The oil and gas industry has used multivariate analysis (MVA) to evaluate how geology, reservoir, and drilling/completion parameters (well characteristics) relate to well production. Although many techniques are used, multiple linear regression (MLR) has been especially popular due to its ease of use and the interpretability of its parameters. However, when the relationship between response and predictor variables is highly complex or nonlinear, this technique can yield erroneous and misleading results. Recent work showed the benefit of combining statistical MLR with fracture and numerical reservoir (physics-based) modeling, which yields a more physically realistic production response to suggested completion changes (Mayerhofer, 2017). However, this work is limited to using the nonlinear relationships between production outcomes and only a few independent variables (i.e., proppant/fluid volumes pumped and fracture spacing). For practicality, other important predictors are still assumed to be linearly correlated to the response variable (e.g., predicted cumulative oil).
In this paper, we describe the implementation of the Alternating Conditional Expectations (ACE) approach and the interpretation of its results, and we highlight the main advantages and limitations of the approach in MVA using a simulated dataset and field data from the Permian Basin. The ACE approach is a non-parametric regression method (i.e., no explicit assumption about the relationships between dependent or response and independent or predictor variables is required). It maximizes the linear correlation between the response and predictor variables in the transformed space (the optimal transformations are derived solely from the given data) resulting in higher R-squared (R2) and smaller Root-Mean-Square-Error (RMSE) values compared to those obtained from the MLR. Because a priori assumptions about the functional form for a transformation (e.g., linear, monotonic, periodic, and polynomial) do not have to be imposed, the ACE-guided transformation can give new insights into the relationship between the response and predictor variables.
We have successfully identified nonlinear relationships between well production and completion/reservoir properties for horizontal wells in the Permian Basin by means of ACE plots, and we have developed closed functional forms for these relationships. When integrated into the overall workflow of MVA, coupled with completion cost models, the ACE model could produce more realistic and accurate well performance predictions— using not only completion/reservoir parameters that are easily calibrated or "history-matched" as in the physics-based models, but also parameters that cannot be conveniently evaluated with the physics-based models.