Predictive Performance Scaling Method
for Hydrodynamic Separators
Mark B. Miller, P.G.
Research Scientist
mmiller@aquashieldinc.com
Chattanooga, Tennessee
(888) 344-9044
EPA Region 6 MS4 Stormwater Conference
July 27 – August 1, 2014
Ft. Worth, Texas
?
How do I predict an HDS performance curve for a different particle
size than the performance curve derived from using the HDS’s lab
test sediment’s particle size distribution?
GET OUT YOUR SLIDE RULE…
OR YOUR TI-30.
Topics of Discussion
 Overview of Hydrodynamic Separators (HDSs)
 The Problem: Evaluating Lab Performance Tests
 A Solution: Performance Prediction Method
 Calculations, Tables & Graphs
 Example Comparison of HDS #1 to HDS #2
 Texas DOT Specification Example for 70% annual
TSS removal and d50 = 75 µm for 38-500 µm PSD
Reference
Derivation
of Peclet
Number
Some Examples of Hydrodynamic Separators
Types of Hydrodynamic Separators
Captures sediment, debris, free-floating oil, floatables
Vortex type =
Vault type =
Gravitational &
Centrifugal Forces
Gravitational Forces
LID Technology Selection Pyramid
Hydrodynamic Separator Applications
Pretreatment or Standalone
On-line
Off-line
HDS Verifications and Use Level Designations
“TARP” (New Jersey)
Technology Acceptance Reciprocity
Partnership Protocol for
Stormwater BMP Demonstrations
 New Jersey DEP Lab Test Protocol for
HDSs 1/25/13 now applies, no field test req’d
 NJ PSD 1-1,000 µm, Scour test 50-1,000
µm for on-line HDS
 NJDEP Certification for HDSs limited to
50% TSS removal credit regardless if higher
rate achieved in lab or field test
 Field test per TARP Tier II 2003/2006
NJDEP 2009 protocol expires w/ new lab test
 Sizing based on MTFR for net annual TSS
removal
“TAPE” (Washington)
Technology Assessment Protocol – Ecology
 Use Level Designations GULD and CULD
require field test in Pacific NW, lab data may
supplement
 PULD based on lab test
 Influent TSS <100 mg/L, Effluent <20 mg/L
 Influent TSS 100-200 mg/L, Effluent ≥80%
removal
 Influent TSS >200 mg/L, Effluent >80%
removal
 ULDs for Dissolved Metals (Cu, Zn), Total
Phosphorus, Oil (TPH), Pretreatment for TSS
 Sizing based on 80% TSS removal per
storm event
Evaluating HDS Laboratory Performance Testing
We’ll explore NJCAT Lab Test Verifications and try to
reduce the level of FRUSTRATION you may have when
evaluating reports and results
HDS Lab Performance Curves from
NJCAT Verification Reports*
100
90
TSS Removal Efficiency (%)
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
Loading Rate (gpm/sqft)
60
* Author does not guarantee accuracy of report interpretations
70
80
HDS Particle Size Distributions for NJCAT
100
90
80
70
% Finer
60
50
40
30
20
10
0
1
10
Particle Size (microns)
* NJDEP 1/25/13 lab protocol d50 <75 µm
100
1,000
Steps for Predictive Performance Method
1. Calculate: Pe = (d · h · Vs) / Q using lab test data
2.
3.
4.
5.
6.
Solve for: Q = (d · h · Vs) / Pe
Convert Q to surface area loading rate (gpm/ft2)
Make table for RE% vs. Loading Rate
Plot performance curve for selected particles size
Make sizing chart(s) for:
a) per storm TSS removal, or
b) annual TSS removal
Peclet Number can be used to predict
performance between different particle sizes
“Peclet Number is defined as the ratio of advection to diffusion,
where advective settling forces are opposed by turbulent diffusion
in the system tending to keep solids in suspension.” (SAFL)
Pe = advection
diffusion
Peclet Number (Pe)
Pe = (d · h · Vs) / Q
Pe = Unitless
d = Horizontal flow dimension in feet
h = Vertical flow dimension in feet
Vs = Particle settling velocity in feet/sec
Q = Flow rate in cubic feet/second
• d in Vortex HDS = diameter of effective treatment area
• d in Vault HDS = long axis of effective treatment area (parallel to flow)
Three Assumptions for Peclet Number (SAFL):
1. Settling Velocity assumes equivalent spherical
particle shapes.
2. Mixing dynamics, and associated removal efficiency,
scales with size (diameter and depth) for each
device.
3. Turbulent diffusion coefficient (Dt) scales with Q/d
across the range of tested flow rates.
Method Variables & Assumptions
1. Stoke’s Law for particle settling velocity using:
a) Specific gravity = 2.65
b) Water temperature 20°C (68°F)
c) Other constant variables for Vs calculation
2. 100% TSS Removal Efficiency @ Zero Loading Rate
3. Calculations based on median (d50) particle size, not full
particle size distribution
4. Performance curve profile does not change for different d50
simulations, but expected to change more as d50
decreases below ~ 50 µm (presently undefined).
Calculate Pe: HDS #1
Test Parameters
Q
(cfs)
Loading Rate
(gpm/ft²)
RE
(%)
Pe
(unitless)
d50 = 110 µm (OK-110)
0
0
100
NA
Vs = 0.021 ft/s
0.20
10.8
89
1.33
SG = 2.65
0.50
27.1
82
0.53
D = 3.3 ft
0.80
43.3
57
0.33
h = 3.83 ft
1.20
64.9
18
0.22
Pe = (d · h · Vs) / Q
Example: Q = 0.2 cfs
Pe = (3.3 ft · 3.83 ft · 0.021 ft/sec) / 0.2 cfs = 1.33
HDS #1 Performance Curve
100
90
TSS Removal Efficiency (%)
80
70
60
50
40
30
20
10
0
0
10
20
30
40
Loading Rate (gpm/sqft)
50
60
70
Calculate Particle Settling Velocity (Vs)
Term
Gs
ρs
ρw
g
T
T
μ
υ
D
Vs
Vs
Vs
Variable
2.65
165.07
62.29
32.20
20.00
68
2.09E-05
1.08E-05
110
0.024
0.02080
0.029
Input Value
Units
Description
Specific gravity of particle
lb/ft3 Density of particle
lb/ft3 Density of water
ft/s2 Acceleration due to gravity
C°
Temperature of water
F°
Temperature of water
lb*s/ft2 Dynamic viscosity of water at given temp.
ft2/s Kinematic Viscosity of water
micron Diameter of particle
ft/s Settling velocity, Cheng Formula
ft/s Settling velocity, Stoke's Law
ft/s Settling velocity, Ferguson & Church
Stoke’s Law Particle Settling Velocities
Particle Size
(µm)
45
50
67
75
90
110
125
Vs
(ft/sec)
0.0085
0.010
0.013
0.014
0.017
0.021
0.024
Performance Summary - 45 µm
Rearrange equation to solve for Q
Q = (3.3 ft · 3.83 ft · Vs) / Pe
RE and Pe constant
Parameters
Q
(cfs)
Loading Rate
(gpm/ft²)
RE
(%)
Pe
(unitless)
d50 = 45 µm
0
0
100
NA
Vs = 0.0085 ft/sec
0.081
4.4
89
1.33
SG = 2.65
0.202
10.9
82
0.53
d = 3.3 ft (8.3 ft2)
0.325
17.5
57
0.33
h = 3.83 ft
0.486
26.3
18
0.22
Loading Rate = Q cfs · 448.83 gpm/cfs / Area ft2
HDS Performance Curves for 45 and 110 µm
100
90
TSS Removal Efficiency (%)
80
70
60
50
40
30
20
10
45µm
110µm
0
0
10
20
30
40
Loading Rate (gpm/sqft)
50
60
70
Parameters
d50 = 50 µm
Vs = 0.010 ft/sec
SG = 2.65
D = 3.3 ft
h = 3.83 ft
Q
(cfs)
0
0.10
0.24
0.38
0.57
50 µm
Loading Rate
(gpm/ft²)
0
5.2
12.9
20.6
30.9
67 µm (d50 from NJDEP PSD)
Q
Loading Rate
Parameters
(cfs)
(gpm/ft²)
d50 = 67 µm
0
0
Vs = 0.0.013 ft/sec
0.124
6.7
SG = 2.65
0.310
16.7
D = 3.3 ft
0.495
26.8
h = 3.83 ft
0.743
40.2
RE
(%)
100
89
82
57
18
Pe
(unitless)
NA
1.33
0.53
0.33
0.22
RE
(%)
100
89
82
57
18
Pe
(unitless)
NA
1.33
0.53
0.33
0.22
Parameters
d50 = 75 µm
Vs = 0.014 ft/sec
SG = 2.65
D = 3.3 ft
h = 3.83 ft
Parameters
d50 = 90 µm
Vs = 0.017 ft/sec
SG = 2.65
D = 3.3 ft
h = 3.83 ft
Q
(cfs)
0
0.133
0.333
0.533
0.800
75 µm
Loading Rate
(gpm/ft²)
0
7.2
18.0
28.9
43.3
RE
(%)
100
89
82
57
18
Pe
(unitless)
NA
1.33
0.53
0.33
0.22
Q
(cfs)
0
0.162
0.405
0.648
0.971
90 µm
Loading Rate
(gpm/ft²)
0
8.8
21.9
35.0
52.6
RE
(%)
100
89
82
57
18
Pe
(unitless)
NA
1.33
0.53
0.33
0.22
Parameters
d50 = 110 µm
Vs = 0.021 ft/sec
SG = 2.65
D = 3.3 ft
h = 3.83 ft
Parameters
d50 = 125 µm
Vs = 0.024 ft/sec
SG = 2.65
D = 3.3 ft
h = 3.83 ft
110 µm (lab test)
Q
Loading Rate
(cfs)
(gpm/ft²)
0
0
0.2
10.8
0.5
27.1
0.8
43.3
1.2
64.9
Q
(cfs)
0
0.229
0.571
0.914
1.371
125 µm
Loading Rate
(gpm/ft²)
0
12.4
30.9
49.5
74.2
RE
(%)
100
89
82
57
18
RE
(%)
100
89
82
57
18
Pe
(unitless)
NA
1.33
0.53
0.33
0.22
Pe
(unitless)
NA
1.33
0.53
0.33
0.22
HDS #1 Performance Summary
45 µm
50 µm
67 µm
75 µm
90 µm
110 µm
125 µm
RE
(%)
LR
gpm/ft2
RE
(%)
LR
gpm/ft2
RE
(%)
LR
gpm/ft2
RE
(%)
LR
gpm/ft2
RE
(%)
LR
gpm/ft2
RE
(%)
LR
gpm/ft2
RE
(%)
LR
gpm/ft2
89
4.4
89
5.2
89
6.7
89
7.2
89
8.8
89
10.8
89
12.4
82
10.9
82
12.9
82
16.7
82
18.0
82
21.9
82
27.1
82
30.9
57
17.5
57
20.6
57
26.8
57
28.9
57
35.0
57
43.3
57
49.5
18
26.3
18
30.9
18
40.2
18
43.3
18
52.6
18
64.9
18
74.2
Note: Removal efficiencies are constant for each particle size
HDS #1 Performance Curves for Different Particle Sizes
100
90
TSS Removal Efficiency (%)
80
70
60
50
40
30
20
45µm
10
50µm
67µm
75µm
90µm
110µm
125µm
0
0
10
20
30
40
Loading Rate (gpm/sqft)
50
60
70
80
HDS Comparison: Lab Test PSDs
100
90
80
HDS #1
70
HDS #2
% Finer
60
50
40
30
20
10
0
1
10
Particle Size (microns)
* NJDEP 1/25/13 lab protocol d50 <75 µm
100
1,000
HDS #2 Performance
HDS #2: 63 µm Lab Test (Calculate Pe)
Q
Loading Rate
RE
Parameters
(cfs)
(gpm/ft²)
(%)
d50 = 63 µm
0
0
100
Vs = 0.013 ft/sec
0.27
6.4
85
SG = 2.65
0.55
12.8
82
D = 5 ft (19.6 ft2)
0.83
19.1
80.2
h = 2.6 ft
1.1
25.5
79
Pe
(unitless)
NA
0.69
0.34
0.23
0.17
HDS #2: Q @ 110 µm by Peclet Method
Q
Loading Rate
RE
Parameters
(cfs)
(gpm/ft²)
(%)
d50 = 110 µm
0
0
100
Vs = 0.021 ft/sec
0.448
11.0
85
SG = 2.65
0.96
22.0
82
D = 5 ft (19.6 ft2)
1.43
32.7
80.2
h = 2.6 ft
1.93
44.2
79
Pe
(unitless)
NA
0.69
0.34
0.23
0.17
Parameters
d50 = 110 µm
Vs = 0.021 ft/sec
SG = 2.65
D = 3.3 ft (8.3 ft2)
h = 3.83 ft
HDS #1: 110 µm Lab Test
Q
Loading Rate
(cfs)
(gpm/ft²)
0
0
0.2
10.8
0.5
27.1
0.8
43.3
1.2
64.9
RE
(%)
100
89
82
57
18
HDS #1: Q @ 63 µm by Peclet Method
Q
Loading Rate
RE
Parameters
(cfs)
(gpm/ft²)
(%)
d50 = 63 µm
0
0
100
Vs = 0.013 ft/sec
0.12
6.5
89
SG = 2.65
0.31
16.8
82
D = 3.3 ft (8.3 ft2)
0.50
27.0
57
h = 3.83 ft
0.75
40.6
18
Pe
(unitless)
NA
1.33
0.53
0.33
0.22
Pe
(unitless)
NA
1.33
0.53
0.33
0.22
HDS #1 and HDS #2 Performance Curves
100
90
HDS #2 110µm
TSS Removal Efficiency (%)
80
70
HDS #2 63µm lab test
60
50
40
30
20
HDS #1 63µm
10
HDS #1 110µm lab test
0
0
10
20
30
40
50
60
Loading Rate (gpm/sqft)
ACME 63 micron
ACME 110 micron
HDS 110 micron
HDS 63 micron
70
HDS #1: 80% TSS Removal Per Storm
100
90
80% TSS Removal Per Storm
TSS Removal Efficiency (%)
80
70
y = -0.0127x2 - 0.4361x + 100
60
50
40
30
20
45µm
10
50µm
67µm
75µm
90µm
110µm
125µm
0
0
10
20
30
40
50
Loading Rate (gpm/sqft)
60
70
80
HDS #1 Particle Size and Peak Loading Rate for
80% TSS Removal Efficiency Per Storm
Particle Size
(µm)
Peak Loading
Rate (gpm/ft2)*
45
50
67
75
90
110
125
10.5
12.2
16.0
17.5
21.0
26.0*
30.0
* Exact Loading Rate can be calculated using
equation for slope of performance curve
Example HDS #1 Sizing Charts: 80% TSS Removal per Storm
Particle Size and Loading Rate
45 µm
50 µm
67 µm
75 µm
90 µm
110 µm
125 µm
10.5
gpm/ft2
12.2
gpm/ft2
16.0
gpm/ft2
17.5
gpm/ft2
21.0
gpm/ft2
26.0
gpm/ft2
30.0
gpm/ft2
WQTF
(cfs)
WQTF
(cfs)
WQTF
(cfs)
WQTF
(cfs)
WQTF
(cfs)
WQTF
(cfs)
WQTF
(cfs)
4.9
0.11
0.13
0.17
0.19
0.23
0.28
0.33
5.0
19.6
0.46
0.53
0.70
0.76
0.92
1.14
1.31
6.0
28.3
0.66
0.77
1.01
1.10
1.32
1.64
1.89
8.0
50.3
1.18
1.37
1.79
1.96
2.35
2.91
3.36
10.0
78.5
1.84
2.13
2.80
3.06
3.67
4.54
5.24
Example
HDS
Model
Diameter
(ft)
Effective
Treatment
Area
(ft2)
2.5
Water Quality Treatment Flow = (Area · Loading Rate) / 448.83 gpm/cfs
Example: WQTF @ 1.4 cfs for 75 µm = HDS Model 8 ft diameter
Special Specification 5848
“The SWTU shall be capable of removing at least 70% of the net annual
Total Suspended Solids (TSS) based on a typical gradation of 38-500
microns with a d50-micron particle size of 75; remove particles greater than
150 –microns (sand-size particles); capture and retain 100% of pollutants
greater than 1 inch in size based on the objects smallest dimension; and
capture and retain total petroleum hydrocarbons.”
Texas DOT Particle Size Distribution 38-500 µm
100
90
80
% Finer
70
60
50
40
30
20
10
0
1
10
100
Particle Size (microns)
Texas DOT PSD
NJDEP (new)
1,000
75 µm TXDOT Specification - HDS #1
Q 75
(cfs)
Loading
Rate
(gpm/ft2)
RE
(%)
Pe
Given
Q 110 µm
(cfs)
Q 75/Q 110
% Flow
75 µm/110 µm
0
0
100
NA
0
NA
0
0.133
7.2
89
1.33
0.2
0.133/0.2
66.5
0.333
18.0
82
0.53
0.5
0.333/0.5
66.6
0.533
28.9
57
0.33
0.8
0.533/0.8
66.6
0.800
43.3
18
0.22
1.2
0.8/1.2
66.7
 HDS lab test showed 80% net annual TSS
removal up to 100 gpm/ft2.
 Make sizing chart based on peak flow, 66.6% of
100 gpm/ft2, or 66.6 gpm/ft2
HDS #1 Performance Curves for 75 µm and 110 µm
100
90
TSS Removal Efficiency (%)
80
70
y = -0.0285x2 - 0.6542x + 100
y = -0.0127x2 - 0.4361x + 100
60
50
40
30
20
80% net annual TSS removal
@ 100 gpm/ft2
10
75µm
110µm
0
0
10
20
30
40
Loading Rate (gpm/sqft)
50
60
70
TXDOT HDS Sizing Chart for HDS #1
80%* Annual TSS Removal for 75 µm
* Exceeds specification of 70% annual TSS removal
HDS Model
Diameter
(ft)
Treatment Area
(ft2)
Water Quality
Treatment Flow @
66.7 gpm/ft2 (cfs)
2.5
4.9
0.73
5.0
19.6
2.92
6.0
28.3
4.20
8.0
50.3
7.47
10.0
78.5
11.67
WQTF = (Treatment Area · Loading Rate) / gpm/cfs
WQTF = (X.X ft2 · 66.7 gpm/ft2) / 448.83 gpm/cfs
Here’s the steps to follow:
1. Calculate: Pe = (d · h · Vs) / Q using lab test data
2.
3.
4.
5.
6.
Solve for: Q = (d · h · Vs) / Pe
Convert Q to surface area loading rate (gpm/ft2)
Make table for RE% vs. Loading Rate
Plot performance curve for selected particles size
Make sizing chart(s) for:
a) per storm TSS removal efficiency, or
b) annual TSS removal efficiency
7. Brag to boss how you solved a mystery of
stormwater life
Mark Miller
mmiller@aquashieldinc.com