Evaluating the Sample Size for LIBS characterisation in Mining Operations

Abstract

In the mining industry, sampling is an essential feature for the characterization of the material when all available material cannot be examined and only a small fraction of the total is evaluated. This study addresses how the minimum number of samples required to obtain a statistically accurate answer. This is important since less sample measurement save time and money. The sample size is related to the homo- and heterogeneity of a rock sample, where the sample size of a homogeneous material is smaller than a heterogeneous material. Many types of research is carried out on the sampling theory, but it is hard to create a formula to determine the sample size beforehand based on a rate of heterogeneity. The homogeneity percentage is not linked to the sample size, but with a spatial elemental distribution, this can be possible. However, further research is needed in order to answer the question more exact for a situation that is more complex. This study first mentions several definitions of homogeneity, second their origin within geology is evaluated. Last this is calculated with theoretical models to explore the minimum sample size required. The project evaluates how the sample size changes when homogeneity, heterogeneity and spatial distribution of the grade varies within a rock image. It is done with the help of an image analysis tool which creates a homogeneity curve, the mean and standard deviations for an increasing sample size. The standard deviations are used to generate answer within different levels of confidence for certain margins of error.
Also, the variogram is used to determine the spatial correlation of the sample and interpolation is made using a general kriging method. Multiple images are evaluated with different rates of homogeneity, the number of elements and their spatial distribution. This study proofs generating more samples increases the accuracy of the characterization. With a lower target grade, the sample size will increase and also with an increasing image or grid size the number of samples will decrease. The variogram gives a first impression of the homogeneity since a smaller range and sill indicates more homogeneous material.