Batch Calculations

How to Calculate Batch Size, Blend Time, and Mixer Fill for Industrial Batch Processing

The five core calculations every batch operator runs, worked through with real units and numbers.

Start with working volume, not vessel volume. A 5,000 L jacketed tank rated to 100% is never run full. Usable working volume is vessel volume times a safe fill fraction, typically 0.70 to 0.85 for agitated liquids and 0.55 to 0.65 for foaming or gas-evolving systems. For a 5,000 L tank at 80%, working volume is 4,000 L. Convert to batch mass using product density: at 1.12 kg/L that batch is 4,480 kg. The Batch Size and Mixer Fill Percentage calculators pin down these two numbers first because every downstream figure, from blend time to cost, scales off them.

Mixer fill percentage is working volume divided by geometric vessel volume, times 100. Watch the freeboard. Below the top impeller you need enough liquid to submerge it by at least one impeller diameter, or you entrain air and lose pumping. For a tank with impeller diameter D of 0.9 m, keep the liquid level at least 0.9 m above the top blade. If your recipe fills only to 62% and the impeller sits at 68% of tank height, the batch will vortex and aerate. Fill percentage is a go or no-go check before you touch the recipe.

Blend time is the clock to reach a target uniformity, usually 95% or 99% homogeneity. The standard model is blend time t95 = C / N, where N is impeller speed in revolutions per second and C is a dimensionless blend number that depends on impeller type and Reynolds number. For a pitched-blade turbine in the turbulent regime, C sits near 30 to 50. At N = 2 rev/s (120 rpm) and C = 40, t95 = 20 seconds per pass, but full recipe blend time also depends on tank turnovers. The Blend Time calculator ties C, N, and tank turnovers together so you stop guessing.

Reynolds number decides which regime you are in, and it changes the blend number C. Re = rho times N times D squared, divided by dynamic viscosity mu. Take rho = 1,120 kg/m3, N = 2 rev/s, D = 0.9 m, and mu = 0.8 Pa·s: Re = 1,120 times 2 times 0.81 divided by 0.8, which is about 2,268. That is transitional, not turbulent, so blend time stretches and C climbs above the turbulent value. Always compute Re before you trust a blend number, because a viscous batch at Re under 100 can take ten times longer to homogenize.

Agitator power draw comes from the power number Np. Power P = Np times rho times N cubed times D to the fifth. For a Rushton turbine at Np = 5, rho = 1,120, N = 2, D = 0.9: P = 5 times 1,120 times 8 times 0.590, roughly 26,400 W, so 26.4 kW, before gearbox and motor losses. Add 15% drivetrain loss and you specify a 30 to 32 kW motor. The Agitator Power calculator runs this so you size the drive to the worst-case viscosity, which is usually cold startup, not steady state.

Ingredient addition rate controls both quality and cycle time. If a minor component is 3% of a 4,480 kg batch, that is 134.4 kg, and dosing it over 12 minutes means 11.2 kg/min. Rate matters because too fast on a reactive or pH-sensitive addition causes local overshoot and off-spec product. The Ingredient Addition Rate calculator converts total charge, target window, and pump capacity into a rate you can actually set on a metering pump, and flags when your pump maxes out below the required rate.

Yield loss is the gap between theoretical and actual output. Yield = (good output mass / total input mass) times 100. Charge 4,480 kg, recover 4,300 kg of on-spec product, and yield is 95.98%, a 4.02% loss to heel, filter cake, transfer lines, and QC rejects. Track it per batch, because a persistent 4% loss on a 4,480 kg batch is 180 kg of material walking out the door every run. The Yield Loss calculator separates recoverable holdup from true destruction so you attack the right loss.

Scale-up ratio keeps a lab recipe valid at plant scale. The common rule is constant power per unit volume, P/V, or constant tip speed, pi times D times N. If a 10 L pilot runs at N1 = 300 rpm with D1 = 0.1 m, tip speed is 1.57 m/s. Hold tip speed constant on a 4,000 L tank with D2 = 0.9 m and required speed N2 = 1.57 divided by (pi times 0.9), about 0.55 rev/s or 33 rpm. The Scale-Up Ratio calculator lets you pick the criterion, P/V or tip speed, and shows how blend time and power shift with each.

Published 2026-07-01.