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In our 1st article (Orr, 2000), we investigated different flow and transport phenomena that could significantly reduce leaching recovery. The combination of such understanding with advanced flow and transport modeling establishes the link between cause and effect, thereby directing operators to optimal design and construction of new heaps. Modeling of flow and transport in heaps could also point to a unique change in application method or rate that would maximize leaching enhancement of an existing heap under existing situation and leaching history. The use of such a model is cost effective in that it can simulate multiple scenarios of alternative leaching enhancement methods. By simulating a large number of irrigation scenarios, such a model can point to optimal and/or most promising alternatives for a particular heap. Our simulations concentrate on the effect of changes in application rates and heap design on changes in flow paths and enhanced leaching recovery. Based on such simulations, an intelligent control agent such as MRDS1 could build a new representation of the complex heap leaching system, and by learning from historical data and current information, it could provide optimal management of heap leaching and heap rinsing.

Putting it all together: From Conceptual Models to Simulations

With the exception of film flow and precipitation/dissolution, all of the preferential flow phenomena discussed above can be captured in a numerical model that is based on mass balance principles. We used a multiphase flow and transport model, FEHM - Finite Element Heat and Mass transport (developed by Los Alamos National Laboratories) to simulate flow and tracer transport in typical heaps. We examined two major types of hypothetical heaps: one is made of lifts of ore crushed and stacked uniformly, and one made of lifts of "run of mine" (ROM) constructed by successive dumping of blasted rocks, using trucks. For each heap type, uniformly stacked crushed ore and ROM, we adopted hydraulic parameters from published analyses of similar materials, and then perturbed these parameters about their mean values to reflect natural heterogeneity (the heterogeneity was somewhat exaggerated to emphasize the effect of heap structure on flow patterns within it. Though each heap is unique, the results show some patterns that provide insight into the general nature of flow and transport in heaps. The following Figures show simulated saturation, flow, and transport in different heaps under different conditions.

Figure 1 shows a cross section of saturation over time, up to 10.5 days from the start of solution application for the uniform heap. Figure 2 (a) and (b) shows saturation profiles during a leaching cycle of 20 days for the ROM heap. The simulations show "dry" zones within the heap throughout the cycle due to significant bypassing of the ore by the leach solution. Figures 3, 4, and 5 show transport of a tracer slug in a "uniform" heap under "high", "medium", and "low" application rates, respectively, while Figure 6 compares the different transport paths of the particles under the three different application rates. In particular, a close look at the high and medium flow rates (uppermost and middle pictures) reveals substantially different flow paths triggered by different flow rates, while flow paths under the "low" application rate are only slightly different from those generated by "medium" rates. That is, a significant change in flow rates does not necessarily imply a substantial change in flow paths. This emphasizes the need in modeling to design changes in application rate that will maximize leaching efficiency. A judicious construction of a heap could enable leaching enhancement that by a careful management of application rates.

It should be kept in mind that our modeling demonstration is compatible with specific (though hypothetical) heaps. For all management purposes, modeling of certain heaps under leaching is site specific and could vary significantly from one heap to another, depending on their hydraulic properties and their specific construction and operation histories. Only with a careful evaluation of heap parameters and careful monitoring over a period of time could a modeler construct a model that resembles the hydraulic behavior of a specific heap.

In order to further examine the effect of changes in application rates on changes in flow paths we took a closer look at the normalized application rate, expressed by the ratio of application rates to mean saturated permeability (q/?k?). Figures 7 and 8 show saturation profiles in square portions of ideal heaps (i.e., heaps constructed with no specific trend or anisotropy in mean permeability; also called "statistically homogeneous and isotropic"), under different q/k ratios. The "rows" consist of identical heap portions (with the same mean saturated permeability and same statistical structure) under different application rates, while the "columns" consist of identical application rates applied to similar heap portions (statistically identical) except for different mean saturated permeabilities. In Figure 7, only saturated permeability is perturbed, while in Figure 8, two inter-related parameters are perturbed - permeability and the pore size distribution parameter. Further, while Figure 7 represents a medium where saturated permeability and the pore size distribution are independent, in Figure 8, these parameters are functionally dependent on each other via scaling, based on the similarity theory (of Miller and Miller). This is reflected by the appearance of identical saturation profiles along the diagonal, implying that the only significant factor is the normalized application rate, q/?k?.

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President and CEO, Shlomo Orr, PhD, Peng, has over 33 years of extensive consulting, research, and project management experience in the field of Hydrology and Water Resources. He earned a PhD in Hydrology and Water Resources with a minor in Soil and Water Sciences, and BSc and MSC in Civil Engineering. Dr. Orr's background includes modeling, planning, and controlling complex subsurface flow and transport phenomena. He has a broad background in conceptual and computational-numerical modeling of fluid flow and solute transport in saturated and unsaturated porous and fractured formations, including stochastic models that account for uncertainties and provide the basis for risk assessment.

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