UNCERTAINTY ASSESSMENT IN 3D RESERVOIR MODELING
BY EMMANUEL GRINGARTEN, EARTH DECISION SCIENCES
AN INTEGRATED APPROACH
Uncertainty is not an inherent feature of
our reservoirs; it is due to our lack of
knowledge and understanding about the
reservoir. Uncertainty can be modeled, but
there is no objective measure of uncertainty.
The uncertainty will be as large as the
modeler decides to make it. Therefore, one
must be open-minded… very open-minded.
This introduces us to a new modeling
paradigm: it is necessary to think in terms of
what we don't know, rather than in terms of
what we know. This paradigm shift
associated with the right tools provides for
better decisions, faster.
(A)
(B)
(C)
MANAGING UNCERTAINTY
We believe that in order to appropriately
manage uncertainty linked to various
aspects of reservoir management, we need a
method and a tool that satisfies the
following requirements:
1) To be able to evaluate the complete range
of uncertainties. It is then necessary to be
able to capture them, i.e., to quantify and
store different structural scenarios and/or
geological models. Last, all of it must be
integrated in a consistent framework to
automatically quantify their cumulative
impact.
2) One must be able to identify the relevant
elements of uncertainty and filter out
those that don't matter.
3) Finally, once key uncertainty elements
have been identified, it is necessary to
rapidly know what actions are required
to reduce their uncertainty to an
acceptable level. For a reservoir modeling
point of view, that would mean: (i) refining
the interpretation, (ii) refining the model,
or (iii) gathering more data because
interpretation and modeling uncertainty
cannot be refined any further with
existing information.
UNCERTAINTY AND 3D RESERVOIR
MODELING
Understanding 3D uncertainties
With today's software, constructing a 3D
geological model of the reservoir is
relatively simple. Once a model is
constructed, it should be easy and automatic
to construct multiple versions (either by
simply changing a parameter and / or
performing stochastic simulation, etc.) We
will postulate that constructing multiple 3D
models is the only way to assess the
cumulative impact of data, interpretation,
and modeling uncertainties on reservoir
management decisions.
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Figure 1. Summary of multiple realizations of a 3D reservoir model: (A) History plot, (B) Histograph, (C) CDF.
3D Uncertainty Analysis
A typical 3D uncertainty analysis workflow
is as follows: (i) evaluate the uncertainties –
taking each step of the workflow along with
all the parameters involved, one must
quantify how much is unknown about each
one of them; (ii) integrate the uncertainties
– through the construction of a complete
reservoir model; (iii) analyze the impact of
constructing multiple models on the
metrics used to make a decision; and (iv)
iterate to reduce the uncertainties until the
risks are minimized sufficiently to allow
decision making.
3D Modeling Workflow
A 3D reservoir model consists of the
following elements: (1) a structural model
consisting of horizons and faults, (2) fluid
contacts – gas-oil (GOC) and oil-water
(OWC), (3) a sedimentological model
(optional), (4) a porosity model, (5) a
permeability model, (6) a net-to-gross
(NTG) model (which may or may not be
related to the sedimentology), (7) a water
saturation model (highly dependent on
everything listed above), (8) a PVT model
describing formation volume factors and
solution gas ratios, etc. and, (9) a reservoir
simulation model.
Each of these elements has its own way of
being quantitatively described, and
uncertainty measures may also be different
for each. However, it is important to think of
them as interconnected members of a single
entity. They are highly dependent on one
another (e.g., water saturation can be a
function of height above contact – itself
dependent on the position of the reservoir
structure and the contacts, and the porosity
and permeability models). Furthermore,
there exists a hierarchy in the way they fit
together to form a 3D reservoir model
giving rise to the concept of “nesting” which
we will come back to later.
Model Uncertainty
Typically, model uncertainty is seen as
multiple realizations of a geostatistic-based
process. Stochastic simulations will
reproduce input parameters “on average,”
and that is done by construction! Variability
in responses from geostatistical simulation is
simply due to what is known as ergodicity –
stochastic fluctuations around the input
parameters.
The uncertainty related to model
parameters is one that is very rarely dealt
with in practice, yet it may be one of
paramount influence on the global
uncertainty. What is essential is to model
“what we do not know”, i.e., what are the
exact values of the modeling parameters.
Multiple Realizations
The only way to assess the cumulative
impact of all uncertainties is to construct
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multiple realizations through a combination
of
scenario-based
and
stochastic
simulations. As mentioned above, once a
model is constructed, i.e., a workflow is put
in place that fits all the pieces together,
changing a piece or part of a piece should be
automatic and require no extra effort from
the modeler. With today's computer
architecture and processing power, this is
quickly becoming a non-issue. It is relatively
fast to generate a static model, even if it
contains millions of cells, to generate a
hundred can be done over lunch, and a
thousand over night!
Summarizing Multiple Realizations
For volumetric computations, different types
of volumes that can be computed are: the
gross rock volume (GRV), the net rock
volume (NRV), the net porous volume
(NPV), the different fluid volumes (OIP and
GIP), and the connected volumes using
various connectivity criteria. These volumes
should be reported not only for the whole
model but also for any regions defined on
the model, i.e., concessions or lease
boundaries, fault-blocks, reservoirs, zones,
facies, and the intersections of the lot.
When a model includes reserves
estimations and fluid flow simulation, one
should also consider looking at produced
volumes, recovery factors, water-cuts, and
GORs – per well, per platform, per field.
These are the “metrics” of the model
allowing its classification. Figure 1 illustrates
the kind of display one should look at: it
includes three important panels: (a) the first
one displays for each model realization, a
summary volume – this is referred to as a
History Plot; (b) the second one shows the
global histogram of that same information
along with the appropriate summary
statistics, and (c) the third panel shows the
cumulative distribution (CDF).
Figure 2b. Hierarchical nesting in reservoir modeling.
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Figure 2a. Independent Simulations
All that is described above and illustrated in
Figure 3 give us our first decision-support
tool. This tool:
(a) yields a list of realistic outcomes that
can be used as input distributions for
Monte-Carlo-based economics analysis,
(b) clearly summarizes the uncertainty in
reserve estimates and shows if a sufficient
number of models have been generated,
and
(c) allows us to understand the spread in
outcomes and the values of important
percentiles.
As the result of an economic risk analysis
may require that the global spread of the
assessed uncertainty be reduced, it is
necessary to identify which factors would
benefit from more rigorous attention.
IDENTIFYING KEY UNCERTAINTIES
One must be able to quickly identify the key
uncertainties, i.e., not necessarily the ones
that have the largest spread, but the ones
whose uncertainty have the biggest impact
on the reservoir management decision at
hand.The metrics defined above are the link
between the estimates and the decision.
From them, the impact of each element is
deduced.
As a simple illustrating example, let's
consider the equation for Oil in Place at
reservoir conditions (no gas):
Equation 1
OIP = GRV * NTG *
ø * (1 - Sw)
The major elements here are the gross rock
volume (GRV), consisting of a structural
piece: horizons and faults – properly
connected together – and fluid contacts; the
Decision Making in the Face of
Uncertainty
Now that we have generated hundreds or
even thousands of models, how do we make
a decision?
There are three major aspects to decisionmaking in 3D uncertainty modeling.The first
one is to rank the alternative reservoir
models and perform more in-depth analysis
of extreme and “average” models. The
second is to be able to optimize the
decision (such as the positioning of a
development well) given all the possible
representations of the reservoir. The last is
to use the resulting distributions as input to
a more complete chain of Monte Carlo
simulations which captures elements beyond
earth sciences (facilities, transports, oil
price, etc).
RANKING
Figure 3: Nested simulations history plots illustrating that, in this particular example, structural uncertainty
has a larger impact on OIP estimates than porosity or water saturation (no NTG specified).
net-to-gross (NTG); the net porosity (ø),
and the water saturation (Sw).
Identifying which of these elements is more
important than the others will help focus
resources on relevant issues, stay at the
right level of technical detail, and in turn
save time and money.
Nested Simulations
In terms of 3D modeling GRV, NTG, ø, and
Sw have a natural “nesting”, or hierarchical
ordering: the GRV represents the envelope
of the reservoir, only part of it defined by
the NTG represents an acceptable type of
rock; ø is the void space in which if there is
no water (Sw), there is hydrocarbon. The
same order is followed when creating a 3D
reservoir model and a hierarchical
dependency is therefore created.
There are two types of approaches when
running multiple realizations, which we will
refer to as Independent simulations and
Nested simulations.
Independent simulations correspond to
drawing one outcome of each element,
reporting the volumes (or any summary
metrics), and starting again at the very top
of the hierarchy and taking a new reservoir
structure as to represent the GRV, then a
new NTG realization, then a new ø
realization, and finally a new Sw realization.
In a more complete reservoir model, the
hierarchy is illustrated in Figure 2a.
Performing Nested simulations implies
drawing multiple sub-elements for each
major element and so on. Nested
simulations are illustrated in Figure 2b. For
example, for each reservoir structure, one
can consider, say 5 NTG; for each NTG:
5 porosities; and for each porosity: 5 water
saturations. The total number of complete
3D models for each sample structure in this
particular example is 125 (5 * 5 * 5). The
total number of realizations becomes very
large, but it very quickly shows also which
element has the largest impact. This is very
important at an early investigation stage
when the 3D model does not need and
should not be unnecessarily fine, and it is
therefore possible to generate quickly a
large number of realizations as shown in
Figure 3.
Tornado Charts
Tornado charts are great to visually
summarize information and more precisely
identify the impact of various plotted
parameters. They are excellent decisionsupport tools for that reason.
If we consider the equation for Oil in Place
(see
Equation
1),
and
multiple
“Independent” realizations, it is possible to
simply de-couple the influence of each
element on the total variability of the
system by considering the P50 value of
each element and by modifying one at the
time to see the positive or negative impact
of the P10 and P90 values. The previous
example would yield the tornado chart of
Figure 4, where it is confirmed that
structural uncertainty has the largest
impact on OIP.
Generating many models is one thing, but
analyzing each one of them is another and is
near impossible. It is therefore necessary to
be able to select representative models for a
more in-depth analysis and understanding of
the possible dynamic responses of the
reservoirs. However, the rank of a particular
model is, of course, dependent on the criteria
or metric chosen to perform the ranking.
This means that a model is representative to
serve as a basis of a given decision only if the
ranking criterion is representative of the
decision that needs to be made. The CDF of
Figure 1 represents the ranking of all models
given the displayed criteria, e.g., the
highlighted realization (# 95) is a P90 with
respect to the original Oil in Place.
CONCLUSIONS
• Modeling uncertainty is a complex issue
that can not be solved using simplistic
scripts of algorithms that use a subset of
the data available. Instead, tools that can
integrate all data and test their effect (or
lack of effect) on the model must be used.
• Uncertainty is the concern of an
integrated asset team.Their integrated 3D
model is the repository of all their
knowledge, but also their lack of it, i.e., the
uncertainties. It also shows the
imbrications and interdependencies of all
modeling stages. A software tool must
exist that enables this to happen, for
example JACTA has been able to
seamlessly
capture
and
integrate
structural, reservoir, and flow uncertainty.
• Uncertainty evaluation, capture, and
integration must be done throughout the
life of the reservoir. The tool must be
flexible enough to allow scalability and fitfor-purpose analysis. There must be a
consistency between quick Monte-Carlo(Continued on page 42...)
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based volumetric estimates – which do not
need to have millions of cells – and 3D
geological models.
Input parameters have a high degree of
uncertainty because they are inferred from
sparse, unreliable, biased interpreted data.
It is fundamental to be able to capture and
use all of it.
Geological modeling software must be
tightly integrated with dynamic flow
simulators to allow a more reliable ranking
of the multiple realization of the reservoir.
It is also an ideal way to investigate and
optimize alternative field development
strategies
Geological modeling software need to be
tightly
integrated
with
economic
evaluation tools to directly measure the
impact of various uncertainties associated
with the different elements of the
subsurface model.
Uncertainty is a constitutive part of the
Shared Earth Model; every element has an
uncertainty associated to it.
Figure 4.Tornado Chart resulting from the example in Figure 3 (no NTG specified).
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