Summary
This paper describes the procedure of building a probabilistic decision tree
on the basis of the integration of data from multiple sources, conditional
probabilities, and the application to map fracture corridors (FCs) in a mature
oil field with abundant production data. A fracture corridor is a tabular,
subvertical, fault-related fracture swarm that intersects the entire reservoir
and extends laterally for several tens or hundreds of meters. Direct indicators
of fracture corridors, such as image logs, flow profiles, well tests, and
seismic fault maps, are sometimes insufficient to map all fracture corridors in
a field. It is also necessary to use indirect fracture-corridor indicators from
well data, such as productivity index (PI), gross rate, water cut, and openhole
logs. Fracture corridors from indirect indicators can be inferred by a
probabilistic decision tree, which makes predictions by integrating data from
multiple sources, giving preference to the indicators with the highest
relevance. Decision trees are constructed by use of a training set that
includes measurements of both direct and indirect fracture-corridor indicators.
In this study, wells with borehole images, production logs (flow profiles), and
injector/producer short cuts are selected as the training set. The resulting
decision trees reveal that total losses, gross production rates, and water cuts
are the three most effective indirect indicators of fracture corridors in the
test field.
Introduction
It is often the case that a particular reservoir attribute, such as
porosity, has only sparse direct measurements. It is possible, however, to
predict values of such a target variable with the help of a set of other
variables that exhibit some degree of correlation to the target variable and
have abundant measurements. A common example is estimating porosity from
seismic attributes. In this paper, the variables that have one-to-one
correspondence to the target variable are called direct indicators and the
variables that have some degree of correlation are called indirect variables.
For example, density and neutron logs are direct indicators of porosity,
whereas seismic impedance is an indirect indicator.
There are several statistical techniques to predict a target variable from a
set of indirect indicators, and these can be collected under two main groups:
supervised prediction techniques and unsupervised prediction techniques.
In the case of supervised prediction techniques, indirect indicators are
correlated to a target variable by use of a training set of data that includes
measurement of both direct and indirect indicators of the target variable. The
generated predictive system can be used to estimate values of the target
variable solely on the basis of indirect indicators in wells that do not have
any measurement of direct indicators. Multiple regression, back propagation,
neural networks, and Bayesian decision trees belong to this category.
In cases where the training set is small or no direct indicators are
available, it is possible to adopt statistical techniques that do not require
extrapolation from a training set. These are termed unsupervised prediction
techniques. Several such techniques exist, including cluster analysis,
unsupervised neural networks, and factor analysis (Wasserman 1989; Chester
1993; Van De Geer 1971). The basic idea is to discover hidden factors that
control indicator variables and to interpret these factors in terms of the
target variable. For example, the density (spacing/relative abundance) of
conductive fractures may affect the rapid water-cut rise, high initial PI, and
high gross rate. These three indirect indicators will be highly correlated to
each other. An unsupervised prediction technique may uncover the hidden factor
(fracture density) that controls all three variables from the high correlation
among them.
Both supervised and unsupervised inferences are methods for making
predictions with incomplete information (Tamhane et al. 2000; Fletcher and
Davis 2002). Most of the applications in the oil industry use fuzzy logic or
fuzzy neural networks. These applications also use soft computing decision
making with incomplete evidence and risk reduction by use of a fuzzy-expert
system (Weiss et al. 2001; Chen et al. 2002; Saggaf and Nebrija 2003). This
idea has found some application, especially in mapping fracture density by use
of seismic attributes (Ouenes et al. 1995; Zellou et al. 2003; Bloch et al.
2003).
Both supervised and unsupervised statistical techniques aim at determining
some global attribute of dispersed fractures, such as density. It is often
fracture corridors, however, rather than dispersed fractures that are
characterized as the main reservoir heterogeneity (Ozkaya and Richard 2006). An
FC is a tabular, subvertical, fault-related fracture swarm that intersects the
entire reservoir and extends laterally for several tens or hundreds of meters
(Fig. 1). FCs could be fluid-conductive or cemented. In this paper, an FC
denotes a fluid-conductive FC unless otherwise specified. FCs may have
significant conductivity and may play a major role in reservoir dynamics by
providing pressure support and, therefore, causing early water breakthroughs
and increased gross rates.
The four main requirements to map an FC are location, strike, length, and
conductivity. Here, we focus primarily on locating FCs and discuss only briefly
how other attributes can be estimated. Our objective is not the actual mapping
of FCs but examining Bayesian decision trees as a viable technique in FC
identification. The basis and procedures for calculating conditional
probabilities, entropy, information Gain (IG), and the construction of decision
trees are explained in the Appendix.
© 2008. Society of Petroleum Engineers
View full textPDF
(
1,780 KB
)
History
- Original manuscript received:
11 November 2006
- Meeting paper published:
11 March 2007
- Revised manuscript received:
9 August 2008
- Manuscript approved:
1 September 2008
- Version of record:
29 December 2008
View Cart
