Отправлено: 04.10.09 07:42. Заголовок: Petrophysical data prediction from seismic attributes using committee fuzzy inference system

Copyright © 2009 Elsevier Ltd All rights reserved.

Petrophysical data prediction from seismic attributes using committee fuzzy inference system

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Ali Kadkhodaie-Ilkhchia, , M. Reza Rezaeea, b, , , Hossain Rahimpour-Bonaba, and Ali Chehrazia, c,

aDepartment of Geology, College of Science, University of Tehran, Tehran, Iran

Department of Petroleum Engineering, Curtin University of Technology, ARRC Building, 26 Dick Perry Avenue, Kensington, Perth, WA 6151, Australia

cGeology Division, Iranian Offshore Oilfields Company, No. 38, Tooraj St., Vali-Asr Ave., NIOC, Tehran 19395, Iran


Received 27 August 2008; revised 16 April 2009; accepted 20 April 2009. Available online 4 September 2009.

Abstract
This study presents an intelligent model based on fuzzy systems for making a quantitative formulation between seismic attributes and petrophysical data. The proposed methodology comprises two major steps. Firstly, the petrophysical data, including water saturation (Sw) and porosity, are predicted from seismic attributes using various fuzzy inference systems (FISs), including Sugeno (SFIS), Mamdani (MFIS) and Larsen (LFIS). Secondly, a committee fuzzy inference system (CFIS) is constructed using a hybrid genetic algorithms-pattern search (GA-PS) technique. The inputs of the CFIS model are the outputs and averages of the FIS petrophysical data. The methodology is illustrated using 3D seismic and petrophysical data of 11 wells of an Iranian offshore oil field in the Persian Gulf. The performance of the CFIS model is compared with a probabilistic neural network (PNN). The results show that the CFIS method performed better than neural network, the best individual fuzzy model and a simple averaging method.

Keywords: Committee fuzzy inference system; Sugeno; Larsen; Mamdani; Hybrid genetic algorithm-pattern search; Probabilistic neural network; Petrophysical data; Seismic attributes

Nomenclature
A, B
input fuzzy sets (membership functions)
αi
firing strength of ith fuzzy rule
β1, β2, β3, β4
constants in constructing output membership functions of the Sugeno model
C
output fuzzy set (membership function)
C′i
truncated output fuzzy set for the ith rule
C′
aggregated output fuzzy set
CC
correlation coefficient
D(x,xi)
distance between the input point x and each of the training points
FCM
Fuzzy c-means clustering
FIS
fuzzy inference system
GA-PS
genetic algorithm-pattern search
k
number of training samples in constructing CFIS and neural network
Li
target petrophysical data
LFIS
Larsen fuzzy inference system
LOM
large of maximum
m
number of clusters
MF
membership function
MFIS
Mamdani fuzzy inference system
MIMO
multiple inputs and multiple outputs
MISO
multiple inputs and single output
MOM
mean of maximum
MSE
mean squared error
n
number of fuzzy rules
Oi
outputs of fuzzy models
ON
output of the probabilistic neural network
ONs
validation result of the probabilistic neural network
PNN
probabilistic neural networks
p, q
coefficients of output membership functions in the Sugeno fuzzy model
ρ
distance scale factor

porosity
Ri
ith fuzzy rule
r
constant of output membership functions in the Sugeno fuzzy model
RB
fuzzy rule base
γ
weight coefficients of MFIS, LFIS, SFIS and average of them, respectively
Sw
water saturation
SFIS
Sugeno fuzzy inference system
SOM
small of maximum
t
number of fuzzy rule base with MISO
τi
Degree of fulfillment of rule i
σij2
variance of cluster i in jth rule

sum operator in fuzzy sets
ui
ith cluster center
μCi(z)
grade of membership of element z in output fuzzy set C for ith rule

firing strength of ith fuzzy rule
μAi(x0)
grade of membership of element x0 in ith input fuzzy set A
μAi(x0)
grade of membership of element y0 in ith input fuzzy set B
μRi
grade of membership for ith fuzzy rule
vij
ith cluster centers of jth rule in input space
wij
ith cluster centers of jth rule in output space
x, y
input data for fuzzy sets and neural network
λ
constant
z
output of fuzzy set
Article Outline
Nomenclature
1. Introduction
2. Methodology
2.1. Fuzzy inference system
2.2. Committee fuzzy inference system
3. Application to the Iranian offshore oilfield
3.1. Correlation of well logs to seismic data
3.2. Selection of optimal seismic attributes
3.3. Fuzzy clustering
3.4. Construction of fuzzy rule base
3.5. Construction of a committee fuzzy interference system—CFIS
3.6. Design of a probabilistic neural network
4. Results and discussion
5. Conclusion
Acknowledgements
References




Fig. 1. Main parts of an FIS (Lee, 2004).

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Fig. 2. Graphical illustrations of MFIS (a), LFIS (b) and SFIS (c).

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Fig. 3. A schematic diagram of CFIS designed in this research.

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Fig. 4. Map showing location of wells in Iranian Offshore Oilfield.

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Fig. 5. A 3D crossline showing general quality of seismic data across study field (Crossline: 1976).

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Fig. 6. A sample of well to seismic tie at well A9.

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Fig. 7. Crossplots showing relationships between seismic attributes and water saturation.

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Fig. 8. Crossplots showing relationships between seismic attributes and porosity.

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Fig. 9. Results of running GA-PS including best and mean fitness values (top left), average distance between individuals (top right), fitness scaling (down left) and calculated scores (down right) for optimizing porosity estimation problem.

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Fig. 10. Correlation coefficient between measured and predicted water saturation for test samples using SFIS (a), MFIS (b), LFIS (c) and CFIS (d).

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Fig. 11. Graphical comparison between measured and predicted water saturation for test samples using SFIS (a), MFIS (b), LFIS (c) and CFIS (d).

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Fig. 12. Correlation coefficient between measured and predicted porosity for test samples using SFIS (a), MFIS (b), LFIS (c) and CFIS (d).

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Fig. 13. Graphical comparison between measured and predicted porosity for test samples using SFIS (a), MFIS (b), LFIS (c) and CFIS (d).

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Fig. 14. Map showing distribution of CFIS estimated water saturation for Top Ghar reservoir.

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Fig. 15. Map showing distribution of CFIS estimated porosity for Top Ghar reservoir.

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Table 1.
Multi-attribute list for predicting water saturation (a) and porosity (b).




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Table 2.
Gaussian membership function parameters derived by FCM for predicting Sw using MFIS and LFIS.




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Table 3.
Gaussian and linear membership function parameters derived by subtractive clustering and gradient descent methods for predicting Sw using SFIS.




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Table 4.
Performance of different fuzzy models for estimating water saturation and porosity.




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Corresponding author at: Department of Petroleum Engineering, Curtin University of Technology, ARRC Building, 26 Dick Perry Avenue, Kensington, Perth, WA 6151, Australia. Tel.: +61 8 9266 7980; fax: +61 8 9266 7063.