非稳态非均相扩散反应模型及解法

非稳态非均相流体固体扩散反应模型具有较大的适应性.通常使用的收缩核心模型、两阶段模型和均相模型都是它的特殊情况.对于自钢渣中用碳酸钠和(或)碳酸氢钠溶液浸取钒的过程,考虑了波相双组份(CO_3~(2-) ,HCO_3~-及固相双组份(Ca(VO_3)_2,Ca(OH)_2)以及固体产物覆盖层对钒浸出率的影响,建立了模型方程.模型方程采用正交配置法和半隐态龙格库塔(Runge-Kutta)法求解,参数估算采用复合形法,计算结果和实验值符合良好.多相非催化流体固体反应的数学模型在广泛的领域内有重要的实用意义.对于这一类数学模型已有较好的综述文章.在冶金及其他工业上待提取的固相物料往往嵌布在惰性介质(脉石)上,体现在微观结构上较大的分散性,宜用体积反应的数学模型.     

MATHEMATICAL MODELING OF NON-CATALYTIC LIQUID-SOLID REACTION AND ITS SOLUTION BY ORTHOGONAL COLLOCATION

The mathematical model of non-catalytic liquid-solid diffusion reactions discussed in this paper can be applied to quite different cases. The models in the literature such as unreacted shrinking core model, two stage model and homogeneous model can be considered as special cases of the above model which has been derived for leaching vanadium from steel slag with sodium carbonate and]or sodium bicarbonate solution reacting with two components in the slag simultaneously. The vanadium leaching reaction is inhibited by the solid product formed during the reaction. The power law equation can be used to represent the kinetic experimental data of leaching reaction. The model equations have been solved by orthogonal collocation and semi-implicit Runge-Kutta method. The parameters of the model have been estimated by the complex method. The calculated results based on this model is in good agreement with experimental data.