Transcript Pneumatic transport

Pneumatic transport
• Basic definition – using gas to transport a
particulate solid through a pipeline
– Ex: grain, flour, plastic, pulverized coal
• Two modes
– Dilute phase – particles are fully suspended, like
entrainment in FB but deliberate, solids less than 1 %
by volume, lots of pumping req’d
– Dense phase – particles not suspended, loading > 30 %
by volume, lots of interparticle interactions
Phase diagram for dilute phase
vertical pneu. transport
(after Rhodes, p. 141, Fig 6.1)
p/L
Static head of
solids dominates
G = G2 > G1
Friction resistance
dominates
G = G1
B
A
Uch for G1
G=0
Superficial gas velocity U
Uch, lowest velocity at which dilute phase transport line can be operated if solids
feed rate is G1
Phase diagram for dilute phase
horizontal pneu. transport
(after Rhodes, p. 142, Fig 6.2)
Saltation, solids begin to settle out in the bottom of the pipe
p/L
G = G2 > G1
G = G1
B
G=0
A
Usalt for G1
Superficial gas velocity U
Definitions
• Superficial gas velocity Ufs = Qf (gas
volumetric flow) /A (cross sectional area of
pipe)
• Superficial solids velocity Ups = Qp/A
(Qp = volumetric flow of solids)
• Actual gas velocity Uf = Qf/Ae (void
fraction)
• Actual particle velocity Up = Qp/[A(1-e)]
Important relationships
• Mass flow rate of particles
Mp  AUp (1  e ) p
• Mass flow of fluid
Mf  AU f e f
• Solids loading = Mp/Mf
Pressure drop in pneumatic transport
Contributors to pressure drop
1. Gas acceleration (gas acting on gas)
2. Particle acceleration (gas acting on particles)
3. Gas/pipe friction
wall friction
4. Solids/pipe friction
“
5. Static head of solids
fighting gravity
6. Static head of gas
“
Not considered: interparticle forces
Force balance on pipe
Net force acting on
pipe contents
Pressure - gas/wall
friction force
= rate of increase in
momentum of contents
- solids wall
friction force
- gravity = rate of increase in force
momentum of gas + rate
of increase in momentum
solids
P1  P2   FfwL  Fpw L   p L(1 e)g sin   f L e g sin 
1
1
2
efU f  (1 e) pU p 2
2
2
Ffw and Fpw are gas to wall and solids to wall friction force respectively,
L = pipe length,  = angle of pipe with horizontal
What happens for steady state? Horizontal flow?
Terms and physical meaning
(you match them up):
P1  P2 
1.
Total pressure drop
2.
Gas acceleration (gas acting on gas)
 p L(1 e)g sin
3.
Particle acceleration (gas acting on particles)
 f L e g sin
4.
Gas/pipe friction
wall friction
1
2
e fU f
2
1
2
(1 e)  pU p
2
5.
Solids/pipe friction
wall friction
6.
Static head of solids
fighting gravity
7.
Static head of gas
fighting gravity
F fw L
Fpw L
Tools to calculate pressure drop
Correlations for Fpw
For vertical transport [G = solids mass flux, mass particles/(area x time)]
Fpw
Horizontal transport
g
L  0.057 G L
D
Fpw L 
where 
and

2f p G U pL
D
U p  U(1 0.0638 x0.3 p )
0.5
2


3 f D
U f  UP
fp 
CD 

8 p x  U p 
For gas/wall friction pressure drop, calculate with friction factor
assuming it is independent of presence of particles.
Simple method for s.s. horizontal
From Particle Technology by Orr (1966)
Ratio of total pressure loss
due to solids/air system
(Pt)
to total pressure loss due to
only air flowing (Pa)
Pt
R
 1
Pa
k
R = mass of solid material
mass of air

k is an empirically
derived coefficient
coefficient k,
dimensionless
k as a function of superficial velocity
4
3.5
3
2.5
2
1.5
1
2000
3000
4000
5000
superficial velocity, ft/min
6000
Bends
Generally problematic. Solids that may be in suspension in
vert/horiz transport may salt out as they go around bends. Worst
case: vertical going to horizontal
blinded tees recommended if
bends are unavoidable
No reliable correlations exist for bend pressure drops.
Only a rough rule of thumb:
Bend P = P for 7.5 m of vertical pipe under same flow conditions
For more info (and movies!)
• http://www.erpt.org/014Q/rhoe-00.htm