Predictive Performance Scaling Method

for Hydrodynamic Separators

Mark B. Miller, P.G.Research Scientist

mmiller@aquashieldinc.comChattanooga, Tennessee

(888) 344-9044

EPA Region 6 MS4 Stormwater ConferenceJuly 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

Vortex type = Gravitational &

Centrifugal Forces

Captures sediment, debris, free-floating oil, floatables

Vault type = Gravitational Forces

LID Technology Selection Pyramid

Pretreatment or Standalone

Hydrodynamic Separator Applications

Off-lineOn-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

0 10 20 30 40 50 60 70 800

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100

HDS Lab Performance Curves fromNJCAT Verification Reports*

Loading Rate (gpm/sqft)

TSS

Rem

oval

Effi

cien

cy (%

)

* Author does not guarantee accuracy of report interpretations

1 10 100 1,0000

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70

80

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100HDS Particle Size Distributions for NJCAT

Particle Size (microns)

% F

iner

* NJDEP 1/25/13 lab protocol d50 <75 µm

Steps for Predictive Performance Method

1. Calculate: Pe = (d · h · Vs) / Q using lab test data

2. Solve for: Q = (d · h · Vs) / Pe3. Convert Q to surface area loading rate

(gpm/ft2)4. Make table for RE% vs. Loading Rate5. Plot performance curve for selected

particles size6. Make sizing chart(s) for:

a) per storm TSS removal, orb) annual TSS removal

Peclet Number can be used to predict performance between different particle

sizes

Pe = advection diffusion

“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)

Peclet Number (Pe)

Pe = (d · h · Vs) / Q

Pe = Unitlessd = Horizontal flow dimension in feeth = Vertical flow dimension in feetVs = Particle settling velocity in feet/secQ = 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 = 2.65b) Water temperature 20°C (68°F)c) Other constant variables for Vs calculation

2. 100% TSS Removal Efficiency @ Zero Loading Rate3. Calculations based on median (d50) particle size, not full

particle size distribution4. 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 ParametersQ

(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

Example: Q = 0.2 cfsPe = (3.3 ft · 3.83 ft · 0.021 ft/sec) / 0.2 cfs = 1.33

Pe = (d · h · Vs) / Q

0 10 20 30 40 50 60 700

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100HDS #1 Performance Curve

TS

S R

emov

al E

ffic

ien

cy (

%)

Loading Rate (gpm/sqft)

Term Variable Units DescriptionGs 2.65 Specific gravity of particleρs 165.07 lb/ft3 Density of particleρw 62.29 lb/ft3 Density of waterg 32.20 ft/s2 Acceleration due to gravityT 20.00 C° Temperature of waterT 68 F° Temperature of waterμ 2.09E-05 lb*s/ft2 Dynamic viscosity of water at given temp.υ 1.08E-05 ft2/s Kinematic Viscosity of waterD 110 micron Diameter of particleVs 0.024 ft/s Settling velocity, Cheng FormulaVs 0.02080 ft/s Settling velocity, Stoke's LawVs 0.029 ft/s Settling velocity, Ferguson & Church

Calculate Particle Settling Velocity (Vs)

Input Value

Particle Size (µm)

Vs(ft/sec)

45 0.008550 0.01067 0.01375 0.01490 0.017110 0.021125 0.024

Stoke’s Law Particle Settling Velocities

Performance Summary - 45 µm

ParametersQ

(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

Rearrange equation to solve for QQ = (3.3 ft · 3.83 ft · Vs) / Pe

RE and Pe constant

Loading Rate = Q cfs · 448.83 gpm/cfs / Area ft2

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100HDS Performance Curves for 45 and 110 µm

TS

S R

emov

al E

ffic

ien

cy (

%)

Loading Rate (gpm/sqft)

45µm 110µm

50 µm

ParametersQ

(cfs)Loading Rate

(gpm/ft²)RE(%)

Pe(unitless)

d50 = 50 µm 0 0 100 NAVs = 0.010 ft/sec 0.10 5.2 89 1.33

SG = 2.65 0.24 12.9 82 0.53D = 3.3 ft 0.38 20.6 57 0.33h = 3.83 ft 0.57 30.9 18 0.22

67 µm (d50 from NJDEP PSD)

ParametersQ

(cfs)Loading Rate

(gpm/ft²)RE(%)

Pe(unitless)

d50 = 67 µm 0 0 100 NAVs = 0.0.013 ft/sec 0.124 6.7 89 1.33

SG = 2.65 0.310 16.7 82 0.53D = 3.3 ft 0.495 26.8 57 0.33h = 3.83 ft 0.743 40.2 18 0.22

75 µm

ParametersQ

(cfs)Loading Rate

(gpm/ft²)RE(%)

Pe(unitless)

d50 = 75 µm 0 0 100 NAVs = 0.014 ft/sec 0.133 7.2 89 1.33

SG = 2.65 0.333 18.0 82 0.53D = 3.3 ft 0.533 28.9 57 0.33h = 3.83 ft 0.800 43.3 18 0.22

90 µm

ParametersQ

(cfs)Loading Rate

(gpm/ft²)RE(%)

Pe(unitless)

d50 = 90 µm 0 0 100 NAVs = 0.017 ft/sec 0.162 8.8 89 1.33

SG = 2.65 0.405 21.9 82 0.53D = 3.3 ft 0.648 35.0 57 0.33h = 3.83 ft 0.971 52.6 18 0.22

110 µm (lab test)

ParametersQ

(cfs)Loading Rate

(gpm/ft²)RE(%)

Pe(unitless)

d50 = 110 µm 0 0 100 NAVs = 0.021 ft/sec 0.2 10.8 89 1.33

SG = 2.65 0.5 27.1 82 0.53D = 3.3 ft 0.8 43.3 57 0.33h = 3.83 ft 1.2 64.9 18 0.22

125 µm

ParametersQ

(cfs)Loading Rate

(gpm/ft²)RE(%)

Pe(unitless)

d50 = 125 µm 0 0 100 NAVs = 0.024 ft/sec 0.229 12.4 89 1.33

SG = 2.65 0.571 30.9 82 0.53D = 3.3 ft 0.914 49.5 57 0.33h = 3.83 ft 1.371 74.2 18 0.22

45 µm 50 µm 67 µm 75 µm 90 µm 110 µm 125 µm

RE (%)

LRgpm/ft2

RE (%)

LRgpm/ft2

RE (%)

LRgpm/ft2

RE (%)

LRgpm/ft2

RE (%)

LRgpm/ft2

RE (%)

LRgpm/ft2

RE (%)

LRgpm/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

HDS #1 Performance Summary

Note: Removal efficiencies are constant for each particle size

0 10 20 30 40 50 60 70 800

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100HDS #1 Performance Curves for Different Particle Sizes

TS

S R

emov

al E

ffic

ien

cy (

%)

Loading Rate (gpm/sqft)

45µm 50µm 67µm 75µm 90µm 110µm 125µm

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100HDS Comparison: Lab Test PSDs

Particle Size (microns)

% F

iner

HDS #2

HDS #1

* NJDEP 1/25/13 lab protocol d50 <75 µm

HDS #2: 63 µm Lab Test (Calculate Pe)

ParametersQ

(cfs)Loading Rate

(gpm/ft²)RE(%)

Pe(unitless)

d50 = 63 µm 0 0 100 NAVs = 0.013 ft/sec 0.27 6.4 85 0.69

SG = 2.65 0.55 12.8 82 0.34D = 5 ft (19.6 ft2) 0.83 19.1 80.2 0.23

h = 2.6 ft 1.1 25.5 79 0.17

HDS #2: Q @ 110 µm by Peclet Method

ParametersQ

(cfs)Loading Rate

(gpm/ft²)RE(%)

Pe(unitless)

d50 = 110 µm 0 0 100 NAVs = 0.021 ft/sec 0.448 11.0 85 0.69

SG = 2.65 0.96 22.0 82 0.34D = 5 ft (19.6 ft2) 1.43 32.7 80.2 0.23

h = 2.6 ft 1.93 44.2 79 0.17

HDS #2 Performance

HDS #1: 110 µm Lab Test

ParametersQ

(cfs)Loading Rate

(gpm/ft²)RE(%)

Pe(unitless)

d50 = 110 µm 0 0 100 NAVs = 0.021 ft/sec 0.2 10.8 89 1.33

SG = 2.65 0.5 27.1 82 0.53D = 3.3 ft (8.3 ft2) 0.8 43.3 57 0.33

h = 3.83 ft 1.2 64.9 18 0.22

HDS #1: Q @ 63 µm by Peclet Method

ParametersQ

(cfs)Loading Rate

(gpm/ft²)RE(%)

Pe(unitless)

d50 = 63 µm 0 0 100 NAVs = 0.013 ft/sec 0.12 6.5 89 1.33

SG = 2.65 0.31 16.8 82 0.53D = 3.3 ft (8.3 ft2) 0.50 27.0 57 0.33

h = 3.83 ft 0.75 40.6 18 0.22

0 10 20 30 40 50 60 700

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100

HDS #1 and HDS #2 Performance Curves

ACME 63 micron Polynomial (ACME 63 micron)ACME 110 micron Polynomial (ACME 110 micron)HDS 110 micron Polynomial (HDS 110 micron)HDS 63 micron Polynomial (HDS 63 micron)

Loading Rate (gpm/sqft)

TSS

Rem

oval

Effi

cien

cy (%

)

HDS #1 110µm lab testHDS #1 63µm

HDS #2 63µm lab test

HDS #2 110µm

0 10 20 30 40 50 60 70 800

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100f(x) = − 0.0126794752977604 x² − 0.436147324269111 x + 100

HDS #1: 80% TSS Removal Per StormT

SS

Rem

oval

Eff

icie

ncy

(%

)

Loading Rate (gpm/sqft)

45µm 50µm 67µm 75µm 90µm 110µm 125µm

80% TSS Removal Per Storm

HDS #1 Particle Size and Peak Loading Rate for

80% TSS Removal Efficiency Per StormParticle Size

(µm)Peak Loading

Rate (gpm/ft2)*

45 10.5

50 12.2

67 16.0

75 17.5

90 21.0

110 26.0*

125 30.0

* Exact Loading Rate can be calculated using equation for slope of performance

curve

Example HDS

Model Diameter

(ft)

Effective Treatment

Area(ft2)

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)

2.5 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 5.24Water Quality Treatment Flow = (Area · Loading Rate) / 448.83 gpm/cfsExample: WQTF @ 1.4 cfs for 75 µm = HDS Model 8 ft diameter

Example HDS #1 Sizing Charts: 80% TSS Removal per Storm

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.”

1 10 100 1,0000

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Texas DOT Particle Size Distribution 38-500 µm

Texas DOT PSD NJDEP (new)

Particle Size (microns)

% F

iner

75 µm TXDOT Specification - HDS #1

Q 75(cfs)

Loading Rate

(gpm/ft2)

RE (%)

PeGiven

Q 110 µm (cfs)

Q 75/Q 110 % Flow75 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

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100f(x) = − 0.0126794752977603 x² − 0.436147324269114 x + 100f(x) = − 0.0285288194199583 x² − 0.654220986403729 x + 100

HDS #1 Performance Curves for 75 µm and 110 µmT

SS

Rem

oval

Eff

icie

ncy

(%

)

Loading Rate (gpm/sqft)

75µm 110µm80% net annual TSS removal

@ 100 gpm/ft2

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/cfsWQTF = (X.X ft2 · 66.7 gpm/ft2) / 448.83 gpm/cfs

TXDOT HDS Sizing Chart for HDS #180%* Annual TSS Removal for 75 µm

* Exceeds specification of 70% annual TSS removal

Here’s the steps to follow:

1. Calculate: Pe = (d · h · Vs) / Q using lab test data

2. Solve for: Q = (d · h · Vs) / Pe3. Convert Q to surface area loading rate

(gpm/ft2)4. Make table for RE% vs. Loading Rate5. Plot performance curve for selected

particles size6. Make sizing chart(s) for:

a) per storm TSS removal efficiency, orb) annual TSS removal efficiency

7. Brag to boss how you solved a mystery of stormwater life

Mark Miller mmiller@aquashieldinc.com