Sludge Volume Index Settleability Calculator

The Sludge Volume Index Settleability Calculator turns one settling-column test on mixed liquor into the sludge volume index and the companion settleability numbers that come out of the same one-litre sample. You give it the settled volume after 30 minutes and the MLSS of the sample that went into the cylinder, and it reports SVI in millilitres per gram, the sludge density index, the settled solids concentration in grams per litre and as percent weight per volume, the settled volume fraction, and the average 30-minute settling rate.

The 30-minute volume can come from a single direct reading, or from a fixed nine-point settling curve at 5, 10, 15, 20, 25, 30, 40, 50 and 60 minutes. In curve mode the tool takes the 30-minute row for every result and separately reports whether any later reading rose above the one before it.

Use it for day-to-day activated-sludge process control. It classifies nothing on its own: there is no bulking or pin-floc verdict here, and the only comparison it offers is against a maximum SVI that you enter yourself.

Purpose and model boundary

This calculator derives sludge volume index (SVI) and related one-litre settleability indicators from MLSS and a 30-minute settled-volume observation. The observation can be entered directly or as part of a fixed nine-point, 60-minute settling curve. An optional user-entered maximum provides a comparison only.

The model summarizes one sample and test. It does not diagnose a settling problem, prescribe an operating range, or substitute for process observations, microscopy, or site-specific troubleshooting.

Inputs and units

• Entry mode selects a direct 30-minute reading or the full 60-minute settling curve.
• MLSS, X, is the concentration of the same representative, well-mixed sample in mg/L.
• Settled volume, V30, is the sludge volume after 30 minutes in a one-litre test, in mL/L.
• Full-curve mode uses exactly the authored times 5, 10, 15, 20, 25, 30, 40, 50, 60 minutes and one settled-volume value from 0 through 1000 mL/L at each time.
• The optional maximum SVI reference is a positive, site-entered value in mL/g. The workbook contains no default process criterion.

Governing relationships

The workbook uses 1000 mg/g and a 1000 mL/L one-litre test basis. Its exact relationships are

SVI (mL/g) = V30 (mL/L) x 1000 / X (mg/L);

sludge density index (g/100 mL) = 100 / SVI;

settled volume fraction = V30 / 1000;

settled solids concentration (g/L) = X / V30;

settled solids (% w/v) = X / (V30 x 10);

30-minute settling rate (mL/L/hour) = (1000 - V30) / 0.5.

When comparison is active,

reference ratio = SVI / maximum entered SVI.

For a full curve, the workbook also checks that every observation is no greater than the preceding observation. The chart intentionally contains only the initial one-litre endpoint (0 min, 1000 mL/L) and the active 30-minute endpoint; it is not a plot of all nine curve observations.

Calculation sequence

1. Resolve direct or full-curve mode and validate positive MLSS.
2. In direct mode, validate the direct V30. In curve mode, require all nine numeric volumes and the exact fixed nine-time schedule, then take row 6 as the 30-minute value.
3. Calculate SVI, density index, settled fraction, settled-solids concentration/percent, and average 30-minute settling rate.
4. In full-curve mode, compare each volume with the preceding observation to classify the curve as nonincreasing or increasing/reversing.
5. If requested, calculate the reference ratio and comparison result.
6. Build the two-point endpoint chart and evaluate status in the order below.

Outputs and interpretation

SVI expresses the 30-minute settled volume per gram of MLSS. Density index is the workbook's reciprocal index; settled-solids concentration and percent restate the same one-litre mass/volume relationship. Settled volume fraction is the occupied fraction at 30 minutes. The settling-rate output is only the average change from 1000 to V30 over the first 0.5 hour.

Curve condition reports NONINCREASING, CHECK INCREASE / REVERSAL, or NOT AVAILABLE. Reference results are AT OR BELOW ENTERED REFERENCE, ABOVE ENTERED REFERENCE, NOT REQUESTED, or NOT AVAILABLE.

Validation and status logic

The workbook evaluates status in this order:

The curve-shape warning precedes the reference warning if both conditions are true.

Assumptions and limitations

The settling test is assumed to use a representative, initially well-mixed one-litre sample, and MLSS must come from the same sample. Times and volume units follow the standard one-litre test basis. Full-curve values are treated as observations, not smoothed or fitted data.

SVI alone does not identify filamentous bulking, denitrification, pin floc, dispersed growth, compression, or zone-settling velocity. The model excludes diluted SVI, stirred SVI, settling-column geometry, temperature correction, blanket behavior, and universal acceptable ranges. The average first-30-minute rate is not a zone-settling regression.

Restrictions and non-computing states

MLSS and the active 30-minute volume must be positive because the reciprocal calculations otherwise divide by zero. Settled volumes are limited to 0 through 1000 mL/L; in full-curve mode only the 30-minute point must be strictly positive, but all nine values and exact times are required. The time column is part of the fixed workbook layout and is not an arbitrary schedule.

An increasing curve is still numerically computable and therefore returns CHECK, not NOT VALID. A reference is optional, but when selected it must be positive.

Errors and warnings

This calculator can refuse out-of-range scalar/grid values or a misshaped grid before calculation. Workbook NOT VALID means the active test data cannot support its reciprocal formulas. Workbook CHECK means SVI is computable but the curve or entered comparison needs review. A connection or calculation-service failure is not a settleability classification.

The workbook implements the settling-test relations directly and reproduces no table, chart, operating band or figure from any publication. SVI is the 30-minute settled volume times 1000 divided by MLSS; the density index, settled solids concentration and settling rate are that same one-litre mass balance rearranged.

• U.S. Environmental Protection Agency. Field Manual for Performance Evaluation and Troubleshooting at Municipal Wastewater Treatment Facilities, which defines SVI as 30-minute settled volume times 1000 divided by MLSS and carries the 200 mL/L at 2,500 mg/L worked example reproduced above. https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=2000C1E0.txt
• U.S. Environmental Protection Agency. Process Control Manual for Aerobic Biological Wastewater Treatment Facilities, for the one-litre settling-test timing, the settled-solids concentration and settling-rate relations, and the limitations of a single 30-minute index. https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=9100NX8X.TXT
• Wikipedia. Sludge volume index. https://en.wikipedia.org/wiki/Sludge_volume_index
• Wikipedia. Activated sludge, for where settleability sits in the process. https://en.wikipedia.org/wiki/Activated_sludge

No operating band, target SVI or settleability classification is shipped with this calculator. Any maximum you compare against is your own site value.