying under forced air at ambient temperatures. This objective is associated with five sub- objectives outlined in 2.1 to 2.5 below. 2.1 MW W Original moisture content, bulk shrinkage, size distribution, particle surface/volume ratio, and resistance to airflow are the physical properties of wood chips to be evaluated in this study. These properties are closely related to the drying process and dryer design. In order to obtain the necessary information for designing the dryers and analyzing the drying process, these properties must be evaluated. Because very limited information is available, the values of some of the properties above will be determined through experiment. 18 In order to simulate fixed bed wood chip drying, a thin layer model will be employed to modify the fixed bed grain drying model. A factorial experiment will be designed to develop a thin layer drying model. Three factors will be included in the experiment: air temperature, air relative humidity, and wood chip size. Multi- factor regression techniques will be used to determine the model. 2.3 MW Because of many assumptions used in developing a semi- theoretical model, the accuracy of the predicted results of the_ model may be reduced in the drying simulation. An empirical fixed bed drying model, however, is expected to give more accurate results, and will be developed in this study. A four factorial experiment will be performed in the model development, which will monitor air temperature, air relative humidity, wood chip size, and air flow rate. Statistical analysis, such as ANOVA table and multi-regression, will be used for developing the model. In order to obtain a quick calculation and an easy application for the empirical wood drying model, a FORTRAN computer program will be written for the model. This program will be designed to simulate the wood chip drying process and to provide basic engineering information for wood chip dryer design. The empirical fixed bed drying model will be developed during a 22-hour drying period in a small dryer. In order to determine whether this model can be used to simulate the drying process in a large dryer, a 14-inch.diameter fixed.bed.dryer'will be designed to perform the drying experiment and to test the model simulations. Three experimental conditions will be chosen to process wood chip drying tests. The results from this experiment will be compared to the values derived from both the semi-theoretical model and the empirical model. Compared to the fixed bed experiment, this experiment will use a larger dryer and a longer drying time. Through the experiment and the comparisons, the accuracy and the stability of the models will be evaluated. CHAPTER III PHYSICAL PROPERTIES OP MOOD CHIPS RELAT. TO PIXED B- DRYING Some physical properties of wood chips evident in fixed bed drying are important in the development of a fixed bed drying model. Many factors may influence drying processes for wood chips, such as original moisture content, wood chip size, surface/volume ratio, bulk shrinkage, and the airflow resistance of the wood chip bed. Some of these properties have already been studied in depth, such as original moisture content. However, because studies on wood chip drying are limited and data on some related properties are unavailable from the literature review, these properties are evaluated and discussed in this chapter. Although the wood chip drying model was developed through an experiment on red pine chips, its application may be extended to other types of chips with physical properties similar to those covered in this study. 3.1 W The original moisture content (OMC) of wood chips in this study refers to the moisture content of green wood. Intensive study 21 22 has been done on green wood moisture content for different species (Peck, 1953). In this study, the gravimetric method, the standard method developed by the American Society of Testing Methods (ASTM, 1990), is employed for measuring moisture content and the dry basis is used to calculate the moisture content of the wood chip samples. Wood chips used as fuel are produced by chipping whole tree in harvesting area or by chipping residual in sawmills, and these combine both sapwood and heartwood. The moisture content of these chips depends on the percentage of each type of wood in the total volume of the combination. According to data from a field sampling study in a wood energy power plant in central Michigan, the moisture content of the wood chip sampled from individual trucks was 44.9-163.2 percent, dry basis, (Nicholls, 1991). The average moisture content of the red pine chips used in the experiment of drying model development was 148.4 percent with the highest at 171.2 percent and the lowest at 127.8 percent. The moisture content of wood chips is considered an independent variable in the model development . 3-2 Wis Compared with some agricultural products, such as corn and soybeans, wood chips are less uniform in their shape and size. Wood chip size is mainly determined by the type of chipper, the chipping operation, and the structure of the wood (FAO, 1976) . 23 Usually, wood chip size is distributed across a wide range, even if the chips are produced at the same chipper. Because chip size was considered an important factor in the drying model, measurement was performed on the different size levels individually. It was found in a preliminary size sorting process that the largest cross section area of the chips was proportional to the size of the screen openings. The correlation between the chip size and screen opening was determined in this study. No previous studies in this area were found in the literature review. The water contained in a single wood chip is proportional to the volume of the chip at a certain moisture content. During the drying processes, water leaving a wood chip must do so through the chip surface by either vapor transformation or water evaporation. Therefore, the drying rate is directly related to the surface/volume ratio of a wood chip. The shape of a wood chip is much less uniform than that of a kernel of grain and the measurement of the surface/volume ratio of wood chips has not been done before. In this study the surface/volume ratio was determined as an average value for each size level. 3 .2.1 Study Methods on Wood Chip Sise and Surface/Volume Ratio Because the size of wood chips was considered a factor in the model development, wood chips were separated by size using a set of wire screens with the holes of four different sizes. The sizes of the screen holes were one-inch, three-quarter-inch, one-half-inch, 24 and one-quarter-inch. square (Figure 3.1). The size sorting separated the wood chips into five groups of different sizes labeled from largest to smallest as 52-0, 82-1, sz-z, 82-3, and 52- 4. Because the sizes of the chips in the 52-0 and the 52-4 were not controlled by an upper or a lower limit, respectively, those two groups were not included in the measurement. Chip size measurements were performed on the wood chip sizes sz-1, 82-2, and 82-3. Three samples were obtained from each size randomly. One hundred wood chips were measured in each sample with a caliper. The typical shape of a wood chip is shown in Figure 3.2. Three dimensions labeled as L (length), W (width), and 2 (thickness) were measured for each chip. The largest cross area and surface/volume ratio were determined from these measurements. Results of the measurements are summarized in Table 3.1. T 25 Figure 3.1 A four-level screen used for size sorting wood chips in the laboratory. The size of the screen openings are 1', 3/4", 8", and k". 26 Figure 3 .2 A typical wood chip shape and its three dimensions labeled as L (length), W (width), and 2 (thickness). 27 3.2.1.1 Largest Cross Section Area of a Wood Chip In size sorting, the largest cross section area of a chip was considered the key control factor directly correlating to the size of the screen opening. As shown in Figure 3.2, the length and width measurements of a wood chip are larger dimensions than its thickness. Therefore, the largest cross section area of a wood chip was defined as L x W in2 and shown in the following formula CA=LxW where CA is the largest cross section area (inz), L is the length (in), and W is the width (in) of a wood chip. The distribution of the largest cross section area of the wood chips with the percentage in total weight was determined for the three different sizes. The average value and standard deviation were also calculated for each sample. 3.2.1.2 Surface/volume Ratio of a Wood Chip Surface/volume ratio (SVR) were determined using the following formula SWhh— S=2x(LxW+LxZ+WxZ) 28 V=LxWxZ where SVR is surface/volume ratio (1/in) , S is surface area (inz) and V is Volume (in3) . The distribution of the surface/volume ratio of the wood chips with the percentage in total wight was determined for the three different sizes. The average values and standard deviation were also calculated for each sample. 3.2.2 Results of the Study on Largest Cross Section Area and Surface/Volume Ratio Results of the measurements of cross section area and surface/volume ratio are summarized in Table 3.2. The average cross section area of wood chips are 529.1 mmz, 284.1 m2, and 144.1 mm2 for the size sz-i, 82-2, and 82-3 respectively. The average surface/volume ratios are 0.78 mm'l, 1.01mm‘1, and 1.41 mm‘1 for the size 82-1, 82-2, and 82-3 respectively. A distribution analysis was done for the pooled samples for the 300 chips in each size group. A normal distribution line was chosen to fit the data (Bhattacharyya, 1977) . Figure 3.3 and Figure 3.4 illustrate the distributions and the related probability for the largest cross section area and the surface/volume ratio, respectively. The statistical data of the distribution curves are illustrated in Table 3.3 and Table 3.4. 29 Table 3.1 Analysis data of the three dimensional measurement on three different sized red pine chips. Sample Group? Length(mm) Width(mm) Thickness(mm) Size Mean Std. Mean Std. Mean Std. Dev. Dev. Dev. 1 28.18 5.10 19.07 6.04 3.99 1.05 82-1 2 28.64 5.45 19.09 4.76 4.08 1.09 3 28.02 5.35 18.81 4.45 3.78 1.18 l 25.62 5.78 11.73 3.26 3.06 0.99 82-2 2 24.59 4.44 12.02 3.07 2.83 0.81 3 24.48 5.30 12.37 3.72 2.90 0.80 1 20.15 7.32 7.26 2.14 2.31 0.72 82-3 2 19.83 7.07 7.27 2.48 2.21 0.73 3 20.75 7.93 7.36 2.26 2.20 0.72 t Each group of wood chips contains 100 individual chips. Table 3.2 Largest cross section area and surface/volume of three different sized red pine chips. Size Group? Cross Section Area Surface/Volume Ratio mm2 mm'1 Mean Std.Dev. Mean Std.Dev. 1 525.48 144.00 0.84 0.21 82-1 2 539.13 138.17 0.73 0.17 3 522.54 137.84 0.76 0.16 1 259.39 90.43 1.01 0.33 82-2 2 292.68 84.36 1.03 0.23 3 300.24 104.16 1.00 0.23 1 143.83 69.49 1.38 0.38 82-3 2 140.26 61.08 1.44 0.39 3 148.08 62.99 1.42 0.38 1 Each group of wood chips contains 100 individual chips. 3O Table 3.3 Largest cross section area (inz) distribution. Sample # Mean Std.Dev. Variance C.V.f 82-1 .9397 .2214 0.04902 0.236 82-2 .5283 .1457 0.02123 0.276 52-3 .3913 .1506 0.02269 0.385 tC.V. - Coefficient of Variation Table 3.4 Surface/volume ratio (1/in2) distribution. Sample I Mean Std.Dev. Variance C.V.T 82-1 17.161 3.734 13.939 0.218 82-2 23.416 5.436 29.548 0.232 82-3 29.571 6.892 47.496 0.233 fc.V. - Coefficient of Variation 31 :ZQQOCA mamwmxmum A‘ \J, 3 1 ‘ sl TL .LutEst—EEPL u 1 . z S e z .1. 3 p .1 h C 11111141141444{114141.414d4414d1111d “ a a n a n 4!. W 9 o a: 33285.. .253 LARGESTCROSSSECTIONAREAOFWOOOWGn') rtgdoza mmmwm... EE...._.£.L:: Chip size SZ-Z . . a A —LE1 . 0 ll LC unassrcnossszcnoumnorwooocmpon') E 83235.. 55; 6 1 P.5i—Es . uLuEPrth .LPP— vs» it Chip size SZ-3 P245555 m w w m. m a u m u w E 33:35.. 553 0. 5 A 1.4, 0.0 014 uncesr caoss szcnou AREA or wooo can: (in') 0.0” Distribution and probability of largest cross section area of wood chips compared to Table 3.3. Figure 3.3 32 .6539... . . a o m m m m m m m m I».....LIIFILIILL:LII-I... m u ... z m S e z m .1 S p M u C i,,//////////.//////////, m ////////////////////////4724 .2,“xv/xxxxéxxx/z/x/xé m 0. .<¢.«4.-...<..a«-4......q4<<<.o x a m r... m 3 0 so 8328...... can; SURFACE/VOLUME M110 (1 fin) E58: . ‘ a o .. a a u w m w m w I.» IL»: - :- :~........L.:Lm I 2 . z m s u o .1 o 8 D. i m m 7////// I/ ///.////////////////////z 7///////////////////// a////////////////////////// m ///////////////. V///////////////////z ..~.z///.////////// , m o. .4..«..<..4...a.1.....4.q.....0 a m u w 9 o c: #328,... 553 MACE/VOLUME RATIO (1 fun) Egg n u u w m m m m m . e a a co ”.’-”.’P’b”Pb”’.’>”b’>”b.”’_9’.Ln 3 . z s e z .1 8 m 0. gnaw... ca 3.53%.. .253 SURFACE/VOLUME mmo (van) Distribution and probability of surface/volume ratio of wood chips compared to Table 3.4. Figure 3.4 33 3.2.3 Discussion on Largest Cross Section and Surface/Volume Ratio The correlation between wood chip size and the opening size of the screen was anticipated. The distribution of the largest cross section area of wood chip fit a normal distribution. Comparing the different sized samples in Figure 3.3 showed that the distribution range tended to be wider for larger chips than for smaller ones. The distribution curves plotted were based on the percentage in of total weight. The water movement along the longitudinal grain direction is much faster than across the grain in a tangential or radial direction because of cell structure (Skaar, 1972) . Most of the surface area of a typical wood chip is parallel to the longitudinal grain direction (Figure 3.1) . Therefore, the two cross-sectioned ends of the wood chip should dry faster than its four other surfaces. The wood chips used in this study were produced by a sawmill. The distribution of wood chip sizes may differ with different sources of supply. The average largest cross section area of the wood chips was used as a unit to represent the chip sizes in the wood chip drying model discussed in the following chapters. 3.3 WW9. Bulk shrinkage is defined as the shrinkage of the total volume occupied by an accumulation of wood chips corresponding to the 34 change in the moisture content of the chips. In the deep bed model, data on bulk shrinkage was used to determine the bed thickness. It is known that wood shrinks considerably during the drying process. In general, average shrinkage is different for the three gain directions of wood: about 0.1 percent in the longitudinal direction, eight percent in the tangential direction, and four percent in the radial direction, with variation by species (Hoadley, 1980) . Many measurements on wood shrinkage for different species have been recorded, but these data are mainly used to indicate the shrinkage of wood at an even moisture content. Bulk shrinkage in the wood chip bed was caused by the volume change of two parts: the wood chips and the air spaces between the chips. Bulk shrinkage in some agricultural products has been studied (Srooker, 1974). A similar study on wood chips has not been found in the literature review. 3.3.1 Study Methods of Bulk Shrinkage Test Sawmill produced red pine chips were chosen for the sample testing in this experiment. The freshly cut wood chips were sorted as in the same manner as the size distribution test. Wood chips of two sizes (82-1 and 82-2) wereneasured and two samples were taken from each size group. The volume of each sample was one-cubic-foot of the freshly cut wood chips at the original moisture content. Measurements of the wet weight and volume of the chips were 35 done at the same time. To measure the volume, the wood chips were put into the container and leveled with a flat cover. A scale was used to measure the settlement of the cover to determine the reduction of the bulk volume. The total weight of the container and the chips was measured with a balance and the moisture content was calculated according to the weight and the final moisture content of the samples. Measurements were performed during the experiment at recorded intervals depending on the drying speed of the chips: shorter interval at higher drying rate and longer intervals at lower drying rate. Between two measurements, the wood chips were spread evenly on the fine screen for air drying. The experiment was performed in a room with a temperature of 70°F and 62 percent relative humidity. The measurement terminated when constant weight of wood chips was reached. Three moisture content samples were taken from each bulk shrinkage sample to determine the final moisture content. The moisture content of the chips at a certain measuring point was then calculated. Nonlinear regressions were used to determine the relationship between the bulk shrinkage coefficient and the moisture content. 3.3.2 Results of Bulk Shrinkage Test Nonlinear bulk shrinkage regressions results on the samples indicate that the regression line fit the experimental data very well (Table 3.5). The following formula was chosen as a bulk 36 shrinkage model 3v:- bi + 192 9’1"" __ ov-wv sv- ov where BV is bulk volume coefficient, MC is the moisture content dry basis (2) , 0V is the original bulk volume (in3) , WV is bulk volume (in3) , and b1, b2 and b; are the constants estimated by the nonlinear regression for the bulk shrinkage model. Table 3.5 Nonlinear regression data on bulk shrinkage test. Container Constant estimated R2 number bl b2 ”3 1-1 -0.003899 0.1363 -0.02775 0.977 1-2 0.004799 0.1449 -0.05526 0.937 2-1 0.004562 0.1877 -0.08277 0.972 2-2 -0.003498 0.1400 -0.04265 0.964 Because of the limitations on wood chip sample supply, only two replications were performed. Based on the T-test (P<0.05) , there are no significant differences between the regression lines for the different sized samples. However, similar regressions performed on pooled experiment data for sz-1 and sz-z samples indicated graphically a slight difference between the two (Figure 3 . 5) . To develop a bulk shrinkage formula for the wood chip drying model, the above regression was also performed on the pooled data of four samples (Figure 3.5) . 37 0.12 ° 0 £sp.(($21)) .. — n sv °-'°‘ e a: ($22) ‘ \ -- R04 (522) 0.“- auu< suamma COEFFICIENT (1 /ucx) p s l o 12 _ Y _ , , + s 55 - ”992155-02. 0.10‘ R. - 9“ om. 3(1) - amass 3(2) II -.4873042£-01 3(3) - .1790986E-02 BULK SHRINKAGE COEFFICIENT (I/MCX) 9 o a A l -0.02 . . u {0 43'60' 30'130'150'110'150'130 uocsrumzcomzmm Figure 3.5 Nonlinear regressions on pooled.experiment data for (1) wood chips of 82-1 and 82-2 sizes and (2) all chip size samples. 38 3.3.3 Discussion on the Bulk Shrinkage of wood Chips Unlike the shrinkage that occurs in a wood block when the moisture content reaches the fiber saturation point (approximately 30 percent), bulk shrinkage began to appear in the wood chip drying when the average moisture content reached about 80 percent. There are three principle reasons for the differences between solid wood and wood chips: (1) During drying, moisture contents for different sized wood chips were not the same. Since wood chip size was distributed over a wide range, the small chips dried more rapidly and started shrinking while the larger chips were still at a very high moisture content. Although the average moisture content was 80 percent, the large chips may have been above this value when the small chips were below even 30 percent (fiber saturation point), which was the point where wood shrinkage started. (2) Because the surface/volume ratio of the wood chips was much larger than that of a big wood block, wood chips dried much faster. Therefore, there is a considerable moisture content gradient in a wood chip which is caused by fast drying. Partial shrinkage may have occurred at the outer layer of a wood chip and, therefore, caused the early bulk shrinkage. ( 3) The stress condition in solid wood and high internal moisture content prevents most shrinkage from occurring. The experiment showed that bulk shrinkage began at a higher average moisture content for large chips than for small chips. 39 There was a wider wood chip size distribution among large wood chip samples than among the small chip samples. Therefore the smaller wood chips in the sample of a large chip size, SZ-l for example, might have dried and shrunk much earlier than the larger sized chips. The wood chips of a small chip sample, SZ-2 for example, were distributed over a smaller range of size and all of them dried at almost the same time. This is why wood chips in a small size sample shrink at a lower average moisture content. (A formula was determined using a nonlinear regression to predict the possible shrinkage at different moisture contents. Because the variation in shrinkage data for different sized chips was very limited, the experimental results did not show significant differences. The bulk shrinkage model was developed using the regression based on the pooled data of the four samples. This model was developed to predict the total bulk volume in the fixed bed drying model discussed in Chapter V and Chapter VI. Variations in drying rates also may influence bulk shrinkage. However, since the drying gradient in a single chip, which is very sensitive to the drying rate, only occurs for a short period of time during drying under forced air, this gradient was ignored and the average moisture content was used as the measurement. 3.4 W Airflow resistance is a very important value in calculating energy consumption in the fixed bed drying operation. Research on 40 airflow resistance has been focused on agricultural products drying (Brooker, 1974). Hukill (1955) developed an equation to explain the airflow resistance for different grains «:0: AP' 1n(1+bo,) where P is airflow resistance (in. 820) , Q is airflow rate (CFM), and a and b - The constants for certain type of grains. A chart related to the above equation was made for many types of grains at various moisture contents, and was widely used in the area of agricultural engineering. A thin layer method was employed to determine airflow resistance during fixed bed drying of grain (Woods, 1987). The material used in the drying experiment was germinated barley. The results indicated that airflow resistance was not affected by the moisture content of the barley, but by compression on the bed. For the convenience of the model application, especially for calculating the energy consumption, the bed resistance on three different chip sizes was tested. 3.4.1 Study Methods for Airflow Resistance A column 14-inches in diameter and 48-inches high was made with sheet metal for this study. (This sheet metal column was also used in the model testing experiment discussed in Chapter VI.) The 41 column consisted of seven sections: the bottom, called the base section, was used to support the whole column, and the remaining six sections, called drying sections, formed the main body of the fixed bed dryer. Each drying section was eight-inches high and.had a layer of 0.25-inch screen soldered at the bottom to support the wood chips in the section. A small air access tube of 0.20-inch interior diameter was soldered near the upper edge of each drying section as an air pressure measurement outlet. Those outlets were connected to '0' water filled pressure meters during the test. A 0.33 horsepower, high-pressure blower, an air distribution box, and three bypass flowmeters were installed at the bottom of the column. The bypass flowmeter was calibrated with a standard airflow meter before each measurement. Red pine wood chips of three different sizes were tested in this experiment: 82-1, 82-2, and sz-a. Wood chips were sorted by the method previously described. During each test, the airflow rate was controlled by the two damper flat valves installed on the air distribution box. The readings from the bypass flowmeter and "U” tube pressure meter were recorded simultaneously. The readings from the bypass flowmeter were converted into flow rate in ft3/hr according to the calibration. 3.4.2 Results of the Study on Airflow Resistance The correlation of airflow resistance in the wood chip bed with airflow rate was determined by nonlinear regressions. The 42 following formula was employed in the regressions Analysis ERW=c1eQJV where FR is airflow resistance (inch water), FV is airflow rate (ft/min), c1 is the first constant (inch water), and c2 is the second constant (min/ft). Table 3.6 shows the statistical analysis of the regressions. The experimental data and regression lines are plotted in Figure 3.6. Table 3.6 Nonlinear regression on airflow resistance in wood chip bed with airflow rate. Wood Chip Size Constant estimated R2 Group by regression c1 62 82-1 0.02005 0.03096 0.986 82-2 0.02591 0.03124 0.998 82-3 0.03857 0.03105 0.996 43 0.5 0 chip size - 0.82 in' 4 0 chip size - 0.46 in' 8 chip size - 0.30 in' ,4 0.4-4 / AIRFLOW RESISTANCE (in. lip/ft) I If r I ' 30 40 50 60 7O 80 90 AIRFLOW RATE (cfm/ft’) Figure 3.6 Airflow resistance of wood chip bed and airflow rate plotted from Table 3.6. 44 3.4.3 Discussion on Airflow Resistance The experiment shows that the wood chip size was well correlated to the airflow resistance; the larger the wood chip size, the less the airflow resistance of the bed. The size of the wood chips is proportional to the volume of empty space in the wood chip bed. Therefore, a bed formed with larger wood chips shows less resistance than one formed with smaller wood chips. According to Woods's study on the airflow resistance of a thin bed of germinated barley, moisture content did not have a significant effect on airflow resistance (Woods, 1987). However, as mentioned earlier, the moisture content of the wood chips would slightly change the bulk volume of the wood chip bed only when the moisture content is less than 80 percent. Because the shrinkage of an individual wood chip is only eight percent in the tangential, four percent in radial directions and 0.1 percent in the longitudinal direction (Wood Handbook, 1988), and the shrinkage does not occur during most of the drying period, the moisture content's influence on airflow resistance is not considered here. A nonlinear regression line was found to illustrate the correlation between the airflow resistance and airflow rate for wood chips of different sizes. This formula was employed in the fixed bed drying model to determine the energy consumed in creating internal airflow. Airflow resistance increases sharply as the airflow rate increases. This result indicates that under commonly acceptable drying rates, the airflow rate should be reduced as low 45 as possible to reduce the energy costs caused by airflow resistance. DEVELOPMENT OF A III” LAYER DRYING MODEL AND IODII'IGNI‘IONG 'l'O T83 GRAIN DRYING HODEL 4.: W11 4.1.1 Wood Drying Principle Extensive studies have been done on lumber drying, practically and theoretically. The water in a tree is stored and transferred mainly in the living cells. One portion of the water is found in the cavities of the cells (free water) and the other in the cell wall (bound water) (Hoadley, 1980). At the beginning of the wood drying process, any free water is removed first, by (1) the evaporation of the water at the cell opening and (2) the movement of water from internal cell cavities to the openings by capillary pressure. Normally, the surface evaporation rate and interior water movement rate controls this process (Siau, 1984). When most of the free water has evaporated, the cell cavities are empty and the bound water starts to dry. The moisture content at this point is called the fiber saturation point. The drying process of bound water is accomplished in three steps: (1) the diffusion of water molecules from the interior to the surface of the cell wall; 46 47 (2) the evaporation of water at the surface of the cell wall; and, ( 3) vapor movement from the cell wall surface to the outside of the wood through cell cavities or pits. This process is controlled mainly by the water diffusion rate within the cell wall (Siau, 1984) . Because the size of wood chips is much smaller than that of lumber, the distances for water and water vapor movement are much shorter in a wood chip. Therefore, under the same drying conditions, wood chips dry much faster than lumber. A preliminary experiment indicated that variations in wood chip size significantly (P<0.05) influence drying rate. Therefore, wood chip size was considered a factor in this experiment. In general, there are two steps to drying biological products: constant rate drying and falling rate drying (Villa, 1973) (Figure 4.1) . During the constant drying period, there is a thin layer of liquid water on the surface of a drying particle, and the drying rate is controlled by external water evaporation. During the falling rate drying period, there is no layer of water on the particle surface and the drying rate is controlled by internal moisture movement. In general, constant rate drying occurs at moisture contents above 233 percent (Brooker, 1974) . Therefore, most biomass particles, including wood chips, dry at the falling drying rate . 48 E '2' t.“ IIlik; z . 8 a 4 I § .9 .- z 9 >- m 2 0 TIME. t Figure 4.1 Two drying steps for biomass material: constant drying rate and falling drying rate (Brooker, 1974) . 49 4.1.2 Thin Layer Drying Equation The thin layer drying is defined as the drying process that occurs when a single layer of particles is exposed to the air of a certain temperature and relative humidity. It comes from agricultural engineers' studies on grain drying and is called single-kernel drying (Brooker,1974). Almost all thin layer drying models were developed for drying agricultural products. Luikov developed a general mathematical model for capillary porous products drying (Luikov,1966) aMC T: 3 sznMC + Vaxufl 4‘ V2K13P 3% = Wave + V “19.6 + We? 6? 3? .. vixnuc + V 319,0 + Viz”? where MC is the moisture content (8), 0 is the particle's temperature ('F), P is vapor pressure (Psi), Kit is the phenomenological coefficient, and K1, is the coupling coefficient.~ After years of studies, it was found that the pressure term was not significant in most drying temperature ranges and that the coupling effects of temperature and.moisture were significant in a few grain products. The temperature gradient in a single particle ‘was not considered in practical grain drying; Therefore, Luikov's model was simplified as follows for cereal grain kernel drying (Brooker, 1974) 50 8MC_ .5? - V2}:11 MC where K11 is the diffusion coefficient, which is also called D. When D is a constant, this equation can be written as follows (Brooker, 1974) auc,D(amc+_gaMc) 5t: 3:3 1’5! where C is a shape coordinate and r is a particle coordinate (ft). An analytical solution for this equation was written for a sphere as follows (Perry, 1963): 2 2 5 1 [-'9” x’] ”3‘72: 7;." Two dimensionless quantities were used in this equation: MR is the moisture ratio and x is dimensionless time (hr) .MC-EMC MR: ouc- EMC' where EMC is the equilibrium moisture content, OMC is the original moisture content, A is the single particle surface area, and D is the volume of the particle body. Later, a simplified solution was written by using only the first term of the analytical solution and was used to predict the drying of grain: Maia 3" sight” ‘3 1:3 Brooker, Bakker-Arkema, and Ball stated that: FAssuming the rate of moisture loss of a grain kernel surrounded by a medium at constant temperature is proportional to the difference between the kernel moisture and its equilibrium moisture content, due- _ 7?-kmc we) Separating the variables and integrating between the proper limits using MC(r,0)-MC(in) and. MC(ro,t)-EMC as initial and boundary conditions yields: m, e-kt ... k the drying constant." The drying constants of cereal grains have been studied intensively. Pabis and Henderson determined the drying constant k for corn through experiment (Pabis, 1961): _ 5023 km.- S . 4 x10"1 9 l“ The drying constants for wheat and barley have also been determined (O'Callaghan, 1971) : In 1971, Young evaluated the diffusion equation for describing the thin layer drying of peanuts in the hull. He put trays containing one layer of peanuts into dryers with air temperatures 52 of 90°F, 100°F, and 110°F and dew points of 52°F, 60°F, and 69°F. He compared four diffusion equations with the experimental data (Young,1971). Some empirical thin layer equations were developed for certain agricultural products. For example, Thompson presented a drying equation for shelled corn in the temperature range of 140° to 300’F: t=AlnMR+B ( lnifl?) 3 A-1.86178+0.004880 3:427 .3640 e"°°°”°1” Another the drying equation for corn was presented in the temperature range of 36° to 70°F (Sabbah, 1968): mse-kt0.“d k39-Xt' x- [6 . 0142+1.453 xlo" (rh)3] °'5-0 [3 .353 x10"+3 .0x10"(rh)3]°'5 y-o.1245-2.197x10'°(rh) +2.3x10”(rh) 0-5.8x10"0 Thin layer equations played an important role in the development of the semi-theoretical fixed bed drying model. The thin layer equation for wood chip drying has not been found in the literature review. In order to simulate the wood chip drying process with the theoretical fixed bed drying model, a thin layer drying model for wood chips had to be developed. 53 4.1.3 Semi-theoretical Fixed Bed Drying Model A theoretical fixed bed drying model can be used to simulate a practical drying process in a fixed bed dryer. This model was developed through the integration of the drying processes for many thin layers. The development of the theoretical model was based on the heat and mass balance in the drying process. Based upon eight assumptions, a grain drying model was written as follows (Bakker, 1973) 37'. -h’a _ '3? c,c,+c,cvw(T o) a - h’a - hfs" Cv( T'O) 3W "6'5 herbage” 0)+ ppCP+pPC,MC '57: awhh due 5} G, 51: 23%" san appropriate thin layer equation where T is air temperature (°F) , 0 is product temperature (°F), MC is moisture content, W'is air’humidity ratio (lb/lb), x is bed coordinate (ft), t is time. (hr), h' is convective heat transfer coefficient (Btu/ft2/°F/hr), 1‘29 is heat of evaporation (Btu/lb), c‘, cp, cv, and cw are the specific heat of dry air, dry grain kernels, water vapor, and liquid water, respectively, (Btu/lb/°F) , c. is air flow rate (lb/hr/ftz) , pp is product density (lb/bu) , and a is particle surface area per unit bed volume (ft2/ft3) . 54 The four differential equations can be solved numerically with a standard finite difference method, and a FORTRAN computer program “Fixed Bed Dryer Model" was developed to execute the calculations of grain drying simulation (Brooker, 1974). The boundary conditions for this fixed bed drying model are listed as follows T(0, t) =T(in1et) 0 (x.0) -0 (initial) W(0, t) -w(in1et) MC(x, 0) -MC(initia1) The fixed bed grain dryer model has not been used for wood chip drying before. To employ this model for wood chip drying, a thin layer equation and an equilibrium moisture content equation had to be determined for wood chips. The method employed in the thin layer experiment was similar to the one used for agricultural products. A single layer of wood chips was distributed on a layer of screen and exposed to controlled air temperature and air relative humidity in a conditioning chamber (Figure 4.2). The drying processes were determined by measuring the moisture contents of the samples during the drying process. A preliminary thin layer drying experiment was performed using red pine chips to evaluate the experimental factors. Three factors had significant influences (P<0.05) on the drying process: air 55 temperature, air relative humidity, and wood chip size. Therefore, a factorial design with three replications was employed (Table 4.1): Table 4.1 Thin layer experimental design for wood chip drying. Independent Variables Level 1 Level 2 Level 3 Level 4 Air temperature (°F) 68.0 82.5 96.8 111.2 Air relative humidity (t) 40.0 55.0 70.0 85.0 Wood chip size (in’) 1.32 0.82 0.46 0.30 The range of the drying conditions (air temperature and air relative humidity) covered the normal conditions for ambient air and slightly heated air. Four levels were chosen for the chip size factor (SZ-O, SZ-l, SZ-Z, and SZ-3). Size SZ-O was included here because only a small amount of the wood chip sample was required and was available from size sorting. The upper limit of the size for sample sz-0 was controlled by a 1.5-inch screen. In general, the wood chip samples can reach their equilibrium moisture content (EMC) within 22 hours under most drying conditions. Twelve sample containers (sample baskets) could be distributed evenly in the cross section of the laboratory conditioning chamber. Therefore, the samples of four different sizes with three replications in each size could be tested at the same time. Sixteen testing days were required to perform the experiment for the total 4x4x4x3-192 samples of wood chips. 56 4.3 WW 4.3.1 Sample preparation for Thin Layer Wood Chip Drying Experiment Red pine chips were supplied from a sawmill in Gladwin, Michigan, for all of the experimental samples because of the reliable supply of one species. In this sawmill, cants were produced from logs of 10 to 12 inches in diameter. Wood chips were produced by chipping the remaining slabs and edgings. The logs used for production had been harvested about two weeks prior. The wood chips were collected immediately after chipping and stored in sealed plastic bags. The wood chip bags were stored at a constant temperature of 40°F. A preliminary storage experiment indicated no significant changes in the moisture content of the wood chips during a 30-day storage period. Usually, the storage time between chip collecting and size sorting was less than seven days and the longest storage time between the size sorting and the drying testing was 16 days. In order to minimize the moisture loss during size sorting, wood chips were sorted in a high humidity room with a temperature of 75°F and relative humidity of 88 percent. The size sorting method described in Chapter III was used. Wood chips of four different sizes (SZ-O, SZ-l, sz-z, and sz-a) were stored separately in the plastic bags after sorting. According to the experimental design, sixteen days were required to complete the whole experiment. Wood chip samples of each size were kept in 16 bags. 57 The sample bags were not opened until the time for the experiment and the moisture loss of the samples was minimized during storage. 4. 3 .2 Equipment Used in the Thin Layer Wood Chip Drying Experiment The thin layer wood chip drying experiment was performed in an AMINCO Conditioning Chamber (Figure 4.2). Wood chip samples were placed in rectangular baskets (five-inch long by four-inch wide by one-inch high) made of a k-inch wire screen. The amount of wood chips contained in each sample was enough to form a single layer of wood chips in each basket. Twelve baskets were evenly placed on the cross section of the chamber. Because of a slight variation in airflow rate along the cross section, especially from the front to the back, a set of fine screens was placed at the bottom level of the chamber to even the airflow rate. To reduce the experimental error caused by differences in the airflow rate, the area of the chamber was divided into three separated blocks from front to back, and the three replications of each sample were assigned to each of the three blocks. The samples of four different chip sizes were randomly assigned to the four spaces in each block using random numbers . 58 Figure 4.2 Thin layer wood chip drying experiment performed in a controlled temperature and relative humidity conditioning chamber. 59 4.3.3 Measurement of the Thin Layer Wood Chip Drying Experiment Because wood chip samples reach their constant weight after 22 hours drying under most experimental conditions, each experiment was performed once a day: 23 hours for the drying test and one hour for setting up the new experimental conditions. Although some samples may not have reached their equilibrium moisture content after 23 hours of drying, especially at high relative humidities and at low temperatures, their data can still be used for regression analysis. Sample moisture contents were determined based on knowing the sample weights vs. the oven dry weights. Since drying was most rapid at the early stages, the weights of samples (including the baskets and the wood chips) were measured every hour for the first 14 hours and, then measured once more after 23 hours. The actual sample weight was calculated by subtracting the basket weight from the total weight. After the moisture measurements, the wood chip samples were placed in beakers and kept in an oven at 217°F until they reached their oven-dry weight. The moisture content for each sample during the drying time was calculated after its oven dry weight was known. The representative drying curves for the four different sizes of wood chips is shown in Figure 4.3. The air temperature and the air relative humidity in the conditioning chamber were measured with a Model 566-2 Psychrometer. The sample weights were measured with a Mettler PJ360 Balance and recorded with a Mettler GA44 Printer. 60 A THIN LAYER EXPERIMENT OF 4 CHIP SIZES (T-96.8F, RII-ssz) N 150 ’ A ‘12 U) <£ CD 120‘ E 1i 8 90 i- .4 I: he . I: 604 8 . m J (K :3 30 i— . e . . 2 0.-.-.-...-.-...-.- 0 4 8 12 16 20 24 DRYING TIME (HOUR) Figure 4.3 Representative drying curves in the thin layer wood chip drying experiment of 4 chip sizes at air temperature 96.S°F and air relative humidity 55%. 61 4 . 3 . 4 Development of a Thin Layer Wood Chip Drying Model 4.3.4.1 Determining Drying Constants for Different Drying , Conditions Although the moisture content of wood chips is generally much higher than that of grain, the drying process for wood chips occurs at a falling drying rate. It can be assumed that the drying process is controlled mainly by moisture transfer inside the wood chips. Therefore, a simplified semi-theoretical solution for the diffusion equation was chosen to simulate the thin layer drying process MR a e’“ where MR is moisture ratio, k is drying constant (1/hr) , and t is time (hr). Moisture ratio is used here in the model to express the moisture content as a dimensionless quantity. In the model, the drying constant (k), the only parameter determined in the regression, represented the most important characteristic in the drying process of the samples. A LOTUS worksheet was used to calculate the moisture contents and the moisture ratios, and a nonlinear regression computer routine (NONL) in SAS was used to perform the regression for each condition. The drying constants (k) were estimated for a total of 192 experimental conditions. A representative regression curve is shown in Figure 4.4. MOISTURE RATIO 62 REGRESSION IN A THIN LAYER EXPERIMENT ( T .. 96.8 F. RH - 55 z. CHIP SIZE .. 0.82 In2 ) 1.0 I 1 \\ 0.0 L . \ dpsae- 'ID Fignure.4.4 fr r V 20 4 a 12 76' 24 DRYING TIME (HOUR) A representative regression curve related to the thin layer drying experiment for wood chip sample sz-i at the experimental condition of temperature 96.S°F and relative humidity 55.0%. 63 4.3.4.2 Determining the Relationship Between Drying Constant and Drying Conditions The correlation between the drying constants and the related experimental conditions (air temperature, air relative humidity, and wood chip size) were determined using multiple regression analysis. A second order polynomial equation was selected as the model to simulate the drying process. This regression was performed by the multiple regression routine (REG) in the SAS program. As this model was used to simulate the thin layer drying process and executed by a computer program, model selection was based on reaching the highest determination of correlation. The results of a backward and forward model selection were also compared and discussed. The residual analysis was performed as part of the model selection to evaluate the fit of the model. 4.3.5 Modification of the Grain Drying Model The Fixed Bed Dryer Model was chosen as a basic model to simulate the drying process of wood chips in a fixed bed dryer. In this model, the standard finite difference methods were used to solve the four differential equations (Section 4.1.3) on a personal computer. The modifications of the grain model included two parts: ( 1) The thin layer wood chip drying model was employed in the fixed bed grain drying model to substitute the thin layer grain drying model. The thin layer wood chip drying model can be written as follows 64 m _ e-kt k I F (T. RH. 52) where F represents the function to calculate the drying constant k (1/hr), T is temperature (°F), RH is relative humidity (percent), and S2 is wood chip size (inz) . (2) The formula calculating the equilibrium moisture content of wood was employed in the model to substitute the formula used for grains. The equilibrium moisture content equation can be written as follows (USDA, 1988) 1800[ 1:): + k1k°h+2k1k,k:h’ m I W 1-koh 1+k1koh+k1k2k3h3 WI330 +0 . 452T+ 0 . 00441531"2 Ito-0 .791 + 0 . 000463T+0 . 0000008441‘2 k1-6.34 +0 . 0007752-0 . 00009352‘2 19:1.09 +0 . 0284 -0 . 000090423 where EMC is the equilibrium moisture content (percent), T is temperature (°F), h is relative vapor pressure. The development of a thin layer wood chip drying model included two parts: (1) a thin layer drying equation and (2) a drying constant equation. The thin layer equation illustrates the relationship between the moisture contents and the drying time; the 65 relationship is represented by the drying constant. The drying constant equation shows the relationship between the drying constants and the experimental conditions. 4.4.1 Thin Layer Drying Equations A total of 192 nonlinear regressions were performed using a SAS NONL routine for the experiment. The drying constants (k) are listed in Appendix A. A representative regression curve for the thin layer drying experiment is illustrated in Figure 4.4. 4.4.2 Drying Constant Equation Studentized residuals were calculated and plotted with a SAS REG computer routine to detect failures in the development of the model. One observation of the total 192 was deleted because of its high residual. An analysis of variance was performed on the results of the nonlinear regressions (Table 4.3). An ANOVA table indicated that three independent variables (T, RH, and 82) and two of their interactions (T*RH and RH*SZ) were found to be significant (P<0.05) in affecting the drying constant (k). Multiple regression was performed to determine the drying constant formula. The maximum R? model selection procedure (MAXR) in the stepwise selection routine (STEPWISE) of SAS program was used to process the model selection. The determination of the 66 final model depended mainly on reaching a higher coefficient of determination (R3). The parameters of this equation are listed in Table 4.3, and this equation is defined as the Drying Constant Equation shown as follows MR'O'“: k I 0°+BIT+82T3+03RH+B, (25cm +B.SZ+B. (1832) +0, (RHXSZ) +8.323 -0.34677801 0.02609468 -0.000068479 -0.001117698 -0.000140584 -0.61144449 -0.001859596 0.005912791 0.10995296 Bo B 1 2 3 I3. 5 6 7 I where MR is moisture ratio, k is drying constant (1/hr), t is drying time (hr), T is air temperature (°F), RH is air relative humidity (percent), and S2 is wood chip size (inz). Table 4.2 Analysis of variance of the drying constant k in the thin layer wood chip drying experiment. Source Degree Sum of F Prob. Freedom Squares Value > F T 3 0.6284 27.62 0.0001* RM 3 4.3776 192.42 0.0001* SZ 3 1.6724 73.51 0.0001* T*RH 9 0.3252 4.76 0.0001* RH*Sz 9 0.4534 6.64 0.0001* T*Sz 9 0.1154 1.69 0.0987 T*RH*Sz 27 0.1764 0.86 0.6634 Error 127 0.9631 * Significant at 5% level. 67 Table 4.3 Parameter estimates of the drying constant equation after the multiple regression analysis. Variable DF Parameter Standard T Prob. Estimate Error Test > IT: Intercept l -0.34677801 0.27214261 -1.274 0.2042 T 1 0.02609468 0.005458704 4.780 0.0001* T*T l -0.000068479 0.000029235 -2.342 0.0202* RR 1 -0.001117698 0.002132946 -0.524 0.6009 T*RH 1 -0.000140584 0.000022593 -6.233 0.0001* 82 1 -0.61144449 0.11841620 -5.164 0.0001* T*82 1 -0.001859596 0.000824734 -2.255 0.0253* RH*82 l 0.005912791 0.000824734 7.468 0.0001* 82*82 1 0.10995296 0.04248953 2.588 0.0104* * Significant at the 5% level. 4.4.3 Discussions on Thin Layer Wood Chip Drying Experiment The thin layer equation is stated in the form of the simplified solution of a diffusion equation, and the drying constant (k) represents the diffusion coefficient. In general, the drying constant is directly related to the drying rate. The contributions of the independent variables to the drying constant are clearly illustrated by the three-dimensional surface graphs in Figure 4.5. CM!’ 881‘ I 0.” N IN Figure 4.5 air relative humidity, 68 “Pm-0.46““. \ m “““““““ ‘ “““““““?““:“‘€“ “““m‘mrrxx: ““‘ ‘ ‘ “““““““““““ \\\\x_\:.x ‘ \\\\\\\\\\\\ \ van-N- “““ ““““ “ ‘ W“‘““‘ mus-140nm. The drying constants change with air temperature, and wood chip size in the thin layer wood chip drying experiment. 69 4.4.2.1 Air Temperature as Related to the Drying Constant Air temperature, is one of the most important factors in wood chip drying and is directly related to the drying constant (Figure 4.5). At a certain relative humidity, the enthalpy (heat content of the air) level increases with the air temperature. The higher the enthalpy level of the air, the more energy the air can transfer to the wood chip drying. The large temperature gradient between the wood chips and the air increases the heat transfer between the two. Fast heat transfer is directly related to the drying rate. Finally, because the activity of water molecules is directly related to temperature, vapor pressure at high temperatures is higher than at low temperatures (Siau, 1984). High vapor pressure improves water evaporation and also increases the water carrying capacity of the air. In wood chip drying, the drying rate can be accelerated when the drying temperature is increased. 4.4.2.2 Relative humidity as Related to the Drying Constant The drying constant is inversely related to the air relative humidity (Figure 4.5). An analysis of variance indicates that air relative humidity, among all the controlled factors, has the strongest influence on the drying process . Relative humidity is defined as the ratio of water vapor in the air to the amount of water the air can hold at saturation at the same temperature. The water absorption tendency of the air, or the drying force, can only 70 be determined when both temperature and relative humidity are known. At certain temperatures, air at a lower relative humidity has a higher water absorption tendency than that of air at a higher relative humidity. During the drying process, if the relative humidity is low, the vapor pressure at the wet surface of a wood chip is much higher than that of the air. The large gradient in water vapor pressure can increase the rate of water vapor transfer. Meanwhile, vapor transfer reduces the vapor pressure at the surface of the wood and, therefore, increases the water evaporation there. 4.4.2.3 Rood Chip Sise as Related to the Drying Constant The drying constant is inversely related to the wood chip size (Figure 4.5) . Analysis of variance shows that the wood chip size, among all the factors, has the second largest influence on the drying constant. The wood chip size refers to the largest cross section area of a chip. There are two reasons for the faster drying of small chips as concluded from the research in Chapter III: ( 1) Small wood chips have a larger surface/volume ratio than large chips. For the same amount of wood chips at certain moisture content, small wood chips have more surface area at which water evaporation can occur than the large chips and, therefore, dry faster. (2) The distance for the mass and energy transfer inside a wood chip is shorter in a small chip than in a big one. The 71 temperature gradient and the moisture gradient are larger in a small chip than in a big one. The larger the gradients are, the faster the related transfers occur. Under the same drying conditions, smaller wood chips not only heat up rapidly, but also dry more quickly than the larger wood chips. 4.4.2.4 Temperature and Relative Humidity as Related to the Drying Constant The influence on the drying constant exerted by the interaction of temperature and relative humidity is shown in Figure 4.5. It shows that, the drying constant is inversely related to relative humidity. However, this relationship is much more obvious at a high temperature (120°F) than at a low temperature (60°F). The drying ability of air depends on two values: (1) the absolute humidity of the air at saturation point, and ( 2) the absolute humidity at a certain air drying condition. The former is directly related to air temperature, and the latter is related to both temperature and relative humidity; The difference between the two values represents the moisture absorption potential of the air. Air at a high temperature and low relative humidity has great drying potential. 4.4.2.5 Relative Humidity and Wood Chip Sise as Related to the Drying Constant The influence exerted by the air relative humidity on the 72 drying constant is greater in drying small wood chips than in drying large ones (Figure 4.5). The drying potential of the air depends mainly on the air relative humidity. At a higher relative humidity, wood chip drying is slow, and the drying process is controlled by the drying capacity of the air. At a low relative humidity, however, drying occurs much faster and the drying process is controlled by the water evaporation at the surface and the water diffusion inside the wood cell. Because the surface/volume ratio is larger and the moisture diffusion distance is shorter in a small chip, the influence on the drying rate relative to wood chip size is much more obvious at a low relative humidity. 4.4.3 Semi-theoretical Fixed Bed Wood Chip Drying Model Both the thin layer wood chip drying model and the equilibrium moisture content model were employed in the Fixed Bed Dryer Model. A FORTRAN computer program, Grain Drying Model, was modified to perform the calculation of the semi-theoretical fixed bed drying model for wood chips. The program was executed for the three drying conditions chosen from the large scale model testing experiment (Chapter VI). The results from the simulation were compared with the results of the related large-scale testing experiments and will be discussed in Chapter VI . CHAPTER V DEVELOPNENT OP EMPIRICAL FIXED BED DRYING NODEL USING TEE REGREBBION METHOD 5.1 W The development of a fixed bed drying model and related experiments were found in the studies of agricultural products drying. Fixed bed experiments were performed on ear corn and grain sorghum (Hukill, 1947). It was found that the grain drying curve underestimated the time required for drying grain. Hukill (1947) developed a grain drying curve, also called bulk drying curves, based on the following assumptions (Figure 5.1): ' ...the drying rate (1) is independent of air velocity; (2) at a given relative humidity it is proportional to the difference between the grain moisture content and the equilibrium moisture content (expressed on the dry basis), and (3) at a given grain moisture content it is proportional to the difference between the dry-bulb temperature of the air and the dry-bulb temperature of air in equilibrium with the grain." A mathematical expression of Hukill's curves is shown in the following formula (Hukill, 1953) 73 74 2D 20 + 21' ... 1 cfmx60xc.x ( '1',- T,) X t1]: uxhafiKOWC-EMCI DM'g C t1/2 Y: where D is a depth factor, Y is a time unit, DM is a dry matter content contained in the depth factor, cfm is airflow rate (ft3/min), c. is specific heat of the air (Btu/lb/°F), T. is air temperature (°F) , T9 is the temperature of air leaving grain mass (°F) , u is the specific volume of air (ft3/lb) , and t“, is the time required for a fully exposed layer of grain to dry from original moisture content (OMC) to a moisture content midway between OMC and equilibrium moisture content (EMC) . Bulk drying curves are based on the assumption that a thin layer of grains dries to a moisture ratio (MR) of 0.50 for the first t1]: , to a moisture ratio of 0.25 during the second t1“, and to a moisture ratio of 0.125 during the third t1”, etc. The thin layer grain drying experiment in the laboratory did not follow this procedure. However, these bulk drying curves do provide a useful illustration of a fixed bed drying process. 75 Figure 5.1 Fixed bed grain drying curves (Hukill, 1954). 75 "7.8 .00. m Figure 5.1 Fixed bed grain drying curves (Hukill, 1954). 76 Most fixed-bed experiments were performed to study the drying procedures for specific agricultural products. For example, a reversed-direction-air-flow drying process for soybean seeds was performed by Sabbah, in 1977. In the study, he found that using a reversed airflow method to a batch-in-bin drying system improved soybean seed quality (Sabbah, 1977). Another soybean drying process involving a fixed bed drying system was performed to analyze the design of a fixed bed dryer. The experiment indicated that the low 'temperature drying of soybeans was feasible if the ambient air temperature was raised by five to eight degrees F and the airflow rate was 1.5 ft9/min/bu (Dalpasquale, 1981). In 1984, Shove performed an experiment in corn drying bins to evaluate the energy consumed in low temperature corn drying. In this study, he found that a more efficient way to use energy is to provide more air rather than to use a portion of the energy to increase the temperature of a smaller quantity of air (Shove, 1984). In 1987, Patil performed an experiment using a recirculating crossflow dryer to develop flexible and generalized drying models which could be used to evaluate the performance of different dryer types. He compared the experimental results with the model simulation and found the model developed from diffusion theory was more flexible and applicable. Because of the difficulties in performing deep bed experiments under different drying conditions, very few experiments have been 77 performed thus far, and no fixed bed drying experiments for wood chips were found in the literature review. Therefore, to develop an empirical fixed bed drying model is an important element in furthering the wood chip drying process. 5.2.1 Experimental Design for Fixed Bed Wood Chip Drying As in the thin layer drying experiment, fixed bed drying was a multi-factor experiment. In addition to the three factors involved in the development of the thin layer model, two more variables (airflow rate and original moisture content) were included in the deep bed model. Because this is a large-scale, multi-factor experiment, a factorial experimental design with a single replication was (selected (Table 5.1). Table 5.1 Experimental design for the empirical fixed bed wood chip drying model. Independent Variables Level 1 Level 2 Level 3 Level 4 Air temperature (°F) 68.0 82.5 96.8 111.2 Air relative humidity (t) 40 55 70 85 Air flow rate (cfmgftz) 44 67 99 -- Wood chip size (in ) 0.82 0.46 0.30 -- Moisture content (4) 140-160 (Not controlled) The factor levels for air temperature and air relative humidity were identical to those in the thin layer experiment. Three wood chip sizes (821, sz-z, and sz-3) were used. The largest 78 wood chip size (SZ-O) was not included in this experiment because it represented only a small percentage of the total weight of the wood chips. The three levels in the airflow rate were selected from the commonly used range of rates used in the forced air drying process for agricultural products. The measure for the air flow rate was cfm/ftz, or cubic feet (air volume) per minute per square feet (cross section of dryer). The original moisture content of the wood chips was distributed over a narrow range and, therefore, was not controlled but was measured in this experiment. The average moisture content of fifteen samples in each dryer was used in the regression analysis of the model. 5.2.2 Equipment Used in the Fixed Bed Wood Chip Drying Experiment The AMINCO Conditioning Chamber mentioned in the thin layer experiment was also used to control air temperature and air relative humidity in the fixed bed experiment. Three small fixed bed dryers, two blowers, and three bypass flowmeters were mounted in the chamber (Figure 5.2). 79 Figure 5.2 The fixed bed wood chip drying experiment was performed in three dryers mounted in a conditioning chamber. D t ’ $ - . The of six 81 (1) 30121 redistril very mu (2) Mid Ioisture (3) TOp Prevent I The drye high: tw liddle 5. Screen w “etion 1 Vere Sea l"“‘et‘l w. the up. tissues c01‘1111113. at Each ‘ Iiclcue p 80 The dryers were made of sheet metal and each one was composed of six sections classified as three portions (Figure 5.3): (1) Bottom portion (one section) -- to support the whole column, redistribute air flow evenly, and hold the moisture samples at the very bottom; (2) Middle portion (four sections) -- to contain wood chips and moisture samples at different levels; and (3) Top portion (one section) -- to hold a layer of wood chips to prevent excessive moisture loss from the top samples. The dryer was eight inches in diameter and a total of 19-inches high: two-inch high for the bottom section, four-inches for each middle section, and one-inch for the top section. A layer of wire screen with k-inch holes was soldered at the bottom of each dryer section to support the wood chips. The connections of the sections were sealed with heavy duty rubber bands. All the sections were marked with numbers and kept in a constant relative position during the experiment. The middle sections were wrapped with thick tissues to reduce heat transformation through the walls of the columns. Three fan-shaped baskets, containing the moisture samples at each depth level, were placed at the top of each section of the middle portion. 81 F':i.gure 5.3 The structure of the dryer and the moisture samples in the fixed bed wood chip drying experiment. each flown two COntI E8381: expez elect incre made board the 1 “58d 144 diff: (air Chip: store B°Ve1 (1) expe; QXpe] were 82 A bypass flowmeter was used to control the airflow rate for each dryer because of its low air pressure drop. The bypass flowmeter included a main pass (two inch PVC tube connected with two ball valves in series) and a bypass (19.6 ml/min valve controlled flowmeter). The bypass flowmeters were calibrated with measured compressed air and a standard flowmeter for each experimental condition. The forced air used for wood chip drying was supplied by two electric blowers (4C446 model, Gralanger) connected in series to increase the static pressure of the air. An air cushion box was made to even the airflow and to support the flowmeters. Particle board was used to support the columns and to hold the top ends of the flowmeter, and a sheet of soft rubber (1/S-inch thickness) was used on the particle board to seal the bottom of the dryers. In accordance with the experimental design, 4 x 4 x 3 x 3, or 144 experiments, were performed. The three dryers containing different size chips were tested under the same drying conditions (air temperature, air relative humidity, and airflow rate). The wood chips used in this experiment were also red pine chips. The methods for sample preparation (size sorting and chip storage) were almost the same as those described in Chapter IV. However, there were two minor differences: (1) The quantity of wood chips used in the fixed bed drying experiment was much larger than that used in the thin layer drying experiment. For convenience in intensive sorting, the wood chips were sorted in a non-conditioning room (T 8 70°F, RH - 50-602) in: 03‘ 83 instead of in the high humidity room; however, the moisture change caused by the size sorting was not significant (P<0.05) because of the large quantity. (2) The plastic bags used to store the wood chips here were much larger than those used in the thin layer drying experiment. The wood chips in one bag were enough for three to four experiments. It only took five minutes to obtain samples from the storage bag and no significant change (P<0.05) in the moisture content was caused by sampling. 5.2.3 Measurement of the Fixed Bed.Wood Chip Drying Experiment Air temperature and air relative humidity in the conditioning chamber were measured by taking the weights of the moisture samples, including the sample container, every two hours for 14 hours of drying, and then again at 22.5 hours. Both a moisture content and a moisture ratio were calculated for each measurement in the same method used in Chapter IV. In each dryer, the moisture samples were located at 0-inch, four-inches, eight-inches, 12-inches, and 16-inches depth levels from the bottom to the top. Wood chip samples held by three fan- shaped baskets were evenly distributed in the cross section of the dryer at each level. The average moisture content of the three samples was used for statistical analysis. The typical curves of the fixed bed drying experiment are illustrated in Figure 5.4. 4|: 1 R 3.93 >28 ezmszoo 5.3.5.03. 84 MOISTURE CONTENT VS. DRYING TIME AND BED DEPTH (‘r - 96.8 F, RH - ssz. CHIP SIZE - 0.82 In') I I H 16 in depth e-e_4a 160 s—s 4“ e—e 0“ WI \ \ I \ " \\\ V T V I ‘r I I W I t I 1 T . 8 12 16 20 - 24 DRYING TIME (HOUR) 5° 8' E // I. : l_1 ‘ 8 nag; s—-"T'fi / MOISTURE CONTENT (DRY BASIS) Z O .1 '1 J G .1. Figure 5.4 Representative drying curves Of the fixed bed wood chip drying experiment. 5.3 5.3.1 with both cons illu dime 85 5.3 WWW 5.3.1 Determining Depth Constant and Time Constant in the Fixed Bed Wood Chip Drying Model In the fixed-bed dryer, the wood chip moisture content changes with the drying time and with the depth of the bed. Therefore, both the drying time (t) and the depth in the dryer (x) must be considered in explaining the drying process. This can be illustrated either with drying curves (Figure 5.4) or with a three- dimensional drying surface model (Figure 5.5) . ‘0' Of to of CC HI. 87 Hukill's bulk drying curves and the curves developed from this wood chip drying experiment are similar. However, the curves for this experiment are based on the depth and the drying time instead of the depth factor and time unit as in Hukill's curves. It was found that if the two numerical numbers "2" in Hukill's formula were substituted with two variables (k‘ and kt) , the shape of the curves changed. Here, it,‘ and kt are defined as the depth constant and the drying time constant, respectively. A modified Hukill's formula is written as follows: It," m.— kx"+kc‘-l where t is drying time (hr), x is depth value in the wood chip bed (in), k, is depth constant, and kt is time constant. This formula can also be illustrated by a three-dimensional surface called the drying surface. The experimental results obtained under each experimental condition can be illustrated by a drying surface which indicates the relationship among the moisture ratio, the drying time, and the depth in the bed (Figure 5.5). Nonlinear regression procedures (NONL) in the SAS program were performed to determine the kx and k1». values for each experimental condition. A total of 144 regressions were executed for this experimental design. 5.3.2 Determining the Models to Explain k, and "n The shape of the drying surface is determined by the depth 88 constant kx and the drying constant kt, which becomes obvious when the drying surfaces are plotted by changingkxand.kt (Figure 5.6). It was found from the experiment that the shape of the drying surface was related to the drying conditions and the properties of the wood chips. Therefore, the two constants, kx and kt, were related to the experimental conditions in some way and this relationship could be determined through regression analysis. Multiple regressions were performed using the SAS computer program to determine the models which would explain the relationship between the constants, k1: and kc, and the experimental conditions, including air temperature (T), air relative humidity (RH), wood chip size (52), airflow rate (V), and original moisture content (OMC). The first four of these variables in the experimental conditions were controlled factors, the last one (OMC) was not. An analysis of variance was performed to evaluate the influences on kit and k1: from the four controlled factors and their interactions. Considering the complicated influences from the multi-factors, second order polynomial equations were chosen as the starting models to present k, and kt. Backward, forward, and maximum R2 model selection . routines in the SAS program were performed to assist model selection. The final models were determined based mainly on the maximum R2 to be reached. Studentized residuals were calculated in the multiple regressions to evaluate the observations from this experiment. u u .... Figu Figure 5.6 The drying surfaces plotted for different 1g and kt. Eli-k,“ KT-kt, T- drying time (hr), and D- bed depth ( n) - 5.3.3 node] cont: unde rela orig SEVe Se: ex] 90 5.3 . 3 Development of a Computer Program from the Empirical Fixed Bed Mood Chip Drying Model Because of the complexity of the empirical fixed bed drying model, a FORTRAN computer program ”CHIP DRY“ was written to execute the calculations using a personal computer. The main program was designed to calculate the moisture content given the drying time (t) and the depth coordinator (x) under certain drying conditions, such as air temperature (T), air relative humidity (RH), wood chip size (82), airflow rate (V), and original moisture content (OMC). For more practical application, several extended functions were also included in this program: (1) to illustrate the moisture distribution along the depth of the wood chip bed and at different drying times; (2) to calculate the average moisture content of the wood chips in the dryer at different drying times; (3) to calculate the average net heating value of the wood chips in the dryer at different drying times; (4) to calculate the airflow resistance of the dryer for different sized wood chips and different airflow rate; and (5) to calculate the bulk shrinkage for different drying conditions. The ”CHIP DRY" program provided the basic information for selecting the drying methods under varied conditions. It is expected to be used as a tool in wood chip dryer design. 91 5-4 Winn W There were two steps taken in developing the empirical fixed bed drying model for wood chips: '(1) determining the drying surface for each experimental condition with nonlinear regressions; and ( 2) determining the relationship between the two constants (kx and kt) and the experimental conditions with multiple regressions. 5.4.1 Determining k‘ and kt for Each Experimental Condition using Nonlinear Regressions A modified Hukill equation was used as the nonlinear regression model to determine kx and kt for the 144 experimental conditions. A typical regression can be illustrated by a three- dimensional surface as shown in Figure 5.3. The two estimates, kx and kt, are listed in Appendix B. The average coefficients of determination for the total 144 regressions in this experiment is 0.95, which indicates that the model fits the experimental data very well. The drying surface shows that the drying process occurs only within a zone of certain thickness at a specific depth and at a certain time. This zone is normally defined as a drying zone. In a dryer, air absorbs the moisture from the wet wood chips, and, after a while, it reaches its saturation point and loses its ability to dry. Therefore, the air can only dry the wood chips within a drying zone in the chip bed, and this zone moves in the SO 5. de 2! 92 same direction as the air does. 5.4.2 The Development of the Models for kx and kt It was found that the drying process can be analyzed by determining two critical values: (1) the moving speed of the drying zone; and (2) the thickness of the drying zone. Comparing the figures.plotted.with the time constant (kt) and.depth constant (k,) (Figure 5.4), it was found that the thickness of the drying zone is inversely related to kx and that the moving speed of the drying zone is directly related to kt and inversely related to k“. Under different experimental conditions, the influence on the two critical values from different independent variables can be explained through R: and kt. Determining the models for kx and k1: was the second step in the development of the empirical fixed bed drying model. Because kx and kt were related to the experimental conditions, multiple regressions were performed to determine the models. 5.4.2.1 Analysis of variance of kx and kt An analysis of variance was performed for both kx and k1: to determine the significant levels for the independent variables and their interactions (Table 5.3, Table 5.4). The ANOVA tables were important references in the model selection. Table I SOURCE model Error Total SOURCE V*SZ WIT Vina 32*‘1‘ 521m Tim V*SZt V‘821 VfiTe} SZRT1 Tabl. soup TOta 93 Table 5.2 Analysis of variance of depth constant kx. SOURCE DP ANOVA 88 MS Model 107 67.185 0.628 Error 34 1.056 0.031 Total 141 68.241 SOURCE DP ANOVA 88 P VALUE PR > F V 2 8.803 141.68 0.0001 82 2 17.145 275.94 0.0001 T 2 1.198 12.85 0.0001 RR 2 23.477 251.89 0.0001 V*82 4 1.359 10.93 0.0001 V*T 6 1.384 7.42 0.0001 V*RH 6 3.137 16.83 0.0001 82*T 6 0.495 2.66 0.0319 82*RH 6 4.183 22.44 0.0001 T*RH 9 1.302 4.66 0.0005 V*82*T 12 1.385 3.72 0.0013 V*SZ*RH 12 0.979 2.62 0.0135 V*T*RB 18 1.623 2.90 0.0036 82*T*Rfi 18 0.713 1.28 0.2632 Table 5.3 Analysis of variance of time constant kt. SOURCE DP ANOVA 88 M8 Model 107 70.729 0.661 Error 34 0.476 0.014 Total 141 71.205 SOURCE DP ANOVA 88 F VALUE PR > F V 2 19.154 684.84 0.0001 82 2 10.318 368.90 0.0001 T 2 10.428 248.56 0.0001 R3 2 10.448 249.04 0.0001 V*82 4 2.773 49.57 0.0001 V*T 6 5.057 60.27 0.0001 V*RH 6 1.903 22.68 0.0001 82*T 6 1.768 21.07 0.0001 82*RH 6 0.888 10.59 0.0001 T*RH 9 1.406 11.17 0.0001 V*82*T 12 2.911 17.34 0.0001 V*SZ*RH 12 0.651 3.88 0.0009 V*T*RH 18 1.503 5.97 0.0001 82*T*RH 18 1.521 6.04 0.0001 94 It was found from the ANOVA tables that almost all of the independent variables were significant. The contribution to the sum square (88) came basically from several independent variables and their second level interactions. , For example, the contribution of SS for kx came from RH, SZ, V, SZ*RH, V*RH, T, and v*sz (in intense order) and for kt from V, S2, RH, T, ViT, v*sz, V*RH, and SZ*T. The original moisture content of the wood chips is not a controlled factor and, therefore, was not included in the ANOVA table. The results of the ANOVA tables were compared to the results of the regression of the models to evaluate the selection of the final models. 5.4.2.2 Regression Analysis of kt and k, The multiple regression procedure was performed to determine the models for kt and 191° The original moisture content was included as an independent variable in the regression. Because the influences to kt and kx from the variables and their interactions were very complicated, second order polynomial equations were chosen as the models to begin with. The maximum R2 stepwise procedure using a SAS computer program was used to select a suitable model. The final models of k1: and kx included the items 'which ‘were significant at 0.05 level in the partial T-test (probability > T). However, some items which were not significant in the T-test were also included in the models because their interactions were significant. The selected models are listed as £011: follows: 95 k.-B..+a., (v1 +8., we) +0., (32) +11“ (522) +85”) +0,“ (RH) «10,,(RH’) +Bu(OMC) +0” (0110’) +Bn,(VS<><fiflbfl"’10*¢>dflQB”"" ' W WWW db1s£hs>«ngfieafl>¢fl£a£5s><>- q} o... o .9.0%%0 0%“. o... ' ; I o O .0 o o o o o r ' '3. ... ’9'} o... o ......” ‘1»«sflt1flfibs>«efifig0*¢>1pw.sfi o o o o \ 'E?W :0 .mg‘.’ \ ”> . - ’ir/ ’0 //:>>fif/// 124 Figure C1 (continued) V I 9903. $2 I 0.30. NC I H4 VI 99.03.32- 0.80. “C I 166 " “.‘ .‘ L 90 125 Figure c1 (continued) V a 99.03. 52 I 0.82. NC I I44 V I 99.03. 82 I 0.82. “C I [66 o O O O O O .‘.o o t ‘ O. O O O... ebqs‘“¢>¢><><fl13» o - 0' '9' 9 O O .psfiaahsfifivfibabsb ‘Efighflhp SO 126 Figure C1 (continued) V I 42.44. 52 I 0.30. NC I 144 / \ ,/’ \ V I 42.44. 82 I 0.30. NC I 186 I? - ¢ - ‘ - - - - - WW 9. ‘8“: ‘ : M.-- - - - ...... - w m.-.“....... ..\ ‘1 G‘ .‘ ‘o‘.’.‘.‘. v f I «‘3.%I>‘.I.I I.’ O- - - - . -‘. - \ ‘:‘:‘:‘- “5%. ‘ - ‘ - - - - to ‘|.. - -..” L” 127 Figure C1 (continued) v -' 42.44. 52 - 0.32. we - 144 V I 42.44. 82 I 0.62. IIC I 166 /W 128 Figure C1 (continued) V I 9903.82- 030.1“: I144 ////“ \\ ‘\\\\\\\\\\\\\ ““‘ ‘ ‘uunnnnuunggfifl‘ ‘uuniflfifs‘ V I 99.03. 82 I 0.30. "C I 166 129 Figure Cl (continued) V I 9903. $2 I 082. NC I 144 “‘ ¢\ \ “ \ \ \ \\ \ \ \\>—\ ‘ J ““““““‘“““‘ \ ““‘ .. “‘ 70 V I 99.03. 82 I 0.62. NC I 166 APPENDIX D LISTING OF THE COMPUTER PROGRAM ”CHIP DRY” 000000 0 APPENDIX D The listings of the computer program "CHIP DRY". PROGRAM REO_MAIN PIXED EED WOOD CMIP DRYING MODEL DESCRIPTION: MAIN PROGRAM POR TEE SIMULATION or A FIXED EED DRYER PUNCTION USED: EMC TIMER DEPTEP RATIO INCLUDE 'rcRAPM.PI' CALL GRAPE () CALL REG () . END Ctttfittiiifiifltt0......i.it.it...O.it.tO..........QOOOOOO..ttitfifiittfittttitit 0 000 10 SUEROUTINE REG() REAL OMC, TEMP. RE, PLO“, SIZE, DEEP, TIME, DP, DEF, TE, TEE, +EHC, EHCC, DH, TH, SUHHC, AVCK, RES, REST, RESTT, CR INTEGER 3.3.JToJD DIMENSION X! (12,12), SE (12, 12) COMMON I (15) , D(15), AVGHC(15), EV(15). AVCSE(15) INPUT CONDITIONS OF DRYER TO DE DIHULAIED WRITE (c.100) OPEN (UNIT-20, PILE-'MODEI.', STATos-'OLD') ONO-150 TEMP-73 RRI78 PLow-vs SIzE-.s DEEP-a TIME-IO GO To 5 CONTINUE WRITE (*,200) READ (...) OMC WRITE (t,201) READ (0,.) TEMP WRITE (*,203) READ (... PLOW WRITE (*.204) READ (t,-) SIZE WRITE(*,250) READ (.,., DEEP WRITE (t,251) READ (.,.) TIME CONTINUE WRITE (t,2ss) OMC, TEMP, RM. PLOW, SIZE, DEEP, TIME WRITE (*,260) READ (*,-) J 10 20 IP (J .E0. 3) GOTO 30 IF (J .29. 4) GOTO go 0 IF (J .E0. 6) OOTO so II (3 .E0. 7) COTO 70 so H H m 'n A A u u n m t) o 2 23 H m L. n o 3 130 Appendix D. 000 000 000 000 000 20 30 40 50 60 70 80 81 82 (continued) WRITE (*,261) READ («,t) OMC OOTO s CONTINUE WRITE (*,262) READ (c,-) TEMP GOTO s CONTINUE WRITE (*,263) READ (*,*) RH GOTO 5 CONTINUE WRITE (*,264) READ (...) PLOW GOTO 5 CONTINUE WRITE (*,265) READ (...) SIzE OOTO 5 CONTINUE WRITE (*,266) READ (...) DEEP GOTO s CONTINUE WRITE (*,267) READ (.,.) TIME OOTO s CONTINUE COMPUTE TIME FACTOR (TPP), DEEP FACTOR (DFP) AND EMC TFPITP (OMC, TEMP. RH, FLOW, SIZE) DPPIDF (OMC. TEMP. RH, FLOW, SIZE) EMCCI EMC (TEMP, RH) RESTI RES (SIZE,PLOW) RESTT I REST * DEEP] 12 00 THROUGH DEEP LOOP DELX I DEEP / 10 DM I 0 JD I 0 DO 81 III, 11 JDIJD+1 D(JD) I DM DM I DM + DELX CONTINUE TIME LOOP DELT I TIME / 10 TMIO JTIO DO 82 II1, 11 IT I JT + 1 T(JT) I TM TM I TM + DELT CONTINUE. DEEP LOOP WRITE (*,212) (T(I), DO 89 II1, 11 TIME LOOP I-l' 131 11) 132 Appendix D. (continued) DO 88 JI1, 11 WRITE (*,*) TFF, DFF, EMCC COMPUTE MOISTURE RATIO FOR PRINT POINTS RATIO IDFF**D(I) /((DFF**D(I))+(TFF**T(J))-l) CONVERT MOISTURE RATIO TO MOISTURE CONTENT DBMCIDBMCC (RATIO, EMCC, OMC) SH (I,J) I SHRINK (DBMC) XM (I,J) IDBMC 88 CONTINUE WRITE (*,211) D(I), (XM (I, JR), JKI1,11) 89 CONTINUE CALCULATE AVERAGE MC AND HEATING VALUE DO 91 JII, 11 SUMMCIO SUMSHIO DO 90 II1, 11 SUMMCIXM(I,J)+SUMMC SUMSHISH(I,J)+SUMSH 90 CONTINUE AVGMISUMMC/ll AVGSHISUMSH/11 AVGMC(J)IAVGM HV(J)IXHV (AVGM) 91 CONTINUE WRITE (*,214) (AVGMC(I),II1,11) WRITE (*,215) (HV(I),II1,11) WRITE (*,216) (AVGSH(I),II1,11) WRITE (*,217) RESTT 000 0000 000 C C CHECK IF NEED ANOTHER CALCULATION C WRITE (*,300) READ (*,*) K C IF (R .E0. 1) GOTO 5 C FORMATE C 100 FORMAT (ll/I, 15X,'WELCOME TO USE CHIP-DRY PROGRAM 2' + ///,10X,'DEAR USER:' + II: 10X,'THIS PROGRAM IS DESIGNED TO CALCULATE THE MOISTURE' + /, 10X,'CONTENT DISTRIBUTION OF WOOD CHIPS IN A FIXED BED’ + /, 10X,'DURING A FORCED AIR DRYING PROCESS. TO USE THIS' + /, 10X,’MODEL PROPERLY, THE ORIGINAL WOOD CHIP CONDITIONS’ + /, 10X,’AND DRYING CONDITIONS SHOULD BE PREPARED FOR THE’ + /, 10X,’CALCULATION.' 200 FORMAT (//,10X,’(1) ORIGINAL MOISTURE CONTENT (¥) I '\) 201 FORMAT (/,10X,'(2) INLET AIR TEMPERATURE (F) I '\) 202 FORMAT (/,10X,'(3) INLET AIR RELATIVE HUMIDITY (A) I '\) 203 FORMAT (/,10X,'(4) INLET AIR FLOW RATE (FT3/HR) I '\) 204 FORMAT (/,10X,'(5) WOOD CHIP SIZE (I) I '\) 1 250 FORMAT (//,10X,'THE FOLLOWING VALUES INDICAT THE SPECIFIC' + I. 10X, 'POINT IN THE DRYER FOR THE CALCULATION.’ + //,10X, '(1) THE DEPTH (LET BOTTOM I 0) (IN) I ’\) //,10X,’(2) THE DRYING TIME (n ) I '\) 251 FORMAT ( 255 FORMAT (I/,10X,'THE CONDITIONS ARE LIST IN THE FOLLOWING TABLE,’ I, 10X,’PLEASE CHECK IT AGAIN BEFORE THE CALCULATION. ’, //,10X, '(1) ORIGINAL MOISTURE CONTENT (A) I ' F9. 4, /,10X,'(2) INLET AIR TEMPERATURE (F) I ' ,F9. 4: +++ Appendix D. 00 +-&+-&+ 260 1++ 261 262 263 264 265 266 267 200 + 210 213 300 350 + //,20X,'IF YES, TYPE '1",//,20X.’IF NO, ... 211 212 214 215 216 217 1133 (continued) I'F904' I'F90" ’,F9.4, .IOX.'(3) .10X.’(‘) / INLET AIR RELATIVE HUMIDITY (t) I /.10X.'(5) / INLET AIR PLOW RATE (FTJ/HR) HOOD CHIP SIZE (I) ,10X,'(6) THE DEPTH (LET BOTTOM - O) (IN) ',F9.4, /,10x,'(7) THE DRYING TIME (HR) ’,F9.4) (//,10X,’PL£ASB TYPE THE NUMBER (1-7) FOR THE VARIABLE’, /,10X,’YOU WANT TO MAKE MODIFICATION AND ENTER (O)’, /,10X,’IF EVERY VALUE IS ox: '\) / iox.'(1) ORIGINAL MOISTURE CONTENT (t) '\) /,10X,'(2) INLET AIR TEMPERATURE (F) ' /, 10x, '(3) INLET AIR RELATIVE HUMIDITY (t) /. 10x,'(4) INLET AIR FLOW RATE (FT3/HR) / 10x,'(5) WOOD CHIP SIzE m FORMAT ,10L '(6) THE DEPTH (LET BOTTOM - O) (IN) FORMAT (1,10x.'(7) THE DRYING TIME (HR) FORMAT (/// 52x F9.4, /, 52x. F9. 4 ,/ 52x, F9. 4 / 52x, F9. 4, 1,52x F9. 4, /. 52L F9. 4) FORMAT (///7(F7.2)) FORMAT(/15F7.2) FORMAT (//,1OX,'DO YOU WANT TO MARE ANOTHER FORMAT FORMAT ( FORMAT ( FORMAT ( FORMAT ( FORMAT ( ( IIIIIII “\“ \ \ \ \ \ \ \ / . vvvvvv 52X,F9.4, TION?’, CALCULA TYPE '0' ’,\) (//,10X,'UNDER ABOVE CONDITIONS,', /,10X,'MOISTURE CONTENT (DRY BASIS) I ',F9.4,' 2’) 1,3X, 11(F6.1)) D / T',2X, 11(F6.1)) AVGMC',2X,11(F6.1)) AVGHV’,2X,11(F6.0)) AVGSH’,2X,11(F6.1)) AIRFLOW RESISTANCE OF DRYER I’,ZX,F6.2,2X,’IN.WATER') FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT RETURN AAAAAA \\\\\3 us QQ ‘: \Q“‘ Cfifitiiiiifititfiiii...iififltfiititifi.itfiitfififittfiiiit...ttitttttfititiiifiiifitiifittt 000 000 000 4. SUBROUTINE GRAPH () INCLUDE ’FGRAPH.FD’ INTEGERcz d , DUMMYl , DUMMY: INTEGERcz coo (3, 2, 2) INTEGERI4 DUMMY4 CRARACTERIZS text1, TEXTz, TEXTS, TEXT4 RECORD / xycoord / xy, xyi RECORD / rccoord / s RECORD I videocontig / vc DATA text1 I ' CHIP-DRY ' / DATA TEXT! / ' Version 1.0, 1991 '/ DATA TEXT: / ' Departsent of Pores '/ DATA szT4 / 'Michigan State Univers ty'l Find graphics node. IF( setvideonode( SMAXRESMODE ) .E0. 0 ) STOP 'Error: cannot set graphics mode' CALL getvideocontig( vc ) Deternine physical (pixel) coordinates Windows. coord(3,1,1) I 0 coord(3,1.2) I o coord(3,2,1) I vc.nunxpixels - 1 coord(3,2,2) I vc.numypixels - 1 Label Windows and frame With rectangles. dummy I setcolor( a ) 1134 Appendix D. (continued) CALL settextposition( 13. 23, curpos ) CALL outtext( texti ) CALL setvieWport( coord(3,1.1). coord(3.1,2) . + coord(3.2.1). coord(3.2.2) ) CALL getviewcoord( coord(3,1,1), coord(3,1,2). xy ) CALL getviewcoord( coord(3.2.1). coord(3,2,2). xyl ) dummy I rectangle( SGFILLINTERIOR, XY.xcoord. xy.ycoord, + xy1.xcoord. xy1.ycoord ) Display rectangles in normal and magnified views. 000 CALL setvieWport( coord(3.1.1). coord(3.1.2) . + coord(3.2,1). coord(3.2.2) ) sctwindow( .TRUE.. 0.0. 0.0, 1000.0, 1000.0 ) dummyl I dummy1 I setcolor (2) dummy1 I rectangle_w( SGBORDRR. 0.0.1000.1000) dummy1 I rectangle W( SGBORDER. 10.10.990.990) dummyl I setcolor Tl) dummyl I rectangle_W( SGBORDER. 295.295.705.705) dummy1 I rectangle W( SGFILLINTERIOR. 300.300.700.700) DUMMY4 I SETBRCOLOR($BLUE) DUMMY! I SETTEXTCOLOR (14) settextposition( 13. 28. curpos ) outtext( text1 ) DUMMYJ I SETTEXTCOLOR (6) settextposition( 15. 28. curpos ) outtext( text2 ) DUMMYJ I SETTEXTCOLOR (7) settextposition( 18. 28. curpos ) outtext( text3 ) settextposition( 19, 28. curpos ) outtoxt( tcxt4 ) READ (*.*) dummy I setvideomode( SDEFAULTHODE ) RETURN EEEE 3% EE Cfiiitiiitttifiiflfifi......COO......iiflifliitflfifiiitfiififiitifififitfififitfifittififiitit c :mmmmnuNEtmmw() C ImumDE 'mauPHJm' ctoeoeoeoaeooooosoeooooeeeeoeoeeeooeoeeoeoeaeegtrounce.ooootooooeooaooat FUNCTION EMC (TEMP, RH) C C DESCRIPTION: TO COMPUTE EMC FOR WOOD C TITEMP HIRH/lOO BI.791+.000463*T-.000000844*T*T BII6.34+.000775*T-.0000935‘T'T BZII.09+.0284‘T-.0000904*T*T WI330+.452*T+.00415*T*T EMCI1800/W*(B*H/(1-B'H)+(BI’B*N+2*BI*BZ*BIB*H*H)/(1+81*B*H* + BI‘BZ‘B*B*H*H)) RETURN Cfififiifii...OQOOOOOO...OOii...tititfifififiiitttitfiiit.iitfitittfifittfiiitflifiitttfi FUNCTION DP (OMC. TEMP. RH. FLOW. SIZE) c . C TO COMPUTE DEEP CONSTANT C DATA BXO, 3X1, BXIXI I +I10.37904712, -.31961232. .000171958/ DATA 3X2, EX1X2, BX2X2 / +24.27485473,-0.02694957. 6.4446486] DATA 8X3, DX1X3 / 135 Appendix D. (continued) +-.30970527, .004217686/ DATA BX4, BX1X4, BX2X4, BX3X4, BX4X4 / +.27417927. -.000774058,-.63756348, .000300598, .000407581/ DATA BXS. BKIXS. BX2X5, BX3X5, BK4X5, BXSXS / +.24743239, .001965759, -.18261486, .001790884, -.001618642, +-.000950171/ DATA 318234. B13335. B2D4B5/ +0.000683442, -.000025603, .003455997/ X1 I FLOW X2 I SIZE X3 I TEMP X4 I RH X5 I OMC DF I BXO + BX1IX1 + BXIXII X1*X1 ++ BX2‘X2 + EX1X2*X1*X2 + BX2X2*X2*X2 ++ BX3*K3 + BX1X3*X1*X3 ++ BX4'X4 + BX1X4‘X1IX4 + EX2X4IX2IK4 + EX3X4IX3IX4 + BX4X4IK4IX4 ++ BX5*X5 + BXIXS‘XI‘XS + BXZXSIK2IX5 + BX3X5*X3*X5 I BX4X5IX4*X5 ++ BXSXS‘KS‘XS ++ BIBZB4‘X1’X2'X4 + E1E3DS‘X1IX3IK5 + BZB4ES‘X2'X4‘X5 RETURN coo...eaeooooeeeeoeoeoooeeeooeooooeooooeeeeooaeeeeeoeoeooeeeeeeaooetto... FUNCTION TF (OMC, Tm, RH, FLOW, SIZE) C C TO COMPUTER TIME CONSTANT C DATA on, Bx1, Bx1x1 / +28.59735622. -.41132229, .000231499/ DATA Bx2 / +-.299129BO/ DATA 3X3. BX1X3 / + -.28020153. .005371459/ DATA 3X4. BXlX4. Bx3x4 / +-.07592159, .000359705, .000195533 / DATA Bxs, BX1X5, Bxaxs, BX4X5 / +-.15436309. .002129935, .001624148. .000374405 / DATA 818334. 318335 / +-.Ooooooozo, -.000029201 / x - FLOW x2 - SIzE x3 TEMP x¢ RH K5 OMC TF EXO + EKI‘KI + EK1X1* KIIXI ++ BX2‘X2 ++ EK3*X3 + BX1K3*X1*X3 ++ EX4‘X4 + BXIX4‘X1IX4 + BX3X4IE3*X4 ++ BX5IX5 + BXIKS'XI‘XS + BXJXS‘K3*X5 + BX4X5IX4*X5 ++ BIE3B4IX1IX3‘X4 + EIE3B5IKIIX3IX5 RETURN C0.0...0.000000000000QOQQOOOOOOOI...ifiififitfititttii.......Otiiififitifiififiitt FUNCTION DBMCC (RATIO. EMCC. OMC) DBMCC I RATIO I (OMC - EMCC) + EMCC RETURN c......tOi0*...0.0...tfitfitfififlfiitt0......0...QOfiififififfittfititti......ttttti FUNCTION‘xHV (xMC) XHV - 9ooo - (.0114-90009100/(ItioolxMC+1)) RETURN coeoooeeeeoeeoOtto.oooeaeaeoooeeoaooottooooeoooaooeooeoateooaoooaoeoooooo FUNCTION RES (SIZE, FLOW) CR I.04521114 - 0.03234395 I SIZE RES I CR * EXP (0.03108 * FLOW) RETURN coeatGEVEGOeoeeoeoooeeoeeesoeooseeeeeaoeetoeooeae«Otooeeoooeaeoooeeeoeeso FUNCTION SHRINK (XMC) SHRINK I 0.152225 0 EXP (I0.0521 * KMC) RETURN END . APPENDIX E RESULTS OF LARGE SCALE TESTING EXPERIMENT AND DRYING MODEL SIMULATIONS Table APPENDIX E Comparison of the results of testing experiment and the simulation results of the empirical drying model and the semi-theoretical drying model. Fixed bed wood chip drying condition: OMCI 133%, TI68'F, 1211-734, sz-o.4o inz, v-az ctm/ttz. Drying Depth Experiment Empirical Theoretical time results model model (hr) (in) HC(§) MC(%) MC(§) O 0 132.06 133.00 132.80 6 0 16.25 24.50 41.10 12 0 15.14 14.80 19.10 18 0 14.81 14.00 14.10 24 0 14.60 13.90 13.00 30 0 14.91 13.90 12.80 42 0 14.45 13.90 12.70 0 8 132.43 133.00 133.00 6 8 115.83 76.40 123.00 12 8 23.53 23.70 91.40 18 8 14.15 14.80 47.90 24 8 13.84 14.00 23.20 30 8 14.06 13.90 15.30 42 8 13.51 13.90 12.80 0 16 134.13 133.00 133.00 6 16 133.47 124.20 133.90 12 - 16 119.03 74.00 132.20 18 16 51.62 23.70 125.80 24 16 16.39 14.80 105.10 30 16 16.16 14.00 64.70 42 16 15.48 13.90 17.60 0 24 131.76 133.00 133.00 6 24 130.83 132.20 134.30 12 24 130.04 123.50 134.20 18 24 116.39 73.90 133.90 24 24 67.74 23.70 132.40 30 24 17.41 14.80 126.60 42 24 14.61 13.90 68.30 0 32 130.00 133.00 - 6 32 125.48 132.90 - 12 32 124.19 132.10 - 18 32 122.71 123.50 - 24 32 113.00 74.10 - 30 32 82.05 23.80 - 42 32 14.48 14.00 - 0 40 130.46 133.00 - 6 40 127.87 133.00 - 12 40 126.54 132.90 - 18 40 125.53 132.10 - 24 40 124.19 123.50 - 30 40 114.19 74.20 - 42 40 42.26 14.90 - 0 48 125.11 133.00 - 6 48 124.83 133.00 - 12 48 125.19 133.00 - 18 48 124.52 132.90 - 24 48 123.83 132.10 - 30 48 122.25 123.50 - 2 48 88.46 23.90 - 136 1137 Table £2 Comparison of the.results of testing experiment and the simulation results ot the empirical drying model and the semi-theoretical drying model. Fixed bed wood chip drying condition: OHCI 130.72, T-70'F, RHI708. sz-o.3o inz, v-Bz ctm/ttz. Drying Depth Experiment Empirical Theoretical time results model model (hr) (in) MC(4) MC(4) MC(4) 0 0 127.15 130.70 129.90 4 0 16.33 27.60 43.10 12 O 14.14 13.30 13.70 20 0 13.82 13.10 11.80 28 0 13.51 13.10 11.70 36 0 13.28 13.10 11.70 44 0 13.13 13.10 11.70 0 8 '129.47 130.70 130.00 4 8 128.36 129.10 124.10 12 8 72.43 70.40 64.40 20 8 13.60 14.80 17.80 28 8 13.20 13.10 12.10 36 8 12.90 13.10 11.70 44 8 12.79‘ 13.10 11.70 0 16 129.58 130.70 130.00 4 16 128.87 130.70 130.80 12 16 127.64 130.50 127.80 20 16 102.60 116.60 97.20 28 16 25.51 24.90 29.40 36 16 14.72 13.30 13.20 44 16 14.46 13.10 11.70 0 24 133.71 130.70 130.00 4 24 132.82 130.70 130.90 12 24 131.93 130.70 130.80 20 24 130.72 130.70 129.10 28 24 114.53 128.70 110.20 36 24 63.39 67.30 41.10 44 24 15.10 13.60 11.70 0 32 130.30 130.70 - 4 32 129.25 130.70 - 12 32 127.95 130.70 - 20 32 126.85 130.70 - 28 32 125.10 130.70 - 36 32 112.17 130.50 - 44 32 79.26 89.60 - 0 40 131.90 130.70 - 4 40 130.78 130.70 - 12 40 130.08 130.70 - 20 40 129.28 130.70 - 28 40 128.21 130.70 - 36 40 126.70 130.70 - 44 40 118.94 130.50 - 0 48 133.10 130.70 - 4 48 132.71 130.70 - 12 48 131.87 130.70 - 20 48 131.27 130.70 - 28 48 130.55 130.70 - 36 48 129.55 130.70 - 44 48 127.90 130.70 - 138 Table E3 Comparison of the results or testing experiment and the simulation results.of‘the empirical drying model and the semi-theoretical drying model. Fixed bed wood chip drying condition: OHCI 1374. T-‘IO‘F, 811-868. sz-O.4s inz, v-99 ctm/ftz. Drying Depth Experiment Simulation Theoretical time results model model (hr) (in) MC(%) HC(%) H C ( 4 ) 0 0 130.51 137.40 137.40 12 0 19.79 19.50 42.40 24 0 19.45 18.40 22.30 36 0 19.08 18.40 18.40 48 0 18.89 18.40 17.60 60 O 18.73 18.40 17.40 72 0 18.92 18.40 17.40 0 8 132.92 137.40 137.00 12 8 94.03 75.60 117.90 24 8 19.01 19.40 72.80 36 8 18.46 18.40 34.90 48 8 18.15 18.40 21.50 60 8 18.05 18.40 18.30 72 8 16.55 18.40 17.60 0 16 134.61 137.40 137.00 12 16 134.82 136.20 137.20 24 16 92.16 72.70 131.30 36 16 20.82 19.30 109.90 48 16 20.21 18.40 66.50 60 16 20.10 18.40 32.60 72 16 20.15 18.40 20.90 0 24 135.94 137.40 137.00 12 24 136.24 137.40 138.50 24 24 133.34 136.10 137.90 36 24 85.36 70.10 135.50 48 24 19.66 19.20 125.50 60 24 19.07 .18.40 95.00 72 24 19.12 18.40 50.70 0 32 148.76 137.40 - 12 32 147.91 137.40 - 24 32 147.06 137.40 - 36 32 140.04 135.90 - 48 32 82.02 67.60 - 6o 32 20.51 19.20 - 72 32 18.36 18.40 - 0 40 142.49 137.40 - 12 40 142.21 137.40 - 24 40 140.97 137.40 - 36 40 139.61 137.40 - 48 40 124.46 135.80 - 60 40 75.82 65.10 - 72 40 22.23 19.10 - O 48 136.67 137.40 - 12 48 136.96 137.40 - 24 48 136.20 137.40 - 36 48 134.80 137.40 - 48 48 133.49 137.40 - 60 48 118.50 135.60 - 72 48 64.97 62.60 - APPENDIX E COMPARISON OF THE RESULTS IN THE TESTING EXPERIMENT ANDTHE RESULTS OF EMPIRICAL MODEL SIMULATION Figure F1 Moisture Content Ratio Moisture Content Ratio APPENDIX E ( 6) 1JT~ .- -.., —._ e ,— , , - r , 1 0‘1?“ .1 e O" depth . . { . g y“ x\\- o a" depth 1 0.9.1 I \ ‘ ‘ \-\\ O 16" depth d . ‘ 0 A .. ‘~. \. e 24" depth . 0.84 \ \ \ \\ o 32" depth -« 0.7: \\ \‘x \ ‘i\. v 40" depth 4‘ J \ ‘~. 0.5 4 i ‘5 \ \ >\. 0.5"j \' \ \\ . \ \ 0.41 \ \ i ‘ \ 0.3 ’ \‘ \ D \ I \ \‘ ‘ ‘5 0.2 ~ X \1 0,1 1 \‘ \ .\ . O 4 \ e \\ \\ \\\ °~° #. r ‘m k - 'r: - 10 ’ 20 30 O 50 Drying Time (hour) (13) ‘.“"’ ‘ I ' - v“ -' r ——v———' .- fl f J o 0" depth "01'7—‘5" jfl\ o 8" depth '4 0.9. \ ° “ \ o 16" depth . i ‘ . ~. \ e 24" depth . 0.34 \ x o 32" depth . ‘ v 40" depth ‘ 0.7~ i 0.614 0.54 J 0.41 0.31 0.2- \ . i 4 \ 004.- .... 1._O~.._. O O 20 30 ‘0 Drying Time (hour) (a) Results of large scale testing experiment and (b) results of empirical fixed bed drying model . simulation, experiment condition: 0MC= 133%, T=68°F, RH-73%, 3220.46 inz, V=82 cfm/ftz. 139 50 140 1 1 (a) ‘ 0 ‘h— 0" depth .1 ' i “r 8" depth + 0,9. 16" depth . o t 24" depth . ‘3, 0.04 32" depth - L: 0.74 40 depth 1 c ‘ 1 8 0.6" q S 4 . U 0.5« . o . L 4 3 0."‘ -t .92 ‘ t o I 0.25-j .i 0.2-4 . mi “‘ j J “0.- i 0.0 g . 0 50 60 (b) ”T - . . . _. -- -7... ,-_,---, _ -,___.__ ‘ O 0” depth ‘ 1.00- : - - - - . r fl\ ' fio 8" depth ‘ 0.94 \\ \ “ \ 0 16" depth 1 9 + '\ ‘ 4 24" depth i ‘6 03: 0 32" depth .. E 0.7. ' 4°" “9‘" i s * i «a 0.64 - 4 o i . 0 0.5+ . e . L0 4 3 0.4- 4 9 J J g 0.34+ . 0.24 . . i \ \ i 0.! J ‘x \ a .. \ ‘\ \\ 0.0+— — 'r o - *— rk - : é\.: r :fi f r 0 10 20 30 40 50 60 Drying Time (hour) (a) Results of large scale testing experiment and (b) results of empirical fixed bed drying model simulation, experiment condition: OMC: 130%, T=70°F, art-70%, sz-o.30 in’, v-az cfm/ttz. Figure E2 Figure F3 Moisture Content Ratio Moisture Content Ratio 141 (a) 1.1 —~- - . 1 , —. 1, e , 1 . a r e I: e 0" depth ‘ OJ 0 8" depth ‘ 0.94 o 16" depth d i a 24" depth . 0.81 0 32" depth - ‘ v 40" depth ‘ 0.7~ -‘ . 1 0.6- .. 1 1 0.5-J .1 ad . 0.3 \ .i 0.2 i \. T 0.: ~ . 1 ‘ 1 0.0«i——-——;—‘ , 0 10 20 30 40 50 60 70 80 Drying Time (hour) 0)) 1-‘1’ ° I I I v I -' 1 "P"! '* “T_" j e 0" depth '-° '77:! \i. x? . . a" mu. .3 0.94 ‘~ 0 16" depth ‘ 1 \ a 24” depth . 0.8? e 32" depth .. v 80 0.7‘ 40 depth 1 1 4 0.6-1 ., J 1 0.5-J J 1 A 0.44 1 1 1 0.34 'i (3.2-1 -4 1 t 1 0‘ 4 x \ d in 20 30 40 50 60 70 80 Drying Time (hour) (a) Results of large scale testing experiment and (b) results of empirical fixed bed drying model simulation, experiment condition: OMC= 137%, T=70°F, RH=86%, SZ=0.46 inz, v=99 cfm/ftz. LI ST OF REFERENCE LIST OF REFERENCE Bakker-Arkema,F.W., Lerew,L.E., De Boer,S.F., and.Roth,M.G., 1974. Grain dryer simulation, Research Report 224. Agr. Exp. Sta., Michigan State University: East Lansing, Michigan. Bhattacharyya, G. K. and.Johnson, R..A. 1977. Statistical Concepts and Methods. John Wiley 8 Sons, New York. Brooker, D. 3., Bakker-Arkema, F. W., and Hall, C. W. 1974. Drying Cereal Grains. AVI: Westport, Connecticut. Carnahan, 3., Luther, H. A. and Wilkes, J. 0. 1969. Applied Numerical Methods. John Wiley 8 Sons, Inc., New York. Cheremisinoff,N.P. 1980. Wood for energy production. Ann Arbor Science. Publishers Inc. Ann Arbor, Mich. Dalpasquale, V. A. 1981. Drying of Soybeans in Continuous-flow Dryers and Fixed-bed Drying Systems. Ph.D Thesis, Michigan State University, East Lansing, Michigan. Del Gobbo,N., 1978. Fuels from biomass systems program overview. Proc. of second annual symposium on fuels from biomass. p.7-24, Troy, N.Y.: Renssalaer Polytechnic Inst., June 20-22. Feist,W.S., Springer,E.L. and Hajny,G.J. 1973. Spontaneous heating in piled wood chips - contribution of bacteria. Tappi. 56(4):148-151. Food and Agriculture Organization of the United Nations, 1976. Wood chips production, handling, transport. 2nd edition, Rome. Hall,D.0. and 0verend,R.P. 1987. Biomass regenerable energy. John Wiley 8 Sons, Chichester. Harris, R. A., McMinn, J.W. and Payne,F.A. 1986. Calculating and reporting changes in net heat of combustion.of wood fuel. Forest Prod. J. 36(6): 57-60. Hawley,C.F., 1952. 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