Particles, Pathogens, and Porous Media:
Physics, Chemistry, and Engineering
Desmond F. Lawler
University of Texas
Assessing Pathogen Fate, Transport, and Risk
in Natural and Engineered Water Treatment
Banff Centre, Banff, Alberta
September 23, 2012
[email protected]
512 471 4595
Conventional Drinking Water
Treatment Plant
Effluent
Concentration
Typical Filter Run
Maximum allowable concentration
Head Loss
B
c
Max. allowable head loss
B
h
Time or Cumulative Volume Throughput
Filtration Complexity
• Two dependent variables of importance
– Head Loss
– Effluent Quality
• Never at Steady State
• Two different modes of operation (filtration
and backwashing)
• Numerous Independent Variables
Independent Variables in Filtration
• Time (or Cumulative Vol. Throughput since last
backwash)
• Particles: size distribution, concentration,
density, shape, surface charge, surface
chemistry
• Water (physical): Temp, and therefore viscosity
and density
• Water (chemical): effects on surface chemistry
of media and particles
• Media: Size, size distribution, density, shape,
porosity, depth, and surface chemistry
• Operation: filtration velocity (Q/A)
Take Home Message (THM) #1
Chemistry matters (a lot)
O’Melia, C.R. (1974)
“The Role of
Polyelectrolytes in
Filtration Processes,”
Report # EPA-670/274-032, U.S.
Environmental
Protection Agency,
Cincinnati, OH.
Alum Dose (mg/L)
50
2.5
2.5
0
1
3
Turbidity (NTU)
40
30
20
10
0
0
60
120
180
Time (min)
240
300
THM #2
Particle size matters
Flow
Sedimentation
Interception
Brownian
Motion
Media
Grain
Streamlines
Yao, K.M., Habibian,
M.T., and O'Melia,
C.R. (1971) "Water
and Wastewater
Filtration: Concepts
and Applications,"
Env. Sci. and Tech., 5,
11, 1105-1112
Yao, Habibian, and O'Melia Model
Sedimentation
Interception
Brownian
Motion
Interception :
3  dp 
ηI =  
2  dc 
Se dim entation : ηG =
2
(ρp − ρl ) g d p 2
18 µ v
Media
Grain
Streamlines
 kT 

Brownian Motion : ηB = 0.9
 µd d v 
 p c 
η = ηI + ηG + ηB
 N out 
3(1 − ε )αηL
ln
=−
2d c
 N in 
2
3
Tot
Single collector removal efficiency
log η
-1
-2
-3
Conventional rapid sand filter
Yao et al. model
-4
-5
-6
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
log of particle diameter (d in µm)
p
1.0
1.5
Tufenkji and Elimelech Model
η Br = 2.4 As Pe −0.715 N R −0.081 N vdW 0.052
1
3
η I = 0.55 As N R 1.675 N A 0.125
η g = 0.22 N R
NR =
NA =
−0.24
NG
1.11
dp
As
dc
AH
2
3πµd p vo
NG =
N vdW =
( ρ p − ρ L ) gd p
18µv o
AH
k BT
N vdw
0.053
Tufenkji, N. and Elimelech, M.
(2004) “Correlation Equation for
Predicting Single-Collector
Efficiency in Physicochemical
Filtration in Saturated Porous
Media,” Env. Sci. and Tech., 38, 2,
529-536.
2(1 − p 5 )
=
2 − 3 p + 3 p5 − 2 p6
1
a
= (1 − ε ) 3
b
vd
Pe = o c
Dp
p =
2
Dp =
k BT
3πµd p
Tot
Single collector removal efficiency
log η
-1
-2
-3
Conventional rapid sand filter
Tufenkji & Elimelech model
-4
-5
-6
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
log of particle diameter (dp in µm)
1.0
1.5
Overall filter removal efficiency
Conventional rapid sand filter
Tufenkji & Elimelech model
1.0
0.8
α =1
0.6
α = 0.1
0.4
0.2
α = 0.01
0.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
log of particle diameter (d in µm)
p
1.0
1.5
Removal Efficiency, η
filter
1.0
d = 0.6 mm
c
0.8
v = 0.14 cm/s
o
0.6
ρp = 1.08 g/cm3
0.4
T = 25 C
α=1
L = 60 cm
o
-13
H = 1 x 10
a
Yao
Rajagopalan & Tien
Tufenkji & Elimelech
0.2
0.0
-1.0
erg
-0.5
0.0
0.5
1.0
1.5
log of Particle Diameter (d in µm)
p
2.0
Assumptions about Pathogens
• In terms of their behavior, pathogens are like any other
particles in a filter, with the critical characteristics being
size and surface chemistry.
• Surface Chemistry:
• Cysts of Giardia and Cryptosporidium are coated with
Natural Organic Matter and are therefore negatively
charged from that adsorbed material.
• Bacteria and viruses are intrinsically negatively
charged due to functional groups that are part of
their surfaces.
Pathogen size
• Viruses: 5 – 100 nm; choose 10 nm as most common; log
dp = -2.0
• Bacteria: 0.7 to 2.5 µm; choose 1 µm; log dp = 0.0
• Cryptosporidium: 2 – 6 µm; choose 3 µm; log dp = 0.5
• Giardia: 7 to 14 µm; choose 10 µm; log dp = 1.0
Pathogen Shapes
• Viruses: Often highly non-spherical, with
varying types of appendages
• Bacteria: Sometimes nearly spherical, but a
variety of shapes (and appendages)
• Cysts and Oocysts: Reasonably spherical
10
Influent
-3
-1
(∆N/∆dp in cm µm )
log of particle size distributiojn funciton
Unripened sand filter
8
6
Effluent
4
2
0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
log of particle diameter (dp in µm)
1.0
1.5
THMs #3 and #4
• Ripening happens
• Detachment happens
Moran, D.C., Moran, M.C., Cushing, R.S., and Lawler, D.F. (1993) “Particle Behavior in
Deep-Bed Filtration: Part 1-Ripening and Breakthrough,” J. Amer. Water Works Assoc.,
85, 12, 69-81.
Moran, M.C., Moran, D.C., Cushing, R.S., and Lawler, D.F. (1993) “Particle Behavior in
Deep Bed Filtration: Part 2-Particle Detachment,” J. Amer. Water Works Assoc., 85, 12,
82-93.
Gear
Pump
Fluid
S ampling
Ports
A
Data Acquisition
S ystem
C
F

Peristaltic
Pump
G
Pressure
S ampling
Ports
Filter
Effluent
3
(∆N/∆d in #/cm -µm)
Exp. SM4
v = 1.8 mm/s
d = 1.85 mm
5.0
4.0
p
c
Time = 17 min.
Port A
Influent
3.0
Port C
193 mm
2.0
1.0
p
LOG(∆N/∆d )
PARTICLE SIZE DISTRIBUTION FUNCTION
6.0
Port G
746 mm
0.0
-1.0
A
-2.0
0.0
0.4
0.8
1.2
Log of Particle Diameter (d in µm)
p
1.6
REMOVAL EFFICIENCY (Number Basis)
Effects of Media Size: Initial Removal
1.0
0.8
0.6
Depth = 746 mm
dc=1.85 mm;
dc=1.85 mm;
dc=0.78 mm;
dc=0.78 mm;
0.4
0.2
Exp. SM4
Model
Exp. SM5
Model
0.0
0.0
0.2
0.4
0.6
0.8
1.0
in
LOG OF PARTICLE DIAMETER
(dµm)
p
1.2
Effects of Media Size
Depth = 746 mm
REMOVAL EFFICIENCY (NUMBER BASIS)
Depth = 193 mm
1.0
A2
A1
0.8
0.6
dc = 1.85 mm; Exp. SM4
dc = 0.78 mm; Exp. SM5
dc = 1.85 mm; Exp. SM4
dc = 0.78 mm; Exp. SM5
0.4
0.2
Window 1 (1.1 µm < d p < 1.8 µm)
Window 1
0.0
0
600
1200
1800
TIME (minutes)
2400
3000
0
600
1200
1800
2400
TIME (minutes)
3000
REMOVAL EFFICIENCY (Numer Basis)
Depth = 193 mm
Depth = 746 mm
1.0
B2
B1
0.8
0.6
0.4
0.2
Window 3 (3.0 µm< dp < 4.8 µm)
Window 3
0.0
0
600
1200
1800
TIME (minutes)
2400
30000
600
1200
1800
TIME (minutes)
2400
3000
According to Yao, for equal removal in two filters,
when removal is dominated by sedimentation:
L1
L2
=
v1 d c1
v 2 d c2
When the two fillters have the same filtration
velocity but different media sizes:
L1
L2
=
d c1
d c2
1.0
REMOVAL EFFICIENCY (Number Basis)
A
B
0.8
0.6
Window 1 (1.1 µm < d p < 1.8 µm)
0.4
dc = 1.85 mm; 416 mm; Exp. SM4
dc = 0.78 mm; 193 mm; Exp. SM5
0.2
Window 3 (3.0 µm < d p < 4.8 µm)
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
CUM. SURFACE AREA CAPTURED
(10
12
0.0
0.5
1.0
1.5
2.5
3.0
CUM. SURFACE AREA CAPTURED
2
µm )
2.0
(10
12
2
µm )
ADDITIONAL HEAD LOSS (cm)
50
dc =1.85; 416 mm; SM4
dc =0.78; 193 mm; SM5
40
30
20
10
0
-10
0
0.5
1
1.5
2
2.5
3
CUMULATIVE SURFACE AREA CAPTURED
µm
( 2)
3
(∆N/∆d in #/cm -µm)
5
4
p
p
LOG(∆N/∆d )
PARTICLE SIZE DISTRIBUTION FUNCTIO
6
3
2
Port A
Influent
Port G
17 min
1
0
Port G
66 min
-1
-2
0.0
0.4
0.8
1.2
Log of Particle Diameter (d in µm)
p
1.6
p
3
(∆N/∆d in #/cm -µm)
5
4
3
2
1
p
LOG(∆N/∆d )
PARTICLE SIZE DISTRIBUTION FUNCTION
6
0
Port A
Influent
Port G
66 min
Port G
2682 min
-1
-2
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
LOG OF PARTICLE DIAMETER (d in µm)
p
p
3
(∆N/∆d in #/cm -µm)
6.0
5.0
A
4.0
Exp. SM3
v = 5.5 mm/s
d = 0.78 mm
3.0
2.0
1.0
p
LOG(∆N/∆d )
PARTICLE SIZE DISTRIBUTION FUNCTIO
Special Detachment Experiments
c
Port A
Influent
(Filtered
effluent)
0.0
-1.0
-2.0
-0.2
0.0
Time = 17 min.
Port C
193 mm
(16 min. after
influent switch)
0.2
0.4
0.6
0.8
1.0
1.2
Log of Particle Diameter (d in µm)
p
1.4
EFFLUENT/INFLUENT (Number Basis)
30
06 min.
29 min.
43 min.
78 min.
25
20
Top 193 mm
15
10
5
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
of Particle
Diameter
(din
µm)
Log ofLog
Particle
Diameter
(d
p inµm)
p
1.4
Application of
Characteristic Reaction Time
Concept to Filtration
Lawler, D.F., and Nason, J.A., “Granular Media Filtration: Old Process, New Thoughts,”
Water Science and Technology, 53, 7, 1-7, 2006.
• In batch system, time
that it would take for a
constituent to reach its
ultimate value, if the
reaction continued at its
initial rate.
• For negative reaction
rate:
c(0)
tchar =
− rc (0 )
Concentration
Definition:
Characteristic Reaction Time
Concentration
Slope = Initial Rate
t
char
Time
Characteristic Reaction Time for First
Order Reactions
dc
rc = = −k1c
dt
c(t ) = c(0) exp( −k1t )
c0
Concentration
• In batch system, time
for a constituent to
reach 1/e of its original
value.
Concentration
c0
e
tchar
tchar
1
=
k1
Time
Filtration “Reaction”
• Removal occurs over space, not time
• Earliest model from Iwasaki, 1937:
dN
= −λN
dx
N (x ) = N in exp(− λx )
or, in full filter :
N out
 L 

= N in exp(− λL ) = N in exp −
 Lchar 
• Characteristic Removal Length = Lchar = 1/λ
Definition: Characteristic Removal Length
 3 (1 − ε )αη 
N out
= exp −
L
N in
 2 dc

Lchar
dc
2
=
3 (1 − ε )αη
 3 (1 − ε )αη 

N out
L 
L = exp −
= exp −

N in
dc
 2

 Lchar 
Decisions
• Characteristic removal length:
Lchar
dc
2
=
3 (1 − ε )αη
• Choice of particle size (η = f ( d p ) )
– For monomedia wastewater filters: dp = 7 µm
– For monomedia drinking water filters: dp = 1 µm
– For dual media filters:
• anthracite dp = 7 µm
• sand dp = 1 µm
• For each particle size, choice of
N out
N in
• For dual media filters, relative sizes of the two media
Removal Efficiency, η
filter
1.0
d = 0.6 mm
c
0.8
v = 5 m/h
0
0.6
ρp = 1.08 g/cm3
0.4
T = 298 K
α=1
L = 60 cm
0.2
0.0
-1.0
Yao
Rajagopalan & Tien
Tufenkji & Elimelech
-0.5
0.0
0.5
A = 1 x 10
-13
H
1.0
1.5
log of Particle Diameter (d in µm)
p
erg
2.0
10
Volume Distribution
(∆V/∆log dp in 106 µm3 cm-3)
Alum Sweep Floc
8
0 min
14 min
6
4
2
0
-0.25
0
0.25 0.5
0.75
1
1.25 1.5
Log of Particle Diameter (dp in µm)
Data from Multimedia Alum Plants
Plant
Glendale,
AZ
California 1
Corvallis,
OR
Spartanburg,
SC
Phoenix,
AZ
Oceanside,
CA
Oakland,
CA
Media
Type
Sand
Anthracite
Sand
Anthracite
Sand
Anthracite
Sand
Anthracite
Sand
Anthracite
Sand
Anthracite
Sand
Anthracite
Effective
Size
(mm)
0.50
0.90
0.60
1.15
0.40
1.05
0.50
1.00
0.46
0.95
0.40
1.00
0.50
0.90
Depth
(cm)
35.6
61.0
30.5
76.2
26.7
49.5
33.0
33.0
25.4
50.8
25.4
45.7
30.5
45.7
L/dc Filtration ηsand
Total Velocity (1 µm)
(--)
(m/h)
ηanth
(7 µm)
1389
11.0
26%
35%
1171
14.7
14%
24%
1138
18.3
26%
19%
991
14.7
22%
16%
1087
14.7
20%
26%
1092
12.2
28%
22%
1118
12.2
22%
27%
Dual media, choose
Media Size
(mm)
d c ,anth = 2d c ,sand
Settling velocity
(cm/s)
Sand
Anthracite
Sand
Anthracite
0.4
0.5
0.8
1.0
5.89
7.59
5.52
7.04
0.6
0.7
1.2
1.4
9.28
10.94
8.51
9.93
g
cm 3
g
= 1.50 3
cm
ρ sand = 2.65
ρ anth
(cm)
req
Required Filter Depth, L
250
d
c,anth
= 2d
v = 10 m/h
c,sand
0
200
150
Anthracite
100
Sand
50
0
0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4
Media Size, d (mm)
c
1.6
(cm)
req
Required Filter Depth, L
250
d
c,anth
200
= 2d
v = 10 m/h
c,sand
0
Total
150
Anthracite
100
Sand
50
0
0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4
Media Size, d (mm)
c
1.6
Required Filter Depth, L
req
(cm)
Dual Media Filter Design: Velocity
250
200
20
15
10
150
5
d
c,anth
= 2d
c,sand
v (m/h)
0
100
50
0
0.3
0.4
0.5
0.6
0.7
Sand Size, d
(mm)
c,sand
0.8
Required Filter Depth, L
req
(cm)
Dual Media Filter Design
250
200
20
15
10
150
5
d
c,anth
= 2d
c,sand
v (m/h)
0
100
L/d = 1000
c
50
0
0.3
0.4
0.5
0.6
0.7
Sand Size, d
(mm)
c,sand
0.8
Required Filter Depth, L
req
(cm)
Current Design Guidelines
500
400
300
200
1500
L/d = 2000
1300
1000
c
100
0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Media Size, d (mm)
c
Summary of This Lchar Proposal
• Know particle characteristics, primarily
particle density
• Choose media size
– For dual media, danth = 2 dsand
• Choose filtration velocity
• Calculate Lchar for dp = 1 µm and 7 µm from
Tufenkji and Elimelech model
• Choose L = 0.29 Lchar
Advantages of This Lchar Proposal
• Much better grounded in filtration theory
than current design guidelines
• More reasonable in accounting for variations
in filtration velocity (and all media and
suspension characteristics)
• Should save on pilot scale tests
• Remarkably, it seems more consistent with
current practice than the simple design
guidelines currently used
Application to slow sand filters
Location
Filtration velocity
(m/h)
0.05
Media depth
(m)
0.30-1.06
Media size
(mm)
0.3
West Hartford,
CT1
0.21
0.61-0.69
0.25-0.35
New Haven, CT1
0.03
0.41-0.56
0.3
Salem, OR2
0.2
0.92
0.3
WWTP Ruhleben,
Berlin, Germany3
0.2-0.25
0.8
1-2
0.2
1.0-1.3
0.15-0.30
0.1-0.3
1
0.15-0.35
Springland, MA1
Kosrae,
Micronesia4
Traditional
design5
Applications to slow sand filters
Characteristics of slow sand filters:
•
•
•
•
•
Far slower velocity ( 0.1 m/h instead of 5 m/h)
Relatively similar depth
Small media size and relatively low porosity
No chemical addition prior to filter
Assume alpha = 0.001
Total filter removal efficiency
1.0
Slow sand filter (Salem OR design)
0.8
0.6
0.4
Yao
Yao
α = 0.01
T&E
α = 0.001
Yao
T&E
0.2
0.0
-2.5 -2.0 -1.5 -1.0 -0.5
0.0
0.5
log of particle diameter (dp in µm)
1.0
1.5
Total filter removal efficiency
1.0
Extremes of slow sand filter design
0.8
New Haven
α = 0.001
0.6
0.4
0.2
Berlin
α = 0.01
0.0
-2.5 -2.0 -1.5 -1.0 -0.5
0.0
0.5
log of particle diameter (dp in µm)
1.0
1.5
Applications to slow sand filters
Results
• Very poor removal with low alpha, especially of small
particles
• What is wrong? Alpha is perhaps much higher
• Why? Conjecture: MOs excrete extracellular polymers
that cover the media and increase alpha
Applications to riverbank filtration
Location
Seepage velocity
(m/h)
Media depth
(m)
Pembrok, NH6
0.46
54.9
Milford, NH6
0.95
22.9
Louisville, KY6
0.51
12.2
Cedar Rapids, IA6
0.16
19.5
Common design7
0.03-1.00
10-600
Media size
(mm)
0.3-0.8
Total filter removal efficiency
Application to riverbank filtration
1.0
0.8
d , v, L, α
c
0.5, 0.5, 10 m, 0.001
or
0.5, 0.5, 100m, 0.0001
0.6
0.4
0.2
0.5, 1.0,
20, 0.0001
0.0
-2.5 -2.0 -1.5 -1.0 -0.5
0.0
0.5
log of particle diameter (dp in µm)
1.0
1.5
Riverbank Filtration (more conjecture)
• These systems behave like gravel flocculators: in the long
run, they don’t remove many small particles, but they
attach small particles that break off as flocs and therefore
show great turbidity reduction.
• They also act as concentration equalization units—holding
up particles in the bank when the concentration is high
and releasing particles when the concentration is low.
• They also are biologically active and release EPS that
contribute to a higher alpha than would otherwise be
present.
THMs for filtration systems
• Chemistry matters (a lot) (and may be influenced
by microbiology)
• Particle size matters (but maybe not quite like the
models suggest)
• Ripening and detachment happen
• Filtration analysis and design should be done
rationally using the characteristic removal length
• Filter systems have more similarities than
differences
Thanks to my Teachers
• Phil Singer
• Charlie O’Melia
•
•
•
•
•
•
•
•
•
Sarah Clark
Bob Cushing
Jeannie Darby
Sara Kau
Ijung Kim
JinKeun Kim
Dan Moran
Melissa Moran
Jeff Nason