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Chemical Engineering

CHEE 481

Edward W Grandmaison

Winter

Description

CHEE 481 – Review Notes
1. PARTICLE SIZING:
Normal distribution:
2
f x = 1 exp - (x - μ)
σ 2 π 2 σ2
1 z x - μ ) 1 1
F(z )= ∫ exp - 2 dx = + erc z 2 )
σ 2 π -∞ 2 σ 2 2
Log-normal distribution:
1 (ln x - ln μ))2
f(x )= exp - 2
ln(σ ) 2 π 2 ln σ) ]
z
1 (ln x - ln μ ))2 1 1
F z = ∫ exp - 2 dx = + erc z 2 )
ln(σ ) 2 π -∞ 2 [ln(σ )] 2 2
2. FLUID-PARTICLE FORCES:
Terminal velocity for particles in gases:
2
g dp ρp
Stokes law: U t 18 μ , K < 3.3
f
g0.71 dp.14 ρp.71
Intermediate law: U t 0.153 0.43 0.29 , 3.3 < K < 43.6
μ f ρ f
1 / 2
g dpρ p
Newton’s law: U =t1.74 ρ , K > 43.6
f
3. DYNAMIC BALANCES – FLUID PARTICLE SYSTEMS:
General formulation: m d U p = F
p d t ∑ i
m d U p = 3 π μfd p U - U )+ m f, where f is a force term (e.g. gravity)
p d t K m f p p
2
d U p d p Kp m
τ + U p = U f τ f, where τ =
d t 18 μ f
For changes in fluid velocity (U )f
d U
τ p + U p U f
d t
Step changes in U fead to exponential changes in U . p
4. STACK SAMPLING:
Sampling locations in round ducts: i 1 / 2
R i N R
2i -11 / 2
ri= R
2 N
Gas density - ideal gas law usually applies:
n P
ρ = =
V R T
5. GRAVITY SETTLING CHAMBERS:
• Collection efficiency is generally poor except for large particles, but very
versatile and useful as a pre-treatment method for more sophisticated
techniques.
No mixing-plug flow model:
L U t
η = H U
f
Vertical mixing-plug flow model:
η =1 - exp - L U t
H U f
where L = settling chamber length
H = settling chamber height
U = gas velocity through settling chamber
f
U t terminal velocity for particle
These relations can be used to design for a suitable L/H ratio.
With chamber dimensions, L, H and W (where W is the chamber width),
Settling chamber “area” = A = WL
Gas flow rate = Q = U H W
L U t A
∴ = U t
H U f Q
This relationship can be used to design for an area A.
6. CYCLONES:
• Better collection efficiency than GSC
• Models more difficult to develop for practical design • For a “conventional” cyclone design, performance is known
1/2
9 μfW
Cut diamet

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