. t‘.‘
lira; .
v3 -
; ..
31'." I...
I 3.7

1:30 .. .
I 31.3.,

5.1

r... 5... .. . ,
fix?

.

 

a .A...z .{m a.
1‘... 4-...XI._:.59 : d...“

 

THSSib

ImmmIiiii‘iiiliiifliiii Ii 1mm»

3 1293 01801 7024

 

LIBRARY
Michigan State
University

 

 

 

This is to certify that the

dissertation entitled

STOCHASTIC MODELING AND AUTOMATIC CONTROL
OF GRAIN DRYERS:
OPTIMIZING GRAIN QUALITY

presented by

Qiang Liu

has been accepted towards fulfillment

of the requirements for
Agricultural

Ph. D . degree in W

/M%

Major professor

 

 

Date DecembL-LLLJM

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINE return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE
3

‘4 ‘r’

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ma W14

 

STOCHASTIC MODELING AND AUTOMATIC CONTROL OF GRAIN
DRYERS: OPTIMIZING GRAIN QUALITY

By

Qiang Liu

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1998

ABSTRACT

STOCHASTIC MODELING AND AUTOMATIC CONTROL OF GRAIN DRYERS:
OPTIMIZING GRAIN QUALITY

By

Qiang Liu

Quality damage to grain during high-temperature drying has become a severe
problem for end users in many grain-processing industries. The problem can not be
solved simply by decreasing the drying-air temperature because this will decrease the
dryer capacity and the energy efficiency. The major objective of this research is to
minimize the quality damage through improving the dryer design and control.

The objective was pursued in two directions, i.e. modeling of the drying process
and developing of the control system. Stochastic maize drying and maize-quality models
were developed, providing the necessary tools for optimizing dryer design; and, automatic
moisture and quality controllers were developed to minimize grain-quality deterioration.
Three aspects of maize quality were investigated, i.e. moisture distribution among grain
kernels, protein denaturation and viability.

The stochastic nature of the moisture content of maize before and afier drying was
analyzed. The moisture content distribution of maize kernels at harvest and after thin-layer
drying, appeared to be normally distributed, and after crossflow-drying to be skewed.

Stochastic models correctly predicted the moisture content distribution in maize kernels

dried in different high-temperature dryer types, i.e. the average moisture content and its
standard deviation of the dried grain.

The stochastic crossflow drying model, and the denatured protein and germination
models, were combined to analyze the quality of individual kernels. The results served as
a guide for operating crossflow dryers.

For the purpose of automatic moisture control, a distributed-parameter process
model of crossflow drying was utilized to develop a model-predictive control system.
The controller has a feedforward loop (i.e. the predictive model and the optimizer) and an
feedback loop (i.e. the parameter estimator and the modifier). It was implemented and
tested on a commercial crossflow dryer and controlled the moisture content of the maize
at the outlet of the dryer to within i 1.3% of the set point, at inlet moisture contents
ranging from 21 to 32% w.b. and drying-air temperatures from 85 tol20°C. The
controller reacted properly to changes in the drying-air temperature.

The strategy of grain-quality control was analyzed. A neural network model was
developed relating the quality of dried grain to various temperature/residence-time
conditions. A control algorithm was selected which to varies the drying-air temperature
with the objective of maintaining the grain quality close to the set point. Simulation tests
showed that a more uniform grain quality is achieved by implementing the quality

controller on a crossflow dryer.

ACKNOWLEDGMENTS

Being associated with Dr. Fred W. Bakker-Arkema was a great turn-point in my
career. He has profoundly influenced my personal and professional life. His generous
help will always be gratefully remembered.

Sincerely appreciation is extended to the guidance committee members: Dr.
William Bickert, Agricultural Engineering; Dr. Lawrence Copeland, Crop and Soil
Science; Dr. Clark J. Radcliffe, Mechanical Engineering; and Dr. R. Lal Tummala,
Electrical and Computer Engineering. Thank you to William D. Crosby, ffi Corporation,
Indianapolis, for serving as an outside examiner.

The financial support of ffi Corporation, Indianapolis, IN; MFS/York, Grand
Island, NE and the Crop and Food Bioprocessing Center (CFBC) at Michigan State
University, are greatly appreciated. Special thanks go to Mr. Curt F ankhauser, Chairman
and CEO of ffi Corporation; Mr. Robert. E. Hines, former General Manager of
MFS/York; and Prof. Kris A. Berglund, Director of the CFBC.

Also acknowledged is the willingness and tremendous cooperation received from
the people at Jorgensen Farm Elevator without whom the experimental field tests would
not have been successful. Special thanks go to Mr. Mike Turner, Manager of Jorgensen
Farm Elevator.

Thanks also due to Jim E. Montross, James S. Labiak, Kyle E. Weidmayer for
their help in the test. Special thanks to Lillian Agranian for her secretarial support.

Deep appreciation to my wife, Xiuli Qi, for her hard work, moral support and

sacrifice, and to my lovely daughters, Xiaoxue Liu and Dana Xiaodan Liu.

iv

TABLE OF CONTENT

 

 

 

 

INTRODUCTION 1
OBJECTIVES .............................................................................................................. 4
OUTLINE OF THE DISSERTATION ................................ . ............. 4
REFERENCES ................................ 8

 

CHAPTER 1. STOCHASTIC MODELING OF GRAIN DRYING: EXPERIMENTAL

 

 

 

 

 

 

 

INVESTIGATION* 9
ABSTRACT ................................................................................................................................................... 9
1.1 INTRODUCTION .................................................................................................................................. IO
1.2 LITERATURE REVIEW ........................................................................................... 10
1.3 EXPERIMENTAL DETAILS . ................................................................... 12
1.3.1 MOISTURE CONTENT MEASUREMENT OF INDIVIDUAL KERNELS ........................................................ 12
1.3.2 LABORATORY THIN-LAYER DRYING ................................................................................................. 13
1.3.3 COMMERCIAL CROSSFLOW DRYING ................................................................................................. 13
1.4 RESULTS .. .................................. 14
1.4.1 MOISTURE DISTRIBUTION AT HARVEST .. ........................................ 14
1.4.2 MOISTURE DISTRIBUTION DURING DRYING . ..................................................... 18
1.4.3 MOISTURE DISTRIBUTION DURING STORAGE .................................................................................... 29
1.5 CONCLUSIONS .................................................................... 29
REFERENCES 31

 

CHAPTER 2. STOCHASTIC MODELING OF GRAIN DRYING: MODEL DEVELOPMENT* 32

 

 

 

 

 

ABSTRACT ................................................................................................................................................. 32
2.1 INTRODUCTION .................................................................................................................................. 33
2.2 THIN-LAYER DRYING MODEL .................................................. 34
2.3 DEEP-BED (ONE-DIMENSIONAL) DRYING MODEL ............................................................................... 35
2.4 DEEP-BED (Two-DIMENSIONAL) DRYING MODEL ............ . ...................... 37
2.5. BASIS CONVERSION OF THE GRAIN MOISTURE CONTENT .................................................................. 38
2.6 MODEL VALIDATIONS ........................................................................................... 39
2.6.1 THIN-LAYER DRYING ...................................................................................................................... 39
2.6.2 CROSSFLOW DRYER. ............................................................................................ 39
2.7 CONCLUSIONS . .............................................................................................. 42
REFERENCES ............................................. 44

 

APPENDIX 2A: THE MOISTURE CONTENT DISTRIBUTION OF GRAIN DRIED IN A ONE-DIMENSIONAL
(CONCURRENT- OR COUNTER-FLOW) DEEP-BED DRYER ........................................................................... 46

V

APPENDIX 23: THE MOISTURE CONTENT DISTRIBUTION OF GRAIN DRIED IN A Two-DIMENSIONAL
(CROSSFLOW) DEEP-BED DRYER .............................................................................................................. 49
SYMBOLS .................................................................................................................................................. 52

CHAPTER 3. STOCHASTIC MODELING OF GRAIN DRYING: ANALYSIS OF

 

 

CROSSFLOW DRYING" 53
ABSTRACT ................................................................................................................................................. 53
3.1 INTRODUCTION ................................................................................................................................... 54
3.2 CROSSFLow DRYER SPECIFICATIONS ................................................................................................. 54
3.3 CROSSFLow DRYER PERFORMANCE CHARACTERISTICS ..................................................................... 55
3.4 STANDARD DEVIATION ....................................................................................................................... 60
3.5 AIR TEMPERATURE ............................................................................................................................. 64
3.6 AIRFLow RATE ................................................................................................................................... 64
3.7 GRAIN INVERSION .............................................................................................................................. 64
3.8 CONCLUSION ...................................................................................................................................... 70

CHAPTER 4. MODELING OF GRAIN QUALITY' 72
ABSTRACT ................................................................................................................................................. 72
4.1 INTRODUCTION ................................................................................................................................... 73
4.2 LITERATURE REVIEW .......................................................................................................................... 74
4.3 MODELS AND SIMULATION ................................................................................................................. 81
4.3.1 QUALITY MODELS ............................................................................................................................ 81
4.3.2 QUALITY SIMULATION ..................................................................................................................... 82
4.3.3 MODEL VALIDATIONS ...................................................................................................................... 84
4.4 GAIN-QUALITY ANALYSIS ................................................................................................................... 86
CONCLUSIONS ........................................................................................................................................... 98
REFERENCES ........................................................................................................................................... 100

CHAPTER 5. DISTRIBUTED-PARAMETER PROCESS MODEL FOR GRAIN DRYING .......... 102
ABSTRACT ............................................................................................................................................... 102
5.1 INTRODUCTION ................................................................................................................................. 103
5.2 REVIEW OF GRAIN DRYING MODELS ................................................................................................ 104
5.3 MODEL DEVELOPMENT .................................................................................................................... 106
5.3.1 ELEMENTAL DRYING MODELS (EDM) ............................................................................................ 106
5.3.2 FULL-SIZE DRYER MODEL .............................................................................................................. 1 13
5.4 VALIDATION OF THE MODELS ........................................................................................................... 1 14
5.5 DISCUSSION AND CONCLUSIONS ....................................................................................................... 1 17
APPENDIX 5A: ONE-DIMENSIONAL CROSSFLOW DRYING MODEL ........................................................... 1 18

Vi

SYMBOLS ................................................................................................................................................ I 2 l

 

 

ABBREVIATIONS ..................................................................................................................................... 1 22
REFERENCES ........................................................................................................................................... 123
CHAPTER 6: DESIGN OF CONTROL ALGORITHM 125
ABSTRACT ............................................................................................................................................... 125
6.1 INTRODUCTION ................................................................................................................................. 126
6.2 PROCESS CHARACTERISTICS AND REVIEW OF THE CONTROL STRATEGIES ........................................ 127
6.3 MODEL-PREDICTIVE CONTROL STRATEGY ........................................................................................ 130
6.3.1 FEEDFORWARD LOOP ..................................................................................................................... 133
6.3.2 FEEDBACK LOOP (PARAMETER ESTIMATOR/MODIFIER) ............... f .................................................. 136
6.4 SIMULATION TESTS AND TUNING OF THE CONTROLLER .................................................................... 138
6.4.1 VIRTUAL GRAIN DRYER AND CONTROLLER .................................................................................... 138
6.4.2 FEEDFORWARD CONTROL .............................................................................................................. 140
6.4.3 FEEDBACK CONTROL ..................................................................................................................... 145
6.4.4 ROBUSTNESS OF THE CONTROLLER ................................................................................................ 148
6.5 CONCLUSIONS ................................................................................................................................... 154
REFERENCES ........................................................................................................................................... 159
CHAPTER 7. FIELD TESTS OF THE CONTROLLER 161
ABSTRACT ............................................................................................................................................... 161
7.1 INTRODUCTION ................................................................................................................................. 162
7.2 IMPLEMENTATION ............................................................................................................................. 162
7.2.1 GRAIN DRYER ................................................................................................................................ 162
7.2.2 CONTROL SYSTEM ......................................................................................................................... 164
7.2.3 PROGRAMMING .............................................................................................................................. 166
7.3 RESULTS AND DISCUSSION ............................................................................................................... 169
7.3.1 ON-LINE CALIBRATION OF THE MOISTURE SENSORS ....................................................................... 169
7.3.2 CONTROL TESTS ............................................................................................................................. 170
7.4 CONCLUSIONS ................................................................................................................................... 186
REFERENCES ........................................................................................................................................... 187
CHAPTER 8. GRAIN QUALITY CONTROL IN HIGH-TEMPERATURE DRYERS ................... 188
ABSTRACT ............................................................................................................................................... 188
8.1 INTRODUCTION ................................................................................................................................. 189
8.2 CONTROL-ORIENTED QUALITY MODELS ........................................................................................... 190
8.3 QUALITY CONTROL ALGORITHM ...................................................................................................... 195
8.4 CONCLUSIONS ................................................................................................................................... 202

Vii

REFERENCES ........................................................................................................................................... 204

 

CHAPTER 9. SUMMARY 205
9.1 STOCHASTIC DRYING MODELING ..................................................................................................... 205
9.2 GRAIN-QUALITY MODELS ................................................................................................................. 205
9.3 MOISTURE CONTROLLER .................................................................................................................. 206
9.4 GRAIN-QUALITY CONTROLLER ......................................................................................................... 206
9.5 SUGGESTIONS FOR FUTURE STUDY: .................................................................................................. 207

viii

LIST OF TABLES

TABLE 1.1 SHRINKAGE IN METRIC TONNES (MT) AND SHRINKAGE COST WHEN 25,400 MT (1,000,000 BU) OF
MAIZE IS DRIED BELow 15.5% w.B. (BROOKER ET AL., 1992). .............................................................. 3
TABLE 1.2 ENERGY REQUIRED PER METRIC TONNE (MT) AND COST (AT DIFFERENT ENERGY PRICES)
RESULTING FROM VARIOUS LEVELS OF OVERDRYING OF 25,400 MT (1,000,000 BU) OF 15.5% W.B.
MAIZE (BROOKER ET AL., 1992) ............................................................................................................. 3
TABLE 1.] X2 TEST FOR NORMALITY IN THE MOISTURE CONTENT DISTRIBUTION OF MAIZE AT HARVEST BEFORE
SMOOTH/NO OF THE DATA ..................................................................................................................... 16
TABLE 1.2 X2 TEST FOR NORMALITY IN THE MOISTURE CONTENT DISTRIBUTION OF MAIZE AT HARI 'EST AFTER
SMOOTH/NO OF THE DATA IN TABLE 1.1. .............................................................................................. 17
TABLE 2.1 EXPERIMENTAL AND SIMULATED STANDARD DEVIATIONS (SD) OF MAIZE DRIED IN CROSSFLOW
DRYERS ................................................................................................................................................ 45
TABLE 2.2 EXPERIMENTAL AND SIMULATED STANDARD DEVIATION (SD) DRIED IN CROSSFLOW DRYERS
EXCLUDING KERNELS A T MOISTURE CONTENTS LOWER THAN 9%. ........................................................... 45
TABLE 3.1 DESIGN SPECIFICATIONS AND OPERATING CHARACTERISTICS OF THE STANDARD CROSSFLOW
DRYER USED IN THE ANALYSIS OF THE MSU STOCHASTIC DRYING MODEL ........................................... 54
TABLE 3.2 MOISTURE CONTENT (MC) AND STANDARD DEVIATION (SD) OF THE MOISTURE CONTENT
(AVERAGE, AT AIR-INLET, AT AIR-OUTLET) OF MAIZE DRIED IN A CROSSFLOW DRYER WITHOUT GRAIN-
INVERSION (AIR TEMPERATURE, 90°C; AIRFLow RATE, 80 M3 MIN" T"). .............................................. 69
TABLE 3.3 MOISTURE CONTENT (MC) AND STANDARD DEVIATION (SD) OF THE MOISTURE CONTENT
(AVERAGE, AT AIR-INLET, AT AIR-OUTLET) OF MAIZE DRIED IN A CROSSFLOW DRYER WITH GRAIN-
INVERSION (AIR TEMPERATURE, 90°C; AIRFLow RATE, 80 M3 MIN" T"). .............................................. 70
TABLE 4.1 EXPERIMENTAL AND PREDICTED TRANSMITTANCE AND DENATURATION OF PROTEIN AFTER DRYING
OF MAIZE IN THREE COMMERCIAL CROSSFLOW DRYERS. ...................................................................... 85
TABLE 4.2 EXPERIMENTAL AND PREDICTED GERMINATION OF MAIZE AFTER Two HOURS OF DRYING IN A
BATCH DRYER IN DRYING MAIZE To 15% MC. ..................................................................................... 85
TABLE 4.3 DRYING CONDITIONS FOR THE GRAIN-QUALITY SIMULATION STUDY IN A CROSSFLOW DRYER. ..... 85
TABLE 4.4A PREDICTED QUALITY OF MAIZE AFTER CROSSFLOW DRYING AT AN AIRFLow RATE OF 40 CFM/BU
(32 M3M'3MIN") ................................................................................................................................... 88
TABLE 4.4B PREDICTED QUALITY OF MAIZE AFTER CROSSFLOW DRYING AT AN AIRFLow RATE OF 60 CFM/BU
(48 M3M'3MIN"). .................................................................................................................................. 88
TABLE 4.4C PREDICTED QUALITY OF MAIZE AFTER CROSSFLOW DRYING AT AN AIRFLow RATE OF 80 CFM/BU
(64 M3M'3MIN"). .................................................................................................................................. 89
TABLE 4.4D PREDICTED QUALITY OF MAIZE AFTER CROSSFLOW DRYING AT AN AIRFLOW RATE OF 100 CFM/BU

(so M3M'3MIN"). .................................................................................................................................. 89

ix

TABLE 4.5 MAIZE QUALITY AFTER CROSSFLOW DRYING WITH AND WITHOUT AIR INVERSION AT THE MIDPOINT
ALONG THE DRYING COLUMN WITH AN AIRFLow RATE OF 60 CFM/BU (48 M3M'3MIN"). ....................... 99
TABLE 4.6 EFFECT OF THE STANDARD DEVIATION (SD) OF THE INLET MOISTURE CONTENT OF MAIZE ON THE
FINAL GERMINATION AFTER CROSSFLOW DRYING ( WITH AN AIRFLOW RATE OF 60 CFM/BU OR 48 M3M‘
3MIN"). ................................................................................................................................................ 99
TABLE 5.1 THE SPECIFICATIONS OF THE ZIMMERMAN VT1210 AND VT4036 DRYERS. .............................. 1 15
TABLE 5.2 PREDICTED CAPACITY OF ZIMMERMAN VT1210 MAIZE DRYER USING THE C.O.D. MODEL AND
P.E.D. MODEL. .................................................................................................................................... 1 16
TABLE 5.3 PREDICTED CAPACITY OF THE ZIMMERMAN VT4036 MAIZE DRYER USING THE C.O.D. MODEL AND
P.D.E. MODEL. .................................................................................................................................... l 16
TABLE 6.1 RESPONSE CHARACTERISTICS OF THE OUTLET MOISTURE CONTENT TO THE MODIFICATION OF THE

DRYING CONSTANT FOR DIFFERENT VALUES OF THE FILTER FACTOR. . ................................................ I48

FIG.
FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG

LIST OF FIGURES

1.1 A SCHEMATIC REPRESENTATION OF THE CONTENTS OF THE THESIS. ................................................... 7
1.1 TYPICAL FREQUENCY DISTRIBUTION OF THE KERNEL MOISTURE CONTENT IN MAIZE REACHING A
DRYER (AVERAGE MOISTURE CONTENT IS 37.5 % D.B.). ...................................................................... 15
1.2 THE FREQUENCY DISTRIBUTION OF THE RAW DATA, SMOOTHED DATA AND THE CORRESPONDING
NORMAL DISTRIBUTION OF THE MOISTURE CONTENT OF MAIZE KERNELS IN A TYPICAL MAIZE SAMPLE
REACHING A DRYER. ............................................................................................................................ 19
1.3 EXPERIMENTAL THIN-LAYER DRYING CURVES (EACH CURVE IS THE AVERAGE OF 60 KERNELS) OF
MAIZE AT THREE DRYING-AIR TEMPERATURES. .................................................................................... 20
1.4 THE STANDARD DEVIATION AT DIFFERENT AVERAGE MOISTURE CONTENTS (60 KERNELS As A GROUP)
DURING THIN-LAYER DRYING OF MAIZE AT THREE DRYING-AIR TEMPERATURE. ................................... 21
1.5 THE MOISTURE CONTENT DISTRIBUTION OF 60 KERNELS AT THREE DRYING STAGES DURING THIN-
LAYER DRYING AT 60°C; THE AVERAGE MOISTURE CONTENTS ARE 24.4 % (INITIAL), 17.6 % AND 14.9
% D.B., RESPECTIVELY, FROM LEFT To RIGHT. ..................................................................................... 22
1.6 THE FREQUENCY DISTRIBUTION OF THE KERNEL DRY MASS OF A TYPICAL MAIZE SAMPLE. .............. 24
1.7 THE DRYING CURVES OF MAIZE KERNELS GROUPED BY DRY WEIGHT DURING THIN-LAYER DRYING OF
60 KERNELS AT 60°C. .......................................................................................................................... 25
1.8 THE STANDARD DEVIATION OF THE MOISTURE CONTENT OF MAIZE KERNELS GROUPED BY DRY
WEIGHT DURING DRYING AT 60°C. ....................................................................................................... 26
1.9 MOISTURE DISTRIBUTION BEFORE AND AFTER DRYING OF MAIZE IN A CROSSFLOW DRYER (CFI);
INLET AVERAGE M.C.=33.0% D.B., STAND. DEV.=8.6% D.B., AND OUTLET AVERAGE M.C.=17.2% D.B.,
STAND. DEV. =7.1% D.B ...................................................................................................................... 27
1.10 MOISTURE DISTRIBUTION BEFORE AND AFTER DRYING OF MAIZE IN ANOTHER CROSSFLOW DRYER
(CF2); AT THE INLET THE AVERAGE M.C. =34.0% D.B., STAND. DEV. =7.9% D.B., AND AT THE OUTLET
THE AVERAGE M.C. =18.6% D.B., STAND. DEV. =7.7% D.B .................................................................. 28
1.1 1 THE CHANGE IN THE STANDARD DEVIATION OVER TIME OF THREE MAIZE SAMPLES AFTER
CROSSFLOW DRYING AND STORAGE AT 20°C. THE AVERAGE MOISTURE CONTENTS OF SAMPLES ARE
22.4 % (A), 15.9 % (X) AND 19.9 % (0) DB, RESPECTIVELY. ........................................................... 30

. 2.I PREDICTED AND EXPERIMENTAL STANDARD DEVIATIONS OF THE MOISTURE CONTENT OF MAIZE

DURING SINGLE-KERNEL DRYING AT 600C AND 700C, RESPECTIVELY. ................................................. 40

FIG. 2.2 PREDICTED AND EXPERIMENTAL STANDARD DEVIATIONS OF THE MOISTURE CONTENT OF MAIZE

DURING THIN-LAYER DRYING AT 80°C. ................................................................................................ 41

FIG. 2. AI SIMULATED DRYER EXIT MOISTURE CONTENT DISTRIBUTION IN A CONCURRENT-FLOW MAIZE

DRYER EMPLOYING DIFFERENT THIN-LAYER DRYING EQUATIONS ......................................................... 5 I

xi

FIG. 3.1 THE AVERAGE MOISTURE CONTENT (AMC) OF MAIZE, THE DIFFERENCE BETWEEN THE AVERAGE
MCS OF THE AIR-INLET AND AIR-OUTLET SUB-COLUMNS (AMCD), AND THE STANDARD DEVIATION
ACROSS THE GRAIN COLUMN (SD), OF A CROSSFLOW DRYER OPERATING AT 90°C ............................... 56

FIG. 3.2 THE DRYING CURVES OF 25 % W.B. INITIAL MOISTURE CONTENT MAIZE AT DIFFERENT POSITIONS
WITHIN THE GRAIN COLUMN OF A CROSSFLOW DRYER OPERATING AT 90°C. ........................................ 57

FIG. 3.3 THE STANDARD DEVIATION OF THE MOISTURE CONTENT AT DIFFERENT POSITIONS WITHIN THE GRAIN
COLUMN. MAIZE INITIALLY AT 25% (W.B.) MOISTURE CONTENT AND DRIED IN A CROSSFLOW DRYER
OPERATING AT 90°C. ............................................................................................................................ 58

FIG. 3.4 THE MOISTURE DISTRIBUTION OF MAIZE BEFORE DRYING, AND AFTER ONE HOUR AND TWO HOURS OF
CROSSFLOW DRYING AT 90°C. MAIZE INITIALLY AT 25% W.B. AVERAGE MOISTURE CONTENT WITH 3%

W.B. STANDARD DEVIATION. ............. .. ............................................................. 59

 

FIG. 3.5 THE STANDARD DEVIATION (SD) OF THE MOISTURE CONTENT OF MAIZE IN A CROSSFLOW DRYER FOR

DIFFERENT INITIAL SD VALUES; THE DRYER OPERATES AT 90°C ......... - - - ................ 6|

 

 

 

FIG. 3.6 THE MOISTURE DISTRIBUTION OF MAIZE DRIED IN A CROSSFLOW DRYER AT DIFFERENT AIR
TEMPERATURES. MAIZE INITIALLY AT 25% W.B. AVERAGE MOISTURE CONTENT AND 3% W.B.

STANDARD DEVIATION. - ........................................................................ 62

 

FIG. 3.7 THE STANDARD DEVIATION OF THE MOISTURE CONTENT IN MAIZE DRIED IN A CROSSFLOW DRYER AT
DIFFERENT AIR TEMPERATURES. MAIZE INITIALLY AT 25% W.B. MOISTURE CONTENT. ........................ 63
FIG. 3.8 THE MOISTURE DISTRIBUTION OF MAIZE DRIED AT 90°C IN A CROSSFLOW DRYER AT DIFFERENT

AIRFLOW RATES (M3 MIN‘l T") . MAIZE INITIALLY AT 25% W.B. AVERAGE MOISTURE CONTENT WITH 3%

 

W.B. STANDARD DEVIATION. ................................... .. ................................................ 65
FIG. 3.9 THE STANDARD DEVIATION OF MAIZE DRIED AT 90°C IN A CROSSFLOW DRYER AT DIFFERENT
AIRFLOW RATES (M3MIN"T"). MAIZE INITIALLY AT 25% W.B. MOISTURE CONTENT. ............................ 66
FIG. 3.10 THE MOISTURE DISTRIBUTION OF MAIZE BEFORE DRYING, AND AFTER ONE HOUR AND TWO HOURS
OF CROSSFLOW DRYING AT 90°C. THE MAIZE IS INITIALLY AT 25% W.B. MOISTURE CONTENT AND IS
INVERTED AFTER 1 HOUR OF DRYING. .................................................................................................. 67
FIG. 3.1 1 THE STANDARD DEVIATION (SD) OF THE MOISTURE CONTENT OF MAIZE DRIED AT 90°C IN A
CROSSFLOW DRYER WITH AND WITHOUT GRAIN-INVERSION. THE MAIZE IS INITIALLY AT 25% W.B.
MOISTURE CONTENT ............................................................................................................................. 68
FIG. 4.1 EXPERIMENTAL (POINTS) AND PREDICTED (LINES) GERMINATION vs. TIME OF MAIZE AT FOUR
LOCATIONS (AT THE AIR INLET, AT 1/2, 2/3 AND AIR OUTLET) IN THE GRAIN COLUMN .......................... 87
FIG. 4.2 DENATURED PROTEIN vs. DRYING AIR TEMPERATURE IN MAIZE DRIED IN A CROSSFLOW DRYER WITH
AN INITIAL MOISTURE CONTENT OF 20% w. B. AT AIRFLOW RATES OF 32, 48, 64, 80 AND 96 M3M'3MIN".
............................................................................................................................................................ 92
FIG. 4.3 DENATURED PROTEIN vs. AIRFLOW RATE IN MAIZE DRIED IN A CROSSFLOW DRYER WITH AN INITIAL
MOISTURE CONTENT OF 20% W.B. AND AT DRYING AIR TEMPERATURES OF 50, 60, 70, 80, 100 AND
120°C. ................................................................................................................................................. 93

xii

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

FIG.

F

G

4.4 DENATURED PROTEIN VS. INLET MOISTURE CONTENT IN MAIZE DRIED IN A CROSSFLOW DRYER AT AN
AIRFLOW RATE OF 48 M3M'3MIN" AND AT DRYING AIR TEMPERATURES OF 50, 60, 70, 80, 100 AND
120°C. ................................................................................................................................................. 94

4.5 GERMINATION vs. DRYING AIR TEMPERATURE IN MAIZE DRIED IN A CROSSFLOW DRYER AT AN
AIRFLOW RATE OF 48 M3M'3MIN" AND WITH INLET MOISTURE CONTENTS OF 17.5, 20, 25, 30 AND
35%W.B ............................................................................................................................................... 95

4.6 GERMINATION VS. AIRFLOW RATE IN MAIZE DRIED IN A CROSSFLOW DRYER WITH AN INITIAL
MOISTURE CONTENT OF 20% AND AT DRYING AIR TEMPERATURES OF 50, 60, 70, 80, 100 AND 120°C.96

4.7 GERMINATION VS. INLET MOISTURE CONTENT IN MAIZE DRIED IN A CROSSFLOW DRYER AT AN

AIRFLOW RATE OF 48 M3M'3MIN" AND AT DRYING AIR TEMPERATURES OF 50, 60, 70, 80, 100 AND

120°C. ................................................................................................................................................. 97
5.1 SCHEMATIC OF CROSSFLOW DRYING. ............................................................................................. 107
5.2 DRYING PROCESSES ON A PSYCHROMETRIC CHART. ....................................................................... 109
5A.1 LINEAR APPROXIMATION OF EQ. 5A.2 AT INLET DRYING-AIR TEMPERATURE OF 100°C (OR 672°R).

.......................................................................................................................................................... 1 l9
6.1 MODEL-PREDICTIVE CONTROL OF GRAIN DRYERS. ......................................................................... 132
6.2 CONTROL PANEL OF THE VIRTUAL GRAIN DRYER FOR CONTROI. TEST ............................................. 139
7 .2 IMPLEMENTATION OF THE CONTROLLER ......................................................................................... 165
7.3 FLOWCHART OF THE CONTROL PROGRAM. ..................................................................................... 168

7.4 COMPARISON OF THE READINGS OF THE TRIME SENSORS AND THE BURROWS METER: (A) INLET
MOISTURE, AND (B) OUTLET MOISTURE .............................................................................................. 171
7.5 MEASURED AND PREDICTED OUTLET MOISTURE CONTENTS AND THE VALUE OF THE MULTIPLIER OF

THE MAIZE DRYmG CONSTANT IN A C ROSSFLOW DRYER OPERATING UNDER ZAE CONTROL (DRYING-AIR
TEMPERATURE = IOSOC, SET POINT =14.5% W.B., FILTER FACTOR B = 0.5). .................................... I73
7.6 INLET AND OUTLET MOISTURE CONTENTS, AND THE AUGER SPEED DURING AUTOMATIC C ONTROL OF

A CROSSFLOW DRYER WITH ZAE CONTROL (DRYING-AIR TEMPERATURE = 105°C, FILTER FACTOR B =
0.5, INITIAL MULTIPLIER y 0 = 0.7, RESIDENCE TIME=2.5-3.5 HOURS). .............................................. 174
7.7 INLET AND OUTLET MOISTURE CONTENTS, AND THE AUGER SPEED DURING AUTOMATIC CONTROL OF
A VT1210 DRYER WITH ZAE CONTROL (DRYING-AIR TEMPERATURE = 105°C, FILTER FACTOR B = 0.5.
INITIAL MULTIPLIER y 0 = 0.6, RESIDENCE TIME =2.0-2.5 HOURs). .................................................... 176

7.8 MEASURED AND PREDICTED OUTLET MOISTURE CONTENTS, AND THE MODEL ERROR (LE. THE
MEASURED MINUS THE PREDICTED OUTLET MOISTURE CONTENTS) DURING THE TEST SHOWN IN FIG. 7.7.
.......................................................................................................................................................... I 77

. 7.9 INLET AND OUTLET MOISTURE CONTENTS, AND THE AUGER SPEED, DURING AUTOMATIC CONTROL OF

A VT1210 DRYER WITH ZAE CONTROL AND AN INLET MOISTURE FILTER (DRYING-AIR TEMPERATURE =

xiii

105°C, FILTER FACTOR B = 0.5, INITIAL MULTIPLIER y 0 = 0.7, SET POINT = 15% W.B., RESIDENCE

TIME=2-2.5 HOURS). .......................................................................................................................... I79
FIG. 7. IO INLET AND OUTLET MOISTURE CONTENTS, AND THE AUGER SPEED, DURING AUTOMATIC CONTROL

OF A VT1210 DRYER WITH LSE CONTROL (DRYING-AIR TEMPERATURE = 105°C, FILTER FACTOR B =
0.5, INITIAL MULTIPLIER y o = 0.7, RESIDENCE TIME = 2.5-3.0 HOURS). ............................................ 180

FIG. 7.] I INLET AND OUTLET MOISTURE CONTENTS, AND THE AUGER SPEED DURING AUTOMATIC CONTROL ()F

A CROSSFLOW DRYER WITH LSE CONTROL AND THE INLET MOISTURE FILTER (DRYING-AIR
TEMPERATURE = 105°C, FILTER FACTOR B = 0.5, INITIAL MULTIPLIER y 0 = 0.7, RESIDENCE TIME =

ABOUT 2.5 HOURS) ............................................................................................................................. 181
FIG. 7.12 RESPONSE TO A STEP CHANGE IN THE DRYING-AIR TEMPERATURE OF A VT1210 DRYER FROM 105

T0 85°C WITH ZAE CONTROL (SET POINT =15% W.B., FILTER FACTOR B = 0.5, INITIAL MULTIPLIER

y 0 = 0.7, RESIDENCE TIME = ABOUT 2.5 HOURs). ............................................................................. 183
FIG. 7.13 RESPONSE TO A STEP CHANGE IN THE DRYING-AIR TEMPERATURE OF A VT1210 DRYER FROM 85 TO

105°C WITH LSE CONTROL (SET POINT = 15% W.B., FILTER FACTOR B = 0.5, INITIAL MULTIPLIER y 0 =

0.7, RESIDENCE TIME = 2.5-3.0 HOURs). ............................................................................................ 184

xiv

INTRODUCTION

Grain is usually harvested at high moisture contents to minimize field losses. The
grain moisture needs to be reduced to a safe level for storage. Therefore, artificial drying
has become prevalent on farms or at elevators. -

Depending on the temperature of the drying-air, artificial drying is categorized
into natural-air drying (i.e. using ambient air), low-temperature drying (the ambient air is
heated a few degrees), and high-temperature drying. High-temperature drying is popular
because of its high drying capacity. The principle high-temperature dryer types are:
crossflow, mixed-flow and concurrent-flow dryers. The drying-air temperature ranges
from 50-300°C (Brooker et al., 1992), depending on the dryer type and type of grain.

The application of high-temperature drying has significantly increased the
harvest/drying rate of farmers. However, severe damage to grain quality, both physically
and bio-chemically, may happen in the drying process. For instance, an average 10—20%
of protein in maize is usually denatured in a conventional high-temperature dryer (Chang
et al., 1989). In the wet-milling industry, the drying conditions have a 2-3 times greater
effect on the starch recovery rate than variety and maturity (Le Bras, 1982); in fact, if the
drying-air temperature in a mixed-flow dryer is higher than 100°C, the maize becomes
unacceptable for wet-milling (Lasseran, 1988).

The diversity of maize utilization has increased rapidly in last a few years. Only
9.9% of US maize was consumed as food and alcohol in 1986 but doubled in 1996,
reaching a total of 1650 million bushels a year (USDA, 1997). Additional non-food

maize products, such as maize-based biodegradable plastics, salt substitutes and ethanol-

containing products, have come on the market recently because of their environmental,
health-related and economic benefits. The non-food uses of maize demand high quality
grain.

Dryer design needs to be improved to produce high-quality grain for non-feed
industries. Conventional high-temperature grain dryers in the US have been mainly
designed for feed grain. The research has focused on dryer capacity and energy efficiency;
grain quality became a major concern only in the late 19803. Limited number of
experimental and modeling studies have thus far been conducted to quantify the major
factors causing quality damage to grain in the drying process.

Adequate control of the dryer is essential to reduce the quality damage because of
overdrying and underdrying of the grain. Overdrying causes breakage and stress-cracks in
maize kernels. Overdrying is also costly because of the unnecessary loss in weight and the
extra energy consumption. Table 1.] lists the shrinkage of 25,400 MT of maize
(1,000,000 bu) caused by overdrying O.25-2.00% beyond 15.5%, and the cost of the
shrinkage at two price levels (Brooker et al., 1992). Thus, the Shrinkage in overdrying
25,400 MT by 1.0% moisture results in a weigh loss of 297 MT, and costs $17,544 when
maize sells for $59.1/MT, and $29,240 when maize sells for $98.4/MT. The additional
energy needed in the drying process and the extra energy cost are tabulated in Table 1.2.
The data Show that 1.0% overdrying requires an additional 87.8 MJ/MT in energy and
costs $10,570 per 25,400 MT, assuming the energy cost is $5.00/ 1,055 MJ.

A limited number of research studies have been conducted on moisture control,
but only a few control algorithms have been implemented on commercial dryers. More
work is needed on moisture control to better address the non-linearity and long delay of

2

Table 1.1 Shrinkage in metric tonnes (MT) and shrinkage cost when 25,400 MT
(1,000,000 bu) of maize is dried below 15.5% w.b. (Brooker et al., 1992).

 

 

 

Overdrying, % Shrinkage Cost (8) at two prices
MT 59.1/MT 98.4/MT
0.25 74.9 4,425 7,375
0.50 149.4 8,823 14,705
1.00 297.1 17,544 29,240
1.50 443.1 26,163 43,605
2.00 587.3 34,682 57,803

 

Table 1.2 Energy required per metric tonne (MT) and cost (at different energy

prices) resulting from various levels of overdrying of 25,400 MT (1,000,000

bu) of 15.5% w.b. maize (Brooker et al., 1992)

 

 

 

Overdrying, % Energy required Natural gas cost ($/ 1055MJ)
MJ/MT 5.00/MT 7.00/MT
0.25 22.1 2,655 3,717
0.50 44.1 5,305 7,427
1.00 87.8 10,570 14,798
1.50 132.2 15,920 22,288
2.00 180.5 21,730 30,422

 

the grain drying process. As grain quality becomes of greater concern, a new issue in

grain dryer operation is the control of the drying-air temperature to optimize grain quality.

Objectives

The major objectives of the research conducted in this study were:

1. To develop stochastic grain drying models, predicting the average and the
standard deviation of the moisture content of individual maize kernels in a
drying process.

2. To develop grain quality models which quantify the quality deterioration of
maize in the drying process.

3. To develop a moisture controller which minimizes the overdrying and
underdrying during the drying process.

4. To develop a grain-quality controller which controls the drying-air
temperature during the drying process according to Specific grain-quality
requirements.

The investigations are primarily concerned with crossflow drying of maize

because the crossflow dryer is prevalent in the US, and maize is the major grain type.

However, the results will be applicable to other dryer types and other grains.

Outline of the dissertation

The thesis is divided into four parts. Part 1, Chapters 1, 2 and 3, present the

development of the stochastic grain drying models. Part 11, Chapter 4, covers the quality

simulation. Part 1H, Chapters 5, 6 and 7, describe the moisture controller. And, Part IV,

Chapter 8, discusses the grain-quality controller.

Part 1: Stochastic Modeling of Grain Drying

In Chapters 1-3, the stochastic nature of the moisture content of maize before and
after drying is explored. Chapter 1 presents experimental data of the moisture content
distribution in maize at harvest time, after thin-layer drying, and afier crossflow drying. In
Chapter 2, the stochastic models are developed of the moisture-content distribution in
maize dried in concurrent-flow, counter-flow and crossflow dryers. In Chapter 3, the

process of maize drying in a crossflow dryer is analyzed stochastically.

Part 11: Modeling of Grain Quality

In Chapter 4, the stochastic drying model and the denatured protein and
germination models are combined to simulate the quality of individual kernels in grain
crossflow dryers. The relationship between the drying conditions and the grain quality

after drying is analyzed.

Part III: Moisture Control of Grain Dryers

A control-oriented grain drying model is developed in Chapter 5. Chapter 6 covers
the design of the control algorithms, and the tuning and simulation tests of the controller.
Chapter 7 presents the implementation and field testing of the controller on a commercial

maize dryer.

Part IV: Grain Quality Control

Chapter 8 discusses the development of the quality-control model and the
associated control algorithm.

The relationship between the various parts of the thesis is shown in Fig. 1.1.

 

 

 

PART I. STOCHASTIC MODELLING PART III. MOISTURE CONTROL

OF GRAIN DRYING

 

 

 

 

 

 

PART II. GRAIN- QUALITY

MODELING

 

 

 

L
PART IV. GRAIN-QUALITY CONTROL

 

 

 

 

 

 

 
  

  
   
 

MOISTURE
CONTROLLER

MOISTURE AND
DRYER DESIGN GRAN-QUALITY

CONTROLLER

 

Fig. 1.1 A schematic representation of the contents of the thesis.

7

 

References

Brooker D.B., Bakker-Arkema, F .W., Hall, CW. 1992. Drying and Storage of Grains and
Oilseeds. Van Nostrand Reinhold, New York, NY.

Chang, C. H. and M. R. Paulsen. 1989. Moisture distribution and starch recovery of
commercially dried maize. Paper No. 89-6525, American Society of Agricultural
Engineers, St. Joseph, MI.

Lasseran, J. C., A. Le Bras. 1988. Improvement of drying techniques to better grain
quality for processing industries. Paper No. 88-323. Presented at the International
Conference on Agricultural Engineering, Ag Eng 88, Paris, France. March 2-5,
1988.

Le Bras, A.1982. Maize drying and its resulting quality for wet-milling industry. In:

Maize: Recent Progress in Chemistry and Technology. Academic Press, Inc., New
York, NY.

USDA. 1997. Feed Situation and Outlook. Economic Research Service, US. Department
of Agriculture, Washington, DC.

CHAPTER 1. STOCHASTIC MODELING OF GRAIN DRYING:

EXPERIMENTAL INVESTIGATION*

Abstract

Previous research has Shown that the variance in the moisture content of individual
maize kernels is Significant at harvest. In this series of three Chapters, the stochastic nature
of the moisture content of maize before and afler drying is explored Chapter 1 presents
experimental data of the moisture content distribution of maize kernels in samples taken at
harvest time, after thin-layer drying, and afler crossflow drying. The moisture content in
recently harvested, and in thin-layer dried maize appears to be normally distributed and in
crossflow-dried maize to be skewed In the Chapter 2, stochastic models are developed of
the distribution of the moisture content in maize kernels dried in concurrent-flow, counter-
flow and crossflow dryers, and in Chapter 3 one of the models is used to analyze the

process ofgrain drying in a crossflow dryer.

*This paper was published in 1997 in the Journal of Agricultural Engineering Research

66:267-273.

1.1 Introduction

The term "grain moisture content" refers in the grain market, and in grain-drying
technology, to the average moisture content of a sample of kernels. Recent studies have
established that a significant variance in moisture content exists among individual grain
kernels (Montross et al., 1994). Thus, the variation in the moisture content between the
kernels should be considered in the evaluation of the processes of grain drying and grain
storage, in addition to the average moisture content.

Present grain drying models assume an uniform initial moisture content of the grain
kernels; they are routinely used in the simulation, design and control of grain dryers
(Brooker et al., 1992). The object of the present study is to develop stochastic models for
the average moisture content and variance in grain dryers operating under non-uniform
initial moisture content of the kernels. Chapter 1 presents the experimental results, Chapter
2 the development of several stochastic models, and Chapter 3 the analysis of crossflow

drying employing a stochastic model.

1.2 Literature Review

Oxley (1948) was among the first to measure the moisture content of individual
grain kernels (i.e. wheat); the standard deviation of the moisture content was in the range of
0.7-7.8% w.b. at harvest and decreased to 0.1-0.4% w.b. afier one month of storage, and
rapid drying produced a skewed distribution in the kernel moisture content. Lasseran (1987)
measured a range in kernel moisture of 23-39% w.b. in freshly-harvested maize at an
average of 30.2% w.b. (and with a standard deviation of 3.8% w.b.); immediately after

drying in a mixed-flow dryer to an average of 16.6% w.b. moisture, the kernel moisture

10

content ranged fiom 6-29% w.b. (with a standard deviation of 4.0% w.b.). Kocher et al.
(1990) established that the moisture range of 20% w.b. rough rice at harvest is 10-23% w.b.,
with a standard deviation between 4-6% w.b.; the mean moisture content of the rice kernels
is different fiom the mode.

Banaszek and Siebenmorgen (1990) studied the drying of individual rice kernels
selected from various maturity groups; differences in moisture content and drying rate were
determined to be related to kernel width, thickness and initial moisture content. Regner
(1995) measured the mass distribution of the kernels in samples of wheat and its effect on
drying rate; light kernels dried faster than heavier kernels but the effect of the kernel mass
was small compared with that of the drying air temperature.

Montross et a1. (1994) determined that at harvest time the smaller tip kernels on
an ear of maize are on average at a lower moisture content than the larger bottom kernels;
at an average sample moisture of 24-25% w.b., the difference is 5-7% w.b., with a range
in the individual kernel moisture of 8-37% w.b. (and in the standard deviation of 0.6-
9.0% w.b.). The authors also measured the moisture content distribution in maize dried
in commercial cross-flow, concurrent-flow and mixed-flow dryers; maize exiting a high-
temperature dryer, regardless of type, was found to have a standard deviation in the

moisture content of 3-5% w.b..

11

1.3 Experimental Details

1.3.1 Moisture content measurement of individual kernels

For the commercial dryer tests, the moisture contents of single maize kernels in a
sample were determined in a Single-kemel moisture meter manufactured by Shizuoka Seiki,
Inc. (Japan). Each kernel is automatically guided to a metallic crusher; the moisture content
(w.b.) is obtained by converting its electric resistance or conductance into a moisture value.

The moisture meter also calculates the average moisture content of 100 kernels, the
frequency in each 0.5% w.b. moisture range, and the standard deviation of the moisture
content of the sample. Calibration studies of the average moisture content readings of the
meter have shown excellent agreement between the meter and the oven methods (Tsai et al.,
1987)

During the thin-layer drying tests, the mass of individual maize kernels was
measured with a Mettler PM 400 digital balance with a precision of 0.001 g. Since the dry
mass of a single kernel of maize is about 0.3 g, the relative error of the measurement is
approximately 0.33%. The dry mass of each kernel was determined subsequently by the
standard oven method (ASAE standard, 1989).

In general, the moisture content in this paper is expressed on a dry basis. In some
cases, the moisture content is also given on a wet basis because its more frequent use in

commerce.

12

1.3.2 Laboratory thin-layer drying

The thin-layer dryer contains 3 0.15m x 0.15m x 0.21m drying platform to which air
is directed at a velocity of 1.2 m/s. The position of individual kernels is nmnbered. The
change of the mass of each kernel is measured afier predetermined drying times.

The grain samples consisted of hand-picked ears of Dekalb 458 maize. It was stored
in a 4°C cooler immediately following the harvest. The cars were kept in the laboratory for
24 hrs, and then were shelled manually just before the start of a drying. Each sample
consisted of 20 arbitrarily selected kernels. The kernels started start a drying test 30 S apart.
Afier predetermined drying periods (i.e. multiples of 10 min), each kernel was weighed.
The tests were conducted at temperatures of 60 °C, 70 °C and 80 °C i 1 and an absolute

humidity of 0.008 kg/kg i 0.00]. Each test was replicated three times.

1.3.3 Commercial crossflow drying

Maize was dried experimentally in two commercial crossflow dryers, CF 1 and CF2.

CF 1 is a cylindrical crossflow dryer with a capacity of 141 m3/h of wet grain at 5%
w.b. moisture removal. The diameter of the dryer is 5.03 m, and the thickness of the grain '
column is 0.305m. The height of the drying section is 16.26 m, and the airflow in the
drying section is 294,000 m3/h. The grain column is turned midway through the drying
section. The height of the cooling section is 5.58 m, and the airflow in the cooling section
is 147,000 m3/h. The exhaust air from the cooling section is re-circulated to the drying
section.

CF 2 is a rectangular three-stage 7.32 m x 0.305 m crossflow dryer with a capacity of

60 m3/h of wet grain at 5% w.b. moisture removal. The air temperatures in the first two
13

stages may differ. The third stage is the cooling section. The thickness of the grain column
is 0.305 m. The height of stage one is 2.44 m; of stage two 1.55 m, and of stage three 0.98
m. The airflow both in the first and second stages is 36,000 m3/h, and in the cooling stage
30,000 m3/h.

Samples were taken every half hour at the inlet and outlet of the dryers afier they
had reached steady—state; the moisture content of individual kernels was measured with the
individual kernel moisture meter immediately after the samples were taken. The residence
time of grain in the dryer was considered in taking the outlet samples to match them with
the inlet samples. The averages of the moisture data of three consecutive samples from the

dryer inlet or outlet were used for analysis.

1.4 Results

1.4.1 Moisture distribution at harvest

The distribution of the moisture content in a typical maize sample reaching a dryer
is shown in Fig. 1.1; the sample had an average moisture content of 37.5% d.b.. Table 1.1
shows the Chi-Square (9(2) results for the normality test of the moisture content distribution
in twenty samples ranging in average moisture content from 19.5 to 38.9% d.b.. The
standard deviation in the moisture content in these samples varied from 0.8 to 11.3% d.b.,
with the higher average moisture contents usually displaying the higher standard deviations.

Table 1.1 shows that the moisture distribution of only 5 of the 20 maize samples
passed the test for normality. This is due (it is believed) to the severe fluctuation in the

frequency values in adjacent moisture content ranges. This was confirmed after the data

14

 

10

 

 

 

 

 

 

8..
x
5; 6i
i:
O
D
I: 4~
LL.
2? W
O 1 l l l l _
10 20 30 40 50 60 70

Moisture content, % d.b.

Fig. 1.1 Typical frequency distribution of the kernel moisture content in
maize reaching a dryer (average moisture content is 37.5 % d.b.).

15

Table 1.1 x2 test for normality in the moisture content distribution of maize
at harvest before smoothing of the data.

 

SAMPLE AVERAGE STANDARD DEGREES OF 7600, x25“... TEST
NUMBER MC DEVIATION FREEDOM VALUE VALUE RESULTS
(% D.B.) (% D.B.)

 

1 38.9 1 1.3 14 23.7 49.3 Fail
2 37.8 11.0 14 23.7 39.3 Fail
3 37.6 10.5 12 21.1 20.8 Pass
4 37.3 12.1 13 22.4 35.1 Fail
5 33.6 11.9 13 22.4 31.3 Fail
6 31.9 8.8 11 19.7 42.5 Fail
7 31.0 5.9 11 19.7 18.5 Pass
8 29.3 I 1.5 20 31.4 56.5 Fail
9 29.2 5.4 11 19.7 45.7 Fail
10 28.7 3.7 14 23.7 104.2 Fail
11 25.5 5.3 10 18.3 48.2 Fail
12 25.3 5.9 12 21.3 29.5 Fail
13 25.3 6.0 12 21.0 63.4 Fail
14 25.0 4.1 14 23.7 29.8 Fail
15 24.6 4.6 12 21.0 33.5 Fail
16 23.7 4.5 14 23.7 51.7 Fail
17 23.1 2.2 8 15.5 9.4 Pass
18 21.5 2.3 6 12.6 97.8 Fail
19 19.7 1.3 4 9.5 6.6 Pass
20 19.5 0.8 3 7.8 6.2 Pass

 

16

Table 1.2 xz test for normality in the moisture content distribution of maize at
harvest after smoothing of the data in Table 1.1.

 

 

SAMPLE AVERAGE STANDARD DEGREES OF X2005 XZSWU, TEST
NUMBER MC DEVIATION FREEDOM VALUE VALUE RESULTS
(% n.3,) (% 0.3.)

1 38.9 11.3 14 23.7 15.2 Pass
2 37.8 11.0 14 23.7 14.3 Pass
3 37.6 10.5 12 21.1 8.9 Pass
4 37.3 12.1 13 22.4 13.2 Pass
5 33.6 11.9 13 22.4 10.5 Pass
6 31.9 8.8 11 19.7 17.0 Pass
7 31.0 5.9 11 19.7 7.4 Pass
8 29.3 1 1.5 20 31.4 20.4 Pass
9 29.2 5.4 1 1 19.7 17.8 Pass
10 28.7 3.7 14 23.7 21.1 Pass
11 25.5 5.3 10 18.3 16.4 Pass
12 25.3 5.9 12 21.3 10.4 Pass
13 25.3 6.0 12 21.0 20.3 Pass
14 25.0 4.1 14 23.7 11.6 Pass
15 24.6 4.6 12 21.0 12.3 Pass
16 23.7 4.5 14 23.7 19.4 Pass
17 23.1 2.2 8 15.5 7.9 Pass
18 21.5 2.3 6 12.6 11.5 Pass
19 19.7 1.3 4 9.5 5.3 Pass
20 19.5 0.8 3 7.8 6.4 Pass

 

17

were smoothed with a Fast Fourier Transform (FFT) filter. The procedure removes any
linear trend in the data, and then uses the FFT technique to filter the data (Press et al., 1986).
The linear trend was reinserted at the end. The number of the data points smoothed each
time was 10. Each of the maize samples then passed the x2 test for normal distribution (see
Table 1.2). Fig. 1.2 shows, in addition to the raw and smoothed data curves, the normal
distribution curve of the frequency of the kernel moistures in a typical maize sample

reaching a dryer.

1.4.2 Moisture distribution during drying

(I) T hin-layer drying

Fig. 1.3 shows the average moisture content of three maize samples during drying at
three temperatures; the change in the value of the standard deviation during the drying
process (i.e. at different average moisture contents) of the three samples in Fig. 1.3 is
illustrated in Fig. 1.4. It appears that the standard deviation of the moisture content
decreases during the course of drying, at least at 60°C and 70°C while at 80°C this decrease
is less pronounced. The rate of decrease in the standard deviation in the high average
moisture content range is larger than in the low average moisture content range.

Fig. 1.5 illustrates the narrowing of the kemel-moisture distribution during the
drying of maize from 24.4% d.b. down to 14.9% d.b.. This is because the lower moisture-
content kernels dry more slowly than the kernels at the average moisture, and the kernels at
the higher than average moisture content dry faster. Note that the distribution of the kernel

moisture remains essentially normal during the drying process, i.e. normal.

18

10 r - w— ___-_ —— __--___.,-__-,____.._-~__ - - --.

 

 

—- normal 1
-D- raw 1
8 - A smoothed I
I
.\° 1
a? 6 ’ l
5 l
:3 l
g 4 ' AA I
u. A ;
A l
2 " AA 1
l
O l l J
0 20 40 60 80
Moisture content, % d.b.

Fig. 1.2 The frequency distribution of the raw data, smoothed data and the
corresponding normal distribution of the moisture content of maize
kernels in a typical maize sample reaching a dryer.

l9

 

 

Moisture content, % d.b.

 

 

 

0 50 100 150 200

Time, min

Fig. 1.3 Experimental thin-layer drying curves (each curve is the average of
60 kernels) of maize at three drying-air temperatures.

20

1.6r--= -

 

 

:. 70°C
.9 1.2
E
5 0°C
'0
“U
E
E 0.8 ~
‘0 60°C
0.4 l l l I
25 20 15 10 5

Average moisture content, % d.b.

Fig. 1.4 The standard deviation at different average moisture contents (60
kernels as a group) during thin-layer drying of maize at three
drying-air temperature.

21

3O ..____ _______._---.__. _____________

Frequency, %
-‘ N
u. o

p—A
O

 

 

28 25 22 19 16 14 11
Moisture content, % d.b.

Fig. 1.5 The moisture content distribution of 60 kernels at three drying stages
during thin-layer drying at 60°C; the average moisture contents are
24.4 % (initial), 17.6 % and 14.9 % d.b., respectively, from left to

right.

22

The frequency distribution of the kernel dry mass of a typical maize sample is
Shown in Fig. 1.6; the individual kernel mass varied from 0.21 to 0.45 g, with the maximum
frequency occurring at 0.31 g.

In order to test the effect of kernel mass on the drying process, some samples were
separated into three kernel-mass categories—large, medium and small. The drying
behavior of three categories and of the Whole sample is illustrated in Figs. 1.7 and 1.8;
Fig. 1.7 shows the drying curves, Fig. 1.8 the standard deviations of the moisture content.

The lighter (i.e. smaller) kernels dry only Slightly faster than the heavier (i.e. larger)
kernels. The standard deviation in each of the three categories is Similar in value than
that of the whole sample. Thus, the distinct difference in kernel mass within a lot of

maize does not affect the standard deviation during drying.

(2) Crosstow drying

The inlet and outlet moisture content distributions of maize in crossflow dryer CFI
are illustrated in Fig. 1.9. The average inlet moisture content was 33.0% d.b. (SD = 8.6%
db.) and the average outlet moisture content 17.2% d.b. (SD = 7.1% d.b.).

Fig. 1.10 Shows the moisture distributions in a second crossflow dryer CF2, in
which maize at an average initial moisture content of 34.0% d.b. was dried to an average of
18.6% d.b. The standard deviation of the maize before drying was 7.9% db. and
immediately after drying 7.7% d.b..

The higher value of the standard deviation in the moisture content afier drying than
before drying is due to the uneven drying treatment of the kernels in a crossflow dryer.
Kernels near the air-inlet in the drying column are usually overheated and overdried, while

23

16 . ‘‘‘‘‘ eeeeeeeeeeeeeeeeeeeeeeeeeee ,

p—s
N
I

Frequency, %
co

 

 

 

O L r I I I
0.20 0.25 0.30 0.35 0.40 0.45

Kernel rmss, g

Fig. 1.6 The frequency distribution of the kernel dry mass of a typical maize
sample.

24

 

26 CH-.. ~=~=~~=~~~~

x kernel mass 0.27-0.31 g
A kernel mass 0.31-0.35 g

 

 

 

I—i 22 - a kernel mass 0.35-0.43g
3 —whole sample
.,\°
*5“
3
g 18 ~
0
a
"5
2 14 -
10 l l l l I
0 50 100 150 200 250

Time, min.

Fig. 1.7 The drying curves of maize kernels grouped by dry weight during
thin-layer drying of 60 kernels at 60°C.

25

+ A kernel mass 027-031 g
+ kernel mass 0.31-0.35g
X kernel mass 0.35-0.43 g

— whole sample

A\;\+1‘ +
A
x4 m

  
  

H
N
1

Standard Deviation, %
P
0‘
"o

 

 

0.0 L I J
25 20 15 10

Moisture Content, % w. b.

Fig. 1.8 The standard deviation of the moisture content of maize kernels
grouped by dry weight during drying at 60°C.

26

10.- 7-.-»-.. .......

Frequency, %

 

 

Moisture content, % d.b.

Fig. 1.9 Moisture distribution before and after drying of maize in a crossflow
dryer (CFI); inlet average m.c.=33.0% d.b., stand. dev.=8.6% d.b.,
and outlet average m.c.=17.2% d.b., stand. dev. =7.1% d.b..

27

 

Frequency, %

 

 

 

 

Moisture content, % d.b.

Fig. 1.10 Moisture distribution before and after drying of maize in another
crossflow dryer (CF2); at the inlet the average m.c. =34.0% d.b.,
stand. dev. =7.9% d.b., and at the outlet the average m.c. =18.6%
d.b., stand. dev. =7.7% d.b..

28

kernels at the outlet side of the column are underheated and underdried. The moisture
content distribution in crossflow-dried maize is skewed because the kernels entering the

dryer at the air-outlet side of the grain column are ofien not dried at all.

1.4.3 Moisture distribution during storage

Fig. 1.11 shows the decrease in the standard deviation of the moisture content of
three maize samples during storage in plastic bag at about 20 °C. Within 24 hs, the standard
deviation in each of the samples diminished to 1-2% w.b., regardless of the initial standard

deviation. After 150 hs storage, the standard deviation equilibrated to 0.6-0.9% w.b..

1.5 Conclusions

(1) The moisture content distribution of maize after harvest can approximately be
expressed by a normal distribution. The distribution is not normal afier drying of maize in a
crossflow dryer.

(2) After thin-layer drying, the kemel-moisture distribution is still normal, but with a
smaller standard deviation than before drying. The difference in kernel mass does not affect
the moisture distribution and the standard deviation.

(3) After cross-flow drying, the moisture distribution is skewed to the low end of
the moisture content range while displaying a tail at in the high moisture range.

(4) The range of the moisture content in stored maize diminishes afier drying.

The standard deviation decreases rapidly, and equilibrates to a value of 0.6-0.9 % w.b..

29

 

 

'3 3
6S 1
C? l
.2 ~
"S 2. A
Q)
"U
“U
a A
: Eu “
WK? 6 X X6 x 3X
0 l l l I l
0 50 100 150 200 250

Fig. 1.11 The change in the standard deviation over time of three maize
samples after crossflow drying and storage at 20°C. The average
moisture contents of samples are 22.4 % (A), 15.9 % (X) and 19.9 °/o
(O) d.b., respectively.

30

References

Montross, M. D., F. W. Bakker-Arkema, C. L. Leppanen and R. E. Hines. 1994. Moisture
content variation and grain quality of maize dried in different high-temperature
dryers. Paper No. 94-6590. ASAE, St. Joseph, MI.

Brooker, D. B., F. W. Bakker-Arkema and C. W. Hall. 1992. Drying and Storage of
Grains and Oilseeds. Van Nostrand Reinhold, New York, NY.

Oxley, T. A. Study water content of Single kernels of wheat. Cereal Chemistry 1948,
25(2):]11-127

Lasseran, J. C. 1987. Grain drying in France. Paper No. 87-6014. ASAE, St. Joseph, MI.

Kocher, M. F., T. J. Siebenmorgen, R. J. Morman and B. R. Wells. 1990. Rice kernel
moisture content variation at harvest. Transactions of the ASAE 33(2):541-547.

Banaszek, M. M. and T. J. Siebenmorgen. 1990. Individual rice kernel drying curves.
Paper No. 90-6589. ASAE, St. Joseph, MI, 1990

Regner, S. Kernel mass related properties of cereal grains. 1995. Ph.D. Thesis. Swedish
University of Agricultural Sciences, Uppsala, Sweden.

Tsai, C., R. Yarnashita and R. Goto. 1987. Moisture distribution of cereal grain in
postharvest processing. Japanese Society of Agricultural Machinery 46(6):599-604

ASAE. Standard 8352.2. 1989. ASAE, St. Joseph, MI.
Press, W. H., B. P. Flannery, S. A. Teukolsky and W. T. Vetterling. 1986. Numerical

Recipes: The Art of Scientific Computing. Cambridge University Press,
Cambridge, MA.

31

CHAPTER 2. STOCHASTIC MODELING OF GRAIN DRYING:

MODEL DEVELOPMENT*

Abstract

In Chapter 1 of this series of three chapters, it was shown that the moisture content
in maize reaching a dryer is approximately normally distributed In Chapter 2, stochastic
drying models are developed for grain initially with an initial normal distribution in
moisture content. It is shown that the moisture content is still normally distributed after
one-dimensional drying (i. e. concurrent- or counter-flow drying), but is skewed after two-
dimensional drying (i. e. crossflow drying). The models predict for dried grain, both the

average moisture content and its Standard deviation to an acceptable accuracy.

*This paper was published in 1997 in the Journal of Agricultural Engineering Research
66:275-280.

32

2.1 Introduction

Drying models are routinely used in the design and analysis of grain dryers
(Brooker et al., 1992). For instance, the Michigan State University (MSU) grain-drying
models which are of the deterministic type, calculate the average moisture content of the
grain exiting a dryer. The assumption is made that the moisture content of each grain
kernel entering a dryer is equal to the average moisture content. This assumption has
proven to be an over-simplification (see Chapter 1), and thus the traditional deterministic
grain-drying models need to be modified to stochastic-type models which accept non-
uniform inlet moisture content data.

Stochastic parameter data have been employed by Sokhansanj (personal
communication, 1996) to account for the effect of random variation of some of the
physical constants in the grain drying model of a batch dryer. However, the model was
not used to simulate the distribution of the moisture content in individual grain kernels.

Ryniecki et a1. (1994) developed a stochastic model for near-ambient in-bin grain
drying. The stochastic nature of the ambient temperature and relative humidity was
considered to be the sole stochastic effect in the drying process; the variability in the
initial grain moisture content of the grain kernels was not accounted for.

Three stochastic grain-dryer models are presented in this paper, a thin-layer drying

model, a concurrent- or counter-flow model, and a crossflow model.

33

2.2 T bin-layer Drying Model

The change in the moisture content of a thin layer of grain dried under constant air

conditions can be expressed by the following empirical equation (Brooker et al., 1992):

M, - M. 2
M0 _ M. f(T.¢,r) (2.1)

Where M0 is the initial dry-basis moisture content, Mythe dry-basis moisture content at
drying time T, and Me the dry basis equilibrium moisture content at the air temperature T

and relative humidity 45.

01'

M = AM, + B (2.2)

where A =f(T, ¢, 1) and B = Me[I-f(T, ¢, 2)]. Thus, A and B are independent of grain
moisture content. If the initial moisture content can be represented by a normal
distribution of N[E(Ma), 0'0], the moisture content after drying is also of the normal type

N[E(Mf), 07] (Press et al., 1986), where

E(M,) = AE(M,) + B (2.3)
and

0f = A00 (2'4)

34

2.3 Deep-bed (one-dimensional) Drying Model

Concurrent- or counter-flow drying are examples of one-dimensional deep-bed
drying. In the deterministic MSU drying models (Brooker et al., 1992), a set of
mathematical equations describes the grain temperature and moisture content, and the air
temperature and humidity, Within a small element in the grain bed. In the simulation of a
one-dimensional deep-bed dryer, the grain bed is divided into thin layers (elements); the
model is solved for each thin-layer by considering the outlet conditions of one layer to be
the inlet conditions of the next layer downstream. After the model is solved for all layers,
the grain and the air conditions in the grain bed are obtained. It is assumed in the
deterministic dryer models that the moisture content of the grain kernels is uniform. In the
MSU stochastic dryer models it is postulated that the moisture content in a lot of grain is
non-unifonn, and normally distributed when grain reaches the dryer.

The Simulation of the one—dimensional drying of grain with a norrnal-type initial
kernel moisture content distribution is accomplished in two steps:

(1) Calculate the distributions of the air temperature and humidity within the
grain-bed with the deterministic drying model, assuming the initial moisture content of all
kernels is equal to the average initial moisture content.

(2) Determine the moisture and grain temperature changes throughout the bed for
the kernels with any initial moisture content other than the average, employing the
deterministic model again, but under the air temperature and humidity distributions
determined in step 1.

Thus, it is assumed that the air temperature and humidity at a particular position in

the drying bed have the same values which they would have had if all kernels had initially
35

been at the average moisture content. This assumption is reasonable because the air
conditions in a grain bed are determined by the average condition of all the kernels
encountered by the air.

In a one-dimensional deep-bed dryer, such as a concurrent-flow (CCF) dryer, the
air temperature and air humidity distributions are one-dimensional, and thus it can be
assumed that each kernel encounters the same drying conditions passing through the
dryer. If the initial grain moisture content distribution is normal, the final grain moisture

content distribution is also normal, i.e. N[E(Mf), 07] (see Appendix 2A). Also,

E(Mf) CE(M0) + D (2.5)
a, = C on, (2.6)

where C and D are dependent on the air temperature and humidity distributions in the
drying-bed.

Two runs of the deterministic dryer simulation program are required to determine
the final distribution of the grain moisture content in a one-dimensional dryer. If E (M, )
is the average of the initial grain moisture content, the average final moisture content
E(Mf) is determined in a run of the deterministic dryer program (step 1). The air
temperature and humidity distributions are stored in a data file. Next, a second initial
moisture content, i.e. M; different from E(Mo), is selected (such as letting M0)” = E(M0)
- 0'0), and the dryer program is run again under the air conditions now stored in the data
fIle. A second dryer-exit moisture content Mf+is obtained (step 2), and the standard

deviation of the exit moisture content is calculated. Thus, from Eq A6:

36

 

Mf+ : (:04!)+ (2'7)
and from Eq. 2.7 and Eq. 2.5:
Mf+ ' E(M/) 2 (CM; + D) - [CE(M0) + D] (28)
: (:[040+ " E(Ma)] .
Then
* - E
C M’, (M’) (2.9)
Mo ' E(Mo)
Finally, substituting Eq. 9 into Eq. 6:
M + - E M
a, = f ( f) (2.10)

 

0'0
Mo+ ' E( M0)
Thus, the moisture content distribution of the grain at the dryer exit in a one-dimensional

dryer is N[E(Mf), 0]].

2.4 Deep-bed (two-dimensional) Drying Model

A crossflow dryer is an example of a two-dimensional dryer. In a two-
dimensional deterministic drying model, the grain column is divided into a number of
equal-depth sub-columns in the direction of airflow. The thickness of a sub-column is
small so that the changes in the air temperature and humidity in the sub-column are
negligible, i.e. the changes in the air temperature and humidity are assumed to be in the

grainflow direction only (as in the one-dimensional model).

37

E(M/) = ZE(Mfl) (2.11)
::1

5|N

The same method employed for the one-dimensional stochastic drying model is
used to determine the dryer-exit moisture content distribution of a sub-column in the two-
dimensional model. If the initial grain moisture content is normal, the exit grain moisture
content of each sub-column is normal. The average moisture content of the grain exiting
the grain column is the result of the average of the sub-columns. If the column is divided
into m sub-columns, the average exit-grain moisture content and its standard deviation in

a crossflow dryer are (see Appendix 2.8):

and

 

1 m 1 m
O'f = JEZO'fii'F'JIZl-EYM/JJZ - [E(Mf)]2 (2.12)

(“I

2.5. Basis Conversion of the Grain Moisture Content

As the wet-basis moisture content of grain is normally used in commercial
transactions, a program is developed to convert the average and standard deviation of the
moisture content from dry basis to wet basis. Assuming the moisture content is normally
distributed on a dry basis, the distribution of the moisture content on a wet basis is not
normal because the conversion of the moisture content from dry basis to wet basis is not

linear, i.e.:

 

M = (2.13)

The Monte Carlo technique (Press et al., 1986) is used in the conversion, i.e. randomly
generating 1000 dry-basis moisture contents with the known distribution function, then
converting each moisture content to a wet basis with Eq. 13, and finally calculating the

average moisture content and the standard deviation on wet basis.

2.6 Model Validations

2.6.1 Thin-layer drying

Figs. 2.1 and 2.2 show the experimental and predicted standard deviations during
the thin-layer drying of maize at 60°C, 70°C and 80°C. [Note: The experimental data
have been presented in Chapter 1.] The predicted standard deviations decrease
approximately linearly with average moisture content. The standard errors between the
experimental and simulated results are 0.11, 0.06 and 0.10 at 60°C, 70°C and 80°C,
respectively. The relative error is in the range of 10% to 15%. The systematic error is
small, except in the low moisture content range of the 80°C run. A possible explanation
is that the drying rate is high at 80°C, and thus a small error in the drying time causes a

relatively large error in the calculated moisture content and its standard deviation.

2.6.2 Crossflow dryer

Table 2.1 shows the experimental and predicted standard deviations for two
crossflow dryers (CF 1 and CF2). [Note: The specifications of the crossflow dryers are
presented in Chapter 1.] The dryer capacities were determined by simulation, i.e. by

matching the experimental dryer-exit moisture content to that obtained by simulation.

39

 

1.6

 

 

 

 

 

, o
L? ‘ ~ .
"a
°\°
c?
.2
E.
>
o
“D o
“O ' ~ . O
a - .
E
m
0.0 1 I 1 l
24 20 16 12 8
Moisture content, % d.b.
A experimental at 60C predicted at 60C
0 experimental at 70 C ------ predicted at 70C

Fig. 2.] Predicted and experimental standard deviations of the moisture
content of maize during single-kernel drying at 60°C and 70°C,

respectively.

40

1.6-~~

 

 

 

.55 0 experimental —- predicted
'2 1.2
k
a.
.2
*5
'5 0.8
Q)
'0
1:
£3
E 0.4
m
0.0 4 4 1 L i
24 20 16 12 8
Moisture content, % d.b.

Fig. 2.2 Predicted and experimental standard deviations of the moisture
content of maize during thin-layer drying at 80°C.

41

[This procedure is justified since model validation for dryer capacity at average
inlet/outlet moisture contents has been proven elsewhere (Brooker et al., 1992).]

The data in Table 2.1 show that the predicted dryer-outlet standard deviations are
higher than the experimental values. The average relative error is 29.9% and is believed
to be caused mainly by the limited range of the single-kernel moisture meter (i.e. the rated
moisture range is 9%-40 % w.b.). This means that the meter incorrectly measured the
moisture content of the kernels below 9% w.b. and above 40% w.b. Since some
crossflow-dried kernels have a moisture content well below 9% w.b. (Brooker et al.,
1992), the measured standard deviation is smaller than the predicted value.

Table 2.2 shows the comparison of the experimental and predicted standard
deviations when kernels with a predicted value of less than 9% w. b. moisture are
excluded in the determination of the standard deviation. The relative error between the
experimental and theoretical standard deviation values now ranges from -8.8% to 17.1%
with an average error of 11.6%. Based on the data in Table 2.2, it is concluded that the
MSU stochastic crossflow drying model shows acceptable agreement with the

experimental results.

2.7 Conclusions

Chapter 1 in this series of three papers showed experimentally that there is a wide
range in the moisture content amongst maize kernels before or after drying, and that the
conventional deterministic grain-dryer models should be complemented with stochastic

models.

42

This Chapter presents the MSU stochastic models for one-dimensional
concurrent-flow and two-dimensional crossflow drying. The models simulate, in addition
to the average final moisture content, the moisture content distribution and standard
deviation of the grain leaving these dryers.

Acceptable agreement was found between the experimental and simulated data.
Thus, it now is possible to predict the moisture content range and distribution of a lot of

maize kernels dried in concurrent-flow and crossflow dryers.

43

References

Brooker, D. B., F. W. Bakker-Arkema and C. W. Hall. 1992. Drying and Storage of
Grains and Oilseeds. Van Nostrand Reinhold, New York, NY.

Ryniecki, A., A. Molinska and D. S. Jayas. 1994. Stochastic modeling of grain moisture
content for near-ambient drying. Paper No. 94-6594, Am. Soc. of Agric. Eng., St.
Joseph, MI.

Kreyszig, E. 1972. Advanced Engineering Mathematics. John Wiley and Sons, New York,
NY.

Pabis, S. and S. M. Henderson. 1961. Grain drying theory: H. A critical analysis of the
drying curve of shelled maize. J. of agric. Eng. Res. 6: 272-277.

Misra, M. K. and D. B. Brooker. 1980. Thin-layer drying and rewetting equations for
shelled yellow corn. Transactions of the ASAE 23(5): 1254-1260.

Thompson, T. L., R. M. Peart and G. H. Foster. 1968. Mathematical simulation of corn
drying - A new model. Transactions of the ASAE 11(4):582-586.

Press, W. H., B. P. Flannery, S. A. Teukolsky and W. T. Vetterling. 1986. Numerical

Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge,
MA.

44

Table 2.1 Experimental and simulated standard deviations (SD) of maize dried
in crossflow dryers.

 

 

 

DRYING CONDITIONS AND EXPERIMENTAL RESULTS SIMULATED RESULTS
TEST DRYER AIR MCIN SD,N MCour SDour MCom SDOUT REL.
No. TEMPS ERROR.
(0C) (% W.B.) (% W.B.) (% w. B.) (% we.) (% W.B.) (% we.) OF :1?”
1 CF] 90 22.9 4.57 15.7 4.87 15.7 5.67 16.4
2 CF] 102 26.2 5.86 14.3 5.70 14.4 6.00 5.3
3 CF] 105 22.2 4.19 12.7 3.68 12.6 5.52 50
4 CF2 155120 24.4 4.12 14.7 5.15 14.8 7.71 49.7
3-stage 2nd'100
3%5
5 CF2 19-88 18.7 3.31 14.4 3.59 14.5 4.59 27.9
3 ta 2“d-88
'S g6 3rd_7

 

* Rel. Error of Sdou, = (simulated SDout - experimental SDom) / (experimental SD00.)

Table 2.2 Experimental and simulated standard deviation (SD) dried in
crossflow dryers excluding kernels at moisture contents lower than

 

 

9%.
TEST N0. 1 2 3 4 5
DRYER CF] CF] CFl CF2 CF2
EXPERIMENTAL soour (%) 4.87 5.70 3.68 5.15 3.59
SIMULATED so,er (%) 5.23 5.25 4.31 5.90 3.96
REL. ERROR or SI)our (%) 7.4 -8.8 17.1 14.6 10.3

 

45

Appendix 2A: The Moisture Content Distribution of Grain Dried in a One-

dimensional (concurrent- or counter-flow) Deep-bed Dryer

Assume the distribution of the moisture content in the grain entering the dryer is
normal, i.e. N[E(Mo), 00]. The grain bed is divided into n thin layers in the direction of
the grain flow. The thin-layer drying equation at constant air conditions is (Brooker et al.,

1992)

M-M. 1.
—————= " 2A.1
Mo-M. e ( )

where Me, k are functions of the air conditions.
For any thin layer of grain i, the relationship between the layer-exit moisture

content, M). 1, and the layer-inlet moisture content, M,-, is:

Mt ' Mei k
——-—-—— = ""4 2A.2
Mo ' Mei e ( )
MI"! " Mei -k'( 4A)
—— = "“1 ’ 2A.3
Mo ' Met 8 ( )
Eliminating 1..., in Eqs A2 and A3 results in:
M,., = M,e""“r + (1 - e’k'A’) M... (2A.4)

where Me,- and k,- are functions of T ,- and ¢,~.
Therefore, the exit moisture content of any grain layer is a function of the air

temperature and humidity, and the initial grain moisture content, i.e. :

46

Ml = M0 e-kgAr + (I _e-k0Ar) Mao
M2 = MIe-k/AT + (I -e-klAt) Me]
= Moe—WW + (I-e'koA’)e""A’ 114.0 + (I -e'*"") M...

Mn _—_ Moe'NO‘kIV-Wkn-IJAY (2A5)
- - . A
+ (I-ekgAT)e(k, 1!. kn-” t M30

- , - 4° A
+ (1_ek,Ar)e(k‘ k3 k,,_,) r Mel

+ (1 ”e.k"-’Ar) Meln-l)

Therefore, the dryer-exit (i.e. final) grain moisture content is

M, = M. = CM. + D (2A.6)
where
C : e-Hto'kl'...°l(,,-[)At
D = (I_e-koAt)e-(k,'k2n..+k,,,,)Ar McO
+ (I_e-kIAt)e-(k2:k3n..*k,,-,)Ar Mel (2A7)

+ (1-8-kn-IAT) Mum-“

Note that C and D are functions of the air temperature and humidity within the drying bed

only.
Since C and D are independent on M0, M13 the normal distribution with (Press et
al., 1986):
E( M,) = CE( M.) + D (2A.8)
0] = C00 (2A‘9)

47

If the thin-layer drying equation (i.e. 2A.1) is not an exponential equation, or if the
drying constant k is a function of the grain temperature or the moisture content, the above
derivation is not strictly correct. Fig. 2A.] shows the simulated grain moisture content
distributions after drying in a one-dimensional (i.e. concurrent-flow) dryer when three
different thin-layer drying equations (i.e. exponential equation (Pabis, et al., 1961), Page
equation (Misra et al., 1980) and Thompson equation (Thompson et al., 1968)) are
employed. It is clear that the final grain moisture content distributions are close.
Therefore, the form of the thin-layer drying equation has only a limited effect on the final

moisture content distribution.

48

Appendix ZB: The Moisture Content Distribution of Grain Dried in a Two-
dimensional (crossflow) Deep-bed Dryer
The grain column is divided into m sub-columns in the direction perpendicular to
the air flow. In each sub-column the grain flowrate is G. The distribution of the exit-
grain moisture content in sub-column i is normal, i.e. N,[E(Mfi), op] (see Appendix 2A).
Within sub-column i, the probability density and the probability of the moisture

content are

 

e-[X—HMM/ 20} (28.1)

f,(/\9 =

2n 0'];
and

g , x
13.00 = 5 = I-.. f,- (M (28. 2)
where g,-(x) is the grain flowrate with a moisture content less than or equal to X in the sub-
column i.
The dryer-exit moisture content is the average of the exit moistures of the sub-

columns. The probability and probability density of the moisture content of the grain

leaving the dryer are

2 Pm (28. 3)

'Ma
Q I99
II

and

49

are:

and

1 m
— 2 f. ()0 (28.4)
m :21

d
M = 7.1; [P00] ==

Therefore, the average dryer-exit grain moisture content and standard deviation

E(M/) = E(M;.) (213. 5)

S|~

'L

N

a; = E(M;)-[E(M,)]’
1 "' ... 2
2 Z Z 1,, X2 f.()OdX- [HM/)1
1 m 2 2 (213.6
= g 2 (0*; + [E(Mf.)]) - [HM/)1 )
1-1
1 ’" 1 "’
= E Z a; + g 2 [Emfiu’ - [Emmi

50

0.10

 

 

 

 

 

0.08
.E‘
U)
c:
% 0.06
.E‘
g 0.04 x‘
e s
a.
0.02
0.00
0 10 20 30 4O
Moisture content, % d.b.
...... Initial distribution —0— Exponential equation
—x— Page equation —-A— Thompson equation

Fig. 2. Al Simulated dryer exit moisture content distribution in a concurrent-
flow maize dryer employing different thin-layer drying equations.

51

A, B, C, D coefficients
grain flowrate in sub-column, dry matter, kg s'I
average value
M moisture content, decimal, d.b.
normal distribution
probability
air temperature, °C
grain moisture content, decimal, d.b.
probability density firnction
flowrate of grain with moisture content lower than or equal to X, dry
matter kg kg 5'1
drying constant. 8"
relative humidity, %
drying time, 8
standard deviation
increment

”\N'fiwzgmm

qqszr

Subscripts

d dry basis

e equilibrium

eq equivalent

i inlet or layer number
f final

0 initial

w wet basis

52

CHAPTER 3. STOCHASTIC MODELING OF GRAIN DRYING:

ANALYSIS OF CROSSFLOW DRYING*

Abstract

In Chapter 3 of the papers on stochastic dryer modeling of grain drying, the MS U
stochastic drying model is used to investigate the distribution of the kernel moisture
content during the crossflow drying of maize. It is shown that the standard deviation of
the moisture content gradually increases during the drying process, and becomes larger
when the drying temperature is increased or the airflow rate is decreased. A grain-
inverter placed in a crossflow dryer is demonstrated to have a beneficial eflect by
decreasing the value of the standard deviation of the moisture content of the grain

leaving the dryer.

*This paper was published in 1997 in the Journal of Agricultural Engineering Research

66:281-286.

53

3.1 Introduction

In Chapters 1 and 2 of this study the stochastic character of the process of grain
drying has been accounted for and has been modelled. First, experimental data were
collected to show the wide variation in moisture content among the kernels in pre—dried
and post-dried samples of maize. Next, stochastic models were developed for the
moisture distribution in the maize before and after drying. In this Chapter in the series,
the MSU stochastic crossflow model is employed to assess the effect of several design
parameters (i.e. air temperature, airflow rate, grain reversal) on the moisture content

distribution in crossflow-dried maize.

3.2 Crossflow Dryer Specifications

The analysis of crossflow grain drying is performed with a commercial-sized
crossflow dryer operating without a cooler (i.e. in a dryeration-type process). The design

specifications along with the operating conditions of the dryer are tabulated in Table 3.1.

Table 3.1 Design specifications and operating characteristics of the standard
crossflow dryer used in the analysis of the MSU stochastic drying

 

model.
COLUMN LENGTH, m 10.0
COLUMN THICKNESS, m 0.305
GRAIN VELOCITY, m h'1 5.0
AIR TEMPERATURE, °C 70, 90, 1 IO
AMBIENT AIR CONDITIONS, °C AND % RH 70 and 60
AIRFLOW RATE, m3 min" t" 60, 80, 100
INITIAL MOISTURE CONTENT, % (W.B.) 25.0
INITIAL STANDARD DEVIATION, % W.B. 2.0, 3.0, 4.0

 

54

The thickness of the grain column is 0.305 m, a standard value in crossflow maize
dryers. The length of the grain column is 10.0 m and the airflow rate is 80 m3 min'1 t",
resulting in a moisture content decrease of maize of 10-12% w.b. after 2 h of drying under
normal drying conditions (i.e. at 90-100°C).

To analyze the effect of the major operating parameters in a crossflow dryer
receiving 25% w.b. maize, the air temperature (70, 90, 110°C), the airflow rate (60, 80,
100 m3 min'l t"), and the initial standard deviation of the moisture content of maize
entering the dryer (2, 3, 4% w.b.), were varied. The selected values of each of these
parameters fall within the range encountered at commercial elevator sites in the U. S. A.
As wet basis is usually used in grain commerce, the moisture content and the standard

deviation of maize are presented on a wet basis in this paper.

3.3 Crossflow Dryer Performance Characteristics

Fig. 3.1 shows the simulated operating characteristics of the crossflow dryer as
calculated by the MSU stochastic crossflow drying model presented in Chapter 2. Maize
at an average moisture content (AMC) of 25.0% w.b. is dried to an average 11.9% w.b. in
2 h at 90 °C. As the maize moves slowly through the dryer, the average moisture content
difference (AMCD) between the maize at the air-inlet and -outlet sides of the drying
column increases from zero to 9.1% w.b.. The standard deviation (SD) of the moisture
content of the maize across the column increases slightly from 3.0% w.b. to 3.4% w.b.,
with the maximum of 3.9% w.b. occurring after about 60 minutes of drying.

Figs. 3.2 and 3.3 show the change in the moisture content and the standard
deviation, respectively, at four positions within the grain column during the drying

55

 

 

 

30~~4 ~ --——- -—-5
25 1: SD c,
' . °\
1; *ATT—XfiI—“k’kx‘x‘ 4 c“
.\° 20 - ““4: g
*5“ ~14 . 3 '5
8 AMC %
g 15 - .c,
0 a
‘9 AMCD 213
5 10 - §
.2 m
E 1
5 l-
0 l L l l l 0
0 20 40 60 80 100 120

Drying time, min

Fig. 3.1 The average moisture content (AMC) of maize, the difference
between the average MCs of the air-inlet and air-outlet sub-columns
(AMCD), and the standard deviation across the grain column (SD),
of a crossflow dryer operating at 90°C.

56

25 m.44444-4-w—H—HH—44—
‘
A“. I
A

 

‘: o .
_d O ‘ I I . e .
' A I 9 .
3 20 ' . . ‘ A l I l . . o .
\° . n .
O . ‘ . I . . o l ' l
a ‘ I O -
E? 15 _ . . . ‘ . _ I arroutet
8 o ‘ ‘ I -
5 ° . ‘ . at 20.3 cm
0 A A
0 10 _ ' . ‘ . at10.2cm
0 . o
. . . o .
1,5, ‘ ° arr-Inlet
.8 5 _
Z
0 1 1 l g 4 l

 

0 20 40 60 80 100 120

Drying time, min

Fig. 3.2 The drying curves of 25 % w.b. initial moisture content maize at

different positions within the grain column of a crossflow dryer
operating at 90°C.

57

3.0

2.5

2.0

1.5

Standard deviation, %

1.0

0.5

 

 

R! I
b ' . ‘ . ' air-outlet
_ ' ° ‘ . l at 20.3 cm
I I A ‘ l
' . ‘ . at 10.2 cm
I ' Ilair-inlet
l
20 40 60 80 100 120

Drying time, min

Fig. 3.3 The standard deviation of the moisture content at different positions
within the grain column. Maize initially at 25% (w.b.) moisture
content and dried in a crossflow dryer operating at 90°C.

58

N

O
I

I

|

initial

(It
I

1 hr drying 2 hrs drying

Frequency, %
3
4

III
I

 

0 l l l l l l l J 1

0 10 20 30 40/0 10 20 30 40/0

Moisture content, % w.b.

 

J

10 2O 30 40

Fig. 3.4 The moisture distribution of maize before drying, and after one hour

and two hours of crossflow drying at 90°C. Maize initially at 25%
w.b. average moisture content with 3% w.b. standard deviation.

59

process, i.e. at the air-inlet and -outlet sides, and at two intermediate locations within the
grain column. The maize at the air-inlet side dries faster (to MCfim} = 7.0% w.b. in 2 h ),
and the standard deviation decreases more quickly (to SDfina] = 0.8% w.b. in 2 h) than the
grain flowing through the dryer at the air-outlet side of the grain column (MCfinal = 16.0%
w.b., SDfina] = 1.9% w.b.).

The change in the moisture content distribution of the maize as it flows through
the crossflow dryer is illustrated in Fig. 3.4. The shape of the frequency distribution
curve changes --fewer kernels are at or near the average moisture content after 1 h and 2 h
of drying than at the start of the drying process. The maximum frequency has shifted to
the higher moisture content range, and the frequency curve has changed from a normal to
bi-modal distribution. Thus, a sample of crossflow-dried maize can be expected to

contain a relatively large number of low and high moisture-content kernels.

3.4 Standard Deviation

The standard deviation in the moisture content of the maize entering a crossflow
dryer influences the standard deviation of the maize exiting the dryer, as is illustrated in
Fig. 3.5. The standard deviation is affected by (1) the standard deviation within each sub-
column, and (2) the standard deviation due to non—uniform heat-transfer/mass-transfer
treatment of the grain across the grain column. During the initial minutes of drying the
standard deviation changes little, but rapidly increases to a maximum value after about 1

h of drying. Subsequently, the standard deviation gradually decreases to about 3.0% w.b..

60

 

 

-¢- ini. SD=4 %
-O-1n1. SD=3 %
-X-1n1. SD=2 %

Standard deviation, %
b)

 

 

 

0 20 40 60 80 l 00 1 20
Drying time, min

Fig. 3.5 The standard deviation (SD) of the moisture content of maize in a

crossflow dryer for different initial SD values; the dryer operates at
90°C.

61

20

 

initial 1 hr drying 2 hrs drying

—A
M

Frequency, %
S

 

 

   

 

 

0 4 %1 Hr ..1§4 4.
0 10 20 3040/010 20 3040/010 20 3O 40

Moisture content, % w.b.

Fig. 3.6 The moisture distribution of maize dried in a crossflow dryer at
different air temperatures. Maize initially at 25% w.b. average
moisture content and 3% w.b. standard deviation.

62

 

 

°\°a 4 - lingoc 1
C I l I I ' I I I
.9 I ' u I
E . . ' 70°C -
g 3 ,4: A ‘ ‘ ‘ . . . ‘
“o i
:3
E
m 2 '

1 l L l l l l

0 20 40 6O 80 100 120

Drying time, min

Fig. 3.7 The standard deviation of the moisture content in maize dried in a
crossflow dryer at different air temperatures. Maize initially at 25%
w.b. moisture content.

63

3.5 Air temperature

The air temperature is a significant parameter in the operation of crossflow dryers.
Fig. 3.6 shows the frequency distribution of the moisture content of 25% w.b. maize as it
is dried at three temperatures. The multi-hump, non-normal character of the frequency
curve (Fig. 3.6) is pronounced at high drying temperatures, and it is curious that at 70°C
the moisture content distribution after 1 h and 2 h is approximately normal.

Fig. 3.7 exhibits the change in the standard deviation under these conditions. Air
temperature, as expected, affects the standard deviation of maize during the process of
crossflow drying. While the change in the standard deviation at 70°C is negligible, at 90-
110°C the standard deviation increases substantially during the first hour of drying and

then decreases to about 0.5% w.b. above the initial value.

3.6 Airflow Rate

The effect of the airflow rate on the moisture distribution is similar to that of the
drying air temperature. This is illustrated in Figs. 8 and 9. At the higher airflow rates, the
standard deviation and the range in the moisture content are smaller than at lower airflow.
Again, the non-normal distribution of the moisture content during and after the crossflow

drying is evident.

3.7 Grain Inversion
Inverting the grain column at the midway point of the drying column has long

been advocated as a means of alleviating the overdrying and underdrying of grain in

64

N
O
1

initial

h—O
U!
I

1 hr drying 2 hrs drying .
100 cub(m)/min 1
d t ‘

Frequency, %
S

Kl!
T

 

0 l I l l
0 10 20 30 40/0 10 2O 30 40/0

Moisture content, % w.b.

   

10 20 30 40

Fig. 3.8 The moisture distribution of maize dried at 90°C in a crossflow dryer

at different airflow rates (m3 min'1 t") . Maize initially at 25% w.b.
average moisture content with 3% w.b. standard deviation.

65

A
r

\
X

Standard devratron, 9
L»)
E
b
‘12
h:
\
\

-X- 60 cub(m)/min-t
—O— 80 cub(m)/m'm-t
+ 100 cub(m)/min-t

N
I

 

0 20 40 60 80 1 00 1 20
Drying titre, min

Fig. 3.9 The standard deviation of maize dried at 90°C in a crossflow dryer at
different airflow rates (m3min'lt'l). Maize initially at 25% w.b.
moisture content.

66

 

Frequency, %

o u. S
I I
I.
a
i
b on

N
M
I

p- ____________

N
O
I

:7.
.
35
L5.

 

 

n-iiverting
0 10 20 30 40/0 10 20 30 40/0 10 20 30 4O
Mo'sture content, % w.b.

Fig. 3.10 The moisture distribution of maize before drying, and after one
hour and two hours of crossflow drying at 90°C. The maize is
initially at 25% w.b. moisture content and is inverted after 1 hour of
drying.

67

 

 

 

\ 4
a“
.9.
E 3 >
5
1:
1::
g 2
E
m 1 L
O L l I l l l
0 20 40 60 80 100 120
Dryingtime,min

Fig. 3.11 The standard deviation (SD) of the moisture content of maize dried
at 90°C in a crossflow dryer with and without grain-inversion. The
maize is initially at 25% w.b. moisture content.

68

crossflow dryers. Figs. 10 and 11 provide proof of this beneficial effect. The moisture
content range of maize dried in a conventional (non-inverting) crossflow dryer is wider
than of maize dried in a dryer fitted with a grain-inverter (see Fig. 3.10). Also, the
standard deviation in the moisture content of maize dried in a grain-inverting dryer is
substantially lower than of the maize dried in a non-inverting model (see Fig. 3.1 1).
The advantages of inverting grain in a crossflow dryer are also illustrated in
Tables 3.2 and 3.3. Without the grain-inverter the maize dries slightly faster than in the
dryer with the inverter, i.e. in 120 min to 11.9% w.b. instead of to 12.6% w.b.. A large
difference between the two designs occurs in the standard deviation of the exit moisture
of the two dryers, 3.4% w.b. without the inverter and only 1.9% w.b. with the device.
Also, note the considerable overdrying occurring of the maize exiting the dryer without
the inverter at the air-inlet side of the column, i.e. a moisture content of the exit grain of
well below 10% w.b..
Table 3.2 Moisture content (MC) and standard deviation (SD) of the moisture

content (average, at air-inlet, at air-outlet) of maize dried in a crossflow
dryer without grain-inversion (air temperature, 90°C; airflow rate, 80 m3

 

 

min'l t'l).

TIME MC... MC...I MCour SDAv SD... SD...”
(MIN) (% W.B.) (% W.B.) (% W.B.) (% W.B.) (% W.B.) (% W.B.)
0 25.0 25.0 25.0 3.0 3.0 3.0
25 21.7 17.5 24.4 3.4 2.2 2.8
50 18.6 13.1 22.5 3.8 1.7 2.6
75 15.8 10.3 20.3 3.8 1.3 2.3
100 13.4 8.4 18.0 3.6 1.1 2.1
120 l 1.9 7.3 16.4 3.4 0.9 1.9

 

69

Table 3.3 Moisture content (MC) and standard deviation (SD) of the moisture
content (average, at air-inlet, at air-outlet) of maize dried in a crossflow
dryer with grain-inversion (air temperature, 90°C; airflow rate, 80 m3 min'

 

 

't“).

TIME MCAv MC.N MCOUT SDAv SD.N SDOUT
(M1N.) (% W.B.) (% W.B.) (% W.B.) (% W.B.) (% W.B.) (% W.B.)
0 25.0 25.0 25.0 3.0 3.0 3.0
25 21.7 17.5 24.4 3.4 2.2 2.8
50 18.6 13.1 22.5 3.8 1.7 2.6
75 16.3 17.1 12.3 2.7 2.1 1.6
100 14.1 12.9 11.9 2.1 1.6 1.5
120 12.6 10.7 11.4 1.9 1.3 1.4

 

*air temperature, 90°C; airflow rate, 80 m3 min'1 t'1

3.8 Conclusion

Deterministic grain drying models provide insight into the course of the average
moisture content of grain during the drying process, and predict the average moisture
content as it exits from a dryer. Stochastic drying models furnish additional information,
namely the distribution of the moisture content during and immediately after drying.

Deterministic grain dryer models assume a uniform inlet moisture content while
the stochastic models presume a more realistic normal distribution of the moisture
content in the grain entering a dryer. Only stochastic modelling can provide essential
design information on the degree of overdrying and of underdrying occurring in crossflow
dryers.

Wet and dry millers in particular will profit from the information provided by the

stochastic dryer models with respect to the uniformity of their base product, i.e. maize.

70

But also, livestock feeders will benefit because of the capability for assessing the likely
breakage susceptibility, and thus the storability, of their feed.

Finally, the MSU stochastic drying models are important tools in the design of
grain drying systems. This has been illustrated in this paper in the analysis of grain

inverters in crossflow maize dryers.

71

CHAPTER 4. MODELING OF GRAIN QUALITY'

Abstract

The objective of this chapter is to develop simulation models of grain-quality
deterioration during crossflow drying. The stochastic drying model and the denatured
protein and germination models are combined to simulate the quality loss of individual
kernels in crossflow dryers. The results of this study lead to a better understanding of

grain-quality deterioration, and provide an improved tool for dryer design and control.

'"Part of the content was published in ASAE Paper No: 97-6030 and was presented at the
1997 ASAE Annual International Meeting sponsored by ASAE, Minneapolis
Convention Center, Minneapolis, Minnesota, August 10-14, 1997.

72

4.1 Introduction

Grain is usually harvested at high moisture content to minimize field losses. High-
temperature dryers are widely used to quickly reduce the moisture to a safe storage level.
The drying-air-temperature ranges from 50 to 300°C, depending on dryer type, the crop to
be dried, and the quality requirements (Brooker et al., 1992). In general, higher drying-
air-temperatures result in higher capacities and energy efficiencies, but degrade the grain
quality. Therefore, the drying air temperature is a compromise between the throughput of
the dryer and the grain quality.

Three reasons make it difficult to predict or control the grain quality in a drying
process: a) the grain quality during drying is affected by multiple factors including the
drying-air temperature, drying time and grain moisture content; b) no dryer (crossflow,
mixed-flow, and concurrent-flow) treats grain uniformly; and c) the moisture content of
each grain kernel is distributed stochastically around an average, and thus each kernel has
a different reaction to the drying treatment. Therefore, the drying conditions for various
dryers are generally determined by rules-of-thumb, and this may lead to substantial
quality damage of the grain.

The objective of this Chapter is to develop a simulation model of the grain quality
in crossflow grain dryers. The model will be used to improve the grain quality through

improved dryer design and through improved automatic dryer control.

73

4.2 Literature Review

This review will focus on the effect of artificial drying on maize quality, quality

criteria of end-users, and the quality modeling in drying process.

(1) Eflect of artificial drying on maize quality

MacMasters et a1. (1959) conducted an extensive test on the wet-milling quality of
maize dried under various conditions in five crop years. The maize was harvested at 30-
20% moisture content, and dried at six air temperatures ranging from 49 to 93°C, and at
relative humidity of 15 and 40%. The starch recovery rate was 82% of the maize dried at
49°C; it decreased to 74% when the drying temperature increased to 93°C. Maize
reaching a temperature above 60°C during drying showed a definite decrease in viability.
The initial moisture content of the maize and the relative humidity of the air were
relatively unimportant with respect to the wet-milling quality.

Brekke et a1. (1973) investigated the effects of the drying-air temperature on the
dry-milling quality of maize. The tests were conducted with a fluidized-bed dryer at five
air temperatures ranging from 32 tol43°C; the maize was dried from approximately 25 to
15% w.b. in 0.5 to 7 hours. The yield of first-break grits (grits passing through a four
mesh sieve and retained on a six mesh sieve) decreased from 45 t012% as the drying-air
temperature was increased to 143°C. The percentage of stress cracked kernels was 56% at
32°C, and 84% at 143°C. The Steinlite breakage susceptibility changed from 7 to 35% as
the drying-air temperature was increased from 32 tol43°C.

Brown et al. (1979) studied the effect of three drying methods on the quality of

maize dried from 20 to 15%: (1) high-temperature crossflow batch drying and cooling, (2)

74

crossflow batch drying followed by dryeration, and (3) low-temperature (ambient air)
drying. The drying air temperature ranged from 45 to 80°C in the crossflow dryer; 60, 80
and 100°C were used in the high-temperature drying stage of dryeration. Viability was
found to be the most sensitive quality factor; it was markedly reduced at temperatures
above 60°C. Grain dried with a low-temperature drying system had a negligible amount
of stress-cracks; dryeration also caused few stress-cracks (i.e. 3-3 0%); batch-dried grain
contained the most stress-cracked kernels, between 45 to 79%. The combination of
viability, test weight, and stress cracks correlated well with the steeping index as a
measure of wet-milling quality.

Le Bras (1982) investigated the effects of the variety, maturity and drying
conditions on the wet-milling quality of maize. The drying condition was the major factor
in degrading the maize quality. A noticeable decrease occurred in starch yield when the
drying-air temperature was raised to 90°C. Five drying methods were investigated: (1)
one-pass drying, (2) two-passes drying with intermediate aeration, (3) dryeration, (4) two-
stage drying, and (5) multi-stage drying processes. Dryeration resulted in the best quality,
followed by drying in two passes with intermediate aeration; drying in one pass resulted
in the worst quality grain.

Weller et al. (1987, 1988) investigated the effects of harvest moisture and drying-
air temperature on starch recovery. The maize was harvested at high, medium, and low
moisture contents of approximately 30, 24 and 18% w.b., and was dried to about 14%
w.b. at 22 (ambient), 49, 71 and 93°C, at an airflow rate of 2 m3m'3min". Starch recovery
was not significantly different for four hybrids but decreased as both the harvest moisture

and the drying-air temperature increased. The test weight decreased as the drying-air

75

temperature increased, and the germination increased from 89% at 22°C to 95% at 49°C.
All samples showed greater than 80% stress cracking at drying air temperature above
49°C except the low moisture content samples. The stress cracks for the soft maize
varieties ranged from 62 to 82% while those for the hard varieties ranged from 39 to 65%.

Maize samples were collected prior to and after drying in four commercial dryers
(three crossflow and one concurrent-flow) by Chang et al. (1989), and their physical and
chemical properties were investigated. The drying-air temperature ranged from 63 to
96°C, the initial moisture content from 18 to 28%, and final moistures from 14.3 to
18.0%. The percentage of stress-cracks increased from almost 0 % to a low of 3-34 %
afier drying. Before drying the individual kernel moistures ranged from 15 to 27%; afier
drying, the kernel moistures ranged from 6 to 20%; a wider variation in the individual
kernel moisture content was indicative of a more severe drying treatment which led to
reduced starch recovery.

Peplinski et al.(1989) investigated the physical and chemical characteristics of six
maize hybrids dried at 25 (ambient) and 60°C, with a moisture removal from 20-24% to
10-13%. Increasing the drying-air temperature from 25 to 60°C had no apparent effect on
the chemical composition but increased the percentage of stress-cracked kernels from 0-3
% to 23-74%, respectively, depending on the maize hybrid. The breakage susceptibility,
as measured in the Stein breakage test, at 25 °C ranged from lto 7 % and at 60°C from 3
to 9%; the grits yield decreased 1% at 25°C and 7% at 60°C.

Maize at 30% moisture was dried in a stationary bed at 25 to 100°C at a depth of
5.1 cm (Peplinski et al., 1994). Drying times to 12% final moisture ranged from 1 hr at

100°C to 38 hr at 25°C. The chemical composition of the maize dried at 100°C was

76

unaltered but the breakage susceptibility ranged from 27 to 67% and the stress-cracked
kernels from were 78-84%. Germination decreased to 0% at air temperatures higher than
70°C. The amount of water-extractable protein (albumin solubility) remained constant in
the maize dried at 25-5 5°C, but rapidly decreased as the drying temperature exceeded
60°C.

Zhang et al. (1991) investigated maize-quality variation in a commercial
crossflow dryer. Samples from 15 points in the dryer were collected. Large variations in
moisture content were observed across the dryer column. Maize at the air-inlet side of the
grain column lost about twice as much moisture as the maize at the air-outlet side. A high
percentage of stress cracked kernels (average of 20.5%) with high breakage-susceptibility
values (205-36.8%) was measured in the samples at the inside layer of the grain column.

The effects of the drying parameters on the various qualities of maize were
studied on a laboratory-size crossflow dryer by Beke et al. (1993). The drying—air
temperature ranged from 60 to 160°C and the superficial air velocity ranged from 0.1 to
1.3 m/s. The drying-milling quality of maize was greatly affected when the drying-air
temperature exceeded 110°C or the air velocity surpassed 0.9 m/s. The protein and starch
content, and the feed value also decreased dramatically when the air-temperature
exceeded 110°C. The maximum air temperature recommended for maize was 100°C for
an initial moisture higher than 32% w.b., and 110°C for an initial moisture lower than

32% w.b..

(2) Quality criteria

77

The quality requirements are different for each end-use of maize, i.e. wet-milling,
dry—milling, and animal feeding; different criteria are used to assess maize quality for
each use. The criteria can be categorized into two types: (a) direct, and (b) indirect. Direct
criteria are, for instance, the grits yield for dry-milling, the starch-recovery for wet-
milling, and the viability for seed grain. An indirect criterion measures a physical or
chemical property associated with grain quality, e. g. moisture content, moisture
uniformity, test weight, stress-cracks, breakage susceptibility, BCFM (Broken Corn and
Foreign Materials), soluble protein, starch viscosity, and sedimentation (Brooker et al.,
1992; Freeman, 1973; Chang et al., 1989). No single indirect criterion adequately predicts
the grain quality, in contrast to a direct criterion which is definitive, but (generally)
cumbersome to determine.

In the U. S. grade standard for yellow maize, five factors are employed to
determine the grade, i.e. maximum moisture, test weight, BCF M, heat damage and total
damage (Brooker et al., 1992). However, the standard does not address the end-use
quality of the grain, and is considered to be inadequate in some industries (Lowell, 1996).
End-users generally use a private grade-description in addition to the general standard in
order to assess grain quality.

The main objective of the dry-milling of maize is to obtain large grits for cereal
food. Wichser (1961) proposed the “milling evaluation factor” (MEF) for rating the dry-
milling quality; the MEF is based on the proportion of grits, meal and flour after the
milling process. Emam et a1. (1981) proposed a modified MEF based upon the yield of
grits larger than 7-mesh and on the percentage of endospenn extraction; the factor is
highly correlated (R=0.92) with flaking-grit yield (Kirleis et al., 1990).

78

Among the indirect maize-quality criteria, kernel density is the best single
predictor of the MEF (Kirleis et al., 1990); floaters and test weight have the highest
correlation with grits yield (Paulsen et al., 1985). No quantitative relationship between the
dry-milling quality and the drying conditions has been established although Peplinski et
al. (1989,1994) recommended (as a rule-of-thumb) a maximum kemel-temperature of
60°C for the drying of maize, regardless of the moisture content.

Direct measurement of the wet-milling quality of maize requires a 2-day
laboratory-scale wet-milling procedure, and is therefore not suitable for examining a lot
of maize on a routine basis (Freeman, 1973; Chang et al., 1989). Viability, test weight,
and stress cracks do not separately predict wet-milling performance (Brown et al., 1979).
Among the indirect criteria, starch content, test weight, and ethanol-soluble protein have
the highest correlation with starch recovery (Weller et al., 1988). Le Bras (1982)
recommended breakage susceptibility, water re-absorption, sedimentation and turbidity as
rapid tests for the measurement of quality damage by artificial drying. Courtois et al.
(1991) and Mourad et al. (1996) used the protein-soluble in saline-water as an indicator

of the wet-milling quality of maize.

(3) Quality models and simulation

A germination model for dried seed grains was developed by Nellist (1981). At
constant temperature and moisture content, seed death is shown to be normally
distributed over time and can be quantified by use of the integral of the normal
distribution. The germination percentage is represented as a probability, which, when
transformed to equivalent values of the standardized normal deviate or ‘probit’, has a

79

linear death rate defined the reciprocal history of seed. A similar germination model was
developed by Lescano et al. (1987) for maize based on thin-layer drying tests; the model
was employed to predict the viability of maize dried in a concurrent-flow dryer.

Courtois et al. (1991) proposed an empirical model for the wet-milling quality of
maize dried in mixed-flow dryers. Transmittance of light through a grain-saline solution
was employed as the quality criterion. The error in the predicted transmittance of mixed-
flow dried maize was generally less than 10%.

Bruce (1992) developed a model for the effect of the heated-air drying on the
bread-baking quality of wheat. Two varieties of wheat at three initial moisture contents
were dried in thin layers with air from 65 to 85°C for periods from 1 min to 4 hours. Two
models were developed to describe the relationship between the loss of loaf volume and
the moisture and temperature histories of the wheat kernels.

Zhang et al. (1992) developed a fuzzy model to predict the breakage
susceptibility of dried maize. The model is based on data obtained from experiments with
a laboratory crossflow dryer with maize of various initial moisture contents.

Mourad et al.(1996) developed a wet-milling maize quality model based on a
number of fluidized-bed drying tests. Protein solubility and the separation index of starch
and protein were the quality criteria. The relationship between the degradation rate of
protein (i.e. the wet-milling quality) and the drying conditions was established.

The aim of this Chapter is to combine two maize-quality models with the
stochastic grain drying model developed in Part 1, Chapter 2, in order to simulate the
change of grain quality in crossflow dryers, and to provide a tool for minimizing the
quality damage of grain in a crossflow dryer.

80

4.3 Models and Simulation

4.3.1 Quality models
The transmittance model developed by Courtois et al. (1991) and the viability
model of Lescano et al.(1987) were employed for the quality simulation of dried maize.

The Courtois transmittance model is:

5A

3 =—KAA2 (4.1)

where

K. = K,“ exp[-1332 x 103 /(8.314(I9+ 273.16))]
K... = 1.9561 x 10'6 +5.4287 x10l7 M+6.8210><10l7 M2

where A is the absorbance unit (dimensionless), 0 the grain temperature (°C), and M the
grain moisture content (dec. d.b.). The relationship between the absorbance unit A and
the transmittance T (%) is:

A = —log.0(T/ 100) (4.2)

The percentage of protein denaturation DP (%) was calculated from (Chang et al., 1989):

DP 100Tf-7° 43
“ 100—T0 (')

where T0 is the initial transmittance and Tfthe final transmittance.

The viability model of Lescano et al. (1987) has the form:

1 *°° 1
G=—- ex ——X2]dX 4.4
E... .1, t >

81

where: X = (t - t) / 0' (4.5)
and G is the germination, X the standardized normal deviate, t the time for 0.5 viability,
and o the standard deviation of the seed viability loss, which is a function of the drying
air temperature T... and the seed moisture content M. For maize,

lno = 4.20 — 0.277; — 33.201n M (4.6)

where Ta is expressed in °C and M in % (w.b.).

4.3.2 Quality simulation

A subroutine for grain quality simulation was added to the stochastic grain drying
program developed in Part 1, Chapter 2. The subroutine predicts the germination and the
percentage of denatured protein of maize during the crossflow drying process.

In the stochastic crossflow grain-drying model, the grain column is divided into a
number of equal-depth sub-columns in the direction of the airflow. Each sub-column is
further divided into stacked grain beds from the inlet to the outlet of the dryer. It was
established that if the grain moisture content is initially normally distributed, the moisture
content keeps the normal distribution during the drying process in a sub-column, but with
a changed average and standard deviation (see Chapter 2.3). The stochastic drying model
predicts the average moisture content of the maize and its standard deviation at the outlet
of each bed.

The quality models of Eqs (4.1) and (4.4) are both functions of the grain
moisture content. With the grain moisture content initially normally distributed, the grain
quality will also be stochastically distributed among the grain kernels (not necessarily as a

normal distribution). In the quality simulation subroutine, 80 values of the moisture

82

content are selected evenly spread in the range of —4 0' to +4 0' of the normal distribution;
the grain quality is predicted for each value of the moisture content. The average grain

quality at the outlet of each bed is subsequently calculated by:

Q = ZflM, )Q. (47)

where Q is the average grain quality; Q. is the predicted quality of the grain with the
moisture content of M ,. ; and f is the probability density of the moisture distribution at
M , , i.e.:

1 M —M
l '*( ' 57*)2

e—2 a (4.8)

 

27:0"

where M is the average grain moisture content and 0' is the standard deviation of the
normal distribution.

For simulation of the denatured protein in a sub-column, the changes in the grain
temperature and moisture content are negligible for the quality simulation. Thus,
assuming constant temperature and moisture content, the solution of Eq. 4.1 is:

1
‘1/Q,_.+KQAT

 

Q. (49)

where QH is the absorbance unit of maize at the inlet of the bed and Q. the predicted

absorbance unit at the outlet of the bed; and AT is the residence time of the maize in the
bed. Then, the percentage of protein denaturation DP (%) is calculated from the
absorbance unit (Q) with Eqs. 4.2 and 4.3.

For simulation of the germination, the solution for germination model of Eq. 4.5

is:

83

At
X, = X,_. +— (4.10)
0'

where X ,_. is the standardized normal deviate at the inlet of the bed, and X , is the
predicted standardized normal deviate at the outlet of the bed; 6 is the standard deviation
of the seed viability loss, and Ar is the residence time of grain in the bed. The viability of
the grain is converted from the standardized normal deviate (X) to germination (G) with
Eq. 4.4.

The procedure of determining the grain quality in a crossflow dryer is: (1) use the
stochastic drying model to predict the average and the standard deviation of the grain
moisture content in each bed in a sub-column; (2) apply Eqs. 4.7-4.10 to each bed in
sequence from the inlet of the dryer to the outlet; and (3) calculate the average of the

values determined in step (2) to obtain the average quality of the dried grain.

4.3.3 Model validations

The experimental data collected from three commercial crossflow maize dryers by
Chang et al. (1989) were used for validation of the wet-milling quality simulation. The
dryers were a Redex R-RT—RX30, a Meyer-Morton 3000 and a Delux DG-1500; the
specifications of the dryers are contained in the paper by Chang et al. (1989). The dryer
capacity in a specific test was found by matching the experimental and simulated final
moisture contents. A comparison of the experimental and predicted transmittance and
denatured-protein percentages in maize is tabulated in Table 4.1.

The average difference between the experimental and predicted values of the

transmittance is 3.0% (32 vs 35%), and of the denatured protein is 3.8% (15.2 vs 19.0%).

84

Table 4.1 Experimental and predicted transmittance and denaturation of protein
after drying of maize in three commercial crossflow dryers.

 

 

 

 

 

 

 

 

Dryer model Redex Meyer-Morton Delux

Test Number 1 2 3 4 5 6 7 8 9 10 l 1 12

Drying air 82 93 82 82 82 93 93 96 63 68 93 96
temp., °C

Initial M.C., % 22.5 20.1 21.4 21.0 28.0 21.4 23.0 18.0 22.4 20.8 20.6 24.1
w.b.

Final M.C., % 15.0 14.3 14.5 14.7 17.5 16.1 17.4 15.0 15.1 14.6 16.5 15.2

w.b.

Initial trans., % 22.5 20.3 24.5 21.3 20.3 25.3 23.1 17.6 24.3 25.6 21.9 25.0

Exp. Final 34.5 30.6 34.2 32.6 35.5 31.6 39.0 39.4 31.4 28.2 42.4 34.5
trans., %

Predicted final 33.5 33.7 34.4 30.9 33.8 36.0 33.8 24.3 27.9 28.6 25.4 35.9
trans., %

Exp. dena. of 15.5 12.9 12.8 14.4 19.1 8.4 20.7 26.5 9.4 3.5 26.2 12.7
protein, %

Predicted dena. 14.2 16.8 13.1 12.2 16.9 14.3 13.9 8.1 4.8 4.0 4.5 14.5
of protein, %

Table 4.2 Experimental and predicted germination of maize after two hours of

drying in a batch dryer in drying maize to 15% MC.

Test Drying air Initial M.C., Final M. C., Initial germ, Final germ., % Predicted final

no. temp., °C % w.b % w.b. % germ, %
1 93 3 I .0 14.9 90 1 1 24
2 93 30.5 14.4 92 5 25
3 93 27.0 13.4 97 3 27

 

Table 4.3 Drying conditions for the grain-quality simulation study in a crossflow

 

dryer.
Drying air temp., °C 50 60 70 80 100 120
Airflow rate , cfrn bu". 40 60 80 100 120
Initial M.C., % w.b. 17.5 20 25 30 35
Initial transmittance, % 25
Initial germination, % 95
Standard deviation of initial M.C., % w.b. 3

 

*1 cfrn bu": 0.804 mjm'3min'l

85

[The experimental percentage of denatured protein in Tests 6 and 10 seems unreasonable
low compared to the values in the similar conditions in the test.]

Experimental germination data of maize was collected by Gustafson (1981) on a
laboratory batch dryer; the dryer has a 30.5 cm wide column, and an airflow rate of
approximately 80 m3 min'l t'l. The predicted germination was higher than the
experimental results as shown in Table 4.2. Fig. 4.1 shows a comparison of the
germination percentage at four positions within the grain column during a two-hour
drying period. Considerable disagreements occurred at 2/3 and at the air-outlet side of the
column, especially in the low germination range. A major reason could either be the
inaccurate prediction of the grain-temperature distribution in the drying column
(Sokhansanj, 1987) or the effect of maize hybrid (Lescano etal., 1987).

In general, it is the opinion of the author that the grain-quality/grain—dryer

simulation models are acceptable for use in further analysis.

4.4 Gain-quality Analysis

A simulation study of the quality change of maize in a crossflow dryer was
conducted. The thickness of the grain column was assumed to be 30.5 cm; the drying air
(or grain stream) is reversed at the midpoint of the drying column. The cooling time is
one-third of the drying time, and the ambient temperature and humidity are 15°C and
60%, respectively. For each drying condition, the drying time and cooling time were
searched for so that the final moisture content would be 15% w.b.. The drying conditions
are tabulated in Table 4.3. A total of 150 drying conditions were investigated. Tables

4.4a-4e show the results.

86

100

 

  
   

 

AA ‘

A outside
80 .

 

 

 

.\° 60
a
.2
g 40
E
Q)
0 20
0 P
_20 1 l A g l l .1 1
0 20 40 60 so 100 120

Drying time, min

Fig. 4.1 Experimental (points) and predicted (lines) germination vs. time of

maize at four locations (at the air inlet, at 1/2, 2/3 and air outlet) in
the grain column.

87

Table 4.4a Predicted quality of maize Table 4.4b Predicted quality of maize

 

 

 

 

after crossflow drying at after crossflow drying at

an airflow rate of 40 an airflow rate of 60

cfm/bu (32 m3m'3min") cfm/bu (48 m3m'3min'l).

Drying Inlet Trans- Dena. Germ, Drying Inlet Trans- Dena. Germ,
air M.C., mittance, protein, % air M.C., mittance, protein, %
temp., % w.b. % % temp., % w.b. % %

°C °C
50 17.5 25.1 0.1 94.7 50 17.5 25.1 0.1 94.7
50 20 25.9 1.2 94.6 50 20 26.0 1.3 94.6
50 25 27.3 3.1 94.3 50 25 27.6 3.5 94.3
50 30 27.9 3.9 93.7 50 30 28.3 4.4 93.8
50 35 28.0 4.0 92.3 50 35 28.3 4.4 92.9
60 17.5 25.2 0.3 94.3 60 17.5 25.3 0.4 94.3
60 20 26.4 1.9 93.2 60 20 26.7 2.3 93.4
60 25 28.4 4.5 70.3 60 25 28.9 5.2 88.8
60 30 29.3 5.7 71.9 60 30 30.0 6.7 76.9
60 35 29.2 5.6 65.2 60 35 29.8 6.4 65.6
70 17.5 25.4 0.5 81.4 70 17.5 25.7 0.9 85.0
70 20 27.1 2.8 66.6 70 20 27.7 3.6 67.6
70 25 29.8 6.4 61.4 70 25 30.8 7.7 58.0
70 30 31.0 8.0 52.7 70 30 32.0 9.3 46.3
70 35 30.8 7.7 44.2 70 35 31.6 8.8 39.9
80 17.5 25.8 1.1 65.9 80 17.5 26.0 1.3 64.4
80 20 28.0 4.0 54.8 80 20 28.7 4.9 46.1
80 25 31.5 8.7 37.7 80 25 32.9 10.5 32.4
80 30 32.7 10.3 34.7 80 30 34.0 12.0 24.7
80 35 32.5 10.0 32.5 80 35 33.4 11.2 21.5
100 17.5 26.7 2.3 39.9 100 17.5 26.9 2.5 38.0
100 20 30.4 7.2 31.3 100 20 31.8 9.1 12.4
100 25 35.3 13.7 11.5 100 25 37.5 16.7 2.3
100 30 36.7 15.6 9.9 100 30 38.8 18.4 0.3
100 35 35.8 14.4 9.8 100 35 37.6 16.8 0.3
120 17.5 27.9 3.9 34.3 120 17.5 28.3 4.4 13.6
120 20 33.5 11.3 12.2 120 20 35.3 13.7 1.0
120 25 39.3 19.1 2.6 120 25 42.5 23.3 0.0
120 30 40.5 20.7 0.3 120 30 43.3 24.4 0.0
120 35 39.1 18.8 0.4 120 35 41.6 22.1 0.0

 

 

88

Table 4.4d Predicted quality of maize

Table 4.4c Predicted quality of maize after crossflow drying at

after crossflow drying at

an airflow rate of 80 cfm/bu an airflow "390:1991
(64 m°m'°min") cfm/bu (80 m m min ).

 

 

Drying lnlet Trans- Dena. Genn.,

DryIng Inlet Trans- Dena. Germ, air M.C., mittance, protein, %

air M.C., mittance, protein, %

 

 

0 0 0

temp., %w.b. % % “L“Cp" /°“"°' /" /°
°C

50 17.5 25.2 0.3 94.7
50 17.5 25.1 0.1 94.7

50 20 26.2 1.6 94.6
50 20 26.1 1.5 94.6

50 25 28.0 4.0 94.3
50 25 27.8 3.7 94.3

50 30 28.9 5.2 93.9
50 30 28.6 4.8 93.8

50 35 28.9 5.2 93.2
50 35 28.6 4.8 93.1

60 17.5 25.5 0.7 94.4
60 17.5 25.4 0.5 94.4

60 20 27.1 2.8 93.6
60 20 26.9 2.5 93.5

60 25 29.8 6.4 89.9
60 25 29.4 5.9 89.5

60 30 31.1 8.1 80.6
60 30 30.6 7.5 79.3

60 35 30.9 7.9 69.2
60 35 30.4 7.2 67.7

70 17.5 25.9 1.2 82.2
70 17.5 25.8 1.1 87.1

70 20 28.4 4.5 71.2
70 20 27.9 3.9 69.5

70 25 32.2 9.6 52.5
70 25 31.5 8.7 55.0

70 30 33.5 11.3 37.6
70 30 32.9 10.5 41.4

70 35 33.1 10.8 33.3
70 35 32.4 9.9 35.9

80 17.5 26.5 2.0 61.3
80 17.5 26.2 1.6 62.9

80 20 30.0 6.7 37.0
80 20 29.4 5.9 40.6

80 25 34.8 13.1 15.8
80 25 33.8 11.7 24.4

80 30 36.4 15.2 6.6
80 30 35.3 13.7 13.1

80 35 35.7 14.3 5.4
80 35 34.6 12.8 11.1

100 17.5 27.6 3.5 23.4
100 17.5 27.3 3.1 32.0

100 20 33.9 11.9 0.0
100 20 32.8 10.4 6.7

100 25 40.8 21.1 0.0
100 25 39.3 19.1 0.0

100 30 42.7 23.6 0.0
100 30 41.0 21.3 0.0

100 35 41.1 21.5 0.0
100 35 39.4 19.2 0.0

120 17.5 30.0 6.7 2.8
120 17.5 29.1 5.5 10.9

120 20 38.6 18.1 1.0
120 20 37.0 16.0 0.0
120 25 449 265 00 120 25 47.5 30.0 0.0

120 30 48.9 31.9 0.0
120 30 46.4 28.5 0.0 120 35 46 6 28 8 0 0
120 35 44.2 25.6 0.0

 

 

89

Table 4.4e Predicted quality of maize
after crossflow drying at

an airflow rate of 120
cfm/bu (96 m3m'3min").

 

Drying Inlet Trans- Dena. Genn.,
air M.C., mittance, protein, %

 

temp., % w.b. % %

°C

50 17.5 25.2 0.3 94.7
50 20 26.3 1.7 94.6
50 25 28.1 4.1 94.3
50 30 29.1 5.5 93.9
50 35 29.1 5.5 93.2
60 17.5 25.5 0.7 94.4
60 20 27.4 3.2 93.6
60 25 30.2 6.9 90.0
60 30 31.4 8.5 81.4
60 35 31.3 8.4 70.0
70 17.5 26.0 1.3 88.9
70 20 28.8 5.1 72.6
70 25 32.7 10.3 49.7
70 30 34.3 12.4 34.2
70 35 33.8 11.7 28.4
80 17 .5 26.6 2.1 60.6
80 20 30.5 7.3 33.7
80 25 35.8 14.4 8.8
80 30 37.5 16.7 2.6
80 35 36.7 15.6 1.8
100 17.5 28.1 4.1 15.7
100 20 34.8 13.1 0.0

100 25 42.8 23.7 0.0
100 30 44.4 25.9 0.0
100 35 42.6 23.5 0.0
120 17.5 30.7 7.6 0.0
120 20 39.8 19.7 0.0
120 25 49.7 32.9 0.0
120 30 51.2 34.9 0.0
120 35 48.7 31.6 0.0

 

The highest transmittance (and thus the worst grain quality) obtained in the tests
was 51.2%, corresponding to a denatured protein value of 34.9%; it occurs (obviously)
with drying conditions of 120°C, 120 cfin/bu (96 m3 m'3 min") initial moisture (Table
4.4e). At a drying-air temperature of 50°C, the germination exceeded 92.3%, regardless of
airflow. A significant change in the germination happened in the temperature range of 60-
70°C; for instance, at initial moisture content of 20% (w.b.) the germination changed
from 93% to about 70%. In general, higher drying- air temperatures, airflow rates and
initial moisture contents resulted in higher denatured-protein values and lower
germination rates. The drying air temperature appeared to be the most significant factor,
especially for germination.

Figs. 4.2, 4.3, and 4.4 show the values of denatured protein at different drying air
temperatures, airflow rates and inlet moisture contents. From Figs. 4.2 and 4.3 it is clear
that the denatured protein percentage increases with increased drying-air temperatures
and airflow rates; at temperatures above 80°C the rate increases. With an increase in the
inlet moisture content, the denatured protein percentage increases rapidly at the lower
moisture contents, and reaches a maximum value at about 28% w.b. moisture content
(Fig. 4.4). The denatured protein percentage decreases at a rate dependent on the drying
air temperature; it is not clear why the denatured protein percentage sharply decreases for
inlet moisture contents above 28% w.b..

Fig. 4.5 demonstrates that the germination does not significantly change until the

drying air temperature exceeds 60°C, except at a moisture of 35%w.b.. Fig. 4.6 shows

91

20

 

 

 

 

airflow rate, m3/m3/min 96 8

15 A
,\°
.5.“ 6 4
Q)
‘2‘
O.

10 -
'U
o 32
E
N
E
Q)
Q

5 .

O A l A 1 j_ l 4

40 60 80 100 120

Drying-air temperature, °C

Fig. 4.2 Denatured protein vs. drying air temperature in maize dried in a
crossflow dryer with an initial moisture content of 20% w. b. at
airflow rates of 32, 48, 64, 80 and 96 m°m‘°min".

92

 

inlet M

 

 

 

 

 

 

 

 

Fig. 4.3 Denatured protein vs. airflow rate in maize dried in a crossflow
dryer with an initial moisture content of 20% w.b. and at drying air
temperatures of 50, 60, 70, 80, 100 and 120°C.

93

25

 

 

 

 

 

 

 

 

 

 

 

 

20 .
,\°
.5.“
g 15 -
a 80°C
"5?: \
g 10 L 70°C
8 60°C
5 P / 50°C
0 / 4L
15 20 25 30 35

lnlet moisture content, % d.b.

Fig. 4.4 Denatured protein vs. inlet moisture content in maize dried in a
crossflow dryer at an airflow rate of 48 m3m'3min" and at drying air
temperatures of 50, 60, 70, 80, 100 and 120°C.

94

100

 

80

60

Germination, %

4O

20

 

 

0 1 l l I I l
50 60 7O 80 100 120

 

 

Drying air temperature, °C

Fig. 4.5 Germination vs. drying air temperature in maize dried in a crossflow
dryer at an airflow rate of 48 m‘lm'3min’l and with inlet moisture
contents of 17.5, 20, 25, 30 and 35%w.b..

95

20

 

 

 

 

 

 

E
.6 ‘ £9
3' 15 I 12
,\° 8
0 GD
‘5 .E
a)
*g 10 5‘
3 “a
*- D
2% E.
E 5 3%
2
O 1 l 1 l 1 1 l 0.5
19:30 21:30 23:30 1:30

Tune, h:min.

Fig. 4.6 Germination vs. airflow rate in maize dried in a crossflow dryer with

an initial moisture content of 20% and at drying air temperatures of
50, 60, 70, 80, 100 and 120°C.

96

100

 

 

 

 

 

50°C

80 ‘ 60°C
9°. 60 - 70°C
:
.2
a
.5
E
8 4° ' 80°C

20 -

100°C
\120°C\
0 \ T _
15 20 25 30 35

Inlet moisture content, % d.b.

Fig. 4.7 Germination vs. inlet moisture content in maize dried in a crossflow
dryer at an airflow rate of 48 m3m'3min'I and at drying air
temperatures of 50, 60, 70, 80, 100 and 120°C.

97

that the airflow rate does not affect the germination significantly below 70°C. Higher
initial moisture contents result in higher germination losses (Fig. 4.7).

Inverting the airflow or grain column at the midpoint along the drying column has
been advocated as a means of alleviating the overdrying and underdrying of grain in a
crossflow dryer, thus improving the grain quality. Table 4.5 compares the predicted final
denatured protein and germination percentage with and without airflow inversion in a
crossflow dryer. The denatured protein percentage is decreased slightly if the air flow is
inverted, but additional germination damage occurs. This can be explained by considering
Fig. 4.1; the germination of the maize at the air-inlet side of the column rapidly drops to
zero. Inverting of the airflow causes the germination of the other side of the column to
approach zero also. At a drying air temperature of 60°C, there is no significant difference
in the quality of maize dried with and without an inversion.

Table 4.6 shows the effect of the standard deviation (SD) of the inlet moisture
content on the final maize germination. The germination decreases slightly when the SD
increases. No difference is found in the denatured protein percentage when the SD

changes from 0 to 4% w.b..

Conclusions

(1) The changes in the denatured protein content and in the germination of maize after
crossflow drying were successfully simulated by combining thin-layer drying-quality
models with the MSU stochastic grain-drying model. Validation of the simulation

models is satisfactory.

98

(1) The quality of maize dried at a wide range of crossflow-drying conditions was

analyzed. The germination decreases rapidly when the drying air temperature exceeds

60°C. The denatured protein percentage increases almost linearly with the drying air

temperature. Inverting the airflow midway through the drying process decreases the

denatured protein percentage slightly, but increases the germination loss.

Table 4.5 Maize quality after crossflow drying with and without air inversion at the
midpoint along the drying column with an airflow rate of 60 cfm/bu (48

m3m‘3min'l).

 

 

 

Drying air temp., °C Drying air temp., °C
Inlet M. C., Airflow 60 70 80 60 70 80

%

Denatured protein, % Germination, %
20 without inv. 2.5 4.1 6.0 93.5 78.4 63.8
20 with inv. 2.3 3.6 4.9 93.4 66.4 46.1
25 without inv. 5.7 8.5 1 1.5 89.5 69.4 52.3
25 With inv. 5.3 7.7 10.5 88.8 58 32.4

 

Table 4.6 Effect of the standard deviation (SD) of the inlet moisture content of maize
on the final germination after crossflow drying (with an airflow rate of 60
cfm/bu or 48 m3m'3min'l).

 

 

 

SD, % w.b.
Air temp., °C 0 2 3 4
Germination, %
60 93.4 93.4 93.4 93.1
70 67.6 67.4 66.7 65.9
80 46.2 45.7 44.6 42.8

 

99

References

Beke, J ., A. Vas, A. Mujumdar.1993. Impact of process parameters on the nutritional
value of convectively dried grains. Drying Technology 1 1(6): 141 5-1428.

Brekke, O. L., E. L. Griffin, Jr., G. C. Shove. 1993. Drying milling of corn artificially
dried at various temperatures. Transactions of the ASAE 16 (4) :761-765.

Brooker, D. B., F. W. Bakker-Arkema, C. W. Hall. 1992. Drying and Storage of Grains
and Oilseeds. Van Nostrand Reinhold, New York, NY.

Brown, R. B., G. N. F ulford, T. B. Daynard, A. G. Meiering, L. Otten. 1979. Effect of
drying method on grain corn quality. Cereal Chemistry 56:529-532.

Bruce, D. M. 1992. A model of the effect of heated-air drying on the bread baking quality
of wheat. J. of Agric. Eng. Res. 52:53-76.

Chang, C. H., M. R. Paulsen. 1989. Moisture distribution and starch recovery of
commercially dried corn. Paper No. 89-6525. ASAE, St. Joseph, MI.

Courtois, F., A. Lebert, A. Duquenoy, J. C. Lasseran, J .J . Bimbenet. 1991. Modeling of
drying in order to improve processing quality of maize. Drying Technology
9(4):927-945.

Emam, A., R. Stroshine, J. Tuite. 1981. Evaluating drying rate and grain quality
parameters of corn inbreds/hybrids: methodology. Paper No. 81-3 522. ASAE, St.
Joseph, MI.

Freeman, J. E. 1973. Quality factors affecting the value of corn for wet milling.
Transactions of the ASAE 16:671-678, 682.

Gustafson, R, R. V. Morey. 1981. Moisture and quality variations across the column of a
crossflow grain dryer. Transactions of the ASAE 24(6):]621-1625.

Kirleis, A. W., R. L. Stroshine. 1990. Effects of hardness and drying air temperature on

breakage susceptibility and dry-milling characteristics of yellow dent corn. Cereal
Chemistry 67 (6):523-528.

Lasseran, J. C., A. Le Bras. 1988. Improvement of drying techniques to better grain
quality for processing industries. Paper No. 88-323. Presented at the International
Conference on Agricultural Engineering, Ag Eng 88, Paris, France. March 2-5,
1988.

100

Le Bras, A. 1 982. Maize drying and its resulting quality for wet-milling industry. In:
Maize: Recent Progres in Chemistry and Technology. Academic Press, Inc., New
York, NY.

Lescano, C. L., D. E.,Tyrrell. 1987. Change in viability of corn during high-temperature
drying. Drying Technology 5(4):497-510.

Lowell, D. H. 1996. Quality of U. S. Agricultural Products. CAST Report, West Lincoln,
LA.

MacMasters, M. M., M. D. Finkner, M. M. Holzaptel, J. H. Ranser, G. H. Dungan. 1959.
Study of the effect of drying condition upon the composition and suitability for
the wet milling of artificial dried corn. Cereal Chemistry 36(3):247-260.

Mourad, M., M. Hemati, C. Laguerie. 1996. Kinetic study and modeling of the

degradation of the maize kernels quality during drying in fluidized bed. Drying
Technology 14(10):2307-2337.

Nellist, M. E. 1981. Predicting the viability of seeds dried with heated air. Seed Science
and Technology 9:439-455.

Peplinski, A. J ., M. R. Paulsen, R. A. Anderson, W. F. Kwolek. 1989. Physical, chemical,
and dry-milling characteristics of corn hybrids from various genotypes. Cereal
Chemistry 66(2):117-120.

Peplinski, A. J ., J. W. Paulis, J A. Bietz, R. C. Pratt. 1994. Drying of high-moisture corn:
change in properties and physical quality. Cereal Chemistry 71(2):]29-133.

Weller, C. L., M. P. Paulsen, M. P. Steinberg. 1987. Viability, harvest moisture and
drying air temperature effects on quality factors affecting corn wet milling. Paper
No. 87-6046. Am. Soc. Agric. Eng., St. Joseph, MI.

Weller, C. L., M. P. Paulsen, M. P. Steinberg. 1988. Correlation of starch recovery with
assorted quality factors of four corn hybrids. Cereal Chemistry 65(5):392-397.

Wicher, W R. 1961. Problems of the dry corn processor. Paper presented at the January
10, 1961 meeting of the Midwest Section of the American Association of Cereal

Chemists, Chicago, Illinois.

Zhang, 0., J. B. Litchfield. 1991. Corn quality distribution within a continuous crossflow
dryer. Transactions of the ASAE 36(6) :2516-2520.

Zhang, Q., J. B. Litchfield, J. Bentsman. 1992. Fuzzy prediction of maize breakage.
Journal of Agricultural Engineering Research 52:77-90.

101

CHAPTER 5. DISTRIBUTED-PARAMETER PROCESS MODEL FOR

GRAIN DRYING

Abstract

A process model is essential for the design of a control system. General-purpose
simulation models can not be directly used in a controller because of the large
computation requirement. A lump-parameter process model is simple, but has several
limitations in representing the grain-drying process. A distributed-parameter process
model of crossflow drying is developed in this Chapter. The model is more flexible and
accurate than a lumped-parameter model, and is of adequate simplicity for use in a

dryer-control system.

102

5.1 Introduction

The moisture content of grain at harvest varies randomly. A variation of 3-5 %
w.b. in the moisture content of maize entering a dryer is common. The discharge rate of a
grain dryer (i.e. the retention time of grain in the dryer) is controlled manually or
automatically in order for the outlet grain moisture content of the dryer to reach the set-
point. Automatic control should outperform manual control, and result in better grain
quality, higher energy efficiency and less manpower.

The grain drying process is difficult to control because of its non-linearity and long
delay. Much research has been conducted on the development of automatic controllers
but only few are in use on commercial dryers. There still exists a need to improve the
quality of control on grain dryers, especially with respect to the robustness of the
controller (i.e. working successfully over a wide range of operating conditions).

Grain quality is rapidly becoming of greater importance to the grain market. High-
temperature grain drying is a main factor in degrading the grain quality (Le Bras, 1982).
In practice, the drying-air temperature is determined by rule-of -thumb, and is seldom
changed during dryer operation. The quality of dried grain is uncertain since it fluctuates
with residence time of grain in the dryer. With the advancement in grain quality
modeling, it is possible to establish the optimum drying-air temperature based on the
quality requirement of the dried grain (Liu et al., 1997).

Automatic quality control is a promising method to alleviate grain-quality damage
during drying. However, quality control requires frequent change of the drying-air

temperature, thereby introducing an extra disturbance to the controller. The moisture

103

controller must be robust to any change in the drying-air temperature to be able to control
a dryer adequately.

The main objective of this series of three Chapters is to design a model-predictive
moisture controller for crossflow grain dryers. Special attention is paid to the robustness
of the controller, and its ability to work in concert with a grain-quality controller. A
distributed-parameter grain drying model is developed in this Chapter, the control

algorithm in Chapter 6, and the results of field tests of the controller in Chapter 6.

5.2 Review of Grain Drying Models

A process model is indispensable for process control. The dynamic characteristics
of a system can be explored with a process model, and subsequently the proper control
strategy can be selected. A process model is also essential in the design of the control
parameters, and in the preliminary testing and fine-tuning of a controller.

A number of general-purpose grain-drying models have been developed
(Cenkowski et al., 1993; Parry, 1985; Sharp, 1982); the authors’ main objectives were to
optimize dryer design. The best known general-purpose grain drying models are probably
the Michigan State University (MSU) (Bakker-Arkema et al., 1974) and the Thompson
(Thompson, 1968) models. The MSU model is based on the fundamental laws of
simultaneous heat and mass transfer, and results in four partial differential equations
(p.d.e.); it has been successfully used for the simulation of high-temperature grain dryers,
i.e. crossflow, concurrent-flow and counter-flow grain dryers (Brooker et al., 1992). The
Thompson model consists of a set of integral heat and mass balance equations and an

empirical thin-layer drying equation. Because of the assumption of temperature

104

equilibrium between the grain and air, the Thompson model is more suitable for low-
temperature drying simulation. The general-purpose grain drying models have most
recently been reviewed by Cenkowski et al. (1993).

The general-purpose drying models are rarely used directly in dryer control
because of the computation requirements. However, they are employed for developing
process models for drying.

Process models for grain drying can be categorized into: (1) lumped-parameter
(LP) models, and (2) distributed-parameter (DP) models. Lumped-parameter models
relate the outlet moisture content of the dryer to the inlet moisture content and the drying
time; the other factors, i.e. the drying air temperature, airflow rate, dryer dimensions and
ambient conditions are lumped into one or two coefficients, and are quantified by
computer simulation, field testing or on-line estimation (Moreira et al., 1990). A LP
model can be linear (Holtman and Zachariah, 1969; Eltigani, 1987), exponential (Forbes
et al., 1984; Merchant, 1985; Whitfield, 1988a) or non-linear(01esen, 1987). LP models
do not predict the moisture profile in the dryer.

Due to their simplicity, LP models are currently employed in some commercial
grain-dryer controllers (see Chapter 6). However, LP models have disadvantages: (1) LP
models are not self-contained (i.e. the values of the lumped parameters have to be
determined, and thus it is inconvenient to transfer 3 LP control model from one dryer
model to another); (2) LP models simplify a spatially-distributed process to a lumped
point, and thus do not represent the characteristics of the process very precisely,

especially not of a drying process with variable drying-air temperatures and airflow rates;

105

and, (3) LP models can not predict the spatial distribution of the moisture content of grain
in the dryer (note: knowledge which is necessary for grain quality).

Only Gui et al. (1988) used a distributed-parameter model to minimize overdrying
and/or underdrying and to optimize grain quality. The model is based on the p.d.e. model
but was not validated.

The objective of this Chapter is to develop a control-oriented, distributed-

parameter (c.o.d.) grain drying model for crossflow dryers.

5.3 Model Development

5.3.1 Elemental drying models (EDM)

In a crossflow dryer, drying-air traverses the grain column perpendicular to the
downward flow of the grain. The graincolumn can be viewed as a stack of rectangular
elements (Fig. 5.1). The thickness (Ax) of the elements is the same as the thickness of the

grain column, but the height (Ay) is so small that the differences of the air temperature

and humidity in the y direction are assumed to be negligible. The element drying model
(EDM) describes the drying process within one element; it can be extended to model the

full-size crossflow dryer.

(1) Assumptions and preliminaries

Assume the dryer is operated under standard environmental conditions, i.e. at
ambient temperature of 20°C and humidity ratio of 0.0087 kg kg'l (i.e. 60%). Further
assume that the air is heated by direct combustion of natural gas or liquefied petroleum,

106

x (thickness) Wet grain

y (height)

Drying-air in Drying-air out

Grain column elements

 

Dried grain

Fig. 5.1 Schematic of crossflow drying.

107

and reaches a humidity ratio of 0.0125 kg kg", regardless of the temperature increase of
the air.

When the drying-air passes through the grain column, the air temperature
decreases and humidity increases, following the process curve 1-2 shown on the
psychrometric chart in Fig. 5.2. If the energy used for the heating of the grain is
negligible, the curve lies on the iso-enthalpy line (i.e. 1-2’) and the process is defined as

an ideal process. The drying process is assumed to be ideal in this Chapter.

(2) Equilibrium moisture content (EMC) function in an ideal drying process
The EMC of grain is defined as the moisture content after the grain has been
exposed to a particular environment for an infinitely long period of time. For maize the

EMC can be described by the modified Henderson equation (ASAE, 1991a):

ln(l- RH) 1,

M =[—A(T+B)]( (5'1)

(3

where M. = EMC, % d.b.

T = drying-air temperature, °C

RH = relative humidity, decimal

A=8.6541x10'5, B=1.8634 and C=49.81 for maize.

In the ideal drying process 1-2’ illustrated in Fig. 5.2, the drying-air temperature
and humidity change from the inlet status at point 1 to the outlet status at point 2’, as does
the EMC of the grain. If the drying-air temperature in the ideal drying process is known,

the humidity of the air can be determined on the psychrometric chart or by the use

108

 

   
  

iso—enthalpy line and
ideal drying process

Humidity
ratio

 

heating of air

 

 

Dry-bulb temperature

Fig. 5.2 Drying processes on a psychrometric chart.

109

of a psychrometric model (ASAE, 1991b). Therefore, the EMC in the drying process can
be expressed as a single-variable function of the drying-air temperature.

The following procedure was used to obtain the EMC for an ideal drying process
at an inlet drying-air temperature of T r and inlet humidity ratio of 0.0125 kg kg". First,
starting from point 1 determined by the inlet drying-air temperature and humidity ratio,
move along the ideal drying process line, and find the corresponding humidity values at
several points. Second, use Eq. 5.1 to determine the EMCS at those points.

The empirical EMC function of the drying—air temperature in the ideal drying

process, obtained by regression analysis, has the form:

M : ea+bllk (5.2)

e

where Mc= EMC, % d.b.

TR: drying-air temperature, (1 .8*(T+273.16)), °R

T = drying-air temperature, °C

a,b =coefficients

Empirical equations of the form of Eq. 5.2 were obtained for maize for nine inlet
drying-air temperatures ranging from 40 t0120°C. The correlation coefficients R are all
higher than 0.99. The values for maize of a and b as functions of the inlet air temperature

(T.) were found to be:

a = —20.39 + 0.0757]

b = 12522.27 — 37.32Tl (5'3)

Note that Eq. 5.2 is valid for determining the EMC along the ideal drying process
line originating at the dry-bulb temperature range of 40-120°C, and for the absolute
humidity of 0.0125 kg kg".

110

(3) Derivation of the elemental drying models
The thin-layer drying rate of grain can be described by the following empirical
equation (Brooker et al., 1992):

d—Jl: = -k(M— M.) (5.4)

where M = grain moisture content, dec., d.b.

Me = EMC, dec., db.

1 = drying time, h

k = drying constant, h'l

The drying constant (k) is a function of the drying-air temperature, the EMC of
the temperature and the humidity. AS the drying-air traverses a grain column, its
temperature and humidity change, and therefore, the drying rate and EMC of the grain
also change across the grain column. In control problems, only the average moisture
content across the column is of concern. By integrating Eq. 5.4 across the grain column,
the average drying rate is obtained:

.1117 1

75:; -k(M—Mc)dx (5.5)

where

_ 1 . .
M = TT [,de , the average morsture content across the gram column, dec., d.b.

H = thickness of the grain column, m

111

Note that the grain moisture content M in the integrand is substituted by M , the average
moisture content across the grain column, in order to simplify the model. Physically, this
can be interpreted as the grain being unifonnly mixed in the x—direction of the column.
The drying constant k is a function of the drying-air conditions (Pabis and
Handerson, 1961 ):
k = ce’WR (5.6)
where for maize c = 1941, r = 5032.
An energy balance between the air and grain in a differential volume (dx dy 1)
gives:
caGa(1-dy)dT= hfg g G(1~ dx)dM (5.7)
where

dT = air temperature increment in the differential volume, °C

dM = moisture content change of the grain in the differential volume, dec. d.b.

c... = specific heat of dry air, J kg" °C'l

G. = dry airflow rate, kg h'1 rn’2

Gg = dry grainflow rate, kg dry product h"1 m'2

hfg = heat of moisture vaporization, J kg'1
The lefi-hand Side of Eq. 5.7 represents the energy transferred from the air to the grain,
while the right-hand side is equal to the energy required to evaporate the moisture. [Note:
the change of grain temperature is neglected]

Solving Eq. 5.7 for T=T1 at the air-inlet (i.e. x=0), yields:

AT“ h_f__gGg _d_Mx
afvx

112

(5.8)

where AT: T-T1.
The residence time dr in a differential element with a height of dy is obtained

from a mass balance. Thus:

pg
(11' = ‘5—05) (5.9)

R
where pg = grain density, kg (dry product) m'3.

Substituting Eqs. 5.2, 6, 8 and 9 into Eq. 5.5, and integrating the right-hand Side
of Eq. 5.5 (see Appendix 5.1), results in the one-dimensional crossflow drying model
which expresses the change in the average grain moisture content in the grain column
(Eq. 5A.5).

If the average inlet moisture content of a bed element is 117,, the height of the

element is AY, the inlet air-temperature is TR) and the EMC at air inlet is Mel ,and

assuming M - M.,l z M, — M.,I within the element, integrating of Eq. 5A.5 results in the

following expression for the outlet moisture content ( 1171]) of the element:

M 417 k.(A7.-M...)AY
f I Gg(1/pg +k1C'qA—jl — kchqMcl)

 

(5.10)

5.3.2 Full-size dryer model
(1) Drying model
Consider the grain column as a stack of elements (see Fig. 5.1). The outlet

moisture content of the top element is found by applying the elemental drying model of

Eq. 5.10 by setting M, equal to the inlet moisture content of the dryer; the calculation is

113

repeated for the next element, using the outlet moisture content of the element above it as
the inlet moisture content of the repeated element. After applying Eq. 5.10 to all the
elements in the grain column, the spatial moisture distribution in the column is obtained.
The model can also be applied to the cooling section (the overall moisture removal in the

cooling section is minor (i.e. 0.5-0.8%».

(2) Inverse drying model
Implementing a control action, an inverse drying model is needed to find the

appropriate grain discharge rate such that the grain is dried to the set-point at the outlet of

the dryer. If the moisture content of the grain is A7” at a distance Y from the outlet of the

drying section, the grain discharge rate (i.e. dryer capacity) for the grain to be dried to the

set point (i.e. M,) can be predicted by Eq. 5A.7 (see Appendix 5 .1), or:

 

G 4'10"), 5 11
X — A7! — Mel — — ( . )
c3 ln iii" M I +c4(M( - My!)
y: e

5.4 Validation of the models

The Zimmerman VT1210 and VT4036 grain dryers manufactured by the ffi Co.,
Indianapolis, Indiana, were chosen as reference dryers. Both dryers are crossflow,
cylindrically shaped dryers with grain tum-flow device midway in the drying sections.
The specifications of the dryer are listed in Table 5.1

The outlet MC of both dryers was modeled using the cod. model of Eq. 5.10,

114

Table 5.1 The specifications of the Zimmerman VT1210 and VT4036 dryers.

 

 

Dryer model . VT1210 VT4036
Overall height, m 17.07 22.89
Outside dryer diameter, m 3.56 5.18
Columns widths, m 0.32 0.32
Column cross-sectional area, m2 3.25 4.89
Drying section

length, m 8.76 17.22

airflow rate, m3/h 97,222 291,134
Cooling section

length, m 3.04 5.76

airflow rate, m3/h 33,685 97,560
Drying-air temperature, 0C 93.3 98.9

Rated capacity (at the outlet, moisture
removal from 20% to 15%), kg/h 27x103 90x103

 

following the procedure described in section 5.3.2. The values of the physical property

parameters for maize are: pg = 560 (dry matter) kg'lm3, ca = 1.007 U kg"k’l, cg: 2.17 k]

kg"k'l (Brooker et al. 1992). The heat loss due to the heating of the grain was accounted
for in the calculations of the heat of vaporization, i.e.:
hf, = 2427 + 2.17 x 35/(M, — 0.183) U kg" (512)
where the temperature increase of the grain in the drying section was assumed to be 35°C,
with moisture removal from M,- to 0.183 kg kg'l d.b. (i.e. 15.5% w.b.).
The moisture removal in the cooling section of the dryer was assumed to be 0.5%,
and was not simulated. The ambient conditions were assumed to be 20°C, 60% relative

humidity, with an initial grain temperature of 20°C.

115

Tables 5.2 and 3 show the cod. model data and the values calculated with the

p.d.e. grain drying simulation model. [Note: the thin-layer drying model of Li et a1.

(1984) was employed to predict the drying rate of maize in the p.d.e. model.]

Table 5.2 Predicted capacity of Zimmerman VT1210 maize dryer using the c.o.d.

model and p.e.d. model.

 

 

 

 

 

Drying air temp., °C 85 95 105

lnlet M.C., % w.b. 20 25 3O 20 25 3O 20 25 30

Capacity by c.o.d. 22.69 11.96 8.32 26.87 14.53 10.07 32.27 17.33 11.99
model, 103 kg/h

Capacity by p.d.e. 22.46 1 1.94 8.17 26.32 14.17 9.69 30.04 16.38 1 1.26
model, 103 kg/h

Relative difference, % -1.6 1.7 1.8 2.1 2.5 3.9 7.4 5.8 6.3

 

 

 

 

 

 

 

 

 

 

Table 5.3 Predicted capacity of the Zimmerman VT4036 maize dryer using the c.o.d.

model and p.d.e. model.

 

 

 

 

 

Drying air temp., °C 85 95 105

lnlet M.C., % w.b. 20 25 30 20 25 30 20 25 30

Capacity by c.o.d. 60.78 33.82 23.31 74.23 41.12 28.23 88.83 49.15 33.68
model, 103 kg/h

Capacity by p.d.e. 67.43 35.99 24.72 76.16 42.84 29.34 91.55 49.87 34.04
model, 103 kg/h

Relative difference, % -9.9 -6.0 -5.7 -2.5 -4.0 -3.8 -3.0 -1.4 -1 .l

 

 

 

 

 

 

 

 

 

 

Table 5.2 shows that the cod-predicted capacities of the VT1210 dryer at 85

t0105°C and inlet moisture contents from 20 to 25% w.b. are slightly higher than those

predicted by p.d.e. model. The maximum difference is 7.4%. The results for the VT4036

116

are listed in Table 5.3; the maximum difference between the cod. and p.d.e. calculated

capacities is -9.9%.

5.5 Discussion and Conclusions

The agreement between the cod. model and p.d.e. model is remarkable
considering the fundamental difference between the two models. The c.o.d. model can
be viewed as the averaging form of the p.d.e. model across the grain column, changing
the two-dimensional p.d.e. model to an one-dimensional model. The reduction in
complexity of the cod. model is reflected in the number of Fortran-code lines required
for the VT1210 dryer, i.e. 67 lines for the cod. model and 1750 lines for the p.d.e.
model.

The agreement between the results of the cod. model and the p.d.e. model
implies that although the c.o.d. model is simple, it represents the characteristics of the
crossflow drying process well. The c.o.d. model retains the advantages of a general-
purpose model, i.e. it is self-contained, provides spatial moisture information on the grain
column, and is flexible for modeling various drying processes.

In conclusion, the cod. drying model has adequate precision, simplicity and

flexibility for implementation on a dryer controller.

117

Appendix 5A: One-dimensional Crossflow Drying Model
Substituting Eqs. 5.2 and 5.6 into Eq. 5.5 yields:

dM 1 ”
dr— — E —(Mce WT" —0.016e“‘("b’fl” )dx (5A1)
0

The exponential terms in the integrand make it impossible to integrate
analytically. Linear approximation of the exponential terms results in:

1—exp(r/T —r/618)
-rlr. z w... H RI AT 5A.2
e e [ TR, —618 R] ( )

 

and

1—exp[(r—b)/TRl —(r-b)/618)]
Tm —618

 

e—(r—b)/'I‘R ze—(r—bflTR.“ +

A7,] (5A.3)

where ATR =TR-TR1.

As shown in Fig. 5A.1, the linear approximation of Eq. 5A.2 is a line passing
through two points on the curve of exp(-r/TR), namely at inlet air temperature TR, (i.e.
100°C) and the intermittent temperature of 61 8°R (i.e. 70°C). A similar explanation can
be given for Eq. 5A.3.

Substituting Eqs. 5A.2 and 5A.3 into 5A.] yields:

d

1” __ ..
7: E]. [k]Me””'“(1+clATR)—k1M,,(1+c2ATR)]dx (5A.4)
0

From Eqs. 5.8, 9, and since ATR =1 .8 AT, integration of Eq. 5A.4 across the grain

column yields the one-dimensional crossflow drying model:

118

 

6.E-04

5.15-04 1

4.E-04 1

3.E-04 F

    
 
  

exp(-r/TR)

Function value

2.E-04
approx. by Eq. A52

l.E-04 -

 

 

 

0.E+00 ‘ ‘
50 60 70 80 90 1 00

Drying-air temp., °C

Fig. 5A.] Linear approximation of Eq. 5A.2 at inlet drying-air temperature
of 100°C (or 672°R).

119

dz

 

 

1 _ _
Gg (— — klclqM + klcquel) = —kl (M —- Mel) (5A.5)
p. dy
where
1—exp(r/TRl -r/618)
C =
' TR, —6l8
_1—exp[(r—b)/TR, —(r-b)/618)
CZ ‘ TR, -618
= h/g (0.9H)
COGO
kI =ce"”"‘I

M,I = 0.019”+"/T’“

If the height of a drying section in a dryer is Y, the solution of Eq. 5A.5 for the

drying section is:

 

Hf —117€l _ _ pgl’
c31n(A7 —}l7 )+c4( f—Mi)=—kl~E—=—klr (5A.6)
1 e1 g
-k]ng
c ln(——z— )+c (M -M,)

where

C3 =1+ kl (cl '62 )pngel
C4 : klclpgq

120

Symbols

0, b = coefficients of Eq. 5.2, defined in Eq. 5.3
c = coefficient for drying constant in Eq. 5.6, 1941 for maize
cl , c2 = constants in Eq. 5A.5

cl , c2 = constants in Eq. 5A.7

ca = specific heat of dry air, J kg'1 °C’l
G = flow rate, kg (dry matter) h'1 m'2
H = thickness of the grain column, m
hfg = heat of vaporization, J kg'l

k = drying constant, h'l

k1 = drying constant at air inlet, h'l

M = grain moisture content, dec., d.b.

M = average grain moisture content across the grain column, dec., d.b.
Me = EMC, dec., d.b.
Me, = EMC at air inlet, dec., d.b.

q = constant in Eq. 5A.5

r = coefficient for drying constant in Eq. 5.6, 5032 for maize
RH = relative humidity, decimal

T = drying-air temperature, 0C

T1 = inlet air temperature, 0C

T R = drying-air temperature, °R

TR] = inlet air temperature, °R
x, y = coordinates, m

Y = height of the drying section, m

AY = height of the grain element, m

r = drying time, h

pg = grain density, kg (dry product) m'3

Subscripts:
1 = air inlet
a = air

e = equilibrium

f = final, outlet

g = grain

i,o = initial

R = temperature, °R
t = target value

121

Abbreviations

c.o.d. = control-oriented distributed-parameter
DP = distributed parameter

EMC = equilibrium moisture content

LP = lumped parameter

p.d.e. = partial differential equation

122

References

ASAE Standards, 38th Ed. 199la. D245.4-Moisture relations of grains. Am. Soc. Agr.
Eng., St. Joseph, MI.

ASAE Standards, 38th Ed. 1991b. D271 .2-Psychrometric Data. Am. Soc. Agr. Eng., St.
Joseph, MI.

Bakker-Arkema, F.W., L. E. Lerew, S. F. DeBoer, M. G. Roth. 1974. Grain drying
simulation. Research report 224. Agr. Exp. Sta., Michigan State University, East
Lansing, MI.

Brooker, D. B., F. W. Bakker-Arkema, C. W. Hall. 1992. Drying and Storage of Grains and
Oilseeds. Van Nostrand Reinhold, New York, NY.

Cenkowski S., D. S. Jayas, S. Pabis. 1993. Deep-bed grain Drying - A review of
particular theories. Drying Technology 1 1(7): 1 553-1581 .

Eltigani, A. Y. 1987. Automatic control of commercial crossflow grain dryers. Ph. D.
Dissertation, Michigan State University, E. Lansing, MI.

Forbes, J. F., B. A. Jacobson, E. Rhodes, G. R. Sullivan. 1984. Model based control
strategies for commercial grain drying systems. Canadian Journal of Chemical
Engineering 62:773-779.

Gui, X. Q., J. Bentsman, J. B. Litchfield. 1988. Control of grain drying: State of the art
and open problems. ASAE Paper No. 88-3502. Am. Soc. Agr. Eng., St. Joseph,
MI.

Holtman, R. D., G. L. Zachariah. 1969. Computer control for grain dryers. Transactions
of the ASAE 12:433-437.

Le Bras, A.1982. Maize drying and its resulting quality for wet-milling industry. In:
Maize: Recent Progressing Chemistry and Technology, ed. by G. E. Inglett.
Academic Press, Inc., New York, NY.

Li, H. Z., R. V. Morey. 1984. Thin-layer drying of yellow dent corn. Transactions of the
ASAE 27(2):581-585.

Liu, Q., F. W. Bakker-Arkema. 1997. Stochastic modelling and control of grain quality in
crossflow dryers. ASAE Paper No. 97-6030. Am. Soc. Agr. Eng., St. Joseph, MI.

Marchant, J. A. 1985. Control of high temperature continuous flow grain dryers.
Agricultural Engineer 40(4): 145-149.

123

Moreira, R. G., F. W. Bakker-Arkema. 1990. A feedforward/feedback adaptive controller
for commercial cross-flow grain dryers. J. agric. Eng. Res.: 107-116.

Olesen, H. T. 1987. Controlling drying percentage. Chapter 3, Appendix E, in Grain
Drying. Innovation Development Engineering APS, Thisted, Denmark.

Pabis, S., Henderson S. M. 1961 Grain drying theory: II. A critical analysis of the drying
curve of shelled maize. J. agric. Eng. Res. 6:272-277.

Parry, J. C. 1985. Mathematical modeling and computer simulation of heat and mass
transfer in agricultural grain drying: a review. J. agric. Eng. Res. 32(1):1-29.

Sharp, J. R. 1982. A review of low temperature drying simulation models. J. agric. Eng.
Res. 27(3):]69-190.

Thompson, T. L., R. M. Peart, G. H. Foster. 1968. Mathematical simulation of corn drying -
A new model. Transactions of the ASAE 11(4):582-586.

Whitfield R D. 1986. An unsteady-state simulation to study the control of concurrent and
counter-flow dryers. J. agric. Eng. Res. 32: 1 71-178.

Whitfield R. D. 19883. Control of a mixed-flow drier. Part 1: Design of the control
algorithm. J. agric. Eng. Res. 41 :275-287.

Whitfield R. D. 1988b. Control of a mixed-flow drier. Part 2: Test of the control
algorithm. J. agric. Eng. Res. 41:289-299.

124

CHAPTER 6: DESIGN OF CONTROL ALGORITHM

Abstract

The grain drying process features non-linearity, long delays and large
disturbances. Model-based control can successful at controlling processes with those
features. In this Chapter, a model-predictive control system is developed for crossflow
drying of maize. The control system has afeedforward loop (i. e. the predictive model and
the optimizer for the control actions) and an indirect feedback loop (i. e. the parameter
estimator and modifier). T we algorithms are proposed for the optimizer. Simulation tests
show that the controller performs well over a wide range of drying conditions, and with

disturbances from the inlet moisture content of the grain, the drying-air temperature and

the sensors.

125

6.1 Introduction

The fundamental requirements of a grain dryer controller are no different from
those of other control systems, i.e.: stable-the system must not oscillate wildly; accurate -
the output moisture content must be close to the desired value; and, robust - it must
perform successfully over a wide range of conditions.

A special strategy has to be found to meet the above requirements because grain
drying is unique: (1) the drying process takes hours, the output of the process (i.e. the
moisture content and quality of the grain at the outlet of the dryer) is determined
collectively by the control actions taken during the drying process; (2) the major
disturbance (i.e. variation in the inlet grain moisture content) enters the system at the inlet
of the dryer, its effect will not be detected at the outlet of the dryer until the grain exits the
dryer; and (3) the drying process is subject to disturbances from ambient conditions, and
from the possible change in genotype and physical properties of the grain.

For a sophisticated process such as grain drying, only a control algorithm which
addresses the dynamic characteristics of the process has a chance for success. The
control-oriented, distributed-parameter (c.o.d.) model developed in Chapter 5 is able to
provide this type of information of the system to the controller.

In this Chapter, a model-predictive control algorithm for crossflow grain dryer is
developed. The performance of the controller is extensively investigated using
simulation. Special attention is paid to the robustness of the controller and its ability to

work in concert with a grain-quality controller.

126

6.2 Process Characteristics and Review of the Control Strategies

In continuous-flow dryers, grain loses most of the moisture when moving through
the drying section; and is usually cooled in the cooling section by ambient air before
leaving the dryer. The moisture content of grain entering a dryer may vary with time, and
thus the required retention time in the dryer changes. It is impossible to control the dryer
such that all of the grain is dried to the set point; when grain with a high initial moisture
is dried to the set point, the grain with a lower initial moisture content has probably been
overdried. The objective of a moisture controller is to minimize the deviation of the outlet
grain moisture content from the set point. Although under-/over-drying is inevitable, it is
desirable to have the same amount of grain overdried as underdried.

The residence time of grain in a high-temperature dryer ranges from one half hour
to several hours, depending on the initial grain moisture content and on the dryer
parameters. As the moisture removal in the cooling section is small, the retention of grain
in the cooling section is considered as the dead-time of the process. The response of the
system to a control action (i.e. a change in grain discharge rate or drying-air temperature)
will not be Observed at the outlet of the dryer until one dead-time later; the transition
period will continue as long as the grain presently in the dryer has not been replaced.
Thus, the outlet grain moisture content is dependent upon the accumulated effects of the
control actions during the retention of the grain in the dryer.

The relationship between the controlled variable (i.e. the grain moisture content
decrease in the dryer) and the manipulated variable (i.e. the grain discharge rate and/or
the drying-air temperature) is non-linear. The non-linearity stems from the fact that grain

dries faster in the high moisture range than in the low moisture range.

127

The long time delay and non-linearity make the grain drying process difficult to
control. The time delay severely limits the performance of conventional feedback control
systems (Perry, 1997; Shinskey, 1994).

Marchant (1985) examined classical proportional and integral (PI) feedback
control Of continuous-flow grain dryers and showed that the stability and response speed
of the controller are unacceptable. Whitfield (1986) tested PI control on concurrent-flow
dryers by simulation and concluded that the control parameters require tuning for
different inlet moisture contents because of the non-linearity of the system; by
linearnizing the system, the stability of the control was much improved, but the response
remained slow.

To speed up the response, McFarlane et a1 (1991) added a first-order lag
feedforward term to the Whitfield controller. The peak error in the outlet MC of a mixed-
flow dryer was approximately half of that occurring with the feedback-only control
system. The oscillating behavior of the original feedback controller was prevented by
varying the sampling period in inverse proportion to the discharge rate. The resulting
dependency on the drying-air temperature required changing the controller gain to
compensate for the temperature changes.

Bruce et al. (1993) improved the McFarlane control system performance for step
changes in the drying-air temperature. Both feedforward and feedback gains were
expressed as functions of temperature in order to adjust the discharge rate of the grain
whenever a change occurred in the drying air temperature. The control strategy during the

start-up period of grain dryer was also addressed. The procedure of applying the Bruce

128

algorithm to dryers other than for which the control algorithm was designed, was
described.

Platt et al. (1992) studied a feedforward-feedback control for crossflow dryers.
The feedforward control was based on a mass balance on the water vapor in the air. The
P1 with scheduled gain control was used for feedback. The disadvantage of this control
type is that the absolute humidity values of the inlet and outlet drying air have to be
measured intermittently.

Courtois (1995) investigated various control strategies theoretically and
experimentally for a mixed-flow dryer, with an inlet moisture content of maize as high as
45% w.b., and residence time as long as 2-5 hours. Classical PID controllers showed poor
stability. The non-linear PI feedforward plus feedback control performed best.

Zhang (1993) implemented fuzzy control on a laboratory grain dryer with the
objective of both controlling the outlet moisture content and the breakage susceptibility of
the maize through manipulation of the drying-air temperature and the discharge-auger
rpm. He concluded that fuzzy logic control may be superior to conventional control for
controlling grain quality.

Model-based control (MBC) has been a significant development in process
control in last two decades. It is especially effective for deadtime-dominant and nonlinear
processes. Forbes et a1. (1984) and Eltigani et al. (1989) developed model-based
controllers for grain dryers. In both, the control action is based upon a process model and
the so-called “pseudo” inlet grain moisture content. A model parameter is updated on-line
according to the difference between the predicted and measured outlet moisture contents.
This type of process model intrinsically compensates for the space time (i.e. in the drying

129

section) and pure dead-time (i.e. in the cooling section) provided the residence time of the
grain in the dryer is accurately estimated. Forbes et al. (1984) established that the model-
based controller is superior to three other control algorithms investigated.

The current control algorithms used in commercial grain-dryer controllers can be
classified as: (1) feedforward plus feedback (FF/F B) (McF arlane, 1991; Oleson, 1987),
and (2) model-based control (MBC) (Forbes et al.,1984, Eltigani et al. 1989). Both types
have feedforward and feedback loops, and require an inlet and an outlet moisture sensors.

The following conclusions can be drawn from the literature review: (1) classical
feedback control is not adequate to control the grain-drying process; (2) an inlet moisture
sensor and a feedforward loop are necessary for adequate response of the controller; and,
(3) the MBC and FF/F B algorithms are effective in controlling the grain moisture of
commercial dryers.

Lumped-parameter drying models are employed in the control algorithms
reviewed above. However, the limitations of lumped-parameter models (see Chapter 5)
negatively affect their performance. With the successful development of the c.o.d.
(control-oriented and distributed-parameter) process model in Chapter 5, new control

algorithms should be investigated. This is done in this Chapter.

6.3 Model-predictive Control Strategy

Model-predictive control or MPC was first employed in the oil refinery industry in
the late seventies. Since then successful commercial applications have been reported in a

variety of industrial processes (Bosley et al., 1991; Perry, 1997). A comprehensive survey

130

of the history and theoretical derivation of model-based predictive control methods can be
found in Camacho et al. (1995) and Garcia et al (1989).

In MPC, a dynamic model of the process is used to predict the outputs over the
next n sampling periods (prediction horizons); an optimizer is employed to determine the
control action. The optimization is repeated each sampling period with up-to-data
information about the process. The main advantages of MPC are: (l) the control strategy
is especially suitable for processes with long-delay times or dead-times, and for non-
linear systems, or for systems with inequality constraints; (2) the performance is
Optimized by an on-line optimizer; and (3) the process model and control strategy can be
updated on-line to compensate for changes in the process conditions or constraints. Thus,
MPC is a perfect candidate for grain dryer control. The disadvantage of MPC is the large
computation requirements for process modeling and control optimization (this is hardly
relevant anymore since the microprocessor costs are rapidly decreasing).

The concept of MPC for grain dryers is shown on Fig. 6.1. The “Drying Model”,
“Inverse Drying Model” and “Optimizer” form a feedforward loop. The inlet grain
moisture content and the drying-air temperature are measured for each sampling time; the
moisture distribution in the dryer, including at the outlet of the dryer, is predicted by the
“Drying Model”. Based on this information, the “Inverse Drying Model” predicts the
necessary flowrate for the grain currently in the dryer. The actual grain discharge rate for
control of the dryer during a sampling period is the optimized rate, taking into account the
flowrate of each bed, thereby minimizing the control error during the prediction horizon.

The “Parameter Estimator and Modifier” constitutes an indirect feedback loop; the
outlet moisture content predicted by the “Drying Model” is compared with the moisture

131

lnlet MC;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Discharge Drying-air Disturbance
rate for next Temperature Measured
)1 Sampling Optimized . Outlet MC
Periods Discharge . Drying
Set point I‘ Rate Process
nverse
—~ - —r_—»
Drymg Model 1 Predicted
Drying ‘ Outlet MC
.__. Model
Moisture Distribution I
in the Dryer Parameter Mode Error

 

 

 

 

 

 

Estimator/Modifier ‘

 

Fig. 6.1 Model-predictive control of grain dryers.

132

content to establish the model error; if not zero, the model parameters in the “Drying
Model” and the “Inverse Drying Model” are adaptively modified by the “Parameter
Estimator and Modifier” according to the size Of the model error.

Each component of the controller is described in the following sections.

6.3.1 Feedforward loop

The grain column in a crossflow dryer is conceptually divided into stacked beds of
identical dimensions. The sampling period equals the residence of the grain in a bed. It is

supposed that there are n beds in the drying section and m beds in the cooling section.

(I) Drying model

Eq. 5.10 and the procedure described in section 5.3.2 in Chapter 5 are employed
to predict the moisture distribution in the dryer during each sampling period. The inlet
moisture content of the dryer (i.e. the inlet moisture content at the top of the bed) is
measured by the moisture sensor, and its value is updated every sampling period. It is

assumed that a total of 0.5% of moisture is removed in the m beds in the cooling section.

(2) Inverse Drying Model

Eq 5.11 in Chapter 5 is applied to calculate the discharge rate for each bed. M y, is

the inlet moisture content of bed i, and Y is the distance from the top of bed i to the end

of the drying section.

(3) Optimizer

133

For each bed element, the calculated grain discharge rate is usually different. The
grain discharge rate during the next sampling period is calculated by the “Optimizer”.
Two optimizing strategies were investigated: (a) zero average error (ZAE), and (b) least
square error (LSE).

(a) Zero Average Error (ZAE)

The objective of the ZAE optimization is for the average control error during the
next n sampling periods to be equal to zero, or the same amount of grain to be overdried
and underdried.

If the inlet moisture content of grain in bed i is M, , and the actual discharge rate
of the dryer is G for the next i sampling periods, the final MC at the end of the drying

section of the grain currently in bed i can be estimated by:

(iAY)
M = M —aEg——

a . G (6.1)

where
M fl = final moisture content after i sampling periods of grain currently in bed i,

where i = 1,2, ..., n is the index of the bed numbered from the outlet to the
inlet of the drying section, dec., d.b.

M, = inlet moisture content of grain in bed i, dec., d.b.
pg = grain density, kg (dry matter) rn'3
AY = height of one bed, m

p g(iAY) / G = time for grain moving down from bed i to the end of drying

section, h

134

a = constant of the dryer depending upon dryer model and operating conditions,
dec., d.b. h"
Given the target moisture content, M, , the necessary discharge rate, G, , i.e. the
discharge rate for the grain currently in bed i (being dried to the target value at the end of

the drying section) is defined by:

iAY)
M = M -QL

. . G (6.2)

If the actual discharge rate of the dryer G is not equal to the required discharge

rate G, during the next i sampling periods, the offset (error) of the final moisture content

of the grain currently in bed i will be:
i i
e, = M, —Mfl :p‘aAY(G—G) (6.3)

The actual error caused by using G instead of G, for grain in bed i is one ith of e,

because G is applied for only one sampling period, and is updated every sampling period.
The average error caused by using G during the next sampling period for the grain in all

beds is:

 

1 l l
e=;;e,/i= n §(6_E) (6.4)

 

(6.5)

(b) Least Square Error (LSE)

135

The average square error resulting by using G in the next sampling period for

grain in all the beds is :

—.(— — —°>2 (6.6)

= o (6.7)

which yields:

 

G = '7‘ (6.8)

Comparing Eqs 6.5 and 6.8, it is clear that the LSE algorithm assigns higher
weights to the discharge rates of the grain beds closest to the inlet of the dryer (i.e. in
sequence of n, ...,i, H, 1 from inlet to outlet), whereas the ZAE algorithm assigns the

same weight to each bed.

6.3.2 Feedback loop (Parameter Estimator/Modifier)

The model error is defined as the difference between the measured and the
predicted outlet moisture contents of the dryer. If the model error is not equal to zero

(which is most frequently the case), the drying constant kl in the drying model (Eqs. 5.10
or 5.1 l) is modified by multiplying by a multiplier y , i.e.:
k 1m = ykl (6'9)

where k,“ = modified drying constant, h'1

136

kI = ce"”"‘I , theoretical drying constant, h'1 (for maize c = 1941 and r = 5032,
Pabis and Handerson, 1961)

Tm = inlet air temperature, °R

y = multiplier of the drying constant

If the initial moisture content of the grain at the inlet of the dryer is called M, , the

measured outlet moisture content M f , and the total residence time of the grain in the

drying section (not including the cooling section) 2', the estimated drying constant (see

Eq. 5A.6 in Chapter 5) is:

 

 

 

— M
k” = r (6.10)
l (cl—62)pngeer+clpgq(Mf_Ml)+T
where
M l M’ '— M“
" - n MI — Mel
_ l—exp(r/TRl -r/618)
6‘ ‘ TR, —618
c =1-exp[(r—b)/Tm—(r—b)/618)
2 Tin-618
= hjg(0.9H)
caGa
kl :ce—r/I'R.

M,l = 0.01e"”’”"“

The average of the drying-air temperature during the residence of the grain in the

drying section should be used in the calculation of the coefficients cI , c2 and M,I in Eq.

6.10 if the drying-air temperature changes during that period.

The estimated multiplier y is:

137

kt’
ye =—'— (6.11)
In

The predicted multiplier is recursively modified by:
7=7’+fl(r"-r’) (6.12)

where y = predicted multiplier for current sampling period
7 I = multiplier used in last sampling period
y e = estimated multiplier from Eq. 6.11

B = filter factor

The filter factorB is determined by tuning of the controller, and is discussed in the

next section.

6.4 Simulation Tests and Tuning of the Controller

6.4.] Virtual grain dryer and controller

A virtual grain dryer was programmed in LabVIEW (Johnson, 1997) based on the p.d.e.
drying model. Fig. 6.2 shows the control panel of the virtual dryer. An arbitrary inlet
grain moisture pattern can be introduced to the dryer at the MC;n entry. The drying-air
temperature and the dryer capacity (i.e. grain discharge rate) can be controlled manually
or by a controller. The inlet/outlet moisture contents and other controlled variables are
traced and printed in real time. The virtual dryer was used as a test bench in the design of
the controller.

Two control algorithms, i.e. ZAE and LSE, were implemented in LabVIEW to

control a virtual Zimmerman VT1210 dryer. The VT1210 has been described in Chapter
138

 

4.09

Manual Contol Knob

 

Fig. 6.2 Control panel of the virtual grain dryer for control test.

139

5; and its specifications are listed in Table 5.1.

To implement the control algorithms, the grain column in the dryer was
conceptually divided into 20 identical beds, 12 in the drying section and 8 in the cooling
section. The sampling time of the controller was set equal to the residence time of the

grain in one bed, i.e. 5-10 min, depending on the discharge rate.

6.4.2 Feedforward control

The response of the controller to step changes in the inlet moisture content and the
drying-air temperature was tested by simulation, assuming the measured outlet moisture
content equaled the value predicted by the process model. Because the model error was
zero (i.e. the measured MC equals the predicted MC), the feedback loop did not take
effect, and thus the responses in Figs 6.3 to 6.5 show the performance of the feedforward
algorithms only.

Fig. 6.3 shows the simulated performance with the ZAE algorithm to a 5% w.b.
step change in the inlet grain moisture content. Responding to a step-up of the inlet
moisture content, the outlet moisture content started to decrease after 8 sampling periods
(i.e. the residence time of grain in the cooling section); when the step change effect
reached the outlet of the dryer, the outlet moisture content responded with a step increase,
changing from overdrying to underdrying; finally the outlet moisture content came back
to the set point. The total transition period lasted approximately one residence time of the
grain in the drying section. About the same amount of grain was overdried and
underdried, i.e. the average control error is close to zero (which is the intention Of the
ZAE algorithm).

140

4O

 

 

 

 

 

 

 

 

 

 

 

 

 

—°I
3 '7 I
e\° = 3 inlet MC
g 30 ' 5 L :
3 : i
i: r-—— :.__._:
8 E 3
QB) 20 —': get MC /outlet MC ‘—_J
as L H A A L A
'5 ‘1' V V V
2 10 l l l l 4 I l
0 500 1000 1500 2000 2500 3000 3500
Time, min
9: .9 120
a 8
3° 80 WM
53 B 40 .
8 E A
'5 °\° 0 r l I 1 L l 41
0 500 1000 1500 2000 2500 3000 3500

Time, min

Fig. 6.3 Simulated response of the feedforward control to step changes in the

inlet moisture content with ZAE optimization (drying-air
temperature = 85 °C).

141

Discharge rate,
% rated capacity

Moisture content, % w.b.

 

 

 

 

 

 

 

 

 

 

 

 

40
inlet MC
30 ' i :
20 —‘: t get MC /outlet MC '———
w v JV 47—4—
1 0 l l J l l L
0 500 1000 l 500 2000 2500 3000
Time, min
80
0 1 l r 1 r 1
O 500 1000 l 500 2000 2500 3000
Time, min

Fig. 6.4 Simulated response of the feedforward control to step changes in the

inlet moisture content with LSE optimization (drying-air
temperature = 85°C).

142

A
O

 

1 II drying-air temp.,

l I o
i , I C

W—

fl
O
O

 

 

 

 

    

 

 

Drying-air temp. and
grainflow rate

 

 

 

 

 

 

 

6O _
gramflow rate,
% of rated capacity
20 l L J_ l l l l
0 100 200 300 400 500 600 700 800
Time, min
16
L2) set point outlet MC, °/o w.b.
5
14 J .L L l 1 l l
O 100 200 300 400 500 600 700 800
Time, min

Fig. 6.5 Simulated response of the feedforward control to step changes in the
drying-air temperature with ZAE optimization (inlet grain moisture
content = 20% w.b.)

143

A similar (but flipped) response pattern was found for a step-down of the inlet
moisture content. The moisture distribution during the transition periods was (again)
symmetric around the set point.

No significant differences were found in the response patterns to the 5% step
changes at different levels of the inlet moisture content, except that the transition periods
lasted longer in the higher inlet moisture range than in the lower range because the
residence times of the grain in the dryer were different. This implied that the controller
performed well over a large range of inlet moisture contents.

The discharge rate (i.e. the manipulated variable) of the dryer is also shown in Fig.
6.3. At each step change in the inlet moisture content, a sharp response in the discharge
rate occurred.

The response of the controller with LSE optimization to a step change in the inlet
moisture content is illustrated in Fig. 6.4. Although the overall pattern is similar to that in
Fig. 6.3, the following differences were found: (1) the response pattern of LSE algorithm
is not as symmetric as that of the ZAE algorithm, i.e. more grain is overdried due to a step
up in the inlet moisture content, and more is underdried due to a step down; (2) the curve
of the outlet moisture content in Fig. 6.4 is straighter than in Fig. 6.3 (which curves in to
the set point); the total area between the response curves and the line of the set point are
smaller in Fig. 6.3 than in 6.4; and thus the ZAE controller is better than LSE type in
terms of the control error; (3) the reaction of the control variable (i.e. the grain discharge
rate) is smoother for the LSE algorithm than for the ZAE algorithm (which, however, is
more favorable in practice because there will be less chance to reach the lower or upper
limits of the unloading system).

144

Fig. 6.5 shows the response of ZAE optimization to step changes in the drying air
temperature. There was an immediate response in the discharge rate to each step change
in the drying temperature. The disturbance in the outlet moisture content is hardly
noticeable ( i.e. less than 0.3% w.b. offset to a 20°C step change in the drying-air
temperature) in the temperature range of 80-120° C. This implies that the temperature

compensation in the drying model was effective.

6.4.3 Feedback control

The p.d.e. drying model employed in the virtual dryer is different from the c.o.d.
process model implemented in the controller (see Chapter 5). Fig. 6.6 compares the outlet
moisture contents predicted by the p.d.e. model and the process model without parameter
modification. The difference between the outlet moisture contents is the model error of
the process model, i.e. -0.71% w.b. at the inlet moisture content of 20% w.b., -O.46% w.b.

at 25% w.b. and 0.2% at 30%w.b..

The filter factor B (in Eq. 6.12) is found by controller tuning. Fig. 6.7 shows the
responses of the system for filter factors ([3) ranging from O to 1.0. When [3 was initially
set to zero, the control error was O.7l%w.b. A value between 0-1 was assigned to B after

320 min of drying; the response of the outlet moisture content is shown in Fig. 6.7a, and

of the multiplier in Fig. 6.7b. For small values of B the outlet moisture content slowly
approached the set point without overshooting. A faster response occurred for [3 values

larger than 0.] (although some overshooting and oscillating occurred). The differences in

rise time and overshoot did not change significantly for

145

35

. 30
£2
3
of
..r 25
c:
3
c:
o
U
0 20
a
'5
2
15
10

 

inlet MC

 

bO—I-I-g

 

 

MC of VD
/ (p.d.e. model)

'

predicted MC
(process model)

M

l

 

 

500

Time, min

1000 1500

Fig. 6.6 Comparison of the outlet moisture contents output from the virtual
dryer (VD) and predicted by the process model without parameter
modification (drying-air temperature = 85°C).

146

16.0

 

 

 

 

 

 

 

' outlet'MC. ~ , .

.0: i"*"“7 .‘ ""’"; 1

3 .

° i l

°\,15.5--' '

E

8

C‘-

O

o J

G.) . .1

g 15.0..

.22 .

O

2

14.5 Ill'....;1“.lll.....gfilrggm...L
300 400 500 600

Time,min
(a)

 

Multiplier

 

 

 

 

 

0.6 1 l 1 l 1 l
300 400 500 600
Time, min
(b)

Fig. 6.7 Response of the system to parameter modification with different
values of the filter factor (B ): (a) outlet grain moisture content of the

virtual dryer, (b) multiplier (y) of the drying constant.

147

values of B in the 0.3 tol .0 range. Table 6.1 lists the rise time and percentage of

overshoot of the moisture response at different B values.

Table 6.1 Response characteristics of the outlet moisture content to the modification
of the drying constant for different values of the filter factor.

 

Filter factor B 0.05 0.1 0.3 0.5 1.0
Rise time, min 130 70 4O 35 30
Overshoot, % 0 12 22 30 34

 

Choosing B is a compromise between rise time and overshoot. A range of 0.3-0.7

is recommended for the controller to achieve a fast response; this will result in 20-3 2%
overshoot which is 0.4-0.7% w.b. offset from the set point (if the model error in MC is

within 2% w.b.).

6.4.4 Robustness of the controller

A grain dryer operates over a wide range of the moisture contents and drying air
temperatures. Besides, random disturbances occur in the ambient conditions and the
sensor noise. Still, a controller should perform relatively unifome over the full range of
operating conditions, and should display adequate disturbance-rej ection ability.
Therefore, the robustness of the controller was tested on the virtual dryer by mimicing
various drying conditions.

The conditions shown in Figs. 6.3 and 6.5 were rerun in Figs. 6.8 and 6.9,
respectively, for the case that the model error was not zero and the feedback loop was on.
The transition period of the outlet moisture content lasted longer in Fig. 6.8 than in 6.3,

and the disturbance to the outlet moisture content from the drying-air temperature was

148

larger in Fig. 6.9 than in 6.5. The parameter modification for compensation of the model
error took time and delayed the response of the controller.

Due to shrinkage of grain during the drying process, the residence time of the
grain in a dryer can not be precisely estimated. A large error in the calculated residence
time may cause wild oscillations of a system with a delay (Shinskey, 1994) because the
predicted outlet moisture content is not of the grain currently at the outlet of the dryer.
The mismatch causes a mistaken modification of the drying parameter. Fig. 6.10 shows
the response of the system to a step increase in the inlet moisture content under different
estimation errors of the grain residence time in the dryer. If the error is less than 10%, the
response is not significantly effected; but at a 20% error, severe over-/under—drying and
large oscillation occurs.

Decreasing the filter factor B can alleviate the effect of incorrectly estimating the
residence time (see Fig. 6.11). When the residence-time error is 20%, decreasing B from

0.5 to 0.1 or less, results in a much improved response pattern. The trade-off is that it
takes longer to compensate the model error with a smaller filter factor.

Both the moisture sensor and the drying-air temperature sensor may be inaccurate.
To test the robustness of the controller regarding these sensors, a i 2% w.b. drift was
introduced in the inlet moisture measurement (Fig. 6.12), and a i 10°C drift in the
drying-air temperature (Fig. 6.13). The system was able to recover from the disturbances
of both sensors with only short offsets in the outlet moisture content.

A grain dryer has a start-up period before reaching normal operation condition. At

the first run of a dryer each drying season, all the grain in the dryer is initially wet. It takes

149

40

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.0: inlet MC
3
.\° 30 L
*a"
8
c
8
2
a
E 20 . outlet MC
0 set pomt /
E; _ \fij... l .4/ r ('4: [‘9 .
IO 4 1 1 1 1 1
0 500 l 000 1500 2000 2500 3000 3 500
'Thne,nfin

Fig. 6.8 Simulated response of the feedforward/feedback controller to step
changes in the inlet moisture content with ZAE optimization (drying-
air temperature = 85 °C. filter factor ,B=0.5).

150

A
O

 

 

 

 

 

 

 

 

 

 

 

 

 

-°:
3 -l
i. 30 L
: cl
0
E - drying-air temp.
o
o I
g 20 +
3; /outlet MC set point
§ ‘ "P J ‘
10 l L I I
400 650 900 l 150 1400
Time, min

140
120
.9
100 95
3
8.
80 e
O
l—
60
40

Fig. 6.9 Simulated response of the feedforward/feedback controller to step
changes in the drying-air temperature with ZAE optimization (inlet

grain moisture content = 20% w.b., filter factor ,6=0.5)

151

MC, % w.b. and
auger speed, % of the 293 rpm

 

30

25

20

15

 

 

 

10 1 l A l a l n L a l a l n I A l l I A l
12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00 8:00 10:00

Time, h:min.

- - O - - inlet MC, °/o w.b. —6— outlet MC, % w.b.
------ auger speed, % max. set point, l4°/ow.b.

 

 

Fig. 6.10 Simulated control responses to a step change in the inlet moisture
content at different estimation errors of the residence time of grain in
the dryer (drying-air temperature = 85°C, filter factor ,6 =0.5).

152

30

 

MC, % w.b. and
N
M

auger speed, % of 293 rpm
N
O

_I
M

 

 

 

 

 

IO . 1 1 1 1 1 1 1 1
14:00 16:00 18:00 20:00 22:00 0:00 2:00
Time, h:min.
- - O - - inlet MC, %w.b. —¢—- outlet MC, %w.b.
------ auger speed, % max. —set point, l4.5%w.b.

Fig. 6.11 Simulated control responses to a step change in the inlet moisture content
at different values of the filter factor (B) (estimation error of residence time
= 20%, drying-air temperature = 85°C).

153

some time before the dryer reaches normal conditions. Fig. 6.14 shows the performance
of the controller during the start-up of the dryer. The moisture content of wet grain was
assumed to be 20% and 25% w.b.. Initially, the outlet moisture content did not change;
once the grain exited the drying section, the outlet moisture content of the dryer rapidly
approached the set point. After some mild oscillations, the outlet moisture content
stabilized at the set point.

To imitate the real situation in a dryer, a random inlet moisture pattern was
generated and fed to the virtual dryer to test the performance of the controller. Fig. 6.15
shows the inlet and outlet moisture contents of the dryer. The inlet moisture varied in the
range of 20-26% with different frequencies; the outlet moisture content was well

controlled around the set point.

6.5 Conclusions

A model-predictive controller was developed for a crossflow grain dryer. Two
feedforward algorithms (i.e. ZAE and LSE) were tested. Both perform well although the
ZAE algorithm showed a slightly smaller control error and the LSE a slightly smoother
control action. An estimator for the drying constant was tested. Computer analysis
established that the controller compensates well for a change in drying-air temperature,
and is robust under various disturbances. The MC controller should be able to work in
concert with a grain-quality controller witch manipulates the drying-air temperature

according to a grain-quality requirement.

154

25

 

 

 

 

 

 

 

 

.0: measuredinletMC
3 ./ , actualinletMC
°\° 20 ' a . /
J a l
s:
o
E
o
o
2
.3
'5
2
10 a l 1 l n l
200 700 1200 1700
Time,min

Fig. 6.12 Simulated control response with the presence of drift in the inlet
moisture sensor (drying-air temperature = 85°C, filter factor ,6 =0.5).

155

 

 

 

 

 
 
   

 

 

 

25 120
£5 / measured air temp. 100
3' . . actual air temp.
°\° 20 - J i _ / .
a E _: - 8°
*2
8 let MC
2 3‘“ ~ 60
g 15 t """"" '/ ' ° '
° set point
2 .. 4o
10 . 1 - 1 1 20
2000 2500 3000 3500

Time, min

Fig. 6.13 Simulated control response with the presence of drift in the

temperature sensor (inlet grain moisture content = 20%w.b., filter
factor ,6 =0.5)

156

Temperature, °C

30

 

inlet MC =25%w.b.

  

Linlet MC=20% . .
20 -—-\

15 \,

Moisture content, % w.b.

set point

 

 

 

IO 1 l 1 l 1 l 1 l

 

 

0 100 200 300 400

Time, min

Fig. 6.14 Simulated control response at the start-up period of the dryer

(drying-air temperature =85°C, filter factor ,6 =0.5).

157

500

30

 

 

 

 

inlet MC
.6
3' 25 - \
°\‘°
J
35
g 20 -
O
2 outlet MC
3
.2 ,
o 15 ..............
2 \
set-point
10 1 l ‘ 1 ‘ 1 1 1 . 1
0 200 400 600 800 l 000 1 200
Time, min

Fig. 6.15 Simulated control response with randomly changing inlet grain

moisture content (drying-air temperature = 85°C, filter
factor ,6 =0.5).

158

References

Bosley J. R., T. F. Edgar, A. A. Patwardhan, G. T. Wright. 1992. Model-based control: A
survey. IFAC Symposia Series 8: 127-136.

Bruce, D. M., N. J. B. McFarlane. 1993. Control of mixed-flow grain dryers: an improved
feedback—plus-feedfomard algorithm. J. agric. Enging Res. 56:225-238.

Camacho E. F ., C. Bordons. 1995. Model predictive control in the process industry.
Springer, London, UK.

Courtois, F ., J. L. Nouafo, G. Trystram. 1995. Control strategies for corn mixed-flow
dryers. Drying Technology 13(5-7):1153-1165.

Eltigani, A. Y. 1988. Automatic control of commercial crossflow grain dryers. Ph. D
Dissertation, Michigan State University, East Lansing, MI.

Forbes, J. F., B. A. Jacobson, E. Rhodes, G. R. Sullivan. 1984. Model based control
strategies for commercial grain drying systems. Canadian Journal of Chemical
Engineering 62:773-779.

Garcia G. E., D. M. Prett, M. Morari. 1989. Model predictive control: theory and practice
- a survey. Automatica 25:335-348.

Johnson, G. W. 1997. LabVIEW graphical programming : practical applications in
instrumentation and control. McGraw-Hill, New York, NY.

Marchant, J. A. 1985. Control of high temperature continuous flow grain dryers.
Agricultural Engineer 40(4): 145-149.

McFarlane, N. J. B., D. M. Bruce. 1991. Control of mixed-flow grain dryers:
development of a feed-back-plus-feedforward algorithm. J. agric. Eng. Res.
49:243-258.

Olesen, H. T. 1987. Controlling drying percentage. Chapter 3, Appendix E, of Grain
Drying. Innovation Development Engineering APS, Thisted, Denmark.

Pabis, S., S. M. Henderson. 1961 Grain drying theory: 11. A critical analysis of the drying
curve of shelled maize. J. agric. Eng. Res. 6:272-277

Perry, R. H., D. W. Green. 1997. Perry’s Chemical Engineers’ Handbook. McGraw-Hill
Companies Inc., New York, NY.

159

Platt, D., A. Palazoglu, T. R. Rumsey. 1992. Dynamics and control of cross-flow dryers
II. A feedforward-feedback control strategy. Drying Technology lO(2):333-363.

Shinskey, PG. 1994. Feedback Controllers for the Process Industries. McGraw-Hill, Inc.,
New York, NY.

Whitfield, R. D. 1986. An unsteady-state simulation to study the control of concurrent
and counter-flow dryers. J. agric. Eng. Res. 32:171-178.

Whitfield, R. D. 1988a. Control of a mixed-flow drier Part 1: Design of the control
algorithm. J. agric. Eng. Res. 41:275-287.

Whitfield R. D. 1988b. Control of a mixed-flow drier Part 2: Test of the control
algorithm. J. agric. Eng. Res. 41:289-299.

Zhang, Q., J. B. Litchfield. 1993. Fuzzy logic control for a continuous crossflow grain
dryer. Food Process Engineering 16:59-77.

160

CHAPTER 7. FIELD TESTS OF THE CONTROLLER

Abstract

The model-predictive control system developed in Chapter 5 was implemented
and tested on a commercial crossflow grain dryer. Both Zero-A verage-Error and Lest-
Squire-Error algorithms showed good accuracy and stability. The moisture content of
was controlled within :t I. 3% of the set point, at inlet moisture contents ranging fiom 21
to 32% w. b. and the drying-air temperatures fi'om 85 t0120" C. The controller also

showed excellent compensation to changes in the drying-air temperature.

161

7.1 Introduction

A distributed-parameter process model (c.o.d.) for high-temperature grain drying
was developed in Chapter 5. In Chapter 6, a model predictive controller for a crossflow
dryer was developed. Two feedforward algorithms, i.e. Zero Average Error (ZAE, Eq.
5.5) and Least Square Error (LSE, Eq. 5.8), were designed with the feedback loop
consisting an estimator (Eqs. 5.10,“) with a filter (Eq. 2.12). The range of the filter

factor B of the modifier was found to be 0.3-0.8. Computer simulations of the control of

a virtual grain dryer showed that the controller has good accuracy and robustness.

This Chapter reports the implementation and field tests of the controller.

7.2 Implementation

7.2.1 Grain dryer

The controller has been implemented and tested on a ZIMMERMANN VT1210
grain dryer (manufactured by ffi Co., Indianapolis) located at the Jorgensen Elevator,
Williamston, MI. The dryer has a cylindrical shape with the drying-air flowing through
the grain column from the inside to the outside. The dryer consists of a drying section,
cooling section, unload system, fan and burner (Fig. 7.1). The upper part of the tower
serves as drying section, with a grain tum-flow located midway in the drying column; the
lower part of the tower consists of the cooling section in which ambient air is used to cool

the grain before it leaves the dryer. The air exiting the cooling section is directed to the

162

Wet grain

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t

\l /— Drying section
Grain tum-flow
/r—_ Fan and burner
/ /— Cooling section

Unload auger

Z /
—— Sampling box
»/

 

 

 

Dried grain

inlet of the burner and is recycled. The specifications of the dryer are listed in Table 5.1

Fig. 7.1 Schematic of ZIMMERMANN VT1210 grain dryer.

163

in Chapter 5.

A sampling box was added to the outlet of the dryer to facilitate installation of a
moisture sensor. The function of the sampling box is to keep the probe of the sensor
surrounded by a constant flow of grain. The grain flowrate in the box is adjustable with a
slide gate in the bottom of the sampling box. Extra grain overflows the box through a by-
pass.

A 100 m3 garner bin is used for temporary storage of wet grain. The dryer receives
grain directly from the dump pit when a truck is dumping grain. Otherwise the dryer

receives grain from the wet garner bin.

7.2.2 Control system

The control system consists of the moisture and temperature sensors, the unload
mechanism of the dryer, and the computer plus software (Fig. 7.2).
The control algorithms are implemented on a personal computer (Gateway 2000, 4DX2-
66, 16MB RAM). The computer communicates with the sensors and the drive motor
through a Lab-PC-l200/AI Data Acquisition Card (DAQ) of National Instrument (Austin,
TX). The card has 24 digital I/O, one 12-bit ADC with eight analog inputs and two 12-bit
DACs with voltage outputs. One digital 1/0 is used to control the auto-control contact,
three analog inputs are used by the sensors (two for moisture and one for temperature),
and one analog output is for the motor control of the unload auger.

The rpm of the unload auger is proportional to a 0-5 voltage input to the controller

of the unload motor. The maximum speed of the auger at 5 V input is 293 rpm and results

164

Wet grain

/. Inlet MC
\_ sensor

 

Isolator lg %
l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Drying-air
/ temp. sensor
LabVIEW ;
£95 E ,_ _ Unload auger
‘ motor
\ / . Outlet MC
E - sensor
DAQ Card [:1 J
COume' (PC-lZOO/Al) Dried grain

Fig. 7.2 Implementation of the controller.

165

in the maximum discharge capacity of 60.2 tonne/h (51.2 tonne of dry matter per hour).

Two moisture sensors (TRIME-GW, MESA Systems Co., Frarningham, MA)
were employed to measure the inlet and outlet grain moisture contents. The TRIME-GW
grain moisture sensor is based on time-domain reflectometry technology; two metal
probes are emerged in the grain column; a high frequency pulse is generated and
propagated along the probes; at the end of the probes, the pulse is reflected back to its
source. The moisture content of grain is related to the transit time of the pulse in the
probes. The inlet sensor was placed at the top of the dryer, and the outlet sensor in the
sampling box (Fig. 7.2).

An 8 m long PTlOO Resistance Temperature Detector (RTD) was installed in the
drying-air plenum to measure the average drying-air temperature. A G418 RTD

conditioner was used to convert the temperature signal to 0-5V output.

7.2.3 Programming

The 12.92 m long grain column between the inlet moisture sensor and the end of
the cooling section was conceptually divided into 20 stacked beds each with a length of
0.646m. The control action was updated each time the grain had moved down 0.646m.
The residence time for the grain in a 0.646m high grain bed was calculated by:

p?‘(AH)A
<D(G

(7.1)

max )
where 1: = residence time of grain in one bed, h
AH = height of one bed, 0.646 m

A = cross-sectional area of the grain column, 3.25 m2

166

CD = relative discharge rate of the unloading auger, % Gmax

Gmax = maximum discharge rate of the unloading auger, 51.2 tonne of dry matter

per hour

U W!

p g = average density of the grain in the dryer, kg (dry matter) rn'3

The average density of the grain is based on the moisture distribution of the grain
in the dryer, and was calculated using the following relationship (Lorenzen,195 8):

M
—)

pg =(816—5.9543M)(1—lOO

(72)

where p g = density of grain, kg (dry matter) in3

M = grain moisture content, % w.b.

The program was written in LabVIEW 4.1, a graphic programming language for
data acquisition and control (Johnson, 1997). A virtual control panel of the grain dryer
was generated on the computer. The dryer could be either manually operated or
automatically controlled from the virtual control panel. The process data were displayed
in real time, in terms of numbers and/or charts and was recorded on disk as text files.
The flowchart of the control program is shown in Fig. 7.3. The computer (i.e. the
controller) takes over the control of the unloading auger (i.e. the dryer) by sending a
digital high signal to the auto control contact. Then, the controller enters the cycle of: (1)
measuring the inlet/outlet grain moisture contents and the drying-air temperature, (2)
calculating and updating the control action, and (3) waiting for the next sampling period.
The period of each cycle is the time for grain to move down one bed, and is calculated

with Eq. 7.1. In the last two minutes of each cycle, 20 readings, one reading every 6

167

 
  
 
 

  
 

Moisture
and temp.
sensors

 
     

Moisture

 

Set initial

 

 

discharge rate

 

 

 

 

Take over dryer control
by turn on auto control
contact

    
 

Auto control

 

contact

 

 

 

 

 

 
 

 

Sample from sensors for

two minutes

 

 

 

 

 

 

Calculate control action

 

 

 

 

 

 

Update control action

 

Unloading
auger

    

 

 

 

 

 

Last two
minutes of this
period ?

 

 

 

and temp.
sensors

     

 

Sample from sensors for
two minutes

 

 

 

 

Fig. 7.3 Flowchart of the control program.

168

 

seconds, are obtained from each sensor, and their averages are used in the calculation of

the control action during the next cycle.

7.3 Results and Discussion

There were three phases in the control test: (1) on-line calibration of the moisture
sensors, (2) preliminary testing of the control algorithm, and (3) testing the controller
under various operating conditions. Initially, the dryer was manually controlled. Next, the
dryer was auto-controlled under close supervision, and was adjusted when necessary.
Finally, the dryer was totally controlled by the controller.

The control tests were conducted during Oct.-Dec., 1997. More than 100 hours of
data were collected while the dryer operated under automatic control, with the inlet
moisture content ranging from 21 to 32%, the drying-air temperature from 85 to 120°C,

and the ambient temperature from -5 to 10°C.

7 .3.1 On-line calibration of the moisture sensors

The inlet and outlet moisture sensors were calibrated dtu'ing manual operation of
the dryer. Grain samples were collected manually at the inlet and outlet sensors at the
same time that the controller was reading the voltage signals from the sensors. The
moisture contents of the samples were measured immediately after sampling using a
BURROWS Grain Moisture Meter( Seedburo Equipment Company, Chicago, IL). The
meter measures the capacitance of a 250g grain sample, and relates it to the moisture
content. The BURROWS meter was calibrated with the standard oven method (ASAE,

1991); it has a precision of i 0.25% near 15% w.b. and i 0.4% near 25% w.b.. The

169

calibration relations for the inlet and outlet sensors were developed by regression analysis
of the data, and were used in the moisture measurement of the sensor.

Fig. 7.4 compares the readings of the BURROWS meter and the calibrated
moisture sensors. The BURROWS meter shows larger fluctuations because only one
reading was obtained for each sample, whereas the sensor took 20 measurements during a
2-minute period.

To check the stability of the moisture sensors, grain samples were taken regularly
during the control tests and their moisture contents were measured with the BURROWS
meter. The outlet sensor was found to be reasonably stable during the testing. The inlet
sensor worked acceptably during the first half of the test period, but was found to be
unstable near the end of the tests. In a few control tests, the inlet sensor was discarded and
the inlet moisture contents were manually entered on the computer. The drifi of the inlet
sensor occurred mainly under extreme weather conditions (i.e. cold and windy) due to

water condensation on the sensor.

7.3.2 Control tests
(1) Initial value of the multiplier

An initial value is assigned to the multiplier of the drying constant (y , see Eq.
6.9) before starting the controller. The multiplier is modified by the feedback loop during
the dryer operation to compensate for the model error. If there is no information on the

error in the control model, a reasonable choice for the initial value of the multiplier is 1.0

(i.e. the model error will not be compensated). If a better initial value of the multiplier can

170

18

16

MC, %

10

 

 

 

 

 

 

 

 

 

 

 

 

11 21 31 41 51
SampleNo.
(a) Inlet sensor
l’i , . 3,...fiEJ‘. E E. :1
334 .. :i-‘z TRIME:.:'.:. .3: i':::: - -
I'l'1.‘ :‘:I' .- '5'. 1 u$:r: I,
' .RE: .' o _, .'_..": KH1 :L
t' - . .,'.,-:: ' - '14-"-
"*1: '2 ..,':-".\:‘.1.~',".E ' ‘ ll.
1 e: - -.- ~~~~~~ +++++++ 2'
L
BURROWS
L
1 21 41 61 81 101 121 141 161 181
SampleNo.
(b) Outlet sensor

Fig. 7.4 Comparison of the readings of the TRIME sensors and the
BURROWS meter: (a) inlet moisture, and (b) outlet moisture.

171

be provided, the transition period for modification of the multiplier will be shorter, and
the desired control precision is reached more rapidly.

Fig. 7.5 shows a test in which the initial value of the multiplier was chosen as 0.9.
The feedback loop was disabled and the multiplier did not change during the first
residence time. After 22:00 of the time, the multiplier decreased because the predicted
outlet moisture content was higher than the measured value. It required another residence
time before the multiplier reached the steady-state value of 0.75.

Several preliminary tests indicated that at steady state the multiplier for the

ZIMMERMAN VT1210 falls in the range of 06-08.

(2) Tests of the control algorithms

Fig. 7 .6 shows a test of the grain dryer operating at 105°C and controlled with
Zero-Average-Error (ZAE) algorithm with ,6=0.5 and yo =0.7, the set-point was 14%
w.b.. During the start-up period (the first 3 hours), the dryer was manually controlled. The
controller was switched on at 15:40. In the next 22 hours of the test, the inlet moisture
content varied from about 30% at the beginning to about 23% w.b. at the end. The inlet
moisture content fluctuated greatly during the first 8 hours of the tests when grain was
delivered directly to the dryer from the field. Less fluctuation occurred in the inlet
moisture content at night when grain entered the dryer from the garner bin. The
fluctuation in the inlet moisture content is reflected in the outlet moisture content after
one residence time (about 2.5-3.5 hours). Excluding the start-up period, the outlet

moisture content was controlled in the range of 13.2-15.5% with an average of 14.08%,

172

 

 

 

 

 

16 ~
:5 * g
B _
5° 12 g
u“ i ‘5
2 3 - 5
e » e
3 o
O 4 . E
1
0 1 1 + 1 1 1 1 1 1 1 1 1 _4
14:00 16:00 18:00 20:00 22:00 0:00 2:00
Time, h:min.
—A- measured outlet MC, %w.b. - - - predicted outlet MC, %w.b. model error, %w.b.

 

Fig. 7.5 Measured and predicted outlet moisture contents and the value of the
multiplier of the maize drying constant in a crossflow dryer
operating under ZAE control (drying-air temperature = 105°C, set
point =14.5% w.b., filter factor B = 0.5).

173

MC, % w.b. and

 

30

 

 

 

 

 

E
9‘ 25
M
a
N
to—
o
0
°\, 20
'o
a)
O)
a.
U)
3 15
on
:3
«3
IO 1 l 1 1 1 .1 1. .l
13:30 15:30 17:30 19:30 21 :30
Time, h:min.
- - D - - inlet MC, % w.b. —o— meadured outlet MC. % w.b.
predicted outlet MC, % w.b. ------ auger speed. % max.

Fig. 7.6 lnlet and outlet moisture contents, and the auger speed during
automatic control of a crossflow dryer with ZAE control (drying-air
temperature = 105°C, filter factor B = 0.5, initial multiplier y 0 = 0.7,

residence time=2.5-3.5 hours).

174

which is in the range of —1 .3% to +1 .0% around the set-point. The auger rpm varied from
40 to 62 rpm.

Fig. 7.7 shows a test with the ZAE algorithm with ,B=0.5 and 70 =0.6. The inlet
moisture content ranged from 29% to 18% w.b.. The outlet moisture content was
controlled withinl3.3 —15.8% with an average of 14.8% (i.e. the offset is —1.2 to +1 .3%
w.b.). The set point of the test was 14.5% w.b.. Comparing Fig. 7.6 and 7.7, no
significant difference is found in the control results although different initial values of the
multiplier (i.e. 0.7 for Fig. 7.6 and 0.6 for Fig. 7.7) were assigned.

The measured and predicted outlet moisture contents in the test illustrated in Fig.
7.7, and the difference between them (i.e. the model error), are shown in Fig. 7.8. There
occurs a spike in the predicted outlet moisture content afier one residence time for each
spike in the inlet moisture content. However, the spikes in the measured outlet moisture
content are not as sharp because of the mixing of grain in the dryer, especially in the grain
tum-flow section. The mixing of grain is favorable for reducing the variation in the outlet
grain moisture content, but exaggerates the model error in Fig. 7.8. It causes a relatively
large error in the estimation of the drying constant, and results in the over-modification of
the multiplier. Therefore, the following filter was added to the inlet moisture content:

M/ = M + 05(M,’ — Mf) (7.3)
where M,f = inlet moisture content after filtering

M," = current sampling value of the inlet moisture content

M,’ = last value of the inlet moisture content after filtering

175

MC, % w.b. and
auger speed, % of 293 rpm

 

N N w w
o M O U]
I If I
”LB
"13:0
.553:
B
a?

—-1
M
I

 

 

 

 

9 ~ 0 l o
. I I. . . .
. ..
IO 1 1 4 ‘1 l 1 1 1 l 1 l

10:00 12:00 14:00 16:00 18:00 20:00
Time, h:min.
------ auger speed, % max. —o— outlet MC, % w.b.

 

- - O - - inlet MC, % w.b. set point, l4%w.b.

Fig. 7.7 Inlet and outlet moisture contents, and the auger speed during
automatic control of a VT1210 dryer with ZAE control (drying-air
temperature = 105°C, filter factor B = 0.5, initial multiplier y 0 = 0.6,

residence time =2.0-2.5 hours).

176

 

30

MC, 0/0 w.b. and

 

 

 

 

 

Q
D 5‘
E (306% dating-'1 ENE-FLU” rd? cfinqua .
E- 25 _ _ .1 i D: g _ on 0%M mm ‘ CF
(45 , Q _- b ti
as :; q:
a 5:
O '. I .v‘ .--.-
o\° 20 _ ”I ".3 . ,s ' ' “~._."~.\
'6 . ’ . I \u’-‘ ----- " \‘-
€13 :3 -’
a-
?» 15
3
IO 1 1 1 1 1 1 1 _l
11:30 13:30 15:30 17:30 19:30

Time, h:min.

--O--in1etMC,%w.b. —-¢—outletMC.°/ow.b.
------ auger speed, % max. ——set point. 15%w.b.

Fig. 7.8 Measured and predicted outlet moisture contents, and the model
error (i.e. the measured minus the predicted outlet moisture
contents) during the test shown in Fig. 7.7.

177

Fig. 7.9 shows a control test after the inlet moisture filter had been added. The
measured and predicted outlet moisture contents are smoother than in Fig. 7.8. The outlet
moisture content was controlled to within i 0.7% w.b. of the set point. The spikes in the
inlet moisture content at 15:30, 16:00 and 17:20 were damped out in the predicted outlet
moisture contents at 18:00, 18:30 and 19:40 (i.e. at r + the residence time).

Fig. 7.10 represents a test with the LSE algorithm without the use of the inlet
moisture content filter. The dryer was manually controlled until 13:20. Since the inlet
moisture content was high (3 2%), the auger speed was set low during the start-up period.
This caused overdrying between 12:00 to 13:00. After 13:20 the controller took over, and
the outlet moisture content was controlled to within i 0.8% w.b. of the set point.

Comparing Fig. 7.10 to Figs. 7.6 and 7.7, it can be seen that the changes in auger
rpm with the LSE algorithm (Fig. 7.10) are less sharp than with the ZAE algorithm. This
agrees with the simulation analysis of the controller presented in Chapter 5.

Fig. 7.11 shows a test of the LSE algorithm with the addition of the inlet moisture
filter. The inlet moisture content variation was relatively smooth. The outlet moisture
content slowly approached the set point after the start-up at 14:20. The outlet moisture
content was controlled to within —1.0% to +0.7% w.b. of the set point after the start-up
period. Comparing the results of Fig. 7.9 and Fig. 7.11, it is clear again that the variation

in the auger rpm is less abrupt with the LSE algorithm than with the ZAE algorithm.

(3) Effects of the drying-air temperature
A step change in the drying-air temperature was introduced intentionally to test
controller response. Because the inlet sensor was unstable, the inlet moisture content of

178

MC, % w.b. and
auger speed, % 293 rpm.

 

 

 

 

 

 

40 120
30 - CD .. 80 g)
.' ': e"
D . : '.
25 PM; %fimmmmm---, ,, ....... .. 60 g
0 .... aFtn mu} m g.
I: .. E
20 t - ".....a'“: _’_.,.-~ .,fl- « 4o 13
15
IO 1 1 1 1 1 0
9:30 1 1:30 13:30 15:30 17:30 19:30
Time, h:min.
- - O - - inlet MC, % w.b. ——a— outlet MC, % w.b.
------ auger speed, % max. — drying-air temperaure. C

Fig. 7.9 Inlet and outlet moisture contents, and the auger speed, during
automatic control of a VT1210 dryer with ZAE control and an inlet
moisture filter (drying-air temperature = 105°C, filter factor B = 0.5,

initial multiplier y 0 = 0.7, set point = 15% w.b., residence time=2-2.5
hours).

179

MC, % w.b. and
auger speed, % of 293 rpm

 

b.)
LI!

1»
(3
CL
0
B
0.
D
‘h

N
M
I
1

N
O
f

—‘
LA
I

 

I a .5...“

 

 

 

10 1 1 1 3' 1 1 1 1 1 1 1
10:00 12:00 14:00 16:00 18:00 20:00
Time, h:min.
------ auger speed, % max. -—o—— outlet MC, % w.b.
- - C} - - inlet MC, % w.b. ——set point, l4%w.b.

Fig. 7.10 Inlet and outlet moisture contents, and the auger speed, during
automatic control of a VT1210 dryer with LSE control (drying-air
temperature = 105°C, filter factor B = 0.5, initial multiplier y 0 = 0.7,

residence time = 2.5-3.0 hours).

180

30

 

N
M

MC, % w.b. and
auger speed, % of 293 rpm
N
O

15

 

 

 

 

 

10 1 1 1 J
11:30 13:30 15:30 17:30 19:30
Time, h:min.
- - c} - - inlet MC, %w.b. —-A-— outlet MC, %w.b.
------ auger speed, % max. ——set point, 15%w.b.

Fig. 7.11 Inlet and outlet moisture contents, and the auger speed during
automatic control of a crossflow dryer with LSE control and the
inlet moisture filter (drying-air temperature = 105°C, filter factor B

= 0.5, initial multiplier y 0 = 0.7, residence time = about 2.5 hours).

181

grain was measured manually with the BURROWS meter and was entered to the
controller from the virtual control panel. The moisture content of the inlet grain samples
was taken every sampling period, and was assumed to be constant during the sampling
period.

Fig. 7.12 shows the response of the controller with the ZAE algorithm to a sudden
drop of 20°C in the drying-air temperature at 14:30. The immediate response of the auger
rpm to the change in the air temperature was significant, but the outlet moisture content
was hardly affected. The outlet moisture content was controlled to within —0.5% to +0.9%
w.b. of the set point. Thus, the controller compensated well for the temperature change.

Fig. 7.13 shows the response of the controller with the LSE algorithm to the 20°C
step up in the drying-air temperature at 11:30. The controller again compensated well for
the temperature change. The outlet moisture content was controlled within —1.3% to
+0.7% w.b. of the set point

In the test shown in Fig. 7.13, there was a step increase in the inlet moisture
content at 14:50, and then a step drop at 16:00. The auger speed and the outlet moisture
first decreased to a minimum point at 16:50, and then increased. During the transition
period, the simulated and measured moisture contents followed a similar trend (see Fig.

5.3 in Chapter 5).

(4) Control of the start-up period of the dryer

During the first run of the dryer in a drying season, the moisture content of all
grain in the dryer is the same. The simulation analysis in Chapter 5 (Fig. 5.14 ) shows that
the controller can quickly steer the outlet moisture content to the set point afier a period

182

MC, % w.b. and
auger speed, % 293 rpm.

40 120

 

 

 

 

 

 

35 -/T TV AWL - A] --— - , - -- - 100
30. , 9:} ~ usooo
. =. 2"
25 WE! %Wmmmfiremm .-__- 60 E
0&th b 1., tdIhj W 8.
.". '. E
20 - .-.-..-..... .... 7,” - - - _,_\ -- 4o 11’
15 20
10 1 L 1 1 1 1 1 1 1 0
9:30 11:30 13:30 15:30 17:30 19:30
Time, h:min.
- - O - - inlet MC, % w.b. —o—- outlet MC, % w.b.
------ auger speed, % max. — drying-air temperaure. C

Fig. 7.12 Response to a step change in the drying-air temperature of a
VT1210 dryer from 105 to 85°C with ZAE control (set point =15%
w.b., filter factor B = 0.5, initial multiplier y o = 0.7, residence time =

about 2.5 hours).

183

MC, % w.b. and
auger speed, % of 293 rpm.

 

 

 

 

 

 

 

40 120

35 . , ,. _fi_‘_ ._-. __'-i' _,‘——1, .,TAT1A'AJ 100

30 :s —————— 7‘ —————————————— 9.0m-— so .0
Mailman .‘Z: q mm 3.;

. 'ED ' .I ‘
25 Plan ------------ “in? —————— “I‘d . 60 g
3 ~ g

20 - ~ ~~ ---—-—- -_ ~ 1, 40 g

15“

10 1 1 1 1 L 1 1 1 0

8:30 10:30 12:30 14:30 16:30 18:30

Time, h:min.

- - O - - inlet MC, % w.b.
------ auger speed, % max.

—o— outlet MC, % w.b.
— drying-air temperaure. C

Fig. 7.13 Response to a step change in the drying-air temperature of a
VT1210 dryer from 85 to 105°C with LSE control (set point = 15%
w.b., filter factor B = 0.5, initial multiplier y 0 = 0.7, residence time =

2.5-3.0 hours).

184

equal to the average residence time of the grain in the dryer. Initially, the moisture content
of the grain is too high and has to be recycled to the inlet of the dryer.

No experimental test was conducted on the control of the start-up period of the
first run of the dryer in 1997 drying season. As this start-up period occurs only once a
season, its control is less important for automatic control.

Most dryers are shut down at the end of the day without emptying the grain in the
dryer, and the drying process is restarted the next day. If the controller does not memorize
the moisture distribution in the dryer when it is shut down, it can not make the correct
decision during the first residence time period (daily start-up period) after the dryer is
restarted.

There are two choices to control the dryer during the daily start-up period: (a) by
manually control, (b) by providing the controller with the current moisture distribution in
the dryer.

Manual control is not only inconvenient, but is also inaccurate. [The daily start-up
periods in Figs 7.5,6,8,9 were manually controlled, and large over-/under-drying was
observed].

A semi-empirical algorithm was developed for the automatic control of the dryer
during the daily start-up period. After the dryer is restarted, the inlet and outlet moisture
contents of the grain are measured for ten minutes. When the controller is switched on,
the grain moisture distribution is approximated as linear from the inlet and outlet. The test
in Fig. 7.13 was a restart after 13 hours shut-down of the test in Fig. 7.12. The semi-
empirical start-up algorithm was used in the start-up period of Fig. 7.13, and resulted in
the outlet moisture content continuing smoothly.

185

The best way for the control of the daily start-up period is to record the moisture
distribution when the dryer is a shut down, and re-enter the value before the dryer is

restarted.

7.4 Conclusions

(1) The moisture controller showed excellent accuracy and stability in all the
experimental tests. The outlet moisture content of grain was controlled to within i
1.3% of the set point with the inlet moisture content ranging from 21 to 32% w.b. and
the drying-air temperature from 85 to 120°C.

(2) Both the ZAE and LSE control algorithms worked well although the auger rpm
changes less abruptly with the LSE algorithm. No conclusion was drawn which
algorithm is superior.

(3) A filter on the inlet moisture measurement is necessary to reduce exaggerated model
errors.

(4) The controller compensated well for a variation in the drying-air temperature when
the grain quality needs to be controlled.

(5) The predicted performance of the controller was validated during the field tests.

(6) Reliable on-line moisture sensors for the controller, especially for inlet grain to the
dryer, still need to be developed before the dryer control system can be

commercialized.

186

References

ASAE Standards, 38‘11 Ed. 1991. D352.2-Moisture measurement-Ungrounded grain and
seeds. Am. Soc. Agric. Eng., St. Joseph, MI.

Lorenzen, C. 1958. The effect of moisture on weight-volume relationships of small grain.
ASAE Paper No. 58-111, Am. Soc. Agric. Eng., St Joseph, MI.

Johnson, G. W. 1997. LabVIEW Graphical Programming : Practical Applications in
Instrumentation and Control. McGraw-Hill, New York, NY.

187

CHAPTER 8. GRAIN QUALITY CONTROL IN HIGH-TEMPERATURE

DRYERS

Abstract

The drying-air temperature is usually determined for conventional grain dryers
by rule-of-thumb and is usually not adjusted during dryer operation. The quality of dried
grain is uncertain since it fluctuates with the residence time of grain in the dryer. The
objective of this Chapter was to develop a control strategy for optimizing the quality of
dried grain by varying the drying-air temperature. A neural network model was
developed to relate the quality of dried grain to the drying conditions. A control
algorithm was tested which varies the drying-air temperature so that the grain quality
approaches the quality set-point at the outlet of the dryer. Simulation tests showed that

the grain-quality controller results in improved grain quality in crossflow drying.

188

 

8.1 Introduction

High temperature drying may cause significant quality damage to the grain. The
major factors influencing the grain quality damage in dryers are the drying-air
temperature and the grain-residence time. The residence time of grain (i.e. dryer capacity)
needs to be controlled to keep the moisture content of the grain at the outlet of the dryer
close to the set-point. Decreasing the drying-air temperature is will reduce the quality
damage to the grain, but it will decrease the dryer capacity and energy efficiency. The
optimal drying-air temperature is the highest temperature at which the grain quality is still
acceptable; it is conventionally determined by rule-of-thumb based on the intended usage
of the grain (i.e. for food, feed or seed).

The drying-air temperature is usually kept constant during the dryer operation.
However, the moisture content of the grain entering a continuous-flow dryer changes
randomly, depending on the variety, growing conditions and the harvest time. The
residence time of the grain in the dryer is varied accordingly; therefore, the quality of the
dried grain will vary significantly because the drying-air temperature is not adjusted. To
achieve the desired and uniform quality of the dried grain, the drying air temperature
needs to be optimized and regulated along with the speed of the unload auger.

The best way to determine the “optimal” drying-air temperature in a grain dryer is
by modeling the quality change in the dryer. The grain—quality models developed in
Chapter 4 of this thesis can not be directly employed for quality control because of the
large computation requirements. First, a control-oriented model relating the quality of
dried grain to the inlet grain moisture content and the drying air temperature, has to be

developed.

189

 

A potential problem for quality control is the disturbance to the moisture control.
The quality control requires frequent regulating of the drying-air temperature, which may
degrade the performance of the moisture controller. This problem has been addressed in
the design of the moisture controller (see Part III, Chapters 5-7). It was shown in
simulation and field tests that the moisture controller is robust under conditions of
moderate changes in the drying-air temperature.

The objectives of this Chapter are to develop control-oriented grain-quality

models and the grain-quality control algorithm for grain dryers.

8.2 Control-oriented Quality Models

Comprehensive simulation tests for the crossflow drying of maize are described in
Chapter 4; the results are presented in Tables 4.4a—e. The drying conditions were: air-
temperature 50-120°C, airflow rate 32-96 m3 In3 min", and initial grain moisture content
17.5-35% w.b.. The thickness of the grain column was 30.5 cm. The final grain moisture
content of 15% w.b. afier drying was searched for by simulation. The standard deviation
of the initial moisture content of grain was chosen as 3% w.b., which is common for
maize entering a dryer. The change in the percentage of denatured protein (PDP) was
chosen as the quality criterion in this Chapter because of its importance in several maize-
processing industries.

Two models are developed based on the data in Tables 4a-e, i.e. a quality
simulation model and a quality control model. In the simulation model, the drying
conditions (i.e. drying-air temperature, airflow rate and initial grain moisture content) are

the inputs and the grain quality is the output. The control model predicts the drying-air

190

temperature for the desired grain quality at a particular airflow and inlet grain moisture
content.

A conventional function approximator (e. g. a polynomial) has been shown to be
effective only in a small range of drying conditions (Liu etal., 1997). Thus, another
approximation technique had to be employed to properly represent the strong non-linear
relationship between the variables in Tables 4.4a-e.

Neural network (NN) approximation has been successful in representing complex
non-linear relationships between multiple inputs and outputs. Huang et al.(1993)
developed a NN model for a tissue-paper dryer; the model was developed with data
obtained from simulation tests, and closely represented the trends of the test data. Trelea
et al. (1997) employed a NN model to predict the drying and the wet-milling degradation
of maize; the agreement between the experimental data and the NN model was good.

The development of the NN models for quality control of crossflow grain dryers
was used. A feed-forward neural network was employed in developing the model. The
architecture of the model is shown in Fig. 8.1. There are two visual layers and one hidden
layer in the network, with three inputs and one output. The neuron number in the hidden
layer, n, was searched.

The mathematical description of the quality simulation model is:

G
Q = ¢, {W2[¢,(W1 T + 131)]} + 32 (8.1)
M0

191

 
   

 

¢2(-)

 

 

 

Fig. 8.1 The structure of the NN model.

and of the quality control model :

G
T = ,1, {W2[¢\(W1 Mo + Bl)]} + 32

Q

where
G = scaled airflow rate
T = scaled drying air temperature
Mo = scaled initial grain moisture content
Q = scaled grain quality
Wl , W2 = weight matrices
Bl, B2 = bias vectors
(111, (1)2 = functions

n = number of neurons in hidden layer

(8.2)

The inputs and outputs were scaled to 0-1 by dividing the maximum values in the

training data. The maximum values of the parameters were found to be 96 m3m'

192

3

min'l for

airflow rate, 120°C for drying-air temperature, 35% w.b. for inlet grain moisture content,
and 35% for denatured protein. (in was chosen as the hyperbolic tangent function and (I); as
the pure linear function. The model parameters of W1, W2, B1 and 82 were determined
by “training” the NN model with the training data in Tables 4.4a-e. A back-propagation
algorithm was used to train the NN model with the function of trainbpx in the Neural
Networks Toolbox of Matlab [Demuth et al., 1992]. The training process continued until
the sum of the square error (SSE) of the NN model had stabilized.

The number of hidden neurons n was searched during the training. Fig. 8.2 shows
the SSE of the control model after 6000 epochs of training at different numbers of hidden
neurons. A higher number of neurons in the hidden layer constitutes a smaller SSE of the
model. It was decided to use three hidden neurons in both models.

The results for the simulation model were (final SSE=0.14):

0.0634 0.1 158 — 4.0228
W1: 1.0417 2.3108 1.8126
0.1604 1.0965 - 45147

2.5246
Bl = — 4.6694
25674

W2 =1 -o.9223 0.4245 0.7375]
32 =[0.3521]

Fig. 8.3 compares the simulation model to the training data at an airflow rate of 64

m3 m’3 min". The agreement between the NN model and the training data is good.

193

SSE

 

 

 

 

 

0.8
0.6 y
0.4 -
0.2 _
0 . . . . . .
1 2 3 4 5

Number of neurons in hidden layer (11)

Fig. 8.2 Sum of the square error (SSE) of the neural network control model
vs. the number of neurons (11) in hidden layer.

194

The results for the control model were (final SSE=0.15):

1.2487 3.6306 0.4423
W1 = 1.1707 - 3.2809 - 1.5777
0.1555 - 1.0397 - 1.3205

- 3.1249
Bl = 1.3498
0.4837

W2 = [- 0.4020 0.5225 - 1.8377]

BZ = 0.1893

Fig. 8.4 compares the control model to the training data. The NN control model
follows the training data well except in the lower and upper ranges of the drying
temperature. Additional neurons in the hidden layer and different nonlinear functions
were investigated but did not improve the results. The ftmdamental reason is that the
temperature does not change smoothly but in steps in the training data, and thus it was a
severe test for the NN model to fully represent the multiple-step function shown in Fig.
8.4. The accuracy of the NN model is acceptable in the range of 60 to 100°C temperature

range.

8.3 Quality Control Algorithm

In the development of the quality control algorithm, it was assumed that the
moisture content of the grain at the outlet of the dryer is always controlled to the set point
(i.e. 15% w.b.) by an “ideal” moisture controller. This allows the design of the quality

controller to be independent of the moisture control, and simplifies the problem. Because

195

 

30

    
 
 

T=l20°C
25 -

   

D T=100°C

NJ

20-

 

 

Percentage of denatured protein, %

 

 

 

15 -
0 T=80°C
10 -
o T=60°C 41)
5 - A °
:1
0 r l I l
15 20 25 30 35

Initial grain M.C., % w.b.

Fig. 8.3 The percentage of denatured protein of maize after crossflow drying
as predicted by the neural-network simulation model (solid lines)
and the training data (marks), at an airflow rate of 64 m°m’°min'l .

196

 

120

    
 

 

 

 

0° Cy
00
00° 0 O
o
. o
o” 100 -
e“
g NN model
Q)
o.
g 80 . .
11' training data
'5
8°
'5
Q 60 h 0
0° 0
o 0%
4O 1 I 1 I 1 1 1 l 1 1 A
l 21 41 61 81 101
Training data No.

moisture controller can not be “ideal”, the accuracy of the quality control depends on the

Fig. 8.4 Comparison of the neural-network control model and the training
data.

197

performance of the moisture controller.

Since accurate on-line measurement of grain quality is not (yet) commercially the
available, no feedback algorithm could be implemented in the quality controller. Thus, a
model-based feedforward control algorithm was used.

If the desired grain quality at the outlet of the dryer is known, the NN control
model can determine the required drying-air temperature corresponding to the inlet grain
moisture content (as measured by a moisture sensor at the inlet of the dryer). At each
sampling period, the inlet grain moisture content is measured and the desired drying-air
temperature is calculated. However, this temperature can not be directly used to control
the air temperature of the dryer because the residence time of the grain in the dryer is
usually much longer than the sampling period. The grain currently in the dryer is the grain
which enters the dryer during previous sampling periods, possibly with different initial
moisture contents each requiring different drying-air temperatures. Therefore, the drying-
air temperature for controlling the dryer needs to be optimized by considering the grain
entering the dryer and the grain currently in the dryer.

To optimize the temperature, a weighted average of the temperatures required by
the grain currently in the dryer is selected. If the residence time of grain in the dryer
constitutes n sampling periods there will be n desired temperatures, i.e. one for grain

entering the dryer at each sampling period. Then, the optimized drying-air temperature is:
T = Z a, T, (8.3)
i=1

where a, = weights, i=1, 2, ..., n

T,- = temperature for ith sampling period, i=1, 2, ..., n

198

T = optimized temperature
The optimized temperature is recalculated every sampling period.

Fig. 8.5 shows the optimized drying-air temperature for different PDP values,
using Eq 8.3 for the crossflow drying of maize at an airflow rate of 64 m3 m'3 min". All
the temperatures were equally weighted (i.e. a,- = 1/ n). The drying column was
conceptually divided into 10 beds; the sampling period was chosen as the time for grain
to move through one bed; therefore, the residence time of grain in the dryer was equal to
10 sampling periods. The inlet grain moisture content ranged from 20-30% w.b. with 5%
step changes, the outlet grain moisture content was controlled at 15% w.b. The optimized
temperatures varied with the inlet grain moisture content and the set-point of the dried
grain quality. When the percentage of denatured protein was changed from 8% to 12%,
and from 12% to 16%, the optimized drying-air temperature increased about 15°C. When
the inlet grain moisture content was changed from 20% to 30% w.b., the drying-air
temperature had to be decreased by about 30°C to maintain the required grain quality.
Conventionally, the drying-air temperature is seldom adjusted in crossflow dryers. Fig.
8.6 shows the predicted outlet grain quality of a crossflow dryer when the drying air
temperature was maintained at 103°C. The grain quality was predicted using the grain-
quality simulation model (Eq. 8.1). The PDP increased from about 10% to 20% when the
inlet grain moisture content changed from 20% to 30%. Thus, the quality of grain dried in
a crossflow dryer varies significantly if the drying-air temperature is not adjusted.

The dried grain quality was relatively uniform when a quality controller was

employed to regulate the drying-air temperature for a set-point of the outlet grain quality

199

 

 
   
     

Air temp., °C

 

 

 

 

 

 

 

 

 

 

 

70
110 L
air temp. for PDP<16%
90 -
a 50
t .
-°.
70 1 . 3
arr temp. for PDP<8°/ °\°
* 02°
50 r ., 30 2
inlet grain MC
10 10
0 20 40 60 80 100 120
Sampling No.

Fig. 8.5 Optimized drying-air temperature for crossflow drying of maize at
different set-points of the outlet grain PDP- percentage of denatured
protein (outlet grain moisture content = 15% w.b., airflow rate = 64

m3m‘3min'l).

200

M. C., % w.b. and PDP, %

 

40 120

 

 

 

 

 

 

 

 

 

 

air temp.
- 100
30 r
I \ inlet grain MC . 80
* é)
; o
,1 PDP of dried grain 1 %-
~ 1 e
PDP setjoint l j 40
1 T
[0 It" “vi“:hr'ttt‘fr'r'fx‘r.‘ ’2'.’ ' '32:. [3,. ...,w
1 20
0 0
0 20 40 60 80 100 120
Smapling No.

Fig. 8.6 Inlet grain moisture content and predicted outlet grain quality of
maize crossflow-dried at 103°C (PDP = percentage of denatured
protein, outlet grain moisture content = 15% w.b., set-point of the
PDP = 12% of denatured protein, airflow rate = 64 m3m'3min").

201

of 12% denatured protein (as shown in Fig. 8.7). For the same pattern of the inlet grain
moisture content as in Fig. 8.6, the variation of the outlet grain quality was small and the
average close to the set-point. There was a small steady-state error in the outlet grain-
quality because different models (i.e. Eq. 8.1 for simulation and Eq. 8.2 for control) were
used for prediction and control of the grain quality, and no feedback was employed in the

quality controller.

8.4 Conclusions

(1) Neural-network models were used for simulating the changes in grain quality in a
crossflow maize dryers.
(2) A model-based feedforward grain—quality controller was developed for controlling the

grain quality of crossflow-dried maize.

202

 

M. C., % w.b. and PDP, %

40

b)
O

N
C

—
O

 

 

 

 

 

 

 

 

 

 

 

air temp.
+
P \
I \ inlet grain MC
PDP of dried grain
PDP set point 1 \l!!!!” ”m” IIIIIII/I q
T
O 20 40 6O 80 100 120
Sampling No.

120

100

80

60

Temperature, °C

40

20

Fig. 8.7 Inlet grain moisture content, optimized drying-air temperature and
predicted outlet maize quality in a crossflow dryer operated with a
grain-quality controller (PDP = percentage of denatured protein, set
point of grain moisture content = 15% w.b., set-point of the PDP =

12% of denatured protein, airflow rate = 64 msm'

3min").

203

References

Liu, Q., F. W. Bakker-Arkema. 1997. Stochastic simulation and control of grain quality
in crossflow grain dryers. Paper No. 97-6030. Am. Soc. of Agric. Eng, St. Joseph,
MI.

Huang, 8., A. S. Mujumdar. 1993. Use of neural network to predict industrial dryer
performance. Drying Technology 11(3):524-541.

 

l3.

Demuth, H., M. Beale. 1992. Neural Networks Toolbox User’s Guide. The MathWorks, '
Inc., Natick, MA.

Trelea, I. C., F. Courtois, G. Trystram. 1997. Dynamic models for drying and wet-milling g

quality degradation of corn using neural networks. Drying Technology 15(3&4):

1095-1102. g

204

CHAPTER 9. SUMMARY

9.1 Stochastic Drying Modeling

The variation of moisture content among grain kernels is significant before,
during and after drying. The stochastic nature of the moisture content of maize in the
drying process was explored experimentally and analytically. Stochastic grain drying
models were developed of the distribution of the moisture content of maize kernels dried in
concurrent-flow, counter-flow and crossflow dryers. The models simulate, in addition to
the average final moisture content, the moisture content distribution and standard
deviation of the grain exiting these dryers.

Deterministic grain drying models assume a uniform inlet moisture content while
the stochastic models presume a more realistic normal distribution of the moisture
content in the grain entering a dryer. Only stochastic modeling can provide essential
design information on the degree of overdrying and of underdrying occurring in grain

dryers.

9.2 Grain-quality Models

The changes in the denatured protein content and in the germination of maize
during crossflow drying were successfully modeled by combining thin-layer
drying/quality models with the MSU stochastic grain-drying model. The application of

quality models was illustrated in the analysis of crossflow drying.

205

Due to lack of quantitative relationships between the dryer parameters and grain
quality, the grain quality is not accounted for in the conventional design of grain dryers.
Usually, the drying-air temperature is compromised between the dryer capacity and grain
quality. The grain-quality models provide an advanced tool to optimize the dryer
parameters so that the dryer reaches maximum capacity and energy efficiency while still

producing grain of acceptable quality.

9.3 Moisture Controller

A distributed-parameter process model of crossflow drying was developed. The
model is more flexible and accurate than the commonly-used lumped-parameter models,
and is of adequate simplicity for use in a dyer-control system.

A model-predictive controller was developed for a crossflow grain dryer
consisting of a feedforward loop and an indirect feedback loop. The controller has an
effective compensation mechanism to changes in the drying—air temperature, and is robust

under various disturbances.

9.4 Grain-quality Controller

A neural-network model was employed for developing process model of grain-
quality in a crossflow dryer. The neural-network model was good in representing the non-
linear relationship between the grain quality and the drying parameters, i.e. air
temperature, airflow rate and the initial grain moisture content. Model-based feedforward

quality controller was developed for controlling the quality of crossflow-dried maize. The

206

 

grain-quality controller optimizes the drying-air temperature, resulting in acceptable and

uniform grain quality.

9.5 Suggestions for Future Study:

(1) To employ the stochastic drying and grain-quality models for the optimal design of
grain dryers.

(2) To improve the reliability of on-line grain moisture sensors.

(3) To test the quality-control algorithm on commercial dryers.

(4) To develop and test the control systems for mixed-flow and concurrent-flow dryer

models.

207

MICHIGAN smrE UNIV. LIBRRRIES
(NI "Ill ll] llll Ill W“ ill” Ill" |||| H Ill! Ill 1W ”HI
31293018017024