SEPTEMBER 2009
The “Better Business” Publication Serving the Exploration / Drilling / Production Industry
Simulation Tools
Maximize Accuracy
Of 3-D Reservoir Models
By Liz Thompson
HOUSTON–Three-dimensional models are becoming part of the standard workflow for
assessing and exploiting hydrocarbon reserves. A key element of the workflow is constructing
3-D grids that accurately represent reservoir geometry, followed by property modeling,
where the grid is populated with reservoir properties such as porosity and permeability.
This modeling usually is based on the detailed analysis of subsurface data carried out
as part of a reservoir characterization study, and employs tools that have been tried and
tested through years of demanding use. These software tools generally are regarded as
robust and reliable, but they cannot get away from the limitations of the data. Models
generally are built from dense, low-resolution seismic data and sparse, very high-resolution
well data. Inherently, such models have a degree of irreducible uncertainty, since the
correlation between the detailed well data and the low-resolution seismic data is an interpretation and may be partially wrong or inaccurate.
In addition, the stochastic modeling techniques used in property modeling give one
possible representation of the reservoir based on the input data and model parameters.
Although this is not a true and complete representation of the reservoir (even with multiple
realizations of the model), it provides a good approximation for calculating in-place
volumes and simulating dynamic behavior. For some time, this has been the most reliable
basis for business decisions.
Reproduced for Roxar with permission from The American Oil & Gas Reporter
SpecialReport: Reservoir Characterization & Exploitation
Given that the user’s knowledge of properties between the
wells is unavoidably uncertain, the use of stochastic techniques
is a pragmatic and effective solution. After all, if the interpreter
knows that the data interpretation has a margin of error, then a
multiple realization approach can embody and visualize that.
But is it possible to do better than simply visualizing it?
Statistical analysis by spreadsheet has become common, but
using a spreadsheet to quantify reserves uncertainty has its limitations. One can assess the impact of ranges of variable values,
but a spreadsheet is a poor tool for working with spatiallyvariable data, since the spatial element is usually lost.
Quantifying Uncertainty
Using 3-D models as the basis for reservoir uncertainty
quantification is now feasible thanks to advances in hardware
and the development of software that supports the automated
generation of multiple 3-D models. Instead of average values,
distributions of input parameters such as porosity, permeability,
velocity, etc., can be used to define a set of equally valid 3-D
structural models and 3-D grid property distributions.
As a result, it is now possible to base all internal rock and
fluid modeling, reservoir flow simulation and volumetric analysis
on models that include not only the best in reservoir characterization and modeling, but also the best in uncertainty assessment.
By combining these two, more reliable decisions can be made
than by using either the 3-D model or the spreadsheets alone.
Three-D uncertainty modeling workflows require the definition
of input distributions for key parameters for all the significant
modeling stages–from velocity modeling and depth conversion
through to facies modeling, saturation modeling and flow simulation. Distributions for parameters such as velocity, surface
FIGURE 1
3-D Uncertainty Modeling Workflow
INPUT
3-D MODELS
OUTPUT
location, porosity and permeability can be repeatedly sampled
to generate multiple equally valid models.
When building full 3-D property models, it is not viable to
generate thousands of 3-D grid models similar to the way in
which thousands of spreadsheet simulations are produced. In one
reservoir modeling solution, for example, Latin hypercube sampling
(LHS) from distributions has been implemented to reduce the
number of realizations needed while still achieving a representative
coverage of the input parameters. As applied to analysis, LHS
technology essentially generates distributions of plausible collections
of parameter values from a multidimensional distribution.
The key point is that 3-D models are three dimensional; they
are built so that the interpreter can use spatial data in their
correct relation to the data around them for visualization and
for calculations, whereas statistical spreadsheet simulations
deal with averaged input values and spatially detached data.
The 3-D workflow is far more appropriate for evaluating
significant contingent resources and for reliably quantifying
commercial reserves. It is also suitable for providing input to
development plans and concept design choices, as well as for
managing fields in early phases of production.
Figure 1 is a schematic of a 3-D uncertainty modeling workflow,
showing the most common inputs, stages in the 3-D modeling
process and corresponding outputs. Multiple 3-D models are generated by stochastic sampling of the input distributions, and all
volumetric calculations are based on the 3-D models.
Simulating Variability
Many vendors are integrating tools for simulating variability
as a result of uncertainty. Uncertain data are not randomly
variable. Both limits and patterns can be set on the ways data
can vary, and it is possible to examine the effects of using
different values sampled, for example, from a normal distribution.
Reservoir modeling software is designed to turn geological understanding derived from the characterization of the reservoir
into a reliable model of the subsurface.
Within reservoir models, key sources of uncertainty are the
structure of the reservoir, porosity (a direct result of the facies
model), water saturation, defining the column height, and the location of hydrocarbon contacts. Connectivity within the reservoir,
a source of uncertainty in simulation modeling, is also largely
controlled by the distributions used in the facies modeling.
Fracture modeling, an area with very significant degrees of uncertainty, also can be integrated into the modeling workflow.
With the right software, it is possible to make assessments of
most of the major sources of uncertainty in geometric reservoir
modeling.
The structural model is a very significant source of uncertainty,
with seismic quality and the fault interpretation contributing irreducible unknowns.
Some reservoir modeling solutions can assess the impact of
variable correctness in the seismic and depth conversion areas,
and although structural modeling still generally requires manual
generation of scenarios, new developments now automate the
process to a far greater degree, making generating multiple
versions of the model a practical goal. Of course, the stochastic
realization structure of facies and petrophysical modeling, which
generates tens or even hundreds of realizations of the model
from the same control input, lends itself naturally to uncertainty
assessment.
SpecialReport: Reservoir Characterization & Exploitation
The most important benefit of working in 3-D is that intrinsic
subsurface dependencies are treated in a realistic manner. This
produces more correct estimations of uncertainty and provides
a better foundation for informed asset management. The 3-D
modeling workflow also produces a variety of additional
products, such as probability maps and cubes that are useful for
quantifying and understanding the spatial variability of uncertainty.
Key Application Areas
So how can uncertainty analysis be applied? One key application area is assessing the volume of reserves. Using statistical
spreadsheet analysis and the standard volumetric equation is
now common in screening and assessing the value of hydrocarbon
assets. Uncertainty in static volumes and recoverable reserves
are quantified by Monte Carlo sampling of probability distributions
for the controlling parameters in the volumetric equation.
Although these approaches are very fast, it is often difficult
to estimate the intrinsic dependencies between input parameters,
such as hydrocarbon contacts and spill points, for example.
They also provide no quantification or visualization of the
spatial location and variability of the uncertainty.
An alternative is to use a 3-D model as the basis for
volumetric calculations. This allows the dependencies between
the various input parameters, such as the shape of the reservoir
and hydrocarbon contact location, to be treated in a realistic
manner and provides information on the spatial variability of
the uncertainty.
Another application area is assessing the effect of uncertainty
on facies variation. Three-D facies architecture models usually
are generated using stochastic modeling algorithms. These algorithms create multiple realizations of facies architecture by
changing the random seed numbers used in the stochastic simulation. However, it is not enough to vary random seeds alone
to quantify realistic uncertainties. From well data and general
paleogeographic knowledge, it is not possible to precisely know
the “true” channel facies volume fraction, average channel sand
body width, or average azimuth.
If the random seed numbers are varied and the geometric parameters are kept constant, the simulated channel geometries
are locally different, but the overall connectivity and architecture
are quite similar. When the input parameters are varied in a
controlled manner using input distributions, the result is a much
richer variation in geometries that more closely reflects true uncertainty in the sand channel architecture and connectivity.
Figure 2 shows realizations of a sand channel architecture
FIGURE 2
Channel Modeling (Seed and Parameter Variation)
Seed Variation
Parameter Variation
FIGURE 3
Simulated Porosity Distribution in Cross Section
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
generated using a stochastic modeling algorithm. The “seed
variation” realizations were generated using identical geometric
input parameters, while the “parameter variation” realizations
were generated with variable sand fraction, channel dimensions
and azimuth.
Full Range Of Values
The benefit of being able to sample a full range of possible
values rather than collapsing the range of possibilities to a
single value is important in all forms of property modeling,
whether porosity, permeability, saturation level, etc. Using a
distribution greatly increases the accuracy of predictions in situations where there is an identifiable trend to the variation in
property value.
Again, where this is a spatially controlled variation, the true
impact of the variability can only be assessed by using a spatial
(or 3-D) model populated using the range of values and the
guiding trend.
An important source of porosity uncertainty that needs to be
taken into consideration when defining input distributions is
related to sampling the wells. Porosity is seldom constant within
a structure. With only a few wells, it is difficult to know whether
the “average porosity” calculated at the well locations is representative of the field. This uncertainty is particularly significant
if there are strong lateral trends or depth-dependent trends.
The impact of internal trends depends on the relationships of
the trends to the structure and contacts, and again, these dependencies need to be modeled in 3-D to be properly understood
and quantified. This is illustrated by a simple example of a
gentle anticline structure with a single discovery well located
near the crest (Figure 3). Note the vertical trend in the porosity
values. The discovery well penetrated 79 feet of fully saturated
sand with an average porosity of 17 percent. The reservoir sand
is characterized by a fining-upward depositional trend. Porosity
values near the base are about 22 percent and decrease to 12
percent near the top of the sand.
This trend can be incorporated into a 3-D uncertainty model.
For example, for the base case structure and a contact 10 meters
under the lowest known hydrocarbon, incorporating the finingupward trend leads to an 8 percent reduction in the pore volumes
estimated from the model when compared with the estimates
derived using no trend and an average value from the well
location. This is because the high-porosity base of the sandstone
dips under the fluid contact and there are larger volumes of the
low-porosity upper part of the reservoir in the hydrocarbon column.
By using uncertainty analysis to map variations in porosity
distribution and structural geometry, multiple models can be
created and their pore volumes measured. These estimates can
be used to define the range of pore volumes to be considered
when making reserves estimates.
SpecialReport: Reservoir Characterization & Exploitation
3-D Modeling Products
In addition to defining histograms and probability distributions
for in-place volumes and reserves, 3-D uncertainty modeling
provides 3-D grids and a wide array of additional products that
are useful for asset management and field development decisions.
Maps can be generated to describe lateral variations in uncertainties. These maps are useful for general quality control
purposes and for communicating the spatial distribution of uncertainty. For instance, a gross pay uncertainty map can provide
useful input for targeting appraisal wells.
At the other end of the spectrum, uncertainty quantification
cannot be divorced from history matching of production data
when dealing with mature fields. Uncertainty modeling and
history match optimization need to be done together. As an example, one software package has been developed to optimize
history matching and quantify uncertainty in future production
profiles. The main controlling parameters are related to the production data and history match. However, the software can be
linked with the geologic models to provide a “big loop” history
match and uncertainty modeling workflow.
Reservoir characterization is a highly skilled part of the hydrocarbon production process, generating an essential understanding of the reservoir. The models that embody that understanding are created by a well established and sophisticated
area of geologic modeling, but even now there is only so far it
can go. However, the limits of the data do not have to represent
the limits of usefulness for the models.
Uncertainty analysis can enhance the models by allowing an
assessment of where any given model is likely to be most
accurate and where it may be unreliable. Using this information
to focus further data collection, locate wells and make justifiable
estimates of reserves can greatly improve the utility of the
model and allow the underlying reservoir characterization work
to contribute even more to the success of an asset.
r
LIZ
THOMPSON
Liz Thompson is technical information manager at Roxar,
responsible for ensuring that all technical information is
gathered and made available to the marketing and product
groups. Thompson was formerly product manager for Roxar’s
fracture modeling software and technical product manager
for Roxar’s structural geologic tools.