Predicting Unconventional Well Performance: R-Squared, Uncertainty, and the Influence of Multiple Dimensions
Scott Lapierre and Paul Duckworth
Pioneer Natural Resources
Current industry consensus seems to suggest that horizontal shale well performance is heavily influenced by no fewer than 5 principal drivers spanning multiple disciplines: engineering, geochemistry, petrophysics and geology. It is common practice among individual disciplines to isolate components and generate X-Y plots in pursuit of predictive relationships. While the cross plots often display obvious and expected relationships, the reliability of the predictions based on empirical regressions is not suitable for making sound investment decisions. A common method for evaluating the significance of regressed relationships is to use correlation coefficients (R-squared) with the assumption that a perfect correlation yields a coefficient of 1. Decision making based upon this outlook underappreciates the role of other parameters not included or considered in the X-Y relationship.
We review general concepts of uncertainty and their impact on R-squared in the 2-dimensional space of an X-Y plot. We simulate an abstract, 3-dimensional relationship and present it as a surface inside of a 3-D cross-plot cube. With R-squared as a guide, we illustrate how even a perfect relationship in three dimensions (R-squared = 1) worsens substantially when viewed, incompletely, from the side in two dimensions. We further demonstrate how the maximum possible R-squared visible in two dimensions will be limited expressly by (1) the total number of variables involved, (2) their relative distributions, and (3) the mathematical formula used to relate them. We bring the notion of incomplete projections of multidimensional problems to bear on common empirical solutions such as Multiple Linear Regression. We also provide a new context for scrutinizing the R-squared of regressed relationships commonly used to predict shale well performance.
AAPG Search and Discovery Article #90164©2013 AAPG Southwest Section Meeting, Fredericksburg, Texas, April 6-10, 2013