DESIGN OF MULTISTAGE GRAIN DRYERS ,

Dissertation for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
ROGER CHARLES BROOK
1977

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ABSTRACT

DESIGN OF MULTISTAGE GRAIN DRYERS

BY

Roger Charles Brook

Grain as a cash crop or a feed crap is economically important
in the United States and Canada for both domestic consumption and for
export. Of the various crops harvested, shelled corn requires drying,
either as ear corn or more commonly as shelled corn. The equipment
used to dry shelled corn can be utilized only during the 4-8 week
period of harvest. Drying other agricultural products with the same
equipment reduces the investment cost per tonne of grain dried. A
second crop often requiring drying in Michigan and in Ontario, Canada
is pea beans, which are very susceptible to damage during the drying
process. Shelled corn and pea beans are the two crops considered in
this thesis.

Previous research has shown that the concurrentflow dryer is
more energy efficient than the conventional crossflow dryer. The con-
currentflow dryer also results in less damage to shelled corn during
the drying process than the crossflow dryer. The objective of the
thesis was to simulate and optimize the drying of grain in a multi-

stage concurrentflow dryer with intermediate tempering stages and a

Roger Charles Brook

counterflow cooler. Experimental tests were conducted using a pilot
model of a three—stage concurrentflow dryer.

A new computer model was developed to simulate the drying per-
formance of such a multistage concurrentflow dryer. Diffusion within
spherical kernels was used to model the drying and tempering process.
Single stage concurrentflow dryer simulations agreed well with pre-
viously published results. A tempering period of 1.25 hours was found
to be satisfactory for a corn kernel temperature of 51°C. The counter-
flow cooler was modeled using a modified version of the Effectiveness-
NTU method derived for a counterflow heat exchanger. The counterflow
cooler simulation was, on the average, within 2°C and 0.4% w.b. of
previously published results. The multistage model agreed well with
the sample data from the experimental samples: (1) fer shelled corn an
average difference of 5°C and 2.3% w.b. and (2) for pea beans an
average difference of 3°C and 0.9% w.b.

The quality of the pea beans and shelled corn as affected by
drying was modeled using data from the experimental tests. An equation
for the percentage of breakage in the Stein breakage test was developed
for shelled corn and one for the percentage of cracked seed coats for
pea beans. The calculations from the quality models agreed well with
the results of the experimental tests but did not adequately reflect
the beneficial effects of the counterflow cooler.

An optimization scheme using dynamic programming was developed
for finding the optimum operational parameters and dimensions of a
multistage concurrentflow dryer with intermediate tempering stages.

The objective function was based on costs for energy consumed during

drying and fixed and variable capital costs. The operational

Roger Charles Brook

parameters were constrained by the desired final moisture content, the
maximum allowable exit temperature of the grain from any drying stage,
and the maximum allowable value of an important grain quality factor.
Costs of 0.447¢/kg and 0.448¢/kg were found for representative two- and
three-stage dryers, respectively. Reuse of the exhaust air reduces the
drying costs to O.424¢/kg and O.405¢/kg, respectively. A representative
drying cost of 0.569¢/kg was found for a single-stage concurrentflow
dryer. About half (4S%-55%) of the total drying cost for multistage
concurrentflow dryers was for energy consumed during the drying process.
Energy costs of O.302¢/kg for a continuousflow crossflow dryer
are greater than an average of O.230¢/kg for concurrentflow dryers.
The internal rate of return for the additional investment in a con-
currentflow dryer instead of a crossflow dryer would be approximately
15% for a single-stage; 9% for a two-stage; 8% for a three-stage. An
investment decision would also include the beneficial effect on grain

quality of a multistage versus a single-stage concurrentflow dryer.

Approved 7. Qt] W - M114,

Maior Proféssor

Approved .
ep ment Chairman

 

DESIGN OF MULTISTAGE GRAIN DRYERS

BY

Roger Charles Brook

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Agricultural Engineering

1977

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ACKNOWLEDGMENTS

The author wishes to express sincere thanks to Dr. Fred W.
Bakker—Arkema for his guidance and encouragement over the past years,
and for serving as major professor.

Appreciation is expressed to the manbers of the guidance
committee, not only for their service but also for help during the
course of study--Dr. Steve Harsh, Agricultural Economics; Dr. Ben
Holtman, Agricultural Engineering; Professor Robert Maddex, Agricultural
Engineering; Dr. Gerald Park, Systems Science.

The partial financial support arranged through the Andersons
Agricultural Research Fund, Columbus, Ohio, and Westlake Agricultural
Engineering, Inc., St. Marys, Ontario, Canada was much appreciated.

A special note of thanks to Mr. Chris Westelaken for his personal
support and for service on the examining committee.

Special thanks to Ms. Pat Brook for encouragement and support

during the course of study and for helping with the typing.

ii

TABLE OF CONTENTS

Page

LIST OF TABLES . . . . . . . '. . . . . . . . . . vi

LIST OF FIGURES. . . . . . . . . . . . . . . . . ix

LIST OF SYMBOLS. . . . . . . . . . . . . . . . . xi
Chapter

1. INTRODUCTION . . . . . . . l

1.1 Trends in grain dryer design. . . . . S

1.2 Dryer energy efficiency . . . . . . . 5

1.3 Maintaining grain quality. . . . . . . . . 8

1.4 Objectives. . . . . . . . . . . . . . 10

2. LITERATURE REVIEW. . . . . . . . . . . . . . 12

2.1 Dryer energy optimization. . . . . . . . . 12
2.2 Drying effects on grain quality. . . . . . . 17

2.2.1 Stress cracking of pea beans . . . . . 18
2.2.2 Stress cracks and broken corn . . . . . 20
2.2.3 Milling quality. . . . . . . . . . 25
2.2.4 Grain viability. . . . . . . . . . 26
2.2.5 Nutritive value. . . . . . . . . . 26
2.3 Concurrentflow grain drying . . . . . . . . 29

3. EXPERIMENTAL INVESTIGATIONS . . . . . . . . . . 34
3.1 Multistage drying of pea beans . . . . . . . 34

3.1.1 Equipment and procedures. . . . . . . 34
3.1.2 Test conditions and results. . . . . . 38

3.2 Multistage drying of shelled corn . . . . . . 4S

2 1 Equipment and procedures. . . . . . . 45
.2.2 Test conditions and results. . . . . . 46

3.
3

iii

Chapter

4. MODEL DEVELOPMENT .

4.1
4.2

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Concurrent heat and moisture transfer .
Auxiliary equations and properties .

4.2.1 Diffusion coefficient . .

4.2.2 Equilibrium moisture content.

4.2.3 Heat transfer coefficient.

4.2.4 Latent heat of vaporization .

4.2.5 Miscellaneous grain and air properties
4.2.6 Energy and static pressure equations .

Tempering stage . . .
Cooling stage . . .
Quality prediction equations .
Model flow chart . . . .
Model validation . . . .

Single-state drying of shelled corn
Multi-stage drying of shelled corn.
Multi-stage drying of pea beans. .
Crossflow dryer comparison--Pea beans.

hat-.5
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5 . OPTIMIZATIONVMODEL.

5.1 Optimization algorithm . . . . .
5.2 Objective function . . . . . . .

S.
5

3
4

5.2.1 Operating cost . . . . . .
5.2.2 Capital investment cost . . . .
5.2.3 Grain quality constraints.

Optimi zat ion imp lementat 1on .
Results of optimization for shelled corn .

Standard input conditions.
Effect of staging . .

Effect of tempering.

Effect of heat recovery .
Effect of quality constraints
Comparison with crossflow drying

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6. CONCLUSIONS . . . .

7. SUMMARY

8. SUGGESTIONS FOR FUTURE RESEARCH

iv

Page
54

SS
58

59
6O
62
63
64
66

71
76
81
86
87

89
93
97
101

103

104
106

107
107
109

109
114

115
118
124
127
127
133

137
139

141

Chapter Page

9. APPENDICES

9.1 Conversion Factors . . . . . . . . . . . 143
9.2 Pea bean tests sample data . . . . . . . . 145
9.3 Shelled corn tests sample data . . . . . . . 149
10. REFERENCES . . . . . . . . . . . . . . . . 151

Table

100

11.

12.

13.

14.

15.

LIST OF TABLES

Drying of corn stored on-farm, 1974-1975 .

Navy bean exports as a percent of North American experts
for the 10 year period 1965-1974 . . . . . .

Shelled corn dried artificially by dryer type, Michigan,
1974-1975. I O O O O O O O I O O O O 0

Approximate energy efficiency for various drying
technologies. . . . . . . . . . .

Estimated fuel use for Michigan, 1960-1975 . . . . .

Percent of inspected receipts by grade for corn two months
following harvest . . . . . . . . . . . .

Grade standard for pea beans . . . . . . . .
Critical kernel temperature as a function of equilibrium
relative humidity for several small grains (criterion:

less than 5% viability decrease) . . . . . . .

Laboratory results of grainflow versus discharge auger
Rm. 0 O O O O O O O O I O O O O O O

Pean bean drying test conditions. . . . .

Summary of sample results for pea bean drying tests .

Results of corn discharge calibrations.

Corn drying test conditions . . .

Sample results for corn drying tests

Diffusion coefficient values (cmZ/hr) for shelled corn (C
calculated using equation 12) and for soybeans (B
calculated using equation 13) as a function of moisture
content and grain temperature. Soybean equilibrium

moisture content Me=5.0% w.b. and initial moisture content
Mo=2800% w.b. O O O O O O O O O O 0

vi

Page

27

37
39
4O
45
48

49

60

Table Page

16. Relative drying rates of various agricultural products as
a percentage of wheat drying rate at 18% w.b. . . . . 61

17. Equilibrium moisture content equation constants . . . . 61

18. Equilibrium moisture content values for pea beans (% d.b.)
as a function of grain temperature and relative humidity.
Calculated (C) from equation (14) and data (D) from
Dexter et a1. (1955). . . . . . . . . 62

19. Grain and air properties . . . . . . . . . . . .. 65

20. Constants for the Sheed pressure-flow relationship for
different agricultural products . . . . . . . . . 68

21. Effect of various grain conditions on the moisture profile
for corn dried in a concurrentflow stage following
tempering for 1.25 hours . . . . . . . . . . . 75

22. Comparison of counterflow process simulator with previously
WbliShed data. 0 O O O O O I O O 0 O O O O 80

23. Sensitivity study of cooler operation using the Effectiveness
simulator for shelled corn. . . . . . . . . . . 82

24. Effect of number of interior nodes in a corn kernel on the
average moisture content profile during the simulated
drying in a concurrentflow dryer. . . . . . . . . 90

25. Comparison of simulated drying conditions with single-stage
experimental drying tests reported in the literature.
Drying only, no cooling. . . . . . . . . . . . 91
26. Simulation results for shelled corn drying tests . . . . 94

27. Average differences between test conditions and simulation
results for the shelled corn drying tests. . . . . . 94

28. Simulation results for pea bean drying tests . . .
29. Average differences between test conditions and simulation
results for pea bean drying tests. Includes cooling
only for test 12 . . . . . . . . . . . . . . 99
30. Average inlet and outlet conditions for pea beans dried

in an Ace crossflow dryer with a heated air temperature
Of 32°C 0 O O O O O O O O O O O O O O O O 102

vii

Table Page

31. Standard conditions for the simulation of dryer performance
for the drying of shelled corn . . . . . . . . . 115

32. Capital and energy cost values used for obtaining
optimization results for shelled corn. . . . . . . 117

33. Ranges for variable design factors . . . . . . . . 118

34. Optimization results for one-stage concurrentflow dryer
at three grainflow rates . . . . . . . . . . . 119

35. Optimization results for two-stage concurrentflow dryer
at three grainflow rates . . . . . . . . . . . 120

36. Optimization results for three-stage concurrentflow
dryer at three grainflow rates . . . . . . . . . 121

37. Cost breakdown and efficiency for one-stage concurrentflow
dryer at three grainflow rates . . . . . . . . . 122

38. Cost breakdown and efficiency for two-stage concurrentflow
dryer at three grainflow rates . . . . . . . . . 122

39. Cost breakdown and efficiency for three-stage concurrentflow
dryer at three grainflow rates . . . . . . . . . 123

40. Optimization results for two-stage concurrentflow dryer at
three tempering lengths for a grainflow of 2.5
tonne/hr-m o o o e o o e e o e o e o o 125

41. Cost breakdown and efficiency for two-stage concurrentflow
dryer at three tempering lengths for a grainflow of 2.5
tonne/hr-m 2 . . . . . . . . . . . . . . 126

42. Cost breakdown and efficiency for two-stage concurrentflow
dryer at three grainflow rates with feed-forward
recycling of exhaust air . . . . . . . . . . . 129

43. Cost breakdown and efficiency for three-stage concurrent-
flow dryer at three grainflow rates with feed-forward
recycling of exhaust air . . . . . . . . . . . 130

44. Optimization results for two- and three-stage concurrent-
flow dryer with an outlet temperature limit of 60°C . . 131

45. Cost breakdown and efficiency for two- and three-stage
concurrentflow dryer with an outlet temperature limit
of 60°C.. . . . . . . . . . . . . . . . 132

46. Costs for drying and storing corn on-farm in Illinois,
1976 . . . . . . . . . . . . . . . . . 134

viii

LIST OF FIGURES

Figure

1. Corn production fer grain in Michigan, 1955 to 1971 and
projected to 1985 . . . . . . . . . . . .

2. Production of dry beans in Michigan, 1955 to 1971 and
projected to 1985 . . . . . . . . . . . . .

3. Block diagram of a two-stage concurrent flow dryer with
counterflow cooler. . . . . .

4. Types of stress cracks in dried corn kernels. . .

5. Block diagram of a single-stage concurrentflow dryer with
a counterflow cooler . . . .

6. Air and product temperatures versus depth for a single-
stage concurrentflow dryer . . . . . . . .

7. Schematic of installed concurrentflow dryer .

8. Scattergram of the change in splits with exit grain
temperature . . . . . . . . .

9. Scattergram of the change in splits with the change in
grain moisture . . . . . . . . . . .

10. Scattergram of the change in cracks with exit grain
temperature . . . . . . . . . . .

11. Scattergram of the change in cracks with the change in
grain moisture . . . . . . . . . . . . .

12. Scattergram of BCFM with the exit temperature of the
grain . . . . . . . . . . . . . . . . .

13. Scattergram of BCFM with the change in grain moisture.

14. Scattergram of Stein breakage percentage with the exit

grain moisture . . . . . . . . . . . . . .

Page

11

22

30

31

35

41

42

43

44

50

51

52

Figure Page

15.

16.

17.

18.

19.

20.

21.

22.
23.
24.

Scattergram of Stein breakage percentage with the change
in grain moisture content . . . . . . . . . . . 53

Moisture content versus tempering time for shelled corn
after drying from 25.0% w.b. in a concurrentflow dryer . 73

Effect of tempering time on corn moisture content profile
in a concurrentflow drying stage following tempering . . 74

Schematic of counterflow process . . . . . . . . . 77
Scattergram of the change in cracks with exit grain

temperature times change in moisture content divided

by grainflow . . . . . . . . . . . . . . . 84

Correspondence plat for single-stage concurrentflow drying. 92

Correspondence plots for'multistage shelled corn drying
tests. I O O O O I O O O O O O O D O O O 97

Correspondence plots for'multistage pea bean drying tests . 100
Basic flowchart of dynamic programming Optimization . . . 110

Schematic of a two-stage concurrentflow dryer with feed-
forward recycling of exhaust air. . . . . . . . . 128

A!

AC

CE

CI

IC

11

IM

IN

IRR

LIST OF SYMBOLS

constant

constant

annual cost, $

constant

Stein breakage, %

budgeted capital cost, ¢/kg product dried

mass flow specific heat, kJ/hr-mz-PC

Capital cost factor, $

energy cost, ¢/kg product dried

95% confidence interval

diffusion coefficient, m2/hr

energy use, kJ/kg product dried

statistic for variance ratio test

dry weight flow rate, kg/hr-m2

air humidity ratio, decimal d.b.

minimum cost summation for dynamic programning
investment cost, $

insurance factor, %
maintenance factor, %
interest rate, %

internal rate of return, %

xi

NS

Nu

Pr

PW

Re

SP

SV

corn fines correction factor

local moisture content, decimal d.b.
Mach number

average kernel moisture content, decimal d.b.
assumed product life, yr

net yearly savings, $

Nusselt heat transfer number

price of energy, ¢/kJ

Prandtl fluid number

present worth, 3

volumetric airflow, m3/m2—min

gas constant

Reynolds fluid flow number

change in pea bean cracks, %

static pressure due to airflow, cm H20
equipment salvage value, $

air temperature, °C

dynamic programming control vector
velocity, m/min

dynamic programming state vector
goodness-of-fit statistic

product specific surface area, mZ/m3
specific heat, kJ/kg-°C

effectiveness ratio for counterflow heat exchanger
percentage of corn fines

enthalpy flow rate, kJ/hr-m2

xii

hf8

hfg'

"1
y

convective heat transfer coefficient, kJ/hr-m2-°C
latent heat of vaporization for water in product, kJ/kg
latent heat of vaporization for free water, kJ/kg
cost function for iEB-stage of dynamic programming
Colburn convective heat transfer factor

thermal conductivity, kJ/hr-m-°C

constant

observed simulation value

linear correlation significance

kernel radial coordinate, m

linear correlation coefficient

equivalent kernel radius, m

relative humidity, decimal

time, hr

kinematic viscosity, m2/hr

bed depth coordinate, m

total bed depth, m

expected experimental value

symbols used as subscripts

a

amb

air

ambient

bulk

critical statistical value
equilibrium

fuel

fan/motor combination

xiii

summation index
initial

product

water vapor

water liquid

xiv

I. INTRODUCTION

Grain as a cash crop or a feed crop is economically important
in the United States (U.S.) and Canada for both domestic consumption
and export. Of the cash crops harvested in.Michigan, corn requires
drying, either as ear corn or artificially dried as shelled corn. The
drying equipment used to dry shelled corn can be utilized only during
the 4-8 week period of harvest. Drying other craps with the same
equipment can help reduce the investment cost per tonne of grain dried.
A second crop which will be considered in the following study is pea
beans. While pea beans do not require drying every year, they are
very susceptible to damage during the drying process.

Shelled corn production.in Michigan ranks tenth in the U.S.
(Hines 35 31., 1976). A projection for production of shelled corn for
grain forecasts a decrease in corn acreage in Michigan with a corre-
sponding increase in grain yield resulting in a fairly constant level
of production as illustrated in Figure l (Anon., 1973).

The field sheller produced dramatic changes in corn harvesting
methods in the l960§t For example, only 18% of the Illinois corn

acreage was field shelled in 1960 as compared to 70% in 1969 (Hill and

Scott, 1969). Shelled corn is usually harvested when the moisture con-
tent in the field is 25-30% w.b. and is commonly dried to 15% w.b. to
prevent heating due to respiration and excessive deterioration due to

mold growth.

Mil. Bu.
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1955 1960 1965 1970 1975 1980 i985

 

Figure 1 Corn . '
° PTOduCtlon for rain ‘ ' °
projected to 1985. g 1“ ”IChISan. 1955 to 1971 and

Source: Anon. (1973).

 

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1955 1960 1965 1970 1975 1980 1985

Figure 2 Production of d
' . ry beans in M' ° .
PrOJected to 1985. 1°h183n. 1955 to 1971 and

Source: Anon. (1973).

The necessary decrease in moisture content of shelled corn is
accomplished through the use of artificial drying equipment either on
the producing farm or at the merchandising elevator. The percentage of
the corn crop which was dried on-farm and off-farm for several mid-
western states is shown in Table 1. Hill (1970) found on-farm drying
to be more profitable than elevator drying when the dried grain is
stored and fed on-farm. Hill predicted that, as seasonal labor becomes
more expensive and as elevators extend drying capacity at competitive

prices, the percentage of grain dried on-farm will decrease.

Table l.--Drying of corn stored on-farm, 1974-1975.

 

 

 

 

Dried naturally in Dried artificially

field or storage On farm Off farm
State

1975 1974 1975 1974 1975 1974
Percent

MICHIGAN 45.3 40.2 51.0 57.0 3.7 2.8
Illinois 33.5 21.0 65.0 77.5 1.5 1.5
Indiana 12.2 12.0 87.2 86.3 0.6 1.7
Iowa 30.6 37.5 68.4 60.2 1.0 2.3
Wisconsin 45.3 39.7 52.0 57.3 2.7 3.0

 

Source: Kenyon 33 21, (1976).

Pea beans (often referred to as Navy beans or white beans) are
a major cash crop in Michigan. Michigan is the leading state in the
U.S. in the production of pea beans (Hines gt_al,, 1976). Production
of dry beans (pea beans represent three—fourths of the production) in
Michigan in 1985 is projected to be 9.9 million bags (100 pounds/bag)

as illustrated in Figure 2 (Anon., 1973). Ontario is presenting

increasing competition to Michigan in the Navy bean export market as

illustrated in Table 2.

Table 2.--Navy bean exports as a percent of North American experts for
the 10 year period 1965-1974.

 

Production (1,000 bags)

 

 

Year
Ontario Michigan

1965 35.0 65.0
1966 24.6 75.4
1967 28.3 71.7
1968 32.4 67.6
1969 26.1 73.9
1970 31.8 68.2
1971 50.5 49.5
1972 41.1 58.9
1973 58.1 41.9
1974 49.7 50.3

 

Source: Anon. (1977).

The weather patterns during growth and maturation of the bean
largely determine whether or not any drying is necessary. Most of the
beans are marketed directly after harvest. If the moisture content is
20-24% w.b. the beans need to be dried to 17.5-18.0% w.b. for storage.
If the moisture content is below 20% w.b. the beans will be placed in
aerated storage and the moisture content reduced by aeration. Very
little drying is done in Michigan with on-farm dryers (Maddex, 1977).
Dry beans stored at 16% w.b. or more can develop mold and musty odors
if the storage temperature is greater than 7°C. Storage below 14% w.b.
with relative humidities above 70% can also result in mold growth and

the development of off-flavors (Adams, 1975).

1.1 Trends in grain dryer design

The on-farm drying of shelled corn started with in-bin drying
utilizing a perforated floor which allowed the forced flow of ambient
air through the corn mass. This drying process is slow and thus the
corn is quite vulnerable to mold for initial moisture contents over
20% w.b. Adding heat to the drying air improves the drying rate but
may result in severe overdrying in the bottom layers of the bin.
Stirring devices in the bin remove the dry grain from the drying floor
and mix it with the partially dried grain. Stirring alleviates to
some extent the overdrying problem with little additional energy
requirement but at the expense of repeated handling of the dried
product.

As the market for corn increased a need arose for high capacity
drying systems. In the column batch dryer, which was designed to meet
this need, the grain is dried while being held in vertical columns
between 40 and 50 cm thick. The natural extension of the column batch
grain dryer was the continuous flow crossflow column dryer with
integral and rapid cooling. Both drying systems are high capacity,
flexible drying devices and are now in common use for drying corn in
Michigan. Table 3 shows the distribution of various dryer types used
for drying corn on-farm in Michigan during 1974-1975. Corn dried at

the elevator is, at the present time, mostly dried in continuous cross-

flow dryers.

1.2 Dryer energy efficiency
Approximate energy efficiencies for various drying devices are

listed in Table 4. Combining these efficiencies with production data

Table 3.--Shelled corn dried artificially by dryer type, Michigan,

 

 

1974-1975.
1974 1975
Continuousflow 45.7 39.5
Batch 38.3 48.1
Bin 14.3 9.2
Natural air 1.7 3.2

 

and dryer type useage date for Michigan, the increase in energy con-
sumption can be estimated. As shown in Table 5, the energy consumption
per kilogram of corn dried has almost doubled during the period 1960-
1975.

Increases in energy prices have prompted interest in reducing
overall energy consumption. There are several possible alternatives
for reducing the energy consumption for drying corn while maintaining
the current high-speed drying capacity:

1. Adjust the operating procedure (Morey gt_al,, 1976) or the
deSign (Johnson, 1973) of current high-temperature dryers.

An improvement in energy efficiency of 10% would reduce average
energy consumption to about 765 kJ/kg corn.

2. Use dryeration (McKenzie gt_31,, 1972) with current or modified
high-temperature dryers. Average energy consumption would fall
to between 620 and 690 kJ/kg corn.

3. Develop new dryer technology such as the concurrentflow dryer
(Graham, 1970; Anderson, 1972).

4. Use heat recovery methods which significantly reduce the energy
consumption for drying corn (Bakker-Arkema gt_al,, 1975; Lai

and Foster, 1975).

Table 4.--Approximate energy efficiency for various drying technologies.

 

Drying Efficiencya

 

Drying Technique kJ/kg corn Comments

1. Drying with - - Slow drying, grain must be

ambient air below 20% moisture content;
vulnerable to mold, weather
conditions critical

2. Electric binb 495 Slow drying rate, mold in-
drying crease, dependent on weather,
(1° - 4°C rise) good grain quality, limits

on moisture content; below
23% w.b.

3. Bin dryingc 655 Overdrying in bottom layers,
without stirring difficult to manage for
(6°C) Optimum performance

4. Bin drying 655 Mechanical reliability may
with stirring be a problem, flexible in
(43° - 60°C) grain depth, fast batch

procedure

5. Batch or 900 High capacity, flexible,
continuousflow high kernel stress from
with cooling fast drying and cooling,
(82° - 104°C) incomplete air saturation

6. Batch or 720 Increased capital invest-
continuousflow ment, two handlings to

with dryerationc
(82° - 104°C)

storage, 50-60% increase in
throughput, improved product
quality

 

Source: Adapted from Anon. (1975).

a kernel temperature of 49° to 60°C.

aBased on drying 10 points (25 to 15% w.b.), 7500 kJ/kg of
water for high-temperature dryer, and 5500 kJ/kg of water for bin
drying systems.

b

Electric drying based on 49.6 kJ/kg/point of moisture removed.

cDryeration response is a constant 2 points of drying, assuming

Table 5.--Estimated fuel use for Michigan, 1960-1975.

 

 

1960 1965 1970 1975
Corn Production (million kg)a 2292 2295 2898 3881
Dryer Types Used, %b
Continuousflow 0 13.2 26.3 39.5
Batch 0 16.0 32.1 48.1
Bin 50 36.4 22.8 9.2
Natural air 50 34.4 18.8 3.2
kJ/kg cornc 328 501 675 849
Energy use, 1010 kJ 75.2 115.0 195.6 329.5

 

aAdapted from yearly issues of Michigan Agricultural Statistics.

b1975 figures from Kenyon 33 51. (1976). 1960 figures assumed.
1965, 1970 results from linear variation between 1960 and 1975.

cAverage by dryer type percentage using energy efficiency
figures from Table 4.
1.3 Maintaining grain quality

The increased use of the column dryer has increased the sus-
ceptibility of the dried corn to breakage during further handling
(Thompson and Foster, 1963). Increases in the percentage of broken
kernels (BCFM) is not evident in surveys of grain receipts as illustra-
ted in Table 6. However, Paulsen and Hill (1976) have found signifi-
cant increases in the percentage of broken kernels as corn moves through
export market channels. The concurrentflow dryer offers improved
quality and reduced susceptibility to breakage as compared to the

crossflow dryer (Thompson 35 21,, 1969; Gygax gt a1., 1974).

Table 6.--Percent of inspected receipts by grade for corn two months
following harvest.

 

 

Year #1 #2 #3 #4 #5 Sample
1966 1.4 15.7 27.4 22.1 23.6 9.8
1967 1.6 15.3 30.2 22.1 20.2 10.5
1968 2.0 28.6 35.6 21.6 8.0 4.2
1969 2.1 23.0 30.3 23.7 12.6 8.4
1970 3.1 36.2 27.5 18.2 9.6 5.4
1971 4.8 34.6 33.5 16.0 6.3 4.8

 

Pea bean drying, when necessary, is usually done at the ele-
vator using crossflow dryers at temperatures of 30°-40°C. Very little
is dried on—farm due to problems with cracking of the seedcoat. The

grade standard for pea beans is presented in Table 7.

Table 7.--Grade standard.for pea beans.

 

Maximum limits of (%)

 

 

Grade Comments
Splits Damage PM
US no. 1 Well screened and of 1.5 trace trace
' good natural color
US no. 2 Well screened and may 3.0 0.1 0.1
be slightly off color
US no. 3 May be of poor color 5.0 0.5 0.5

 

Source: USDA (1969).

10

1.4 Objectives

The concurrentflow dryer is more energy efficient than the
crossflow dryer (Mfihlbauer gt_313, 1971; Bakker-Arkema gt_al,, 1972)
and results in less grain damage due to the drying process (Thompson
3511., 1969; Gygax 9331., 1974).

The objective of this study is to simulate drying in and to
analyze the design of a multistage concurrentflow dryer with inter-
mediate tempering stages and a counterflow cooler. A block diagram of
a two-stage concurrentflow dryer is given in Figure 3. The grain enters
at the top of the drying column and flows continuously through the
drying column at a controlled rate. The heated air flows through a
drying stage in the same direction as the grain flow and is used to
reduce the moisture content of the grain in that stage. The moisture
laden air is exhausted from each drying stage prior to a succeeding
tempering stage. Ambient (unheated) air enters the bottom of the
counterflow cooler and flows in a direction opposite to the grain. The
cooling air is exhausted at the same point as the exhaust air from the
previous drying stage.

The first step of the study was to conduct an experimental
investigation of a multi-stage concurrentflow dryer using pea beans
and shelled corn. 1n the second step these results were used to
verify the computer model developed for the multi-stage drying process.
Finally a dynamic programming optimization algorithm using the multi-
stage model was constructed to help study the effect of grainflow,
staging, tempering and heat recovery on the design and operation of

multi-stage concurrentflow drying systems.

11

GRAIN

IN
| I HEATER m AMBIENT AIR

CONCURRENT
DRYING

 

 

 

 

 

L———->BXHAUSI

[TEMPERING I
1 L... a m...

CONCURRENT

 

 

 

 

 

 

—-"-—'-—"EXHAUST

 

 

 

COUNTER
FLOW
COOLING

 

 

 

r fl—mmam AIR

GRAIN OUT

 

Figure 3. Block diagram of a two-stage concurrent flow dryer with
counterflow cooler.

2. LITERATURE REVIEW

The following section presents a literature review of selected
areas concerned with the drying of cereal grains.

The review begins with previously published optimization studies
concerning the design of convection grain dryers. Next is a summary
of the effect of artificial drying on the quality of pea beans and
shelled corn. Last is a review of laboratory and computer simulation
studies of single-stage concurrentflow dryers.

Other pertinent studies and published results will be reviewed
to provide necessary background when needed fer a particular subsection

in the remainder of the thesis.

2.1 Dryer energy optimization

The design and operational control of cereal grain dryers has
been studied using computer simulation for evaluation of dryer per-
formance. The model is often coupled with an optimization algorithm
which predicts optimal design and operational parameters.

The objective function used in an optimization procedure varies
depending on the specific interest of the program. It may include:
(1) drying capacity, (2) various grain quality factors, (3) energy costs
for heating and moving the drying air, (4) capital cost considerations
for the drying equipment involved, and (S) the amount of moisture

removed.

12

13

Thompson (1967) defined a general performance function for a
dryer operating at fixed drying capacity while removing a specified

amount of moisture:

Cost = C1(drying speed) + C2(drying temperature) + C3(heat energy
supplied) + C4(fan energy supplied) + C5(size of the dryer

required) (1)

1, C2 are penalty costs for stress cracks and breakage,

respectively; C3, C4 are the Operating costs per unit Of energy; and

where C

CS is the fixed cost per cross-sectional drying area. The Optimization
algorithm develOped was applied to both crossflow and concurrent flow
grain dryers using a gradient search technique.

Morey and Peart (1971) studied Optimum horsepower and depth in
a natural air corn drying system. The Objective function was based on
the fan energy used and the capital cost Of the system. The allowable
time befOre storage (which is a function Of grain temperature and
moisture content) was used as an Operational constraint. Overdrying
or underdrying costs were neglected. The Optimum system was determined
graphically.

Farmer (1972) developed an Optimization program for the design
and economic analysis of batch-in—bin grain drying systems. The
Objective function was based on the heat and electrical energy cost
equations developed by Bloome (1970). Grain quality was not considered
explicitly by the computer program but was constrained implicitly by
constraints placed on the dryer operation variables. A two-dimensional
Optimization routine used a one-dimensional search algorithm to find

the optimum values of airflow and heated air temperature. A sensitivity

14

study of operating costs was performed with regard to (Farmer and
Bakker-Arkema, 1971): (1) economic conditions, (2) design parameters,
and (3) variations in Operating and marketing practice.

Thygeson and Grossman (1970) studied the Optimum design of
through-circulation dryers (crossflow type) for the case of constant
rate drying Of an arbitrary particulate solid. The Objective function
was the throughput rate constrained by the power fOr moving the air and
the maximum allowable local final moisture content. Optimization was
accomplished through the application of the Kuhn-Tucker Optimality
conditions.

Brook and Bakker-Arkema (1976) developed a computer simulation
model which minimized the Operating costs for drying shelled corn in
three frequently used dryer types: (1) the continuous crossflow dryer,
(2) batch-in-bin dryer, and (3) the column-batch dryer. The Objective
function is based on the heat and electrical energy costs per bushel
Of corn dried. After calculating the optimum drying costs, several
associated corn quality factors are estimated for the optimum drying
conditions: (1) change in test weight, (2) average temperature Of the
corn leaving the dryer, (3) allowable storage time permitting only
1/2% dry matter loss, and (4) changes in broken kernels due to harvest
and drying. Optimization was accomplished through the use of an
algorithm which defines a number of points randomly scattered through
the variable space. These points are reflected through the centroid
until the Optimum condition (minimum drying cost) is achieved.

A multiple column crossflow dryer was studied as a means to
increase the efficiency Of drying and reduce the moisture gradient Of

the grain at a given drying capacity (Morey and Cloud, 1973). The

15

Objective function was based on the moisture content differential, the
energy required to move the air and the thermal efficiency (kilograms
Of water removed per 1000 kJs of energy supplied). A trial and error
procedure was used in estimating the relative Speeds of grain in the
various drying columns to insure that the grain discharged at the
desired final average moisture content.

Ahn gt_al, (1964) proposed dividing the grain column of a con-
ventional crossflow dryer into several sections. The effect of varying
the airflow in each section was studied using dynamic programming. The
Objective was to maximize a profit function based on the amount of
moisture removed and the cost Of supplying the airflow to each stage.
Grain quality was not considered.

Schroeder and Peart (1967) also studied the Optimal air distri-
bution pattern in a crossflow dryer using dynamic programming. They
defined the "biostrain index," based on the Optimal solutions for up
to seven sections, as the ratio of the amount of moisture removed in
each section to the average moisture content in that section. For the
Optimal air distribution patterns the biostrain index was essentially
constant with a mean of 0.270. The biostrain index for a uniform
airflow pattern begins at 0.170 and rises to 0.470 at the end of the
drying process.

Bakker-Arkema.gtnal. (1973b) studied a modified crossflow
dryer using reversed airflow direction and air recycling in part Of
the column. Three main parameters were investigated in a sensitivity
study: (1) section length, (2) grain column thickness, and (3) drying
air distribution. Optimization was accomplished using a bound con-

vergence technique. The objective function was based on the energy

16

requirements for drying with no direct consideration of grain quality
factors except the final average moisture content.

The Optimal design of the concurrentflow dryer, with or without
a counterflow cooler, has also been studied using computer simulation.
Thompson (1967) developed a simulation model for a concurrentflow
dryer. General performance graphs using the model were developed to
study and optimize the design of the dryer. Thompson 33 a1. (1969)
compared the performance characteristics of crossflow and concurrent-
flow grain dryers using general performance graphs for each dryer type.

Farmer (1972) developed a dynamic programming algorithm for a
single-stage concurrentflow dryer with a counterflow cooler. The
Objective function considered energy costs and employed grain quality
constraints. Two cases were studied: (1) exhausting the air leaving
the dryer and (2) recycling the cooler exhaust air to the inlet of the
heater for the drying section. Bakker-Arkema gt_31, (1973b) compared
results Obtained using the Farmer algorithm with a commercial con-
currentflow grain dryer with a counterflow cooler. The results
indicated that the concurrentflow dryer should be Operated at higher
air temperatures and lower airflow rates (to increase the relative
humidity of the outlet air).

Computer simulation for analyzing and optimizing the design of
grain dryers is fairly well developed at the academic level. Cost
functions for heat and electrical energy use are available for most
any air/grain flow configuration (Thompson, 1967; Farmer, 1972;
Mfihlbauer and Isaacs, 1975; Young and Dickens, 1975). Adequate models
for calculating the effect of drying on various grain quality factors

are beginning to appear for crossflow and batch dryers (Schroeder and

17

Peart, 1967; Brook and Bakker-Arkema, 1976). Research work in West
Germany is defining some new directions in grain quality determination
and its application to grain dryer design and analysis (Mfihlbauer and
Christ, 1974; Mfihlbauer £E.El:’ 1976).

Recently dryer manufacturers and dryer Operators have.become
interested in the Optimization programs which are available for minimi-
zing energy use in the drying process. The current emphasis on energy
conservation and improved grain quality is generating more interest
in using computer simulation for establishing standardized ratings for
commercially available grain dryers such as proposed by Bakker-Arkema
gt El: (1973a). Standardized ratings would encourage manufacturers to
improve the design of their drying equipment or to be innovative in
developing new dryer types (Graham, 1970; Anderson, 1972). The new
dryer types can be fairly easily simulated and Optimized using esta-

blished expertise.

2.2 Drying effects on grain quality
Product quality and its determination are important fer the

marketing and processing Of cereal grain. Desirable properties Of high
quality grain are (Brooker 33 21., 1974):

l. appropriately low and unifOrm moisture content

2. low percentage of broken and damaged kernels

3. low susceptibility to breakage

4. high test weight

5. high starch yield

6. high Oil recovery

7. high protein quality

18

8. high viability

9. low mold count

10. high nutritive value
An exhaustive determination Of grain quality is not a simple task.
The grain dealer is especially interested in (l), (2), (3), and (4);
the wet or dry miller in (5), (6), or (7); the farmer seeding corn in
(8); the animal feeder in (9) and (10). While not all quality factors
are important to every user, they are all affected by the cereal grain

drying process.

2.2.1 Stress cracking of pea beans

The U.S. grade standard for pea beans was listed previously in
Table 7. Moisture content is not a grade factor. Pea beans which con-
tain more than 18% moisture w.b. are graded according to Table 7 and
then designated "high.moisture" beans.

Hall and.Maddex (1952) dried pea beans at 38°C both with and
without partial recirculation of the drying air. As the percentage
Of recirculation increased the percentage Of cracked seed coats (cracks)
decreased. NO air recirculation resulted in 12 to 18% cracks; cracks
decreased to 1.75% at 50% recirculation and 1.25% at 75% recirculation.
Even though the drying time increased the reported fuel consumption did
not vary significantly due to the increased enthalpy Of the air which
was recirculated.

Wang (1956) theorized that the cracking Of the seed coat was
due to unequal shrinkage because Of moisture differences between the
seed coat and the inner part Of the kernel. Applying the theories of

engineering mechanics Wang developed an equation for determining whether

19

or not the seed coat was going to crack during a given drying period.
The equation was based on: (1) thermal expansion coefficient, (2) mois-
ture contraction coefficient, (3) modulus Of elasticity, (4) Poisson's
ratio, (5) rate Of tauperature change, (6) rate of moisture change, and
(7) the force exerted on the skin by the kernel due to unequal
shrinkage. NO attanpt was made to define the necessary parameters as
a function of drying. An intermittent drying process using air at 38°C
was devised consisting of: (1) 15 min. heating at high humidity
(adjusted so that the vapor pressure was equal for the air and the
beans), (2) 30 min. drying with air at 38°C and 50% RH, (3) 10 min.
heating at high humidity, and (4) 30 min. drying with heated air. The
process was then repeated after a four hour resting (tempering) period
which allowed the strain caused by moisture differences to be relieved
as the moisture diffused from the interior Of the bean. For beans
dried from 20 tO 15% moisture, w.b., 1.3% cracks were Observed as
compared to over 2.0% for a conventional continuous process. Little
difference were reported for resting periods Of 3, 4, 5, and 6 hours.
Zoerb (1958) studied the mechanical and rheological properties
Of several grains including pea beans as related to harvesting and
handling: (1) yield strength, (2) maximum compressive strength,
(3) average shear stress, (4) modulus Of elasticity in compression,
of resilience, and of toughness, and (5) energy for rupture by both
impact and static shear. The parameters which affect these mechanical
prOperties were found to be: (1) moisture content, (2) rate of deforma-
tion, and (3) kernel position. The study was made from a macroscopic

viewpoint with respect to the pea bean kernel and no attempt was made

20

to separate the effects on the seed coat from those on the interior of
the kernel.

Perry (1959) investigated pea bean mechanical damage occurring
during commercial handling. The effect of moisture content, temperature
and height of drop on mechanical damage was studied. Perry noted that
dampening Of dry beans restored their ability to resist damage.
Bakker-Arkema gt_31, (1968) modeled the absorption rate in beans as a
means to toughen the pea bean kernel to prevent damage during handling.

Narayan (1969) computed the elastic modulus Of pea beans for
various moisture contents in the range of 11.5-28.8% moisture w.b. for
beans quasi-statically loaded. Narayan concluded that beans suffer
the least damage due to impact when the moisture content is in the
range of 13.4-15.6% w.b.

Soybeans are very similar in structure to pea beans with an
outer seed coat and two inner cotyledon halves and thus may be expected
to behave very similarly to pea beans. Walker and Barre (1972) studied
the effect Of drying on soybean germination and cracking. Tests were
conducted for the following range Of drying conditions: (1) air tem-
peratures 32°C-66°C and (2) 20-60% RH. They concluded that no seed

coat cracks develOped for relative humidities greater than 40%.

2.2.2 Stress cracks and broken corn

Drying shelled corn with hot air increases the percentage of
stress cracks found in the kernels. Stress cracks are cracks in the
starchy endosperm inside the kernel which do not rupture the seed
coat. Stress cracks are generally divided into three categories

according to the pattern formed in the kernel: (1) single, (2) multiple,

21

and (3) checked. The three categories are compared in Figure 4.
Thompson and Foster (1963) related the extent Of the development of
stress cracks for yellow corn dried in a crossflow dryer to the overall
drying rate, expressed as moisture loss in percentage points per hour.
Drying air temperatures in the range of 60°-117°C were used. The
relationship between stress cracks and drying rate has been confirmed
for white corn (White and Ross, 1972) and for east EurOpean yellow corn
varieties (Katic, 1973).

Grain is Often cooled as the last step in the drying process.
White and Ross (1972) found that rapid cooling of high temperature
corn causes a high percentage Of stress crack development. Slow
,cooling (cooling to ambient temperature in a polystyrene insulated
chamber) resulted in a significant reduction in the percentage of
stress cracked kernels. Foster (1973) reported that while a con-
ventional crossflow dryer with rapid cooling may produce as much as
90% stress cracked kernels, delayed cooling (dryeration) could reduce
this to 40% as compared to natural air drying producing 8% stress
cracked kernels.

'The susceptibility of corn to breakage during handling is
related to the amount of stress cracking Of the kernels which occurs
during the harvesting and drying processes. Thompson and Foster (1963)
found that shelled corn artificially dried using heated air was two
to three times more susceptible tO breakage than corn dried with
natural air. McGinty (1970) confirmed that heat dried corn showed
higher susceptibility to breakage with increasing drying air temperature

and airflow rate.

22

 

\

 

Figure 4. Types of stress cracks in dried corn kernels.
A--Whole kernels
B—-Single stress cracks

C--Mu1tiple stress cracks
D--Checked kernels

Source: Thompson and Foster (1963).

23

Agness (1968) described a breakage test which can be used to
provide an evaluation of the mechanical damage inflicted on corn during
harvesting, handling and drying. The corn sample is placed in an
aluminum container. An impeller revolves around inside the container
for a period of two minutes. The sample is removed and the percentage
of material passing through a 0.48 cm round-hole screen is the percentage
of breakage. The test is commonly referred to as a Stein breakage test.
The grain samples should be carefully conditioned to a common moisture
content to make comparisons valid. Stephens and Foster (1976) related
the amount of breakage due to handling to the results of the Stein
breakage test. Corn dried in the field resulted in 3.0% breakage, corn
dried in a low temperature (38°-53°C) bin dryer in 11.6%, and corn
dried in a high temperature (93°-106°C) batch dryer in 36.6%. Multiple
runs with four different spouting arrangements yielded a linear corre-
lation between handling breakage and tester breakage with a correlation
coefficient of rc = 0.98.

The theories of engineering mechanics have application in
describing stress crack formation in shelled corn. Thompson and Foster
(1963) reported that corn kernels dried at 143°C were puffed_and the
crown almost completely inflated. Ekstrom gt_al, (1966) determined
the coefficient Of cubical thermal expansion Of corn kernels as a
function of kernel temperature and moisture content. The strain
produced by the expansion can be related to the stress inside the
kernel. Hammerle 33 31. (1971) found that the horny endosperm of
corn kernels is thermo- and hydro-rheologically simple. Therefore the
time behavior of the mechanical properties of the material can be

analyzed at one common temperature and moisture content. The

24

properties at other temperatures and moisture contents are computed
through multiplication by a temperature or moisture shift-factor based
on the standard and the desired temperature or moisture. The complete
mechanical behavior of corn horny endosperm was described by the
following rheological properties: (1) bulk modulus, (2) shear modulus,
(3) tension modulus, (4) Poisson's ratio, (5) failure stress, and

(6) the time-temperature and time-moisture shift factors. Mensah
g§_§g: (1976) studied the effect Of various drying conditions on the
impact fracture resistance of different corn varieties as related to:
(1) energy absorbed per unit shear area, (2) maximum resistive shear
stress, and (3) impulse imparted by an impact apparatus. Overall
kernel strength was reduced in kernels dried at 93°C compared to
kernels dried at 60°C. Genetic differences were found to be signifi-
cant; for the three varieties tested, one was found to be more resistant
to damage than the other two.

When applying engineering mechanics to grains such as corn one
has to recognize that the kernel is not homogeneous. Corn consists of
four distinct parts: (1) horny endosperm, (2) floury endosperm,

(3) germ, and (4) seed coat. Analysis of the kernel must include all
factors and their interrelationships. For structural quality the

floury endosperm and the seed coat are most important. For oil recovery
or when used for seed the germ is most important. While inroads have
been made in this area, there is more research necessary before a

useable, stochastic model Of the kernel can be developed.

25

2.2.3 Milling quality

Kernel temperature during drying has a significant effect on
starch quality and yield. Lasseran and Boigneville (1973) dried
western European shelled corn in a batch dryer at temperatures from
40° to 150°C. When the drying temperature was greater than 100°C a
depressive effect on starch yield was Observed, decreasing from 67% at
90°C to 58.7% at 150°C. Further tests in a continuous crossflow dryer
showed that drying at an air temperature of 140°C resulted in an 11.6%
decrease in starch yield as compared to drying at 80°C. Lasseran and
Boigneville speculated that two-stage drying with intermediate storage
under aeration may be acceptable. French (1973) stated that when
native starch (either corn or potato) is gradually heated (up to 55°C)
the change in the starch granule is reversible and so the starch remains
essentially unaltered after drying and cooling. If heating is con-
tinued in the range Of 60°-80°C irreversible gelatinization occurs such
that after cooling the starch will be a semi-rigid gel.

Oil recovered by wet milling of corn is derived entirely from
the germ. Vojnovich gt 31, (1975) studied quality Of corn dried in an
experimental fluidized-bed batch dryer. A regression analysis of oil
recovery versus drying temperature in the range Of 49°-149°C showed
that recoverable oil decreased with increasing temperature at the rate
of 0.3%/°C (rc = 0.95). Stress cracked and broken kernels may result
in a damaged germ. Freeman (1973) reported that as much as 90% of the
oil in these damaged germs may be absorbed by the gluten in the
endosperm prior to or during processing. Overhults gt_al, (1975) con-
cluded that the overall quality Of the Oil obtained from soybeans did

not significantly deteriorate when beans were dried in thin layers at

26

air temperatures up to 100°C. Some interior breakdown was evident at
the higher temperatures indicating that at temperatures greater than
100°C soybeans may begin to Show deterioration in oil quality.
Peplinski £3 31. (1975) recommended that, on the basis of
several quality factors, the temperature of corn used for milling
should not exceed 80°C; no time-temperature relationship was established.
Mfihlbauer and Christ (1974) have shown that not only is the temperature
of the corn important but the time at that temperature is equally
important. For example, only a light browning of the kernel was
evident for exposure to 140°C air for 16 min. while a very strong
browning was evident after 30 min. The cause of the browning was
suggested to be a chemical reaction between the carbohydrates and the

proteins.

2.2.4 Grain viability

Seed grains require a high germination percentage. High kernel
temperatures kill the germ and thus grain used for seed cannot be dried
under excessive kernel temperature conditions. Kreyger (1972) deter-
mined the critical kernel temperature for a number of small grains as
a function of equilibrium relative humidity as given in Table 8. It
is obvious that there is a significant difference between the various
grain species. Wheat germination is the least heat sensitive followed
by oats, corn and rye. Germination of all grains is more heat sensitive

at high than at low moisture contents.

2.2.5 Nutritive value
A large part of the shelled corn harvested in the U.S. is used

as animal feed. Williamson (1975) suggested several physical

27

Table 8.--Critical kernel temperature as a function of equilibrium
relative humidity for several small grains (criterion: less
than 5% viability decrease).

 

 

RH, % 60 70 80 90
Oats 59 55 50 --
Wheat 63 62 58 52
Corn 52 51 48 46
Rye 53 50 45 41

 

Source: Kreyger (1972).

characteristics which are important when considering corn for animal
feed: (1) provides a unifOrm and consistent ration, (2) provides a
relatively high energy content, (3) provides a palatible ration,

(4) generally is free of mold and other toxic factors, and (5) provides
a major portion of the protein needs.

Assessing the effect of heat treatment on the nutritive value
of corn is a very difficult task; different animals have different
nutritive requirements. The energy contained in the starch of a corn
kernel provides a consistent energy level in many ruminant rations.
However, mink and broilers require a more concentrated energy source in
the form of fat for Optimum performance (Williamson, 1975). Sullivan
g£_gl, (1975) reviewed the work of several researchers on the effect
of heat treatment on corn used for swine and beef rations. They con-
cluded that heat treatment has the following effects: (1) increases
bulk of the grain, (2) increases feed value fOr ruminants, and (3) heat
damaged corn has a greater economic value than allowed under U.S. grade

standards.

28

Mfihlbauer and Christ (1974) investigated the influence of
kernel temperature and time at that temperature on the nutritive value
of corn used for animal feed. The quality criterion used was the con-
tent of the amino acids methionine, cystine and lysine. Rapid drying
of corn kernels in a single layer with heated air at 180°C resulted in
less decrease in amino acid content than longer drying at lower tem-
peratures (140°, 160°C). Wall gt_al, (1975) dried corn in a fluidized
bed dryer with air temperatures in the range of 15°-143°C. Significant
variations in amino acid content were found only for lysine and arginine.
They concluded that at grain temperatures less than 100°C little or no
damage to amino acids occurs (no time-temperature relationship noted).
Vojnovich gt 31. (1975) concluded that higher drying temperatures affect
the solubility of certain proteins and sugars normally present in corn.

Nutritive changes in grain due to drying can be determined
using a combination of analytical methods and animal feeding trails.

The latter, however, is time consuming and expensive. A rapid method
to evaluate the effect of drying on the nutritive value of grain is
necessary. Bjarnason and Carpenter (1969) stated that enzyme-resistant
linkages between the carbonyl groups of sugars and the free amino
groups of proteins, particularly lysine, can make a portion of the
amino acids nutritionally unavailable after drying. Mfihlbauer gt_al,
(1976) conducted an extensive investigation using various drying con-
ditions and concluded that changes in lysine content (which can be
related to nutritive value) could be correlated linearly (rc =

0.74-0.82) with color changes in the kernels.

29

2.3 Concurrentflow grain drying

Concurrentflow grain dryers have only recently become available
commercially. In a concurrentflow dryer the air and the product both
flow in the same direction through the dryer as illustrated in Figure 5.
The hottest air encounters the wettest grain so that the air is cooled
rapidly due to the high rate of evaporation as illustrated in Figure 6.
The kernel temperature remains considerably below the air temperature
in the t0p layers of the dryer because the kernels are not exposed to
the heated air for a long period of time during this period of high
evaporation (Farmer 33 31., 1972).

The concurrentflow dryer has advantages over the crossflow
dryer because of its favorable energy efficiency, grain quality
characteristics, and pollution qualities. The initially high rates of
evaporation allow the use of drying air temperatures as high as 148°-
260°C without causing excessive grain kernel temperatures. The high
drying air temperature results in a high energy efficiency for the
dryer. Energy efficiencies between 4185-5120 kJ/kg of water evaporated
are common for concurrentflow grain dryers.l Crossflow dryers average
about 7500 kJ/kg of water evaporated (Mfihlbauer and Isaacs, 1975).

The concurrentflow dryer subjects all grain kernels to the same
drying treatment thus avoiding non-uniformity in moisture content
inherent in crossflow dryers. The grain temperature continually
decreases through the last portion of the drying bed (Figure 6). This
helps to reduce drying stress, stress cracking, and subsequent
mechanical damage when the dried grain is handled. The increase in

checked and multiple stress cracked kernels in a crossflow dryer is

3O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

GRAIN
IN
AIR
RI — ' IN
\ . ,
\
\ HEATER
\
\ _ .
. 9 1L_
4 L
CONCURRENTFLOW DRYING
[I n DRYING
. 3 AIR OUT
* 3 COOLING
h a AIR our

 

COUNTERFLOW COOLING

 

 

 

 

 

1‘?!
14
GRAIN AIR
OUT IN

Figure 5. Block diagram of a single-stage concurrentflow dryer with
a counterflow cooler.

Source: Brooker £2 31. (1974).

31

 

 

 

 

 

 

300
550 -—
500 -
250 1..
450
.0 5‘ 400
Q 200 - G
u.)
53 g 350 T’
E—
: E
2.” 150 _ o. 300 L AIR
5 E
E- E—
250 L
100 - 200 P
150 ..
50 .. PRODucr
100
n J n 1 1 l l 1 L
1 2 3 4 s 6 7 9

DEPTH, feet

 

L 1 ~ L L L

 

 

0.5 1.0 1.5 2.0 2.5
DEPTH, meters

Figure 6. Air and product temperatures versus depth for a single-
stage concurrentflow dryer.

Source: Brooker 93 21, (1974).

32

markedly higher than the increase from a comparable capacity concurrent-
flow dryer (Thompson gt_al,, 1969; Gygax gt_al,, 1974).

The Clean Air Act of 1970 established standards that must be
adhered to by the grain handling industry. The pollution character-
istics of the various dryer types differ partially due to differences
in the quantities of air discharged to the atmOSphere. The air moved
and exhausted through a crossflow dryer is eight to ten times as large
as in a comparable concurrentflow dryer (Bakker-Arkema gt_al,, 1972).

Several experimental studies of concurrentflow drying have been
conducted. Thompson gt_§1, (1969) conducted concurrentflow drying tests
under the following drying conditions: (1) drying air temperature
93°-204°C, (2) bed depth 0.61 and 1.22 m, (3) air velocity 30-75 m/min.,
(4) grainflow rate 22.0-175.0 kg/hr, and (5) initial moisture content
18.0 and 23.0% w.b. Samples of the dried grain were tested fOr stress
cracks, Stein breakage and wet millability based on starch recovery.
Drying air temperatures of less than 121°C gave acceptable millability
scores. Increasing temperatures resulted in unacceptable and continually
decreasing millability scores. The percentage of kernels with a checked
stress crack pattern and the Stein breakage percentage both increased
with increasing temperature.

Carrano gt_al, (1971) investigated the design of a laboratory
scale concurrentflow dryer with a counterflow cooler for drying shelled
corn. They noted that some drying was done in the counterflow cooling
section. No quality tests were conducted.

Mfihlbauer 35 a1, (1971) conducted concurrentflow drying tests
in the drying air temperature range of 125°-250°C. Only slight changes

in the nutritive value of the corn dried where observed. They

33

concluded that by correctly balancing the air and grain flow rates any
damage to the nutritive value of the corn (which developes because of
high grain temperatures) could be avoided. Thus the energy efficiency
advantage of the higher temperature air could be safely utilized.
Baughman gt_al, (1971) simulated the drying of shelled corn in
a concurrentflow dryer. The model was based on heat and mass balances
and radial diffusion in an assumed spherical kernel. Drying parameters
were studied for the purpose of controlling the moisture of the grain
leaving the dryer. The final moisture content decreased 1.0% d.b. when
the initial grain temperature was increased from 11° to 33°C and when
the initial air humidity decreased from 0.010 to 0.001. Increasing
the airflow rate from 1200 to 2200 kg/hr-m2 decreased the final
moisture content about 5.0% d.b. The inlet air temperature increase
from 66° to 177°C resulted in a 9.0% d.b. decrease in final moisture

content at a grainflow rate of 500 kg/hr-mz.

3. EXPERIMENTAL INVESTIGATIONS

The following section presents the conditions and results of
field experiments conducted with pea beans and shelled corn. Other
cereal grains and agricultural products may also be dried in a con-
currentflow dryer. The two products choosen serve to illustrate the
advantages and possible limitations of the multistage concurrentflow

drying process.

3.1 Multistage drying of pea beans

3.1.1 Equipment and procedures

Drying tests were conducted during the fall, 1976 harvest
season using Canadian pea beans (varieties unknown). A three stage
concurrent flow dryer with a counterflow cooler was supplied by West-
lake Agricultural Engineering, Inc., St. Mary's, Ontario, and erected
at the Cook's Elevator, Kirkton, Ontario (Figure 7). Each drying
stage consists of a two meter long drying bed followed by a 3.7 meter
tempering stage. The third drying stage is followed immediately by a
one meter counterflow cooler. The cross-section of the drying and
cooling column is 1.5 square meters. The wet inlet grain for the dryer
is obtained from the same elevator which fed the wet grain to an Ace

model 1850D crossflow dryer already installed at the site. The dry

34

35

Wet Grain

Westlake
Concurrentflow
Dryer

—_. Ace
Crossflow
Dryer

D1

H

 

 

 

 

T1

 

 

 

 

Fl

T2

E
8:.“
1:55

 

u___. Dry Grain
F.Eli. to Storage

 

 

T

 

 

 

 

 

 

 

 

 

Figure 7. Schematic of installed concurrentflow dryer-—
D1, D2, D3--Drying stages
El, E2, E3--Exhaust ports
T1, T2--Tempering stages
C--Cooling stage

36

outlet grain is augered into the same elevator leg serving the cross-
flow dryer.

Each drying stage employes a separate centrifugal blower with
adjustable louvers for supplying the drying air. The airflow rate in
each stage was measured using a "Velometer" manufactured by Alnor
Instruments. A nine point grid was defined in the one meter square air
supply duct ahead of the gas burner. An arithmetic average of these
nine points was used to set the air velocity for each stage at 30.5 1
3.0 m/min. LP gas was used to heat the air. The drying air temperature
for each stage was maintained by a Honeywell controller (11°C) utilizing
a platinum resistance feedback thermocouple located in the center of
the airduct just prior to the point where the air entered the moving
grain mass.

Air/grain temperatures within the dryer were monitored using
iron-constantan thermocouples. Temperatures were recorded continuously
on a Texas Instruments Multi-Riter multi-point potentiometer. Thermo-
couples were located in each drying stage in the center of the moving
grain mass: (1) 15 cm above the air inlet, (2) 15 cm below the air
inlet, (3) 30 cm below the air inlet, and (4) in the air exhaust
stream. The cooling stage thermocouples were similarily located:

(1) 20 cm below the air exhaust, (2) 40 cm below the air exhaust, and
(3) 60 cm below the air exhaust. Ambient dry and wet bulb temperatures
were monitored using a Princo hand-held sling-psychrometer.

The flow rate of the grain through the drying column is con-
trolled by a variable speed DC motor connected to the three dryer
discharge augers. The grainflow was correlated with the auger RPM.

Laboratory tests conducted by Westlake personnel showed that the

37

discharge rate varied linearly with auger RPM as indicated in Table 9.
Two grainflow tests were conducted with the Kirkton dryer at a discharge
auger speed of 63 rpm with grainflow rates of:

1. 1080 kg at 804 kg/m3 discharged in 11 min 48 sec

2. 1250 kg at 804 kg/m3 discharged in 13 min 12 sec
During the drying tests the RPM of the discharge angers was measured
and recorded and the grainflow calculated at 1.478 :_0.025 kg per auger

revolutions.

Table 9.--Laboratory results of grainflow versus discharge auger RPM.

 

RPM Grainflow, tonne/hr-m2

 

10 0.812

20 1.625

30 2.437

40 3.250

50 4.062

60 4.875
Pea Bean conditions Moisture 15.8% w.b.
Test weight 837.0 kg/m3

 

Source: Westlaken (1976).

The conditions for each drying test were set up and the dryer
operated until an equilibrium condition was achieved (one complete
grain pass through the dryer). A total of four samples were taken at
20 minute intervals from five locations: (1) grain inlet, (2) air/grain
exit from each of the three drying stages, and (3) outlet from the

cooling section. The samples were tested immediately for temperature

38

(mercury bulb thermometer) and moisture content (Motomco moisture

meter calibrated by the Canadian Department of Agriculture). The
samples were sealed in plastic bags and stored at 5°C for later analysis.
After the drying tests were completed, 100 grams of each sample were
separated using a Boerner divider and examined visually to determine

the percentage of cracked seed coats (cracks) and of beans which had
been split into two halves or otherwise damaged (splits). Percentages
were calculated by weight using a Pennsylvania mechanical balance

scale.

3.1.2 Test conditions and results

A total of twelve drying tests were conducted using pea beans.
Tests 1 and 7 were interrupted by mechanical failures and are not
reported. The test conditions are presented in Table 10. Tests 2
through 9 were two stage drying tests during which the t0p drying stage
of the dryer was not operated. Tests 10 through 12 were three stage
drying tests. The cooler was operated only on test 12.

The results of the analysis on the dried samples are summarized
in Table 11. The change in splits for one drying section showed no
apparent correlation with the exit temperature or the change in
moisture for that stage (Figures 8 and 9). The occurrence of splits
is probably due to random factors other than the drying process, such
as harvest conditions, method of obtaining samples or variations
occurring due to sample analysis.

The change in cracks for one drying stage showed a correlation
of rc = 0.48 (significance of p > 0.01) with the exit temperature of
the grain (Figure 10), and a correlation of rc = 0.42 (significance of

p > 0.01) with the change in moisture content in that stage (Figure 11).

39

 

 

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3.2 Multistage drying of shelled corn

3.2.1 Equipment and procedures

Drying tests were conducted during the fall, 1976 harvest
season using shelled yellow corn (varieties unknown) using a three
stage concurrent flow dryer with a counterflow cooler as described in
section 3.1.1.

The flow rate of the grain through the drying column was corre-
lated with the discharge auger RPM. Tests were conducted at three
different RPM using 12% w.b. corn with a test weight of 721 kg/ms.

The results of the tests are given in Table 12. -During the drying
tests the RPM of the discharge angers was measured and recorded and

the grainflow calculated at 5.289 I 0.063 kg per auger revolution.

Table 12.--Resu1ts of corn discharge calibrations.

 

 

 

Discharge Grainflow
RPM ._________
Weight (kg) Time (min) kg/rev

”5 1141 43.17 5.286
9 1835 39.00 5.228
13 1531 22.00 5.353
Average -- -- 5.289
Range -- -- 30.063

 

The dryer was operated until an equilibrium condition was
achieved (one complete pass through the dryer). Samples at the grain
outlet were taken at 15 minute intervals after equilibrium conditions

were attained. Samples at the grain inlet were taken hourly. The

46

samples were tested immediately for temperature (mercury bulb thermo-
meter), moisture content GMotomco moisture meter), BCFM (broken corn
and foreign material passing through 0.48 cm round-hole screen), and
visually inspected for heat damaged kernels. All samples were sealed
in plastic bags and stored at 5°C. After the drying tests were com-
pleted, the samples were conditioned and subjected to a Stein breakage
test to test their susceptibility to damage.

In the conditioner air was circulated through the sample and
over a saturated sodium-chloride salt solution. Thus the air was
maintained at approximately 75% relative humidity at 27°C. Moisture
contents of about 12.5-13.5% w.b. were obtained. The samples were
conditioned for a period of six days before being tested in the Stein
breakage tester.

One hundred grams of each sample were separated using a Boerner
divider. After the two minute breakage test the samples were removed
from the tester and screened using a 0.48 cm round-hole screen. The
percentage lost through the screen was the percentage of breakage for

the Stein breakage test.

3.2.2 Test conditions and results

A total of nine drying tests were conducted using yellow corn
(varieties unknown). The results of tests 2 and 9 are questionable
due to mechanical problems encountered. Test 6 was invalid due to a
fire in the dryer and therefore not reported. The author feels that
the fire was due to overdrying caused by intermittent starting and
stopping of the dryer because of mechanical problems encountered.

Proper start-up and shut-down procedures would eliminate the danger

47

of fire. The test conditions are presented in Table 13 and the results
of the sample analysis are summarized in Table 14.

BCFM showed no correlation with either the exit temperature
of the corn (Figure 12) or the change in moisture content of the corn
(Figure 13). The occurrence of BCFM immediately after drying is
probably due to random factors other than the drying process such
as corn variety and harvest conditions.

The percentage of breakage in the Stein breakage tester showed
no correlation with the exit temperature of the corn (Figure 14). A
correlation of rc = 0.59 (significance of p > 0.01) was observed
between the breakage tester results and the change in moisture content

of the corn (Figure 15).

48

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4. MODEL DEVELOPMENT

Previous simulation research for concurrentflow dryers use
different models. Thompson (1967) derived a set of algebraic equations
based on heat and mass transfer at the kernel surface. The moisture
transfer was based on a thin layer equation developed by recording
moisture content versus time for a thin layer of kernels when subjected
to an airflow of constant temperature and humidity. Bakker-Arkema
g£_al, (1974) derived a set of ordinary differential equations based
on heat and mass transfer at the kernel surface with moisture transfer
based on Thompson's thin layer equation. The system of equations is
solved numerically using an integration routine.

Thin layer models for corn are available for several temperature
ranges. A good review of equations available for a limited number of
other products is presented by Brooker g£_§l, (1974). The thin layer
models suffer from one severe limitation in that they do not consider
what is occurring within the kernel. The structure of the kernel is
stressed during drying which may lead to cracking of the kernel. The
degree of damage has been related to many different variables but the
exact cause of the stress is not really known. Possibly it is due
to variations of moisture content within the kernel.

A model based on heat and moisture diffusion within the kernel

overcomes this limitation. Baughman 33 El' (1971) derived a set of

S4

55

ordinary differential equations for a concurrentflow dryer using
diffusion to account for moisture transfer.

A diffusion model has a number of other advantages. First, it
would be easily applicable to a number of agricultural products for
which diffusivity coefficients are known. Second, the assumed shape
of the product could be easily varied. Differential diffusion
equations are available for flat plates, spheres, cylinders and other
shapes. As more is learned about what occurs within the grain kernel
during drying, a different kernel shape may be necessary. Third, the
diffusion model can be used to approximate the tempering period when
little or no heat and mass transfer occurs at the kernel surface.
During tempering the kernel reacts in some manner to relieve the
internal stresses caused by drying.

The following section outlines the development of a computer
model for simulating the drying performance of a multistage concurrent-
flow dryer with intermediate tempering stages and a final counterflow
cooling stage. The model output is compared with previously published
data for single-Stage concurrentflow drying of shelled corn. The
effect produced by the cooling and tempering stages is evaluated.
Lastly the multistage model output is compared with the multistage.

experimental results presented in the previous section.

4.1 Concurrent heat and moisture transfer

The phenomena of heat and mass transfer can be visualized from
the viewpoint of the individual kernels. The transfer of heat and
mass within the kernel occurs by diffusion. The corn kernel is shaped

somewhat like a brick and was analyzed as such by Pabis and Henderson

S6

(1961). The temperature and moisture distributions at any point within
the kernel were represented as a function of the three coordinate
directions. The diffusion coefficients were assumed to be independent
of the location within the kernel; i.e., the kernel was assumed to be
homogeneous with respect to heat and moisture diffusion. Chu and
Hustrulid (1968) showed that "two solids of different size and shape

are considered to be equivalent if their volume-to-surface-area ratios
are the same." Thus the corn kernel was represented by a sphere with

a properly determined equivalent radius. The equivalent radius approach
was also used for wheat by Ingram (1976).

To analyze the drying of a grain kernel one can visualize a
sphere of radius ro with a moisture content distribution which varies
from the center radially outward. The surface of the sphere is exposed
to varying environmental temperature and humidity as the drying process
proceeds along the length of the drying column. The transfer of heat
and.mass within the kernel occurs by diffusion of heat and mass,
respectively. Young and Whitaker (1971) concluded that for most agri-
cultural products (including cereal grains) the diffusion of moisture
alone adequately describes the drying process of the grain kernel.
Therefore, it can be assumed that no thermal gradient exists within the
kernel even though the kernel temperature may change with time as it
loses moisture and loses heat with the environmental air. The diffusion
of moisture within the kernel can be represented by the diffusion
equation for a sphere (Crank, 1957);

BM 2 3M

_=2_(r____ (2)
St 1.2 3r2

S7

The diffusion equation is a second order partial differential
equation. For ease in solving the equation numerically on a digital
computer, equation (2) is transformed into a set of coupled ordinary
differential equations (0055) by the method of lines. The method of
lines approximates the spatial derivatives by an appropriate finite
difference formula (Carver, 1976). Using a second order difference

formula the coupled ODE system becomes:

dMi__D M M ._

-E_._ :5-(31 1+1 - 2Mi + bi i-l)’ 1-2,3,...,n (3)
where:

ai = i/(i-l) (4)

bi = (i-2)/(i-1) ‘ (5)

At the center of the sphere, i=1 and the diffusion is symmetric so

that the moisture derivative becomes:

dM
1 6D
F’ijz‘Mfl (6)

At the surface of the sphere, i=n and the diffusion rate can be cal—
culated by assuming the existence of a psuedo-point outside the kernel
with the moisture content equal to the equilibrium moisture content.
Therefore the moisture derivative becomes:
dMn D
'dt_ 8 *—§'(anMe-2Mn+bnanl? (7)
o

The derivation given above may be found in similar form in Crank (1957).

58

At the surface of the kernel, interaction with passing air
transfers both heat and moisture. The conditions of the air and of
the grain vary from the inlet point through the length of the dryer.
The variation can be described by differential equations developed

from energy and mass balances as presented by Brooker 33 El: (1974):

 

 

dT = -hca(T-6) (8)
32' G (c +c H)
a a v

19- : hca(T - e) _ 33“:ch - 9) G 9.5 (9)
dx Gpicp+cwfi) GPCcp+cwfi) a dx

-G did
dH =
32’ Ga 3x (10)
(it dt

The basic equations for simulating the concurrent flow drying
process are equations 3 through 11. The solution to this system can
be obtained numerically with the help of a digital computer. For this
purpose a Runge-Kutta fourth-order single-step integration algorithm
was used because of its availability at Michigan State University and
the author's familiarity with the algorithm. The routine uses an
Adams-Moulton technique for starting the integration and features

automatic step size adjustment using relative error checking.

4.2 Auxiliary equations and prOperties
The solution of the ODE system presented in section 4.1
requires knowledge of several grain and air properties. Some vary

with the changing grain and air conditions and need to be recalculated

59

after each distance step (e.g., diffusion coefficient and equilibrium
moisture content). Some may be considered as dependent only on the
initial grain and air conditions (e.g., heat transfer coefficient).
Others are independent of the grain and air conditions both before
and during drying but may be dependent on the grain type being dryed

(e.g., specific heat and specific surface area).

4.2.1 Diffusion coefficient

Chu and Hustrulid (1968) studied diffusion in corn kernels
assuming that the kernel can be represented by a sphere of equivalent
radius. Previously published experimental results of several thin
layer drying studies were used for the following parameters: (1) product
temperature 49°-71°C, (2) relative humidity 10-70%, and (3) corn

moisture content 5-35% d.b. The fellowing equation was developed:

2513.00
9 + 273.13

 

D = 1.513x10-4 (0.045 e I 6.806)“ - (12)

Sabbah g£_al, (1976) studied moisture diffusion in soybeans
assuming that the kernel can be represented by a sphere of equivalent
radius. Unpublished thin-layer data from Ohio State University was

used to develop the following equation:

-o.590 - -3137.67
( M -M 3* °°°18(M’"e)]ex9(e + 273.13) (13)

0 e

D = 0.360[0.049exp

 

 

The ranges of the drying data from which the equation was develOped
were not reported. The diffusion equation was used in a reversed-air
crossflow drying model with good results.

The diffusion coefficient values for shelled corn and pea

beans are compared in Table 15. The diffusion coefficient and thus

60

Table 15.--Diffusion coefficient values (cmZ/hr) for shelled corn (C
calculated using equation 12) and for soybeans (B calculated
using equation 13) as a function of moisture content and
grain temperature. Soybean equilibrium moisture content
Me=5.0% w.b. and initial moisture content Mo=28.0% w.b.

 

Moisture content, % w.b.

 

 

Temperature
°C 12 16 __}0 24 28
C B C B C B C B C B

100 .0084 .0080 .0155 .0088 .0304 .0097 .0646 .0106 .1460 .0117
80 .0051 .0050 .0089 .0055 .0166 .0060 .0328 .0066 .0703 .0072
60 .0029 .0029 .0049 .0032 .0086 .0035 .0161 .0039 .0324 .0042
40 .0016 .0016 .0025 .0018 .0043 .0019 .0075 .0021 .0141 .0024
20 .0008 .0008 .0012 .0033 .0011 .0057 .0012

.0009 .0020 .0010

 

the drying rate of pea beans increases as the temperature increases,
similar to shelled corn. More importantly, the drying rate of pea
beans is less than that of corn and is much less sensitive to in—
creasing moisture content. The cause of this is probably in the
structure of the bean: two cotyledon halves surrounded by a fairly
impervious seed coat. This can also be seen in the data presented

by Kreyger (1972) in Table 16 fer peas, which have a similar structure.

4.2.2 Equilibrium moisture content
Pfost 33 21. (1976) gathered and summarized equilibrium
moisture content data for many grains and develOped the following

equation for calculating the equilibrium moisture content:

Me = A-B{£n[-l.987(6+A')£n(rh)]I (14)

61

Table l6.--Re1ative drying rates of various agricultural products as
a percentage of wheat drying rate at 18% w.b.

 

Moisture content, % w.b.

 

 

Product

14 16 18 20 22
Peas 15 23 35 55 9S
Corn 15 30. 50 90 135
Wheat 35 65 100 150 210
Rye 35 70 115 175 225
Oats 60 100 150 250 450
Sugarbeet seed 300 500 800 1200 1650
Rapeseed 500 800 1150 1500 ~-

 

Source: Kreyger (1972).

Data from several previously published sources was used with a grain
temperature of 0°-50°C and a relative humidity range of 20-90%. The
values for the constants in equation (14) are given in Table 17. The
constants for edible beans (a class of beans which includes pea beans)
are given by Pfost gt 21" Calculated values using equation (14) for
edible beans are compared with some experimental data from Dexter §t_al,
(1955) in Table 18. The equilibrium values for 85% rh and high tem-

peratures were affected by mold development.

Table 17.--Equilibrium moisture content equation constants.

 

 

Constant Corn Edible beans
A 0.379212 0.480920
B 0.058970 0.066826
A' 30.305000 120.098000

Std. Error 0.012100 0.017400

 

Source: Pfost g£_gl, (1976).

62

Table 18.-~Equi1ibrium moisture content values for pea beans (% d.b.)
as a function of grain temperature and relative humidity.
Calculated (C) from equation (14) and data (0) from Dexter

.e_t. §_1_. (1955).

 

Relative Humidity,

%

 

 

Temperature
°C
D C D C D C D C

10 14.84 14.41 16.74 16.60 19.57 19.30 24.33 23.11
21 14.05 13.87 16.27 16.06 19.46 18.75 24.05 22.57
32 13.13 13.36 15.49 15.55 18.09 18.25 21.79 22.07
43 12.47 12.90 14.73 15.09 18.34 17.79 23.87 21.60
54 13.20 12.46 15.25 14.65 19.10 17.75 26.81 21.17

 

Source: Dexter gt_al. (1955).

4.2.3 Heat transfer coefficient

McAdams (1954) recommended the following

transfer between spheres and a flowing gas:

Nu

where Nu

Re

0 60

0.37 Re '

2h r

Nusselt number = -—9—9-

Reynolds number =

k

20 r
o

 

a

equation for heat

(15)

(16)

(17)

Equation (15) provides a convenient formula to calculate the

convective heat transfer coefficient of grain kernels which are

represented by a sphere of equivalent radius.

heat transfer coefficients for corn kernels and recommended the

following:

Sabbah (1971) studied

63

Nu = 0.389 Reo'850 (18)

for air velocities in the range 1.74-52.43 m/min.
Ngoddy gt_§l, (1966) studied heat transfer in beds of pea beans.
An equation for packed beds of spheres based on the Colburn j-factor

was found to be satisfactory for pea beans:

j - -——lfli—-— = 0.992 Re’°°34° (19)

Re Pr1/3

0.660 Pr1/3

or Nu = 0.992 Re (20)

Referring to Figure 6 a normal air temperature range during
concurrentflow drying is 300°-500°K. In this temperature range the
thermal conductivity of air varies from 0.026-0.040 W/m-°C; the dynamic
viscosity varies from l.983-2.67l x 10.5 kg/m-sec; the Prandtl varies
from 0.708-0.680 (Holman, 1976). Average values in these ranges are
used in the drying simulation to calculate an average heat transfer

coefficient.

4.2.4 Latent heat of vaporization
The latent heat of vaporization is the energy necessary to
evaporate moisture from the product being dried. Othmer (1940) proposed

the following equation for the latent heat of vaporization:

h = hf

fg '[1.0 + Aexp(B)] (21)

8

Equilibrium moisture content curves furnish the necessary data to

calculate the product-temperature-moisture dependent constants.

64

Rodriguez-Arias (1956) developed the constants for corn with
equilibrium moisture data in the range 8.70-35.l4% d.b. and temperatures
in the range 5°-40°C. Using these constants the latent heat of water

evaporated from corn kernels was determined:
hfg = (2502.100-2.386 e)(1.0+4.349exp(-28.2sfi)) (22)

Alam and Shove (1973) developed constants from the equilibrium
moisture data for soybeans in the range of 5.66-27.51% d.b. and bean
temperatures in the range of 5°-55°C. The constants for soybeans can
be used for calculating the latent heat of vaporization of water

evaporated from pea beans:
hf8 = (2502.100-2.386 e)(1.0+0.z16exp(-6.2330)) (23)

The first parenthetical expression in both equations (22) and
(23) are expressions for the latent heat of vaporization for free water
as a function of water (grain) temperature as determined by Rodriguez-

Arias (1956).

4.2.5 Miscellaneous grain and air properties

Brooker §£_al, (1974) described a SYCHART package for calculating
any property of moist air given any two other properties. The SYCHART
package of routines has been recently converted to SI units by Rugumayo
(1976). I

Several grain and air properties are independent of the grain
or air conditions before or during drying. These properties are listed

in Table 19 along with the reference source where they were obtained.

65

Table 19.-—Grain and air properties.

 

 

 

Property Corn Pea Beans
. 3 a e
Dry bulk den51ty, kg/m 620.1 929.0
Equivalent kernel radius, cm 0.488b 0.457e
Specific heat, kJ/kg-°C 1.122c 1.675c
Specific surface area, m2/m3 784.1d 1522.3e
Specific heat, kJ/kg-°C dry air 1.013:
water vapor 1.884

water liquid 4.187f

 

aBakker-Arkana 33 _a_1_. (1974).

bSabbah (1971).

cKazarian and Hall (1965).

dBakker-Arkema gt 31. (1971)

eNgoddy g£_91, (1966).

fHolman (1976).

66

Conversion to SI units was accomplished in all cases using the SI con-

version table contained in Appendix 9.1.

4.2.6 Energy and static pressure equations

The energy consumed during the concurrentflow drying process
is composed of two components: (1) fuel for heating the drying air, and
(2) electricity for running the motor which drives the fan to force
the heated air through the drying bed.

The energy to heat the air can be calculated from an enthalpy
balance on the air flowing through the heating apparatus assuming an

85% efficiency (Westelaken, 1976):

E = Ga(ca+cvflg(T-Tamb)
a .85 Gp

 

(24)

The humidity value is the ambient humidity when the heat added by com-
bustion is determined from the fuel's lower heat value. The combustion
of fuel does add some additional water as a combustion by-product. The
main fuel used for grain drying in.Michigan is LP gas which is mostly
propane (Kenyon gt_al,, 1976). Propane has the chemical formula C3“

8

and undergoes combustion by the fellowing formula (Raznjevic', 1976):

C H + 50 + 3C0

38 2 2‘4“

20 + (48651 kJ/kg propane) (25)

A typical concurrentflow dryer uses 3000 kgair/hr-m2 at a temperature
rise of 200°C with an ambient humidity of 0.005. In this case the

added humidity due to combustion is 0.008 kgwater/kg The results

air'
presented by Baughman gt_§l, (1971) indicate that the added humidity

increases the outlet moisture by approximately 0.3% d.b.

67

The electricity to run the fan is dependent on the static
pressure which the fan operates against. The energy required can be
calculated as given by Perry gt_al, (1963) assuming a 50% efficiency
(Farmer, 1972):

S.75(Qa)SP

fm ’ .s c
P

E (26)

 

Pressure drop data for many agricultural products was presented
in graphical form by Shedd (1953). The data was reported for loose
filled, clean, relatively dry grains and seeds. The following obser-
vations were reported by Brooker st 21: (1974):

l. loose filled, clean grain with high moisture content (equili-
brium RH greater than 85%) results in about a 20% reduction
in pressure drop

2. packing of the grain may cause a 50% higher pressure drop

3. fine material mixed with whole grain increases the pressure
drop

4. course material mixed with whole grain decreases the pressure
drop

The curves presented by Shedd (1953) have been represented by the

following pressure-flow relationship:
Q = MSP/x )B (27)
a 1

Using this ferm of the pressure-flow relationship, constants A and B
for several agricultural products are presented in Table 20.

A comprehensive study on the resistance of grain to airflow
was presented by Matthies (1956). Based on Reynold's law of similarity

an effort was made to determine the relationship between pressure dr0p

68

Table 20.--Constants for the Sheed pressure-flow relationship for
‘ different agricultural products.

 

Airflow Range

 

Product A 1./B mS/mZ-min Source
Shelled corn 18.90 1.471 3.0-12.2 Shedd (1953)
Shelled corn 17.68 1.528 12.2-45.0 Farmer (1972)
Wheat 9.75 1.250 3.0-12.1 Shedd (1953)
Pea Beans 19.81 1.431 3.0-30.5 Maddex (1953)*

 

*Data presented fit to the form of the equation by author.

and the independent variables affecting pressure drop. The results
confirmed that the pressure drop varied linearly with the depth of the
grain mas and inversely with the fourth power of the porosity.

Patterson gt 21, (1971) calculated static pressure using a
modified form of the Ergun equation for packed beds. The equation is
based not only on the superficial air velocity but also the porosity
of the product bed and an empirical factor which is product temperature
and moisture dependent. Matthies and Peterson (1974) have shown that
the form of the equation presented by Shedd deviates from the Ergun
equation for wheat by only 7.4%. The simplified equation (27) pre-
sented above is thus acceptable for use in the concurrentflow model.

A question raised which is pertinent to concurrentflow dryers
especially is in regards to the effect of the change in temperature on
the pressure drop which the fan senses. Assume the situation to be
frictionless flow through a heat duct with heat transfer, a derivation
which may be found in fluid mechanics texts such as Streeter (1971).
The following four assumptions are made in the derivation: (1) steady,

plug flow, (2) air is a perfect gas with constant Specific heat,

69

(3) the duct has a constant cross-section, and (4) friction is negli-

gible. The appropriate equations are:

continuity: Ga = pV (28)
momentum: SP + pV2 = constant (29)
Mach number: Ma = V/(1.4R(T+273))l3 (30)

The continuity equation (28) is substituted into the perfect gas

equation giving:
SP = GaR(T+273)/V (31)

The Mach number equation (30) is combined with the perfect gas equation

giving:
SP = pVZ/(l.4Ma2) (32)

From the momentum equation (29) the preSsure at two points (before and

after heating) can be transformed into a ratio:

SP 1+1.4Ma 2
EFI- = ———7"1 (33)
2 1+1.4M82

Equation (33) is used to estimate the change in static pressure
due to the heating process. A realistic situation for a concurrentflow
heater is air entering at 45 m/min. and exiting the heater at 65 m/min
with a temperature rise from 25° to 200°C. The Mach number for the two

3 3

points would then be: (1) Ma1 = 2.2 x 10’ and (2) Ma2 = 2.4 x 10' .

Substituting into equation(33) results in a static pressure ratio of

70

0.9999987. Therefore, it can be concluded that the effect of the
heating is negligible on the static pressure which the fan senses.
Another factor to be considered is the effect of the percentage
of fines and foreign material on the static pressure. Henderson (1943)
presented a fairly complete set of data for static pressure versus
percentage of corn fines. The data can be approximated by a linear

equation for a multiplicative correction factor:
K = 1.0-3.75 f (34)

Haque gt_al, (1976) studied the effect of fines in shelled corn on the
static pressure and concluded:

1. for an airflow rate in the range 4.6-12.2 m/min, the pressure
drop increased linearly with the increase in percentage of
fines in the range 0-20% fines

2. a modification to the Shedd equation (27) allows prediction of

pressure drop as affected by corn fines:
K = (1.0+(14.556-0.4403 Qa)f)/Qa (35)

The static pressure data and prediction equations currently
available are generally at airflow rates below those in use in com-
mercial concurrentflow dryers. The following simulation and optimization
uses the Shedd equation (27) for estimating the static pressure even
though the airflow rates may exceed the range for which the equation
was developed. In addition it is assumed that the corn has been ade-
quately cleaned such that no effective percentage of fines is left to
affect the static pressure. It is further assumed that the continuous

flow nature of the dryer does not significantly affect the porosity of

71

the grain mass. The affect of porosity could be included in a porosity
multiplicative factor if desired. Such a factor would include the
actual value of the porosity which may also be influenced by the
moisture of the product being dried. For shelled corn Bern and Charity
(1975) studied the effect of varying bulk density on the pressure drop
for airflow through corn. The porosity value was replaced by a function

of the bulk density and the kernel density:
a = 1.0 — (ob/1170) (36)

Gustafson and Hall (1972) studied the effect of drying temperature in
the range 21°-104°C on the change in density of a bed of shelled corn.
The true bulk density was found to be a linear function of the moisture

content of the corn (constants A and B were not explicitly stated):
=A-BM (37)

Similar equations can be developed for other agricultural products and

for additional airflow ranges following appropriate experimentation.

4.3 Tempering stage

Tempering of warm grain from the first stage of a multistage
dryer accelerates the drying rate in the following drying stage.
Increased capacity and better grain quality result when corn is dried
from 32 to 18% w.b. followed by drying from 18 to 14% in the second
crossflow stage after a tempering period as compared to drying directly
from 32 to 14% in one crossflow stage (Katie, 1975).

Sabbah (1971) studied tempering as a part of the dryeration

process. Tempering had a significant effect on the cooling rate and

72

on the moisture removed during in-bin cooling. An index of tempering
was constructed which redefined the initial moisture of the corn after
tempering. The index was used to calculate the moisture removed during
subsequent cooling. During the tempering period the grain did not
exchange heat and moisture with the surrounding air.

The effect of tempering after concurrentflow drying can be
estimated using the ODE integretion algorithm previously described for
any desired length of tempering time. The derivatives in equations
(8) thru (11) become zero since no transfer occurs between the grain
and the air. The moisture within the kernel then redistributes by
diffusion as shown in Figure 16. As the tempering time increases the
moisture concentration at any point within the kernel will asymptoti-
cally approach an average value.

Since the moisture loss from the kernel to the air occurs only
at the surface, the overall moisture transfer rate would indeed
increase after tempering. Figure 17 compares the effect of tempering
time on the moisture content profile for a two meter long concurrentflow
dryer following the tempering stage. Tempering times beyond 1.25 hours
appear to have a negligible effect on the final average moisture con-
tent and temperature of the grain. Sabbah gt_al, (1972) found that
tempering for eight hours following crossflow drying resulted in a
higher moisture removal rate during subsequent cooling than tempering
for two, four or twelve hours. The concurrentflow dryer requires less
tempering time for maximum tempering effect than the crossflow dryer
because of the uniformity of the average moisture contents and temper-

ature between kernels after drying in a concurrent flow dryer.

Moisture content, % d.b.

73

 

 

 

 

 

 

 

 

34
Kernel Center

32-

1/2 Radius
soI-

3/4 Radius
23r-

Surface
26k-
240

Tempering Time, hr.

Figure 16. Moisture content versus tempering time for shelled
corn after drying from 25.0% w.b. in a concurrentflow
dryer. Kernel temperature during tempering 51°C.

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m a“ ofiflmoum ueoucoo onsumfioe shoe no mafia wcwnomaou mo uoommm .NH onsmfim

a £0an
o.~ m; o; a me o

 

74

 

— q q - mH

 

mN.H
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m o .1oH
o.o
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75

Sabbah (1971) found that grain did not change temperature or
moisture content significantly during tempering. The corn entering
the tempering stage illustrated in Figures 16 and 17 had a temperature
of 51°C. If the grain temperature is less than 51°C the moisture
removal would decrease (see Table 21) and a longer tempering time
would be necessary for a similar tempering effect. Correspondingly, a
higher inlet grain temperature would decrease the tempering time for a
similar tempering effect.

Table 21.-~Effect of various grain conditions on the moisture profile
for corn dried in a concurrentflow stage following tempering

for 1.25 hours.

 

 

 

Tegpering Depth, m

rain

T°mpfgatur° 0.0 0.4 0.8 1.2 1.6 2.0
51 19.95 17.55 16.75 16.28 15.98 15.78
43 21.15 18.78 17.98 17.55 17.29 17.14
40 21.74 19.38 18.60 18.19 17.96 17.83
47 20.56 18.15 17.37 16.92 16.63 16.45
39 23.06 20.52 19.77 19.42 19.26 19.20
51 19.63 17.33 16.49 16.00 15.69 15.48
46 19.98 17.75 16.92 16.46 16.17 15.97
42 21.95 19.48 18.72 18.31 18.09 17.97
48 19.29 17.17 16.35 15.87 15.55 15.35
41 23.28 20.57 19.81 19.47 19.33 19.29

 

76

4.4 Cooling stage

Simulation of the counterflow cooling stage using heat and mass
transfer equations is very difficult because the problem is a two-point
boundary value problem (Figure 18). Hence there does not exist a
straightforward, short (computer time) solution algorithm for the
differential equations describing the heat and mass transfer. Thompson
(1967) simulated a counterflow process assuming the bed to be a number
of thinlayer which were continuously moving downward. At successive
time intervals a layer was removed from the bottom of the stack and
anOther placed on the top. Since the algebraic equations derived
assumed a steady-state situation a search algorithm was necessary to
find the appropriate solution. Evans (1970) applied invariant pro-
gramming and invariant imbedding techniques to the simulation of the
counterflow process. The approach produces a family of solutions which
yield a particular solution upon the application of a dynamic pro-
gramming type solution retrieval technique. Bakker-Arkema gt_al,
(1974) develOped a counterflow simulation program which used a shooting
technique to arrive at the appropriate solution. The differential
equations derived for the heat and mass transfer assumed a steady-state
situation. The algorithm's stability was particularly sensitive to
the initial guesses and did not always yield a reasonable solution.
Roth (1977) used an approach similar to that of Thompson except
utilizing a set of differential equation written to include the
transient as well as the steady state part of the counterflow process.
The counterflow cooler process was simulated as a transient system

until steady state operation was achieved.

77

A'
1r outlet Tout’Hout

J

Grain inlet ein’Min

Counterflow

Process

 

 

 

Air inlet T. ,H.
in in

 

 

V

G .
rain outlet eout’Mout

Figure 18. Schematic of counterflow process.

78

All the algorithms presented above use too much computer time
for estimating the effect of the counterflow cooler as a part of the
multistage drying system. During the counterflow cooling process the
exit grain temperature does not reach thermal equilibrium with the
inlet air temperature. Likewise, the exit air temperature does not
always reach thermal equilibrium with the inlet grain temperature.
The counterflow cooler may be considered as basically a counterflow
heat exchanger for transferring heat from the inlet grain to the air
flowing through the cooler. Some mass transfer occurs which assists
in the heat transfer through evaporative cooling. The counterflow
cooler can then be approximated by a modified version of the
Effectiveness-NTU method presented by Holman (1976). The effectiveness

for a counterflow heat exchanger is defined:

e = actual heat transfer (38)
maximum possible heat transfer

The value of the effectiveness is calculated from a convective heat

transfer analysis using the energy capacity flowrate for each product:

Ca = [Ga(c +c H. )Tin+ G

a V in (39)

ahngin] lTin

CP= Gp(cp+cwMin) (40)

The relations listed above were modified to account for the transfer
of energy based on the mass transfer and associated latent heat. There
are two distinct cases that could occur during the counterflow cooling

process: (1) Ca §_C , and (2) Cp fi-Ca' The two cases affect the

P
equations to be used for calculating the effectiveness and the

associated outlet grain and air temperatures.

79

Case (1): e = (1.0-A)/(1.0-(Ca/CP)A) (41)
where: A = exp((-hcx1a/Ca)(1.0-Ca/Cp) (42)
Tout = Tin+e(ein-Tin) (43)
6out = Bin-e(Ca/Cp)(ein-Tin) ‘ (44)
Case (2): e = (l.0A)/(1.0-(Cp/Ca)A) (45)
where: A = exp((-hcx1a/Cp)(1.0-Cp/Ca) (46)
6out = Gin-3(6in'Tin) (47)
Tout a Tin+e(cp/Ca)(ein'Tin) (48)

Using the above calculated outlet temperatures the outlet moisture can

be estimated from an enthalpy balance on the counterflow cooler:

Mout = (A Min-B)/A' (49)
where: A = Gp(chout'cwein+hfg) (50)
A. = Gp(chout'cweout+hfg) (51)

B = Ga(°a+°vHin)(Tout'Tin)'GaHinhfg (52)

The calculated outlet moisture is then used in an iterative process
where the humidity in equation (39) is replaced by the average of the
inlet and outlet humidity (calculated from a mass balance). The
moisture in equation (40) is replaced by the average of the inlet and
outlet moisture, and the outlet moisture is recomputed. The iterative

process is continued until the change in outlet moisture between

80

successive iterations is insignificantly small.

Effectively this

process recalculates the outlet temperatures based on the evaporative

cooling due to the mass transfer taking place in addition to the

previously calculated heat transfer.

The calculated results produced by the above described method

are compared in Table 22 with results preSented by Farmer (1972) for

counterflow cooling simulations using a model-fit algebraic algorithm.

The model was constructed from simulation output prepared by the

counterflow cooler processor described by Bakker-Arkema et_al, (1974)

for shelled corn. The simulator described above matches well with the

results of Farmer and can be applied to products other than corn.

Table 22.-2Comparison of counterflow process simulator with previously

published data.

 

 

 

 

Data set I Data set 11
Model Farmer Model Farmer
(e-NTU) (e-NTU)
Inlet air conditions: 2
temperature °C 11 11 11 ll
humidity, decimal d.b. .003 .003 .003 .003
flow rate, kg/hr-mz 1275 1275 1275 1275
Inlet grain conditions:
temperature, °C 62 62 55 55
moisture, % w.b. 16.8 16.8 16.8 16.8
flow rate, kg/hr-mz 2460 2460 2460 2460
Outlet air temperature, °C 61 62 55 55
Outlet grain conditions:
temperature, °C 29 26 26 25
moisture, % w.b. 15.9 15.2 15.6 15.5

 

Source: Farmer (1972).

81

A sensitivity study using the Effectiveness model is presented
in Table 23. One aspect noted by Roth (1977) but not always fully
recognized is that there is a point where supplying more airflow to
the cooler actually results in less moisture removal. For the results
in Table 22 for corn this occurs at an airflow of 25 m/min. At this
airflow, the energy capacity flow rates (defined in equations (39),
(40)) have inverted in relative magnitude. Before this point the air
energy capacity flowrate was less than the grain energy capacity flow-
rate. When the inversion occurs the outlet air temperature (which had
previously been almost equal to the inlet grain temperature) begins

to decrease. Therefore the moisture removal will decrease.

4.5 Quality prediction equations

Several grain quality factors may be considered as shown in
Section 2. For shelled corn the majority of the U.S. harvest goes for
feed grain. The handler and shipper are interested in shipping a
product which meets U.S. grade standards at minimum cost. The buyer
wants to receive the product in as good a condition as possible.
Stress cracks lead to broken corn which is expensive for the handler to
remove and downgrades the product received. The results of the Stein
breakage test can be used toestimate the effect of drying on the
susceptibility to damage of the artificially dried corn. The data
collected during the experimental investigations was plotted in
Figure 15. The correlation for a straight line yielded the following

equation:

85 = 143.6S*AM-8.40; rc=0.59, p50.01 (53)

82

Table 23.--Sensitivity study of cooler operation using the Effectiveness
simulator for shelled corn.

 

 

 

Inlet Conditions Outlet Conditions
Grain Grain Air Air Grain Grain Grain
Temp Moisture Temp Flow Rate Flow Rate Length Temp Moisture
°C % w.b. °C m/min kg/hr-m2 m °C % w.b.

50 16.0 15 10 2000 1.0 34 15.6
30 16.0 15 10 2000 1.0 24 15.9
70 16.0 15 10 2000 1.0 43 14.9
50 14.0 15 10 2000 1.0 34 13.4
50 18.0 15 10 2000 1.0 35 17.4
50 16.0 5 10 2000 1.0 21 15.0
50 16.0 10 10 2000 1.0 29 15.2
50 16.0 20 10 2000 1.0 39 15.6
50 16.0 15 5 2000 1.0 42 15.7
50 16.0 15 15 2000 1.0 27 15.1
50 16.0 15 20 2000 1.0 19 14.9
50 16.0 15 25 2000 1.0 15 14.8
50 16.0 15 30 2000 1.0 15 14.9
50 16.0 15 40 2000 1.0 15 14.9
50 16.0 15 10 g 1000 1.0 19 14.9
50 16.0 15 10 1500 1.0 29 15.2
50 16.0 15 10 2500 1.0 37 15.5
50 16.0 15 10 3000 1.0 40 15.6
50 16.0 15 10 2000 0.1 34 15.4

50 16.0 15 10 2000 2.0 34 15.4

 

83

The results indicate the same trend noted by Thompson and Foster (1963)
for crossflow drying of corn. The susceptibility of corn to breakage
during subsequent handling (as indicated by the Stein breakage test)
increases as the drying rate increases.

Processers of pea beans are concerned about the percentage of
cracked seed coats (cracks). Cracks often become beans with loose
pieces of skin or even split beans. During the final processing phase
the loose skin may separate from the bean. The exposed cotyledons
become mushy as solids are released to the surrounding fluid (Anon.,
1974). An equation which uses the theory of engineering mechanics
similar to that presented by Wang (1956) and recognizing the stochastic
properties of the process could be used to predict the percentage of
cracks occurring. However, adequate experimental data is not yet
available for this type of approach. The data collected during the
experimental investigations can be used to develop a prediction equation
for the percentage of cracks. Figure 10 showed that the percentage
of cracks increases as the exit temperature of the beans increased.
Figure 11 showed that the percentage of cracks decreased as the
moisture removed in one stage decreased. Taking these two factors into
account plus the influence of the grainflow rate, a new variable is
defined for estimating the percentage of cracks in pea beans due to

the concurrentflow drying process (Figure 19):
S = 0.199 + 5.554*0*AM/Gp; rc = 0.59, p>0.01 (54)

The above equation predicts the change in skin cracks which occurs due
to a single concurrentflow drying stage. Again the influence of the

drying rate on grain quality is evident. Also included in the above

84

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equation is the effect of the grain temperature which is important for
beans as noted by Walker and Barre (1972). Not included is the possible
influence of the humidity of the drying air. Hall and Maddex (1952)
indicated that humidity is an important parameter which affects the

percentage of cracked seed coats for pea beans dried with heated air.

86

4.6 Model flow chart

m-———I(Read input conditions

Retrieve product constants

Calculate - dry weight flow rates
heat transfer coefficient
dry basis mois

 

 

 

 
   
 
 

i

Initia iz

 

 

 

 

Surface moisture greater 4‘\\,N°
‘< Ia .1.] . . 7 ,r4*
Yes,

elative humidity less‘\\lN°
- A/V”

 

 

 

 

 

100952 _ I
Yes I Set flag
- that next step

   

is te

 

 

< Time towfis
'5 No
Total 1e 1 7

Yes

‘No

 

 

 

Print grain and air properties for I
current r ' ted

Exit fla set?
Yes

Calculate - energy use and efficiency
and Print qua11 ' '

_ A0 No!

< Tempering length 232W
Yes

nitialize integration algorithm I

 

 

 

 

H

 

 

 

 

 

 

 

 

Yes ?

 

 

87

4.7 Model validation

The experimental results used in this section were results from
tests conducted in English units. The conversion of the results to
SI (Standard International, see ASAE, 1977) units was done by the
author using the conversion table presented in Appendix 9.1.

Several methods may be used for comparing the predictions of
the computer simulation model with experimental results. The methods
can be grouped into three general categories: (1) graphical, (2) para-
metric statistical, and (3) non-parametric statistical.

One graphical method is called a correspondence plot. The
experimental result for the desired parameter is plotted as the
abscissa while the predicted value of the parameter is plotted as the
ordinate. Ideally the plotted points would fall along a 45° line
beginning at the origin (perfect correspondence). The deviation from
this line can be measured by a linear regression coefficient:

2(01'62(yi'9)

[2 (oi-15)2 (xi-9)2] 1’2

 

r =

c (55)

for the matched coordinate pair (oi, yi) where °i is the estimated
value of the experimental results yi.

A second graphical method uses residuals which are the differ-
ence between the actual and predicted parameter values. A plot of
residuals versus time or versus the actual parameter value may indicate
any systematic deviation from perfect linear correspondence. Himmelblau
(1970) presented an excellent review of the use of residuals under the

heading of "Process Control Charts." Only the correspondence plots

will be used in the model validation which follows.

88

There are several parametric statistical tests. Gilmour (1971)

 

discussed several of these in the context of simulation model validation.
The goodness-of-fit test based on the Chi-Square statistic is a measure
of the discrepancy between observed and expected frequencies. The
goodness-of-fit statistic is calculated:
(oi-vi)2
x2 = 2—97— (56)
1

A value of zero (0) implies perfect correspondence between the actual
and predicted parameter values. For a given level of significance the
critical X2 value can be read from a Chi-Squared distribution table.
If the x2 statistic is less than the critical value, the correspondence
is acceptable at the given level of significance.

A second parametric statistical test is based on the F-
distribution. The F statistic is the ratio of the variances of the
two sample sets and may be calculated:

£(oi-B)Z
F a —""171? (57)
ZIYi'Y)

The degrees of freedom for the predicted values is one less than the
number of tests. The degrees of freedom is one less than the product
of the number of tests times the sample replication for each test. An
P value of one (1) implies identical variance. For a given level of
significance the critical P value can be read from a table of the F
distribution. If the F statistic is less than the critical value, the
variances of the actual and predicted parameters are considered

essentially equal at the given level of significance. Both of the

89

parametric statistical methods reviewed above will be used in the
model validation which follows.

Himmelblau (1970) reviews several nongparametric statistical

 

tests which may be used in model validation. The Sign Test may be used
instead of the t-test and relates the median difference in paired
observations. The Mann-Whitney U test is another acceptable alternative
to the t-test and is used to test whether or not two sample populations
are identical. The Siegel-Tukey test is an alternative to the F test.
The test determines if the dispersions of the underlying population of
two independent samples are the same. The non-parametric statistical
tests are allowable alternatives to the parametric tests but are not
used in the following validation of the computer simulation model
primarily due to the lack of readily available computer programs for

carrying out the necessary computations.

4.7.1 Single-stage drying of shelled corn

The concurrentflow drying simulation equations presented in the
previous section are dependent on the number of interior nodes within
the grain kernel. Table 24 shows the effect of the number of interior
nodes on the moisture content profile during drying of shelled corn.
The simulation results presented in the following subsections use
four (4) interior nodes as a reasonable compromise between accuracy and
necessary computing time.

The single-stage concurrentflow dryer has been previously
studied (Thompson, 1967; Carrano gt_gl,, 1971; Baughman g£_al,, 1971;
Mfihlbauer gt_al,, 1971). Comparison between randomly selected experi-

mental results from several of these studies and the simulated results

90

Table 24.--Effect of number of interior nodes in a corn kernel on the
average moisture content profile during the simulated drying
in a concurrentflow dryer.

 

Number of Interior Nodes

 

 

Depth

2 3 4 5 6 7
0.00 25.00 25.00 25.00 25.00 25.00 25.00
0.25 22.61 22.03 21.56 21.17 20.83 20.82
0.50 21.69 21.12 20.66 20.32 20.05 20.04
0.75 21.14 20.60 20.20 19.95 19.79 19.78
1.00 20.77 20.27 19.95 19.77 19.71 19.70

Ambient conditions: 15°C
0.005 kg/kg

Drying conditions: 250°C
50.0 m/min
2.5 tonne/hr-m2

 

using the above described model are presented in Table 25. Some
simulated moisture contents are greater than the experimental results,
some are less than the experimental results. The average of the
absolute differences in grain moisture content is 0.933% w.b. Likewise
some of the simulated grain temperatures are greater than the experi-
mental results, some are less. The average of the absolute differences
in grain temperature is 7.73°C. Much of the temperature difference is
due to the tests presented by Carrano gg_§l, (1971). In obtaining the
data, a single stage concurrentflow dryer with a counterflow cooler
was used. Grain samples were taken between the drying and cooling
stages and the temperatures reported are a combination of outlet dryer
and outlet cooler air temperatures.

Correspondence plots for grain temperature and moisture content
are presented in Figure 20. The linear correlation coefficient for

grain temperature including all tests is rc = 0.746; for grain

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91

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Figure 20.

92

 

 

 

 

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Actual Moisture Content, % w.b.

 

 

 

 

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Actual Grain Temperature, °C

Correspondence plot for single-stage concurrentflow
drying: T = Thompson (1967), C a Carrano gg_gl, (1971),
B = Baughman gt_al, (1971).

93

temperature excluding the Carrano tests rc = 0.789; for moisture
content rc = 0.743.

The grain temperature goodness-of-fit test (excluding Carrano
tests) yields x2 = 6.253 which is less than the critical Chi-Squared
value at 95% significance of xc2 = 14.07 (CI: 1.69 - 16.01). The p
value is F(7,31) = 1.173 which is less than the critical value at 95%
significance of PC = 2.75 (CI: 0.36 - 2.75). The grain temperature
correspondence is significant at the 95% level.

The moisture content goodness-of—fit test yields X2 = 1.19 which
is less than the critical value at 95% significance of xc2 = 19.68
(CI: 3.82 - 21.92). The F value is F(47, 11) = 1.78 which is less
than the critical value at 95% significance of Fc = 3.02 (CI: 0.33 -
3.02). The moisture content correspondence is significant at the 95%

level. Therefore the model is accepted for single-stage drying at the

95% significance level.

4.7.2 Multi-stage drying of shelled corn

The previously described multi-stage concurrentflow computer
model was used to simulate the drying of shelled corn. The effect of
drying on the susceptibility to breakage (Stein breakage test) was
determined using equation (53). Computer simulation runs were produced
for the test input conditions given in Table 13. The results of the
simulations are presented in Table 26.

The test results from Table 14 can be compared with the simula-
tion results in Table 26 to help verify the accuracy of the computer
simulation results for use in the design of a multistage concurrentflow

grain dryer. Table 27 shows the absolute values of the differences

94

Table 26.--Simulation results for shelled corn drying tests.

 

 

Test Number 1 2 3 4 5 7 8 9
Stage 1
temperature, °C 36 39 40 41 40 41 43 41
moisture, % w.b. 25.2 21.5. 24.5 24.0 22.2 20.2 19.7 22.6
Stein breakage, % 15.2 16.3 12.1 13.8 25.6 28.0 39.0 39.8
Stage 2
temperature, °C 41 49 46 50 53 60 56 49
moisture, % w.b. 21.8 16.9 18.8 17.8 14.0 11.3 11.9' 14.3
Stein breakage, % 21.2 26.1. 25.5 28.2 43.4 46.1 50.1 57.9
Stage 3
temperature, °C 44 60 58 66
moisture, % w.b. 18.1 12.8 13.1 11.8
Stein breakage, % 29.6 34.2 37.0 40.0
Cooler**
temperature, °C 23 23 28 24 29 29 23 17
moisture, % w.b. 17.3 11.6 12.0 10.5 13.1 10.3 10.8 13.2
Efficiency, kJ/kg H20* 3778 4197 3738 3910 3832 3981 3853 3986

 

*Does not include the energy used or the removed during cooling.

**Cooler airflow 10 m/min test 1-4, 5 m/min tests 5-9.

Table 27.--Average differences between test conditions and simulation
results for the shelled corn drying tests.

 

 

Average Maximum Minimum x2* F**
Before cooling
temperature, °C 33 43 23 -- --
moisture, % w.b. 2.3 5.1 0.1 -- --
Stein breakage, % 18.9 25 7 9.1 -- --
After cooling
temperature, °C 5 11 l 14.54 1.06
moisture, % w.b. 3.2 6.4 0.5 6.49 1.06
Stein breakage, % 18.9 25.7 9.1 155.60 1.27

 

2

*X = 14.07 (CI:

C

1.69 - 16.01) at 95% significance.

**Fc(7,31) = 2.75 (CI: 0.36 - 2.75) at 95% significance.

95

between the test results and the simulation results for exit grain
temperature, moisture content and percentage for the Stein breakage
test. The discrepancy between the simulation and test results for
moisture content is fairly large. This is primarily due to the way in
which the test data was obtained. The corn drying tests were conducted
as would be done commercially, i.e., varying the grainflow rate in
order to achieve a unifbrm.moisture product from the dryers. This was
indeed accomplished as can be seen in the range of moisture contents
given in Table 14 which is about :.0.5% w.b. The grainflow rates used
in the simulation are time-weighted averages and do not account for all
the effects of variable grainflow.

Correspondence plots for grain temperature and moisture content
are presented in Figure 21. The linear correlation coefficient for
grain temperature is rc = -0.136; for moisture content rc = 0.454; for
Stein breakage percentage (not shown) rc = 0.729.

The goodness-of—fit and F-value statistics are included in
Table 27. The variance comparison (F-test) of all three parameters is
significant at the 95% level. Only the moisture content correspondence
is significant at the 95% level. The variation in the moisture con-
tent causes most of the deviation in Stein breakage percentage.
Likewise the grain temperature is dependent on the moisture content.
The correspondence is marginally significant at the 95% level. It is
expected that the correspondence in all parameters would improve for
multistage tests conducted with relatively constant inlet conditions.
The agreement between the simulation model and the experimental tests
is considered sufficient for the model to be used in the design of

multistage concurrentflow grain dryers.

96

 

 

 

 

 

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Actual Moisture Content, % w.b.

 

Predicted Grain Temperature, °C

 

 

 

 

10 1 ' ! ‘
10 15 20 25 30
Actual Grain Temperature, °C

Figure 21. Correspondence plots for multistage shelled corn drying
tests. Numbers refer to test number listed in Table 26.

97

It should be noted here that the overall breakage for the tests
listed in Table 13 and 14 of 23.7% is lower than a previously reported
average of 36.6% for a high—temperature crossflow dryer (Stephens and
Foster, 1976). It is also lower than the average of 52.6% for samples
taken from an Ace crossflow dryer operated at 104°C which was tested

at the same time as the concurrentflow drying tests were conducted.

4.7.3 Multi-stage drying of pea beans

The previously described multi-stage concurrent flow computer
model was used to simulate the drying of pea beans. 'The effect of
drying on the percentage of cracked beans was determined using equation
(54). Computer simulation runs were produced for the test conditions
given in Table 10. The results of the simulations are presented in
Table 28.

The test results from Table 11 can be compared with simulation
results in Table 28 to verify the accuracy of the computer simulation
results for use in the design of a multistage concurrentflow grain
dryer. Examination of Tables 11 and 28 shows that some simulation
results are greater than and some less than the test results. Table 29
shows the absolute values of the differences between the test results
and the simulation results for exit grain temperature, moisture con-
tent, and percentage of cracked beans. The percentage of cracks
calculated is, in most cases, less than the observed percentage. Some
of the difference is attributed to the variability in moisture contents
(the change in moisture content is one factor in the estimation
equation). The estimation equation for cracks is representative of

the test data. However, the test samples were removed hot from each

98

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99

Table 29.--Average differences between test conditions and simulation
results for pea bean drying tests. Includes cooling only
for test 12.

 

 

Temperature Moisture Cracks
°C % w.b. %
First stage-~average* 2.0 0.65 0.62
maximum 5.0 1.10 2.20
minimum 0.0 0.10 0.00
Second stage--average* 2.9 1.20 2.26
maximum 5.0 2.10 5.20
minimum 1.0 0.20 0.40
Third stage-~average** 1.0 0.80 1.83
maximum 1.0 1.20 4.20
minimum 1.0 0.60 0.30
Total weighted average 3.1 0.91 1.49
XZIII 2.92 1.11 11.00
F(9, 35)**** 2.09 1.34 5.72

 

*Average of 10 absolute differences.

**Average of 3 absolute differences.
***xc2 16.92 (CI: 2.70 - 19.02).
****F 2.51 (CI: 0.40 - 2.51).

drying section it is felt that the sudden exposure to the cooler air
increased the percentage of cracks observed. Second, the counterflow
cooler provides a gentle cooling process as compared to a crossflow
cooler. The beans leaving the cooler in Test 12 showed 2.9% cracks.
Correspondence plots for grain temperature and moisture content
are presented in Figure 22. The linear correlation coefficient for

grain temperature is r = 0.825; for moisture content rc = 0.714; for

c
the percentage of cracked seed coats (not shown) rc = 0.651.
The goodness-of-fit and F-value statistics are included in

Table 29. The parameters are all significant at the 95% level except

100

 

 

 

 

 

 

 

 

 

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Figure 22. Correspondence plots for multistage pea bean drying tests.
Numbers refer to test number listed in Table 28.

101

the cracks which fail the F-test. The correspondence between the
simulation model and the experimental tests is considered sufficient
for the model to be used in the design of multistage concurrentflow

grain dryers.

4.7.4 Crossflow dryer comparison--Pea beans

Pea bean samples were collected and tested form the Ace cross-
flow dryer on a regular basis by Cook's personnel. Each sample was
immediately tested for temperature, moisture, and percentage of splits
and cracks. The procedure used by the Cook's personnel was different
and less critical than the procedure employed by MSU personnel for
determining the percentage of cracked beans in a sample. Therefore
direct comparison of the two is difficult. From personal observations
the author feels that an analysis by MSU personnel would show cracks at
a level of 1.5-2.0 times that observed by Cook's personnel.

Silo measurements were kept to determine the total quantity of
beans dried and thus the average grainflow rate through the crossflow
dryer. The total gas used was recorded and used to calculate the
average energy efficiency of the crossflow dryer. Table 30 presents
average inlet and outlet conditions for the pea beans dried in an Ace
crossflow dryer operated at a heated air temperature of 32°C.

A multistage concurrentflow dryer could be operated and perform
as well as, if not better than, a crossflow dryer with respect to grain
damage. The major advantage of the multistage concurrentflow dryer is
in regard to energy consunption which is less than for a crossflow
dryer. The smaller air exhaust area would also allow easier reuse of
air exhausted from the concurrentflow dryer for additional energy and

operating cost savings.

102

Table 30.--Average inlet and outlet conditions for pea beans dried in
an Ace crossflow dryer with a heated air temperature of

 

 

32°C.
Average Variance N
Inlet--moisture, % w.b.* 21.5 0.84 38
cracks, %* 1.0 0.32 38
splits, %* 0.2 0.02 38
0ut1et--temperature, °C 22.0 3.90 253
moisture, % w.b. 17.0 0.10 253
cracks, % 2.0 1.23 243
splits, % 1.0 0.38 249

Efficiency, kJ/kg water removed 5552 -- --

 

*Ca1culated from inlet samples taken from the concurrentflow
dryer.

S. OPTIMIZATION MODEL

The previously developed multistage concurrentflow dryer model
can be utilized with a trial and error approach to help design a multi-
stage concurrentflow dryer for field use. Alternatively one can con-
struct an optimization algorithm to help find a design which dries
grain with a minimum value of a specified objective (cost) function.

The objective function.may include drying costs, capital equipment cost,
costs for.changes in grain quality, or other important factors.

The following section outlines the development of a dynamic
programming algorithm for finding the optimum Operational parameters
and size of a multistage concurrentflow dryer with intermediate tempering
stages. The objective function is based on costs for energy consumed
during the drying and for fixed and (design) variable costs. The
operational parameters are constrained by the desired final moisture
content, the maximum allowable exit temperature of the grain from each
drying stage, and the maximum allowable value of an important grain
quality factor. For shelled corn the quality factor used is the
susceptability to breakage as measured by the Stein breakage test. For
pea beans a quality factor is the percentage of cracked beans. For

wheat one is interested in an index based on baking quality factors.

103

104

5.1 Optimization algorithm

Thompson (1967) and Farmer (1972) developed multi-variable
search techniques, based on a single-dimensional search algorithm, for
study of the optimal design of convection grain dryers. Thompson
studied single-stage crossflow and concurrentflow, and Farmer the
optimum design of batch-in-bin dryers.

Dynamic programming, developed by Bellman (1957), is an extremely
powerful approach for solving optimization problems. Dynamic pro-
gramming is especially applicable to multistage optimization problems.
Ahn.gt'gl, (1964) and Schroeder and Peart (1967) applied dynamic pro-
gramming to the study of optimal air distribution along the length of a
crossflow dryer column. Farmer (1972) used dynamic programming in the
optimization of a single—stage concurrentflow dryer with counterflow
cooler (a two stage process); the effect of recycling the exhaust air
from the cooler to the dryer inlet was also studied. -

The standard form of dynamic programming used in the previously
cited references was "backward" dynamic programming. Backward dynamic
programming begins the computations at the final time and proceeds to
the initial time in order to find the Optimum solution. A useful
technique outlined by Larson (1968) is "forward" dynamic programming
~where the computations begin at the initial time and proceed to the
final time in order to find an optimal solution. Forward dynamic
programming is utilized in this thesis because of the form of the
drying system equations involved. The following outline of forward
dynamic programming is adapted from Larson (1968):

1. Let X denote the state vector which describes the dynamic

 

behavior of the multistage system,

105

2. Let U denote the control vector, the components of which are

 

varied by the dynamic programming algorithm so that the
progress of the state vector with time is controlled in an
optimal fashion.

3. The system equations relate the dynamic behavior of the state

 

vector to the applied control vector. The system equations are

usually non-linear, time-varying differential equations; e.g.:

dX
a- = F(X,U,t) (58)

4. The objective function (cost function) determines the effective-
ness of the applied control vector and is minimized by the
dynamic programming procedure. The cost function is dependent
on the applied control vector and the associated state vector
for the nEE-stage and also the minimum of the sum of the cost
functions for the proceeding stages:

n-l
I(X,n) = i(X,U,n) + minjili(xj_1, Uj_1,j) (59)

The procedure starts at the intial time (t=0) with an initial
state vector (X0) and divides the feasible range of state vector values
at the end of the first stage into a suitable number of feasible sets.
For each set of state vector end points the set of feasible control
vectors is applied. The resultant set of cost function values is
searched to find the value of the control vector which minimizes the
cost function. The procedure is then repeated for each set of state
vector end points.

The succeeding stages have a feasible set of initial state

vectors defined from the proceeding stage. A feasible set of state

106

vector end points is again defined. The set of feasible control
vectors is applied for each set of vector end points for all sets of
the initial state vector. The resultant set of cost function values is
searched to find the value of the control vector which minimizes the
cost function. The procedure is then repeated for each set of state
vector end points and for each succeeding stage.

The final result is a super-set of control vectors which
defines the dynamic behavior of the system for the initial state vector
and a terminal set of state vector end points.‘ The super-set will
yield the overall optimal set of control vectors necessary to proceed
from the initial state vector to any particular terminal set of state
vector end points.

The state vector for the multistage concurrentflow dryer
problem studied consists of a single component-~the moisture content of
the grain. The control vector consists of three components for each
stage: (1) heated air temperature, (2) airflow, and (3) stage length.
The objective of the dynamic programming algorithm is to find the
optimum values of the three components of the control vector for each
stage which result in the minimum possible cost for drying grain from a

specified initial moisture to a desired final moisture content.

5.2 Objective function

The objective function (total cost) utilized consists of three
parts: (1) operating cost based on energy consumption, (2) capital
investment cost, and (3) grain quality constraints. The total cost is
the sum of the energy and capital investment costs budgeted per unit
mass of grain dried. If the quality factors exceed a preset value, a

large cost is added to the above total cost.

107

5.2.1 Operating cost

The two Operational parameters included in the control vector
are: (l) heated air temperature, and (2) airflow. The cost for the
energy used to heat the air is based on the air energy equation (24)
and the price of the fuel per unit of energy supplied:

Ga(ca+ch)(T-Tamb)Pfue1

CEa z .85 GP (60)

 

The cost for the energy used to Operate the fan is based on the fan
energy equation (26) and the price of electricity per unit of electri-
city supplied:

5.575(Qa)(SP)P

.5 G
P

electricity

 

CEfm = (61)

5.2.2 Capital investment cost

The two parameters included in the control vector which influ-
ence the capital cost are: (1) length of the drying stage, and (2) air-
flow. In addition to these two design variable capital costs, there is
a fixed capital cost for auxiliary equipment which is not affected by
changing the length of the drying stages or the operational parameters.

The total investment is calculated from:

IC 3 CCfixed + CCfanQa + CClengthxl (62)

The investment cost must be converted to an equivalent
annual cost. Riggs (1977) describes two methods for calculating annual
costs for a given investment: (1) approximate calculation, and (2) exact

calculation.

108

The approximate annual cost calculation is based on straight-

 

1ine depreciation and average interest. A grain dryer would have an

annual cost of:

IC—SV IC+SV IN

AC = N + 2 (1569

(63)

Brake (1976) suggested an expanded version of the approximate annual

cost calculation which includes yearly maintenance and insurance costs:

IC-SV IC+SV IN+IM+II

AC = N + 2 I 100 )

 

 

(64)

The exact annual cost calculation given by Riggs (1977) includes

 

the time value of money. The discounting of the annual cash flow is
normally the preferred means for investment analysis and capital
budgeting. However, for use in the Optimization procedure the simpli—
city of equation (64) is preferred. The author feels that the optimiza-
tion results are not affected by using the approximate instead of the
exact annual cost calculations.

Dividing the annual cash flow by an assumed yearly throughput
yields budgeted capital cost (cost per kilogram of grain dried) values
that can be directly incorporated with the operational costs. The
multistage concurrentflow dryer will be used mainly at an elevator.
Operational time is estimated at 24 hours/day and 30 days per corn
harvest season. The resulting;budgeted capital cost is calculated

from:

AC*1O
24*30 Gp

BC = (65)

109

5.2.3 Grain quality constraints

The cost associated with deterioration in grain quality can be
used as an additional cost factor. At the present time the estimation
models for grain quality are not sufficiently accurate for this
approach. In addition, if the quality factors are maintained within a
reasonable range they do not affect the value of the grain when it is
later marketed. One factor for corn is the kernel temperature at the
end of each drying stage. Corn to be used for feed can withstand a
higher temperature than corn which is to be used for wet or dry milling.
Corn which is to be used for seed is very sensitive to high grain
temperatures (see Table 8). A second constraint for corn is the
kernels' susceptibility to breakage as measured by the Stein breakage
test. The breakage test percentage is estimated using equation (53).

During the analysis of the cost function in the dynamic pro-
gramming procedure, the quality cost is initially set to zero. If
either of the quality parameters (temperature or breakage percentage)
exceed some predetermined limit the quality cost is set to a value
high enough to effectively render the current set of control vector

values infeasible.

5.3 Optimization implementation

Dynamic programming (DP), unlike linear programming.or
other Optimization techniques, is not supported by a standard com-
putational package. The software programmer must tailor the DP
procedure for each application.

The basic flowchart for the DP optimization algorithm used in

this study is presented in Figure 23. The problem being studied

110

 

Glead inputs )

 

 

 

Find outlet moisture content

 

 

 

 

rIncrement inlet moisture I

cont ent range

l4 Increment outlet moisture I
content,ran2e

 

 

 

[ Increment airflow range __]

for drying?

Increment heated air temper- ]
ature for drying

 

Simulate drying until current
outlet moisture content is
reached. Store required
stage depth

[#JC ompute dryingicost _]

Computed cost :::>
i cost?

Yes

! Store cost and control vector _]
rncf

u11 temperafure range
. . 9

 

 

 

 

   
   

 

 

 

 

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No .2/9611 airflow range ::>>
ted?
Yes

 

 

 

No /Fu ll outlet moisture :>

content ran e
to?
IYes
ull inlet moisture

 

 

 

 

 

N-—< AllS stages investigated? >
es

 

Figure 23. Basic flowchart of dynamic programming optimization.

111

involves known initial and final values for the state vector (moisture
content of the grain). Therefore, during computations for the first
stage, the inlet moisture content range consists of a single point.
Similarily for the last stage the outlet moisture content range consists
of a single point. Making use of these known points considerably
reduces the number of calculations required.

As the calculations proceed the specified ranges of the controls
Cheated air temperature, airflow, and stage length) are investigated to
find the proper combination which results in a minimum overall drying
cost. The cost value used for the minimization process is the sum of
two costs (see equation (59)): (l) the cost using the current set of
control values to dry the grain from the current inlet moisture content
to the current outlet moisture content for the current stage (from
equations (60), (61), and (65)), and (2) the minimum cost to dry the
grain from the initial moisture content of the first stage to the
current inlet moisture of the current stage. In this way the cost
obtained and the associated control vector is always for the minimum
overall total cost.

Here again knowledge of the process being optimized helps
reduce the number of calculations required. Several such heuristic
methods are used in the optimization algorithm of this study.

The outlet moisture content range is determined for each stage
using the minimum and maximum, respectively, allowable values of the
control vector elements. The minimum value of the range thus defined
is checked and reset to, if less than, the desired overall final
moisture content. In this way the outlet moisture range used for

each stage is always a set of feasible points, and moisture contents

112

less than the desired final moisture are not included in the com-
putations.

The reader can note in Figure 23 that the innermost loop is
the dryer length for the current stage. The algorithm then determines
the necessary dryer length for the current values of inlet and outlet
moisture content, heated air temperature, and airflow. This is
accomplished by starting the drying simulation at the current inlet
moisture content (for the Specified temperature and airflow) and con-
tinuing along the length of the dryer until the grain reaches the
current outlet moisture content. The necessary dryer depth is stored
and used for later cost calculations. The above procedure is allowable
because the grain moisture content is a continuously decreasing function
of depth during drying. The author does not feel that this method
introduces any bias in the optimization in regard to minimizing the
cost. Generally the minimum cost will occur when the dryer length
trends toward a minimum value.

The next outermost loop shown in Figure 23 is for heated air
temperature. The firSt step in this loop (before any simulation as
previously described) is to check the moisture content obtained using
the maximum allowable heated air temperature and the maximum allowable
dryer length for the current stage. If this calculated moisture
content is greater than the current outlet moisture content, there is
no allowable temperature and length combination for the current airflow.
Since the airflow starts at the maximum allowable and decreases during
the calculations, when the condition stated above occurs, the current
and all lower airflow values are infeasible for the current outlet

moisture content. The program then terminates the airflow loop and

113

increments the outlet moisture content loop. If the calculated moisture
content is equal to the current outlet moisture content, the program
calculates an approximate cost using the current heated air temperature
and the minimum allowable length for the current stage (no drying
simulation necessary). If the approximate cost is greater than the
current minimum cost then no further calculation is necessary for the
current heated air temperature. The temperature is incremented
(increased) and the approximate cost recalculated. When a temperature
is found where the approximate cost is less than the current minimum
cost, the necessary stage length is found as described previously. The
exact cost is then calculated and compared against the current minimum
cost. If the exact cost is less than the minimum cost, the exact cost
becomes the minimum cost to dry the grain from the initial moisture
content to the current outlet moisture content. The associated control
vectors and an index indicating the current inlet moisture content are
also stored.

The above procedures are repeated fer all possible sets of
inlet and outlet moisture content for all desired stages. After all
computations are complete the optimal trajectory for the moisture
content is obtained starting at the outlet moisture content of the
last stage. The printed output indicates the inlet moisture content
index for finding the outlet moisture content from the previous stage.
Then the associated cost and control vector elements are found.

Backing up one stage to the indicated moisture content the process is
repeated through the first stage.

The performance of the optimization algorithm can be estimated

based on knowledge of the concurrentflow drying process and the

114

associated cost functions. The algorithm will attempt to maximize the
heated air temperature (maximum drying rate), minimize the airflow
(maximum utilization of the energy in the drying air), and minimize the

dryer length (minimum capital cost) fOr each stage.

5.4 Results of optimization for shelled corn

The dynamic programming type optimization routine described
above is used to analyze the design of a multistage concurrentflow
dryer for shelled corn. Like any design tool, the Optimization routine
is not an end in itself. Four comparisons are made:

1. Staging: Compare one-, two-, and three-stage dryers.

2. Tempering: A good tempering time was found to be 1.25 hours
for a concurrentflow dryer. Compare tempering times less than
1.25 hours for their effect on total drying cost.

3. Heat recovery: One method of heat recovery is to use the
exhaust air from one drying stage as the input air to the
following drying stage. Compare the dryer performance using
this feed-forward recycling with a conventional concurrentflow
configuration.

4. The predominant dryer for drying shelled corn currently is the
column crossflow dryer. Compare the drying and capital costs
for this type of dryer with the multistage concurrentflow two-
and three-stage dryers.

Each comparison is conducted at three grainflow levels using
the standard conditions listed in the following section. The grainflow
rates are based on advertised rates for'multistage concurrentflow
dryers manufactured by Westlake Agricultural Engineering, Inc., St.

Marys, Ontario, Canada.

115

5.4.1 Standard input conditions

Simulation of grain drying and optimization of the performance
of a grain dryer is accomplished using any reasonable set of input
conditions. However, when comparing basic parameter changes or
different dryer types, the performance evaluation requires a standard
set of input conditions in order to have an adequate basis for com-
parison. Bakker-Arkema g£_§g: (1973a) proposed the standard conditions
listed in Table 31 for the drying of shelled corn. These conditions
are used in obtaining the optimization results in the following
sections. The optimization routine assumes that the counterflow cooler
will remove 1% d.b.

Table 31.--Standard conditions for the simulation of dryer performance
for the drying of shelled corn.

 

Inlet corn moisture content, % w.b. 25.0
Outlet corn moisture content, % w.b. 15.0*
Ambient air temperature, °C 15.0
Ambient air humidity ratio, decimal d.b. .0065
Inlet corn temperature, °C 15.0
Inlet corn foreign material, % 3.0
Inlet corn breakage, % 10.0
Outlet corn temperature, °C** 20.0

 

*Original table value from Bakker-Arkema g£_gl, (1973a) was
20.0% w.b. The author feels that for the drying of shelled corn the
value given is more representative of actual field practice.
**The final reduction in grain temperature is accomplished using
a counterflow cooler which is not considered in the Optimization.
The optimization routine includes two grain quality constraints.
The first is the temperature of the grain which leaves a concurrentflow

drying section. The grain temperature within the dryer will be greater

than the exit temperature at some time during the drying process, but

116

drops rapidly as drying progresses (see Figure 6). Mfihlbauer and
Christ (1974) have shown that the time-temperature relationship is
important fer grain. The time-temperature history during drying is a
more accurate quality criterion. However, the author feels that outlet
grain temperature is an adequate quality constraint. Using the results
and conclusions of Peplinski 33 El: (1975) a value of 80°C is used as
a constraint in obtaining the optimization results in the following
sections. 1

The second quality factor for shelled corn is the kernel
breakage percentage obtained from the Stein breakage test. The U.S.
grade standards for shelled corn limit broken corn to 3.0% for no. 2
yellow corn (the most common trade grade). Stephens and Foster (1976)
found that a handling breakage of 3.0% resulted from repeated handling
of shelled corn with a Stein breakage percentage of 17.0-23.0%. A
value for the maximum allowable Stein breakage percentage of 23.0% is
used in obtaining the optimization results in the following sections.

The optimization routine includes three capital cost factors:
(1) fixed cost independent of variable design factors, (2) fan costs
per unit of air velocity (m/min), and (3) cost per meter of drying
column length based on the combined drying and tempering lengths.
Sales costs for 1976 were obtained from Westlake Agricultural Engi-
neering, Inc. for one-, two-, and three-stages concurrentflow dryers.
The sales costs and a non-linear least-squares algorithm (Meeter and
Wolfe, 1965) were used to approximate the capital cost factors in
equation (62). The values of the three cost factors obtained are
listed in Table 32. Also listed in Table 32 are the fuel and electri-

cal energy costs used in the optimization. The cost factors were

117

Table 32.-~Capital and energy cost values used for obtaining optimiza-

tion results for shelled corn.

 

Fixed cost, $lm2/stage $7225.00 (bottom stage)
3270.00 (tOp stages)
Fan cost, $/(m/min) 5.00
Length cost, $/m3 975.00 (bottom stage)
250.00 (top stages)
Fossil fuel cost, ¢/kJ* 0.0004
Electricity cost, ¢/kJ** 0.0014

 

*Based on L.P gas at 40¢/ga1 and 96532 kJ/gal.

**Based on electricity cost of 5¢/kWh.

determined as cost per square meter of dryer column area so as to be

applicable for a wide range of dryer sizes. Realistically, an economy

of scale does exist (approximately -$ l72/m2) which is not considered

by the optimization routine.

Five capital budgeting factors are used in equation (64):
Salvage value--Assume zero salvage value. The dryer is made
of mostly sheet metal. While the metal may have some scrap
value, the cost of dissassembling the dryer would make the
total salvage value negligible.
Equipment 1ife--Assume a ten year life for the drying equipment.
Interest rate--Assume an interest rate of 8%.
Maintenance factor--Woods (1975) gives a range for maintenance
factors of 2-15% of investment cost per year. A grain dryer
is a relatively simple piece of equipment. Assume a maintenance
factor of 5% of investment cost per year.

Insurance factor--Woods (1975) gives a range for insurance
factors of 0.4-1.0% of investment cost per year. A grain dryer

is a relatively high risk piece of equipment due to the open

118

flame used to heat the air. Assume an insurance factor of 1% of

investment per year.

The optimization algorithm as previously flowcharted considers
three variables for each drying stage: (1) heated air temperature,
(2) airflow rate, and (3) length. The tempering time and thus the
length of the tempering stages is, in most cases, set at a length
resulting in 1.25 hours tempering time. The range of the variables
listed in Table 33 are used to obtain the results in the following

sections.

Table 33.--Ranges for variable design factors.

 

 

One-Stage Two-Stage Three-Stage
Stage 1: temperature, °C ISO-200 200-230 200-230
airflow, m/min 30-60 30-60 30-60
length, m 1—2 1-2 1-2
Stage 2: temperature, °C 150-200 150-200
airflow, m/min 30—60 30-60
length, m 1-2 1-2
Stage 3: temperature, °C 150-200
airflow, m/min 30-60
length, m 1-2

 

5.4.2 Effect of staging

Results for one-, two-, and three-stage concurrentflow dryer

optimizations are given in Tables 34 through 36. Each different staging

configuration is presented for three grainflow rates chosen to be

representative of commercial concurrentflow dryers. The grainflow

ranges overlap and cover the composite range of 1.0-4.0 tonne/hr-mz.

Generally, within each configuration the total drying cost decreases

as the grainflow increases.

The decrease is primarily due to drying

119

Table 34.--Optimization results for one-stage concurrentflow dryer at
three grainflow rates.

 

Grainflow, tonne/hr-m2

 

 

1.0 1.5 2.0
Inlet air temperature, °C 200 200 200
Airflow, m3/min.-m2 42 60 60
Dryer length, m 1.5 2.0 2.0
Tempering time, hr -- -- --
Inlet moisture, % w.b. 25.0 25.0 25.0
Outlet grain temperature, °C 53 53 45
Outlet moisture, % w.b. 15.7 16.2 18.5
Stein breakage, % 22.7 21.7 16.9
Outlet air temperature, °C 53 53 45
Outlet air humidity, decimal d.b. .0559 .0559 ..0563
Drying cost, ¢/kg .569 .464 .348

 

more grain with similar capital investment cost. When reviewing
Table 34 the reader should note that the single stage dryers with
grainflows of 1.5 and 2.0 tonne/hr-m2 did not dry the grain to the
desired final moisture content; the results presented are the maximum
possible with the design factor ranges used (Table 33).

The cost breakdown for the one-, two-, and three-stage dryers
are given in Tables 37, 38, and 39, respectively. The total energy
costs does not vary significantly between the various drying con-
figurations. The average energy efficiency for the one-stage dryers
is 3858 kJ/kg water; for the two-stage dryers, is 3819 kJ/kg water;
for the three-stage dryers 3857 kJ/kg water. The variation in energy
cost and energy efficiency between the three configurations is not
considered significant. The proportion Of the drying cost due to
capital equipment investment is similar between the two- and three-stage

configurations. At higher grainflows the capital cost is about 45%

120

Table 35.—-Optimization results for two-stage concurrentflow dryer at
three grainflow rates.

 

Grainflow, tonne/hr-m2

 

 

2.0 2.5 3.00
Stage l--
inlet air temperature, °C 230 230 230
airflow, m3/min-m2 48 48 60
dryer length, m 1.0 1.1 2.0
tempering time, hr 1.25 1.25 1.25
inlet moisture, % w.b. 25.0 25.0 25.0
outlet grain temperature, °C 51 48 46
outlet moisture, % w.b. 19.4 20.7 20.3
Stein breakage, % - 14.3 11.9 ' 12.9
outlet air temperature,°C 51 48 46
outlet air humidity, decimal d.b. .0610 .0593 .0621
drying cost, ¢/kg .243 .198 .200
Stage 2--

inlet air temperature, °C 190 200 200
airflow, m3/min-m2 30 48 54
dryer length, m ' 1.1 1.7 1.9
tempering time, hr -- -- ~-
inlet moisture, % w.b. 19.4 20.7 20.3
outlet grain temperature, °C 62 62 63
outlet moisture, % w.b. 15.7 15.7 15.7
Stein breakage, % 22.7 22.7 22.7
outlet air temperature, °C 62 62 63
outlet air humidity, decimal d.b. .0580 .0618 .0600
drying cost, ¢/kg .238 .245 .219

Total drying cost, ¢/kg .481 .443 .418

 

121

Table 36.--Optimization results fOr three-stage concurrentflow dryer

at three grainflow rates.

 

Grainflow, tonne/hr-m2

 

 

3.0 3.5 4.0
Stage l--
inlet air temperature, °C 200 200 212
airflow, m3/min-m2 30 30 60
dryer length, m 1.0 1.0 1.1
tempering time, hr 1.25 1.25 1.25
inlet moisture, % w.b. 25.0 25.0 25.0
outlet grain temperature, °C 43 41 43
outlet moisture, % w.b. 23.5 23.8 22.3
Stein breakage, % 10.0 10.0 10.0
outlet air temperature, °C 44 41 43
outlet air humidity, decimal d.b. .0381 .0359 .0506
drying cost, ¢/kg .120 .105 .143
Stage 2--
inlet air temperature, °C 190 180 200
airflow, m3/min-m2 54 60 54
dryer length, m 1.1 1.1 1.3
tempering time, hr 1.25 1.25 1.25
inlet moisture, % w.b. 23.5 23.8 22.3
outlet grain temperature, °C 56 54 57
outlet moisture, % w.b. 19.5 20.3 19.1
Stein breakage, % 14.7 12.8 15.5
outlet air temperature, °C 56 54 57
outlet air humidity, decimal d.b. .0572 .0533 .0589
drying cost, ¢/kg .161 .145 .130
Stage 3--
inlet air temperature, °C 200 200 190
airflow, m3/min-m 42 60 54
dryer length, m 1.2 1.8 1.5
tempering time, hr -- -- --
inlet moisture, % w.b. 19.5 20.3 19.1
outlet grain temperature, °C 67 66 68
outlet moisture, % w.b. 15.7 15.7 15.7
Stein breakage, % 22.7 22.7 22.7
outlet air temperature, °C 67 66 68

outlet air humidity, decimal d.b.
drying cost, ¢/kg

Total drying cost, ¢/kg

.0624 .0630 .0587
.186 .197 .156

.467 .447 .429

 

122

Table 37.--Cost breakdown and efficiency for one-stage concurrentflow
dryer at three grainflow rates.

 

Grainflow, tonne/hr-m2

 

 

1.0 1.5 2.0
Inlet temperature, °C 15 15 15
Inlet humidity, decimal, d.b. .0065 .0065 .0065
Fixed cost, $ 7225 7225 7225
Fan cost, $ 210 300 300
Length cost, $ 1463 1950 1950
Electrical energy cost, ¢/kg .0037 .0081 .0061
Fuel energy cost, ¢/kg .226 .215 .161
Total drying cost, ¢/kg .569 .464 .348
Efficiency, kJ/kg water 3867 3881 3827

 

Table 38.-~Cost breakdown and efficiency for two-stage concurrentflow
dryer at three grainflow rates.

 

Grainflow, tonne/hr-m2

 

 

2.0 2.5 3.0
Stage l--
inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ ' 3270 3270 3270
fan cost, $ 240 240 300
length cost. $ 1250 1525 2000
electrical energy cost, ¢/kg .0017 .0015 .0040
fuel energy cost, ¢/kg .150 .120 .125
total drying cost, ¢/kg .243 .198 .200
Stage 2--
inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ 7225 7225 7225
fan cost, $ 150 240 270
length cost. $ 1073 1658 1853
electrical energy cost, ¢/kg .0006 .0023 .0029
fuel energy cost. ¢/kg .076 .101 .097
total drying cost, ¢/kg .238 .245 .219
Two-stage drying cost. ¢/kg .481 .443 .418
Efficiency, kJ/kg water 3860 3782 3814

 

123

Table 39.--Cost breakdown and efficiency for three-stage concurrentflow

dryer at three grainflow rates.

 

Grainflow, tonne/hr-m2

 

 

3.0 3.5 4.0
Stage 1--
inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ 3270 3270 3270
' fan cost, $ 150 150 300
length cost, $ 1750 2000 2275
electrical energy cost, ¢/kg .0004 .0002 .0017
fuel energy cost, ¢/kg .054 .055 .086
total drying cost, ¢/kg .120 .105 .143
Stage 2--
inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ 3270 3270 3270
fan cost, $ 270 300 270
length cost, $ 1775 2025 2325
electrical energy cost, ¢/kg .0017 .0019 .0015
fuel energy cost, ¢/kg .092 .081 .073
total drying cost, ¢/kg .161 .145 .130
Stage 3-- .
inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ 7225 7225 7225
fan cost, $ 210 300 270
length cost, $ 1170 1755 1463
electrical energy cost, ¢/kg .0010 .0031 .0017
fuel energy cost, ¢/kg .075 .092 .069
total drying cost, ¢/kg .186 .197 .156
Three-stage drying cost, ¢/kg .467 .447 .429
Efficiency, kJ/kg water 3779 3908 3883

 

124

of the total cost. As grainflow decreases the proportion increases to
about 53% at the lowest grainflow rates. Therefore, within each con-
figuration the total drying cost decreases as the grainflow increases.
Comparing the one-, two—, and three-stage configurations, the one-
stage dries corn for a total cost of 0.569¢/kg; the two-stage for an
average total cost of 0.447 ¢/kg; the three-stage for 0.448 ¢/kg. The
multistage dryers have an apparent cost advantage as compared to the
single-stage dryer. There is no significant advantage (on the basis of
average total drying cost) of two- or three-stage concurrentflow grain

dryers.

5.4.3 Effect of tempering

The Optimization and cost breakdown results for two-stage
dryers with different tempering times are presented in Tables 40 and 41.
Again the total fuel cost does not vary significantly; 0.223¢/kg for
tempering times of 1.20 and 1.00 hours as compared to 0.236¢/kg for a
tempering time of 0.75 hours.

One factor not adequately covered by the optimization routines
is the effect of tempering on the quality of the corn which has been
dried. Very likely a longer tempering time is beneficial for the
kernel to relieve some of the internal stress caused by the drying
process. The tempering time and thus the length of the tempering
stage has a significant effect on the drying cost. The capital cost
of the additional volume of drying column required by tempering indi-
cates a small tempering length should be used for minimum drying cost
(see Table 32). A decision about tempering length would have to be

balanced against the effect of tempering on grain quality and the

125

Table 40.--Optimization results for two-stage concurrentflow dryer at

three tempering lengths for a grainflow of 2.5 tonne/hr-mz.

 

Tempering length, m

 

 

3.0 4.0 5.0
Stage l--
inlet air temperature, °C 230 230 230
airflow, m/min 48 48 48
dryer length, m 1.1 1.1 1.1
tempering time, hr 0.75 1.00 1.25
inlet moisture, % w.b. 25.0 25.0 25.0
outlet grain temperature, °C 48 48 48
outlet moisture, % w.b. 20.7 20.7 20.7
Stein breakage, % 11.9 11.9 11.9
outlet air temperature, °C 48 48 48
outlet air humidity, decimal d.b. .0593 .0593 .0593
drying cost, ¢/kg .191 .194 .198
Stage 2--
inlet air temperature, °C 200 200 200
airflow, m/min 54 48 48
dryer length, m 1.1 1.8 1.7
tempering time, hr -- -- --
inlet moisture, % w.b. 20.7 20.7 20.7
outlet grain temperature, °C 69 62 62
outlet moisture, % w.b. 15.7 15.7 15.7
Stein breakage, % 22.7 22.7 22.7
outlet air temperature, °C 69 62 62
outlet air humidity, decimal d.b. .0556 .0620 .0618
drying cost, ¢/kg .249 .246 .245
Total drying cost .440 .441 .443

 

126

Table 41.--Cost breakdown and efficiency for two-stage concurrentflow
dryer at three tempering lengths for a grainflow of 2.5

tonne/hr-mz.

 

Tempering length, m

 

 

3.0 4.0 5.0.
Stage l--
inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ 3270.00 3270.00 3270.00
fan cost, $ 240.00 240.00 240.00
length cost, $ 1025.00 1275.00 1525.00
electrical energy cost, ¢/kg .0015 .0015 .0015
fuel energy cost, ¢/kg .120 .120 .120
total drying cost, ¢/kg .191 .194 .198
Stage 2--
inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ 7225.00 7225.00 7225.00
fan cost, $ 270.00 240.00 240.00
length cost, 8 1073.00 1755.00 1658.00
electrical energy cost, ¢/kg .0020 .0025 .0023
fuel energy cost, ¢/kg .116 .103 .103
total drying cost, ¢/kg .249 .246 .246
Two-stage drying cost, ¢/kg .440 .441 .443
Efficiency, kJ/kg water 4036 3817 3816

 

127

necessity to provide the adequate physical separation between drying

stages.

5.4.4 Effect of heat recovery

The small exhaust area of the concurrent dryer as compared to
the crossflow dryer makes it readily amendable to some type of reuse
of the exhaust air. One type of recycling considered is the use of the
exhaust air from one drying stage as the input air to the heater of
the next drying stage. Such situations are illustrated in Figure 23
for a two-stage drying configuration.

The extra humidity in the inlet air to each drying stage has
little effect on the amount of drying which occurs. Therefore the
optimization results remain essentially the same as presented in
Tables 35 and 36. The cost breakdown for the two-stage and three-stage
configurations with the feed-forward recycling of the exhaust air are
presented in Tables 42 and 43, respectively. The recycling does indeed
decrease fuel energy consumption and thus total drying costs. However,
the capital cost (as given in Table 43) does not include the necessary
ducting to accomplishthe recycling. Using this heat recovery method
the three—stage drying configuration has a distinct advantage over the

two-stage dryer with respect to the energy consumed during drying.

5.4.5 Effect of quality constraints

The optimization runs previously presented used an exit temper-
ature limit of 80°C. No problems were encountered in satisfying this
constraint. Tables 44 and 45 present the optimization and cost-
breakdown results for one two-stage and two three-stage concurrentflow

dryers using a temperature limit of 60°C. In the first two cases the

128

 

 

 

 

Grain
In
I Heater Ambient
1; | Air
Concurrent
Drying

 

 

 

 

LI————-—-.:_

[Tempering J
6 1 Heat er a

Concurrent
Drying

 

 

 

 

 

 

 

 

 

———-—. Exhaust Air

 

 

 

Counterflow
Cooling

 

 

 

:_' Fan _ I Aggient

 

 

 

 

I

Grain
Out

Figure 24. Schematic of a two-stage concurrentflow dryer with feed-
forward recycling of exhaust air.

129

Table 42.--Cost breakdown and efficiency for two-stage concurrentflow

dryer at three grainflow rates with feed-forward recycling

of exhaust air.

 

Grainflow, tonne/hr-m2

 

 

2.0 2.5 3.0
Stage l--
inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ 3270.00 3270.00 3270.00
fan cost, $ 240.00 240.00 300.00
length cost, $ 1250.00 1525.00 2000.00
electrical energy cost, ¢/kg .0017 .0015 .0040
fuel energy cost, ¢/kg .150 .120 .125
total drying cost, ¢/kg .242 .198 .200
Stage 2--
inlet temperature, °C 51 48 46
inlet humidity, decimal d.b. .0610 .0593 .0621
fixed cost, $ 7225.00 7225.00 7225.00
fan cost, $ 150.00 240.00 270.00
length cost, $ 1072.00 1658.00 1852.00
electrical energy cost, ¢/kg .0006 .0023 .0029
fuel energy cost, ¢/kg .055 .077 .078
total drying cost, ¢/kg .216 .219 .196
Two-stage drying cost, ¢/kg .459 .417 .395
Efficiency, kJ/kg water 3502 3373 3491

 

Table 43.--Cost breakdown and efficiency for three-stage concurrentflow
dryer at three grainflow rates with feed-forward recycling

of exhaust air.

 

Grainflow, tonne/hr-m2

 

 

3.0 3.5 4.0
Stage l--
inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ 3270.00 3270.00 3270.00
fan cost, $ 150.00 150.00 300.00
length cost, $ 1750.00 2000.00 2275.00
electrical energy cost, ¢/kg .0004 .0002 .0017
fuel energy cost, ¢/kg .054 .055 .086
total drying cost, ¢/kg .120 .105 .143
Stage 2--
inlet temperature, °C 44 41 43
inlet humidity, decimal d.b. .0381 .0359 .0506
fixed cost, 3 3270.00 3270.00 3270.00
fan cost, $ 270.00 300.00 240.00
length cost, $ 1775.00 2025.00 2325.00
electrical energy cost, ¢/kg .0017 .0019 .0015
fuel energy cost, ¢/kg .070 .064 .057
total drying cost, ¢/kg .139 .127 .114
Stage 3--
inlet temperature, °C 56 54 57
inlet humidity, decimal d.b. .0888 .0827 .1030
fixed cost, $ 7225.00 7225.00 7225.00
fan cost, $ 210.00 300.00 270.00
length cost, $ 1170.00 1755.00 1463.00
electrical energy cost, ¢/kg .0010 .0031 .0017
fuel energy cost, ¢/kg .052 .065 .048
total drying cost, ¢/kg .163 .169 .134
Three-stage drying cost, ¢/kg .422 .402 .391
Efficiency, kJ/kg water 3012 3159 3277

 

131

dryer with an outlet temperature limit of 60°C.

Table 44.--Optimization results for two- and three-stage concurrentflow

 

Number of Stages

 

 

2 3 3*
Stage 1--
inlet air temperature, °C 214 230 200
airflow, m/min 40 >48 30
dryer length, m 1.0 1.0 1.0
tempering time, hr 1.25 1.25 1.25
inlet moisture, % w.b. 25.0 25.0 25.0
outlet grain temperature, °C 47 45 41
outlet moisture, % w.b. 21.0 21.6 23.8
Stein breakage, % 11.3 10.0 10.0
outlet air temperature, °C 47 45 41
outlet air humidity, decimal d.b. .0543 .0572 .0362
drying cost, ¢/kg .207 .168 .105
Stage 2--
inlet air temperature, °C 166 200 180
airflow, mfimin 50 42 60
dryer length, m 2.0 1.2 1.1
tempering time, hr -- 1.25 1.25
inlet moisture, % w.b. 21.0 21.6 23.8
outlet grain temperature, °C 58 53 54
outlet moisture, % w.b. 15.7 18.1 20.3
Stein breakage, % 22.7 17.7 12.8
outlet air temperature, °C 58 53 54
outlet air humidity, decimal d.b. .0512 .0619 .0532
drying cost, ¢/kg .293 .143 .145
Stage 3--
inlet air temperature, °C 170 200
airflow, m/min 30 6O
dryer length, m 1.2 1.8
tempering -- --
inlet moisture, % w.b. 18.1 20.3
outlet grain temperature, °C 54 66
outlet moisture, % w.b. 15.7 15.7
Stein breakage, % 22.7 22.7
outlet air temperature, °C 54 66
outlet air humidity, decimal d.b. .0555 .0630
drying cost, ¢/kg .154 .196
Total drying cost, ¢/kg .500 .466 .447
Grainflow, kg/hr-m2 2000 3000 3500

 

132

Table 45.-~Cost breakdown and efficiency for two- and three-stage
concurrentflow dryer with an outlet temperature limit of

60°C.

 

Number of Stages

 

 

2 3 3*
Stage l—-

. inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ 3270.00 3270.00 3270.00
fan cost, $ 200.00 240.00 150.00
length cost, $ 1250.00 1750.00 2000.00
electrical energy cost, ¢/kg .0011 .0012 .0003
fuel energy cost, ¢/kg .116 .100 .046
total drying cost, ¢/kg .207 .168 .105

Stage 2--
inlet temperature, °C 15 15 15
inlet humidity, decimal d.b. .0065 .0065 .0065
fixed cost, $ 7225.00 3270.00 3270.00
fan cost, $ 250.00 210.00 300.00
length cost, $ 1950.00 1800.00 2025.00
electrical energy cost, ¢/kg .0038 .0010 .0019
fuel energy cost, ¢/kg .110 .075 .082
total drying cost, ¢/kg .293 .143 .145
Stage 3--
inlet temperature, °C 15 15
inlet humidity, decimal d.b. .0065 .0065
fixed cost, $ 7225.00 7225.00
fan cost, $ 150.00 300.00
length cost, $ 1170.00 1755.00
electrical energy cost, ¢/kg .0004 .0031
fuel energy cost, ¢/kg .045 .092
total drying cost, ¢/kg .154 .196
Three-stage drying cost, ¢/kg .500 .466 .447
Efficiency, kJ/kg water 3873 3759 3772

 

133

drying cost increased in order to satisfy this temperature constraint.
The fuel energy costs are not significantly different among the three
cases. Cost differences are due to necessary changes in the airflow
and length of the drying stages.

The third analysis is included to indicate some possible limita-
tions of the constaint checking method used in the optimization pro-
cedure. In this case the optimization algorithm could not find any
conditions which accomplish the required amount of drying and still
meet the temperaeure constraint. However, this may not necessarily be
true. The calculations are done in a sequential manner on the basis of
minimum cost. The temperature constraint does not usually become
effective until the last drying stage; only then does the grain temper-
ature approach the temperature limit. The effect of the drying in the
first stage on the grain temperature in the last stage is not adequately
represented not accounted for in the program. Consequently, a set of
operational parameters for the first two stages may exist (e.g., higher
temperature and lower airflow) which results in a higher drying cost
without satisfying the temperature constraint. It is especially in
this regard where knowledge of the process involved is very helpful in
choosing the ranges for the variables used during the Optimization

procedure.

5.4.6 Comparison with crossflow drying

In a 1970 study of on-farm drying costs in Illinois, the drying
cost data shown in Table 46 were computed (Anon. 1976). The capital
investment cost included the necessary auxilliary storage costs,

erection costs and costs for other needed equipment for a complete

134

Table 46.--Costs for drying and storing corn on-farm in Illinois, 1976.

 

 

Capital Variable Fixed Total
Cost Cost Cost Cost
4 HR: ¢/kz ¢/k8
Low temperature, in-bin
305 tonne 15,000 .394 .591 .984
915 tonne 42,500 .394 .512 .905
1525 tonne 68,600 .394 .472 .945
High temperature, in-bin batch with multiple auger stirring
305 tonne 15,100 .433 .591 1.024
915 tonne 31,200 .276 .354 .630
1525 tonne 41,800 .276 .315 .591
Automatic batch
305 tonne 23,600 .354 .945 1.299
915 tonne 44,100 .276 .512 .787
1525 tonne 70.500 .276 .472 .750
Continuous crossflow
305 tonne 22,200 .354 .866 1.220
915 tonne 42,700 .276 .512 .787
1525 tonne 72,200 .276 .472 .750

 

Source: Anon. (1976).

drying and storage system. A drying time of 20 days was used for
removing 10 points of moisture from the corn.

The drying costs in Table 46 will be used along with the
previously presented costs for multistage concurrentflow dryers for
evaluation of investment feasibility. The comparison method used is
the Internal Rate of Return (IRR) as presented by Riggs (1977).

The IRR method is based on present worth calculations which
include the time value of the future yearly cash-flOws. Essentially,
the IRR method seeks to determine at what rate of cash flow discounting

does the present worth of the yearly increase in returns equal the

135

additional investment for the two projects being compared. The present

worth is calculated from:

PW

II
II [‘12

NSi(A,IRR,i) — AIC = o (66)

i 1

where: (A,IRR,i) = 1/(1+1RR)i (67)

The IRR figure computed from equation (66) is a percentage which is the
approximate yield for the particular use of capital involved.
A single-stage concurrentflow dryer rated at 8.0 tonne/hr can

be purchased for $43,000*; an equivalent two-stage dryer for $48,000;
an equivalent three-stage dryer for $49,000. All concurrentflow dryers
were shown previously to have an operating cost of about 0.230¢/kg. The
average Operating cost for an equivalent crossflow dryer is 0.302¢/kg
as given in Table 46 and can be purchased for approximately $21,000
(based on 30% of capital investment cost listed in Table 46). Based
on the previous assumption of 720 yearly operating hours, the net
yearly savings would be $4150. The corresponding IRR for the additional
investment in a concurrentflow dryer instead of a crossflow dryer
would be:

1. 14.6% for a single stage dryer; additional investment $22,000,

2. 8.7% for a two-stage dryer; additional investment $27,000,

3. 7.9% for a three-stage dryer; additional investment $28,000.
The corresponding break-even periods for the three concurrentflow

drying configurations are 5.3/6.5/6.7 years.

 

*Concurrentflow dryer purchase costs supplied by Westelaken
(1976).

136

The above analysis does not include the effect of inflation and

(possibly) steeply increasing energy prices which are tied very closely

to oil prices. Woods (1975) has tabulated and compared several indices

which can be used for evaluating the effect of inflation. .Inflation

of the evenly prices will improve the advantage of the concurrentflow

dryer over the crossflow dryer.

6. CONCLUSIONS

On the basis of either operating costs or IRR figures the
multistage concurrentflow dryer is preferrable to a crossflow dryer.
The two- or three-stage dryers have a higher investment cost than a
single-stage dryer, but, on a per square meter of column area basis,
the single-stage concurrentflow dryer is more expensive to operate than
a two- or three-stage concurrentflow dryer.

The quality of the end-product is affected by the drying
process. The concurrentflow dryer produces dried corn which is less
susceptible to damage than that produced by a crossflow dryer. Since
the increase in Stein breakage (and thus increased susceptibility to
breakage) is related to the moisture removal rate, a multistage con-
currentflow dryer with tempering is preferrable to a single-stage con-
currentflow dryer, and also to a conventional crossflow dryer. Imposing
a 60°C temperature limit versus an 80°C temperature limit during the
drying of shelled corn increases the drying cost. Changing constraints
on the quality factors of shelled corn and other agricultural products
produces similar results.

Feed-forward recycling of exhaust air significantly reduces the
energy use in the concurrentflow dryer. A three-stage dryer with
recycling has about a 16% advantage in energy cost over a similar

two-stage dryer. However, the added capital cost required for the

137

138

equipment necessary to capture and conduct the exhausted air is not
considered. A dryer purchased today has a known capital cost which is
budgeted over the estimated life of the equipment. At the same time
inflation causes energy purchase costs to increase (perhaps dramatically)
during the same time period. Therefore, a dryer using recycling has a
continuously increasing advantage over a dryer not using recycling, and
also over a conventional crossflow dryer.

The numerical results obtained are dependent on the factors
used fer estimating capital costs. However, operational and design
factors calculated by the optimization routine are unaffected by even
major changes in the capital cost factors. The IRR figures are com-
puted assuming zero inflation. Inflation and other market factors are
a fact of life which increase energy purchase costs and thus increase

the advantage of the concurrentflow dryer over the crossflow dryer.

7. SUMMARY

A computer model was developed to simulate the drying perfor-
mance of a multistage concurrentflow dryer with intermediate tempering
and a counterflow cooler. Diffusion within spherical kernels was used
to model the drying and tempering process. The counterflow cooler was
modeled using a modified version of the Effectiveness-NTU method
derived for a counterflow heat exchanger. The multistage model agreed
reasonably well with sample data obtained from field experiments for
the multistage drying of shelled corn and pea beans.

The quality of the shelled corn and pea beans as affected by
drying was modeled. An equation for the percentage of breakage in the
Stein breakage test was developed for shelled corn and for the per-
centage of cracked seed costs for pea beans. The calculations from
the quality models agreed well with the results of the experimental
tests but did not adequately reflect the beneficial effects of the
counterflow cooler.

An Optimization.mode1 using dynamic programming was developed
for finding the Optimum operational parameters and size of a multistage
concurrentflow dryer with tempering. The objective function was based
on energy costs for energy consumed during drying and capital investment

I

costs budgeted over a 10 year period. The operational parameters were

139

140

constrained by the desired final moisture content, the maximum allowable
exit temperature of the grain from any drying stage, and the maximum
allowable value of an important grain quality factor. Comparisons were
made for different number of stages, and with a conventional crossflow
dryer. The effect of feed-forward recycling of exhaust air was
investigated for the multistage concurrentflow dryer.

Costs of 0.447¢/kg and 0.448¢/kg were found for representative
two- and three-stage dryers, respectively. Feed-forward recycling of
the exhaust air reduces the drying costs to 0.424¢/kg and 0.405¢/kg,
respectively. A representative drying cost of 0.569¢/kg was found for
a single-stage concurrentflow dryer. About half (45%-55%) of the total
drying cost for multistage concurrentflow dryers was for energy consumed
during the drying process.

Energy costs of 0.302¢/kg for a continuousflow crossflow dryer
are greater than an average of 0.230¢/kg for concurrentflow dryers.

The internal rate of return for the additional investment in a con-

currentflow dryer instead of a crossflow'dryer would be approximately
15% for a single-stage; 9% for a two-stage; 8% for a three-stage. An
investment decision would also include the beneficial effect on grain

quality of a multistage versus a single-stage concurrentflow dryer.

8. SUGGESTIONS FOR FUTURE RESEARCH

The concurrentflow drying model used was based on uniform
diffusion within an assumed spherical kernel. A mass transfer surface
convection coefficient of infinity was assumed. It has been theorized
that a grain kernel does not lose moisture uniformly over the whole
surface but rather at one point (the germ) unless there are open cracks
in the seed coat and underlying aleurone layer. The impervious nature
of the seed coat of pea beans helps explain why the bean exhibits a
relatively constant diffusion coefficient with re5pect to changing
kernel moisture content. A better understanding of the moisture
diffusion process within grain kernels is necessary, not as much for
calculation of drying rates, but for its importance in understanding
how the quality of the grain kernel is affected by drying and tempering.

The tempering period apparently has an important effect on the
quality of the grain. The beneficial effect may be related to stress
caused by moisture gradients which are relieved as the moisture
migrates during tempering. Improved knowledge of the extent to which
tempering affects grain quality is important for determining not only
the necessary tempering time but also the number of drying stages to be
utilized.

The overall effect of drying and tempering on the quality of

agricultural products is not well understood. Attempts have been made

141

142

to relate average quality changes to drying conditions. Engineering
mechanics approaches have mostly assumed that grain kernels are homo-
geneous which is not actually true. Research is necessary to study the
interrelationships of the various parts of the kernel. When developing
quality prediction equations it must be recognized that different
kernels will react in different manners; the stochastic nature of the
process must be included. As understanding of these factors is
improved they can be incorporated into the quality models used for
optimization.

The Optimization algorithm developed was applied only to the
drying of shelled corn. The pea bean drying equations presented can
also be used toIstudy dryer design. The equation determined for
predicting seed coat cracking is fairly representative of the data
collected, however a better understanding of the effect of drying
and tempering is needed. Counterflow cooling and recycling of exhaust
air may have a beneficial effect on quality, as well on the energy
used during drying. Higher humidities during drying reduce the
moisture difference between the seed coat and the cotyledon halves
thereby reducing the relative difference in the amount of shrinkage

and the resulting stress on the seed coat structure.

9. APPENDICES

APPENDIX 9.1

CONVERSION FACTORS

 

Unit Conversions English or Metric 51
Area 1 ft2 9-290 xlo'zn2
Convective Heat-Transfer 1 Btu/h ftz °F 5-678 W/m2°C
coefficient
Density 1 1b/f’t3 1°602 x10kg/m3
Energy 1 kcal 4-187 x103J
1 Btu’ 1-055 x103J
1 kWh 3:600 x106J
Enthalpy, specific 1 Btu/lb 2-326 x103J/kg
Force 1 lbf 4:448 N
Heat flux 1 kcal/h m2 1-163 W/m2
1 Btu/h ftz 3-155 W/n2
Heat release rate (mass) 1 Btu/h lb 6:461 x10'1W/kg
Length 1 ft 3°048 xlO'lm
Mass 1 lb 4-536 x10‘1kg
1 tonne 1-000 x103kg
1 ton 1-016 x1o3kg
Power 1 Btu/h 2-931 x1001W
1 hp 7-457 x102W
Pressure 1 standard atmosphere 1-013 x105N/m2
1 bar 1-000 x105N/n2
1 lbf/inz 6:895 x103N/m2
1 in water 2.491 xlogN/m2
1 mm Hg 1-333 xIO‘N/mz

143

144

 

 

 

 

 

Unit Conversions English or Metric 81
2 3 2 3
Surface per unit volume 1 ft /ft 3°280 m /m
Specific heat 1 Btu/lb F 4-187 xlo3J/kgx
Temperature difference 1 deg F (deg R) 5/9 deg C (deg K)
Thermal Conductivity l Btu/h ft2 (°F/ft) 1'731 W/m2(°C/m)
Velocity 1 ft/h 8-467 xlo'Sm/s
Viscosity, absolute (or dynamic) l lb/ft h 4'134 x10'4kg/m s
Viscosity, kinematic 1 ftZ/h 2-581 xlo'snz/s
Volume 1 bu (volume) 3-523 xlo’zm3
1 ft3 2°832 x10-2m3
1 U.S. gal 3-785 x10'3m3
Miscellaneous Conversions English or Metric 51
Airflow 1 cfm 2-832 x10'2m3/nin
1 cfm 4-719 x10-4m3/sec
l cf’m/ft2 3-048 x10'1m/min
l cfm/ft2 5-080 xlO'sm/sec
Drying Cost 1 ¢/bu 3.937 x10'2¢/kg
corn
3-392 x10’2¢/kg
beans
Grainflow (corn) 1 bu/hr 2°540 x10-2tonne/
hr
2'540 x10 kg/hr
1 bu/hr/ft2 2°734 xlO'ltonne/
hr m2
2°734 x10 kg/hr/
m2
Grainflow 1 bu/hr 2.948 xlo‘ztonne/
hr
2:948 x10 kg/hr
1 bu/hr/ft2 3-174 x10'150nne/
hr m
3'174

x10 kg/hr/
m2

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'nz.o:.oa..oooass PAGES PRINT.

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