Research -- Papers
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The Random Choice Method: Structural Stability of a Conservation Equation in Reservoir Dynamics, SIAM J. Numer. Anal., Vol 24 no. 5 (1987)
Abstract
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Simulation of Two-Phase Flow on a Laboratory Scale: Diffusion Operator Splitting and Consistency, Comp. Meths. Appl. Mech. Engrg., 65 (1987)
Abstract
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Operator Splitting and Domain Decomposition Techniques for Reservoir Problems, Proc. Math. of Oil Recovery, Cambridge UK, Jul. 1987
Abstract
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The Gullfaks Field -- A Modelling Challenge, Proc. Fourth Int. Forum on Reservoir Simulation, Salzburg, Austria, Aug-Sep 1992
Abstract
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Building, Managing, and History Matching very large and Complex Grids -- with examples from the Gullfaks Field,
Proc. ECMOR IV, Røros, Norway, June 1994
Abstract
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Some Aspects of Modelling Rock Fabric and Impact on Fluid Flow in Sandstone Reservoirs -- Faults and Compaction, 2004 (*PG)
Abstract
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Effects to be Considered When Planning Late Stage Depressurisation,
Proc. 13th Eur. Symp. on Improved Oil Recovery, Budapest, Hungary, (w. Standnes, D.C. and Skauge, A.) Apr. 2005
Abstract
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Sandstone Compaction Modelling and Reservoir Simulation, Proc. 67th EAGE conf. & exhibition (ext. abstr), Madrid, June 2005 (**PG)
Abstract
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A Predictor for Accelerated Coupled Rock Mechanics and Reservoir Simulation, Proc. ECMOR X, Amsterdam, the Netherlands, Sep 2006 (**PG)
Abstract
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Sandstone compaction, grain packing and Critical State Theory, Petroleum Geoscience 13(1) (2007) (**PG)
Abstract
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Using relations between stress and fluid pressure for improved compaction modelling in flow simulation and increased efficiency in coupled
rock mechanics simulation, Petroleum Geoscience 14(4) (2008) (**PG)
Abstract
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Improved Compaction Modeling in Reservoir Simulation and Coupled Rock Mechanics / Flow simulation, With Examples From the Valhall Field,
SPE Reservoir Evaluation & Engineering 12(2) (2009)
Abstract
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Compaction, Permeability, and Fluid Flow in Brent-Type Reservoirs Under Depletion and Pressure Blowdown,
The Open Petroleum Eng. J. 3 (2010), 1-13 (http://www.bentham.org/open/topej)
Abstract
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Horizontal Simulation Grids as Alternative to Structure-based Grids for Thin Oil-zone Problems, Proc. ECMOR XII, Oxford, UK, 6.- 9. Sept. 2010
Abstract
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Horizontal Simulation Grids as Alternative to Structure-based Grids for Thin Oil-zone Problems: A comparison study on a Troll segment,
Comput. Geosci 16 (2012) 211-230
Abstract
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Coupled Flow-- and Rock Mechanics Simulation: Optimizing the Coupling term for Faster and Accurate Computation,
Int. J. of Num. Anal. and Modeling 9 (3) (2012), 628-643
Abstract
(*PG) This work has been submitted to The Geological Society of London and European Association of Geoscientists and Engineers for possible publication.
Copyright may be transferred without notice, after which this version may no longer be accessible
(**PG) This material has been published in Petroleum Geoscience. the only definitive repository of the content that has been certified and accepted after peer review. Copyright
and all rights therein are retained by The Geological Society of London and EAGE (Copyright © The Geological Society of London and EAGE)
The validity of representing the nonlinear part of a
conservation equation by a finite number of node points
is discussed. The difference between the solutions of
the original and approximate problems obtained by the
random choice method is analyzed in a probabilistic
manner, and is found to stay small with a probability
close to one for a finite time depending on the
discretization.
Key words: nonlinear PDE, Riemann problem, random
choice method, stability
![[x]](index_htm_files/close.png "Close")
The one-dimensional nonlinear saturation convection-
diffusion equation in reservoir dynamics is solved
numerically by an operator-splitting technique. This
splitting, the implicit boundary conditions, and a
saturation constraint give rise to an ill-conditioned
system of nonlinear discretized equations allowing for
multiple solutions which is analyzed. The consistency
of the problem regarding grid spacing versus diffusion
is discussed, and a simple criterion is given for when
diffusion should be omitted in the numerical model.
This space intentionally left blank.
(I’ll complete it when I re-find the abstract....)
The Gullfaks Field has by many been described as the world's most
complex offshore oil reservoir, being characterized by a dense fault pattern
and a large number of layered sands with strongly varying quality. Pressure
and flow communication between layers and between the 50+ mapped fault
blocks show no general trend and must be handled individually for each
barrier. Modelling the reservoir is further complicated by faults which have
a sloping angle of up to 70 degrees from vertical; hence a vertical fault
model must be abandoned in many cases. A multitude of problems have
been encountered during the production history, representing a continuous
challenge to the reservoir engineers, but nevertheless present production is
better than originally predicted, based on solutions that supply Statoil and
the Norwegian oil industry in general with invaluable experience and
knowledge within petroleum technology. Modelling aspects covered in this
talk include generation and maintenance of large irregular corner point
grids with sloping faults and coordinate lines and handling of grids with a
vast number of non-neighbour connections, and the problems these factors
impose on history matching. Identification of potential areas for efficiency
increasy within real world model building where better tools are called for
is emphasized, rather than the description of presently used techniques.
Some examples of case studies are presented in the last part of the talk.
The Gullfaks Field has by many been described as the world's
most complex offshore oil reservoir, being characterized by a
dense and irregular fault pattern and a large number of layered
sands with strongly varying quality. Pressure and flow
communication between layers and between the many fault
blocks show no general trend and must be handled individually
for each barrier. Modelling the reservoir is further complicated by
faults which have a sloping angle of up to 70 degrees from
vertical; hence a vertical fault model must be abandoned in many
cases. With such complex geometry the grid building process
becomes a science of its own, often requiring several man-months
of work, partly due to the shortcomings of commercially availble
software. Advantages and disadvantages of using sloping grids in
general will be discussed, with a critical evaluation of the
foundations for the construction methods in common use, and
how insufficiencies in these algorithms have been overcome.
This paper addresses aspects of fluid flow related to rock fabric, that
are difficult or impossible to model in a flow simulator by standard
methods, but which may have significant impact on fluid flow. For
some reservoirs, the described procedures will be a necessary
ingredient in a simulation model if production history is to be
validated and understood.
For flow across faults the standard model of defining sand-to-sand
contacts with fault transmissibilities can be replaced by a more general
procedure, based on recent studies of fault composition. The typical
rock compaction model, where pore volume modifications are based
on pore pressure, is generally not sufficiently sophisticated to predict
actual pore volume and permeability changes during production. A
systematic overview of different compaction causes and implications
is given, accompanied by appropriate modelling aspects. Some results
from reservoir rock parameter experiments are presented to support
the theory, as well as examples from field simulations
Key words: Reservoir coomunication, fault plane, sealing
characteristic, compaction, reservoir simulation
This paper addresses a special effect related to rock compaction which may
occur during depressurization (DP) in mature oil fields. Empirical data indicate
that reservoirs containing high-permeability channels in a background of more
low-permeability soil will experience selective compaction when the fluid
pressure is decreasing significantly (such reservoirs are common in the North
Sea). Thereby the permeability will be reduced relatively more for weak, high-
permeability material than stronger, low-permeability soil (also supported by
empirical data) resulting in what we denote permeability homogenization with
decreasing fluid pressure (the ratio k
channel
/k
background
will decrease). Permeability
homogenization has been demonstrated qualitatively by performing numerical
simulation of generic reservoirs of Brent type, containing layers with high-
permeability channels enclosed in a background of more low-permeability soils.
The results show that increased sweep efficiency of oil may occur in certain
layers as a result of the permeability homogenization effect). However,
improved oil recovery due to permeability homogenization on field scale was
difficult to demonstrate due to the simplicity of the model. Improved modeling
of the rock compaction process and better understanding of modeling fluid flow
in channel systems is required before the effect of permeability homogenization
can be quantified more realistically
Key words: Rock compaction; Depressurization; Permeability homogenization
Soil compaction has a great influence on reservoir pressure
development and hydrocarbon production by depletion. Still this factor
is often treated in a simplistic manner in reservoir simulation studies,
mainly due to lack of data in the early stages of production history.
Later in field history the compaction parameters can often be
satisfactorily estimated by material balance analysis, but for field
development feasibility studies this option is obviously not available.
In this paper a general model for behaviour of sand or sandstones under
compaction is presented. If necessary rock parameters are not
available, it is shown how reasonable estimates can be deducted from
petrophysics. Available methodology for compaction modelling in
reservoir simulators is shown to be at best only approximate, and can
be a source of grave errors. A systematic approach to improved
compaction modelling is presented.
The impact of the stress field on reservoir fluid flow and production can be significant for many
kinds of reservoirs, and hence coupled Rock Mechanics and Reservoir Simulation has been seeing a
growing popularity. A much used scheme is iterative coupling, where compaction is computed at
each stress step by iteratively updating cell pore volumes in the reservoir simulator by values
calculated from strain in the stress simulator. Although the procedure works satisfactory, it may be
slow, as often many iterations are needed. Further, the pore volume corrections will only be
performed at selected stress time steps, such that pressure and compaction in the flow simulator are
not continuous in time. Many reported schemes assume specific poro-elasto-plastic models, as e.g.
linear elastic, and also require modification of code. It is well known that compaction is a function
of strain, while reservoir simulators use fluid pressure, the only compaction energy available. On
this background few if any coupled procedures utilize the compaction vs. fluid relationship at all. In
this paper we show that the relationship can nevertheless be used as basis for constructing a
predictor for the actual stress / strain computations, which leads to significant speed-up. Many of the
features of the predictor can be determined from the first stress time step only, and for later stress
steps it can be improved with small effort. The scheme is valid irrespective of the poro-elasto-
plastic model, and is based on information exchange, so no simulator code modification is
necessary. The compaction state is primarily dependent on the materials, boundary conditions, and
the production process, with the geometry dependency as the governing. The predictor is
constructed by modifying compaction vs. fluid pressure to take account of geometry variation. A
good predictor will result in an improved pressure field as computed by the reservoir simulator,
hence providing the stress simulator with a better pseudo-initialiser, such that it converges quicker,
and in the pore volume iteration scheme fewer if any iterations are required. In total we have
experienced a reduction in total computer time of more than 90% in some cases, and as a bonus the
fluid pressure field is continuous in time.
Based on the physics of grain packing in a granular material, we
demonstrate that sands or sandstones are most correctly modelled by
Critical State Theory, and show how this model can be used to define a
consistent compaction relationship for use in rock mechanics or reservoir
simulation. The theoretical model is compared to experimental data for
volume and permeability variation during loading or unloading.
Key words: Compaction, Failure model, reservoir simulation, rock
mechanics, sandstone
The conventional compaction model used in reservoir simulators defines
compaction as a function of fluid pressure, whereas in reality it is a function
of effective stress. The inter-relationship between fluid pressure, effective
stress, and reservoir parameters (materials distribution, geometry, production
scheme) is investigated. By modifying the conventional concept of flow
simulator compaction a predictor is constructed for the rock mechanics
computations in a coupled flow – rock mechanics simulation. This predictor
reduces the time to converge the stress computations by reducing or
eliminating the number of pore volume iterations in the coupling scheme.
Overall computing time is thereby considerably reduced while maintaining
accuracy in the stress computations. Additionally, the compaction state in the
flow simulator will be more accurate than in a conventional iterative coupling
scheme.
Key words: Compaction, reservoir simulation, rock mechanics, coupled
simulation, effective stress
In traditional flow simulation compaction is modeled as a function of fluid pressure, whereas in reality it is
dependent on effective stress (e.g. mean effective and shear stress). Therefore, although compaction computed by a
flow simulator may be correct on a regional average basis, the true variation throughout the reservoir (both spatial
and temporal) cannot be accounted for by a traditional approach. A stress simulator (i.e., geomechanics model)
honoring material properties, rock mechanical boundary conditions, and material-to-materialinteraction is needed to
achieve this compaction. Especially for sands, chalk, and other weak materials which in general, have a
compactiondependentpermeability, the spatial variation of compaction may have significant impact on the flow
pattern. The industry standard approach for computing true compaction is by either doing a fully coupled
simulation, or by using partial coupling with pore-volume iterations, both typically being expensive in terms of
computer processor time. For this reason the simplified compaction calculations are often used in practice thus
disregarding actual physics in the reservoir simulation.
In this paper we describe a procedure whereby a modified (pseudo) material definition is constructed and used to
improve compaction calculations by the flow simulator. The construction is based on results from a simplified
coupled flow–stress simulation, typically consisting of three to six explicit stress steps. The resulting compaction
field is comparable to the true one and represents a significant improvement over the traditional approach. This
compaction state is the optimal input to the stress simulator in a coupled scheme, and hence assures that the rock
mechanics calculations can be performed with maximum efficiency. By using our suggested procedure the pore-
volume iterations in a coupled scheme are eliminated or significantly reduced, and the simulated reservoir state will
be accurate at all times–not only when stress simulations are performed. Our main goal is to reduce total computer
time in iterative-coupled simulations without loss of accuracy, especially focusing on two mechanistic models from
the Valhall field, which is a highly compacting chalk reservoir in the North Sea.
We also demonstrate benefits of using the procedure in a simplified form to increase accuracy in reservoir
simulation for reservoirs in which coupled simulation is traditionally not seen as needed because of either a
perceived lack of complexity or the computing costs. In this paper, we demonstrate that the developed construction
methodology is general in use. Further, the maximum permitted difference between flow-simulator calculated
compaction and true compaction (i.e., computed from strain using a geomechanics simulator) is user-controlled,
such that by proper definition of this parameter, the coupled simulation in most cases can be guaranteed to converge
at the first pore volume iteration.
Compaction-induced permeability reduction in a producing reservoir rock/soil
can be significant, but neverthelessis often neglected or overly simplified in
reservoir simulations. Provided examples show that the commonly used
compaction models in reservoir simulators are not capable of capturing the actual
spatial variation of the compaction, which generally is more complex than the
simplified models predict. The only way to compute a reliable compaction state is
by rock mechanics simulation. The computing time can be considerably reduced
by an accurate and efficient procedure, which has been used to do the compaction
modeling and study the effects of permeability reduction on fluid flow and
production.
Weak, moderate, and strong materials behave differently when loaded, such that
large contrasts in initial permeability can be reduced by increasing load
(depletion), resulting in more homogeneous flow. It is demonstrated how this can
be utilized to achieve better sweep efficiency, reduced water production and
increased oil recovery. The effects are especially pronounced when the pressure
reduction is considerable (“pressure blowdown”). The data used are from Brent-
type reservoirs, but the results also apply to a wider range of reservoirs
Key words: Compaction, permeability reduction, reservoir simulation, sandstone
reservoir, material homogenization
As a general rule, the layering in reservoir simulation grids is based on the
geology, e.g. structure tops. In this paper we investigate the alternative of using
horizontal layers, where the link to the geology model is by the representation of
the petrophysics alone. The obvious drawback is the failure to honor the structure
in the grid geometry. On the other hand a horizontal grid will honor the initial
fluid contacts perfectly, and horizontal wells can also be accurately represented.
Both these issues are vital in thin oil-zone problems, where horizontal grids may
hence be a viable alternative.
To investigate this question, a number of equivalent simulation models were
built for a segment of the Troll Field, both geology-based and horizontal, and
various combinations of these. In the paper it is demonstrated that the horizontal
grid is able to capture the essentials of fluid flow with the same degree of
accuracy as the geology-based grid, and near-well flow is considerably more
accurate. For grids of comparable resolution, more reliable results were obtained
by a horizontal grid than a geo-grid. A geo-grid with local grid refinement and a
horizontal grid produced almost identical results, but the ratio of computing times
was more than 20 in favor of the horizontal grid. In the one-phase regions of the
reservoir, relatively coarse cells can be used without significant loss of accuracy.
The layering in reservoir simulation grids is often based on the geology, e.g.,
structure tops. In this paper we investigate the alternative of using horizontal
layers, where the link to the geology model is by the representation of the
petrophysics alone. The obvious drawback is the failure to honor the structure
in the grid geometry. On the other hand, a horizontal grid will honor the initial
fluid contacts perfectly, and horizontal wells can also be accurately represented.
Both these issues are vital in thin oil-zone problems, where horizontal grids
may hence be a viable alternative. To investigate this question, a number of
equivalent simulation models were built for a segment of the Troll Field, both
geology-based and horizontal, and various combinations of these. In the paper,
it is demonstrated that the horizontal grid was able to capture the essentials of
fluid flow with the same degree of accuracy as the geology-based grid, and
near-well flow was considerably more accurate. For grids of comparable
resolution,
more reliable results were obtained by a horizontal grid than a geo-grid. A geo-
grid with local grid refinement and a horizontal grid produced almost identical
results, but the ratio of computing times was almost 20 in favor of the
horizontal grid. In the one-phase regions of the reservoir, relatively coarse cells
can be used without significant loss of accuracy.
Key words: Reservoir simulation, Thin oil-zone, Well modeling
Coupled flow and rock mechanics simulations are necessary to
achieve sufficient understanding and reliable production
forecasts in many reservoirs, especially those containing weak
or moderate strength rock. Unfortunately these runs are in
general significantly more demanding with respect to computing
times than stand-alone flow simulations. A scheme is presented
whereby the number of needed rock mechanics simulations in
such a setting can be reduced to a minimum. The scheme is
based on constructing optimal input for flow simulations from a
few rock mechanics runs. Results obtained with the scheme are
at least as accurate as traditional coupled runs, but computations
are considerably faster, often as much as two orders of
magnitude.
Key Words: Reservoir simulation, Coupled simulation, Rock
mechanics, Compaction
