Prediction of Air Flows Through Broken Rock by Finite Difference Grids

A numerical technique is described which can be used to model the quantity and distribution of air flow through broken rock. The method can also describe gas concentration and temperature distribution. A computer code implementing the numerical approach was developed to assist in determining the feasibility of a proposed modified in-situ leaching method for extracting copper from sulfide porphyry deposits. This mining method requires air to be forced through cells of rubblized ore. The flow serves to supply oxygen for the leaching reactions and to dissipate heat that would other-wise build due to the exothermic reactions. The method substitutes the Carman equation into the Laplace equation. The solution of the resulting non-linear formulation is done on a finite difference grid using SOR with iteration improvement of coefficients. This procedure yields the required air flow pattern and pressure drop. An equation for advection with absorption is then solved over the same grid using explicit schemes to yield oxygen concentration. Finally, a similar technique is applied to the convective heat transfer formula to yield the temperature profile. The model is potentially applicable to such mining problems as the prediction of leakage through caved ground, the prediction of methane concentration in gobbed ground, and the prediction of heat build-up in caved workings.