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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    Examples of solid-fluid operations Include:

    1. Sedimentation2. Centrifugation

    3. Filtration

    4. Desliming

    5. Clarification

    6. ..

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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    1.1. SOLID - FLUID CONTACTING AND PROCESSING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    1.1. SOLID - FLUID CONTACTING AND PROCESSING

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

    phase system include:

    transport through pipelines

    holding / storage

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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    1.2. SOLID - FLUID SEPARATIONS

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    1.2. SOLID - FLUID SEPARATIONS

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    1.2.2. Driving forces used to effect separation

    1. Gravity

    2. Drag

    3. Centrifugal

    4. Pressure gradient

    5. .

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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    Typical separation processes include:

    1. ..2. .....

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

    4.

    5. .

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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    PARTICLE SIZE DISTRIBUTIONS

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    PARTICLE SIZE DISTRIBUTIONS

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    DEPARTMENT OF CHEMICAL ENGINEERING

    PARTICLE SIZE DISTRIBUTIONS

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    DEPARTMENT OF CHEMICAL ENGINEERING

    Particle size distribution representation

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    DEPARTMENT OF CHEMICAL ENGINEERING

    Particle size distribution representation

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    100

    10 100 1000 10000

    Size, um

    Cum.

    %p

    assing

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    DEPARTMENT OF CHEMICAL ENGINEERING

    PARTICLE SIZE DISTRIBUTIONS

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    PARTICLE SIZE DISTRIBUTIONS

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    Particle size distribution representation

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    DEPARTMENT OF CHEMICAL ENGINEERING

    SolidFluid OperationsCHE 3040S

    Measures of separationefficiency

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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    EVALUATION OF SEPARATIONPERFORMANCE

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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    Efficiency Curves III

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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    Scale-up and Efficiency Curve VI

    Fish hook effect

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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    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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    DEPARTMENT OF CHEMICAL ENGINEERING

    Efficiency Curve Model - I

    2)(

    )1(C=E50

    )50

    o(

    ee

    e

    cd

    dcd

    d

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    DEPARTMENT OF CHEMICAL ENGINEERING

    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)