Scaling Up a 900-Million-Cell
Static Model to a Dynamic Model
T
he Greater Burgan field began
producing in 1946. It remains
under primary depletion with natural
waterdrive. Subsurface modeling is an
integral part of reservoir management.
In 2001, the first comprehensive fullfield geological model was built with
65 million cells, encompassing all of the
major reservoirs. A reservoir-simulation
study (1.6-million-cell dynamic model)
was conducted in 2003 by use of
parallel-simulation technology. During
the last decade, active field-development
plans have resulted in major surfacefacility upgrades and the drilling of
+more than 300 new wells. This paper
discusses scaling up the high-resolution
geological model and specific problems
encountered by the study team.
Introduction
The Greater Burgan field is in southeastern
Kuwait, with an area of 320 sq miles. Fig. 1
shows the five main reservoir units of the
Greater Burgan field complex: the Wara
sand, Mauddud, Burgan Upper sand, Burgan Middle sand, and the Burgan Lower
sand. Areally, the field is separated into
three producing areas, Burgan, Magwa,
and Ahmadi. Mauddud, the only carbonate reservoir in the sequence, is relatively tight and, together with the extensive
Wara shale, acts as a barrier separating the
Wara sand from the massive sands of the
underlying Burgan formation. However,
extensive faulting prevents communication between the Wara and Burgan sands.
The Burgan oil field was discovered
in 1938, with first oil production in 1946.
Burgan has good energy support from
strong natural aquifers, and after 66
years of production, most of the field is
still under primary depletion. More than
1,200 wells have been drilled across the
field. While drilling spacing is dense in
the crestal area, well control in the flanks
is relatively weak, giving rise to more
geostatistical uncertainty. As the field has
matured, the reservoir pressure has declined, reducing productivity.
Scaling-Up Approach
Because the field comprises significantly
different reservoir units, a detailed geological description is required. A veryfine-scale geological model with 900 million cells was required. This geological
model was constructed as a master model
integrating all types of data available, and
will be maintained and updated over time
with new data from drilling, production,
and other activities. For dynamic modeling, the very-fine-scale geological model
is too big and must be scaled up.
A multiscale approach is needed for
the Greater Burgan field. Several studies, including reservoir management and
optimization, facilities design and planning, recovery optimization, and enhanced oil recovery, are envisaged for the
field. These studies are expected to require different resolutions and different
levels of reservoir-description detail. Use
of a single model with the highest possible resolution for all of the studies is im-
This article, written by Senior Technology Editor Dennis Denney, contains highlights
of paper SPE 164187, “Answering the Challenge of Scaling Up a 900-Million-Cell
Static Model to a Dynamic Model—Greater Burgan Field, Kuwait,” by Eddie Ma,
SPE, Kuwait Oil Company; Sergey Ryzhov, SPE, Schlumberger; Yuandong Wang,
SPE, Petrobras; Reham Al-Houti, SPE, Laila Dashti, SPE, and Farida Ali, Kuwait Oil
Company; and Muhammad Ibrahim, SPE, Schlumberger, prepared for the 2013 SPE
Middle East Oil and Gas Show and Exhibition, Manama, Bahrain, 10–13 March. The
paper has not been peer reviewed.
practical for a field this size. Thus, each
study had to formulate model-­resolution
requirements in accordance with the
phenomena to be studied, which resulted
in different scaling of the models.
Of these models, one is the master
model and is used for the flow simulation. Choice of model size in this case
was dictated by reasonable turnaround
time, which in turn warranted that model
history matching could be completed
on schedule. However, certain aspects
of field redevelopment could require a
finer-resolution model, here called the
Finer model, and should benefit from the
groundwork of the Coarse master model.
The Coarse master model is used for
full-field history matching and is expected to capture the general energy balance
and the water-front movement. It can be
used to generate reliable production forecasts for certain redevelopment scenarios such as infill drilling and waterflood.
However, the reliability of the forecast
profiles is expected to be limited to the regional level. Resolution of the Finer model
would enable accuracy beyond the regional level (i.e., the Finer model is expected
to produce the cube of r­ emaining-oil saturation that can be used for actual well
planning and water-­injection design). In
addition to the Coarse and Finer models, the team also proposed the use of an
even coarser model with resolution just
high enough to capture the major geological features of the Greater Burgan
field. This Very Coarse model can be used
for fast-track screening and sensitivity
analysis, as well as for computer-aided
history-matching exercises.
Areal scaleup, or upgridding, is
needed for the model. In most reservoirsimulation studies, scaling up is performed only in the vertical direction because areal grid size of the geological
model is already suitable for simulation.
However, the immense size of the field,
the depositional-environment variation
For a limited time, the complete paper is free to SPE members at www.spe.org/jpt.
Copyright 2013, Society of Petroleum Engineers. Reprinted from the Journal of Petroleum Technology with permission.
82
JPT • JULY 2013
State of Kuwait
Greater Burgan Field
20 km×40 km
Fig. 1—Greater Burgan field, Kuwait.
within each stratigraphic unit, and the
major differences in the degree of heterogeneity between different reservoir
zones require the geological model to
retain geological features at the highest
possible level of detail, which results in
small grid-cell sizes of 50×50 m.
Special attention must be given to
reservoir connectivity. The degree of heterogeneity differs significantly from one
stratigraphic unit to another, particularly
when comparing the two main reservoir
units: Wara sand and Burgan Third Middle sand. Burgan Third Middle sand is associated with a channel belt and is a clean
massive sand, well-connected both laterally and vertically. The Wara sand has features of depositional environments from
distributary channels to the tidal shallow marine with individual sand bodies
with less width and often separated from
their neighbors by tidal flats and shales.
However, in a structured grid, the same
areal dimensions must be used for the entire productive interval, which links the
choice of the areal grid-cell size with the
possible effect it may have on reservoir
connectivity of heterogeneous reservoirs
in a scaled-up model.
Model-Size Determination
The size of the master (Coarse) model
was linked directly to the simulation
model run on the operator’s hardware.
JPT • JULY 2013
Requirements for the model run time
were formulated upfront. To meet the
deadline, it was agreed that turnaround
time of a history-match simulation run
should be within 1 day. This requirement
translates to a run time between 15 and
20 hours, with additional time for postprocessing and analyses.
It is worth mentioning that the start
of model scaling up coincided with the
deployment of the operator’s new PC
cluster. To estimate the optimal size of
the Coarse dynamic model, a series of
benchmarking runs was performed with
different numbers of CPUs on the new
cluster using the 2009 Greater Burgan
parallel model (1.6 million cells). The resulting run time was used to estimate the
run time required for the Coarse model,
assuming scalability of run time with
model size and CPU use. Benchmarking
indicated that the optimal choice was
32 CPUs, which corresponds to a model
size of 2–3 million cells.
The sizes of the Finer and Very Coarse
models were derived from the numbers
accepted for the Coarse model. Thus, the
Finer grid had approximately 30 million
cells, while the size of the Very Coarse
grid does not exceed 0.2 million cells.
Upgridding
Although three grids of different resolutions (Coarse, Finer, and Very Coarse)
Wara Formation
Type Log
were generated, the focus here is on the
Coarse model because it was chosen as
the master model for the study.
Areal cell size of the dynamic grid
was selected on the basis of simple practical considerations. Ideally, while coarsening the grid, one should fit as many grid
cells as possible between two neighboring wells. However, there will always be
a compromise between lateral and vertical resolution of the grid. Areal grid-cell
size of the geological model is 50×50 m.
Therefore, the choice of areal grid-cell
size for the Coarse dynamic model was
restricted to between 100×100 m and
300×300 m. The average distance between wells in the field is approximately 500 m; thus, use of 300×300-m grid
cells was not recommended because it
leaves a maximum of one cell between
two wells.
A 100×100-m grid resulted in at
least four cells between two neighboring
wells. However, to comply with a model
size of 3 million cells, the 100×100‑m
grid would require sacrificing vertical
resolution. In the process of upgridding,
every 15 geological-model layers had
to be merged into a single layer of the
Coarse grid. The vertical resolution of
such a grid was deemed unacceptable for
adequate representation of field geology, especially in the more-heterogeneous
reservoirs such as the Wara.
83
Fig. 2—Streamlines showing water-saturation distribution 15 years after start of the waterflood, with slices of the 3D
grid superimposed on the streamlines. Fine grid on the left and coarse grid on the right.
Therefore, use of the 200×200-m
grid appeared to be a reasonable compromise. It allowed at least two cells between most of the neighboring wells, but
did not require significant coarsening of
the grid in the vertical direction. On average, areal grid-cell dimensions of the
Coarse grid would be 200×200 m, with
a cell thickness of approximately 12 ft.
Lateral coarsening of the grid was performed by rerunning the pillar-gridding
process with the areal size set to 200 m.
For vertical coarsening, a variabilitybased approach was used (i.e., layers
were merged together on the basis of the
similarity of property distribution within the layer). A reservoir-quality index
(RQI) was used for variability analysis.
The RQI distribution within each finegrid layer was presented as a proportion
to the grid cells falling inside predefined
bins of RQI and was visualized in the
form of vertical-proportion curves for
each zone of the model grid.
Layers that demonstrate similar distribution of RQI then were selected for
merging. Technically, remapping was
required for zones in the Coarse grid
such that each of the new zones contained only layers intended for merging.
In an attempt to preserve the conceptual
depositional framework reflected in the
­geological-model layering, layer lumping was performed that used exactly the
same layering scheme (i.e., proportional, follow top, or follow base) as was
used originally for this zone in the geological model. Grid coarsening thereby
preserved pinch­outs and dipping angles
84
defined by geological modelers in each
of the particular stratigraphic units of
the model.
Scaling Up Model Properties
Before scaling up, the team conditioned
the geological-model properties. First,
two cutoffs were introduced to differentiate between reservoir and nonreservoir cells in the geological model. Any
cell with porosity less than 2 porosity
units or permeability less than 0.1 md
was considered nonreservoir. Then, a
binary-distributed (0 or 1) net-to-gross
(NTG) property was created: All nonreservoir cells were assigned a zero NTG,
while the rest of model cells had a unit
NTG. Subsequently, NTG was used as a
weighting factor for scaling up porosity,
permeability, and saturation. Permeability and saturation-computation properties were given special attention in the
property scaling-up process. Different
algorithms were examined, and choice
of the most-suitable algorithm was made
subject to validation by streamline simulation on a sector model, as shown in
Fig. 2.
Regarding water saturation, the
team considered several ways of transferring saturation values from the geological model to the simulation model. In the
geological model, water saturation was
populated by use of three relationships
derived from core-analysis data:
◗◗Irreducible-water saturation as a
function of RQI
◗◗Maximum capillary pressure as a
function of RQI
◗◗An equation that links water
saturation with normalized
capillary pressure and with RQI
Multiple possibilities were available
for repopulating water saturation in the
scaled-up model, from direct scaling up
of geological-model water saturation to
calculating water saturation from the
scaled-up rock properties. The complete
paper details the permeability and watersaturation scaling-up process.
Quality Check
Quality checks were performed at each
step of the scaling-up process. First, gridcell geometry needed to be checked during the upgridding, This was necessary
because areal upgridding requires reperforming the pillar-gridding step, which
may result in irregular cell geometries.
The inside-out check resulted in negative volumes and unfavorable cell angles,
leading to highly twisted and distorted
cells. Cells with irregular geometry needed to be identified and fixed, or flagged to
be deactivated during simulation, to prevent potential problems.
Second, areal scaling up coarsens
the grid and, consequently, reduces the
resolution of the zigzagged faults. Part
of the fault plane could be shifted slightly. If a well penetrated the fault plane
or was in the vicinity of a fault, the well
could appear on the incorrect side of
the fault because of the fault shifting.
The result would be incorrect formation
markers or perforated intervals. This
problem had to be fixed during scaleup.
JPT • JULY 2013
To fix the problem, wells were shifted
slightly to the correct location relative to
the fault.
Third, validation of the volumetric and flow-property conservation
was needed. Of the multiple approaches to determine water saturation, the
best approach was selected on the
basis of volumetric validation. Flowproperty conservation was validated by
running streamline simulations on both
fine and upscaled sector models to check
whether reservoir connectivity was preserved. Because of the substantial heterogeneity in the Wara formation and
significant scaling up, this check became
very important.
JPT • JULY 2013
Conclusions
To succeed, the scaling-up process required the use of an elaborate approach
for grid coarsening and scaleup/transfer
of the properties from the fine-scale static model to the coarse simulation grid.
The following solutions were used.
◗◗Multiscale approach (i.e.,
scaling up to dynamic models of
different size).
◗◗Upgridding that combined both
areal and vertical (variabilitybased) coarsening. Use of the
original (geological-model)
layering scheme that allowed
preserving geological input into
the gridding process.
◗◗Translating fine-scale watersaturation values to the coarse
model, ensuring necessary
preservation of model
volumetrics.
◗◗Use of mechanistic modeling at
different stages of the scaling-up
process.
The Burgan geological model was
scaled up successfully to a dynamic
model at three different scales. The approach chosen for the scaling-up procedure proved its value by demonstrating
small-to-negligible discrepancy in volumetric comparisons between the fine
and coarse models. This holds true for
the results of the permeability validation
that used streamline simulations on sector models. JPT
85