Conventional Surface Water Treatment for Drinking Water Paddle - - PowerPoint PPT Presentation

Conventional Surface Water Treatment for Drinking Water

Paddle Flocculators at Everett WTP

The Rate of Collisions by Each Mechanism Can be Predicted from Theory

floc ij i j

r n n β =

( )

3

1 6

Br ij i j

G d d β = +

( ) ( )( )

2 3

4 72

DS ij i j i j p w i j i j

v v d d g d d d d π β π ρ ρ µ = − + = − + −

( )

2 1 1 3

Br B i j i j

k T d d d d β µ ⎛ ⎞ = + + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ Brownian Motion: Particles Collide Due to Random Motion Fluid Shear: Particles on Different Streamlines Travel at Different Velocities Differential Sedimentation: Particles Collide Due to Different Terminal Velocities

Each mechanism of flocculation is predicted to dominate for certain ranges of particle properties (primarily size)

Considering the short- range interactions leads to a decrease in the predicted flocculation efficiency

Short-range forces are predicted to reduce the effectiveness of shear as a mechanism of flocculation more than the

• ther

mechanisms

(From Opflow, June 2000)

( )

( )

,CV ,CV L L p

d NV QN Q N dN V r dt = − + + Q Av =

Assume pseudo-steady state, so (

)

,CV L

d NV dt =

,CV L p

Av dN V r = − +

,CV L p

Av dN V r =

,CV

Rate of Removal of Particles Number of by a Single Collector Collectors in Layer Rate of Approach of Removal Efficiency of Number Particles to a Collector a Single Collector

L p

V r ⎡ ⎤ ⎡ ⎤ = − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎡ ⎤ ⎡ ⎤ = − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

• f

Collectors in Layer ⎡ ⎤ ⎢ ⎥ ⎣ ⎦

2

Rate of Approach of Particles to a Collector 4

c

d Nv π ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ Removal Efficiency of a Single Collector η ⎡ ⎤ ≡ ⎢ ⎥ ⎣ ⎦

( )

3

Total Volume of Number of 1 Collector Media Volume of a Collectors in Layer / 6 Single Collector

c

AdL d ε π ⎡ ⎤ ⎢ ⎥ − ⎡ ⎤ ⎣ ⎦ = = ⎢ ⎥ ⎡ ⎤ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦

[ ]

( ) ( )

2 3

1 4 / 6 1 3 2

c c c

AdL d Nv d Nv AdL d ε π η π ε η − ⎡ ⎤ ⎡ ⎤ = − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ − = −

,CV

Rate of Approach of Removal Efficiency of Number of Particles to a Collector a Single Collector Collectors in Layer

L p

V r ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = − ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

“Single Collector Removal Efficiency”

,CV L p

Av dN V r =

Av

( )

1 3 2

c

dN N v A d ε η − = − dL

( )

1 3 2

c

dN dL dL N d ε η λ − = − = − ln

• ut

in

N L N λ = −

( )

exp

• ut

in

N N L λ = −

“Filter coefficient”

Summary: Mass Balance Analysis of Particle Removal in a Granular Filter

• Based on relative sizes of particles and

collectors, sieving is unimportant and removal can be modeled based on interactions with isolated “collector” grains

• Assuming pseudo-steady state, concentration of

any given type of particle is expected to decline exponentially with depth

• Each type of particle has a different coefficient

for the exponential loss rate

• If we could predict η for a given type of particle,

we could predict Nout/Nin for that particle

2/3

0.905

B Br c p

k T d d v η µ ⎛ ⎞ = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

“Filter Ripening”

S=Standard case; L=longer bed; c=concentration; h=headloss

S=Standard case; d=larger diameter grains; c=concentration; h=headloss