CE20226 - Bernardo Particle Tech

Question 1

What’s hindered settling?

Answer 1

Particle settling where there are additional forces acting on the settling particle I.e. from contact with other particles, the wall etc.

It mainly considers density difference and concentration.

(Alternative to free settling)

Question 2

What causes hindered settling?

Answer 2

Hindered settling results from collisions between particles and also between particles and walls.

In addition high particle concentration reduces the flow area and increases the velocity of the fluid (moving upwards) with a consequent decrease in settling rate.

Furthermore particle concentrations increase the apparent density and dynamic viscosity of the fluid.

Question 3

How do the settling characteristics of hindered settling systems differ from those for free settling?

(5 ways)

Answer 3

1) The interactions of particles-particles and particles-vessel wall is significant.
2) The large particles are hindered by the small particles, which increase the effective resistance of the suspending medium for large particles.
3) Upward velocity of the displaced fluid flowing in the interstices between the particles is significant
4) The velocity gradients in the suspending fluid flowing upward between the particles are increased (since the area available for flow is now smaller), resulting in greater shear forces.
5) Because of the high surface area to volume ratio for small particles, surface forces (e.g. shear) are important, resulting in flocculation and ‘‘clumping’’ of the smaller particles into larger effective particle groups.

Question 4

What are the 2 modes of (hindered) settling?

Answer 4

Settling with narrow particle size ranges - more distinct layers form between the different components

Settling with broad particle size ranges. Components with more variable compositions exist.

Question 5

What does thickening involve?

Answer 5

Increasing the solids content of a slurry or suspension by gravity settling in order to achieve separation (or partial separation) of the solids and the fluid.

Because concentrated suspensions and/or fine particle dispersions are often involved, the result is usually not a complete separation of the solids from the liquid but is instead a separation into a more concentrated (underflow) stream and a diluted (overflow) stream.

Thickening is often used as a pre-treatment step before a more capital intensive operation, such as filtration, is used.

Question 6

How do thickeners and clarifies differ?

Answer 6

Thickeners and clarifiers are essentially identical. The only difference is that the clarifier is designed to produce a clean liquid overflow with a specified purity, whereas the thickener is designed to produce a concentrated underflow product with a specified concentration.

Question 7

What is epsilon? (Richardson and Zaki equation)

How is it calculated?

Answer 7

Voidage

Voidage = total volume of liquid / total volume

Question 8

What’s lambda (in particle tech / Richardson and Zaki equation)?

Answer 8

The ratio of particle-to-tube diameter

y = dp/db

Question 9

What is c (particle tech / Richardson and Zakinequation)

Answer 9

Solid concentration by volume fraction

Question 10

How do you derive an equation to calculate average particle velocity from terminal velocity?

Answer 10

1) Derive uf from volume conservation (uf = actual velocity of suspension relative to container wall)

2) Derive uc from u.RZ
(uc is the actual average velocity of a particle in suspension)

Question 11

What does u.cs represent in particle tech?

Answer 11

u. cs is the volumetric settling flux
u. cs = Qc/Ab

= vol flowrate of solids / cross sectional area of tank

Question 12

What is u.t?

Particle tech

Answer 12

Relative / terminal velocity of a single particle

Question 13

What’s u.f?

Answer 13

Actual / observed velocity of the fluid

Question 14

What’s u.RZ?

Particle tech

Answer 14

Hindered settling velocity of a particle in a suspension of multiple particles.

Question 15

What’s u.p?

Particle tech

Answer 15

Actual velocity of particle

Question 16

What’s u.c?

Particle tech

Answer 16

Actual average velocity of a particle in suspension

Question 17

What’s C?

Particle tech

Answer 17

Solid fraction

Question 18

What are the 2 approaches to determining velocity in hindered settling?

Answer 18

1) Using a correction factor to the free settling velocity
2) Using modified suspending fluid properties (I.e. viscosity and density), considering functions involving voidage/porosity

Question 19

What are the main principles of packing / packed beds?

Answer 19

High interfacial area

Low resistance to flow

Uniform flow distribution

Costing (minimise reactor size and footprint)

Question 20

What is a packed bed?

Answer 20

A packed bed normally consists of tightly packed, uniformly-sized particles and can be used in a wide variety of applications:

Adsorption columns – water removal, air separation, (bio)chemical purifications
Catalytic reactions – hydrocracking of crude oils
Ion exchange – water purification
Car exhausts with catalytic converters
Kitchen cooker hoods

They have typical void fractions of 0.4-0.5

Question 21

What’s Darcy’s law?

Answer 21

Darcy’s Law is one of the simplest method of estimating pressure drop across a packed column and is an empirical equation that relates the superficial velocity of flow through a bed, u, to the pressure gradient along the bed, dp/dl, and the viscosity of the fluid, μ:

u = -K/mu dp/dl

NB: the (-ve) sign signifies that there is a pressure loss, where the constant K is called the permeability of the bed (units = m2).

Darcy’s law predicts that the pressure drop along a bed of length l is given by:

dp = muul/K

Question 22

What are the 2 methods obtaining permeability, K?

Answer 22

Carman-Kozeny equation (for laminar flow only)

Ergun equation (for laminar or turbulent flow)

Question 23

How is the modified Reynolds number calculated?

Answer 23

Re’p = rho.fud.p/((1-e)*mu)

Where e is epsilon = voidage or porosity

Question 24

At what modified Reynolds number does deviation (in pressure drop) begin to occur, and Re’p transition (from laminar to turbulent in packed beds)?

Answer 24

15

15 is the transition Re’p in packed beds

Question 25

When calculating pressure drop in packed beds, which equation must you use (depending on flow regime)?

Answer 25

Carman Kozeny equation if Re.p’ < 15 (laminar)

Ergun equation if Re.p’ > 15 (lam to turbulent)

Question 26

What’s fluidisation?

Answer 26

To give the characteristics of a fluid - is the result of an upward flow of fluid through a bed of particles. Note that in fluidised beds, the bed is not confined i.e. there is a free surface at the top of the bed.

Question 27

How does pressure typically vary in fluidisation?

Answer 27

As u increases the pressure drop across bed due to friction, Δp, increases.

As Δp increases, the upward drag force on the particles increases.

However, once fluid is able to flow past the packing, The is a small, quick pressure drop.

Δp can be predicted from either the Carman-Kozeny or Ergun equation.

Question 28

What happens as fluid velocity is increased in fluidisation?

Answer 28

Before the point of minimum fluidisation, mf, the fluidised bed behaves like a packed bed because the particles are stationary.
The pressure drop across the bed can be described using the Carman-Kozeny or Ergun equation depending on the flow regime.

When u reaches umf (the minimum fluidising condition) the upward drag force imposed by the flowing fluid is just sufficient to overcome the static friction of the particles so that the particles are no longer rest on one another.

As velocity is further increased, pressure drop through the bed falls slightly because of the sudden increase in area of fluid flow.

After this point, the bed is said to be fluidised.
As u is increased further the bed starts to rise (expand), i.e. its height, h, increases and as a consequence the bed voidage, ε, also increases.

It is for this reason that the pressure drop attains an approximately constant value that is independent of the fluid velocity.
Increase in bed height will continue until the height of the bed reaches that of its container and thereafter particles are swept out of the bed in the fluid flow; this is called elutriation.

Question 29

What happens as fluid velocity is decreased in fluidisation?

Answer 29

If the fluid velocity is reduced, the bed contracts until it reaches the condition where particles are just resting on one another.

The porosity then has the maximum stable value which can occur for a fixed/packed bed of the particles.

If velocity is further decreased, the structure of the bed then remains unaffected provided that the bed is not subjected to vibration.
The pressure drop across this reformed fixed bed at any fluid velocity is then less than that before fluidisation.

Question 30

Why does pressure drop decrease slightly during fluidisation as velocity is increased?

Answer 30

Due to a sudden increase in the area of fluid flow.

After this point, the bed is said to be fluidised and the bed will rise/expand with increasing velocities.

Question 31

What is minimum fluidisation velocity?

Answer 31

The superficial gas velocity at which the drag force of upward moving gas becomes equal to the weight of particles in the bed.

Pressure drop remains approximately constant at this point.

Question 32

What is superficial velocity, u?

Answer 32

A hypothetical velocity for if the given phase were the only phase present/flowing.

u = Q/A

Question 33

When is the Carman-Kozeny equation used?

Answer 33

When calculating pressure drop across packed beds with laminar flow

Question 34

When is the Ergun equation used?

Answer 34

When calculating pressure drop in packed beds with laminar and turbulent flow

Question 35

What are the 2 main fluidised bed systems?

Answer 35

Liquid-solid

Gas-solid

Question 36

What are the 4 main results of non-uniform bed expansion?

Answer 36

Bubbling (aggregation fluidisation)
(particle free zones form and coalesce - there’s good mixing but some bypassing occurs)

Slugging (large bubbles comparable to the diameter of the bed)

Channeling (and cracks forming)

Spouting (fountain-like from the centre of the bed)

Question 37

What are the 4 classifications of air fluidised bed with increasing mean particle diameter and density difference?

Answer 37

(From lowest particle diameter and density difference to highest)

Cohesive

Aeratable

Sand-like

Spoutable

Question 38

How does cake thickness change over time in a filtration time with constant velocity?

Answer 38

dl/dt = constant

Integrating, filter cake depth (l) increases at a constant rate.
dp is also proportional to l, so applied pressure must be increased proportionally to the time of filtering to maintain constant u.

Question 39

What are the 2 filtration operating regimes?

Answer 39

Operating at constant flow rate (I.e. u is constant)

Operation at constant pressure drop (dp) across the cake

Question 40

What does the Carman-Kozeny equation tell us about pressure drop across the cake in filtration units?

Answer 40

dp is proportional to ul (velocitycake thickness).

For a constant dp, u ∝ 1/l therefore dl/dt ∝ 1/l.

Integrating, l^2 ∝ t // l ∝ t^0.5

Thus to maintain constant dp, we must operate filtration such that u proportional to 1/t^1/2

Question 41

What are the 4 main cases of gas/solid fluidised bed expansion?

Answer 41

Bubbling

Slugging (sand-like)

Channelling

Spouting

Question 42

How do gas/solid and liquid/solid fluidised bed expansions differ?

Answer 42

For gas/solid, the expansion is NOT uniform.

Question 43

What are the 2 main types of solid conveying?

Answer 43

Pneumatic (compressed gas)

Hydraulic (pressurised liquid)

Question 44

How can pneumatic conveying be classified?

Answer 44

By:

The angle of inclination of the pipelines (horizontal and vertical)

Flow characteristics (dilute or dense transport)

Operational modes (negative or positive pressure operation)

Question 45

What factors cause pressure drop?

Answer 45

Solid-to-pipe friction
Gas-to-pipe friction
Particle acceleration
Gas acceleration
Static head of solids
Static head of gas

Question 46

What are the characteristics of dilute phase (lean) vertical transport?

Answer 46

High gas velocities (above 20 m/s)

Low solid concentrations (below 1 vol %)

Low P drops per unit length

Is the only system capable of operating under negative pressure

Solid particles behave as individuals

Fully suspended in the gas

Question 47

What’s chocking velocity?

Answer 47

U.ch

Lowest velocity for dilute phase (vertical transport) operation

Can not predict it theoretically

Question 48

What’s the saltation velocity?

Answer 48

U.salt

The lowest velocity before solids begin to settle out in the bottom (during dilute-phase horizontal transport)

Question 49

What are the different types of dense phase flow (with increasing superficial velocity)?

Answer 49

Continuous dense phase flow

Plug flow

Discrete plug flow

Dune flow

— once velocity is high enough, there is transition to the dilute phase where there will be dilute phase flow —

Question 50

What are the advantages and disadvantages of dense-phase pneumatic conveying?

Answer 50

Adv:
Low gas requirements

Low solid velocities

Lower E requirements per kg product

Less erosion and product degradation

Disadv:
Limited to granular materials

Used only in short straight pipes

Requires very high pressures

Question 51

What are the 3 classifications of slurry flow behaviour?

Answer 51

Homogeneous - particles uniformly distributed. Particles remain in suspension. ‘Non-settling slurries’

Heterogeneous - there are conc gradients. Particles tend to settle and there are minimal effects on the liquid carrying the particles

Saltation regime

Question 52

What’s the standard velocity and critical deposition velocity?

Answer 52

Standard - When the slurry classification changes from homogeneous to heterogeneous

CD - When slurry classification changes from saltation to homogeneous

Question 53

What’s sludge?

Answer 53

High concentrated slurry of fine particle material

Question 54

What’s a pseudo plastic fluid?

Answer 54

A fluid whose apparent viscosity or consistency decreases instantaneously with an increase in shear rate.

Question 55

What are the 2 main flows in conical hoppers?

Answer 55

Mass flow

Core flow