Section 1 _Solid-Fluid Ops Lecture 1-Vula
Transcript of 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)