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 straightforward
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.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
6 April 2004
- Revised manuscript received:
22 December 2004
- Manuscript approved:
27 January 2005
- Version of record:
15 April 2005
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