Hindered Systems & Thickening
Chapter 6 in Fundamentals
Professor Richard Holdich
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Introduction
Hindered settling
Porosity/voidage and
Concentration
Introduction
Hindered settling - thickener design
Hindered settling – pharma crystallisation
Hindered Systems & Thickening
Buoyancy correction – p61 Viscosity correction – p61 Hindered settling relations – p55 Zones in batch sedimentation – p57 Kynch's analysis – p60 Flux theory & thickener designs –
p57/8
Buoyancy Correction
Archimede’s Principle When a body is wholly, or partially,
immersed in a fluid it experiences an upthrust equal to the weight of fluid displaced.
Buoyancy - hence buoyed weight is:
gxF sW )(6
3
Buoyancy Correction
However, when measuring the buoyancy in a continuum consisting of suspended particles Archimede’s Principle tells us that the buoyancy correction is the density of the continuum not fluid alone (e.g. for a hydrometer in a slurry):
gxF msW )(6
3
)1( CC sm where
Viscosity correction
When a body is moving relative to a suspension made of others (usually finer).
NOT appropriate for sedimentation and filtration of a homogeneous suspension.
Krieger’s equation:K
e KC /)1( K is crowding factor 1/CMAX, and equal to 1.56 for spheres
eta is intrinsic viscosity, which is 2.5 for spheres
Viscosity correction
Hindered settling relations
Free settling
Hindered settling relations
Hindered settling
Hindered settling relations
Hindered settling
Hindered settling relations
Hindered settling
U = Ut (1-C)n
Richardson and Zaki’s equations
Zones in batch sedimentation
Hindered settling
Zones in batch sedimentation
Time
Height
t
At time t:
Supernatant
Originalconcentration
Variableconcentration
Sediment
Zones:
Co
Zones in batch sedimentation
Height
Supernatant
OriginalconcentrationVariableconcentration
Sediment
Zones:
Concentration
Co
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Kynch's analysis
Material balance on thickening element:
hsCUA
sAhhCUCU d/)(d
Kynch's analysis
Material balance on thickening element:
Input:
Output:
Accumulation:
Giving:
sCUA
sAhhCUCU d/)(d
hAt
Cs
d
d
C
CU
t
h
d
)(d
d
d
Kynch's analysis
Material balance on thickening element:
Time
HeightGiving:
C
CU
t
h
d
)(d
d
d
The rate at which the concentration propagates up the vessel is equal to the differential of the ‘solids flux’ withrespect to solids concentration.
Kynch's analysis
Experimental measurements:
Introduction
Hindered settling - thickener design
Flux theory & thickener design
Thickeners - hindered settling
Flux theory & thickener design
Thickeners - hindered settling
Picket fence rake - plunging feed
Flux theory
Settling curves
Batch flux curveCU
Flux theory
Flux?
sACU m2 v/v m s-1 kg m-3 i.e. kg s-1
sCU v/v m s-1 kg m-3 i.e. kg m-2 s-1
or
i.e. mass flow rate of solids (per unit area) - input & output.
Area and solid density are assumed to be constant - hence simply velocity by concentration (v/v) are used.
Flux theory
Batch flux curve
Flux theory
Flux theory
Underflow withdrawal flux
Flux theory
Composite flux
Flux theory
Limiting flux
Flux theory
Limiting flux F m3/s
A
Coe and Clevenger
Flux at any point:
G = (U + T) A C
Flux in underflow: G = (Uu + T) A Cu
Flux in feed:
G = F Co
Rearrange equations for T then G gives:
U
O
CCCU
FCA
11
)(
Coe and Clevenger
U
O
CCCU
FCA
11
)(
Where U(C) is U at values of C between Co and Cu. Solve the above equations for various values of C and U(C) and select the area that is the greatest for the design.
Thickener designs - others
Lamella settler - increased capacity:
Thickener designs - others
Lamella settler - increased capacity:
Thickener designs - others
Potable (drinking) water treatment - floc bed clarifier:
Upward flow clarification, coagulation using ferric sulphate or polyectrolyte. Solids collected in the blanket are removed by cone de-sludging.
Sedimentation
Stokes law ok for small particles Particles of given size settle fastest
in free settling Increasing concentration slows
particles - hindered settling If a PSD then smaller particles
dragged down by the larger ones Empirically relate U=f(C): U=Ut(1-C)n
Recap:
Sedimentation
On line thickener design available on the www (freely available) using Coe and Clevenger technique:
http://www.filtration-and-separation.com
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