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Hydrometallurgy

Kiln Residence Time Calculator

Computes rotary-kiln solids residence time from the Sullivan, Maier & Ralston (1927, U.S. Bureau of Mines Technical Paper 384) relation t = 0.19 · L / (N · D · s), with the 0.19 constant cited to that source and the slope shown converted to the m/m ratio that enters the formula.

Mean solids residence time in an inclined rotary kiln from the Sullivan, Maier & Ralston (1927) empirical relation. Enter the kiln length, the INTERNAL diameter, the rotation speed and the slope — slope in m/m, per cent or degrees, always shown converted to the m/m ratio the formula consumes, because 3° and 3 % are not the same number. The result is the mean residence time in minutes and as h:min, with the peripheral speed π·D·N reported as a labelled sanity figure. SI primary; foot toggles on length and diameter only.

TypeInteractive engineering calculator

Calculator

Kiln geometry & motion

Effective length material travels. SI primary; ft accepted.

INTERNAL diameter (inside the shell / lining bore). SI primary; ft accepted.

rpm

Entered as m/m (rise ÷ run). 3° ≠ 3 % — the converted m/m value below is what enters the formula.

Converted slope

s = 0.03 m/m (entered directly)

Residence time (min)38 min
Residence time (h:min)0 h 38 min
Length L30 m
Internal diameter D2.5 m
Rotation speed N2 rpm
Slope s (m/m)0.03
Peripheral speed π·D·N15.708 m/min

First estimate from the Sullivan form only — verify for critical service.

Audit trail
  • Constant 0.19 — Sullivan, Maier & Ralston (1927), U.S. Bureau of Mines Technical Paper 384
  • Slope: s = 0.03 m/m (entered directly)
  • t = 0.19 · L / (N · D · s) = 0.19 × 30 / (2 × 2.5 × 0.03)
  • t = 5.7 / 0.15 = 38 min = 0 h 38 min
  • Peripheral speed π·D·N = π × 2.5 × 2 = 15.708 m/min (labelled sanity figure; not in the residence-time formula)
Copyable summary

Worked example: L = 30 m, D = 2.5 m, N = 2 rpm, s = 0.03 m/m → t = 0.19 × 30 / (2 × 2.5 × 0.03) = 5.7 / 0.15 = 38.0 min. The same case loads by default above.

Related: Leach tank sizing · Hydraulic residence time · Heat duty · Slurry density · Leach reagent consumption

Formulas

Residence time — Sullivan, Maier & Ralston (1927)
t = 0.19 · L / (N · D · s)
Slope conversion (per cent)
s = value / 100
Slope conversion (degrees)
s = tan(θ)
Peripheral speed (sanity figure)
v = π · D · N

Diagram

DLs = tan θN (rpm)

Worked example

A rotary kiln 30 m long, 2.5 m internal diameter, turning at 2 rpm on a 0.03 m/m slope. Find the mean solids residence time.

  1. 01Slope already in m/m: s = 0.03 (no conversion needed; 3 % would also give 0.03, but 3° would give tan 3° = 0.0524)
  2. 02Numerator: 0.19 × L = 0.19 × 30 = 5.7
  3. 03Denominator: N × D × s = 2 × 2.5 × 0.03 = 0.15
  4. 04t = 5.7 / 0.15 = 38.0 min = 0 h 38 min
  5. 05Peripheral speed π·D·N = π × 2.5 × 2 = 15.71 m/min (labelled sanity figure; not in the formula)
Result

The mean solids residence time is 38.0 min (0 h 38 min) — a first estimate from the Sullivan form.

FAQ

Where does the 0.19 constant come from?
It is the empirical constant of the Sullivan, Maier & Ralston (1927) residence-time relation for inclined rotary kilns, published in U.S. Bureau of Mines Technical Paper 384. Most online calculators state the constant uncited; this page names the source in the lead sentence and the audit trail so the figure can be traced.
Why does the slope mode matter so much?
The formula consumes slope as a dimensionless m/m ratio. A 3 % grade is 0.03 m/m, but a 3° incline is tan 3° = 0.0524 m/m — about 75 % larger, which would shorten the predicted residence time by the same proportion. The calculator always shows the converted m/m value so the grade that actually entered the formula is unambiguous.
What about Friedman & Marshall?
Friedman & Marshall (1949) is a separate, more elaborate correlation that uses a different constant and exponents and adds terms for material properties and air flow; it gives different answers. Implementing it partially would misrepresent it, so this page names it and computes the Sullivan form only.
Is this good enough for design?
It is a first estimate of mean residence time for a free-flowing material with no flights, dams or end constrictions. For critical service, verify against operating data or a tracer test — the page reports the value, not a design guarantee.

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