Download Scientific Visualization in Oil and Gas Exploration

Scientific Visualization in Oil and Gas Exploration
Leon Fedencznk University of Calgary
Brian Wyvill University of Calgary
Kristina Hoffmann Gambit Consulting Ltd.
analyses are means of analyzing data to extract
and summarize information. Through statistical
analysis, one can develop a meaningful
information summary in order to understand
historical data, develop predictive models, and
have the ability to quantifY the results. Statistical
techniques enable patterns and trends to be
extracted from the data, and to establish relations
between the different data sets.
In brief,
statistical techniques compress and organize large
amounts of data into a small set of information.
They aid in the identification of any valid
relationships and patterns hidden in exploration
databases. This can be useful in directing
exploration and development efforts in areas with
the highest possible potential.
ABSTRACT
In this paper we
present a method for
interpretation of statistical results from
discriminant analysis. The specific attention has
been given to the application of Scientific
Visualization to the presentation of results from
statistical analysis. Techniques are presented to
aUow a geologist in oil and gas exploration, to
make a visual analysis of the statistical results.
In particular, we explain how to convert
multidimensional geological data into a single
parameter, which is later presented in 2D and 3D
space.
A discriminant criterion is developed and then
used to classifY each of the multivariate
observations into one of two groups: producers
and nonproducers. The posterior probability of
membership in each group for the test data is
presented as the production probability.
Furthermore, this probability governs the colour
and density during the rendering process.
Statistical modelling can be used to:
locate areas favourable for exploration;
to determine the "when" and "where" for
the treatment, in order to optimize the
exploitation programs of the reservoirs;
INTRODUCTION
implement quality programs and the
identification of potential bypasses.
Successful exploration in the oil and gas industry
is the result of careful data acquisition and
creative data analysis techniques. Geological
data is multidimensional, often noisy,
nonreproducible and worst of all, the majority of
geological samples are mixtures of simpler
components. Statistical methods help earth
scientists to take a closer look at some of the
geological hypothesis and find hidden patterns,
variance, and original compositions of sample
data. Unfortunately, it is often difficult to
translate statistical results into geologically
meaningful statements. Statistical and numerical
In addition, we show how scientific visualization
helps in the statistical data interpretation.
Scientific visualization of geological data
[Sabella88] [Connolly86] and the results of the
statistical studies in [Fedenczuk9l] has taken on
an increasingly important role in exploration. This
is due to the quantitative nature of the geological
and geophysical data and the increasing amounts
and availability of that data. We feel that
statistical techniques could be applied more
successfully in predicting oil and gas discoveries
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if advanced visualization tools were used to
improve the interpretation.
example, the production capacity as a
function of the subset of parameters;
DATA ANALYSIS AND MODELLING
discrimination functions to distinguish
between on/off-field anomalies;
contour maps
probability;
Statistics in Oil and Gas Exploration
Finding oil or gas is inherently probabilistic,
which is supported by the rather limited success
of drilling programs. The entire process of oiUgas
exploration is made up of a large component of
chance factors. Therefore, it is highly probable
that oil and gas reservoirs of appreciable size still
remain undetected. So far, discovered reserves
are a reflection of currently applied technology
(including technology used in data analysis) and
current economic realities. New innovative data
interpretation techniques will help in locating yet
undiscovered reserves. Improved data analysis
can be achieved by the use of advanced
visualization techniques to interpret results from
multivariate statistical procedures (e.g. factor
analysis) [Fedenczuk92]. Statistical processing
can establish the degree of uncertainty
surrounding
exploration
events
while
visualization techniques provide a presentation
and interpretation tool.
of
the
production
a list of possible bypasses (abandoned
wells which could be producers, but were
probably damaged during the completion).
The Scope of Statistical Analysis
The following is a list of tasks in geostatistical
analysis:
perform necessary data checks, develop
frequency
distributions,
check
correlations, find relevant differences
between group of objects, and establish
level of confidence for obtained results;
develop mathematical models to predict
production rates;
develop models allowing a discrimination
between several groups of objects;
Objectives
The primary objective of data analysis and
modelling is to estimate the production capacity
or production probability, based on available
geological, petrophysical, and engineering data.
Statistical models allow for the selection of
regions of interest or specific sites (wells) which
represent higher potential than the surrounding
locations. The possible deliverables of statistical
models are:
find similarity between individual wells;
apply advanced graphical tools to display
multidimensional data.
Multivariate Statistical Procedures
One of the most useful statistical procedures is
the Linear Discriminant Function. It can provide
a numerical criterion or set of criteria for help in
assigning an individual observation or object to
one of several populations (e.g. good or bad
performers). In addition, Factor Analysis and
specially Q-mode Factor, Analysis have been
successful in investigations of patterns, order and
similarity in data. These methods yield new
numerical values corresponding to a smaller
number of factors that are useful in reproducing
an optimal set of geological, log,
hydrodynamic,
geochemical,
and
completion parameters necessary to
represent a statistical model and to
support geological interpretations;
mathematical models describing, for
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the original data matrix. Often, this approach is
described as the unmixing technique intended to
find similarity between observations [Ehrlich87].
This contrasts with techniques dealing with
similarity between variables. This is a very useful
tool to trace the well connectivity and response.
The interpretation of statistical results can be
facilitated by advanced visualization tools which
are capable of presenting close data sets of more
than three dimensions [Fedenczuk92].
diagnostics indicate when more terms should be
added to the model, and how to identifY outliers.
Application of the Discriminant Function
Discriminant analysis results in a function, which
is a linear combination of variables and provides
the best discrimination between the classes in
the data set. In the initial stage Univariate
analysis should be performed for each variable.
Tables with Min,_Max, Average, and Std. values
are very useful for cleaning data In addition, the
correlations between all of the variables should be
tested. In the next step the smallest subset of
significant variables should be selected using
stepwise procedures. This subset of variables
should predict the dependent variable, the
perfonnance class, or the response variable used
to describe a phenomenon.
Regression techniques are used for quantitative
variables (continuous scale), such as production
rates. However, in additi on to the quantitative
variables, predictive models must often
incorporate qualitative variables, such as the
response group or formation.
Typically, the
dependent variable is associated with the oil/gas
production rate, the weIl quality, or the weIl
response to a specific treatment.
Discriminant Analysis can act as a tool to overlay
multidimensional infonnation. The discriminant
criterion is developed and then used to classifY
each ofthe multivariate observations into one of
the groups.
In the simplest case the
classifications can be based on:
Diagnostics and parameter selection
The selection and diagnostics help to identifY the
independent variables which significantly
influence the outcome of the dependent variable.
Typically, the data contains more information
than is required for the model. The procedures
used to identifY the significant parameters
required to describe the phenomenon are:
the initial production (pr<x,!ucers and
nonproducers);
c-,
response to a treatment (yes/no).
Stepwise Regression;
The discriminant function should be built on a
base of the preselected set of variables from
stepwise discriminant analysis. The verification
of the function should be done on a test set. In
general, a proper application of the discriminant
analysis is done on two data sets: learning and
testing set. They can be created by random
selection of the observations from the total data
into these sets. For more information please refer
to SAS/STA1"'" manual. The fmal result of such
analysis is mappable information, the posterior
probability of membership in each group for the
test data can be presented as the production
probability.
Backward Regression Analysis;
Rsquare Regression;
Stepwise Discriminant Analysis.
Through these procedures one can identifY a
suitable and optimal subset of variables. All
possible subsets of variables can be tested by
adding and deleting variables one at a time until,
by some criteria, a reasonable stopping point has
been reached. The diagnostics are used to
determine whether models adequately represent
the data upon which they are based The
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can be derived from simulations, statistics, etc.
The modelling leads to a series of numbers
representing data in the experimental space, with
additional time dependence (ifrequired).
VISUALIZATION
Components of visualization
The scientific visualization process can be viewed
as a sequence of transformations that convert a
data set into a displayable form which leads to an
enhanced capability for prediction and discovery.
There are typically three stages in this process:
Multidimensional View of 3D Information
The visualization of a scalar function of three
variables, in a form p=p(x,y,z) can be regarded as
a function which maps the fourth dimension (P)
into a 3D space. In some cases we can map
information into 2D space in the form of the
contour map (equivalent to the elevation map as
p=p(x,y). For volume data we can use the 3D
analog of 2D contour plots and pseudo-colour
maps in the form of isosurfaces [Wyvi1l86], 3D
points [Cline88],
3D self-emitting voxels
[Sabella88],
translucent voxels [Levoy90],
viewing colour-roded density data [Nielson91], or
opaque voxels [Chen85].
data manipulation, must identifY the
dimensionality and features in data
sequences, determine how they change
relative to time and position, and how
they interact;
modelling, maps the previously processed
data into data structures and a set of
visualization primitives, with positional
parameters, colour, texture, reflection and
so on;
Data Presentation
The probability obtained from Discriminant
Analysis can be presented as a contour map. This
is equivalent to a simultaneous analysis of several
contour maps on the light table. Furthermore, for
more advanced users of the visualization tools
this probability can govern the colour and density
during the rendering process. For the purpose of
visualization, one needs to apply a threshold or
cut-{)ffvalue as a criterium for the selection of the
area of the interest For example, an 80%
probability of the well to be a producer can serve
as a criterion. Similarly, the discriminant score
can be applied with a value that corresponds to
the same success probability. A choice of the
high value of the probability as a cut-off will
cause that some of the potentially producing areas
will not be included in the area of the interest. On
the opposite side, shifting the cut-off value below
80% will increase a risk of drilling dry wells. In
the second case we will not overlook too many
potential producers.
rendering, produces an image of the data,
as defmed in the visualization modelling,
using such operations as projection,
shading, and hidden surface removal.
Data Manipulation
Any data associated with the petroleum
exploration is transformed into a form that is
suitable for subsequent visualization operations
and may include such operations as griding,
interpolation, and smoothing. For example, real
data is often provided on a sparse grid.
IdentifYing which characteristics of data are
relevant for modelling, is the first important step
in designing effective data visualization
techniques. Each 3D point acquires data for:
colour, density, opacity, surface properties
(reflection. rock, water, etc.), volume properties
(refraction, density, viscosity, sonic velocity,
strength, elasticity, etc.)
Optionally, this stage involves the construction of
a mathematical model, to be used as a data source
for the visualization. In many cases, the model
that is used to describe a particular phenomena
The best approach is a creation of two areas of
interest which are based on two tails. One of the
areas corresponds to the highest values of
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production probability, and the second
corresponds to a very low probability of the
producer membership. The gray area between
these two borders (contour lines) often represents
the opportunity area, where the advanced
technology can improve the odds of the correct
prognosis. Special attention in the higher end of
the gray area should be placed to all abandoned
wells. This is especially true in the case of
fonnations which are prone to the damage during
the drilling process and where wells could be
abandoned due to the misinterpretation of the
DST tests. In the case of the old fields for which
there is available information in the public data
bases, the analysis can produce a simple list of the
abandoned wells, which were misclassified by the
discriminant function.
union
PuQ=PnQ
These operations allow us to construct
expressions to add and extract regions of interest
from the statistical solutions and enhance their
graphical representations. Thus, interactions
between different data sets and their responses
can be extracted for the purpose of the
interpretation and visualization. However, these
operations do not form a complete boolean
algebra due to the fact that P n P " P and P n Ap
"tP.
Boolean Operations
We applied the boolean operations (union,
complement, intersection, and difference) to
posterior probabilities. If two sets P and Q
represent posterior probabilities, spatially defined
as P(X,Y;I.) and q(x,y,z), which have been derived
from two discriminant functions, then the
operations can be defined as:
SUMMARY
The volume of information available to industry
has increased several fold in the past decade.
Nowhere is this more evident than in the data
related to oil and gas exploration. Statistical
techniques and advanced graphics can help us to
gain a better understanding of this information by
providing insight into the meaning of variations in
specific parameters and by providing meaningful
summaries of specific information. In general,
statistical and numerical techniques were
developed to deal with large quantities of data
and are therefore efficient and effective means of
processing large volumes of data. Statistical
techniques provide methods of summarizing large
quantities of data into manageable and usable
estimates, while Scientific Visualization provides
better tools to interpret the results of the
statistical modelling. The final 2D or 3D image
allows geologists to identifY the most probable
areas, which are potentially productive with
respect to hydrocarbon exploration. Furthermore,
these techniques enable the risk factor to be
qualified and confidence limits to be determined.
Informed decisions regarding large capital
intersection
complement
difference
P-Q=PnQ
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expenditures can only be made when the risk
factor is properly understood.
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International Sixteenth Annual
Conference,
New
Orleans,
Louisiana, February 1991, pp.
771-778..
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If you have any questions or comments, or desire
further information, the authors may be contacted
at:
Department of Computer Science
The University of Calgary
2500 University Drive NW.
Calgary, Alberta
T2N IN4 Canada
[email protected]
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other countries.
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