铝土矿连续球磨过程建模与关键参数优化
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摘要
铝土矿选矿是我国首创的处理高硅铝矿石的新工艺,该工艺通过提高矿石的铝硅比使其适用于拜耳法氧化铝生产,以降低氧化铝的生产成本,具有很好的发展前景。球磨是选矿中一个十分重要的环节,它将经过破碎的铝土矿磨碎至一定细度,得到有用矿物基本单体解离或富集合的颗粒,再经过分级过程后供浮选,其经济和技术指标的好坏直接关系着整个选厂的经济和技术指标。
由于铝土矿来源复杂、品位波动频繁,其球磨过程由人工凭经验控制,造成流程指标波动大、效率低等问题。建立铝土矿球磨过程模型,对研究流程的行为和实现优化控制具有重要意义。然而,球磨过程影响因素众多且相互耦合,包括物料的性质、介质参数、操作变量、磨机规格、转速等,是一个非常复杂的系统。同时,这些因素的多变性和过程中的随机因素大大增加了建模的难度。
获得物料的破碎分布函数(B)、物料在磨机内的停留时间分布(RTD)函数和连续磨矿物料的比破碎速率函数(S)是建立球磨过程模型的关键,因此,本论文深入研究并优化确定了这三个函数参数,从而建立了球磨机磨矿过程的总体平衡模型,并将其引入磨矿分级过程的数据协调。对实际生产数据的预测结果表明了球磨机模型的有效性。论文主要研究工作及创新性如下：
(1)针对矿石粒度分布严重不均造成自然粒级给料的磨矿数据无法准确确定破碎分布函数,而传统单粒级给料方法试验工作量大的问题,基于组合粒级给料方式的分批磨矿试验方法,获取了大量的试验数据,揭示了铝土矿破碎的非一阶特性,即铝土矿粗粒级和细粒级的破碎速率随时间的增加逐渐减小,而引起非一阶的最可能原因是铝土矿本身的非均质性。
(2)针对铝土矿不同粒级破碎速率随时间变化快慢不同,且磨矿开始时减速快,然后逐渐趋于一阶的特点,提出了分段线性化的非一阶破碎描述方法。该方法对磨矿时间进行分段,假设每一时间段内破碎符合一阶规律,以前一时间段的产品作为后一时间段的给料来计算物料的破碎速率和产品粒度分布,进而准确地确定了分批磨矿破碎速率随粒度和时间变化的三维关系,且简化了模型的求解。在此基础上,优化确定了铝土矿的破碎分布函数。基于所获参数,对分批磨矿产品粒度进行预测,累积粒度分布的相对误差均位于±5%以内,非累积粒度分布的绝对误差均位于±2%以内,表明了所获参数具有较高的准确性。
(3)结合磨机本身的分级作用,采用两个小混合器加一个大混合器的等价模型表示RTD。针对等价模型参数示踪测量方法难度大,而从实际生产数据辨识的方法会影响破碎速率函数精度的问题,提出基于实测数据直接估算平均停留时间的方法,从而确定了铝土矿连续球磨的RTD,并避免了RTD对破碎速率函数的影响。
(4)针对铝土矿的非均质性,基于分批磨矿结果,提出了连续磨矿的非一阶破碎速率函数模型；针对破碎速率函数优化辨识的边界约束不确定问题,提出了基于软约束调整的优化方法,保证破碎速率满足给定目标的同时减小了搜索代价,进而确定了不同生产条件下最优的破碎速率函数；分析破碎速率与磨矿条件和矿石性质的关系,建立了破碎速率函数的最小二乘支持向量机(LS SVM)软测量模型。
(5)针对磨矿分级过程数据存在采样和分析误差的问题,结合数据的层次特点,提出了磨矿分级过程三层数据协调模型,并将球磨机单元模型引入粒度数据协调中,增强了数据的冗余性。提出了基于PSO算法的分层协调方法,保证协调精度的同时加快了协调的求解效率。协调结果的统计分析,以及与商业软件协调结果的对比证明了协调模型和方法的有效性,也进一步证明了球磨机模型的有效性。
Beneficiation of diasporic bauxite, created firstly in China, is one of the new potential technologies to process high silica bauxite, which eliminates some silica minerals to increase the grade of the ores so that they are suitable for the Bayer process, and in consequence, the cost of alumina production is reduced. Ball milling is an important operation unit in the beneficiation process, which grinds the comminuted ores to small particles and liberates the alumina from silica minerals for classification and then flotation. The economical and technical indices of the benification plant are directly influenced by the grinding process.
In practice, the ores come from many mine resources and the grade of the ores varies frequently, and the process is controlled empirically by the operators. All of these result in large fluctuation of the grinding circuit and low efficiency. So, modelling the process is significant to understand and to optimally control the process. However, the ball milling process is influenced by many factors, including the properties of the materials, the media characteristics, operating conditions, mill size and speed etc., so that it is a complex process. Meanwhile, time-varying of these factors and other stochastic factors make it even more diffcult to model the process.
The breakage distribution function (B), residence time distribution (RTD) of the miaterial in the mill and the specific breakage rate function (S) of the continuous milling process are the key parameters to establish the ball milling model. Therefore, these three functions are studied and optimally determined to establish the population balance model. Finally, data reconciliation of the grinding-classification process based on the ball mill model is studied. The prediction results of the industrial process show the effectiveness of the model. The main contributions are as follows:
(1) The size distribution function can not be correctly determined because there are too few medium size particles in the natural size distribution of the bauxite. Meanwhile the mono-sized grinding method is time-consuming and expesive. So, a test method with make-up feed is adopted to get a large amount of test data. The breakage rates of the bauxite are found to be non-first order from the test data. That is, the coarse and the fine size intervals break slowly and follow non-first order, and the medium size intervals break fast and follow the first order. The non-first order is most probably caused by the heterogeneity of the ore.
(2) According to the characteristic that breakage rates of different size intervals decrease fast at different rates with time at the beginning and then become to be first order, piecewise linearized method is proposed to describe the non-first order. In the method, grinding time is devided into pieces, and breakage is assumed to be first order in each time piece. Breakage rates and product size distribution are then calculated by taking the product of last piece as feed. So, the 3D relationship of the breakage rates varying with particle size and grinding time is accurately determined and the model solving problem is simplified. The breakage distribution function is then optimally determined by using back-calculation method. Validation results show that relative errors of the cumulative size distribution are all within±5%, and absolute errors of noncumulative size distribution are all within±2%, which means high accuracy of the obtained parameters.
(3) Based on the mechanism of the material transportation through the mill and the exit classification of the mill, the two small-one large reactors model is used as the RTD model. Because it is difficult to use the radio tracking method to get the RTD parameters in the bauxite grinding process and fitted RTD will influence the accuracy of breakage rate function, a mean RTD estimation method based on measured and empirical data is then proposed to avoid the influence of RTD on breakage rate.
(4) Considering of the heterogenerity of the bauxite, a non-first order breakage rate model is proposed for the continuous grinding process. Due to the uncertainty of the boundary constraints of the breakage rate identification problem, an optimization method based on soft constraints adjusting is proposed, which insures the breakage rates are satisfying and cost of searching is reduced. The optimal breakage rates under different operating conditions are then identified from the industrial data. A soft sensor using least square support vector model (LS_SVM) is proposed to calculate the breakage rates using milling condition parameters.
(5) In order to correct the sampling and analysis errors of the process data, a triple-layer data reconciliation model is proposed for the grinding-classification process based on the characteristic of the process data. Meanwhile, the ball mill unit is introducted into the size distribution reconciliation to increase the redundancey the process data. Then, the method of solving the reconciliation problem layer by layer based on PSO is proposed to reduce the time complexity of the problem. The statistical analysis of the reconciliation results and comparison of them with the reconciliation results using a commercial software validate the effectiveness of the reconciliation model and the method, and also the ball mill model.
由于铝土矿来源复杂、品位波动频繁,其球磨过程由人工凭经验控制,造成流程指标波动大、效率低等问题。建立铝土矿球磨过程模型,对研究流程的行为和实现优化控制具有重要意义。然而,球磨过程影响因素众多且相互耦合,包括物料的性质、介质参数、操作变量、磨机规格、转速等,是一个非常复杂的系统。同时,这些因素的多变性和过程中的随机因素大大增加了建模的难度。
获得物料的破碎分布函数(B)、物料在磨机内的停留时间分布(RTD)函数和连续磨矿物料的比破碎速率函数(S)是建立球磨过程模型的关键,因此,本论文深入研究并优化确定了这三个函数参数,从而建立了球磨机磨矿过程的总体平衡模型,并将其引入磨矿分级过程的数据协调。对实际生产数据的预测结果表明了球磨机模型的有效性。论文主要研究工作及创新性如下：
(1)针对矿石粒度分布严重不均造成自然粒级给料的磨矿数据无法准确确定破碎分布函数,而传统单粒级给料方法试验工作量大的问题,基于组合粒级给料方式的分批磨矿试验方法,获取了大量的试验数据,揭示了铝土矿破碎的非一阶特性,即铝土矿粗粒级和细粒级的破碎速率随时间的增加逐渐减小,而引起非一阶的最可能原因是铝土矿本身的非均质性。
(2)针对铝土矿不同粒级破碎速率随时间变化快慢不同,且磨矿开始时减速快,然后逐渐趋于一阶的特点,提出了分段线性化的非一阶破碎描述方法。该方法对磨矿时间进行分段,假设每一时间段内破碎符合一阶规律,以前一时间段的产品作为后一时间段的给料来计算物料的破碎速率和产品粒度分布,进而准确地确定了分批磨矿破碎速率随粒度和时间变化的三维关系,且简化了模型的求解。在此基础上,优化确定了铝土矿的破碎分布函数。基于所获参数,对分批磨矿产品粒度进行预测,累积粒度分布的相对误差均位于±5%以内,非累积粒度分布的绝对误差均位于±2%以内,表明了所获参数具有较高的准确性。
(3)结合磨机本身的分级作用,采用两个小混合器加一个大混合器的等价模型表示RTD。针对等价模型参数示踪测量方法难度大,而从实际生产数据辨识的方法会影响破碎速率函数精度的问题,提出基于实测数据直接估算平均停留时间的方法,从而确定了铝土矿连续球磨的RTD,并避免了RTD对破碎速率函数的影响。
(4)针对铝土矿的非均质性,基于分批磨矿结果,提出了连续磨矿的非一阶破碎速率函数模型；针对破碎速率函数优化辨识的边界约束不确定问题,提出了基于软约束调整的优化方法,保证破碎速率满足给定目标的同时减小了搜索代价,进而确定了不同生产条件下最优的破碎速率函数；分析破碎速率与磨矿条件和矿石性质的关系,建立了破碎速率函数的最小二乘支持向量机(LS SVM)软测量模型。
(5)针对磨矿分级过程数据存在采样和分析误差的问题,结合数据的层次特点,提出了磨矿分级过程三层数据协调模型,并将球磨机单元模型引入粒度数据协调中,增强了数据的冗余性。提出了基于PSO算法的分层协调方法,保证协调精度的同时加快了协调的求解效率。协调结果的统计分析,以及与商业软件协调结果的对比证明了协调模型和方法的有效性,也进一步证明了球磨机模型的有效性。
Beneficiation of diasporic bauxite, created firstly in China, is one of the new potential technologies to process high silica bauxite, which eliminates some silica minerals to increase the grade of the ores so that they are suitable for the Bayer process, and in consequence, the cost of alumina production is reduced. Ball milling is an important operation unit in the beneficiation process, which grinds the comminuted ores to small particles and liberates the alumina from silica minerals for classification and then flotation. The economical and technical indices of the benification plant are directly influenced by the grinding process.
In practice, the ores come from many mine resources and the grade of the ores varies frequently, and the process is controlled empirically by the operators. All of these result in large fluctuation of the grinding circuit and low efficiency. So, modelling the process is significant to understand and to optimally control the process. However, the ball milling process is influenced by many factors, including the properties of the materials, the media characteristics, operating conditions, mill size and speed etc., so that it is a complex process. Meanwhile, time-varying of these factors and other stochastic factors make it even more diffcult to model the process.
The breakage distribution function (B), residence time distribution (RTD) of the miaterial in the mill and the specific breakage rate function (S) of the continuous milling process are the key parameters to establish the ball milling model. Therefore, these three functions are studied and optimally determined to establish the population balance model. Finally, data reconciliation of the grinding-classification process based on the ball mill model is studied. The prediction results of the industrial process show the effectiveness of the model. The main contributions are as follows:
(1) The size distribution function can not be correctly determined because there are too few medium size particles in the natural size distribution of the bauxite. Meanwhile the mono-sized grinding method is time-consuming and expesive. So, a test method with make-up feed is adopted to get a large amount of test data. The breakage rates of the bauxite are found to be non-first order from the test data. That is, the coarse and the fine size intervals break slowly and follow non-first order, and the medium size intervals break fast and follow the first order. The non-first order is most probably caused by the heterogeneity of the ore.
(2) According to the characteristic that breakage rates of different size intervals decrease fast at different rates with time at the beginning and then become to be first order, piecewise linearized method is proposed to describe the non-first order. In the method, grinding time is devided into pieces, and breakage is assumed to be first order in each time piece. Breakage rates and product size distribution are then calculated by taking the product of last piece as feed. So, the 3D relationship of the breakage rates varying with particle size and grinding time is accurately determined and the model solving problem is simplified. The breakage distribution function is then optimally determined by using back-calculation method. Validation results show that relative errors of the cumulative size distribution are all within±5%, and absolute errors of noncumulative size distribution are all within±2%, which means high accuracy of the obtained parameters.
(3) Based on the mechanism of the material transportation through the mill and the exit classification of the mill, the two small-one large reactors model is used as the RTD model. Because it is difficult to use the radio tracking method to get the RTD parameters in the bauxite grinding process and fitted RTD will influence the accuracy of breakage rate function, a mean RTD estimation method based on measured and empirical data is then proposed to avoid the influence of RTD on breakage rate.
(4) Considering of the heterogenerity of the bauxite, a non-first order breakage rate model is proposed for the continuous grinding process. Due to the uncertainty of the boundary constraints of the breakage rate identification problem, an optimization method based on soft constraints adjusting is proposed, which insures the breakage rates are satisfying and cost of searching is reduced. The optimal breakage rates under different operating conditions are then identified from the industrial data. A soft sensor using least square support vector model (LS_SVM) is proposed to calculate the breakage rates using milling condition parameters.
(5) In order to correct the sampling and analysis errors of the process data, a triple-layer data reconciliation model is proposed for the grinding-classification process based on the characteristic of the process data. Meanwhile, the ball mill unit is introducted into the size distribution reconciliation to increase the redundancey the process data. Then, the method of solving the reconciliation problem layer by layer based on PSO is proposed to reduce the time complexity of the problem. The statistical analysis of the reconciliation results and comparison of them with the reconciliation results using a commercial software validate the effectiveness of the reconciliation model and the method, and also the ball mill model.
引文
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