Section 1 _Solid-Fluid Ops Lecture 1-Vula

8/13/2019 Section 1 _Solid-Fluid Ops Lecture 1-Vula

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DEPARTMENT OF CHEMICAL ENGINEERING

SolidFluid OperationsCHE 3040S

Introduction

&Particle Size Characterisation

Aubrey Mainza


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SOLID FLUID OPERATIONS

SECTION 1

Topics

I. Introduction to solidFluid Operations

II. Motion of Particles

III. Terminal Settling velocity of Particles

IV. Deviations from Free Settling of Spherical Particles


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1. INTRODUCTION TO SOLIDFLUID OPERATIONS

Three main categories of solid-fluid operations

1. Contacting of solid and fluid phases

2. Processing of multi-phase streams, including a solid

phase

3. Separation of solid and liquid phases


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Examples of solid-fluid operations Include:

1. Sedimentation2. Centrifugation

3. Filtration

4. Desliming

5. Clarification

6. ..


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1.1. SOLID - FLUID CONTACTING AND PROCESSING

Important operations in this category include:

mixing and agitation

solid suspension

gas dispersion (in 3-phase system)

provision of a reaction environment


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Systems used to facilitate solid - fluid contacting

include:

the stirred tank reactor (mechanically agitated

contactor) the fluidised bed reactor

the packed column


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Typical operations in the processing of a 2- or 3-

phase system include:

transport through pipelines

holding / storage


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1.2. SOLID - FLUID SEPARATIONS

This involves separation of any of the

following two phases:-

I. Solid

II. Liquid

III. gas

from a suspension (or slurry)


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First part of course:- solidliquid separations

I. Recovering the valuable solids (discarding the

liquid)

II. Recovering the liquid (discarding the solids)

III. Recovering both the solid and the liquid, &

Other possible areas to look at may include:

I. Recovering neither (i.e preventing pollution)


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Perfect separation would result in:

I. A stream of liquid

II. A stream of solids

Process imperfection lead to:

I. Fine solids reporting to the liquidII. Some liquid reporting to the solid stream

Characterisation of Imperfection in separation:

I. Mass of fraction of solids recovered (separation

efficiency)

II. The dryness or moisture content of the solids

(percentage solids by weight)


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It is sometimes desirable to remove: coarse or

fine particles from the product

1. De-gritting

2. De-sliming

The process is called classification (solidsolid

separation)

Size separation is important:

Most principles involved in solidliquid separation are:

dependant on particle size.

sometimes principles used for solid - liquid separation

can be used two types of solids from each other.


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1.2.1. Properties used for solidliquid separation

1. Density difference

2. Particle size

3. Particle shape

4. Affinity to water

5. .


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1.2.2. Driving forces used to effect separation

1. Gravity

2. Drag

3. Centrifugal

4. Pressure gradient

5. .


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1.2.3. Solidliquid separation processes

Classified on basis of principles involved:

If liquid constrained & particles can move freely within it(due to fields of acceleration)

Sedimentation and flotation

For sedimentation a density difference between solids & liquids is

necessary

If particles are constrained by a medium & liquids can

flow through them :-

Filtration and screening

In Fluidisation (used for solidfluid contacting or solid

liquid separation processes)

Both particles & fluid are in motion


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Typical separation processes include:

1. ..2. .....

3. ............

4.

5. .


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SOLIDFLUID OPERATIONS

SECTION 1- Particle characterisation

Topics

I. Introduction to particle characterisation

II. Particle characterisation

III. Characterisation methods

IV. Particle size distribution

V. Slurry & pulp density (units & conversions)

VI. Evaluation of separation performance

I. Efficiency of separations

II. Partition curve


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1. INTRODUCTION TO PARTICLE CHARACTERISATION

In solid fluid operations we handle collection of particles

with a distribution of properties.

Three most important characteristics of an

individual particle:

1. Composition: determines density, conductivity, etc

Provided particle is completely uniform

2. Sizeaffects settling rates & surface area to volume ratio

3. Shaperegular (crystals, spheres), irregular

Irregular shapes are expressed in terms of regular shaped particles


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1. SINGLE PARTICLE

Spherical particles are the most simple todescribe.

Symmetrical: orientation can be ignored

Hence particles are described in terms of

equivalent spheres


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Some definitions of particle size properties equivalent to

sphere

Name Equivalent property of sphere

1 Volume diameter Volume

2 Surface diameter Surface

3 Surface Volume diameter Surface to Volume ratio4 Drag diameter Resistance to motion(Same fluid and

at same velocity

5 Free-falling diameter Free falling speed(Same liquid &particle density

6 Stokes diameter Free-falling speed, Stokes law used(Re


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Example I

What is the diameter of the sphere that has the

equivalent volume to a cube with side length 1 unit.

What is the diameter of the sphere that has theequivalent surface area to a cube with side length

1 unit.

What is the surface to volume diameter of a cube with sidelength 1 unit?


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SHAPE

A measure of particle shape frequently usedis sphericity, defined as:

Surface area of sphere of same volume as particle

Surface area of particle

Another method: using factors by which a cube of the

size of a particle must be multiplied to give volume.


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Example II

What is the sphericity of the sphere?

What is the sphericity of a cube with side

length 1 unit?


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Example III

What is the projected area diameter of abrick with side lengths 5 x 3 x 1 units?

Definition: The projected area diameter, or

equivalent diameter, is the diameter of a circle

having the same area as the projected area of

the particle in some stable position.


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PARTICLE DENSITY

True density: is that of material making up particle

(excludes pores).

Apparent density: Includes pores

Effective density: Found when liquid does notpenetrate pores

Bulk density: density of a pile of solids

Includes packing & size distribution effects.


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MEASUREMENT OF PARTICLE SIZE

Screening/sieving

Microscopic analysis

Sedimentation & Elutration

Permeability

Electronic particle counters

Laser diffraction method

X-Ray or pho sedimentometers

Sub-micron sizing


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PARTICLE SIZE DISTRIBUTIONS

Easy to see distribution by plotting frequency

curve:

Slope of continuous curve or measured (F(x) are

plotted against particle size x.

This may show a single or more than one peak

for mixtures of particles or product of a process.

Representative particle size of a class is geometricmean of lower & upper size.


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Four types of particle distributions, which differgraphically, are defined:

1. By number

2. By length (not generally used)

3. By surface area

4. By mass (or volume).

This is the most commonly used.


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Size distribution

Relationships that form basis of conversions (only

when shape factor is constant:

1( ) ( )L Nf x k xf x

22( ) ( )S Nf x k x f x

3

3( ) ( )M Nf x k x f xDistribution by

Volume

Distribution by

Surface

Distribution by

number

What about Distribution

by mass???


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Particle size distribution representation


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0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Size, um

Cum.

%p

assing


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Often useful to have quantitative analysis of:

mean particle size.

Each mean conserve two properties of original population

Arithmetic mean of surface distribution: Surface and volume

Spread of particle sizes present. Results of size analysis can be represented using cumulative mass

fraction:

F(x) plotted against x

F(x) is usually expressed as a percentage


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Describing population by single number:

1. The mode

2. The median

size which 50% of the particles are larger & 50% smaller.

3. The mean depends on mathematical function describing the

distribution & type of mean diameter required;

often used are arithmetic and geometric means.

4. Terms: d80 implies 80% of particles smaller than this

size.


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SolidFluid OperationsCHE 3040S

Measures of separationefficiency


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SLURRY AND PULP DENSITY

Pulp density is usually given either as the %

solids, or as the density (kg/m3).

The conversion between these is important.

The following equation holds:

( 1)% 100

( 1)

s p

p s

solids

Where; s- dry solids density

p- pulp density


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Important: Please attempt to derive this

equation & the equivalent one to determine

the percentage solids from the pulp densityfrom a solids & liquid volume balance for a

unit volume of slurry.

The mass flow of solids, M, is given by:

M = F px/ 100

Where; F is the slurry volumetric flow, x is the %

solids


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EVALUATION OF SEPARATIONPERFORMANCE


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EFFICIENCY OF SEPARATIONS:

Total efficiency, ET, is mass flow of solids in

coarse product stream, Mu, divided by solids

flow rate in the feed, MF:

E M

MT

U

F

where; MU& MFare underflow & feed flowrates of solids (usually tph)

Note that this does not describe the dewatering in any way.


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ETis also given by the two product formula:

E f o

u oT i i

i i

where; fi, ui& oiare mass fractions of solids of size iin feed,

coarse & fine streams, respectively.

The Part i t ion Numberquantifies the efficiency of separation

within a particular size class

The Part i t ion Numberquantifies the efficiency of separation

within a particular size class


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Separation efficiency

The Part i t ion Numberquantifies the efficiency of

separation within a particular size class;

It is the fraction of material in that size class in the

feed that reports to the coarse stream. To calculate the Part i t ion Numberfor sizei:

P M uM f

E uf

f i ou o

uf

iU i

F i

Ti

i

i

i i

i

i

..

.


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EVALUATION OF SEPARATION PERFORMANCE

Solids flow rate, tph 4.69 2.21 2.48

Size, microns % retained % retained % retained1000 0 0 0

710 1.65 0 3.07

500 4.76 0 8.87

355 6.71 0 12.5

250 6.15 0 11.46

180 5.1 0 9.5127 3.9 0 7.23

90 3.38 0.01 6.31

63 3.6 0.35 6.4

45 8.25 7.5 8.9

32 12.09 18.48 6.62

22 18.38 30.2 8.19

16 17.71 29.55 7.5

11 8.32 13.91 3.45


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Efficiency Curves - I

0.00.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.01 0.10 1.00 10.00

Size (mm)

Fraction

to

Coarse Actual

Efficiency

Curve


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Efficiency Curve II

0.0

0.10.2

0.3

0.4

0.5

0.60.7

0.8

0.9

1.0

0.01 0.10 1.00 10.00

Size (mm)

F

raction

to

Coars

e

D50 Act

Actual

Water

Split


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Efficiency Curves III


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Efficiency Curves - IV

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.01 0.10 1.00 10.00

Size (mm)

Fraction

to

Coarse

D50 Act

D50 Corr

Actual

Corrected


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Separation efficiency

Corrected curve for coarse fraction;

Corrected curve for fine fraction;

1

aU f

UC

f

E RE

R

aO

OC

EE

C


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Efficiency Curves - V

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.1 1 10

D/D50c

F

raction

to

Coar

se

Reduced

Efficiency

Curve


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Scale-up and Efficiency Curve VI

Fish hook effect


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Fish hook effect

0

20

40

60

80

100

0.1 1 10 100 1000

Particle size, microns

Percent

toU/F

fs-0.3/sp-75/P-50kpa

fs-0.3/sp-75/P-100kpa

fs-0.3/sp-75/P-125kpa

fs-0.3/sp-51/P-50kpa

fs-0.3/sp-51/P-100kpa

fs-0.3/sp-51/P-125kpa


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Efficiency Curve - Varying b

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.10 1.00 10.00 100.00 1000.00

Size (m)

Fractiont

o

Fin

0.0

0.2

0.5

1.0

2.0


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Efficiency Curve Model - I

2)(

)1(C=E50

)50

o(

ee

e

cd

dcd

d


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SG Effects - 1

0.00.1

0.20.30.40.50.6

0.70.80.91.0

10 100 1000

Size (m)

FractiontoFine

Galena

Sphalerite

Silica

d50c (Ga) d50c (Sp) d50c (Si)


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SG Effects - 2

0.00.1

0.20.30.40.50.60.70.80.91.0

10 100 1000

Size (m)

FractiontoF

ine

Galena

Sphalerite

Silica

Average

d50c (Ga) d50c (Sp) d50c (Si)

Documents

Section 1 _Solid-Fluid Ops Lecture 1-Vula