Solids Retention Time MCRT Calculator

The Solids Retention Time and MCRT Calculator answers two questions about an activated-sludge solids inventory. Given the solids you are holding and the solids leaving each day, how many days is the average particle staying in the system? And, running it the other way, what waste flow would you have to pull to hit a target SRT?

In actual mode it reports the solids retention time in days, the total system solids inventory, the daily solids loss split between the waste stream and the effluent, the share each of those carries, and the daily turnover as the reciprocal of SRT. In planning mode it reports the allowed daily loss at your target, the waste flow required to produce it, and whether that solution exists at all.

Inventory can come from aeration volume times mixed-liquor concentration plus an optional additional mass, or from a total system mass you enter directly. Everything runs on either a total-solids or a volatile-solids basis, in US customary or SI units.

Purpose and model boundary

This calculator evaluates actual solids retention time/mean cell residence time (SRT/MCRT) from system solids inventory and daily waste/effluent solids losses, or solves the nonnegative waste flow required for a user-entered target SRT. Inventory can be calculated from volume and concentration plus an additional mass or entered directly.

The result is a solids mass-balance indicator for the entered system boundary and TSS/MLSS or VSS/MLVSS basis. It is not hydraulic retention time, an operating recommendation, or proof of biological treatment performance.

Inputs and units

• Unit system selects US customary or SI metric flow, volume, and mass labels. It does not convert values already entered.
• Calculation mode selects actual SRT/MCRT or required waste flow for a target SRT.
• Solids basis selects consistent TSS/MLSS or VSS/MLVSS labels; it does not change the arithmetic.
• Inventory method uses aeration volume, mixed-liquor concentration, and optional additional solids mass, or a direct total system mass.
• Waste and effluent flows are in MGD or m3/day; their solids concentrations are in mg/L on the selected basis.
• Actual-mode target minimum/maximum and planning-mode target SRT are in days and must be site-entered values.

The US mass factor is exactly 8.34540445201933 lb / (MG x mg/L); the SI factor is 0.001 kg / (m3 x mg/L).

Governing relationships

With unit factor k, calculated inventory is

M_primary = V_aeration x X_mixed-liquor x k

and

M_total = M_primary + M_additional.

Direct-inventory mode instead uses M_total = M_direct. Daily solids losses are

L_waste = Q_waste x X_waste x k;

L_effluent = Q_effluent x X_effluent x k;

L_total = L_waste + L_effluent.

Actual SRT and turnover are

SRT = M_total / L_total

and

daily solids turnover = 1 / SRT.

Waste- and effluent-loss shares divide their respective loss by L_total.

In planning mode for target SRT_t:

L_planned = M_total / SRT_t;

L_waste,raw = L_planned - L_effluent;

L_waste,required = max(L_waste,raw, 0) within the workbook tolerance;

Q_waste,required = L_waste,required / (X_waste x k).

The planning tolerance is 1e-12 x max(abs(L_planned), abs(L_effluent)). Actual target-band comparisons use 1e-12 x max(1, abs(SRT), abs(target minimum), abs(target maximum)).

Calculation sequence

1. Resolve unit, calculation, solids-basis, inventory, and active comparison branches; hidden branch fields are ignored.
2. Validate nonnegative active plant quantities and calculate or accept total system inventory.
3. Calculate effluent loss and, in actual mode, waste loss and total daily loss.
4. In actual mode, divide positive inventory by positive daily loss, calculate turnover/shares, and optionally compare with an ordered target band.
5. In planning mode, divide inventory by target SRT, subtract effluent loss, apply the 1e-12 planning tolerance, and divide the required nonnegative waste loss by waste concentration and unit factor.
6. Build the published waste-flow sensitivity chart and evaluate status in the exact order below.

Outputs and interpretation

Total inventory and the two daily loss outputs expose the mass-balance boundary. Actual SRT/MCRT is in days; turnover is its reciprocal. Loss shares show which exit governs the daily loss. Inventory basis identifies the selected TSS/VSS branch and inventory method.

Planning outputs report planned total daily loss, required waste solids loss, required waste flow, and a feasibility interpretation. INFEASIBLE: EFFLUENT LOSS EXCEEDS ALLOWANCE means the entered effluent loss alone is greater than the total loss permitted by the target, within tolerance; increasing waste cannot solve that condition.

Validation and status logic

The workbook evaluates status in this order:

The planning and actual branches are mutually exclusive after the first two common checks. Within each branch, earlier rows take precedence.

Assumptions and limitations

Inventory and every loss must use one consistent TSS/MLSS or VSS/MLVSS basis and the same daily time basis. The modeled boundary must include all intended solids inventory and exits. Additional inventory is assumed to be an independently estimated mass within that boundary.

Planning holds inventory, effluent flow/concentration, and waste concentration fixed while solving waste flow. The model does not project how those quantities respond to a changed wasting rate. It excludes solids in unmodeled units/streams, recycle effects on the system boundary, growth/decay kinetics, temperature, nitrification targets, settleability, hydraulic residence time, and universal SRT ranges.

Restrictions and non-computing states

All active plant quantities are nonnegative. Total inventory must be positive. Actual mode requires positive combined daily loss. Planning requires positive target SRT and waste concentration. If effluent loss exceeds the target's allowed total loss beyond tolerance, the requested target is infeasible under the fixed planning assumptions.

Actual target comparison requires a nonnegative minimum strictly below a nonnegative maximum. Unit-system changes alter labels and factors but do not convert submitted values. Very large finite values can leave the primary result valid while making the sensitivity chart nonnumeric, producing the documented chart-range warning.

Errors and warnings

This calculator's input rules can reject out-of-domain values or unknown options before calculation. A workbook NOT VALID response means a required mass-balance denominator or active state is unusable. A workbook CHECK response identifies a computed zero-loss path, target shortfall, planning infeasibility, or chart-range issue. A connection or calculation-service failure is not an SRT result.

The workbook implements the mass-balance definition of SRT and MCRT and the exact dimensional conversions behind its mass factor. No operating range, design table or figure from any publication is reproduced.

• U.S. Environmental Protection Agency. Field Study Training Program, Volume II, the federal MCRT mass-balance equation, the consistent solids-basis requirement, and the 1.0 MG at 2,400 mg/L worked example replayed above. https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=94002GLG.TXT
• U.S. Environmental Protection Agency. Field Study Training Program, Volume I, for the definition of mean cell residence time as process solids inventory divided by solids removed per day. https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=94002G8S.TXT
• California State Water Resources Control Board. Wastewater Formula Sheet, a government cross-check confirming that system inventory may include clarifier as well as aeration solids, and that daily loss includes both waste and effluent solids. https://www.waterboards.ca.gov/water_issues/programs/operator_certification/docs/proposed_equivalent_formula_sheet.pdf
• Michigan Department of Environment, Great Lakes, and Energy. Wastewater Operations Formula Sheet, a current state cross-check on cell-retention-time and mass-loading relations. https://www.michigan.gov/egle/-/media/Project/Websites/egle/Documents/Programs/WRD/Operator-Certification/Wastewater-Operations-Formula-Sheet.pdf
• National Institute of Standards and Technology. Handbook 133, Appendix E: General Tables of Units of Measurement, which fixes the US gallon at exactly 3.785411784 litres and the international pound at exactly 0.45359237 kilograms. https://www.nist.gov/document/14-app-e-14-hb133-finalpdf

No target SRT is supplied or implied. The band you compare against is your own.