Leach Residence Time: Calculation and Tank Sizing

Last updated: 2026-11-02

For a typical 500 t/d gold plant treating 25% solids pulp, the leach residence time that delivers 90% recovery in four agitated tanks is about 5.7 hours total, or 1.4 hours per tank, using a 0.55 per hour rate constant from bottle roll test work. This guide converts that kinetics figure into slurry flow and tank volume for a continuous leaching duty, and audits every number.

Key Takeaways

• Residence time is working volume divided by slurry volumetric flow; use working volume, never geometric tank volume.
• Dead volume, bypassing, and short-circuiting typically push effective residence time 20–40% below nominal.
• Four to six CSTRs in series approach plug flow; one large tank of equal volume recovers far less.
• Convert bottle roll kinetics with care: oxygen mass transfer often limits full-scale rate below batch performance.
• Budget 15–25% freeboard and 0.8–1.2 kW/m³ of installed agitator power for gas-sparged leach duty.

What Is Leach Residence Time and Which Volume Counts?

Leach residence time is a measure of the average time that slurry spends inside a leach vessel or train, written as tau = V/Q, where V is the working volume of slurry held and Q is the volumetric slurry flow rate through it. It is the single most consequential number in leach tank sizing, because recovery, reagent consumption, and capital cost all hang on it.

Three definitions anchor the calculation. Working volume is a fraction of the geometric tank shell that is actually filled with circulating slurry, typically 75–85% of geometric volume, with the remaining 15–25% left as freeboard for gas holdup, foam, and flow surges. The CSTR-in-series model is a representation of a tank train that treats each vessel as perfectly mixed, with concentration dropping stepwise from tank to tank rather than smoothly as in true plug flow. Dead volume is a stagnant region of slurry that sits behind baffles, below the agitator, or in corners and exchanges little material with the active stream.

The distinction that matters is nominal versus effective residence time. Nominal residence time is what you calculate on paper: working volume divided by feed flow. Effective residence time is what the slurry actually experiences after dead volume, bypassing, and short-circuiting take their toll. Plant surveys commonly show effective residence time running 20–40% below nominal in poorly performing circuits — exactly the gap that explains a plant missing design recovery even though the tankage was “correct” on the flowsheet. For the underlying test-work methods, see our leaching resources library.

How Do You Calculate Leach Residence Time From Slurry Flow?

The basic relation is simple; the work is in getting Q onto a consistent slurry basis. Since leach reactions consume and release solution but the solids are conservative, the mass balance starts from dry solids throughput and converts to slurry flow using solids density, liquid density, and pulp density. The parameters you need, with typical ranges, are:

The conversion from dry solids to slurry volume uses three steps. First, slurry mass flow is ṁs/w, because wet pulp is part solids and part solution. Second, pulp specific gravity follows from the volume-weighted mixture rule:

ρp = 1 / (w/SGs + (1 − w)/SGl)

Third, slurry volumetric flow is Q = (ṁs/w) / ρp: divide dry solids flow by the solids fraction for slurry mass flow, then by pulp specific gravity for cubic meters per hour. Total working volume for any target leach residence time is V = Q × tau, and per-tank volume is simply V/N.

Keep solution-basis and slurry-basis flows strictly separated. Heap leach liquor balances are usually quoted on solution basis; a tank sizing calculation must use slurry basis, or the volume will be understated by roughly the solids fraction — a 25% solids pulp has a slurry volume about 33% greater than the solution alone. Mixing up the two bases is the most common error in third-party sizing reviews; the companion leaching recovery calculation guide carries the recovery math.

Why Do Four Tanks Beat One Tank of the Same Volume?

Because real tanks are neither plug flow nor perfectly mixed, the standard design model is a train of N continuous stirred-tank reactors (CSTRs) of equal stage residence time tau_stage = tau/N. For first-order leach kinetics with rate constant k, the predicted recovery is:

R = 1 − 1/(1 + k × tau_stage)^N

The key insight is that the same total residence time produces very different recoveries depending on how it is divided. In a single large tank, fresh feed mixes instantly with fully leached slurry, so a fraction of the feed effectively leaves early and dilutes the average. Splitting the volume into a train narrows the residence time distribution step by step; four to six tanks in series is generally accepted as a practical approximation of plug flow, and beyond six to eight the incremental recovery gain no longer justifies another pump box, agitator, and sampler.

Numbers make the point concrete. Take k = 0.55 h⁻¹ and a total nominal residence time of 5.66 h. A single 351 m³ tank gives R = 1 − 1/(1 + 0.55 × 5.66) = 1 − 1/4.113 = 75.7%. Four tanks of 87.8 m³ each, same total volume, give R = 1 − 1/(1 + 0.55 × 1.415)⁴ = 1 − 1/10.0 = 90.0%. Fourteen recovery points for free, purely from flow configuration — that is why continuous leach trains are built as four or more vessels rather than one big tank. Where a compact footprint matters, a purpose-built three-stage continuous CSTR leaching train is the reference configuration for this duty.

The model also cuts the other way: it tells you how much recovery you lose when effective residence time erodes. If dead volume removes 25% of the working volume, the effective stage time drops to 1.06 h and four tanks deliver only 1 − 1/(1 + 0.55 × 1.061)⁴ = 1 − 1/6.29 = 84.1%. Six recovery points lost to hydraulics that never appeared on the flowsheet.

How Do You Convert Bottle Roll Kinetics to a Full-Scale Train?

Bottle roll tests are the cheapest source of leach kinetics, and extracting k from them is straightforward. At timed intervals, measure dissolved metal and compute fractional recovery R(t). For a first-order model, plot ln(1/(1 − R)) against time; the slope of the straight-line portion is k. In the worked example below, a bottle roll on the design ore gave R = 67% at 2 h and R = 89% at 4 h, corresponding to ln(1/0.33)/2 = 0.55 h⁻¹ and ln(1/0.11)/4 = 0.55 h⁻¹ — a clean first-order fit.

Converting batch kinetics to continuous performance is where judgment enters. A batch bottle roll is a closed system: the solution-to-solids ratio stays constant, oxygen is usually abundant at the 40–50% solids typical in the bottle, and every particle experiences exactly the same time. A continuous tank offers none of these luxuries. The continuous equivalent for an N-tank train is the R = 1 − 1/(1 + k × tau_stage)^N relation above, which always predicts lower recovery than the batch curve at the same total time — for the example kinetics, 90% needs 4.19 h in batch but 5.66 h in a four-tank train.

The most important caveat is oxygen mass transfer. In a bottle roll, the required oxygen is modest and the rolling film resupplies it easily; in a production tank at 30–40% solids with high reagent demand, the rate is frequently limited not by surface chemistry but by how much oxygen the agitator and sparging system can transfer into the pulp. When that happens the plant k is lower than the bottle roll k — a derating commonly reported as typical when oxygen demand is high — and no amount of tank volume compensates for a starved impeller. Design with sparging capacity to match peak oxygen demand, confirm the kinetics are not gas-limited with an ORP profile down the train, and cross-check against the shrinking core model for leaching kinetics for coarse or passivation-prone feeds.

What Are Typical Residence Times by Leaching Duty?

Residence time is duty-specific, and the table below is indicative only — ore mineralogy, grind size, and reagent regime move these numbers by a factor of two or more in either direction. Treat them as scoping-level starting points, never as design values.

Several field patterns recur across commodities. Gold CIL plants in Australia, West Africa, and South America typically run 8–12 hours in CIP plus 12–24 hours in CIL tanks — always indicatively, because refractory ores push well beyond. Copper oxide plants in Chile and Peru commonly show k around 0.5–1.0 h⁻¹ for oxide ores at 40–80 °C, which is why 2–8 h of residence is typically sufficient at fine grind. Surveys of underperforming CIL circuits repeatedly find effective leach residence time 20–40% below nominal, with the first two tanks the worst offenders due to frothing and short-circuiting. Atmospheric duty is not the only option — compare tank versus heap leaching before committing to agitated tankage, and review the copper oxide ore processing route as a worked case.

Worked Example: Sizing a 500 t/d Four-Tank Train

The brief: 500 t/d dry solids, pulp density 25% w/w, solids SG 2.7, liquid SG 1.15, four agitated tanks, target recovery 90%, k = 0.55 h⁻¹ from bottle roll test work. Every intermediate number is shown so the arithmetic can be audited line by line.

1. Dry solids feed. Convert the daily figure to hourly: 500 t/d ÷ 24 h = 20.83 t/h of dry solids.
2. Slurry mass flow. At 25% w/w solids, slurry mass flow = 20.83 ÷ 0.25 = 83.33 t/h, of which water and solution make up 62.50 t/h.
3. Slurry specific gravity. Volume-weighted mixture: 1/(0.25/2.7 + 0.75/1.15) = 1/(0.0926 + 0.6522) = 1/0.7448 = 1.343 t/m³.
4. Slurry volumetric flow. Q = 83.33 t/h ÷ 1.343 t/m³ = 62.1 m³/h. Sanity check: 25% solids at SG 2.7 in liquid at 1.15 gives a pulp well above 1.0 but far below the solids density, as expected.
5. Stage residence time from the recovery target. R = 0.90 with N = 4 requires (1 + 0.55 × tau_stage)⁴ = 1/(1 − 0.90) = 10, so 1 + 0.55 × tau_stage = 10^0.25 = 1.778, giving tau_stage = 0.778 ÷ 0.55 = 1.415 h per tank. Total nominal leach residence time = 4 × 1.415 = 5.66 h.
6. Total and per-tank working volume. V = Q × tau = 62.1 × 5.66 = 351 m³ total; per tank = 351 ÷ 4 = 87.8 m³.
7. Geometric volume. At 80% working fill (midpoint of the 75–85% typical band), geometric volume per tank = 87.8 ÷ 0.80 = 110 m³.
8. Tank dimensions. For atmospheric leach tanks a height-to-diameter ratio near 1:1 is typical. With H = D, geometric volume = pi × D³/4, so D = (4 × 110/3.14159)^(1/3) = 5.19 m. Specify D = 5.2 m, H = 5.2 m, giving 3.1416 × 5.2²/4 × 5.2 = 110.4 m³ — the check closes.
9. Agitator power. At the 0.8–1.2 kW/m³ typical for gas-sparged, 25–40% solids slurries (basis: working volume), each tank needs 87.8 × 0.8 to 87.8 × 1.2 = 70–105 kW. Specify 90 kW nominal per agitator, roughly 360 kW installed for the train.
10. Batch curve check. The bottle roll predicts R = 1 − e^(−0.55t): 67% at 2 h, 89% at 4 h, and 90% at t = ln(10)/0.55 = 2.303/0.55 = 4.19 h. The four-tank train at 5.66 h total reproduces the same 90%, and the ratio 5.66/4.19 = 1.35 quantifies the CSTR-series penalty. Had the train been a single 351 m³ tank, recovery would have been 75.7% — the configuration check in step 5 is what makes the design work.

How Much Freeboard, Steel, and Power Does the Tank Train Need?

Freeboard converts working volume into geometric volume, and getting it wrong is expensive in both directions. Under-freeboarded tanks foam over during reagent surges and gas spikes; over-freeboarded tanks waste steel on volume that never contacts slurry. For open, gas-sparged leach duty, working volume is typically 75–85% of geometric — that is, 15–25% freeboard — with the higher end where fine carbon, frothers, or high pulp viscosities promote stable froth. Covered tanks can justify the lower end.

Geometry and power interact. Height-to-diameter ratios of roughly 0.8–1.2 are typical for atmospheric leach tanks in the 100–1,000 m³ class: taller, narrower tanks give better plug-flow character and lower agitator tip speed for the same turnover, but cost more per cubic meter and strain foundations on poor ground. Installed agitator power of 0.8–1.2 kW/m³ (working volume basis) covers most gas-sparged slurry duties; above about 1.5 kW/m³ question whether the duty needs it, because power draw is a permanent operating cost. Impeller tip speed is the classic scale-up trap: keeping tip speed below roughly 5 m/s (typical) protects liners and carbon particles, which means large tanks need larger, slower impellers rather than scaled-up lab geometry.

Steel mass scales almost linearly with shell area in this size class. A 110 m³ tank at 5.2 m diameter and 5.2 m height has roughly 127 m² of shell, roof, and floor plate; at 8 mm wall, indicative plate mass is about 8 t before stiffeners, railings, and liners — call it 8–12 t per tank as a scoping figure. Tankage capex tracks geometric volume closely, so oversizing the train by 25% “for safety” adds roughly a quarter to the steel, agitation, and foundation budget while the extra volume sits unproductive and oversized agitators burn 25% more power forever. The economical buffer is design margin in the k value and the residence time, not in steel. Our agitated leaching tank design guide carries the full geometry and mechanical detail.

Why Do Plants Miss Design Recovery?

When a plant underperforms its bottle roll predictions, the effective leach residence time is almost always the first suspect, because hydraulics degrade silently while the flowsheet looks correct. Six causes account for most cases:

1. Frothing and foaming in the first tanks. Symptom: slurry surging at the inlet, visible froth layer, erratic density. Cause: fine carbon, organics, or excessive air entraining stable froth that displaces working volume. Action: fit or clean froth control, derate aeration in lead tanks, and re-survey actual slurry level against design.
2. Dead zones behind baffles and below the agitator. Symptom: tracer tests show slurry elements held far longer than nominal. Cause: baffle damage, insufficient agitation at low turndown, or solids settling into a static bed. Action: raise agitator speed or impeller diameter, inspect baffles, and confirm suspension at design pulp density.
3. Short-circuiting through level control or launder design. Symptom: feed appears in the tail sample well before one nominal residence time. Cause: open interstage launders or plugged overflows allowing density-driven bypass. Action: inspect interstage screens and launders, restore design level differentials, and re-run a tracer test.
4. Operating above design throughput. Symptom: recovery drops gradually as feed rises. Cause: Q has grown but V has not, so tau = V/Q has fallen — a 20% feed increase cuts residence time by a sixth. Action: re-rate the train honestly, add parallel capacity, or accept the recovery loss knowingly.
5. Oxygen mass transfer limitation. Symptom: ORP falls along the train and never recovers; k from plant data sits well below bottle roll. Cause: sparging or agitation cannot deliver the oxygen demand of the feed. Action: upgrade spargers, increase agitator gas handling, or pre-oxidize the feed.
6. Pulp density creep. Symptom: tanks run heavier than design and agitator current climbs. Cause: mill water balance drift or upstream thickener upset pushing solids above the 20–40% design window. Action: restore water balance discipline and alarm on pulp density so the volume basis of the residence time calculation stays valid.

Most audits find a combination: perhaps 10–15% lost to dead volume, 5–10% to foaming, and the remainder to throughput creep. The compounding effect on recovery is why the effective-versus-nominal gap deserves its own line in every plant model — the worked geometry, hydraulic, and instrumentation fixes are collected in our resources library.

Frequently Asked Questions

Should residence time be based on slurry flow or solution flow?
Slurry flow, always, for tank sizing. The tank must hold everything that flows through it — solids and solution together — so tau = V/Q with Q on slurry basis. Solution-basis flows understate the required volume by roughly the solids fraction: at 25% solids, sizing on solution flow alone yields a train about a quarter too small. Solution basis is legitimate only for heap leach liquor balances and downstream circuits, never for leach tank volume.

How many tanks should a leach train have?
Four to six is the standard answer for atmospheric duty. Below four, short-circuiting costs meaningful recovery — a single tank at the example kinetics loses 14 recovery points against a four-tank train of equal volume. Above six to eight tanks, the plug-flow approximation is already close and each added vessel brings an agitator, pump box, and sampler that cost more than the marginal recovery they buy. Autoclaves typically use four to six compartments for the same reason.

How do I derate bottle roll k for a full-scale tank?
Start with the R = 1 − 1/(1 + k × tau_stage)^N relation using the bottle roll k, then check oxygen: if plant oxygen demand per tonne exceeds what 0.8–1.2 kW/m³ agitation and your sparger can transfer, the plant k will sit below the bottle roll value. Confirm with an ORP profile and plant data fitting after commissioning. Where gas transfer is not limiting, four to six CSTRs usually run close to batch-predicted recovery at 1.3–1.5 times batch time.

Does higher pulp density reduce the tank volume I need?
Yes, and materially. Raising pulp density from 25% to 35% solids cuts slurry volumetric flow — the denominator effect in tau = V/Q — so the same residence time needs less working volume, roughly 15–20% less across that range for SG 2.7 solids. The limit is agitation and oxygen transfer: above about 40% solids, power demand, viscosity, and gas dispersion degrade quickly, and the kinetic benefit of denser pulp can reverse if oxygen becomes limiting.

How much freeboard does a leach tank need?
Typically 15–25% of geometric volume for open, gas-sparged leach tanks, so working volume is 75–85% of the shell. Use the upper end with fine carbon, frother carryover, high-viscosity pulps, or widely varying feed; the lower end suits covered tanks with stable hydraulics. Size agitator mounting and overflow weir positions on the geometric height, but calculate residence time only from the working volume — conflating the two silently overstates tau.

What agitator power per cubic meter is typical for leach tanks?
0.8–1.2 kW/m³ installed, on a working volume basis, covers most gas-sparged duties at 20–40% solids. Low-solids, fine-grind duties can sit at the bottom of the range; high-solids or gas-hungry pressure-oxidation-style duties push the top. Remember power is an operating cost forever: specifying 1.5 kW/m³ where 1.0 would do adds half again to the train’s connected load, and tip speed, not power, usually governs impeller selection.

Can I use this model for pressure oxidation and HPAL autoclaves?
Partially. The CSTR-in-series recovery equation applies, since autoclave compartments behave as staged reactors, and the residence time arithmetic is identical. What changes is the volume basis — slurry volume fraction at operating temperature and pressure, with vapor space inside the shell — and the kinetics, which follow temperature-dependent autoclave chemistry rather than ambient bottle roll work. Use autoclave test data for k, and treat the 0.5–2 h POX and 0.5–1.5 h HPAL figures as indicative only.

Conclusion

The verdict: leach residence time is a calculable quantity — working volume divided by slurry volumetric flow, corrected for how many tanks you build in series — and for the worked 500 t/d example that is 5.66 hours across four 110 m³ tanks to reach 90% recovery. Action: run this calculation on your own feed with bottle roll kinetics, then request a quote for a tank train sized to the audited numbers rather than to a rule of thumb.

References

• Levenspiel, O. Chemical Reaction Engineering, 3rd ed. John Wiley & Sons.
• Wills, B.A. and Finch, J.A. Wills’ Mineral Processing Technology, 8th ed. Butterworth-Heinemann / Elsevier.
• Fuerstenau, M.C. and Han, K.N. (eds.). Principles of Mineral Processing. SME.
• Weiss, N.L. (ed.). SME Mineral Processing Handbook. SME-AIME.
• Perry, R.H. and Green, D.W. Perry’s Chemical Engineers’ Handbook, 8th ed. McGraw-Hill.
• Marsden, J.O. and House, C.I. The Chemistry of Gold Extraction, 2nd ed. SME.
• Oldshue, J.Y. Fluid Mixing Technology. McGraw-Hill.
• Gates, L.E., Morton, J.R., and Fondy, P.L. “Selecting Agitator Systems to Suspend Solids in Liquids.” Chemical Engineering, 1976.

Changelog

• 2026-11-02: First publication.