Evaluating Early-Time Eagle Ford Well Performance Using Multivariate Adaptive Regression Splines (MARS)
Authors: Gao Chao (Chad) , Gao Hong (Heidi) 
Published: September 2013

Abstract
Horizontal wells with multi-stage hydraulic fracturing have dramatically boosted Eagle Ford production since 2008. Due to the high drilling and completion costs, compared to the wells with conventional drilling and completion, operators have been trying to improve development economics by understanding unconventional plays and optimizing stimulation treatments using various data analysis techniques. In this paper, the multivariate regression analysis method is used to evaluate the Eagle Ford production and completion data for wells within 3-5 years’ production as a means to determine the correlations of production performance with completion and other variables. A ‘big-picture’ view with 174,000 acres were initially chosen for the study, where 487 wells were selected in the portion of the Eagle Ford oil "window" located in Karnes and Live Oak counties. 2D heat maps and 3D plots were applied to illustrate the correlation and the relative importance of each variable. Among 487 wells selected for data evaluation, only 273 wells were used for the multivariate regression analysis due to the data incompleteness for some of the wells. In the data analysis and multivariate regression analysis of this paper, it was demonstrated that the proppant tonnage and horizontal lateral length are not the most important variables affecting the early-time production in the study area, as may be expected by many engineers. We have nine (9) variables selected for this study. Those variables (proppant tonnage and horizontal lateral length) are generally less important than formation depth and tubing flowing pressure. However, frac fluid amount shows importance in the gas condensate area, between reservoir depth between 12,000 to 12,500 ft. In the same depth region (12,000 to 12,500 ft), the proppant tonnage and horizontal lateral length don't correlate with production well in the region of (2000 - 5000 tons of sand and 2000 - 6000 ft of lateral), meaning that this could be the water frac candidate area (more water, less proppant). They may even be less important than fluid properties (gas oil ratio (GOR) and oil API gravity, which are related to oil viscosity). Approximate linear relationships of early-time production vs. tonnage or lateral length could be observed when a well group is selected in a small area where the geological, petrophysical, reservoir and fluid properties are nearly constant. Optimizations of proppant tonnage, lateral length and/or frac fluid amount may be performed based on the relationships.
The main operators in this study area are Marathon (147 wells), Burlington Resources (137 wells), Plains Exploration & Production (53 wells). Other major players like EOG, Pioneer, Petrohawk, Hilcorp and Murphy are also in the area.
Multivariate Adaptive Regression Splines (MARS) is a form of regression analysis introduced by Jerome Friedman in 1991.[1] It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models non-linearities (locally spline fitting) and interactions among variables. The MARS acronym was used for the multivariate regression calculation engine developed by Salford-Systems. This paper introduces the MARS algorithm of Friedman for estimating the transformations of a response and a set of predictor variables in multiple regression problems in the petroleum industry, especially for unconventional play analyses. In particular, we present the results from the MARS calculation engine developed by Salford-Systems to evaluate early-time Eagle Ford well production performance utilizing publicly available production and well completion data. It appears that this is the first documented application of the MARS algorithm to analyze and interpret petroleum industry data. We demonstrate that the MARS method has certain advantages in some fitting problems of the petroleum industry over other multivariate regression algorithms. In this paper, we demonstrate our model built using MARS in a mathematical function form with more than 40 linear basis functions. Basis functions with two variables reveal the interaction between the two variables. We are able to achieve the naive R^2 in a range of 0.7 - 8.5 with a small data set (273 wells). The ANOVA decomposition analysis of the MARS model really enhances our understanding about our complex unconventional data.