Data processing: measuring – calibrating – or testing – Measurement system – Statistical measurement
Reexamination Certificate
1999-02-11
2001-08-07
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system
Statistical measurement
C702S006000, C702S011000, C367S025000, C367S026000
Reexamination Certificate
active
06272444
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to a method of characterizing the coherence of measurements of characteristics of a medium and, more particularly, of logging data, said method making it possible, in particular, to characterize the relationships between, on the one hand, a qualitative variable whose origin is not logging-related and, on the other hand, logging measurements.
An oil field may, for example, comprise a number of wells which may be close together or far apart.
When studying such a field, geologists generally have available only a small number of core samples taken from one or more wells, which are then considered as being reference wells, the various measurements made on the core samples being considered as being reference measurements. On zones containing wells which are referred to as application wells and from which no core sample has been taken, specialists use other means for studying them, such as logging, seismic, etc. The data provided by these other means make it possible to determine petro-physical or other parameters and, in particular, to check their coherence with the measurements made on the available core samples. Checking and/or extrapolating data which are not related to core samples make it possible to characterize both quantitative variables and qualitative variables.
A geologist or another specialist, such as a sedimentologist, divides the zone from which core samples are available into a certain number of slices representative of various qualitative variables such as facies, sedimentary body, sedimentary environment, etc. Each of these variables is generally assigned a number.
For example, clay facies is referenced by the number 1, sand facies by the number 2, sandstone facies by the number 3, and so on. In this way, a qualitative variable is obtained which is referenced in depth and contains whole values, each value corresponding to one class of one logging viewpoint.
It should be noted that the measurements or descriptions on core samples may greatly exceed the resolution of conventional logging tools as used currently and, in particular, by the company SCHLUMBERGER. However, these descriptions are sometimes visual, and therefore subjective because they depend directly on the quality of observation by the geologist or the sedimentologist. It is not easy to obtain a comparison or a parallel between logging measurements made on one or more application wells because numerous “mixing” zones are often observed, that is to say the logging measurements may belong to several classes.
In order to reduce the specialist's subjectivity as far as possible, the use of statistical or neural classification methods has been advocated. Conventional statistical methods, such as those developed by TETZLAFF et al. at SPWLA in 1989, JIAN et al. in “Journal of Petroleum Geology, V. 17, January, p. 71-88, or GREDER et al. at SPWLA in 1995, give poor results when the classes overlap too much, because these so-called parametric methods assume that each class follows a Gaussian law. However, the shape of a class is generally more complex than a simple Gauss curve.
Neural classification methods, described in particular by CARDON et al. in 1991, ROGERS et al. in AAPG Bulletin 1992, V. 76, No. 5 p. 38-49, HALL et al. at SPWLA in 1995 or MOHAGHEGH in 1995 and 1996, also give poor results owing to the fact that the methods are highly sensitive to incoherences observed in the measurements. In neural networks whose learning is supervised, the network learns to recognize one shape from examples. However, a logging measurement may be attributed to one class in a first step, then be attributed to another class in another step. Neural networks with overlaid levels do not succeed in recognising that a single measurement is involved.
Reference was made above to core samples which are taken from one or more reference wells and on the basis of which classifications have been made using the methods summarized above. It should, however, be noted that the methods have also been applied to logging measurements produced directly in one reference well or several reference wells, for which the logging measurements have been considered as satisfactory because of their accuracy or since they were representative of qualitative variables of the well or wells. It is nonetheless true that the results obtained with the methods on reference logging measurements were unsatisfactory and suffered from the same drawbacks. Specifically, these methods give poor results when a facies not described in the learning set is encountered in an application well and/or when the quality of the logging measurements is compromised by defective calibration or corrections, or on account of poor acquisition conditions.
BRIEF SUMMARY OF THE INVENTION
The object of the present invention is to overcome the aforementioned drawbacks and to provide a method of characterizing the coherence of logging data which is not parametric and which permits to objectively evaluate whether a learning set, formed from logging data, can be used in application sets which are formed by logging data to be identified, by picking out the depth intervals over which a problem is detected. Indeed, the method according to the present invention does not require the knowledge of any a priori probabilistic model by virtue of the fact that each domain in the learning set is determined by k nearest neighbours searching.
The method of characterizing the coherence of measurements made in a given medium, is of the type consisting in:
taking N types of reference measurements at each point (P
i
) of a given reference set of said medium, each point (P
i
) being defined by a depth dimension, the group of N measurements which are associated with each point (P
i
) constituting a reference observation (X
i
),
forming at least one N-dimensional learning set containing all the points (P
i
),
taking at least N application measurements at each point (Q
i
) of an application set of said medium, which is different from the reference set, each group of application measurements which are associated with the point (Q
i
) constituting an application observation (x),
comparing each application observation (x) with all the reference observations (X
i
) of the learning set,
characterized in that it furthermore consists in:
constructing a neighbourhood domain (D
i
) for each reference observation (X
i
) of the learning step using the k nearest neighbours process (K-NN), said neighbourhood domains constituting the said learning set which defines an acceptance class (C
a
) for application observations (x) in the application set,
defining a degree of membership of each application observations (x) to the acceptance class (C
a
) each application observation (x) being assigned to the acceptance class (C
a
) when its membership degree is at least greater than a first threshold (S
1
).
According to another characteristic of the invention, each application observation (x) is assigned to one of three classes consisting of the acceptance class (C
a
), an ambiguity class (C
o
) or a reject class (C
d
).
According to another characteristic of the invention, the membership degree comprises at least two thresholds (S
1
, S
2
), the second threshold being less than the first threshold (S
1
).
According to another characteristic of the invention, an application datum (x) is assigned to the reject class (C
d
) when its membership degree is less than the second threshold (S
2
)
According to another characteristic of the invention, an application datum (x) is assigned to the ambiguity class when its membership degree lies between S
1
and S
2
.
According to another characteristic of the invention, the membership degree is defined by the membership function:
μ
i
(
x
)
=
ⅇ
[
-
x
-
X
i
σ
i
]
(
1
)
in which
X
i
is an observation in the learning set, i lying between 1 and n
a
,
n
a
corresponds to the number of reference observations in the learning set,
&sgr;
i
is the radius of the domain centred on the observation X
i
,
x is an applicat
Rabiller Philippe
Thevoux-Chabuel Hugues
Bui Bryan
Elf Exploration Production
Hoff Marc S.
Ostrolenk Faber Gerb & Soffen, LLP
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