episode 38 : bin and hopper design

SAJJAD KHUDHUR ABBASCeo , Founder & Head of SHacademyChemical Engineering , Al-Muthanna University, IraqOil & Gas Safety and Health Professional – OSHACADEMYTrainer of Trainers (TOT) - Canadian Center of Human Development

Episode 38 : Bin and Hopper Design

Introduction

< 1960s storage bins were designed by guessing Then in 1960s A.W. Jenike changed all.- He

developed theory, methods to apply, inc. the eqns. And measurement of necessary particles properties.

WHY HOPPER?

For protection and storage of powdered materials It must be designed so that they are easy to load and

more importantly easy to unload

The Four Big Questions

What is the appropriate flow mode? What is the hopper angle? How large is the outlet for reliable flow? What type of discharger is required and what is the

discharge rate?

Hopper Flow Modes

Mass Flow - all the material in the hopper is in motion, but not necessarily at the same velocity

Funnel Flow - centrally moving core, dead or non-moving annular region

Expanded Flow - mass flow cone with funnel flow above it

Mass Flow

Typically need 0.75 D to 1D to

enforce mass flow

D

Material in motion

along the walls

Does not imply plug flow with equal velocity

Funnel Flow

“Dead” or non-flowing region

Act

ive

Flow

C

hann

el

Expanded Flow

Funnel Flow upper section

Mass Flow bottom section

Problems with Hoppers

Ratholing/Piping

Ratholing/Piping

Stable Annular Region

Voi

d


Ratholing/Piping Funnel Flow

Funnel Flow-Segregation

-Inadequate Emptying

-Structural Issues

Coa

rse

Coa

rse

Fine


Ratholing/Piping Funnel Flow Arching/Doming

Arching/Doming

Cohesive Arch preventing material from exiting hopper


Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow

Insufficient Flow- Outlet size too small

- Material not sufficiently permeable to permit dilation in conical section -> “plop-plop” flow

Material needs to dilate here

Material under compression in

the cylinder section


Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing

Flushing

Uncontrolled flow from a hopper due to powder being in an aerated state- occurs only in fine powders (rough rule of thumb - Geldart group A and smaller)- causes --> improper use of aeration devices, collapse of a rathole


Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate Emptying

Inadequate emptyingUsually occurs in funnel flow silos where the cone angle is insufficient to allow self draining of the bulk solid.

Remaining bulk solid


Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate Emptying Mechanical Arching

Mechanical Arching

Akin to a “traffic jam” at the outlet of bin - too many large particle competing for the small outlet

6 x dp,large is the minimum outlet size to prevent mechanical arching, 8-12 x is preferred


Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate Emptying Mechanical Arching Time Consolidation - Caking

Time Consolidation - Caking

Many powders will tend to cake as a function of time, humidity, pressure, temperature

Particularly a problem for funnel flow silos which are infrequently emptied completely

Segregation

Mechanisms- Momentum or velocity- Fluidization- Trajectory- Air current- Fines

What the chances for mass flow?

Cone Angle Cumulative % of from horizontal hoppers with mass flow

45 060 2570 5075 70

*data from Ter Borg at Bayer

Mass Flow (+/-)

+ flow is more consistent+ reduces effects of radial segregation+ stress field is more predictable+ full bin capacity is utilized+ first in/first out- wall wear is higher (esp. for abrasives)- higher stresses on walls- more height is required

Funnel flow (+/-)

+ less height required- ratholing- a problem for segregating solids- first in/last out- time consolidation effects can be severe- silo collapse- flooding- reduction of effective storage capacity

How is a hopper designed?

Measure- powder cohesion/interparticle friction- wall friction- compressibility/permeability

Calculate- outlet size- hopper angle for mass flow- discharge rates

What about angle of repose?

Pile of bulk solids

Angle of Repose

Angle of repose is not an adequate indicator of bin design parameters

“… In fact, it (the angle of repose) is only useful in the determination of the contour of a pile, and its popularity among engineers and investigators is due not to its usefulness but to the ease with which it is measured.” - Andrew W. Jenike

Do not use angle of repose to design the angle on a hopper!

Bulk Solids Testing

Wall Friction Testing Powder Shear Testing - measures both powder

internal friction and cohesion Compressibility Permeability

Sources of Cohesion (Binding Mechanisms)

Solids Bridges-Mineral bridges-Chemical reaction-Partial melting-Binder hardening-Crystallization-Sublimation

Interlocking forces

Attraction Forces-van der Waal’s-Electrostatics-Magnetic

Interfacial forces-Liquid bridges-Capillary forces

Testing Considerations

Must consider the following variables- time- temperature- humidity- other process conditions

Wall Friction TestingWall friction test is simply Physics 101 - difference for bulk solids is that the friction coefficient, , is not constant.

P 101

N

FF = N

Wall Friction TestingJenike Shear Tester

Wall Test Sample

Ring

CoverW x A

S x A

Bracket

Bulk Solid

Wall Friction Testing Results

Wall Yield Locus, constant wall friction

’

Normal stress, W

all s

hear

stre

ss,

Wall Yield Locus (WYL), variable wall friction

Powder Technologists usually express as the “angle of wall friction”, ’

’ = arctan

Jenike Shear Tester

Ring

CoverW x A

S x A

Bracket

Bulk SolidBulk Solid

Shear plane

Other Shear Testers

Peschl shear tester Biaxial shear tester Uniaxial compaction cell Annular (ring) shear testers

Ring Shear Testers

W x ABottom cell rotates slowly

Arm connected to load cells, S x A

Bulk solid

Shear test data analysis

C fc 1

Stresses in Hoppers/Silos

Cylindrical section - Janssen equation Conical section - radial stress field

Stresses = Pressures

Stresses in a cylinder

h

dh

Pv A

D

(Pv + dPv) A

A g dh

D d

h

Consider the equilibrium of forces on a differential element, dh, in a straight-sided silo

Pv A = vertical pressure acting from above

A g dh = weight of material in element

(Pv + dPv) A = support of material from below

D dh = support from solid friction on the wall

(Pv + dPv) A + D dh = Pv A + A g dh

Stresses in a cylinder (cont’d)Two key substitutions

= Pw (friction equation)

Janssen’s key assumption: Pw = K Pv This is not strictly true but is good enough from an engineering view.

Substituting and rearranging,

A dPv = A g dh - K Pv D dh

Substituting A = (/4) D2 and integrating between h=0, Pv = 0 and h=H and Pv = Pv

Pv = ( g D/ 4 K) (1 - exp(-4H K/D))

This is the Janssen equation.

Stresses in a cylinder (cont’d)

hydrostatic

Bulk solids

Notice that the asymptotic pressure depends only on D, not on H, hence this is why silos are tall and skinny, rather than short and squat.

Stresses - Converging Section

r

Over 40 years ago, the pioneer in bulk solids flow, Andrew W. Jenike, postulated that the magnitude of the stress in the converging section of a hopper was proportional to the distance of the element from the hopper apex.

= ( r, )This is the radial stress field assumption.

Silo Stresses - Overall

hydrostatic

Bulk solidNotice that there is essentially no stress at the outlet. This is good for discharge devices!

Janssen Equation - ExampleA large welded steel silo 12 ft in diameter and 60 feet high is to be built. The silo has a central discharge on a flat bottom. Estimate the pressure of the wall at the bottom of the silo if the silo is filled with a) plastic pellets, and b) water. The plastic pellets have the following characteristics:

= 35 lb/cu ft ’ = 20º

The Janssen equation is

Pv = ( g D/ 4 K) (1 - exp(-4H K/D))

In this case: D = 12 ft = tan ’ = tan 20º = 0.364

H = 60 ft g = 32.2 ft/sec2

= 35 lb/cu ft

Janssen Equation - Example

K, the Janssen coefficient, is assumed to be 0.4. It can vary according to the material but it is not often measured.

Substituting we get Pv = 21,958 lbm/ft - sec2.

If we divide by gc, we get Pv = 681.9 lbf/ft2 or 681.9 psf

Remember that Pw = K Pv,, so Pw = 272.8 psf.

For water, P = g H and this results in P = 3744 psf, a factor of 14 greater!

Types of BinsConical Pyramidal

Watch for in-flowing valleys in these bins!

Types of BinsWedge/Plane Flow

B

L

L>3B

Chisel

A thought experiment1 c

The Flow Function

1

c

Flow function

Time flow function

Determination of Outlet Size

1

c

Flow function

Time flow function

Flow factor

c,i

c,t

Determination of Outlet Size

B = c,i H()/

H() is a constant which is a function of hopper angle

H() Function

Cone angle from vertical10 20 30 40 50 60

1

2

3

H(

)

Rectangular outlets (L > 3B)

Square

Circular

Example: Calculation of a Hopper Geometry for Mass Flow

An organic solid powder has a bulk density of 22 lb/cu ft. Jenike shear testing has determined the following characteristics given below. The hopper to be designed is conical.

Wall friction angle (against SS plate) = ’ = 25º

Bulk density = = 22 lb/cu ft

Angle of internal friction = = 50º

Flow function c = 0.3 1 + 4.3

Using the design chart for conical hoppers, at ’ = 25º

c = 17º with 3º safety factor

& ff = 1.27

Example: Calculation of a Hopper Geometry for Mass Flow

ff = /a or a = (1/ff)

Condition for no arching => a > c

(1/ff) = 0.3 1 + 4.3 (1/1.27) = 0.3 1 + 4.3

1 = 8.82 c = 8.82/1.27 = 6.95

B = 2.2 x 6.95/22 = 0.69 ft = 8.33 in

Material considerations for hopper design

Amount of moisture in product? Is the material typical of what is expected? Is it sticky or tacky? Is there chemical reaction? Does the material sublime? Does heat affect the material?

Material considerations for hopper design

Is it a fine powder (< 200 microns)? Is the material abrasive? Is the material elastic? Does the material deform under pressure?

Process Questions

How much is to be stored? For how long? Materials of construction Is batch integrity important? Is segregation important? What type of discharger will be used? How much room is there for the hopper?

Discharge Rates

Numerous methods to predict discharge rates from silos or hopper

For coarse particles (>500 microns)Beverloo equation - funnel flowJohanson equation - mass flow

For fine particles - one must consider influence of air upon discharge rate

Beverloo equation

W = 0.58 b g0.5 (B - kdp)2.5

where W is the discharge rate (kg/sec)b is the bulk density (kg/m3)

g is the gravitational constantB is the outlet size (m)k is a constant (typically 1.4)dp is the particle size (m)

Note: Units must be SI

Johanson Equation

Equation is derived from fundamental principles - not empirical

W = b (/4) B2 (gB/4 tan c)0.5

where c is the angle of hopper from verticalThis equation applies to circular outletsUnits can be any dimensionally consistent setNote that both Beverloo and Johanson show that W B2.5!

Discharge Rate - Example

An engineer wants to know how fast a compartment on a railcar will fill with polyethylene pellets if the hopper is designed with a 6” Sch. 10 outlet. The car has 4 compartments and can carry 180000 lbs. The bulk solid is being discharged from mass flow silo and has a 65° angle from horizontal. Polyethylene has a bulk density of 35 lb/cu ft.

Discharge Rate Example

One compartment = 180000/4 = 45000 lbs.Since silo is mass flow, use Johanson equation.6” Sch. 10 pipe is 6.36” in diameter = B

W = (35 lb/ft3)(/4)(6.36/12)2 (32.2x(6.36/12)/4 tan 25)0.5

W= 23.35 lb/secTime required is 45000/23.35 = 1926 secs or ~32 min.In practice, this is too long - 8” or 10 “ would be a better choice.

The Case of Limiting Flow Rates

When bulk solids (even those with little cohesion) are discharged from a hopper, the solids must dilate in the conical section of the hopper. This dilation forces air to flow from the outlet against the flow of bulk solids and in the case of fine materials either slows the flow or impedes it altogether.

Limiting Flow Rates

Vertical stress

Bulk

density

Interstitial gas pressure

Note that gas pressure is less than ambient pressure

Limiting Flow Rates

The rigorous calculation of limiting flow rates requires simultaneous solution of gas pressure and solids stresses subject to changing bulk density and permeability. Fortunately, in many cases the rate will be limited by some type of discharge device such as a rotary valve or screw feeder.

Limiting Flow Rates - Carleton Equation

gd

vB

v

ps

ff 3/5

3/40

3/23/120 15sin4

Carleton Equation (cont’d)

where v0 is the velocity of the bulk solid

is the hopper half angles is the absolute particle density

f is the density of the gas

f is the viscosity of the gas

Silo Discharging Devices

Slide valve/Slide gate Rotary valve Vibrating Bin Bottoms Vibrating Grates others

Rotary Valves

Quite commonly used to discharge materials from bins.

Screw FeedersDead Region

Better Solution

Discharge Aids

Air cannons Pneumatic Hammers VibratorsThese devices should not be used in place of a

properly designed hopper!They can be used to break up the effects of time consolidation.

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