Active Learning Method for Estimating Missing Logs in Hydrocarbon Reservoirs

Characterization and estimation of physical properties are two of the most important key activities for successful exploration and exploitation in the petroleum industry. Pore-fluid pressures as well as estimating permeability, porosity, or fluid saturation are some of the important example of such activities. Due to various problems occurring during the measurements, e.g., incomplete logging, inappropriate data storage, or measurement errors, missing data maybe observed in recorded well logs. This unfortunate situation can be overcome by using soft computing approximation tools that will estimate the missing or incomplete data. Active learning method (ALM) is such a soft computing tool based on a recursive fuzzy modeling process meant to model multi-dimensional approximation problems. ALM breaks a multiple-input single-output system into some single-input single-output sub-systems and estimates the output by an interpolation. The heart of ALM is fuzzy measuring of the spread. In this paper, ALM is used to estimate missing logs in hydrocarbon reservoirs. The regression and normalized mean squared error (MSE) for estimating density log using ALM were equal to 0.9 and 0.042, respectively. The results, including errors and regression coefficients, proved that ALM was successful on processing the density estimation. ALM is illustrated by an example of a petroleum field in the NW Persian Gulf .

[1]  Nakaji Honda,et al.  A NEW METHOD FOR ESTABLISHING AND SAVING FUZZY MEMBERSHIP FUNCTIONS , 1997 .

[2]  M. Rider,et al.  The Geological Interpretation of Well Logs , 1986 .

[3]  Gustavo Deco,et al.  Two Strategies to Avoid Overfitting in Feedforward Networks , 1997, Neural Networks.

[4]  M. Reza Rezaee,et al.  Intelligent approaches for the synthesis of petrophysical logs , 2008 .

[5]  Karen Drukker,et al.  A study of the effect of noise injection on the training of artificial neural networks , 2009, 2009 International Joint Conference on Neural Networks.

[6]  Elena Bautu,et al.  Using Gene Expression Programming to estimate sonic log distributions based on the natural gamma ray and deep resistivity logs: A case study from the Anadarko Basin, Oklahoma , 2010 .

[7]  Zhen Zhu,et al.  Optimized Approximation Algorithm in Neural Networks Without Overfitting , 2008, IEEE Transactions on Neural Networks.

[8]  A. Ghaffari,et al.  Effective partitioning of input domains for ALM algorithm , 2013, 2013 First Iranian Conference on Pattern Recognition and Image Analysis (PRIA).

[9]  Nakaji Honda,et al.  Recursive Fuzzy Modeling Based on Fuzzy Interpolation , 1999, J. Adv. Comput. Intell. Intell. Informatics.

[10]  C. Crânganu,et al.  Quantitative estimation of expelled fluids from Oligocene rocks, Histria Basin, Western Black Sea , 2008 .

[11]  Emad A. El-Sebakhy,et al.  Functional networks as a new data mining predictive paradigm to predict permeability in a carbonate reservoir , 2012, Expert Syst. Appl..

[12]  Rene Preusker,et al.  Application of the Active Learning Method for the estimation of geophysical variables in the Caspian Sea from satellite ocean colour observations , 2007 .

[13]  M. Murakami,et al.  A comparative study of the IDS method and feedforward neural networks , 2005, Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005..

[14]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  S.B. Shouraki,et al.  Genetic Ink Drop Spread , 2008, 2008 Second International Symposium on Intelligent Information Technology Application.

[16]  Masayuki Murakami,et al.  Model Accuracy of the IDS Method for Three-input Systems and a Basic Constructive Algorithm for Structural Optimization , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[17]  Joseph Rynkiewicz.  General bound of overfitting for MLP regression models , 2011, ESANN.

[18]  Nakaji Honda,et al.  Outlines of a living structure based on biological neurons for simulatig the active learning method , 1997 .

[19]  Fouad Bahrpeyma,et al.  Fast fuzzy modeling method to estimate missing logsin hydrocarbon reservoirs , 2013 .

[20]  G. Wahba,et al.  A note on generalized cross-validation with replicates , 1992 .

[21]  M. Murakami,et al.  Hardware for a new fuzzy-based modeling system and its redundancy , 2004, IEEE Annual Meeting of the Fuzzy Information, 2004. Processing NAFIPS '04..

[22]  Mihaela Breaban,et al.  Using support vector regression to estimate sonic log distributions: A case study from the Anadarko Basin, Oklahoma , 2013 .

[23]  Jack P. C. Kleijnen,et al.  Cross-validation using the t statistic☆ , 1983 .