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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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