11.3 Hydraulic Retention Time (HRT), Surface Overflow Rate (SOR) & Weir Overflow Rates

Hydraulic Loading, Retention & Clarification Mechanics

Sedimentation basins, clarifiers, flocculators, and filters depend on specific hydraulic flow regimes to achieve optimal particle settling and filtration efficiency. If flow rates exceed hydraulic design criteria, retention times drop, fluid velocities rise, and floc particles are carried over into effluent launders or driven deep into filter media. Certified operators in Colorado must regularly calculate Hydraulic Retention Time (HRT), Surface Overflow Rate (SOR), Weir Overflow Rate (WOR), and Filter Hydraulic Loading Rates (HLR) to diagnose process upsets and adjust operational unit sequencing.

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Hydraulic Retention Time (HRT) / Detention Time

Hydraulic Retention Time (also termed Detention Time) represents the theoretical average time that a given parcel of water or wastewater resides within a treatment vessel. It is fundamentally calculated as volume divided by flow rate:

$\mathbf{\text{Retention Time} = \frac{\text{Basin Volume}}{\text{Volumetric Flow Rate}}}$

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|                   DETENTION TIME FORMULA VARIATIONS                     |
+-------------------------------------------------------------------------+
| 1. Detention Time in Days:                                              |
|    DT (days)  = Volume (gal) / Flow Rate (gpd)                          |
|    DT (days)  = Volume (MG) / Flow Rate (MGD)                           |
|                                                                         |
| 2. Detention Time in Hours:                                             |
|    DT (hours) = [Volume (gal) × 24 hr/day] / Flow Rate (gpd)            |
|    DT (hours) = [Volume (MG) × 24 hr/day] / Flow Rate (MGD)             |
|                                                                         |
| 3. Detention Time in Minutes:                                           |
|    DT (min)   = [Volume (gal) × 1,440 min/day] / Flow Rate (gpd)        |
|    DT (min)   = Volume (gal) / Flow Rate (gpm)                          |
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Typical Industry Hydraulic Retention Standards

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Clarifier Surface Overflow Rate (SOR) / Hydraulic Loading Rate

The Surface Overflow Rate (SOR)—also termed the Hydraulic Surface Loading Rate—measures the volume of water applied daily per square foot of clarifier surface area:

$\mathbf{\text{SOR (gpd/sq ft)} = \frac{\text{Influent Flow Rate (gpd)}}{\text{Basin Surface Area (sq ft)}} = \frac{\text{Flow (MGD)} \times 1,000,000}{\text{Surface Area (sq ft)}}}$

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|                    CLARIFIER SURFACE AREA FORMULAS                      |
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| Circular Clarifier:     Surface Area (sq ft) = 0.785 × Diameter² (ft²)  |
| Rectangular Clarifier:  Surface Area (sq ft) = Length (ft) × Width (ft) |
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Physical Significance of SOR

Under Hazen's Theory of Ideal Sedimentation, a settling particle will be successfully captured if its downward settling velocity ($v_s$) equals or exceeds the upward hydraulic surface overflow velocity ($v_o = \text{SOR}$). The depth of the basin influences retention time but has no theoretical effect on the critical particle settling velocity cutoff; only surface area determines the overflow velocity threshold. Typical secondary clarifier SOR design values range from 400 to 800 gpd/sq ft under average flow conditions and up to 1,000 to 1,200 gpd/sq ft during peak hydraulic events.

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Weir Overflow Rate (WOR) & Launder Hydraulics

Clarifier effluent is collected across perimeter or inboard v-notch weirs. The Weir Overflow Rate (WOR) (or Weir Loading Rate) measures the volume of clarified effluent passing over each linear foot of weir crest per day:

$\mathbf{\text{WOR (gpd/linear ft)} = \frac{\text{Influent Flow Rate (gpd)}}{\text{Total Active Weir Length (linear ft)}}}$

+-------------------------------------------------------------------------+
|                    WEIR LENGTH DETERMINATION RULES                      |
+-------------------------------------------------------------------------+
| 1. Peripheral Circular Weir (single outer edge):                        |
|    Length (ft) = π × Diameter = 3.1416 × D                              |
|                                                                         |
| 2. Inboard Double-Sided Circular Launder (weir on both walls):          |
|    Length (ft) = (π × D_inner) + (π × D_outer) ≈ 2 × π × D_centerline   |
|                                                                         |
| 3. Rectangular Clarifier End / Finger Weirs:                            |
|    Length (ft) = Sum of all active weir crest edges                     |
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Regulatory Standards: Both CDPHE Design Criteria and the Ten States Standards generally mandate that Weir Overflow Rates not exceed 10,000 to 15,000 gpd/linear foot for standard plants, or 20,000 gpd/linear foot for larger facilities with inboard launders. Excessive WOR generates high localized exit velocities that pull settled sludge up into the effluent trough (scouring/pin floc carryover).

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Granular Media Filter Loading Rate & Backwash Rise Rate

Granular media filters (sand, dual-media anthracite/sand, mixed-media) treat water downward during filtration and expand upward during backwash cycles.

Filter Hydraulic Loading Rate (HLR)

Filter loading rate evaluates flow applied per square foot of media surface area and is expressed in gallons per minute per square foot ($\text{gpm/sq ft}$):

$\mathbf{\text{Filter Loading Rate (gpm/sq ft)} = \frac{\text{Operating Flow Rate (gpm)}}{\text{Filter Surface Area (sq ft)}} = \frac{\text{Flow (gpm)}}{\text{Length (ft)} \times \text{Width (ft)}}}$

• Conventional Rapid Sand Filters: $2.0\text{ to }3.0\text{ gpm/sq ft}$
• High-Rate Dual/Mixed Media Filters: $4.0\text{ to }6.0\text{ gpm/sq ft}$
• Membrane Microfiltration: $0.5\text{ to }1.5\text{ gpm/sq ft}$ (expressed as flux in gfd)

Filter Backwash Rise Rate

During backwash, clean treated water is pumped upward at high rates ($15\text{ to }22\text{ gpm/sq ft}$) to fluidize the media bed and release trapped solids. The upward vertical velocity is termed the Rise Rate and is expressed in inches per minute ($\text{in/min}$):

$\text{Rise Velocity (ft/min)} = \frac{\text{Backwash Rate (gpm/sq ft)}}{7.48\text{ gal/cu ft}}$

$\mathbf{\text{Rise Rate (in/min)} = \frac{\text{Backwash Rate (gpm/sq ft)} \times 12\text{ in/ft}}{7.48\text{ gal/cu ft}} = \text{Backwash Rate (gpm/sq ft)} \times 1.604}$

$\text{Rise Rate (in/min)} = \frac{\text{Total Backwash Flow (gpm)} \times 12\text{ in/ft}}{\text{Filter Area (sq ft)} \times 7.48\text{ gal/cu ft}}$

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Step-by-Step Worked Exam Calculations

Worked Example 1: Rectangular Primary Clarifier HRT & SOR

Problem: A rectangular primary sedimentation basin has interior dimensions of $80.0\text{ ft length}$, $25.0\text{ ft width}$, and a water depth of $12.0\text{ ft}$. The plant flow rate entering this clarifier is $2.40\text{ MGD}$. Calculate:

1. The hydraulic retention time (HRT) in hours.
2. The Surface Overflow Rate (SOR) in gpd/sq ft.

Step 1: Calculate basin surface area and total liquid volume. $\text{Surface Area} = 80.0\text{ ft} \times 25.0\text{ ft} = 2,000.0\text{ sq ft}$ $\text{Volume (cu ft)} = 2,000.0\text{ sq ft} \times 12.0\text{ ft} = 24,000.0\text{ cu ft}$ $\text{Volume (gal)} = 24,000.0\text{ cu ft} \times 7.48\text{ gal/cu ft} = 179,520\text{ gallons}$

Step 2: Calculate Hydraulic Retention Time (HRT) in hours. $\text{HRT (hours)} = \frac{179,520\text{ gal} \times 24\text{ hr/day}}{2,400,000\text{ gpd}} = \frac{4,308,480}{2,400,000} = \mathbf{1.795\text{ hours}} \approx \mathbf{1.80\text{ hours}}\text{ (or } 107.7\text{ min)}$

Step 3: Calculate Surface Overflow Rate (SOR). $\text{SOR (gpd/sq ft)} = \frac{2,400,000\text{ gpd}}{2,000.0\text{ sq ft}} = \mathbf{1,200\text{ gpd/sq ft}}$

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Worked Example 2: Circular Clarifier SOR & Weir Overflow Rate

Problem: A circular secondary clarifier with a diameter of $75.0\text{ ft}$ treats a peak secondary flow of $3.50\text{ MGD}$. Clarified effluent discharges over a peripheral weir running the full circumference of the tank. Calculate:

1. The Surface Overflow Rate (SOR) in gpd/sq ft.
2. The Weir Overflow Rate (WOR) in gpd/linear ft.

Step 1: Calculate surface area. $A = 0.785 \times (75.0\text{ ft})^2 = 0.785 \times 5,625\text{ ft}^2 = 4,415.63\text{ sq ft}$

Step 2: Calculate Surface Overflow Rate (SOR). $\text{SOR} = \frac{3,500,000\text{ gpd}}{4,415.63\text{ sq ft}} = \mathbf{792.6\text{ gpd/sq ft}} \approx \mathbf{793\text{ gpd/sq ft}}$

Step 3: Calculate peripheral weir length. $\text{Weir Length (ft)} = \pi \times D = 3.1416 \times 75.0\text{ ft} = 235.62\text{ linear ft}$

Step 4: Calculate Weir Overflow Rate (WOR). $\text{WOR} = \frac{3,500,000\text{ gpd}}{235.62\text{ ft}} = \mathbf{14,854.4\text{ gpd/linear ft}} \approx \mathbf{14,854\text{ gpd/linear ft}}$

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Worked Example 3: Filter Hydraulic Loading & Backwash Rise Rate

Problem: A dual-media gravity filter cell measures $18.0\text{ ft by } 22.0\text{ ft}$. During standard filtration, the cell processes $1,500\text{ gpm}$. During backwash, the backwash supply pump delivers $6,000\text{ gpm}$. Calculate:

1. The filter hydraulic loading rate in gpm/sq ft.
2. The backwash rise rate in inches per minute (in/min).

Step 1: Calculate filter surface area. $A = 18.0\text{ ft} \times 22.0\text{ ft} = 396.0\text{ sq ft}$

Step 2: Calculate filter loading rate (HLR). $\text{HLR (gpm/sq ft)} = \frac{1,500\text{ gpm}}{396.0\text{ sq ft}} = \mathbf{3.79\text{ gpm/sq ft}}$

Step 3: Calculate backwash loading rate. $\text{Backwash Loading} = \frac{6,000\text{ gpm}}{396.0\text{ sq ft}} = 15.15\text{ gpm/sq ft}$

Step 4: Calculate backwash rise rate in inches per minute. $\text{Rise Rate (in/min)} = \frac{15.15\text{ gpm/sq ft} \times 12\text{ in/ft}}{7.48\text{ gal/cu ft}} = \frac{181.80}{7.48} = \mathbf{24.3\text{ in/min}}$