Alternating Conditional Expectation (ACE) Algorithm for Permeability Estimation in Bahariya Formation
Authors: Mokhtar Ali Hesham , Abu El Ela Mahmoud , El-Banbi Ahmed 
Published: May 2021

Summary
The nonparametric transformation is a data-driven technique, which can be used to estimate optimal correlations between a dependent variable (response) and a set of independent parameters (predictors). This study introduces a systematic methodology using the nonparametric transformation concept and the alternating conditional expectation (ACE) algorithm to estimate the effective gas permeability using conventional logs and the core data. The ACE algorithm was employed in the current work using the MATLAB® (The MathWorks, Inc., Natick, Massachusetts, USA) code and the open-source GRaphical ACE (GRACE) software (Xue et al. 1997) for deriving the optimal nonparametric correlations for predicting the permeability. The methodology was applied to a heterogeneous formation [Bahariya (BAH)] in Egypt to understand its characteristics and predict its permeability more accurately.
The BAH Formation is considered one of the main sources for oil production throughout the Western Desert (WD) of Egypt. The cumulative oil production from the BAH Formation is estimated to be approximately 40% of the total WD production. The reservoir characteristics of the BAH Formation range from highly permeable to tight sandstone interbedded with shale and siltstone. It usually depicts low-resistivity and low-contrast (LRLC) log behavior. Thus, regional and accurate determination of the reservoir permeability for the different rock units of the BAH Formation across the WD is a challenge. Conventional well log data from approximately 100 cored wells and corresponding 5,500 core measurements were used to provide a regional permeability correlation that can be used in a large number of reservoirs.
The methodology of this work included two main steps:
Applying the nonparametric transformation technique to identify the collective log responses for deriving optimal correlation Predicting the permeability profiles using the selected log responses
The model was applied to many wells that address different petrophysical characteristics of the BAH Formation. The established permeability profiles showed reliable correlation coefficients relative to the measured core data. The correlation coefficient was 0.893 for the training data points (75% of the collected database) and 0.913 for the testing data points (25% of the collected database). In addition, the mean absolute percentage error (MAPE) between the predicted and the measured permeability for the training and testing data points were 5.93 and 4.14%, respectively.
Permeability prediction using ACE is compared with other techniques such as k-ϕ crossplots, multiple linear regression (MLR), Coates, and Wyllie-Rose correlations.
This work is considered an original contribution to present regional permeability prediction correlations using the conventional well logs for reservoir characterization and simulation applications. The ACE algorithm was successfully applied to the BAH Formation and proved its capability to identify the best predictors that are required to establish a rigorous model.