Leaching Equipment

Leaching Reactor Volume Calculator from Residence Time

Residence time is the parameter most often traded away to raise throughput, and it is usually the wrong thing to trade. This calculator works the sizing in the practical direction: give it the slurry flow and the residence time your leach kinetics need, and it returns the total working volume, the volume per tank for the number of tanks you choose, and the physical dimensions for a stated height-to-diameter ratio.

Inputs

Slurry flowm³/h

Volumetric slurry flow through the leach circuit.

Required residence timemin

Time the slurry must stay in contact with the lixiviant to reach your target extraction. Establish it from batch leach kinetics rather than from a rule of thumb — it varies enormously with particle size and temperature.

Working volume fraction%

Fraction of the vessel's geometric volume occupied by slurry at operating level. A freeboard is needed for aeration, foam and surge.

Tanks in series

Splitting the volume across several tanks in series narrows the residence time distribution towards plug flow, which raises recovery for a given total volume.

Height : diameter

Vessel aspect ratio. Taller vessels use less floor area but need more agitator shaft length and more air for a given power input.

How to use it

Runs entirely in your browser — nothing you enter is sent anywhere. Defaults are typical lab/pilot values so you can see the arithmetic move; replace them with your own numbers before you rely on the result.

Results

Total working volume —m³

Total geometric volume —m³

Working volume per tank —m³

Tank diameter —m

Tank height —m

Actual residence time per tank —min

The results appear here and update as you type. Each result is followed by the conditions under which it holds.

Read the assumptions before you use a number. A sizing figure without its conditions is not a result — it is a guess with a decimal point. The assumptions listed below are part of this calculator's output, not small print.

How to use it

Establish the kinetics, not the rule of thumb
Run a batch leach at your intended temperature, pulp density and lixiviant concentration, and plot extraction against time. The residence time you need is the point where the curve flattens towards your target — anything beyond it is reactor volume you have paid for but do not use.
Convert flow and time into working volume
Working volume is slurry flow multiplied by residence time. This is the volume the slurry must actually occupy, and it is independent of how you divide it among vessels.
Add freeboard to get geometric volume
Vessels need freeboard for aeration, foam, and surge during flow changes. Working fraction is the share of the vessel that is slurry at normal operating level.
Choose the number of tanks in series
The same total volume split across several tanks in series behaves closer to plug flow, so recovery rises without spending more volume. It also costs more vessels, more agitators and more interconnecting pipework.
Fix the aspect ratio and read off dimensions
Height-to-diameter ratio trades floor area against agitator shaft length and air requirements. A very tall, slender vessel is harder to agitate evenly and is more prone to solids settling in the base.

Formulas used

Total working volume  V = Q × (τ / 60)
Geometric volume      = V / (working fraction)
Volume per tank       = V / N                          N = tanks in series
For volume of one tank:  V_tank = π (D/2)² × (H/D × D)
   solve D = ( 4 V_tank / (π × (H/D)) )^(1/3) ,  H = D × (H/D)

Assumptions & applicability

Ideal mixing within each tank, with tanks in series to model the residence time distribution. Real vessels have dead zones, short-circuiting and stagnant corners, so the effective volume is normally less than the geometric volume.
The required residence time is an input that must come from batch leach kinetics on your own material. Leach rates vary by orders of magnitude with particle size, mineralogy, temperature and lixiviant strength, so a generic figure is not usable for design.
Constant slurry density and flow. In reality pulp density changes along the circuit as solids dissolve and as wash water is added.
No allowance is made for solids settling out in the vessel, for agitator power limits, or for the increase in viscosity and the fall in mixing quality at high pulp density.
Heat input and temperature control are not modelled, although leach kinetics depend strongly on temperature.
The scaling and abrasion behaviour of the vessel and agitator material is not considered.

FAQ

Why use several tanks in series instead of one large tank?

Because the total residence time is the same but the distribution is much narrower. Part of the slurry cannot short-circuit straight through, so more of it actually receives the full contact time. That translates into higher recovery for the same total volume, which is why leach circuits are almost always built as a series of agitated tanks rather than one large vessel.

What pulp density can I run?

The practical ceiling is usually set by mixing, not by chemistry. As pulp density rises, slurry viscosity rises sharply, the power needed to keep solids in suspension rises, and the driving force for dissolution falls because the liquid-to-solid ratio drops. Establish the achievable density in an agitated test vessel at your intended geometry before committing to a reactor design.

Should I use an agitated tank or a column or autoclave?

It depends on the kinetics and on why you are leaching. Atmospheric agitated tanks suit slow kinetics and coarse solids, autoclaves are needed when the chemistry requires elevated temperature and oxygen overpressure, and columns or heaps suit very low-grade material where long residence times are acceptable because the cost per tonne is low. The decision is normally made by kinetics together with the required oxygen or pressure, not by tank volume.