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Conference:
Assessing pathogen fate, transport and risk in natural and engineered water treatment
Banff Alberta, Canada September 26, 2012
Jeff D. Senders &
M. R. Collins University of New Hampshire
Department of Civil & Environmental Engineering Durham, NH USA
1
Acknowledgements
The USEPA and TACnet
Prof. J. P. Malley, Jr.
Prof. P. J. Ramsey
Kellen Sawyer
Damon Burt
Varouna Appiah
Durham NH DWTP Operators:
Wes and Brandon 2
Presentation Outline
I. Overview of slow-rate biofilters
(SRBFs) II. Problem statement III. Research objective &
hypotheses IV. Modeling depth filtration in
SRBFs V. Developing and evaluating a
phenomenological SRBF model
VI. Model calibration and validation VII. Application to multiple
organisms VIII. Conclusions
3
Slow-Rate Biofiltration Systems (SRBFs)
http://jhu.edu
http://megphed.gov.in/gallery/sustainsource/slides/sustain4.htm
http://geosciencewater.com
Slow Sand Filtration (SSF)
Riverbank Filtration (RBF) 4
Artificial Recharge Systems (ARS)
Winthrop, Maine SSF
Pawtuckaway State Park, NH
Problem Statement
Even though these robust SRBF systems are among the oldest drinking water treatment technologies in existence, no model
exists that accurately describes microbial removals within SRBFs.
• Depth filtration models predict microbial transport in
saturated granular media. Unfortunately, these models assume the media is clean solid spheres, uniform in size.
• Slow-rate biofilters (SRBFs) utilize non-uniform granular
media and deposited substances at the fluid/media interface to enhance filtration efficiency; however, current filtration models do not account for this removal mechanism.
5
Research Objective
Develop a model that can be used to predict E. coli removals for drinking water treatment
in SRBFs.
6
Source: http://healthierprograms.com
E. coli modeling parameters:
(treated as constants)
Density (ρp) = 1090 kg/m3 Diameter (dp) = 1 x 10-6 m
Working hypotheses in SRBF model
I: Depth filtration can be modeled by accounting for non-uniform media using a surface area per
unit volume (as) designation.
II: Cake filtration is governed by an interfacial ripening phenomenon that can be
qualified/quantified.
7
Modeling depth filtration
∂C/∂L = λC
Integrated:
C/Co = exp-(λL)
= filter coefficient or impediment modulus (Length-1) L = length or depth of filter C = concentration of colloid
Iwasaki, 1937
8
The Filter Coefficient (λ)
Current depth filtration models define the filter coefficient as:
λ = 3(1- Є)ηα /2dc
Where 3(1-Є)/2dc is the Happel Sphere-in-Cell model that is used to represent the surface area per unit volume of uniform media
Є = porosity (unitless)
η = transport efficiency (# ℎ𝑖𝑡𝑠
# 𝑎𝑝𝑝𝑟𝑜𝑎𝑐ℎ𝑒𝑠 = 0 - 1)
α = sticking coefficient (# 𝑠𝑡𝑖𝑐𝑘𝑠
# ℎ𝑖𝑡𝑠 = 0 - 1)
dc = diameter of collector (meters)
Yao, Habibian, O’Melia, 1972
9
Accounting for non-uniform media
SRBFs are not comprised of marbles This necessitates substituting the media surface area per unit volume back in for the Happel Sphere-in-Cell Model
= asηα/Ψ
as = spherical surface area per unit volume (m2/m3m-1)
Ψ = sphericity (0-1) where 1 is a perfect sphere
10
Estimating the media surface area from a sieve analysis
Calculating the surface area per unit volume (as) from a standard sieve analysis
(Assuming the media is spheres of one size between two sieve pans)
as (meters-1) = [∑(# of grains di)( πdi2)]/[(∑ (# of grains di)( πdi
3/6))(Є/(1- Є) + 1)]
di = median diameter between two sieve sizes (meters) Є = media porosity
11
Comparison of media characteristics and hydraulic loading rate between SSF and RBF data sets
Parameter Units SSF RBF ASR
as m2/m3 6,446.92 10,388.79 9,207.45
das mm 0.53 0.38 0.41
d10 mm 0.32 0.14 0.20
d50 mm 0.57 0.65 0.65
UC d60/d10 2.03 5.93 4.25
Є 0.43 0.34 0.37
Ψ 0.84 0.84 0.84
HLR m/hr 0.175 0.045 0.074
0
10
20
30
40
50
60
70
80
90
100
0.01 0.1 1 10 100
% p
as
sin
g
D, mm
Particle Size Distributions of SRBF Media
RBF
SSF
ASR
dc as a function of as (das)
Total Unit Volume (Vt) = Void Volume (Vv) + Volume of Sand (Vs)
Vv = (Є/(1- Є))Vs Vt = (Є/(1- Є))Vs + Vs = Vs((Є/(1- Є)) + 1)
Substitute the volume of a sphere for the volume of sand (Vs)
Vt = πdas3/6((Є/(1- Є)) + 1)
Then the surface area per unit volume (as) may be expressed as
as = πdas2/ (πdas
3/6(Є/(1- Є)) + 1) = 6/das(Є/(1- Є) + 1)
Some algebra and a quick slide of hand
das= 6(1- Є)/as
12
The modified depth filtration model
C/Co = exp
-(asηαL/Ψ)
Within η, substitute dc for das.
das= 6(1- Є)/as
13
Do the modifications help us?
Pilot-scale SRBFs
Slow Sand Filters (SSF)
Riverbank Filter (RBF)
14
Artificial Recharge System (ARS)
The sticking coefficient (α) of pilot-scale SRBFs
15
Modified
The modified model reduces the sticking coefficient by an order of
magnitude and brings mathematical continuity to modeling with non-
uniform media.
α follows a power based trend that is a function of the empty
bed contact time (EBCT)
y = 0.6035x-1.074 R² = 0.8155
0.001
0.010
0.100
1.000
10.000
0 10 20 30 40 50 60
α
EBCT, hrs
α = -ψln(C/Co)/asηL
y = 2.8736x-1.074 R² = 0.8155
0.001
0.010
0.100
1.000
10.000
100.000
0 10 20 30 40 50 60
α
EBCT, hrs
α = -2dasln(C/Co)/3(1-Є)ηL
Traditional
Accounting for cake filtration
16
Changes observed in the sticking coefficient (α) are correlated to biomass, pH, and deposited substances.
0.001
0.010
0.100
1.000
10.000
100.000
1,000.000
0 5 10 15 20 25 30EBCT, hrs
α nmolPO43-/gdw10000[H+]CEC
17
In 1937, Tomihisa Iwasaki proposed a method to account for deposited
substances (specific deposit) that effect the filtration efficiency. He defined the impediment modulus (λ) with the following relationship:
𝝀 = 𝝀𝟎 + 𝒌𝝈 𝜎 = 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑑𝑒𝑝𝑜𝑠𝑖𝑡 𝑝𝑒𝑟 𝑏𝑒𝑑 𝑣𝑜𝑙𝑢𝑚𝑒 𝑖𝑛 𝑢𝑛𝑖𝑡𝑠 𝑜𝑓
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
𝑘 = 𝑟𝑎𝑡𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑑𝑒𝑝𝑜𝑠𝑖𝑡 𝑤𝑖𝑡ℎ 𝑢𝑛𝑖𝑡𝑠 𝑜𝑓 𝜎−1𝑚𝑒𝑡𝑒𝑟𝑠−1
Defining the initial impediment modulus (i.e. depth filtration) as:
𝝀𝟎 =𝒂𝒔𝜼𝜶
𝚿
The proposed generic definition of the impediment modulus for SRBFs then becomes:
𝝀 =𝒂𝒔𝜼𝜶
𝚿+ 𝒌𝝈
Expanding the modified model to account for deposited cake substances:
Phenomenological SRBF Model
Developing a SRBF PhenMod
18
Acknowledging that multiple substances affect filtration efficiency, a generic
form of the impediment modulus can be defined as:
𝝀 = 𝝀𝟎 + 𝒌𝟏𝝈𝟏 + 𝒌𝟐𝝈𝟐 +⋯+ 𝒌𝒏𝝈𝒏
Through some calculus and selecting the concentration of hydrogen ions ([H+]), biomass (Bio), cation exchange capacity (CEC), metal oxides (Mox), and clay/silt (CS)
deposits as modeling parameters, this SRBF PhenMod may be expressed as:
lnC
C0= −
𝑎𝑠𝜂𝛼𝐿
Ψ+ 𝑢
𝑘[𝐻+] 𝜎𝐻+𝑑τ
𝜏
𝜏0+ 𝑘𝐵𝑖𝑜 𝜎𝐵𝑖𝑜𝑑τ
𝜏
𝜏0
+𝑘𝐶𝐸𝐶 𝜎𝐶𝐸𝐶𝑑τ
𝜏
𝜏0
+ 𝑘𝑀𝑜𝑥 𝜎𝑀𝑜𝑥𝑑τ
𝜏
𝜏0
+ 𝑘𝐶𝑆 𝜎𝐶𝑆𝑑τ
𝜏
𝜏0
Where: τ = residence time or empty bed contact time (EBCT, sec)
u = bulk fluid velocity or hydraulic loading rate (HLR, m/sec)
The initial SRBF PhenMod
19
Noting that the specific deposit follows a power-based trend that is a function of residence time or empty bed contact time (EBCT) of the
plug flow reactor, this Phenomenological SRBF Model integrates to:
𝑪
𝑪𝟎= 𝒆−(
𝒂𝒔𝜼𝜶𝑳Ψ
+𝒖𝑲𝒍𝒏𝝉)
τ = EBCT (seconds) u = HLR (m/second)
L (meters) K (meters-1)
A new unknown that might account for surface specific deposit characteristics-
a sight specific parameter.
Initial determination of K
20
Modeling Parameters
Average log removal difference: 0.4
Maximum over estimate: 1.9 log removal There is room for improvement…
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0.0 0.5 1.0 1.5 2.0 2.5 3.0
C/C0
Depth, m
ASR 18C
ASR 23C
ASR 22C
ASR 18C obs
ASR 23C obs
ASR 22C obs
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
C/C0
Depth, m
U-SSF 17C
U-SSF 17C obs
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0 1 2 3 4 5 6
C/C0
Depth, m
RBF 16C
RBF 17C
RBF 16C obs
RBF 17C obs
ASR RBF SSF Units
η 0.0246-0.0409 0.0167-0.0181 0.0064 N/A
α 0.005 0.005 0.005 N/A
u 0.050 0.074 0.193 m/hr
K 1.20E+04 1.20E+04 1.20E+04 m-1
22
Bench-scale results for the rate constant K
Sums of Squares = 4.97 x 109 F Ratio = 88.35
R2adj = 0.57
𝑲 = −[𝟕. 𝟕𝟓 × 𝟏𝟎𝟒 + 𝟗. 𝟎𝟐 × 𝟏𝟎𝟑𝒍𝒏 𝑯𝑳𝑹 ]
Sums of Squares = 6.09 x 108 F Ratio = 127.38
R2adj = 0.66
HLR, m/s HLR, m/s 𝑲 = 𝒆(𝟗.𝟔𝟑−𝟏.𝟏𝟔×𝟏𝟎
𝟖𝑯𝑳𝑹𝟐)
Selected Regression
K K
Number of observations: 65
The current SRBF PhenMod
23
𝑪
𝑪𝟎= 𝒆−(
𝒂𝒔𝜼𝜶𝑳Ψ
+𝒖𝑲𝒍𝒏𝝉)
τ = EBCT (seconds) u = HLR (meters3/meters2-second)
L (meters)
𝑲 = −[𝒄𝟏 + 𝒄𝟐𝒍𝒏 𝑯𝑳𝑹 ]
Average log removal difference 0.09
Maximum log over estimate: 1.75 …getting a little better…
For Durham NH:
c1 ~ 𝟕. 𝟕𝟓 × 𝟏𝟎𝟒
c2 ~ 𝟗. 𝟎𝟐 × 𝟏𝟎𝟑
Application to multiple organisms
24
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0.0 0.5 1.0 1.5 2.0 2.5 3.0
C/Co
Depth, m
Enterococci PhenMod Enterococci
Depth ModEnterococci
Enterococci obs
1.E-02
1.E-01
1.E+00
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
C/Co
Depth, m
Aerobic Spore Forming Bacteria (ASFB)
PhenMod ASFB
Depth Mod ASFB
1.E-02
1.E-01
1.E+00
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
C/Co
Depth, m
MS2
PhenMod MS2
Depth Mod MS2
MS2 obs1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0.00 0.25 0.50 0.75 1.00 1.25
C/Co
Depth, m
Bacillus 17.7C PhenMod11.5C PhenMod5C PhenMod5.5C PhenMod12.9C PhenMod21C PhenMod10.6C PhenMod5C PhenMod17.7C obs11.5C obs5C obs5.5C obs12.9C obs21C obs10.6C obs5C obs
Application to multiple organisms
25
𝑪
𝑪𝟎= 𝒆−(
𝒂𝒔𝜼𝜶𝑳Ψ
+𝒖𝑲𝒍𝒏𝝉)
𝑲 = −[𝒄𝟏 + 𝒄𝟐𝒍𝒏 𝑯𝑳𝑹 ]
Diameter (μm) Density (kg/m3) α c1 c2
1.00 1090 0.005 77500.00 9020.00 0.09 1.75
1.00 1090 0.200 15501.42 1803.91 -0.13 2.67
1.00 1090 0.003 15501.42 1803.91 0.06 0.49
0.50 1090 0.005 77500.00 9020.00 -0.37 -0.25
0.20 1090 0.0005 15501.42 1803.91 0.20 0.50
-0.03 1.03
0.22 1.17
Average log
removal
difference
Maximum log removal
over estimate
overall average
overall standard deviation
ASFB
MS2
SRBF Phenomenological Filtration Modeling Parameters
Enterococci
Organism
E. coli
Bacillus
Conclusions
26
Both cake and depth filtration must be accounted for when
modeling microbial removals in SRBFs.
This SRBF PhenMod is an inexpensive way to estimate microbial removals.
The efficacy of this model can help provide safe potable water to
impecunious regions around the world.
Current research is focusing on increasing model resolution by analyzing various substances within the cake filtration layer.
27
Thank You
Contact information Jeff D. Senders
447 Molyneaux Rd. Camden, ME 04843 USA [email protected]
The Specific Deposit (σ)
28
Based on a mass balance through a differential slice of a filter, the specific deposit may be expressed as:
𝜎𝑡 =𝒟
Є(𝑡 − 𝑡0)𝐶 0 − 𝐶1 𝑑𝑡 + 𝑟
Where:
𝐷𝑖𝑙𝑢𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒 𝒟 =1
𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑐𝑒 𝑡𝑖𝑚𝑒=
1
𝐸𝐵𝐶𝑇=1
𝜏
𝑟 = 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑙𝑎𝑤
𝐶 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 (𝑚𝑎𝑠𝑠
𝑉𝑜𝑙𝑢𝑚𝑒)
Є = 𝑓𝑖𝑙𝑡𝑒𝑟 𝑝𝑜𝑟𝑜𝑠𝑖𝑡𝑦
𝑡 = 𝑓𝑖𝑙𝑡𝑒𝑟 𝑟𝑢𝑛 𝑡𝑖𝑚𝑒
Experimental Approach
30
Phase I: An Interface Study 22 full factorial designed to evaluate the modeling parameters surface
area (as) and hydraulic loading rate (HLR)
*Also used for measurement systems analysis (MSA)
Phases II - IV: Further Assessment of the Interface
Phase II: 23 factorial experiment assessing clays, CEC, and BDOC
Phase III: HLR follow-up and further assessment of CEC and BDOC
Phase V: Validation Model validation using field observations
Phase I
31
VII
Column as HLR
1 + +
2 + +
3 - +
4 - +
5 - -
6 - -
7 + -
8 + -
High (+) Surface
Area (as) 13438.617
m2/m3
Low (-) Surface
Area (as) 4269.583
m2/m3
HLR High (+) = 0.5
m/hr Low (-) = 0.1
m/hr
Phase I Results: HLR is Significant
33
VII
Column As HLR
1 + +
2 + +
3 - +
4 - +
5 - -
6 - -
7 + -
8 + -
Slow Sand Filtration (SSF)
Headspace
Supernatant Water
Schmutzdecke
Raw water
Filter drain & backfill
Sand media
Support gravel
Drain tile
Adjustable weir
Overflow weir
Vent
Control valve
Effluent Flow Control Structure
34
Comparison of Modeling With Different Diameters of SSF
Media
35
00.10.20.30.40.50.60.70.80.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
C/C
o
Depth, m
TE model predictions using differing diameters representative of
Winthrop media
d50
das
d10
da
dc
dg
dSB
Parameters Used in Depth
Model
36
attachment efficiency (α) = 0.005 Hamaker constant = 1E-20
Boltzman constant (Kb) = 1.38E-23 particle diameter (dp) = 1μm
particle density (ρp) = 1090 kg/m3
Ψ
37
Ψ
1
0.95-0.98
0.83-0.94
0.73-0.81
0.65-0.70
0.6
0.43
0.28
Crushed
Jagged (Wilcox sand)
Jagged flakes (Flint sand)
Flakes (Mica)
Description
Spherical
Nearly spherical (Ottawa sand)
Rounded or worn
Angular or Sharp
List of Terms
38
filter coefficient (Length-1
)
η total transport or single collector efficiency, dimensionless
α attachment efficiency or sticking coefficient, dimensionless
L depth of filter, meters
C particle concentration at depth L
Co initial particle concentration
as surface area per unit volume (Length-1
, m2/m
3)
Ψ sphericity (0-1)
Є porosity
γ porosity function, dimensionless
As porosity function, dimensionless
Pe Peclet number, dimensionless
dp diameter of particle, meters
ap radius of particle, meters
ρp density of particle (1090 kg/m3 used)
dc diameter of collector as a function of the Happel Cell, meters
ρc density of collector (sand: ρ = 2650 kg/m3)
Kb Boltzmann constant, 1.3805x10-23
J/K (kg*m2/s
2)
T absolute temperature, (oK= 273.15 +
oC)
vf fluid velocity (m/s)
vs Stoke’s settling velocity (m/s)
μ dynamic viscosity (kg/m*s)
g gravity (9.81 m/s2)
NLo London-van der Waals group, dimensionless
Ha Hamaker constant, 3x10-21
- 4x10-20
J (1x10-20
kg*m2/s
2 used)
Nr or R* relative-size group (dp/dc, dimensionless)
Ng transport efficiency due to gravity, dimensionless
di diameter of media retained in sieve #
at total surface area of sieve analysis (m2)
da arithmetic mean collector diameter
d10 effective size (10% passing by mass)
dsb sphere in box collector diameter
das surface area per volume collector diameter
dg geometric mean collector diameter
d50 50% passing by mass
d60 60% passing by mass
filter coefficient (Length-1
)
η total transport or single collector efficiency, dimensionless
α attachment efficiency or sticking coefficient, dimensionless
L depth of filter, meters
C particle concentration at depth L
Co initial particle concentration
as surface area per unit volume (Length-1
, m2/m
3)
Ψ sphericity (0-1)
Є porosity
γ porosity function, dimensionless
As porosity function, dimensionless
Pe Peclet number, dimensionless
dp diameter of particle, meters
ap radius of particle, meters
ρp density of particle (1090 kg/m3 used)
dc diameter of collector as a function of the Happel Cell, meters
ρc density of collector (sand: ρ = 2650 kg/m3)
Kb Boltzmann constant, 1.3805x10-23
J/K (kg*m2/s
2)
T absolute temperature, (oK= 273.15 +
oC)
vf fluid velocity (m/s)
vs Stoke’s settling velocity (m/s)
μ dynamic viscosity (kg/m*s)
g gravity (9.81 m/s2)
NLo London-van der Waals group, dimensionless
Ha Hamaker constant, 3x10-21
- 4x10-20
J (1x10-20
kg*m2/s
2 used)
Nr or R* relative-size group (dp/dc, dimensionless)
Ng transport efficiency due to gravity, dimensionless
di diameter of media retained in sieve #
at total surface area of sieve analysis (m2)
da arithmetic mean collector diameter
d10 effective size (10% passing by mass)
dsb sphere in box collector diameter
das surface area per volume collector diameter
dg geometric mean collector diameter
d50 50% passing by mass
d60 60% passing by mass
η is a function of a collector diameter (dc)
Differences in diameters used for modeling (d10, d50, d60,..etc.) in non-uniform media confounds comparisons
between researchers.
η = 2.4As1/3Nr
-0.081Pe-0.715NvdW
0.052
+ 0.55AsNr1.675NA
0.125 + 0.22Nr
-0.24Ng1.11NvdW
0.053 or
η = 4[2(1-γ5)/(2-3γ+3γ5-2γ6)]1/3(3μπvfdpdc/KbT)-2/3
+ [2(1-γ5)/(2-3γ+3γ5-2γ6)](4Ha/9πμdp2vf
1/8)(dp/dc)15/8
+ 3.38x10-3[2(1-γ5)/(2-3γ+3γ5-2γ6)](g(ρp-ρw)dp2/18μvf)
1.2(dp/dc)-0.4
Tufenkji & Elimelech, 2004
39
Rapid vs. Slow Rate Biofilters
Slow
40
Rapid
Filtration Mechanisms
Media Characteristics
Hydraulic Loading Rate (HLR)
Empty Bed Contact Time (EBCT)
5 – 30 m3/m2-hr
0.05 - 0.4 m3/m2-hr
Non-uniform UC > 2.5
Cake & Depth
Uniform UC < 2
Depth
Hours-days Minutes
But…
The Happel Sphere-in-Cell Model only applies to solid spheres uniform in size
3(1- Є)/2dc = as
as = surface area per unit volume (meters-1) dc = diameter of collector (meters)
Є = porosity (unitless)
John Happel, 1958
41
Accounting for cake filtration
Clay/silt deposits and higher natural organic matter
(NOM) removals in the upper region of SRBFs corresponds to viable biomass, and an increase in the cation exchange capacity (CEC). The increase in CEC
allows for greater retention of metal oxides and cations. This ripening phenomenon then relates to the enhanced
E. coli removals associated with SRBFs.
42