Solids Handling

Method used with low conc/large particles + dense solids

Settling tank

Driving force of settling tank

Gravity

Method used with low conc + large solids

Centrifuge

Method used for very fine particles

Membrane/filter

Driving force of filter/membrane

Pressure/conc driven

Method used for high concs

Gravity thickener

5 factors of hindered settling

• Interactions of particles

• Large particles hinder smaller ones

• Upwards velocity of the displaced fluid

• Velocity gradients in the fluid are increased

• Flocculation and clumping of particles

2 methods of modelling hindered settling

• Correction factor

• Modify the fluid properties

Why can we assume that lambda is 0

It is often extremely small so doesn’t contribute to the value of n

How can we find the region where free settling turns to hindered on a velocity vs conc graph?

Take the first derivative to find the stationary point

What 2 properties of the fluid do we modify

• Viscosity

• Density

Example of a system to use modified fluid properties on

Thickener due to different modes of settling in different sections

Applications of Packed Beds

• Absorption 

• Catalytic reactions 

• Ion exchange – water purification 

• Car exhausts w/catalytic converters 

• Kitchen cooker hoods 

Principles of packing

• High interfacial area 

• Low resistance to flow 

• Uniform distribution of flow 

• Costing 

Voidage

Ratio of voids in the bed compared to total volume

Superficial Velocity

Hypothetical maximum velocity if the solids weren't in the bed 

Interstitial Velocity

Represents the actual velocity of the liquid by taking into account solids

What equation is used for laminar flow

Carman-Kozeny Equation

hat equation is used for tuburlent flow

Ergun Equation

Why does deviation occur between the Carman-Kozeny and Ergun Eq, as Re’ increases?

The turbulent term in the Ergun equation dominates

Re’ boundary for using Carman-Kozeny Equation

Re’ < 15

Re’ boundary for using Ergun Equation

Re’ > 15

How do you choose a packed bed equation in an exam setting

Assume one of the equations, then validate it with Re’, if not valid recalculate with the other equation

Features of Fluidisation

• High interfacial area 

• High level of inter mixing 

• Frequent particle-particle and particle-wall interactions 

Why is the shutdown profile different to the start-up one for fluidisation

On shutdown, frictional forces do not need to be overcome like on startup, meaning we don’t get the 'bump' at u_mf

What direction is drag force during fluidisation

Upwards as it is against the direction of weight

Galileo Number

Ratio of gravitational forces to viscous forces

How to solve Ergun Equation with Galileo Number

Quadratic formula

How to find U_mf

1) Find voidage at mf

2) Find Ut, stokes (laminar) or Galileo (turb)

3) Find Umf

4) Check if CK or Ergun is valid

What are voidage and bed heighr functions of after the point of fluidisation

Velocity

2 types of fluidised bed expansion

1) Liquid-Solid

2) Gas-Solid

Liquid-Solid Bed Expansion Assumptions

• Uniform Expansion 

• Non-bubbling (density of fluid and particles are similar 

Examples of Liquid-Solid bed systems

• Water and Sand

• Water and Glass Beads

Gas-Solid Bed Expansion

• Not uniform 

• e.g air + sand, air + glass beads 

• Greater density difference than solid-liquid 

4 Flow regimes in gas-solid beds

• Bubbling

• Slugging

• Channeling

• Spouting

Bubbling

• Also known as aggregative 

• Bubbles are generated similar to gas bubbles in liquids 

• Bypassing of bubbles – negative consequences for chemical reactions 

Slugging

• Similar to bubbling but bubbles are large 

• Bubbles have around the same diameter of the bed 

• These large bubbles are called slugs 

Channelling

• Beds of fine cohesive particles display channels or cracks 

• Particles have a strong particle-particle adherence 

Spouting

• Occurs when particles are large 

• Gas passes through the central channel 

• Produces a spouted bed – loose packing 

Difference between filtration and other beds

Bed height changes over time

Filtration Design Parameters

Flux: u

Pressure drop: delta P

Cake Thickness: l

Cake

Collected solids after filtation

Slurry

Mix of solids and liquid before filtration

Filtration mat balance assumptions

Out = 0 as nothing leaves

Gen = Cons = 0 as no reaction occurs

2 modes of operation for filtration

1) Operation at constant flowrate

2) Operation at constant pressure drop

Why is ratio of mass of solids to fluid constant

No solid enters or leaves the system

Filtration assumption

Laminar flow so initial always use CK Eq

Solids Conveying

Using fluids to transport solids

2 types of solid conveying

• Pneumatic

• Hydraulic

Angles of conveying

• Horizontal

• Vertical

Flow Characteristics for conveying

• Diluted

• Dense

Operational modes for conveying

• Positive

• Negative

Pneumatic Conveying

Uses compressed gas to move solids

Positive Conveying

• Solids are fed to air stream 

• System uses positive pressure 

• Max pressure is 1 bar gauge 

Negative Conveying

• Often used when air is not desirable 

• Uses vacuum or negative pressure 

• Max vacuum of 0.4bar 

Dilute Phase Transport

• High gas velocities (>20m/s) 

• Low solids conc ( <1 vol%) 

• Low pressure drops per unit length 

• Only system capable of operating under negative pressure 

• Solid particles behave as individuals  

• Fully suspended in the gas 

• Fluid-particle forces dominate 

What causes pressure drop

• Solid-pipe friction 

• Gas-pipe friction 

• Particle acceleration 

• Gas acceleration 

• Static head of solids 

• Static head of gas 

Choking Velocity

Minimum velocity where particles can be held up in the flow

Saltation Velocity

Velocity at which particles settle on the bottom of the pipe

When is saltation and choking velocity used?

Saltation - Horizontal

Choking - Vertical

Dense Phase Saltation

• Solids are conveyed such that they are not entirely suspended in the gas 

• Transition point is defined by both choking and saltation velocities 

Advantages of dense phase conveying

• Low gas requirements

• Low solids velocity

• Lower energy requirement per kg of product

• Less erosion or product degradation

Disadvantages of dense phase conveying

• Limited to granular materials

• Used only in short start pipes

• Requires very high pressures

Hydraulic conveying

Uses pressurised liquid to move product

Main application of hydraulic conveying

Slurry transport

Sludge

High conc slurry of fine particulate material

Flow behaviours in hydraulic conveying

1) Homogenous

2) Heterogenous

3) Saltation

Homogenous flow

• Particles uniformly distributed

• Particles remain in suspension

• Referred as non-settling slurries

Heterogenous Flow

• Concentration gradients

• Particles tend to settle

• Minimal effects on the liquid carrying the particles

Saltation regime

• Particles settle and roll

• A liquid flow later exists above the moving bed

Shear thinning liquids

n < 1

Toothpaste and ketchup

Shear thickening liquid

n >1

Oobleck

Where are colloids found

• Biotechnology 

• Food Industry 

• Consumer Goods

• Wastewater treatment

Small particle characteristics

• Dominated by surface forces (VDW, Electron Double Layer) rather than body forces (friction, gravitational) 

• High SA: V

• Surface for is a function of distance and potential difference

VDW Forces

• Group of electrodynamic interactions: Keeson, Debye and London dispersion 

• Dominant contribution is dispersion forces that come from Columbic interactions 

• Depends on a constant

Electron Double Layer Forces

When particles are immersed in a liquid they might develop a surface charge 

Applications of Electron Double Layer Forces

• Production of aerated concrete blocks 

• Food additive 

• Paper 

• Biofuel applications 

• Flame retardants 

Isoelectric point

Where the M-OH₂ ⁺ and M-O^- have the same number of sites per unit area

If we want a positive charge

• Use an acid

If we want a negative charge

• Use an alkali

Zeta potential

How much energy needed to stick/slide atoms to molecules

Low zeta yields flocculation and high causes separation

How to control forces

Use polymers

• High MW help flocculation

• Low MW can stabilise