-
SPE-173270-MS
Capturing Geologic Complexity in a Simulation Grid
Larisa Branets, ExxonMobil Upstream Research Company; Valeriy
Kubyak, Elena Kartasheva, Valeriy Shmyrov,and Dmitry Kandybor,
NeurOK Software
Copyright 2015, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Reservoir
Simulation Symposium held in Houston, Texas, USA, 2325 February
2015.
This paper was selected for presentation by an SPE program
committee following review of information contained in an abstract
submitted by the author(s). Contentsof the paper have not been
reviewed by the Society of Petroleum Engineers and are subject to
correction by the author(s). The material does not necessarily
reflectany position of the Society of Petroleum Engineers, its
officers, or members. Electronic reproduction, distribution, or
storage of any part of this paper without the writtenconsent of the
Society of Petroleum Engineers is prohibited. Permission to
reproduce in print is restricted to an abstract of not more than
300 words; illustrations maynot be copied. The abstract must
contain conspicuous acknowledgment of SPE copyright.
Abstract
It is well recognized that structural and stratigraphic
frameworks are the geologic features that have thehighest impact on
the flow simulation results. Great advances are being made in
modeling complexstructural scenarios with either truncated or
stair-step grids. However some key stratigraphic features
arecommonly modeled with simplified geometries (e.g. use of simple
layering styles) that are limited in theirability to represent
stratigraphic concepts. Due to high geometric complexity of the
combined structuraland stratigraphic assumptions, simulation grid
is bound to further simplify them and thus lose the abilityof
recapturing geologic concepts and closing the feedback loop of the
reservoir modeling and simulationworkflow.
Preserving sound structural and stratigraphic concepts from
geologic modeling all the way to flowsimulation is critical for
reliably predicting flow streams. In this paper we propose an
approach to addressfull geometric complexity of geologic frameworks
description by integrating stratigraphic modeling withthe
generation of truncated simulation grids. We start by defining a
continuous volume (e.g., so calleddepositional space) created by
removing discontinuities in the original faulted model according to
asuitable geometric criterion. Stratigraphic modeling of interfaces
and regions, such as channels or sandlobes, shale drapes or high
permeability streaks, is carried out in this continuous space.
Stratigraphicconcepts are represented in this space by volumetric
functions including, in particular, an indicatorfunction to
designate each different layer or stratigraphic region. After the
stratigraphic models are createdfor all reservoir zones, we
generate a grid, which can be either geologic model grid or
simulation grid,directly in the original faulted domain. The grid
is built honoring both stratigraphic region definition fromthe
depositional space (through layer reconstruction) and structural
framework of the faulted domain(through truncation). We compare the
set of technical challenges our approach presents with other
knowntruncated grid generation techniques.
Examples of the grids adapted to both structural and
stratigraphic frameworks according to theproposed methodology are
included and flow simulation results are demonstrated on these
simulationgrids. Examples are based on common geologic environments
with a range of complexity of stratigraphicframeworks, e.g., from
shoreface to lobes and channelized clastic environments.
-
IntroductionStructural and stratigraphic frameworks have
thegreatest impact on flow pathways in the subsurface(Figure 1).
Surfaces of both frameworks need to becaptured in a simulation grid
in order to have effecton the simulation and to relate dynamic
results backto geologic model and interpretation. In terms ofgrid
generation this means two sets of independent/ conflicting
constraints on the grid geometry, sincegenerally fault networks are
unrelated to deposi-tional surfaces, and both types need to be
honored.
Traditional modeling workflow, with geocellulargrid for geologic
modeling and different simulation grid for flow simulation does not
adequately solve theproblem of capturing geologic frameworks in the
simulation grid. Gocellular grid of the geologic modelneeds to be
close to structured and cells need to be same size and shape to
enable efficient and accurateapplication of geostatistical
algorithms. Combining this requirement with structural and
stratigraphicconstrains is a significant challenge. In the recent
years, the structural complexity was tackled bystair-stepping
faults (Gringarten et al.) or by grid truncation at the faults
(Mallison et al.). Faultstair-stepping allows great flexibility in
handling complex intersected fault networks, but cannot
guaranteethat cross-fault connectivity is preserved in the
stair-step approximation. Grid truncation at faults is lesssuitable
for uniform or structured grid generation, but preserves exact
fault geometry and connectivity. Inadvanced techniques,
stratigraphic framework is added through layering in depositional
space. How-ever, stratigraphic framework is often lost in transion
from depositional space to simulation grid / modelor replaced by
standard layering options.
We propose a methodology for enabling preservation of geologic
complexity in the simulation modelthrough a geometry-centric
workflow where structural and stratigraphic frameworks are put
directly intothe simulation grid. Our stratigraphic model has a
geometrical representation which is independent ofgeocellular grid,
similar to the spirit of surface-based modeling techniques (Jackson
et al.). Only one gridrepresentative of both geology and simulation
is generated. Thus, grid generation can work directly withthe
stratigraphic model to build layering and truncate cell geometries
by the structural framework surfaces(horizons and faults) for
un-compromised representation of geologic complexity. Geometry
descriptionand grid generation tools are implemented on the base of
implicit complexes (Kartasheva et al.) whichprovide topologically
correct representation of heterogeneous spatial objects.
Geometry focused modeling workflow: from concept to
simulationHere we describe in detail how we build a
geometry-centric geologic modeling workflow aimed ataccurately
representing geologic features of potential importance to flow. The
workflow is illustrated inFigure 2. It incorporates the following
technology components:
Mapping to continuous space: geometric mapping from a zone in
the faulted structural frameworkto a continuous depositional space
zone is built by removing fault discontinuities in the zone.
Functional Form Modeling (FFM): model is built in the continuous
space using functional formsto represent stratigraphic features of
the depositional environment of the zone, including surfacesand
volumetric property distributions.
Grid generation and layer reconstruction: unstructured grid is
built in the real space zone usingfunctional indicators from the
FFM to deduce layering and truncating cells at the surfaces of
thestructural framework, rock properties are transferred from the
FFM.
Figure 1Relative importance of geologic features to flow.
2 SPE-173270-MS
-
Process is repeated for each reservoir zone and final simulation
grid is combined from the zonal grids.We assume that modeling
inputs for structural framework come in the form of watertight
surface-basedrepresentation (B-rep) of the structural compartments.
Modeling is done by zone which is a volumebetween two horizons
corresponding to a certain geologic environment of deposition.
Mapping to continuous space
Geologic concepts are best described in a continuous or
depositional region which needs to beconstructed such that
discontinuities caused by fault juxtaposition as well as different
types of truncationsare removed from the zone of a model.
In our workflow, we do not rely on existense of the inverse
mapping from the continuous space to realfaulted space and only
evaluate forward mapping. Consequently, geometric mapping to a
continuousspace can be simple. For example, datuming to a horizon
by z-value shift of both horizons bounding azone is a very simple
and efficient mapping technique that we successfully use with the
frameworks thatdo not exibit too much structural complexity.
Functional Form modelingStratigraphic features are modeled in
the depositional space based on the input data (wells,
seismic)mapped from the real space as well as based on the geologic
concept of the environment. Concept playsimportant role in bridging
the gap in the available data and in providing insights into
connectivity /compartmentalization of the volume by the
stratigraphic framework of regions and interfaces. Due to
itsnature, geologic concept is highly uncertain and creation of
multiple scenarios is required for evaluatingthe effect of the
uncertainty on the flow pathways.
Functional Form Modeling (FFM) is the technology we developed
for efficiently parameterizinggeologic concepts (Gai et al.). It
focuses on flexible geometric modeling of geologic interfaces and
regionsbetween them, where surfaces and volume properties are
modeled and distributed using mathematicalfunctions. The functions
are based on geometric skeletons consisting of reference surfaces,
lines, and/orpoints. Given a geologic setting, the continuous
modeling region is divided into conceptual regionsbounded by
conceptual and explicit interfaces. These regions correspond to
depositional and erosionalevents as depicted in a geologic theory
for that specific setting. A conceptual region can be treated as
amodeling region and the above procedure can be repeated to form a
hierarchy of conceptual regions atdecreasing scales. The
hierarchical modeling can be adaptive only those conceptual regions
that requiremore detailed modeling need to be enriched with
conceptual regions and interfaces at smaller scales.Reservoir rock
properties are modeled within each conceptual region. Since abrupt
changes in reservoir
Figure 2Modeling workflow diagram.
SPE-173270-MS 3
-
properties are captured by the interfaces, the properties within
a conceptual region are relatively smoothand can be modeled using
smoothly varying functions that can be controlled by a few
parameters.Traditional geo-cellular property modeling techniques
can still be used, if a geo-cellular grid is generatedwithin each
conceptual region. Thus, Functional Form Models are hierarchical,
multi-scale and non-stationary, and their representation does not
rely on a geo-cellular grid.
Although Functional Form Model is created in a continuous
depositonal space, the functionalrepresentation simulataneously
exists in the real space of the model: every function of the FFM
can besampled in the real space using superposition with the
mapping. Our gridding technology is built to takefull advantage of
this fact.
Grid generation and layer reconstructionIn order to assess the
effect a particular geologic concept or scenario have on a flow
pathways in areservoir, simulation grid needs to capture this
geologic concept and represent it accurately in the flowsimulation.
For multiple scenario evaluation it is also important to fully
automate the grid generationprocess by enabling automatic linkage
between simulation grid and geologic representation.
Our grid generation approach establishes such linkage through
the layer reconstruction procedure. Gridis generated directly in
the real space, in the domain defined by a boundary representation
of a watertightframework. First, a 2D areal template mesh is
generated covering extent of the current zone. This arealmesh can
be structured or unstrucuted and adapted to a cell density
specification. Areal mesh is extrudedin the third dimension by
building rays from each of its nodes. The direction for mesh
extrusion can bedifferent for each volume part (or fault block).
Even further, variable extrusion directions can be built,adapting
to a stratigraphic cross-strata directoion from FFM. Next, the
functional indicator of thestratigraphic regions from FFM is
sampled along each ray and region boundaries are reconstructed
assurface patches in real space, providing layer boundaries
definintion for the simulation grid such thatprismatic grid faces
may be placed on those layer boundaries. Layer definition and
reconstruction can behierarchical based on the geologic concept
hierarchy, i.e., if smaller-scale regions are modeled as
fullycontained inside a main region of the FFM, they will be
reconstructed in a hierarchical manner after themain region is
reconstructed.
After the layers are reconstructed, the resulting prismatic
(2.5D) layer grid is truncated by the surfacesof the watertight
framework (faults, horizons, and boundaries). Truncation is
performed through compu-tation of intersections between the cells
of prismatic layer grid and the volumes of the
watertightframework.
Rock properties are sampled onto the grid cells from the FFM.
Various types of averaging can be usedin sampling, e.g. cell
center, arithmetic average of vertical edge centers, arithmetic or
harmonic averageof quadrature points. Consistent layering improves
accuracy of property transfer from the stratigraphicmodel to the
simulation grid.
Figure 3a) Parallel rays for property sampling in one volume of
the domain; b) Sampled FFM region ID property along the rays; c)
Grid resolvingproperty contrasts.
4 SPE-173270-MS
-
Finally, cell connections across faults and zone boundaries are
established through split-face calcula-tion and post-processing
grid quality improvements are performed to reduce number of small
elementsproduced in truncations.
Application examples
Full workflow applicationIn this section we demonstrate our
modeling workflow application to an example reservoir
setting.Modeling inputs include a watertight structural framework,
and geologic concepts for environments ofdeposition for 3 different
zones of the reservoir. The concepts are derived from input
observations andinterpretations (see Fugure 5). Geologic concepts
identify the reservoir regional setting to be retrogradingover time
from the shoreface environment in the lower zone, through shallow
water deltaic environmentin the middle zone and into a deep-water
channelized environment in the top zone. For each of the
threemodeled zones we provide short description of its geologic
concept, its functional parameterization andrepresentation, and
example simulation grid.
Shoreface environment is a transitional environment controlled
by shorelines and gradational trends.Shoreline position deliniates
rock property contrasts, and change of its position in time guides
the regiondefinition (quite similar to weighted proportional
layering). Regions boundaries have potential for beingbarriers or
baffles to flow, they also separate contrasts in rock properties
caused by shoreline movementback-and-forth. Concept modeling inputs
and parameters are shoreline polylines, EOD/facies
propertythicknesses or boundaries, and smooth functional trends for
porosity distribution inside those EODregions.
Delta-lobe environment of the middle zone containes depositional
lobe elements, laterally extensivemud drapes between lobes and
erosion at the base of channels and inner stream mouth bars.
Regions aredefines by lobe and channel geometries, and the property
distribution inside each region uses localcoordinates derived from
the region shape parameterization. Mud drapes represent flow
barriers andincrease model compartmentalization, on the other hand,
erosive channels increase connectivity in themore proximal part of
the channel-lobe model. Concept modeling inputs and parameters are
lobe
Figure 4Comparison of FFM and standard layering for different
geologic environments. FFM layering allows for precise
representation of shaledrapes of high permeability streaks.
SPE-173270-MS 5
-
Figure 5Modeling inputs
Figure 6Shoreface zone: a) concept modeling inputs and
functional form model in continuous space, b) simulation grid in
real space (colored byEOD property).
Figure 7Channel-lobe concept: a) inputs and functional form
representation in continuous space, b) cross-section through the
concept model(erosional elements are orange and mud drapes are
white), c) simulation grid in real space (colored by EOD
property).
6 SPE-173270-MS
-
Figure 8Channel-belt concept: a) inputs and functional form
representation in continuous space, b) lateral accretion package
surfaces, c)cross-section through the concept model, d) simulation
grid in real space (colored by EOD property).
Figure 9Truncated simulation grids based on a) triangular
adaptive areal grid, and b) quadrilateral areal grid. Areal grid
resolution is differentin each zone.
Figure 10Oil saturation after 20 years of pattern water
injection, a) view from the top of the model, b) view from the
bottom of the model.
SPE-173270-MS 7
-
centerline polylines, widths and thicknesses forlobes and
channels, as well as coverage and thick-ness of the mud drapes.
Deep-water channel environment consists of ero-sional channel
belts. Each channel-belt is formed bydepositional point bars and
erosional abandonmentchannel regions. Properties inside each region
arespecified in its local coordinates. Point bars aresubdivided
into subregions by lateral accretionpackage boundaries which are
potential baffles toflow. Channel belts erode into each other
creatingcomplex connectivity in the model. Concept mod-eling inputs
and parameters include centerlines for channel-belts and
abandonment channels, channel beltand abandonment channel
thicknesses and widths, number and angle of inclanation of lateral
accretionpackage surfaces, and style of channel migration.
The final simulation grid of the model is obtained by combining
three zonal grids together andcomputing cell connectivity across
faults and zone boundaries. Different areal grids can be used in
eachzone, varying both cell type (triangular, quadrilateral, etc.)
and size. The grid is truncated by fault andhorizon surfaces of the
watertight framework, in the upper zone the truncation of layers
conforming tochannel shape at the top horizon of the zone can be
seen in both grids of Figure 9. After the wellconnections to the
grid are computed, the grid is ready for flow simulation. Results
of a flow simulationrun are shown on Figure 10.
Figure 11Truncated grid generation performance.
Figure 12Left: truncated grid and layering, right: conforming
grid and pinch-outs.
Figure 13Near-well refinement of the truncated grid.
8 SPE-173270-MS
-
Challenges and alternatives in the proposed workflowThe main
difference between the grid generation workflow we present and
other known techinques thataim at the same goal of representing
both structural and stratigraphic complexity of the subsurface in
asimulation grid is that we build the grid directly in the faulted
space of the model, where others griddepositional space model and
map the grid back to real space (as stair-step by Gringerten et al.
or astruncated by Mallison et al.). The benefit of our approach is
greater flexibility in handling complexgeometries and less strict
requirements on the quality of the mapping to the depositional
space. It comesat a cost of a more challenging truncation problem
with the real-space geometries of structural framework.
The major complexity of the truncation in real space is in
finding solution to a 3D volume intersectionproblem between a
prismatic cell (simple geometry) and a compartment of the
watertight framework (canbe arbitrarily complex, non-convex volume
with internal surface cuts, described by a surface mesh of
itsboundary). The complexity translates into performance
challenges. We have implemented multipleperformance improvement
strategies, including, e.g., localization / search structures and
shared memoryparallelization for certain algorithms. Current
performance results are shown in Figure 11, a million cellgrid can
be generated in under 20 mins.
The benefit of building a grid directly in the faulted space is
the larger range of options for controllinggrid geometry. The
direction of areal mesh extrusion (rays) does not have to be fixed
or constant vector,it can vary to better conform to a cross-strata
direction of the stratigraphic FFM model. Alternatively, therays
for mesh extrusion can be constructed to follow structural
features, such as faults, instead of thestratigraphic features of
the FFM. In this case, truncation can be avoided and grid faces
will conform tothe faults and other surfaces of the structural
framework, see Figure 12.
Engineering constraints (such as wells) are also present in the
real space and can be taken into accountduring grid generation
together with the geologic ones (Fung et al.). For example, if
strong gravity effectsare present, the vertical extrusion direction
might be preferable to any other choices mentioned above.Wells can
be taken into account during gridding through, e.g., areal grid
refinement, as illustrated inFigure 13.
The main reason for truncated grids is their ability to
represent complex structural scenarios. See Figure14 for and
example of framework geometries that are easily treated by
truncation, but can be challengingfor generation of conforming
prismatic grids. We are currently implementing a hybrid gridding
workflowwhich combines truncating and conforming relationships in
the same grid. Such a hybrid grid will allowto simplify (and speed
up) grid generation without compromising the ability to handle
structuralcomplexity.
ConclusionsWe have presented an integrated geometry-centric
modeling workflow that ensures preservation ofgeologic concepts
through simulation by coupling unstructured grid generation with
Functional FormModels. FFM is a flexible representation of geologic
concepts that provides efficient parameterization ofstratigraphic
model and enables us to easily generate multiple geologically
meaningful scenarios.Automatic linkage of simulation grid geometry
and concept geometry enables smooth updates and rapidexploration of
multiple concepts and scenarios on field development strategies. We
have demonstrated
Figure 14Truncated grid of a model with listric (Y-) faults
(colored by layer Id).
SPE-173270-MS 9
-
application of the proposed modeling workflow on an example
reservoir setting, from input geologicconcept all the way to flow
simulation results.
We have discussed the differences with other known advanced
simulation grid generation techniques,as well as pros and cons of
our approach. The main advantage of our workflow is the enhanced
flexibilityin adapting grid geometry not only to geologic, but also
to engineering constraints. This comes at a costof tackling a more
computationally intensive problem in grid truncation. We have
outlined the directionsfor future research and improvement in the
proposed technology by aiming at hybrid combinations ofdifferent
gridding options available to us due to the flexibility mentioned
above.
ReferencesGringarten, E.J., Haouesse, M.A., Arpat, G.B., Nghiem,
L.X. 2009. Advantages of Using Vertical
Stair Step Faults in Reservoir Grids for Flow Simulation. Paper
SPE 119188 presented at the SPEReservoir Simulation Symposium, 2-4
February 2009, The Woodlands, TX, USA.
Mallison, B.T., Sword, C., Viard, T., Milliken, W.J., Cheng, A.
2013. Unstructured Cut-Cell Grids forModeling Complex Reservoirs.
Paper SPE 163642 presented at the SPE Reservoir
SimulationSymposium, 18-20 February 2013, The Woodlands, TX,
USA.
Jackson, M.D., Gomes, J.L.M.A., Mostaghimi, P., Percival, J.R.,
Tollit, B.S., Pavlidis, D., Pain, C.C.,El-Sheikh, A.H., Muggeridge,
A.H., Blunt, M.J. 2013. Reservoir Modeling for Flow SimulationUsing
Surfaces, Adaptive Unstructured Meshes and
Control-Volume-Finite-Element Methods.Paper SPE 163633 presented at
the SPE Reservoir Simulation Symposium, 18-20 February 2013,The
Woodlands, TX, USA.
Kartasheva, E., Adzhiev, V., Comninos, P., Fryazinov, O., Pasko,
A. 2008. An Implicit ComplexesFramework for Heterogeneous Objects
Modelling. Heterogeneous Objects Modeling and Appli-cations,
Lecture Notes in Computer Science, vol. 4889, pp. 141,
Springer-Verlag, 2008.
Gai, X., Wu, X., Branets, L., Sementelli, K.M., Robertson, G.D.
2012. Concept-Based GeologicModeling Using Function Form
Representation. Paper SPE 161795 presented at Abu
DhabiInternational Petroleum Conference and Exhibition, 11-14
November 2012, Abu Dhabi, UAE.
Fung, L.S., Ding, X., Dogru, A.H. 2013. An Unstructured Gridding
Method for Densely-SpacedComplex Wells in Full-Field Reservoir
Simulation. Paper SPE 163648 presented at the SPEReservoir
Simulation Symposium, 18-20 February 2013, The Woodlands, TX,
USA.
10 SPE-173270-MS
Capturing Geologic Complexity in a Simulation
GridIntroductionGeometry focused modeling workflow: from concept to
simulationMapping to continuous spaceFunctional Form modelingGrid
generation and layer reconstruction
Application examplesFull workflow applicationChallenges and
alternatives in the proposed workflow
Conclusions
References
