Optimal Transformations for Multiple Regression: Application to Permeability Estimation From Well Logs

Abstract

Conventional multiple regression for permeability estimation from well logs requires a functional relationship to be presumed. Because of the inexact nature of the relationship between petrophysical variables, it is not always possible to identify the underlying functional form between dependent and independent variables in advance. When large variations in petrological properties are exhibited, parametric regression often fails or leads to unstable and erroneous results, especially for multivariate cases.In this paper, we describe a nonparametric approach for estimating optimal transformations of petrophysical data to obtain the maximum correlation between observed variables. The approach does not require a priori assumptions of a functional form, and the optimal transformations are derived solely based on the data set. Unlike neural networks, such transformations can facilitate physically based function identification. An iterative procedure involving the alternating conditional expectation (ACE) forms the basis of our approach. The power of ACE is illustrated using synthetic as well as field examples. The results clearly demonstrate improved permeability estimation by ACE compared to conventional parametric-regression methods.

Integrating well log interpretations for lithofacies classification and permeability modeling through advanced machine learning algorithms

“…These algorithms include multiple linear regression (Dahraj and Bhutto 2014;Mohaghegh et al 1997;Xue et al 1997), generalized additive modeling (Al-Mudhafar and Mohamed 2015; AlMudhafar and Bondarenko 2015; Lee et al 2002;Rafik and Kamel 2016), multivariate adaptive regression splines (Al-Mudhafar and Al-Khazraji 2016;Xie 2008), neural networks (Lee and Datta-Gupta 1999;Lee et al 2002;Mohaghegh et al 1997), fuzzy logic (Nashawi and Malallah 2009), and support vector regression (Al-Anazi and Gates 2011).…”

Inflow Performance Relationship Correlation for Solution Gas-Drive Reservoirs Using Non-Parametric Regression Technique

“…Neural Network modeling can be considered as one of the nonparametric modeling approaches and has wide range of applications in oil industry. However, the method that was used here is based on the Alternating Conditional Expectation (ACE) algorithm [26,27]. A comparison between Neural Network and ACE algorithm was used to build bubble point pressure correlation for oil reservoirs [28] and it was found that the predictive strength of ACE is much higher compared to Neural Network for the studied samples.…”

“…(20). The 550 several combinations of the 9 sensitive parameters which represent the independent variables with one dependent variable that is C 1 were used in the ACE Algorithm [27] to find the best correlation between the dependent and the independent variables. The resulted IPR correlation is given in Eq.…”

Predicting CO2Minimum Miscibility Pressure (MMP) Using Alternating Conditional Expectation (ACE) Algorithm

“…It can be applied both in bivariate and multivariate cases and it yields maximum correlations in transformed space (Malallah et al, 2006). A modification of ACE algorithm with graphical (GRACE) interface was later proposed by Xue et al (1997).…”