A coupled DEM + SPH model can be used to predict the motion and breakage of resolved coarser particles within a SAG mill. The fine product from coarse particle fracture can then be included in the slurry phase modelled using SPH. This allows, in principle, the prediction of the breakage and transport of coarser material and the transport of the finer material within the grinding and pulp chambers of a SAG mill including discharge performance of the mill. It also allows the effect of the changing solids loading on the slurry rheology to be included. In this paper we will explore the development of an extension of this model that also allows prediction of the grinding of the finer particles embedded in the slurry phase due to the collisions and shear of the coarser particles (rocks and grinding media). The size distribution of the slurry fines is discretised into a set of size fractions so that its change due to grinding can be tracked at each point in the slurry. This is formulated as a system of coupled advection-diffusion equations. An SPH discretisation of this system is then developed. The resulting coupled SPH ODE's are solved using the SPH method in a way that is fully coupled to the DEM and SPH parts of the model. The proposed model includes a diffusive component that allows for the shear induced dispersion of the slurry size fractions and allows prediction of the spatial distribution of these fine size fractions within the slurry phase. The advection of the slurry is automatically accounted for by the motion of the SPH particles which is an important benefit of using the SPH method for such wet mill modelling. The local fine grinding behaviour arising from the coarse DEM resolved components of the charge are characterised at each location in terms of the local energy dissipation rate. This information is used in conjunction with a first order grinding law to predict the grinding of each slurry size fraction at each location in the mill due to the collisional action of the coarser particles. The ability of this new model to predict fine particle grinding and transport within the slurry phase is demonstrated for an industry standard 1.8 m diameter by 0.6 m long AG/SAG pilot mill.

中文翻译：

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使用耦合 DEM + SPH 模型预测 3D 中试 SAG 磨机中由于介质和粗岩相互作用引起的泥浆研磨

耦合的 DEM + SPH 模型可用于预测 SAG 磨机内解析的粗颗粒的运动和破碎。然后可以将粗颗粒破碎的精细产品包含在使用 SPH 建模的浆料相中。原则上，这允许预测在半自磨机的研磨和纸浆室中较粗材料的破碎和运输以及较细材料的运输，包括磨机的卸料性能。它还允许将改变的固体负载量对浆料流变学的影响包括在内。在本文中，我们将探索该模型扩展的发展，该模型还允许预测由于较粗颗粒（岩石和研磨介质）的碰撞和剪切而嵌入浆料相中的较细颗粒的研磨。浆料细粒的粒度分布被离散为一组粒度级分，以便可以在浆料中的每个点跟踪其因研磨而发生的变化。这被公式化为耦合对流-扩散方程的系统。然后开发该系统的 SPH 离散化。生成的耦合 SPH ODE 使用 SPH 方法以完全耦合到模型的 DEM 和 SPH 部分的方式求解。所提出的模型包括一个扩散分量，它允许浆料尺寸部分的剪切引起的分散，并允许预测这些细尺寸部分在浆料相内的空间分布。SPH 颗粒的运动自动考虑了泥浆的平流，这是使用 SPH 方法进行这种湿磨建模的一个重要好处。由装料的粗 DEM 解析分量引起的局部细磨行为在每个位置根据局部能量耗散率进行表征。由于粗颗粒的碰撞作用，该信息与一阶研磨定律结合使用，以预测磨机中每个位置的每种浆料粒度级分的研磨。这种新模型预测浆料相内细颗粒研磨和传输的能力已在工业标准 1.8 m 直径 x 0.6 m 长 AG/SAG 中试磨机中得到证明。由于粗颗粒的碰撞作用，该信息与一阶研磨定律结合使用，以预测磨机中每个位置的每种浆料粒度级分的研磨。这种新模型预测浆料相内细颗粒研磨和传输的能力已在工业标准 1.8 m 直径 x 0.6 m 长 AG/SAG 中试磨机中得到证明。由于粗颗粒的碰撞作用，该信息与一阶研磨定律结合使用，以预测磨机中每个位置的每种浆料粒度级分的研磨。这种新模型预测浆料相内细颗粒研磨和传输的能力已在工业标准 1.8 m 直径 x 0.6 m 长 AG/SAG 中试磨机中得到证明。