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GUSS14 - 29
Uncertainty Analysis in Geomodeling: How Much Should We
Know About What We Don’t Know?
Y. Zee Ma, Schlumberger, Denver CO, USA
This paper has been selected for presentation for the 2014 Gussow Geosciences Conference. The authors of this material have been cleared by all interested
companies/employers/clients to authorize the Canadian Society of Petroleum Geologists (CSPG), to make this material available to the attendees of Gussow 2014
and online.
ABSTRACT
As the demand for hydrocarbon resources continues to
grow, reservoir modeling and uncertainty analysis have
become increasingly important for optimizing field
development. Optimal valuation and exploitation of a field
requires a realistic description of the reservoir, which in turn
requires reservoir characterization and modeling, and
quantification of the uncertainty by integrating multi-
disciplinary data. An integrated approach for reservoir
modeling helps bridge the traditional disciplinary divides and
tear down interdisciplinary barriers, leading to better
handling of uncertainties, and improvement of reservoir
modeling for its use in the petroleum industry. Uncertainty
analysis should be conducted for investigational analyses, and
for decision analysis under uncertainty and risk. Constructing
a realistic reservoir model, and reducing and quantifying the
uncertainty are the topics discussed in this article.
INTRODUCTION
Reservoir characterization and modeling have seen
significant leaps in the last two to three decades, driven by
the development of computational horsepower, advances in
seismic technology, logging tools, geological understanding of
depositional systems and natural fracturing of subsurface
systems, and applications of probabilistic methods. It has
evolved from fragmentary pieces into a discipline of
geoscience applications for the petroleum industry, from
university research to value-added resource developments,
from 2D mapping of structures and reservoir properties to 3D
geocellular representations of hydrocarbon reservoirs, and
from dealing with discipline-specific problems to integrated
multidisciplinary reservoir modeling.
The division of tasks between geologists and reservoir
engineers in the early time was that geologists explored for
hydrocarbon resources, and engineers produced
hydrocarbons from the reservoirs. This separation of the
tasks was based on the low usage of fossil fuel relative to the
amount of the resources in the ground and high reservoir
quality of formations. As hydrocarbon consumption has
dramatically increased worldwide, reservoir management has
become more and more important. Integration of geology
with reservoir engineering has become critical for better
reservoir management (Haldorsen and Lake, 1984, Ma et al,
2008), especially for unconventional reservoirs (Du et al.,
2011; Cipolla et al., 2012).
Geology has traditionally been considered as descriptive,
although some quantitative branches including geophysics,
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mathematical geology and geostatistics have significantly
increased the breadth of geoscience. We believe that in the
future, most geoscientists will conduct geologic or reservoir
modeling as routine work. By performing geologic modeling,
geoscientists can test and quantify their geologic concepts
and hypotheses. In doing so, they use data to prove or
disprove the concepts, and use statistics and geostatistics to
resolve inconsistencies in various data and integrate them in
a coherent manner (Ma, 2010). As a result of the
convergence of descriptive geology and quantitative geology,
geoscientists need to use the modeling as a process for
understanding the reservoir, not just producing a numeric
model. The convergence should make reservoir modeling a
synonym of reservoir characterization.
Reservoir management and field development planning
are important for maximizing the economics of the field,
which requires accurate reservoir characterization. Reservoir
modeling was the missing link between geosciences and
reservoir engineering in field development before the mid-
1980s. Since then reservoir characterization has shown
significant values in identifying both prolific and marginal
reservoirs, extending the production life of existing fields and
increasing the hydrocarbon recovery of reservoirs. Successful
reservoir characterization projects typically show high degree
of integration. In fact, reservoir modeling is the best way to
integrate all the data and disciplines, and the only way in
which all the data and interpretations come together into a
single 3D numeric representation of a reservoir. In
integration, the data include not only quantitative data such
as well-logs, cores, and seismic data, but also the geologic
concepts and descriptive interpretations (Mallet, 2002; Ma,
2009; Cao et al., 2014).
A reservoir is the result of geologic processes and is not
randomly generated. However, the complexity of subsurface
reservoir properties coupled with limited data leads to
substantial uncertainty in a reservoir model. Uncertainties
can be mitigated by gaining more information and/or using
better science and technology. How much uncertainty should
be mitigated depends on the needs of decision analysis for
reservoir management and the cost of information.
Uncertainty analysis should be conducted for investigational
analyses, and for decision analysis under uncertainty and risk.
Knowing what needs to be known and what can be known
should be the main focal points of uncertainty analysis in
reservoir modeling.
RESERVOIR MODELING
“A good model can advance fashion by ten years.”
Yves Saint-Lauren
The essence of reservoir modeling lies in using all the
available data to build an accurate reservoir representation
that is fit-for-purpose to the field’s development needs. In a
significant hydrocarbon resource asset, a good reservoir
model can be an essential element for increasing the
production and extending the field development life for
years.
Why build a reservoir model?
The most common use of reservoir models is to provide a
3D numeric input to reservoir simulation. Reservoir modeling
and simulation provide a basis for maximizing economic value
for field development and operational decisions. The typical
motivation for reservoir simulation is to increase profitability
through better reservoir management. These include
development plans for new fields and depletion strategies for
mature fields. Reservoir modeling and simulation can address
liquid (oil, and water) and gas volume forecasting, decline
analysis, infill drilling uplift, secondary or tertiary recovery
options, well management strategies, water/gas handling
strategies and facility constraints, contact movement, liquid
dropout, reservoir surveillance strategies, injection strategies,
and well and completion designs. Reservoir modeling and
simulation can also be used for reserve confirmation, equity
determination, or support for funding large projects.
Traditional mapping and cross-section methods worked
relatively well for homogeneous reservoirs, but they tend to
overestimate sweep efficiency for heterogeneous reservoirs.
These methods may significantly under- or over-estimate in-
place hydrocarbon resources because they lack 3D
examination of reservoir heterogeneities. Reservoir modeling
and simulation provide powerful tools for more accurate
reservoir description and hydrocarbon production forecasting
(Dubrule, 1989; Yu et al., 2011), and can help reservoir
management and field development. Accurate reserve
assessment through reservoir modeling and simulation could
help reduce cost and increase recovery.
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Besides reservoir simulation, reservoir modeling itself
can be used as support for reservoir surveillance activities,
such as monitoring fluid contacts and reservoir pressures,
analyzing fault transmissibility and performing production
fault seal analysis. It can also be used for an accurate
determination of stock-tank original oil in place (STOOIP), for
example, by incorporating capillary pressure effects, new
opportunity identification and prioritization, well planning
and well placement optimization, visualization and
communication of the detailed 3-D reservoir architecture and
properties between various disciplines, reviewing data and
their quality controls, resolving inconsistencies between
various disciplines, support for time lapse seismic analyses,
for example, by identifying bypassed oil, and reservoir
uncertainty and risk analysis.
Reservoir modeling is critical to rapid successful
commercialization of discovered and undeveloped
hydrocarbon resources, as well as to optimizing depletion of
mature fields. As a rapidly growing discipline, reservoir
modeling has become an integral part of the field asset
management. For large and capital-intensive development
projects, reservoir modeling and simulation have almost
become a necessity. Even for small to medium reservoirs,
modeling and simulation can enhance efficient development,
and depletion planning, and potentially increase reserves and
yield cost saving. Modeling can also help in moving static
resources to reserves.
In some cases using traditional 2D mapping methods,
reserves have originally been grossly overestimated, leading
to false optimism. Expensive modern platforms may be
installed, but later may be found under used because of the
over-estimation of the resource. On the other hand, some
large oil fields have been mistakenly farmed out because of
the underestimation of the resource by traditional methods,
leading to false pessimism. In many of these cases, reservoir
modeling could have helped make the decisions more
objectively and realistically.
Reservoir modeling is a critical link between seismic
interpretation and reservoir simulation. Without reservoir
modeling, integrated approaches to E&P solution and
accurate reservoir evaluation are almost impossible. Building
a reservoir model used to be very costly, but availability of
increasingly versatile and sophisticated software packages
has made reservoir modeling much more efficient and
affordable.
Cases for building a reservoir model
Reservoir modeling generally brings significant value that
is higher than its cost, and the majority of reservoir modeling
projects have been successful. For individual reservoirs, the
asset team needs to assess the cost, benefits, and availability
of skills to decide if a reservoir model should be built. The
following criteria are important considerations in deciding
whether a model will be constructed.
• A reservoir simulation study is planned.
• The field is a major asset that warrants a significant
reservoir management and depletion planning effort.
• Reservoir performance is not well understood due to
complex geology, fluid, etc.
• Significant drilling or workover activity is planned.
• Reserves need a confirmation through accurate STOOIP
determination and history-matched simulation to compare
with other studies, such as material balance, and decline
curve analysis.
• A secondary recovery plan may be warranted.
• Manage risk by evaluating multiple scenarios and
realizations based on sensitivity of important parameters.
• Guide the operations team in selecting well locations using
a living/evergreen model.
• Identify the need, type and value of additional data.
• Rapidly feed decision-making information.
• Understand the reservoir system before hydrocarbon
production to improve the cost effectiveness of the
project.
• Reduce the chance for dry holes by feeding information
back to the operations team.
• Update the development plan and reserve.
How should the model be built?
A reservoir is complex in its geometry as well as in the
variability of its rock properties. Yet improving hydrocarbon
recovery requires detailed and accurate descriptions of
reservoir properties. Integrated modeling attempts to
improve quantitative reservoir descriptions by incorporating
geologic knowledge, well data and seismic data. Proper
integration of diverse data can help build a more realistic
geologic model and reduce the uncertainty in describing the
reservoir properties. Geologic modeling provides us with an
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excellent platform for uncertainty analysis in reservoir
characterization.
A model should be built according to business and/or
technical needs, i.e., fit-for-purpose, optimally using the
available data, and conveying the uncertainty of reservoir
geology and production. With the complexity of reservoir
geology and limited data, building a model that exactly
replicates every detail of the subsurface is impossible.
However, it is possible to build a model that fits technical and
business needs by optimally integrating all the available data.
The objective of the model needs to be realistic based on
needs, available technology, data quantity and quality, and
timeline.
Capabilities for building models in all stages of field
development are important considerations. As the objectives
change through time and business stage, a reservoir model
must address business or technical needs (volumetrics,
reservoir compartments, and production driving mechanism,
targeting wells, and aiding drilling decisions etc.), so it cannot
have everything. Models are different for exploration,
discovery, development, early production, and mature and
depletion stages. However, the model should be updateable,
allowing for rapid updates as more data become available.
Initial modeling should be simple so that it enables an early
evaluation. As more data become available, modeling can
incorporate more complexity.
A reservoir model typically includes
Structural and stratigraphic models
Lithofacies models
Petrophysical property models
Dynamic simulation models
The structural model deals with how the major geological
elements are in play for reservoir architecture, and how these
different elements are related in space. Facies are the rock
properties that reflect the depositional characteristics, such
as facies relationships, stacking patterns, and stratal
geometry. Petrophysical properties are descriptions of fine-
scale characteristics of the reservoir, typically including
porosity, fluid saturations, and permeability. Dynamic
simulation model generally represents a coarse grid that
contains all the necessary reservoir properties that define
reservoir volumetrics, and flow properties. Geostatistical and
object-based modeling approaches provide tools for
integrating diverse data and analyzing uncertainty associated
with the description of the reservoir. Integration is one of the
most important characteristics of modeling, as shown in
Figure 1.
Figure 1 Illustration of integrated reservoir modeling
UNCERTAINTY ANALYSIS
“I’d rather be vaguely right than precisely wrong.”
John M. Keynes
Reservoirs are not random; they were deposited geologically and evolved into hydrocarbon-bearing entities. There is no uncertainty in a reservoir; there is only uncertainty in our understanding and description of it because of the subsurface complexity—and thus the difficulty in formulating a complete and precise description. The subsurface complexity and limited data make the reservoir characterization and modeling complex and indeterministic, which explains the large uncertainty space in managing a hydrocarbon resource project (Massonnate, 1997).
Uncertainty is ubiquitous in reservoir characterization,
and it exists in various disciplines, including
Seismic processing
Interpretations of faults and horizons
Time-to-depth conversion
Structural modelling
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Petrophysical analysis
Geological interpretation
Fluid contact determination
Spatial and frequency distributions of reservoir
properties
Fault transmisibilities
Pressure/volume/temperature and saturation model
Production and drilling scenarios
Economic parameters
It is a paradox that sometimes uncertainty appears to
increase as more data becomes available (Ma, 2011). In fact,
in these cases the uncertainty space was not correctly
defined and the uncertainty model was overly simplified. To
reconcile them, further analysis is warranted, including
acquiring additional data and mitigation of sampling bias if
present (discussed later) to adequately define the correct
space of uncertainty.
We don’t analyze uncertainty for the sake of uncertainty.
Describing uncertainty generally is not the ultimate goal of a
project; reducing it and/or managing it is the goal. The
question is, “How much should we try to know about what we
don’t know?” Subsurface complexity, coupled with limited
data, prevents us from completely describing every detail of
the heterogeneities. Our main emphasis in reservoir
modeling should be to define relevant objectives that impact
the business decision, and to find realistic solutions
accordingly.
A pitfall is to reduce the model uncertainty at all costs. In
some cases reducing the model uncertainty actually increases
the true uncertainty because the process increases the
conceptual uncertainty without being noticed. For example,
integrating more data should logically always decrease the
model uncertainty, but actual uncertainty might increase if
the data are inaccurate.
Reservoir modeling provides an efficient platform for
performing uncertainty analysis related to field development.
A double goal of uncertainty analysis is to quantify and
reduce the uncertainty. This is critical because optimal
reservoir management, including production forecasting and
optimal depletion, requires knowledge of the reservoir
characterization uncertainties for business decision analysis.
Resource development projects frequently fail because of the
failure to study subsurface heterogeneity and of the lack of
uncertainty analysis for resource estimates and risk
mitigation in the reservoir management process. A successful
drilling technology project sometimes becomes an economic
failure for these reasons.
Quantification of uncertainty should consider as many as
possible uncertainty factors to approach the total uncertainty
space. Uncertainty of each factor also should be correctly
represented by a statistical distribution. Where uncertainty
increases as more data are introduced, the original model did
not include all uncertainty factors in the first place and
consequently underrepresented the true uncertainty. When
data that correlate with the target variable are introduced
into the modeling, the uncertainty space can be narrowed. If
the uncertainties in the input factors are reduced, the
uncertainty space will be narrowed.
Data integration and uncertainty analysis
“We don’t see things as they are, we see things as we are.”
Anais Nin
Three approaches can be used to reduce uncertainty:
using additional direct information or hard data, e.g., well
data; capitalizing on relatable indirect information or soft
data, such as seismic data and geological concepts; and
employing robust inference and prediction methods. These
approaches should be integrated coherently in applications
whenever possible. We show the effectiveness of these
approaches in this section using various geostatistical and
other analytical methods for data integration and uncertainty
assessment.
Because the purpose of uncertainty analysis is reducing
and managing it, we must first fully exploit the available data
and build a baseline or technically most sound model. In
many projects, multiple realizations of the reservoir model
are generated before the data are fully explored, which is not
a good practice. Here we show an example of incorporating
geological principles into the model, which requires an
understanding and objective interpretation of the physical
setup.
One of the best examples of the importance of
understanding the physical setup in applying probability is
the Monty Hall problem (Rosenhouse, 2009), of which many
researchers get the answer wrong, not because they do not
know how to calculate the conditional probability, but
because they mis-interpret the physical setup. The Monty
Hall problem shows the importance of discerning the non-
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randomness from a seemingly “random” event in a physical
process.
Figure 2 shows an example of comparing a facies model
that is not constrained to the conceptual depositional model
interpreted using geological knowledge and a facies model
that has integrated the geological knowledge. The conceptual
depositional characteristics can be objectively interpreted
and quantified through propensity analysis and incorporated
in the facies modeling by use of probability maps or cubes
(Ma et al., 2009). Moreover, two different methods,
sequential indicator simulation and truncated Gaussian
method, were used to build these facies models, which
illustrates the inference uncertainty in modeling. Without
understanding the physical setup, it is difficult to objectively
develop a conceptual depositional model, and accurately
construct the reservoir model.
(b)
In reservoir characterization and modeling, true
integration is very important, just assembling a group with a
geologist, a geophysicist, a petrophysicist, and a reservoir
engineer doesn’t mean it will be an integrated team. In some
cases, a team of heterogeneous skills is like the old tale about
the blind men and the elephant. One grabs his long trunk,
one touches his large ears, and one pats his broad side; each
comes away with a totally different conclusion. The geologist
may think it is all about reservoir geology; the geophysicist
claims it is all about rock physics; the reservoir engineer
deems that the bottom line is economics. They are all right,
and they are all wrong, simply because they are all partial. In
the end, the integrated project may become disintegrated.
The best solution lies in optimally integrating everything
while resolving the inconsistencies between different data
and capitalizing on values from different disciplines.
(c)
(d)
Facies
(a)
Figure 2 Facies modeling example. (a) Facies data at 8 wells. (b) Facies model built with Sequential Indicator Simulation
(SIS). (c) Facies model built with SIS using geological prior knowledge or a conceptual depositional model. (d) Facies
model built with truncated Gaussian simulation using geological prior knowledge or a conceptual depositional model.
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Figure 3 shows an example of a reservoir model constructed using several different approaches. Although well-log porosity data are honored as a result of using Gaussian Random Function Simulation, or GRFS (Gutjahr et al., 1997), conditional to the data in building the model, they are not enough to constrain the porosity model to be realistic, partly because of the lateral trend or nonstationarity in the porosity data, as the different facies have different porosity histograms (discussed later) and the depositional facies model shows distinct spatial transitions (Figure 2).
(a)
(b) (c)
This is also reflected by the lateral variogram (Figure 3b).
The seismic attribute has a similar lateral trend, and it is
significantly correlated to the porosity, with a correlation
coefficient equal to 0.705 (Figure 3f). By using Collocated
Cosimulation (CoCosim), the lateral trend is quite well
integrated in the model (Figure 3g). CoCosim can deal with
nonstationarity better than single variable simulation through
the correlation between the primary and secondary variables
when the trend is reflected in the secondary variable.
(e)
(f)
Figure 3 Illustration of uncertainty reduction through integration. (a) Porosity data from wireline logs at 8 wells. (b) Lateral variogram for the well-log porosity that shows a nonstationary linear trend. (c) Vertical variogram. (d) Porosity model built using Gaussian Random Function Simulation (GRFS) with a spherical variogram. (e) Seismic attribute. (f) Crossplot between seismic attribute in (c) and well log porosity in (a). (g) Porosity model built using Collocated Co-simulation (CoCosim) by integrating the well-log porosity in (a) and seismic attribute in (e). Both models in (d) and (g) were built with the variograms in (b) and (c).
(d) (g)
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Spatial uncertainty, frequency uncertainty and their impact
on volumetrics and field development
Statistics that have great impact on reservoir modeling
and resource evaluation include frequency statistics and
spatial statistics (Ma et al., 2008). Frequency statistics is
especially important for the overall heterogeneity and mass
balance; spatial statistics is especially important in describing
the continuity, local heterogeneity, facies pattern, and
connectivity of the reservoir properties (Journel and Alabert,
1990). These two schools should be coupled in reservoir
modeling and uncertainty analysis (Ma et al., 2011).
Reproduction of the histogram in stochastic simulation is
such an issue that involves both frequency and spatial
statistics, and it has drawn significant attention (Soares,
2001; Robertson et al., 2006). However, honoring the
histogram of the data is generally not a good idea when a
sampling bias exists (Ma, 2010).
Figure 4a shows a good histogram match between the
porosity model in Figure 3g and the well-log porosity data.
But the model is actually biased as a result of the sampling
bias in the wells. The same can be said to the model in Figure
3d. Specifically, more wells were drilled in the eastern part,
wherein reef facies are dominant and porosity is generally
higher. Propensity analysis and subsequent facies modeling
can mitigate sampling bias, such as the models in Figures 2c
and 2d. Thus, use of such a facies model as a constraint to the
porosity model enables the mitigation of sampling bias.
Figures 4b and 4c show two porosity model realizations
generated using GRFS–based collocated cosimulation
constrained to the facies model in Figure 2d and the seismic
attribute (Figure 3e). Although the histogram of the model
does not match the well-log porosity histogram (Figure 4d),
the histogram matches between the model and the data are
actually good for each facies (Figures 4e, 4g, 4i). On the other
hand, although the global histogram match between the
model and the data is good for the model without mitigation
of the sampling bias (Figure 3g), the histogram matches are
not good for each facies (Figures 4f, 4h, 4j).
When a sampling bias is present and is not accounted
for, it produces an estimation bias in all the petrophysical
models, often in the same direction (over- or
underestimation), and can result in a systematic error in the
estimated in-place hydrocarbon volumes. The porosity
models in Figures 4b and 4e have approximately a 20% bias;
the hydrocarbon saturation can have a similar magnitude of
bias; so the in-place hydrocarbon volume can be biased more
than 40% as the fluid volume compounds the biases in
porosity and fluid saturation.
On the other hand, two reservoir properties, such as
porosity and hydrocarbon saturation, are sometimes biased
in different directions, one over-estimation and one
underestimation, with a similar magnitude. Then the
estimated hydrocarbon volume may appear correct in the
reservoir model. This is a composite error of false positive
and false negative (Ma, 2010), which will cause problems in
reservoir dynamic simulation and production forecasting.
Uncertainty quantification and reduction are highly
related. Optimally, quantifying uncertainty is a process of
reducing it, because the best use of all the available
information reduces the uncertainty compared to not fully
using the data. Figure 5a shows an example of hydrocarbon
pore volume (HCPV) uncertainty quantification based on the
model realizations, in which the P50 model honors the
statistics of the well-log porosity without mitigation of the
sampling bias.
Figure 5b shows an example of HCPV uncertainty
quantification based on the model realizations, in which the
P50 model honors the statistics of the well-log porosity after
discounting the sampling bias and constraining the model to
the facies model. The sensitivity was mainly focused on the
porosity, and thus the uncertainty range of the HCPVs is not
large. However, comparing the two HCPV uncertainty
histograms, P10 of the reservoir model without discounting
the sampling bias is greater than the P90 model with its
mitigation of the sampling bias.
How the model is built impacts not only the global
volumetrics but also the spatial distribution of pore and
hydrocarbon volumetrics. This has implications for the
positioning of future wells and field development planning
strategies. Figure 6 compares the average spatial
distributions of the two HCPVs based on the two models used
for HCPV computation in Figure 5. The field development
planning should be different for these two different HCPV
spatial distributions.
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(a)
(b)
(d)
(e) (f)
(g) (h)
(i) (j)
Figure 4 Comparing reservoir models that handle spatial and
frequency uncertainties. (a) Histogram of the porosity
model in Figure 3g (Blue) compared to the well-log data
histogram (green). (b) Porosity model built using CoCosim
constrained to the facies model in Figure 3d and the seismic
attribute in Figure 4e. (c) Same as (a) but with a different
random seed. (d) Histogram of the porosity model in Figure
4b (blue) compared to the well-log data histogram (green).
(e)-(j) Histogram comparisons by facies between the
porosity model (blue) in (b), porosity model (blue) in Figure
3g and the well-log data (green). (e) and (f) for reef, (g) and
(h) for tidal flat, and (i) and (j) for lagoon.
(c)
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(a)
(b)
Figure 5 Description of volumetric uncertainty
quantification. (a) HCPV uncertainty description based on
the 200 realizations in which the P50 model was built
honoring the statistics of the well-log data without
mitigation of the sampling bias. (b) HCPV uncertainty
description based on the 200 realizations in which the P50
model was built honoring the statistics of the well-log data
after mitigation of the sampling bias.
(a)
(b)
Figure 6 Average HCPV maps. (a) Based on the reservoir
model without propensity analysis and no conditioning to
the seismic attribute (Figure 3e). (b) Based on the reservoir
model with propensity analysis, mitigation of sampling bias,
and conditioning to the seismic attribute.
Known knowns, known unknowns and unknown unknowns
In uncertainty and risk evaluation, three categories of
variables can be distinguished: known knowns, known
unknowns and unknown unknowns, to use the terminology
of Rumsfeld (Girard and Girard, 2009, p. 54). Here we will use
these terms loosely by extending the meanings for reservoir
modeling. Known knowns include core and wireline log
measurements, histograms of reservoir properties from core
and wireline logs (e.g., green histogram in Figure 4a),
empirical correlations between reservoir properties (e.g.,
Figure 3f). Known unknowns, in its original meaning, imply
the variables that we know that we don’t know, but we may
use them loosely for the variables that we know a little, but
not fully; for example, the conceptual depositional model
that is typically interpreted from limited data and general
geological principles or reservoir model constrained to such a
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conceptual model (e.g., Figure 2), and histograms that
describe the uncertainties of reservoir properties based on
petrophysical analysis (Moore et al., 2011).
In all rigor, unknown unknowns are totally unpredictable
variables that may have a large impact on the outcome; Taleb
(2009) called them black swans. In reservoir modeling, the
uncertainty regarding different interpretations of conceptual
depositional models may be loosely considered to be in this
category; for example, all the geologists may initially
interpret the depositional environment of a reservoir to be a
carbonate ramp based on the limited data, but as more data
come in, the depositional environment turns out to be a
platform.
When unknown unknowns are dominant, uncertainty
analysis is highly challenging. In a nutshell, the most difficult
tasks are to define and quantify these known knowns, known
unknowns, and possibly unknown unknowns in an
uncertainty analysis project. When all the input uncertainties
are defined, uncertainty analysis becomes a sensitivity
analysis that evaluates the various outcomes based on the
input uncertainty ranges and distributions.
Transferring uncertainty from static to dynamic modeling
Transferring uncertainty analysis of static modeling into
dynamic modeling (Ballin et al., 1993) is another important
topic that is not discussed here. Because of the intense
demand of dynamic simulation and the large number of
possible realizations in the static model to deal with the
uncertainty space, ranking the static models is almost a
prerequisite for uncertainty analysis in forecasting production
characteristics and risk analysis for reservoir management.
Several approaches have been proposed for handling multi-
dimensional ranking and transfer of static uncertainty to
dynamic uncertainty (Deutsch and Srinivasan, 1996; Scheidt
and Caers, 2009; Caers and Scheidt, 2011; Vanegas et al.,
2011). Transferring uncertainty analysis of static modeling
into dynamic modeling is a wide, important subject, and
should be a focus of future research.
CONCLUSION
A reservoir model is a description of a reservoir through
integration of various disciplines and data, including
stratigraphic architecture, facies types, dimensions and
relationships, and petrophysical properties. A model should
be fit for purpose, integrated, and updatable. It should also
provide a platform for uncertainty analysis.
Generally, many types of uncertainties exist in reservoir
characterization. With limited data, it is impossible to
describe subsurface heterogeneities at all levels of detail. But
it is possible to describe them in relevant details. One of the
main reasons to analyze and quantify uncertainty is to
enhance decision analysis. In general, business decisions are
made under uncertainty because uncertainty may be
mitigated but cannot be completely eliminated. How much
we should attempt to mitigate uncertainty depends on the
needs of decision analysis and the cost of information.
Uncertainty analysis should not be for its own sake, but
rather should support investigational analyses, decision
analysis under uncertainty, and risk management.
ACKNOWLEDGMENT
The author thanks Schlumberger Ltd. for permission to
publish this work.
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