Bioleaching: Monod Growth & Shrinking-Core Ore Extraction (2D)

Inoculum & Environment

Initial bacteria population 10%

pH 2.0

Temperature 33 °C

Ore Charge

Particle radius (R₀) 0.50 mm

Simulation speed 1.0×

Live Readout

Elapsed time

0.0 d

Bacterial population

0.0%

Metal recovery

0.0%

Particles depleted

0 / 0

Growth rate μ

0.000 /h

Leach rate factor

0.00

How it works

Acidophilic iron/sulfur-oxidizing bacteria (e.g. Acidithiobacillus ferrooxidans) colonize crushed sulfide ore and regenerate the Fe³⁺ oxidant that attacks the mineral lattice. The population follows logistic-Monod growth limited by the exposed mineral surface area S (normalized to the initial charge), with Gaussian pH/temperature response functions typical of mesophilic acidophiles:

f(pH) = exp(-(pH-2.0)²/(2·0.5²))
f(T)  = exp(-(T-33)²/(2·7²))
μ     = μmax·f(pH)·f(T)·S/(Ks+S)
dX/dt = μ·X·(1-X/K) - kd·X,   K = 100·S

Each ore particle shrinks under a reaction-controlled shrinking-core model: the unreacted core radius R falls at a rate set by the environmental factors and a Monod-type dependence on active biomass X (biofilm coverage saturates, it does not scale linearly forever):

dR/dt = -kL·f(pH)·f(T)·X/(Xhalf+X)
recovery_i = 1 - (R/R0)³        (spherical shrinking core)

Field view — every circle is an unreacted ore core; it shrinks as it is bioleached, and green motes around it represent the local bacterial biofilm density.
Recovery chart — cumulative metal extraction (teal) and bacterial population (amber) plotted against elapsed heap time.
Feedback loop — population growth depends on remaining mineral surface, and leach rate depends on population: as ore depletes, both curves saturate together, the same coupling that governs real heap/tank bioleaching operations.

Unreacted ore core Bacterial biofilm Population curve