Summary
Predicting permeability from well logs typically involves classification of the well-log response into relatively homogeneous subgroups based on electrofacies, Lithofacies, or hydraulic flow units (HFUs). The electrofacies-based classification involves identifying clusters in the well-log response that reflect "similar" minerals and lithofacies within the logged interval. This statistical procedure is straightforward and inexpensive. However, identification of lithofacies and HFUs relies on core-data analysis and can be expensive and time-consuming. To date, no systematic study has been performed to investigate the relative merits of the three methods in terms of their ability to predict permeability in uncored wells.
The purpose of this paper is three-fold. First, we examine the interrelationship between the three approaches using a powerful and yet intuitive statistical tool called "classification-tree analysis." The tree-based method is an exploratory technique that allows for a straight forward determination of the relative importance of the well logs in identifying electrofacies, lithofacies, and HFUs. Second, we use the tree-based method to propose an approach to account for missing well logs during permeability predictions. This is a common problem encountered during field applications. Our approach follows directly from the hierarchical decision tree that visually and quantitatively illustrates the relationship between the data groupings and the individual well-log response. Finally, we demonstrate the power and utility of our approach via field applications involving permeability predictions in a highly complex carbonate reservoir, the Salt Creek Field Unit (SCFU) in west Texas. The intuitive and visual nature of the tree-classifier approach also makes it a powerful tool for communication between geologists and engineers.
Introduction
The estimation of permeability from well logs has seen many developments over the years. The common practice has been to crossplot core porosity and core permeability and to define a regression relationship to predict permeability in uncored wells based on the porosity from well logs.
However, permeability predictions in complex carbonate reservoirs are generally complicated by sharp local variations in reservoir properties caused by abrupt changes in the depositional environment. Another distinctive feature in carbonate reservoirs is the porosity/permeability mismatch (that is, low permeability in regions exhibiting high porosity and vice versa). All these features are extremely important from the point of view of fluid-flow predictions, particularly early-breakthrough response along high-permeability streaks.
A variety of approaches have been proposed to partition well-log responses into distinct classes to improve permeability predictions. The simplest approach uses flow zones or reservoir layering. Other approaches have used lithofacies information identified from cores, electrofacies derived from well logs, and the concept of HFUs. However, because of the extreme petrophysical variations rooted in diagenesis and complex pore geometry, reliable permeability predictions from well logs have remained an outstanding challenge, particularly in complex carbonate reservoirs. A major difficulty in this regard has been the proper classification of well logs in uncored wells.
Several problems are encountered in practical applications of current methodologies to data classification in uncored wells. These methods generally are based on a specific set of well logs; therefore, any missing well log can result in misclassification. This situation frequently occurs in field applications. Also, the impact of each well log in the final prediction is not clear. The situation is complicated by the fact that very often, the well logs are transformed into new variables such as principal components before classification. Furthermore, discriminant analysis, a statistical technique commonly used to assign classification on the basis of log response, is restricted to simple linear (or quadratic) additive models that may be inadequate, particularly for complex carbonate reservoirs. The current procedure for data partitioning and classifications using multivariate statistical analysis also tends to obscure communication between engineers and geologists. A simple and intuitive approach that works directly with well logs rather than transformed data can significantly improve this communication gap.
In this paper, we present a powerful graphical approach for data classification or partitioning for permeability predictions using well logs based on a statistical approach called classification-tree analysis. Tree-based modeling is an exploratory technique for uncovering structures in the data. It is a way to present rules to predict or explain responses both for categorical variables such as lithofacies or electrofacies and for continuous variables such as permeability. When we have continuous data as the response variable, the procedure is called "regression trees"; if the response variable is categorical data, it is called "classification trees." Although tree-based methods are useful for both classification and regression problems, we focus here on the former because our main concern is data partitioning or grouping for permeability predictions. The classification rules are obtained by applying a procedure known as recursive partitioning of the available data, applying splits successively until certain stop criteria are satisfied. Then the rules can be displayed in the form of a binary tree, hence the name.
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