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Hydrometallurgy

Leach Tank Sizing Calculator

Sizes leach tanks for a stated residence time from the slurry flow, the required residence time τ, the number of tanks in series and a live-volume fraction — flow entered directly as Q or derived from a solids basis using the house slurry-density relation — giving total live volume, per-tank volume and optional flat-bottom-cylinder geometry.

Plain tank-volume arithmetic for a stated residence time, in two flow-input modes. Enter the slurry volumetric flow Q directly, or work from a solids basis — dry solids t/h, % solids by mass, solids SG and liquor SG — and the slurry density and flow are derived using the same relation the slurry-density calculators publish, with every step shown. Then the total live volume is Q·τ and the per-tank volume divides that across the tanks in series and the live-volume fraction. Optional flat-bottom-cylinder geometry returns the per-tank diameter and height from an H/D ratio. SI primary throughout. The required residence time comes from metallurgical testwork for the specific ore and conditions; this calculator sizes vessels for a stated residence time — it does not predict leach performance.

TypeInteractive engineering calculator

Calculator

Flow input
Slurry flow
m³/h
Sizing
h

From metallurgical testwork for the specific ore and conditions.

count
–

Working volume ÷ geometric volume. Default 0.85 — a labelled assumption to verify.

–

Flat-bottom cylinder basis. Default 1.0 — a labelled assumption. No freeboard beyond f_live.

Per-tank volume V_tank880.188 m³
Total live volume V_live4488.96 m³
Slurry flow Q187.04 m³/h
Residence time τ24 h
Tanks in series N6
Live-volume fraction0.85
Per-tank diameter D10.3871 m
Per-tank height H10.3871 m

The required residence time comes from metallurgical testwork for the specific ore and conditions; this calculator sizes vessels for a stated residence time — it does not predict leach performance.

Audit trail
  • Slurry flow Q = 187.04 m³/h (entered directly)
  • V_live_total = Q · τ = 187.04 × 24 = 4488.96 m³
  • V_tank = V_live_total / (N · f_live) = 4488.96 / (6 × 0.85) = 880.188 m³
  • D = (4·V_tank / (π·(H/D)))^(1/3) = 10.3871 m; H = (H/D)·D = 10.3871 m (flat-bottom cylinder; no freeboard/agitation allowance beyond f_live)
Copyable summary

Worked example (solids basis): 100 t/h dry solids, 40 % w/w, solids SG 2.70, liquor SG 1.000 → slurry SG 1.337, slurry mass 250 t/h, Q ≈ 187.0 m³/h; τ = 24 h, N = 6, f_live = 0.85 → V_tank ≈ 880 m³ (D = H ≈ 10.4 m at H/D = 1.0). The same case loads by default above.

Slurry density is derived via the house relation shared with Slurry density · Percent solids (mass ↔ volume) · Slurry mass balance. Related: Kiln residence time · Leach reagent consumption

Formulas

Slurry density (solids basis, house relation)
ρ_slurry = 1 / (Xs/ρ_solids + (1−Xs)/ρ_liquor)
Slurry volumetric flow
Q = (solids ÷ Xs) ÷ ρ_slurry
Total live volume
V_live = Q · τ
Per-tank volume
V_tank = V_live / (N · f_live)
Geometry (flat-bottom cylinder)
D = (4·V_tank / (π·H/D))^(1/3), H = (H/D)·D

Diagram

Q, τV_tankDHV_tankV_tankN tanks in series · V_tank = Q·τ / (N·f_live)

Worked example

Solids basis: 100 t/h dry solids at 40 % w/w, solids SG 2.70, liquor SG 1.000. Required residence time 24 h across 6 tanks in series, live-volume fraction 0.85, H/D = 1.0.

  1. 01Solids mass fraction Xs = 40 / 100 = 0.40; ρ_solids = 2700 kg/m³, ρ_liquor = 1000 kg/m³
  2. 02Slurry density = 1 / (0.40/2700 + 0.60/1000) = 1 / 0.00074815 = 1336.6 kg/m³ (slurry SG 1.337)
  3. 03Slurry mass flow = dry solids / Xs = 100 / 0.40 = 250 t/h
  4. 04Q = 250 t/h × 1000 / 1336.6 = 187.0 m³/h
  5. 05Total live volume V_live = Q · τ = 187.0 × 24 = 4488.9 m³
  6. 06Per-tank volume V_tank = V_live / (N · f_live) = 4488.9 / (6 × 0.85) = 880.2 m³
  7. 07Geometry at H/D = 1.0: D = (4 × 880.2 / π)^(1/3) = 10.39 m; H = 1.0 × D = 10.39 m
Result

Each of the 6 tanks holds about 880 m³ of live volume — a flat-bottom cylinder roughly 10.4 m diameter by 10.4 m high at H/D = 1.0; total live volume 4489 m³.

FAQ

Does this calculator predict leach recovery or kinetics?
No. The required residence time comes from metallurgical testwork for the specific ore and conditions; this calculator sizes vessels for a stated residence time — it does not predict leach performance. It returns volumes and geometry, not recovery.
What is the live-volume fraction and why 0.85?
It is the working (live) volume divided by the geometric volume of the tank — the part actually holding mixed slurry, below freeboard and clear of internals. The 0.85 default is a labelled assumption to verify against the real freeboard, launder and internals arrangement; change it to match the design.
How is the solids-basis flow derived?
From the solids mass fraction and the solids and liquor SGs, the slurry density is computed with the house relation ρ_slurry = 1/(Xs/ρ_solids + (1−Xs)/ρ_liquor) — the same relation the Slurry Density and Slurry Mass Balance calculators publish. The slurry mass flow is the dry solids divided by the mass fraction, and Q is that mass flow divided by the slurry density. Every step is shown in the audit trail.
Why do the two flow modes give the same size?
The solids-basis mode simply derives the slurry volumetric flow Q and then sizes the tanks from that Q exactly as the direct mode does. Enter the derived Q in the direct tab and the per-tank volume is identical — the sizing maths is independent of how Q was obtained.

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