Rotary Kiln Residence and Heating

What is modelled

In a rotary kiln the whole tube turns slowly on a slight slope. The bed of solids is lifted by the wall and tumbles back, and with every turn it creeps a little way downhill. The hot gas from the burner flows the other way, so the feed meets the coolest gas first and the hottest gas last. The time the bed spends inside and the heat the gas can pass to it decide whether the solids come out hot enough.

Equations

• Residence time t = 1.77 √θ L / (D N s) with the dynamic repose angle θ and slope s in degrees, diameter D in metres and speed N in rpm (Sullivan-Saeman form).
• Hold-up = feed × t and fill = hold-up / (ρb Vkiln).
• Counter-current exchange Cm dTm/dx = Cg dTg/dx = U′ (Tg − Tm).
• Effectiveness ε = (1 − e−NTU(1−Cr)) / (1 − Cr e−NTU(1−Cr)).

Checks run in the page

• The residence time against a seeded random-advance particle simulation.
• Hold-up and fill against the feed rate.
• The shooting-method temperature profile against the effectiveness-NTU result.
• The heat balance and the scaling of residence time with length and speed.

Honest simplifications

The bed and gas have constant specific heats, there is no reaction heat, no wall loss, no radiation from the flame and a single volumetric heat transfer coefficient, and the residence time formula is an empirical fit for a rolling bed. Real cement kilns have a calcining zone, a burning zone with the flame, a dust cycle and coating, so this is a first look at the transport, not a kiln model.

• Press Fast rotation to see the stay shorten and the bed leave cooler.
• Press Overfed kiln to watch the fill pass the warning line.
• Press Short kiln, weak transfer and compare the effectiveness with the reference kiln.