Summary
A fuzzy model is applied for permeability estimation in heterogeneous
sandstone oil reservoirs using core porosity and gamma ray logs. The basic
concepts of a fuzzy model are described, and we explain how to use the
constructed model to analyze and interpret the results. The fuzzy-logic
approach is used to represent a nonlinear relationship as a smooth
concatenation of local linear submodels. The partitioning of the input space
into fuzzy regions, represented by the individual rules, is obtained through
fuzzy clustering. The results from the fuzzy model show that it is not only
accurate but also provides some insight into the nonlinear relationship
represented by the model. Furthermore, the results of the blind test developed
a good agreement between the measured core permeability and the output of the
fuzzy model.
Introduction
Many oil reservoirs have heterogeneity in rock properties. Understanding the
form and spatial distribution of these heterogeneities is fundamental to the
successful characterization of these reservoirs. Permeability is one of the
fundamental rock properties, which reflects the ability to flow when subjected
to applied pressure gradients. While this property is so important in reservoir
engineering, there is no well log for permeability, and its determination from
conventional log analysis is often unsatisfactory (Mohaghegh et al. 1997; Malki
et al. 1996).
Estimation of permeability in a heterogeneous reservoir is a very complex
task; a poorly estimated permeability will make the model inaccurate and
unreliable, thus affecting the degree of success of many oil and gas operations
that are based on such models. Major efforts have been made by many researchers
to establish a complex mathematical function that relates permeability to other
reservoir characteristics. These studies have helped in understanding the
factors controlling permeability but have not provided an accurate estimation
of permeability. The internal processes of a reservoir correspond to complex
physical phenomena where many factors are interacting. Definition of an exact
expression for each of these factors as a function of others is an impossible
task. The best that can be done is approximate methods that somehow give a hint
about the permeability distribution in the reservoir (Berg 1970; Timur
1968).
One of the first practices was finding correlations between permeability and
other reservoir characteristics such as porosity, or well logs. Samples
extracted from cored wells were used in the laboratory to find values of
permeability and porosity; likewise, logs were taken in the same wells.
Correlations were obtained from permeability vs. porosity plots or from
functional transformation on the well logs wherever enough information existed.
These correlations were extrapolated to wells in which little or no information
was available. For this method to work, a high amount of
reservoir-representative samples was required, something expensive to achieve.
Besides, when heterogeneity of a well is high, these correlations become
unreliable (Yao and Holditch 1993).
Statistical multivariate techniques arise as a better choice, providing a
potential solution through regression analysis. These techniques offer
appealing solutions; however, their main drawback is the need to exhaustively
identify all the factors affecting permeability and then establish a linear or
nonlinear model that best represents interactions among such factors. Because
permeability is controlled by both depositional characteristics (such as grain
size and sorting) and digenetic features, a precise model should take into
account the fundamentals of geology and physics of flow in porous media
(Abbaszadeh et al. 1996). Relationships between core-derived pore-throat
parameters and log-derived macroscopic petrophysical attributes can be
established (Soto B. et al. 1999).
Fuzzy logic uses the benefits of approximate reasoning. Under this type of
reasoning, decisions are made on the basis of fuzzy linguistic variables such
as “low,” “good,” and “high,” with fuzzy set operators such as “and” or “or.”
This process simulates the human expert’s reasoning process much more
realistically than do conventional expert systems. Fuzzy-set theory is an
efficient tool for modeling the kind of uncertainty associated with vagueness,
imprecision, and/or a lack of information regarding a particular element of the
problem at hand (Soto B. et al. 2001).
In this paper, the fuzzy model was applied for permeability estimation in
heterogeneous oil reservoirs using core porosity and gamma ray log. Also, the
basic concepts of the fuzzy model are described. Finally, a method is presented
for using the constructed models to analyze and interpret the results.
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
29 June 2004
- Revised manuscript received:
3 January 2006
- Manuscript approved:
7 March 2006
- Version of record:
20 June 2006
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