Gold CIL Control Room: Cyanide Leach Kinetics, Carbon Isotherm and Six-Tank Mass Balance (2D)

Presets

Events and faults

Speed1x

Alarms

Live readouts

Graphs

Gold along the six-tank cascade: solids (g/t) and solution (mg/L x10)

Carbon loading on the Freundlich isotherm (log10 C versus kg/t)

Recovery, tails grade and loaded-carbon grade versus plant time

Cyanide (tanks 1 and 6), dissolved oxygen and dosing versus plant time

Numerical checks

running...

How to use

Read the P&ID: slurry flows left to right through six agitated tanks. Activated carbon moves the other way (brown dashed lines), so the barren slurry meets the freshest carbon and the richest slurry meets the most loaded carbon. Tank 1 is a pre-leach tank (no carbon) in the baseline.
The coloured bars under each tank show solids gold (amber), gold in solution (blue), carbon loading (brown), cyanide (green) and dissolved oxygen (violet). The first graph is the same profile along the cascade, the second places every carbon tank on the Freundlich isotherm.
Press a preset. Disturbance presets start from the healthy baseline and let you watch the plant react: cyanide starvation, oxygen starvation with high sulphide, a coarse grind, low pH, fouled carbon, preg-robbing ore, dense pulp or richer ore. Raise time compression to see the slow carbon circuit (hundreds of hours) respond in seconds.
Cyanide dosing is a PI loop (AIC-101) holding tank 1 at its set-point. Try Kp too high, a long Ti, a manual dose, or the Cyanide pump trip event, and read the alarms: low cyanide, low dissolved oxygen, HCN risk at low pH, gold in tails, loaded carbon above the elution capacity, gold lost on carbon fines.
Four numerical checks run in the page (Habashi limits, cascade closed form, closed batch isotherm, whole-plant gold balance). Space pauses, R resets. In 3D drag to orbit, wheel to zoom, use the camera buttons and the X-ray tank toggle.

The science

A carbon-in-leach plant dissolves gold with cyanide and adsorbs it on activated carbon in the same agitated tanks (Elsner reaction):

4 Au + 8 CN^- + O₂ + 2 H₂O -> 4 Au(CN)₂^- + 4 OH^-

Dissolution is limited by mass transfer of cyanide and oxygen to the gold surface (Habashi). With diffusion coefficients D and boundary-layer thickness delta, the flux per unit area is

r = 2 D_CN D_O2 [CN-] [O2] / ( delta ( D_CN [CN-] + 4 D_O2 [O2] ) )
limits: r -> (1/2) (D_CN/delta) [CN-] (oxygen in excess), r -> 2 (D_O2/delta) [O2] (cyanide in excess)

Only the CN^- ion leaches: [CN-] = alpha [NaCN] with alpha = 1/(1 + 10^(pKa - pH)), pKa = 9.31. Below pH 10 a growing share is HCN, which is lost to the air and is toxic, so lime keeps the pulp at pH 10.5 or higher. The model turns the flux into a first-order rate on the liberated gold of each tank, with an Arrhenius factor (Ea 15 kJ/mol), a 1/P80 surface-area factor and a pulp-viscosity factor. Two gold populations are tracked (fast, 70 % of leachable gold, and slow, at 12 % of the fast rate), plus a refractory fraction that never dissolves:

dg_i/dt = (g_(i-1) - g_i)/tau - k_i g_i , k_i = K_L (r_i / r_ref) f_T f_d f_eta^(1/2) , tau = V / Q

Gold in solution C, carbon loading q (g/t carbon), film-diffusion adsorption on the Freundlich isotherm and a counter-current carbon flow F_c through carbon inventory M_c:

q*(C) = K C^n (n = 0.4, K = 20 000 g/t per (mg/L)^n at 25 C, scaled by carbon activity)
dC/dt = (C_(i-1) - C)/tau + (c_s/phi_L) k g - k_f (rho_c/rho_ref)(C - C*(q))
dq/dt = (F_c/M_c)(q_(i+1) - q) + 1000 phi_L k_f (C - C*(q)) / rho_ref

Cyanide has dosing, first-order cyanicide consumption (copper and iron minerals), HCN loss and 2 mol per mol of gold complexed; dissolved oxygen has air transfer, sulphide-oxidation demand and gold consumption:

dCN/dt = (CN_(i-1) - CN)/tau - k_cc s CN - k_H (1 - alpha) CN - 2 (M_NaCN/M_Au) r_Au + dose/(V phi_L)
dDO/dt = (DO_(i-1) - DO)/tau + k_La (DO_sat - DO) - R_O2 s 0.7^i - (1/4)(M_O2/M_Au) r_Au , DO_sat(T): fresh-water polynomial, about 4.3 times higher with oxygen enrichment

Preg-robbing carbonaceous matter in the ore is a second sorbent that moves with the solids and leaves in the tails. A torn interstage screen lets carbon fines leave one tank. The tank equations are integrated with fourth-order Runge-Kutta; the dosing PI controller has anti-windup, a sensor lag and a pump limit.

Numerical checks run in the page

The Habashi rate reproduces both analytic limits (cyanide-excess and oxygen-excess).
For fixed cyanide and oxygen the integrated six-tank steady state of the leachable solids gold matches the closed-form product 1/(1+k tau)^6.
A closed batch of carbon and solution reaches the equilibrium found independently by bisecting the gold mass balance with the Freundlich isotherm.
Over 120 h the whole plant satisfies feed = tails (solids + liquor) + net gold to carbon + carbon fines + change in gold inventory, with preg-robbing, a torn screen and cyanide dosing active.

Honest simplifications

Ideal, well-mixed tanks of equal volume; the carbon moves continuously rather than in pulses; a single Freundlich isotherm without competition from copper, calcium or organic fouling beyond the activity factor; first-order leaching on a two-component gold distribution instead of a particle-by-particle shrinking core; no tank-level or slurry-density control; all rate constants, volumes and the carbon properties are illustrative round numbers chosen to give industry-typical recoveries (about 90 to 96 %) and loaded-carbon grades (1 to 8 kg/t), not data from a specific mine. This is an educational process model, not a design tool; real plants must follow site cyanide-management practice.