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
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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
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)
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
Now what, calibration?
21
Bench-scale experiments were designed and executed for model calibration.
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…