Reservoir characterization analysis resulting from incorrect applications of statistics can be found in the literature, particularly in applications where integration of various disciplines is needed. Here, we look at three misapplications of ordinary least squares linear regression (LSLR), show how they can lead to poor results, and offer better alternatives, where available. The issues are
Application of algebra to an LSLR-derived model to reverse the roles of explanatory and response variables that may give biased predictions. In particular, we examine pore-throat size equations (e.g., Winland’s and Pittman’s equations) and find that claims of overpredicted permeability may in part be because of statistical mistakes.
Using a log-transformed variable in an LSLR model, detransforming without accounting for the role of noise. This gives an equation that underpredicts the mean value. Several approaches exist to address this problem.
Misapplication of the coefficient of determination (R2) in three cases that lead to misleading results. For example, model fitting in decline curve analysis gives optimistic R2 values, as is also the case where a multimodal explanatory variable is present.
Using actual and synthetic data sets, we illustrate the effects that these errors have on analysis and some implications for using machine learning results.