2- emc & drying rate (1)

CHAPTER 2 :

MOISTURE CONTENT AND DRYING RATE

CALCULATIONS Ms Noor Rosyidah Binti Sajuni

School of Engineering

[email protected]

OBJECTIVES

At the end of this lessons, students should

be able to: Define the drying process Explain the classification of dryers Explain the principles of drying Perform calculation in this topics

INTRODUCTION

Drying -Definition:

The removal of water or other solute from the solid material to reduce the content of residual liquid to an acceptable low value.

Drying is the final step in a series of manufacturing process. Drying is carried out before the products undergo packaging

or dispatched to the warehouse.

INTRODUCTION

Water or other liquid may be removed from the solid:

a) mechanically by presses or centrifuges

b) thermally by vaporization – drying It is cheaper to remove liquid mechanically than

thermally. The product contain no liquid – bone dry Commonly, product does contain some liquid

Example: dried table salt (0.5%), dried coal (4%)

INTRODUCTION

The solid to be dried may be in many different forms: flakes, granules, crystals, powder, slabs or continuous sheets.

The liquid to be vaporized may be:

a) on the surface of solid

b) entirely inside the solid

c) partly inside and partly outside of solid

INTRODUCTION

Drying is carried out for one of the following reasons:

a) to reduce the cost of transport

b) to make a material more suitable for handling

c) to provide definite properties

d) to remove moisture which may otherwise lead to corrosion.

MOISTURE CONTENT RELATIONSHIPS

Moisture/solid equilibrium relationships

Figures 9.4-1 and 9.4-2 for several types of systems

Defined on the basis of relative humidity at a specific temperature

Equilibrium amount of moisture tends to decrease with increasing temperature

RATE OF DRYING CURVES FOR CONSTANT DRYING CONDITIONS

RATE OF DRYING CURVES FOR CONSTANT DRYING CONDITIONS

MOISTURE CONTENT VARIABLES

Based on the mass of moisture relative to the mass bone dry solid

)MoistureSurface(

.XXBoundAboveContentMoistureX

MoistureUnbound

%100HwithSaturation@ContentMoistureX

)25.9(XXContentMoistureFreeX

ContentMoisturemEquilibriuX

15.9BDSSolidDryMass

LiquidMassX

BtU

RB

*t

*

t

IMPORTANT TERMS

Equilibrium moisture, X*

The lowest moisture content obtainable at equilibrium under the drying conditions used.

Free moisture

The moisture that can be removed by drying under the given % relative humidity: Xt – X*

IMPORTANT TERMS

Bound moistureThe minimum moisture a material can carry.

Unbound moistureThe excess moisture content in the material.

DRYING EQUIPMENTS

Batch Operation Tray Dryers Agitated Dryers

Continuous Operation Spray Dryers Tunnel Dryers Rotary Dryers Drum Dryers

SOLID HANDLING IN ADIABATIC DRYERS

Figure 2.1: Patterns of gas-solid interaction in dryer

Rate of Drying Curves

In the drying process, it is desired to

estimate: the size of dryer needed, the various operating conditions of humidity and temperature

for the air used the time needed to perform the amount of drying required.

Rate of Drying Curves

Equilibrium moisture content cannot be predicted and must be determined experimentally.

The data obtained from the experiments can be converted to drying rate.

Rate of Drying Curves: Method 1

Plot X versus t

- get the slopes of tangents at different values of t which give values of dX/dt.

- determine drying rate, R from each point.

where Ls = mass of dry solid used

A = exposed surface area for drying

dt

dX

A

LR s


Drying curve is obtained by plotting R versus moisture content as in Figure 9.5-1b.


Calculate weight loss ∆X for a ∆t time (Eqn 9.5-3).

Drying rate, R is the average over the period ∆t and plotted at the average concentration X.

dt

dX

A

LR s

Rates of drying for constant-drying conditions

Drying Curve (pg 577-578) Point A : 1. At zero time the initial free moisture content is shown

Point A’: 1. Solid quite hot

Point B : surface temp rises to its equilibrium value

Point B-C : 1. line is straight 2. slope and rate are constant during this period 3. Constant rate of drying period is shown

Point C : 1. Drying rate starts to decrease in the falling rate period until it reaches point D

Point CD : 1. First falling rate period. 2. The line is often linear

Point D : 1. surface completely dry. 2. The rate of drying falls even more rapidly until it reaches point E 3. EMC is 0

Point D-E : second falling-rate period evaporation from interior of solid.

Point E : equilibrium moisture content X*.

X = X* - X* = 0

no further drying.

Critical moisture content

Critical moisture content is the point at which the constant rate period ends (whether or not the drying rate is truly constant).

If the initial moisture content of the solid is below the critical value, there will be no constant rate period.

The critical moisture content depends on:

- the thickness of material

- the rate of drying

- the resistances to heat and mass transfer within the solid.

Rates of drying

Graph A:

Total moisture content decrease when liquid start vaporized from the solid.

Value become stable which indicates a little water left in the solid (allowable min. moisture content).Figure 2.7:

Plots of total moisture contents and drying rate vs drying time

Rates of drying

Graph B:

The drying rate increases until a certain period where the drying rate is constant (constant rate period)

This shows that liquid continues to vaporize which is due to constant supplying of heat.

The drying rate decreases which shows that less liquid being vaporize from the wet solid (falling rate period).

When the stage of equilibrium moisture content has been achieved between the solid and hot gas, the drying rate has stopped (no more liquid has vaporized from the solid)

Calculation methods for constant rate drying period

Method using experimental drying curve Using drying curve (Ex 9.6-1):

- based on actual experimental data- the time required for constant rate period can be determined directly from drying curve (free moisture content vs. time)

Using rate of drying curve for constant rate period:- the drying rate R is defined as (Eqn 9.5-3)

dt

dX

A

LR s

Calculation methods for constant rate drying period pg 580

Rearrange and integrate over the time interval to dry from X1 at t1 = 0 to X2 at t2 = t. (Eqn 9.6-1)

If the drying takes place within the constant rate period, X1 and X2 are greater than the critical moisture content Xc,

R = constant = Rc (Eqn 9.6-2)

1

2

2

1 0

X

X

stt

t R

dX

A

mdtt

)( 21 XXAR

mt

c

s

Example 9.6.1 (using graph 9.5-1a)

A solid whose drying is represented by Figure 2.6 is to be dried from a free moisture content X1 = 0.38 kg H2O/kg dry solid to X2 = 0.25 kg

H2O/kg dry solid. Estimate the time required.

Example 9.6.2

9.7 Calculation methods for falling rate drying period pg 585

Method using graphical integration In the falling rate period, the rate of drying, R is not constant but decrease

when drying proceeds past the critical free moisture content, Xc

When the free moisture content, X is zero, the rate drops to zero. The time for drying between X1 and X2 is (Eqn 9.6-1):

If the rate is constant, this equation can be integrated to give Eq. 9.6-2 This equation can be graphically integrated by plotting 1/R versus X and

determining the area under the curve.

1

2

X

X

s

R

dX

A

Lt

Example 9.7.1 A batch of wet solid whose drying rate curve is represented by Figure

9.5-1b is to be dried from a free moisture content of X1 = 0.38 kg H2O/kg dry solid to X2 = 0.04 kg H2O/kg dry solid . The weight of the dry solid is 399 kg dry solid and A = 18.58 m2 of top drying surface. Calculate the time for drying.

SOLUTION

1. FOR CONSTANT RATE PERIOD

2. FOR FALLING RATE PERIOD

1

2

X

X

s

R

dX

A

Lt

To determine this area by numerical integration using a spreadsheet, the calculations are given in this following table

X R 1/R ∆X (I/R)av (∆X)(1/R)av

0.195 1.51

0.150 1.21

0.100 0.90

0.065 0.71

0.050 0.37

0.040 0.27

TOTAL 0.1889

Calculation methods for falling rate drying period –Special case in falling rate period (pg 587)

1. Rate is linear function of X If X1 and X2 are less than Xc and the rate R is linear in X over

this region,

a = slope of lineb = constant

1)-(9.7 baXR

adXdR

Calculation methods for falling rate drying period

Substitute into equation;

Since R1 = ax1 + b and R2 = aX2 + b,

2

1sR

R

s

R

Rln

aA

L

R

dR

aA

Lt

1

2

21

21

XX

RRa


Substitute into equation Eqn (9.7-3) into (9.7-2);

(9.7-4)

2. Rate is a linear function through origin The rate of drying is directly proportional to the free moisture

content

2

1

21

21s

R

Rln

)RR(A

XX(Lt

aXR


Differentiating, dX = dR/a;

The slope a of the line is Rc/Xc and for X1 = Xc at R1 = Rc

2

1ln1

2 R

R

aA

m

R

dR

aA

mt s

R

R

s

2

lnR

R

AR

Xmt c

c

cs


Rc/R2 = Xc/X2,

(9.7-8)

cc

2

c

c

cs

X

XRR

OR X

Xln

AR

XLt

Example 9.7.2Repeat example 9.7-1, but as an approximation assume a straight line of

the rate R versus X through the origin from point Xc to X = 0 for the falling rate period.

DRYING RATE CURVES Depend on whether heat or mass transfer controls

free moisture vs. time drying rate vs. moisture content

http://www.ias.ac.in/sadhana/Pdf2005Oct/PE1280.pdf

ADDITIONAL NOTES

DRYING REGIMES

constant rate - no limit to mass transfer in solid phase surface moisture transfer near surface

falling rate –moisture flux through the solid is hindered

critical points occur between constant rate and falling rate with a change in the falling rate drying mechanism

DRYING MODELS

RATES FROM EMPIRICAL DATA

CONSTANT RATE DRYING CONTROLLED BY HEAT TRANSFER TO VAPORIZE

THE MOISTURE OR MASS TRANSFER

)35.9(

tA

XLR S

76.9)(

HHMkTTh

R WByW

WC

FACTORS THAT AFFECT h

AIR VELOCITY (G) GAS HUMIDITY (T – TW) AND (HW-H) GAS TEMPERATURE (T – TW) AND (HW-H) SOLID THICKNESS - NO EFFECT ON RATE FOR

SURFACE MOISTURE MATERIALS SURFACE FINISH OR ANY

CONDITION THAT STIMULATES TURBULENCE J. E. SUGARMAN & T. J. VITALE, OBSERVATIONS ON THE DRYING

OF PAPER: FIVE DRYING METHODS AND THE DRYING PROCESS Journal of the American Institute for Conservation , 1992, Volume 31, Number 2, Article 3 (pp. 175 to 197) http://www.jstor.org/stable/3179491?seq=1

CONSTANT RATE DRYING TIME

DRYING TIME CAN BE CALCULATED BY INTEGRATING (9.5.-3) LOWER VALUE OF X > XC (CRITICAL POINT)

1

22

X

X CC

SR XXWHERE

R

dX

A

Lt

C

FALLING RATE DRYING

CONTROLLED BY GAS PHASE MASS TRANSFER FROM SOLID OR HEAT TRANSFER INTO THE SOLID TO

VAPORIZE THE MOISTURE. GENERAL FORM OF THE EQUATION:

X1 < XC

16.9)(

1

2

X

X

SF XR

dX

A

Lt

FALLING RATE DRYING NUMERICAL CALCULATION FOR COMPLEX SYSTEMS

SEE EXAMPLE (9.7-1) FOR NUMERICAL INTEGRATION SIMPLIFICATIONS FOR LINEAR RELATIONSHIPS: R(X) = aX + b

FOR b = 0, LINEAR THRU ORIGIN

)47.9(ln)(

)(

2

1

21

21

21

21

R

R

RRA

XXLtSO

XX

RRa S

F

)87.9(lnln22

X

X

AR

XL

R

R

AR

XLtSOaXR C

C

CSC

C

CSF

FALLING RATE EXAMPLE

Shibata, H.; Iwao, Y., Vacuum Drying of Sintered Spheres of Glass Beads,Ind. Eng. Chem. Res.; 1999; 38(9); 3535-3542

FALLING RATE EXAMPLE

Carmen Rossello, Jaime Canellas, Susana Simal, Angel Berna, Simple mathematical model to predict the drying rates of potatoes, J. Agric. Food Chem.; 1992; 40(12); 2374-2378.

2- emc & drying rate (1)

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