JKSimMet can be used to predict the performance of a grinding circuit through the use of a circuit model which incorporates models of each unit operation in the circuit. The unit operations are linked to create a single circuit model using connecting streams. The model can be used to predict the circuit behaviour under different operating conditions, including differing breakage properties of the feed ore, changing throughput requirements or changes to the product P80 specification. 

Comminution theory is an integral part of JKSimMet. Every unit operation is represented by a mathematical model describing the breakage and/or classification in that unit. The development of each model is based on years of research at the JKMRC. The details of each mathematical model in JKSimMet can be found in the User Manual or the Monograph. 

The general theory behind using JKSimMet to mass balance a set of circuit data and tailor the mathematical models (model fit) to the specific circuit is covered below. 

Mass Balancing 

When developing a model of an existing grinding circuit, the first step is to take a set of survey data and mass balance it. Mass balancing is a process in which the measured survey data is adjusted according to a minimisation of error method to give a set of data which balances perfectly across all units and for all components. The process is described by the following equation: 

(1)

Where:    WSSQ = Weighted Sum of Squares 
                Mi= measured value of component i 
                Bi = balanced value of component i 
                SDi = Standard Deviation of measured value Mi 

In mass balancing, the measured values include flows, densities, size fractions and components. 

The mass balancing method aims to minimise the Weighted Sum of Squares. For every measured value Mi there is a corresponding balanced value Bi which is an adjusted approximation of the measured value. Weighting is applied to each measured value according to the degree of confidence in the measurement of that value. The weighting or standard deviation of the measured data (SDi) affects how much the data is adjusted during mass balancing.

A high degree of confidence in a measured value equates to a small SD. The mass balancing process minimises the adjustment to values with small SDs since any adjustment will contribute greatly to the overall sum of squares error, according to Equation (1). Conversely, a large SD means that there is less confidence in a measured value and the mass balancing process will allow larger adjustments to that value since the adjustments will not contribute as significantly to the overall sum of squares. 

In this way, the data is adjusted so that a fully balanced set of data is achieved which results in a minimum sum of squares error. 

Model Fitting 

The next step in developing a model of the grinding circuit is to take the mass balanced data and use it to customise the equipment models so that the predicted outputs from the models match the measured outputs. This process is called ‘model-fitting’. 

JKSimMet contains models of many types of equipment commonly found in grinding circuits including: ball mills, AG/SAG mills, rod mills, hydrocyclones, crushers, screens and high pressure grinding rolls (HPGRs). Although the models for each unit operation are different, they have a number of characteristics in common. 

Each model has two sets of parameters: machine dependent parameters and ore dependent parameters. The ore dependent parameters for a given circuit can be measured by carrying out tests on samples of the actual ore. The value of the machine dependent parameters vary depending on the specific operation and the best possible value for a given machine is determined in a process called “model-fitting”. 

Model-fitting is similar to the mass balancing process. The following diagram describes the process: 

Parameters in the model are adjusted until the difference between the measured outputs from a process, Mi, and the predicted outputs from the model of the process, Pi, result in a minimum weighted sum of squares. 

As in mass balancing, the measured values are assigned a weighting, or standard deviation, which defines how accurate the measured value is expected to be based on the confidence in the measurement procedure. A small SD means that there is a high degree of confidence that the measured value is accurate. The model parameters will be adjusted so that the measured and predicted values agree very closely. Conversely, a large SD means that the degree of confidence in the measurement technique of a value is not high and the model parameter adjustment will not be so sensitive in ensuring that the measured values agree closely with the predicted values. 

The best values of the model parameters are those which give the lowest weighted sum of squares error between the measured and predicted outputs. 

Simulation Studies – Existing Plants and New Plants 

Once the two steps of mass balancing and model fitting are completed, the circuit model is ready to be used for simulation and optimisation studies. The comminution consultant is able to use the model to investigate the various options and determine the predicted results with changes in circuit details. 

If the circuit does not exist, it is not possible to survey the plant and have real data to balance and model fit. In this case, the mass balancing and model fitting processes are impossible. Instead, suitable model parameters from a similar circuit treating similar ore are borrowed from the JKTech database of previous jobs and used in the model of the proposed new circuit. The model is developed based on these borrowed parameters and the simulation study is able to proceed.