Calculate the Food to Microorganism (F/M) ratio for activated sludge systems.
Volume of wastewater entering the system per day (m³/day)
Biochemical Oxygen Demand in the influent (mg/L)
Total volume of the aeration basin (m³)
Concentration of suspended solids in the reactor (mg/L)
function calculateSludgeLoading() {
var flowRate = document.getElementById('flowRate').value;
var bod = document.getElementById('bodInput').value;
var volume = document.getElementById('tankVolume').value;
var mlss = document.getElementById('mlssInput').value;
var resultDiv = document.getElementById('result');
// Validation
if (flowRate === "" || bod === "" || volume === "" || mlss === "") {
resultDiv.style.display = "block";
resultDiv.innerHTML = "Please fill in all fields.";
return;
}
var q = parseFloat(flowRate);
var b = parseFloat(bod);
var v = parseFloat(volume);
var m = parseFloat(mlss);
if (v <= 0 || m <= 0) {
resultDiv.style.display = "block";
resultDiv.innerHTML = "Volume and MLSS must be greater than zero.";
return;
}
// Calculation Logic
// 1. Calculate Mass of BOD (Food) in kg/day
// Formula: (Flow m3/d * BOD mg/L) / 1000 = kg/day
var massBOD = (q * b) / 1000;
// 2. Calculate Mass of MLSS (Microorganisms) in kg
// Formula: (Volume m3 * MLSS mg/L) / 1000 = kg
var massMLSS = (v * m) / 1000;
// 3. Calculate F/M Ratio (Sludge Loading Rate)
// Formula: Mass BOD / Mass MLSS
var fmRatio = massBOD / massMLSS;
// Determine Process Type Estimation
var processType = "Unknown Range";
if (fmRatio = 0.05 && fmRatio 0.15 && fmRatio 0.5 && fmRatio <= 1.5) {
processType = "High Rate Aeration";
} else {
processType = "Very High Rate (Dispersed)";
}
// Output Construction
var htmlOutput = "
The Sludge Loading Rate (SLR), commonly referred to as the Food to Microorganism (F/M) ratio, is a critical parameter in the design and operation of biological wastewater treatment processes, specifically the activated sludge system. It represents the amount of organic "food" (measured as Biochemical Oxygen Demand or BOD) entering the system relative to the quantity of microorganisms (biomass) available in the aeration tank to consume that food.
Maintaining the correct SLR ensures that the bacteria decompose organic matter efficiently while settling properly in the secondary clarifier. If the rate is too high, the bacteria multiply rapidly but do not form dense flocs, leading to poor settling. If the rate is too low, the bacteria may begin to consume their own cell mass (endogenous respiration), leading to "pin-floc" and turbid effluent.
The Formula
The calculation for the F/M ratio is derived by dividing the daily mass of organic load by the total mass of microbes in the system. The standard formula is:
F/M = (Q × BOD) / (V × MLSS)
Where:
Q = Influent Flow Rate (m³/day)
BOD = Influent BOD₅ Concentration (mg/L)
V = Volume of the Aeration Tank (m³)
MLSS = Mixed Liquor Suspended Solids (mg/L)
Note: Since mg/L is equivalent to g/m³, the conversion factors usually cancel out, leaving the unit as kg BOD per kg MLSS per day (d⁻¹).
Typical Ranges for Activated Sludge Processes
Different variations of the activated sludge process operate effectively at different F/M ratios. Operators use these ranges to diagnose system health:
Extended Aeration: 0.05 – 0.15 kg BOD/kg MLSS/day. This process has a long retention time, resulting in less sludge production but higher aeration costs.
Conventional Activated Sludge: 0.2 – 0.5 kg BOD/kg MLSS/day. This is the standard range for municipal wastewater treatment plants.
High Rate Aeration: 0.5 – 1.5 kg BOD/kg MLSS/day. Used when partial treatment is acceptable or space is very limited.
Why Calculate Sludge Loading Rate?
Wastewater operators perform this calculation daily or weekly to determine if they need to adjust the wasting rate (WAS).
To Increase F/M: Increase the wasting rate. This removes biomass from the system (lowering the denominator), giving the remaining bugs more food per capita.
To Decrease F/M: Decrease the wasting rate. This keeps more biomass in the tank (increasing the denominator), spreading the food supply thinner across a larger population.
Frequently Asked Questions
Does temperature affect the target F/M ratio?
Yes. Microorganisms are less active in colder temperatures. Consequently, operators often maintain a higher MLSS (resulting in a lower F/M ratio) during winter to compensate for the slower biological metabolic rates.
Should I use MLSS or MLVSS?
While MLSS (Mixed Liquor Suspended Solids) measures all suspended solids, MLVSS (Mixed Liquor Volatile Suspended Solids) measures only the organic fraction that can burn off at 550°C. MLVSS is a more accurate representation of the living biomass. However, MLSS is commonly used for general SLR calculations because it is faster to test. If you use MLVSS, the target ratio numbers will be slightly higher because the denominator (mass of solids) will be smaller.
What happens if the F/M ratio is too high?
A high F/M ratio means there is too much food and not enough bugs. The bacteria remain in the "log growth" phase. They are dispersed and do not stick together to form heavy flocs. This leads to sludge bulking, where solids wash out of the clarifier and into the effluent, violating discharge permits.