Summary
In this paper, we present a field example in which multiple reservoir
descriptions were generated to capture uncertainties in reservoir performance;
a streamline simulator was used to rank these multimillion-cell geostatistical
realizations and to determine the optimum level of vertical upscaling.
During geostatistical reservoir characterization, it is a common practice to
generate a large number of realizations of the reservoir model to assess the
uncertainty in reservoir descriptions and performance predictions. However,
only a small fraction of these models can be considered for comprehensive flow
simulations because of the high computational costs. A viable alternative is to
rank these multiple “plausible” reservoir models on the basis of an appropriate
performance criterion that adequately reflects the interaction between
heterogeneity and the reservoir flow mechanisms. One can generate thousands of
geostatistical realizations with a minimal cost; however, the cost of ranking
such realizations can be prohibitively expensive, even if fast streamline
simulators are used. The objective is to generate a manageable number of
realizations and represent the possible range of uncertainty in reservoir
descriptions. Here, we propose a “hierarchical methodology” in designing
uncertainties to be represented in reservoir descriptions.
In this paper, we also show how a streamline simulator can be used to design
vertical upscaling of fine-scale reservoir descriptions. The biggest challenge
of upscaling is to reduce model size without losing the heterogeneity level of
the original geological model.
We use streamline time-of-flight connectivity derived from a streamline
simulator. The time of flight reflects fluid-front propagation at various
times, and its connectivity at a given time provides us with a direct measure
of volumetric sweep efficiency for arbitrary heterogeneity and well
configuration. The volumetric sweep efficiency is the simplest measure that
reflects the interaction between heterogeneity and the flow field. It is a
dynamic measure that can be updated easily to account for changing
injection/production conditions.
Our field study involves a Middle Eastern carbonate reservoir under a
moderate-to-strong aquifer influx. The reservoir is on primary depletion and
has no injectors. In our streamline-simulation exercise, the aquifer pressure
support is modeled by pseudoinjectors, and pressure updates are used to reflect
changing field conditions.
Background
With the widespread use of geostatistics, it has now become a common
practice to generate a large number of realizations of the reservoir model to
assess the uncertainty in reservoir descriptions and performance predictions.
Most commonly, these multiple realizations account for spatial variations in
petrophysical properties within the reservoir as well as the random order in
which unsampled locations are visited and, thus, represent a very limited
aspect of uncertainty. For reliable risk assessment, we need to generate
realizations that capture a much wider domain of uncertainty, such as
structural, stratigraphic, and petrophysical variations. From a practical point
of view, we want to quantify the uncertainty while keeping the number of
realizations manageable. In this study, we will adopt an approach that is based
on hierarchical principles. Thus, the uncertainty having the greatest potential
impact is identified first. For example, with limited well control, the
structural uncertainty derived from the seismic interpretations can have the
most impact on the flow performance, or (for faulted reservoirs) the
uncertainty with respect to fault locations can have the most impact. Then, the
next level of uncertainty is identified, and so on. The last level of
uncertainty is the multiple geostatistical realizations of reservoir properties
for a given set of input parameters. The petrophysical uncertainties generally
tend to have a much lower impact on the reservoir performance compared to
factors affecting large-scale fluid movements.
There is, of course, a variety of other sources of uncertainties.
Uncertainties may exist related to fault representation or log- vs.
core-porosity representation or inclusion of seismic data to modify porosities.
For practical applications, we must keep the number of realizations to a
manageable level. One way to accomplish this objective is to use, for each
level of uncertainty, discrete distributions that can bound the uncertainties.
For example, to represent structural uncertainties, we can define low,
most-likely, and high surfaces as a discrete way to capture the
uncertainties.
One criticism often leveled at geostatistically generated realizations is
that only a select few are ultimately used in the history-matching process. The
question is often raised about the purpose of multiple realizations if
ultimately only one or very few will be used for history-matching purposes. The
second criticism is the upscaling of geostatistical realizations. Geocellular
models tend to have millions of gridblocks. It is practically infeasible to use
these models directly in the conventional flow simulators. We need to upscale
these realizations before we can include them in a simulator. A relevant
question here is, what is the appropriate level of upscaling so that critical
heterogeneity details are still captured?
Streamline simulation, which has developed rapidly over the past 10
years,1–4 helps to address these criticisms effectively. To address the first
criticism, we need to conduct history matching of more than one realization so
that we can capture the uncertainties represented by these realizations. A
crucial issue here is to select representative realizations that will
adequately represent the uncertainties in the reservoir performance
predictions. We will resort to a streamline-based ranking criterion for this
purpose.5–7 Currently, several ways exist to rank multiple realizations.
Realizations can be ranked on the basis of the highest pore volume, highest
average permeability, closest reproduction of input statistics, and so on. Some
type of permeability threshold connectivity can be used to calculate connected
pore volume and rank the realizations based on such connectivity.8 The drawback
of these simple techniques is that they do not account for dynamic flow
behavior.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
13 November 2003
- Revised manuscript received:
24 November 2004
- Manuscript approved:
9 December 2004
- Version of record:
15 February 2005
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