Episode 38 : Bin and Hopper Design < 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. SAJJAD KHUDHUR ABBAS Ceo , Founder & Head of SHacademy Chemical Engineering , Al-Muthanna University, Iraq Oil & Gas Safety and Health Professional – OSHACADEMY Trainer of Trainers (TOT) - Canadian Center of Human Development

1. SAJJAD KHUDHUR ABBAS
Ceo , Founder & Head of SHacademy
Chemical Engineering , Al-Muthanna University, Iraq
Oil & Gas Safety and Health Professional – OSHACADEMY
Trainer of Trainers (TOT) - Canadian Center of Human
Development
Episode 38 : Bin and Hopper
Design

2. 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.

3. 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

4. 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?

5. 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

6. 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

7. Funnel Flow
“Dead” or non-
flowing region
ActiveFlow
Channel

8. Expanded Flow
Funnel Flow
upper section
Mass Flow
bottom section

9. Problems with Hoppers
Ratholing/Piping

10. Ratholing/Piping
Stable Annular
Region
Void

11. Problems with Hoppers
Ratholing/Piping
Funnel Flow

12. Funnel Flow
-Segregation
-Inadequate Emptying
-Structural Issues
Coarse
Coarse
Fine

13. Problems with Hoppers
Ratholing/Piping
Funnel Flow
Arching/Doming

14. Arching/Doming
Cohesive Arch
preventing material from
exiting hopper

15. Problems with Hoppers
Ratholing/Piping
Funnel Flow
Arching/Doming
Insufficient Flow

16. 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

17. Problems with Hoppers
Ratholing/Piping
Funnel Flow
Arching/Doming
Insufficient Flow
Flushing

18. 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

19. Problems with Hoppers
Ratholing/Piping
Funnel Flow
Arching/Doming
Insufficient Flow
Flushing
Inadequate Emptying

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

21. Problems with Hoppers
Ratholing/Piping
Funnel Flow
Arching/Doming
Insufficient Flow
Flushing
Inadequate Emptying
Mechanical Arching

22. 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

23. Problems with Hoppers
Ratholing/Piping
Funnel Flow
Arching/Doming
Insufficient Flow
Flushing
Inadequate Emptying
Mechanical Arching
Time Consolidation - Caking

24. 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

25. Segregation
Mechanisms
- Momentum or velocity
- Fluidization
- Trajectory
- Air current
- Fines

26. What the chances for mass flow?
Cone Angle Cumulative % of
from horizontal hoppers with mass flow
45 0
60 25
70 50
75 70
*data from Ter Borg at Bayer

27. 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

28. 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

29. How is a hopper designed?
Measure
- powder cohesion/interparticle friction
- wall friction
- compressibility/permeability
Calculate
- outlet size
- hopper angle for mass flow
- discharge rates

30. What about angle of repose?
α
Pile of bulk
solids
α
α

31. 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!

32. Bulk Solids Testing
Wall Friction Testing
Powder Shear Testing - measures both powder
internal friction and cohesion
Compressibility
Permeability

33. 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

34. Testing Considerations
Must consider the following variables
- time
- temperature
- humidity
- other process conditions

35. Wall Friction Testing
Wall friction test is simply Physics 101 - difference for bulk
solids is that the friction coefficient, µ, is not constant.
P 101
N
F
F = µN

36. Wall Friction Testing
Jenike Shear Tester
Wall Test
Sample
Ring
Cover
W x A
S x A
Bracket
Bulk Solid

37. Wall Friction Testing Results
Wall Yield Locus,
constant wall friction
ϕ’
Normal stress, σWallshearstress,τ
Wall Yield Locus (WYL),
variable wall friction
Powder Technologists usually express µ as the
“angle of wall friction”, ϕ’
ϕ’ = arctan µ

38. Jenike Shear Tester
Ring
Cover
W x A
S x A
Bracket
Bulk SolidBulk Solid
Shear plane

39. Other Shear Testers
Peschl shear tester
Biaxial shear tester
Uniaxial compaction cell
Annular (ring) shear testers

40. Ring Shear Testers
W x A
Bottom cell
rotates slowly
Arm connected to load
cells, S x A
Bulk
solid

41. Shear test data analysis
σ
τ
C fc σ1

42. Stresses in Hoppers/Silos
Cylindrical section - Janssen equation
Conical section - radial stress field
Stresses = Pressures

43. Stresses in a cylinder
h
dh
Pv A
D
(Pv + dPv) A
γ A g dh
τπDdh
Consider the equilibrium of forces on a
differential element, dh, in a straight-
sided silo
Pv A = vertical pressure acting from
above
γ A g dh = weight of material in element
(Pv + dPv) A = support of material from
below
τ π D dh = support from solid friction on
the wall
(Pv + dPv) A + τ π D dh = Pv A + γ A g dh

44. Stresses in a cylinder (cont’d)
Two key substitutions
τ = µ 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 = γ A g dh - µ K Pv π D dh
Substituting A = (π/4) D2
and integrating between h=0, Pv = 0
and h=H and Pv = Pv
Pv = (γ g D/ 4 µ K) (1 - exp(-4H µK/D))
This is the Janssen equation.

45. 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.

46. Stresses - Converging Section
r
σ
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.
σ = σ ( r, θ)
This is the radial stress field
assumption.

47. Silo Stresses - Overall
hydrostatic
Bulk solid
Notice that there is essentially no stress at
the outlet. This is good for discharge
devices!

48. Janssen Equation - Example
A 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:
γ = 35 lb/cu ft ϕ’ = 20º
The Janssen equation is
Pv = (γ g D/ 4 µ K) (1 - exp(-4H µK/D))
In this case: D = 12 ft µ = tan ϕ’ = tan 20º = 0.364
H = 60 ft g = 32.2 ft/sec2
γ = 35 lb/cu ft

49. 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 = ρ g H and this results in P = 3744 psf, a factor of 14
greater!

50. Types of Bins
Conical Pyramidal
Watch for in-
flowing valleys
in these bins!

51. Types of Bins
Wedge/Plane Flow
B
L
L>3B
Chisel

52. A thought experiment
σ1
σc

53. The Flow Function
σ1
σc
Flow function
Time flow function

54. Determination of Outlet Size
σ1
σc
Flow function
Time flow function
Flow factor
σc,i
σc,t

55. Determination of Outlet Size
B = σc,i H(θ)/γ
H(θ) is a constant which is a function of
hopper angle

56. H(θ) Function
Cone angle from vertical
10 20 30 40 50 60
1
2
3
H(θ)
Rectangular outlets (L > 3B)
Square
Circular

57. 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) = ϕ’ = 25º
Bulk density = γ = 22 lb/cu ft
Angle of internal friction = δ = 50º
Flow function σc = 0.3 σ1 + 4.3
Using the design chart for conical hoppers, at ϕ’ = 25º
θc = 17º with 3º safety factor
& ff = 1.27

58. Example: Calculation of a Hopper Geometry for Mass
Flow
ff = σ/σa or σa = (1/ff) σ
Condition for no arching => σa > σc
(1/ff) σ = 0.3 σ1 + 4.3 (1/1.27) σ = 0.3 σ1 + 4.3
σ1 = 8.82 σc = 8.82/1.27 = 6.95
B = 2.2 x 6.95/22 = 0.69 ft = 8.33 in

59. 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?

60. 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?

61. 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?

62. Discharge Rates
Numerous methods to predict discharge rates from
silos or hopper
For coarse particles (>500 microns)
Beverloo equation - funnel flow
Johanson equation - mass flow
For fine particles - one must consider influence of air
upon discharge rate

63. Beverloo equation
W = 0.58 ρb g0.5
(B - kdp)2.5
where W is the discharge rate (kg/sec)
ρb is the bulk density (kg/m3
)
g is the gravitational constant
B is the outlet size (m)
k is a constant (typically 1.4)
dp is the particle size (m)
Note: Units must be SI

64. Johanson Equation
Equation is derived from fundamental principles - not
empirical
W = ρb (π/4) B2
(gB/4 tan θc)0.5
where θc is the angle of hopper from vertical
This equation applies to circular outlets
Units can be any dimensionally consistent set
Note that both Beverloo and Johanson show that W α B2.5
!

65. 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.

66. 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
)(π/4)(6.36/12)2
(32.2x(6.36/12)/4 tan 25)0.5
W= 23.35 lb/sec
Time required is 45000/23.35 = 1926 secs or ~32 min.
In practice, this is too long - 8” or 10 “ would be a better choice.

67. 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.

68. Limiting Flow Rates
Vertical
stress
Bulk
density
Interstitial gas pressure
Note that gas pressure is less than
ambient pressure

69. 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.

70. Limiting Flow Rates - Carleton Equation
g
d
v
B
v
ps
ff
=+ 3/5
3/4
0
3/23/12
0
15sin4
ρ
µρα

71. Carleton Equation (cont’d)
where
v0 is the velocity of the bulk solid
α is the hopper half angle
ρs is the absolute particle density
ρf is the density of the gas
µf is the viscosity of the gas

72. Silo Discharging Devices
Slide valve/Slide gate
Rotary valve
Vibrating Bin Bottoms
Vibrating Grates
others

73. Rotary Valves
Quite commonly used to discharge
materials from bins.

74. Screw Feeders
Dead Region
Better Solution

75. Discharge Aids
Air cannons
Pneumatic Hammers
Vibrators
These devices should not be used in place of a
properly designed hopper!
They can be used to break up the
effects of time consolidation.

76. Thanks for Watching
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