An empirical determination of the minimum number of measurements needed to estimate the mean random vitrinite reflectance of disseminated organic matter

Abstract

In coal samples, published recommendations based on statistical methods suggest 100 measurements are needed to estimate the mean random vitrinite reflectance ( R v−r ) to within ±2%. Our survey of published thermal maturation studies indicates that those using dispersed organic matter (DOM) mostly have an objective of acquiring 50 reflectance measurements. This smaller objective size in DOM versus that for coal samples poses a statistical contradiction because the standard deviations of DOM reflectance distributions are typically larger indicating a greater sample size is needed to accurately estimate R v−r in DOM. However, in studies of thermal maturation using DOM, even 50 measurements can be an unrealistic requirement given the small amount of vitrinite often found in such samples. Furthermore, there is generally a reduced need for assuring precision like that needed for coal applications. Therefore, a key question in thermal maturation studies using DOM is how many measurements of R v−r are needed to adequately estimate the mean. Our empirical approach to this problem is to compute the reflectance distribution statistics: mean, standard deviation, skewness, and kurtosis in increments of 10 measurements. This study compares these intermediate computations of R v−r statistics with a final one computed using all measurements for that sample. Vitrinite reflectance was measured on mudstone and sandstone samples taken from borehole M-25 in the Cerro Prieto, Mexico geothermal system which was selected because the rocks have a wide range of thermal maturation and a comparable humic DOM with depth. The results of this study suggest that after only 20–30 measurements the mean R v−r is generally known to within 5% and always to within 12% of the mean R v−r calculated using all of the measured particles. Thus, even in the worst case, the precision after measuring only 20–30 particles is in good agreement with the general precision of one decimal place recommended for mean R v−r measurements on DOM. The coefficient of variation ( V = standard deviation/mean) is proposed as a statistic to indicate the reliability of the mean R v−r estimates made at n ⪡ 20. This preliminary study suggests a V < 0.1 indicates a reliable mean and a V > 0.2 suggests an unreliable mean in such small samples.