Deep Bed Drying

(Calculations)

In deep bed drying,

• All the samples in the dryer are not fully exposed to the same condition of drying air

• Condition of dry air at any point in mass changes with time and with the depth of sample bed

• Drying in the deep bed can be taken as a sum of several thin layers

• Humidity and temperature of air entering and leaving each layer vary with time depending upon the stage of drying, the moisture removing from the dry layer until equilibrium moisture content is reached

Some examples for deep bed drying

Drying grain (e.g., shelled corn) with the

drying air flowing through more than two to

three layers of kernels

Dehydration of solid food materials

inaoutaa ,,

Fan

grain of mass totalgm

ina, :ratiohumidity

MCgrain in change gW

outa, :ratiohumidity

am

Basic Drying Process

(Mass Conservation)

Total moisture conservation equation

compare: moisture added to air

to

moisture removed from product

Drying time

ggaa Wmtm

kga

ss

kgw

kga

kgw

kgg

kgg

aa

gg

m

Wmt

Heat balance for drying

Q- Air flow rate m3/min

v – specific volume

Ca – specific heat of air kJ/kg

Ta- Temperature of air in plenum 0C

Tg- Temperature of air leaving grain mass 0C

hfg –latent heat of vaporization kJ/kg moisture

DM – Dry matter content kg

M0 – Initial Moisture content (db - decimal)

Me – Final equilibrium moisture content (db-decimal)

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( 0 efggaa MMDMhtTTcQ

Time taken by the drying front to reach the top of the bed can be calculated using following equation

Where,

Mi = % Dry basis initial moisture content of the sample

Mx = % Dry basis average moisture content at the end of the drying front advance to the top

ti = Time of advance (hr)

A = Cross sectional area of the dryer through which air passes

G = Mass flow rate of dry air (kg/ hr.m2)

Hs= Humidity of air leaving the dryer

Hi = Humidity of air entering the dryer

Wd = Mass of the dry sample in the bin (kg)

iis

xid tHHAGMMW

100

For the changes in drying air conditions

psychrometric principles can be applied

Hard wheat at 75°F is being dried from 18% to

12% w.b. in a batch grain drier. Drying will be

stopped when the top layer reaches 13%.

Ambient conditions: Tdb = 70°F, RH = 20%

Determine the exit air temperature early in the

drying period?

Determine the exit air RH and temperature at

the end of the drying period?

Example

Twb

emc=13%RHexit

Texit

Part II

At inlet ambient air enters

T db = 70°F RH =20%

During drying air enthalpy doesn’t change

Loewer, et al. (1994)

13%

T exit air = 58°F RH exit = 55%

Part I

inlet ambient

T db = 70°F RH =20%

emc = 18%

Texit air = 53.5°F

Twb

emc=18%

Tdb,e

Loewer, et al. (1994 )

Mathematical models for

Deep- bed drying process

Mathematical models are needed to predict temperature and moisture profiles in the deep-bed and inside the grain

The models propose that the system with two control volumes Grain where moisture is at liquid phase

Humid air outside the kernel

To pull the moisture from grain and to enter to the vapor phase sensible and latent heat is needed

Models assume the steady state drying

According to Hukill ( 1947,1954) bulk drying curves can be used to find:

approximate moisture content at any depth in the deep bed drying system at any time after drying has started

Three parameters were used to represent any deep drying systems

Moisture ratio ( MR)

Depth factor ( D)

Time unit ( Y)

Moisture ratio

122

2

YD

D

MR

Where,

MR = ( M – Me ) / ( Mo - Me )

Mo = Moisture content at the start of drying ( d.b. ,decimal )

M = Grain Moisture ( d.b. ,decimal )

Me = Moisture content when the grain as reached equilibrium with air

D = Depth factor

Y = Time unit

Depth factor (D) DM’ is needed to calculate depth factor

DM’ is constant throughout the drying periodDM’ = dry matter per depth factorTg = Temperature of exit airTa = Temperature of inlet airhfg = Btu/ lbcfm = Air flow rate in cubic ft per minuteca = Btu/lb v = ft3 / lb

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2/1

eofg

gaa

MMvh

tTTccfmDM

Depth factor zero (D=0)

However,

D=0 contains half of the grains of the other

depth factors

DM’ – is considered as a constant value

throughout the drying period

(volume of grain/depth factor depends on density, it

changes with drying ?? But to simplify the analysis

assume no shrinkage. Select a logical value, ie at M0 )

Time unit ( Y)

Y = t / t1/2

t1/2 = Time required for fully exposed grain to dry from MR=1 to MR = 0.5 ( obtained from a table )

t = Drying time

Values of t1/2 for shelled corn

Temp F

Original

MC

%wb

60

15.55 C

80

26.66 C

100

37.77 C

120

48.88 C

140

60 C

160

71.11 C

180

82.22 C

35 5.6 5.5 4.5 3.3 2.4 1.5 1.2

30 6.0 5.0 3.9 3.0 2.6 2.1 1.7

25 6.3 5.2 4.3 3.2 2.9 2.6 2.4

20 6.6 6.4 5.6 4.4 4.0 3.5 3.4

(t1/2 –Time required for fully exposed corn to dry from MR=1 to MR=0.5 at given

temperatures. The air has a dew point temperature of 50 F

Example1. Air flow rate in a dryer = 16330 cfm

Ta = 83.5 F -Air temp at the plenum

Фa = 35% (RH)

Tg = 64.0 -exit air temp,

Ca- 0.24 BTU/lb F

v = 13.86 ft3/lb specific volume of air

M0 = 33.33% db

Me = 9.28% db -at plenum air conditions

Dia of the dryer -27 ft-Floor area = 573 ft2 - height of grain 8 ft -Given

Drying time 75 h

Find a). Location of the drying zone

b). The thickness of the zone

c). The average moisture content of the grain

T1/2 = 5 h

MR= M - Me / (M0- Me )

M = Me + MR (M0- Me)

MR M

0 - 9.28

0.1 - 11.69

0.2 14.09

. .

1.0 33.33

Y = t/ t1/2

t = Y * 5

Y = 75/5 = 15 Refer to the drying curves pgs 197-98

a) after 75h drying, bottom of the drying zone is 8.5

depth factors (or 2.78 ft) from the bottom

Top of the zone is 21.5 depth factors (or 7.03 ft)

from the bottom

To calculate the height of a depth factor

Use the DM’ equation

b) Drying zone = 7.03- 2.78 ft

= 4.25 ft

DM’ – Dry matter per depth factor

)(

)(60*'

2/1

eofg

gaa

MMvh

tTTccfmDM

0928.03333.01200*86.13

0.5*0.645.8324.0*60*16330'

DM

= 5732 lb dry matter per depth factor

Grain density at M0 (25% (w.b.) = 40.8 lb/ft3

Dry mass per 1 ft3 = 40.8 * 0.75 lb

Volume per Depth factor = 5732/40.8*0.75

= 187.32 ft3

Floor area of the dryer = 573 ft2 - Given

The thickness of a depth factor = Vol of a depth factor/floor area of the dryer

= 187.32 ft3 / 573 ft2

= 0.327 ft

But “0” DF = ½ * 0.327 = 0.163 ft

Mc (d.b.) can be read from the graph

Mc along the 15 Y line for curves or can be calculated from

122

2

YD

D

MRMR = ( M – Me ) / ( Mo - Me )

M av = weighted %/total No of Depth factors= 455.83%/24.5 = 18.61 d.b.Or 15.69 w.b.

DDepth factor

Y Time unit

MR Moisture Ratio

MMC-decimal

0 15 3.05176E-05 0.092807

1 15 6.10333E-05 0.092815

2 15 0.000122059 0.092829

3 15 0.000244088 0.092859

4 15 0.000488058 0.092917

5 15 0.00097564 0.093035

6 15 0.001949377 0.093269

7 15 0.003891169 0.093736

12 15 0.111114125 0.119523

20 15 0.969697866 0.326012

21 15 0.984615847 0.329600

22 15 0.992248297 0.331436

23 15 0.996109068 0.332364

24 15 0.998050742 0.332831

24.5 15 0.998620879 0.332968

Depth factor

D

Depth of

Grain

% MC d.b. Weighted %

0 0.163 9.28 4.64

1-8 2.779 9.28 74.24

9 3.106 9.65 9.65

10 3.433 10.00 10.00

11 3.760 10.69 10.69

12 4.087 11.95 11.95

13 4.414 14.05 14.05

14 4.741 17.30 17.30

15 5.068 21.31 21.31

16 5.395 25.31 25.31

17 5.722 28.52 28.52

18 6.049 30.66 30.66

19 6.376 31.92 31.92

20 6.703 32.6 32.60

21 7.030 32.96 32.96

22-24 8.011 33.33 99.99

455.83

End

A simple model for drying rice grains in a

deep bed dryer

The deep bed drying can be described as several

thin layers

If height of the bed is Z,

air entering at Z=0 and

air leaving from the bed at Z=L

Uniform temperature distribution across the grain

phase is assumed. But the temperature is changed.

Drying process inside the grain requires a two

phase model. At the second falling rate period,

diffusion of bound water takes place.

Xms= Maximum sorption water content

X0 = Initial moisture content

Xeq = Equilibrium moisture content

D0 = Diffusion coefficient at initial time(m2s-1)

Equilibrium moisture content is calculated using isotherm

)

)(

eqms

eq

obedXX

XXDD

D1 = Constant of Arrhenius type equation (m2s-1)

Ea = Activation energy per unit mass (Jkg-1)

R = Ideal gas constant ( Jkg-1k-1)

T = Time (s)

)exp(10RT

EDD a

D0 = Diffusion coefficient at initial time

Conservation of mass equation state the moisture

loss by the grain phase

X = Grain moisture content ( kg moisture / kg

drain )

Wa = Axial drying air flux per unit of deep bed

cross sectional area ( m s-1)

H = Absolute air humidity ( kg moisture/kg dry

air)

Z

HW

t

Xa

ss

a

Energy conservation for each of the thin layer

Heated air can evaporate water coming from the

grain and increase the temperature from Ts to Tg

Energy balance,

Z

HTTcpTlW

t

Txcpcp

Z

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swsss

g

vaaa

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Change of rice temperature in solid and liquid

phase

t

TXcpcpTTha s

wssssgeff

)()()(

cpv = Specific heat of vapor (Jkg-1k-1)

Cpw = Specific heat of water ( Jkg-1k-1)

haeff = Volumetric pseudo convective heat

transfer coefficient (Wm-3k-1)

Tg = Air temperature

Ts = Temperature of solid

ρss = Apparent density of dry grain

ρa = Density of dry air

lv = Vaporization heat of water ( Jkg-1)

Modeling of temperature changes in air phase

Z

HTTcpTlTT

W

ha

Z

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aa

eff

va

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)()(

Thank You