Date post: | 01-Mar-2018 |
Category: |
Documents |
Upload: | saifulislam9442 |
View: | 217 times |
Download: | 0 times |
of 19
7/26/2019 Bostrom 2009
1/19
SPE 124307
Development of a Geomechanical Reservoir Modelling Workflowand SimulationsB. Bostrm, StatoilHydro
Copyright 2009, Society of Petroleum Engineers
This paper was prepared for presentation at the 2009 SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 47 October 2009.
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not beenreviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, itsofficers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission toreproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract
A Geomechanical Earth Model (GMEM) is wanted for every field development and should be maintained for the life-time ofthe field. These models are needed in order to contribute to safe and optimum drilling and production in depleting and
complex reservoirs. This strategy is only possible if an automated workflow is developed.
Links between the stress simulator Abaqus and the geological software Irap RMS and between Abaqus and the reservoir
simulator ECLIPSE are established in order to have; (1) faster and better generation of geomechanical reservoir simulationmodels, (2) to better account for geomechanical effects in the reservoir simulation and 4D feasibility studies. Abaqus
scripting interface is used to link Irap RMS and Abaqus. The link consists of a set of Python scripts that rebuilds the reservoir
geometry in the CAD, meshing and visualization program Abaqus/CAE. This is believed to be a unique feature of thedeveloped workflow as opposed to earlier developments that reuse the reservoir grid. In addition, a link between Abaqus and
ECLIPSE is developed transferring reservoir pore pressure data, initial porosity and degree of water saturation between
ECLIPSE and Abaqus through the file system. Verification and demonstration of capabilities of the developed workflow isdone using a faulted North Sea oil and gas field.
Introduction
Both commercial and research simulators that take the fully coupled nature of three-phase-flow and deformation into account
exists today. Stone et al 2000 have extended ECLISPE-300
(trademark of Schlumberger) to include geomechanics in afinite difference context, while for instance Li and Zienkiewics 1992 have developed a similar approach using the finite
element method. It is then natural to ask if this will make the partly coupled approach described here superfluous. Our
experience is however that a partly coupled approach between a conventional reservoir simulator and a stress simulator is the
best approach for the near future when advanced geomechanical issues must be taken into account. This is also the industrytrend as for instance Schlumberger now is marketing the partly coupled approach between ECLIPSE and the finite element
stress simulator VISAGE
(trademark of Schlumberger). The partly coupled approach benefits from the latest developmentsin physics and numerical techniques of both simulators.
Computer programs from three vendors are involved in the geomechanical reservoir modelling workflow illustrated in Figure
1: (1) Irap RMS (trademark of Roxar Technologies) for geological modelling, (2) ECLIPSE
(trademark of
Schlumberger) for reservoir modelling and (3) Abaqus(trademark of Dassault Systmes) for geomechanical reservoirmodeling/stress analysis. A standard procedure is to build the faulted reservoir geometry with the geological tool Irap RMS.
After gridding and upscaling a simulation ready model is exported to the reservoir simulator ECLIPSE. A similar coupling
between the stress-simulator Abaqus and Irap RMS did not exist starting this project.
Parts and assemblies can be imported into Abaqus/CAE (Computer Aided Engineering) from a third-party CAD (ComputerAided Design) system. However Irap RMS does not support the CAD industry standards implying that the reservoir
geometry must be generated from scratch within Abaqus/CAE using the geometry creation tools: Solid features, cut features,
shell features, wire features, datum geometry and partition tools.
7/26/2019 Bostrom 2009
2/19
2 SPE 124307
It is also necessary to modify the Irap RMS geometry in order to address the important question of fault reactivation during
depletion. This question will be answered introducing the geometry of the fault fill material with its mechanical properties
into the Abaqus/CAE simulation model.
Figure 1 also indicates the two way data exchange between ECLIPSE and Abaqus. Here we focus on the transfer of pore
pressure data from the reservoir simulator to the stress simulator. In addition the specification, programming and verification
of the link between Irap RMS and Abaqus are main issues of this paper.
Figure 1: Geomechanical reservoir modelling workflow.
Modelling strategy
Two apparent choices exist regarding establishing a geomechanical reservoir simulation model for Abaqus: (1) Rebuild thegeometry within Abaqus/CAE or (2) Use the grid of the geological model or the reservoir model directly in Abaqus.
Earlier developments within this field typically generate the simulation model or input file to the stress simulator, i.e. re-use
the reservoir simulation grid. This is normally done by extending the reservoir simulation grid up in the surrounding shale as
shown in Figure 2. Commericial reservoir simulators that use this approach are ECLISPE 300 with geomechanics and
STARS with internal geomechanical model (trademark of CMG). Examples of this approach may also be found in Samierand Gennaro 2007; Kristiansen et al 2005; Marchina and Onaisi 2006. This last approach lack the flexibility needed to handledisplacement localization in the overburden that may occur when reservoir is produced by huge depletion.
The first approach is chosen here as we aim at: (1) High quality mesh with a limited total number of elements in the model,
(2) Adaptive re-meshing requires tetrahedron meshing (localization), (3) Extend fault fill material geometry out in the
surrounding shale and (4) Finer discretization level for the fault fill material utilizing cohesive elements.
ECLIPSE
Reservoir geometry
Simulation modelInp file
Irap
RMS
Irap
RMS
Abaqus
, kP,T,Sw
7/26/2019 Bostrom 2009
3/19
SPE 124307 3
Figure 2. ECLIPSE 300 grid for a North Sea oil and gas field (structured gridding).
Tool specificationsSpecifications of the tool that link Irap RMS and Abaqus will be given below.
Reservoir geometry from Irap RMS
The starting point for generating a faulted reservoir model in Irap RMS is the irregular fault surfaces that penetrate thereservoir. Interpreted horizons from the seismic are added in a consistent way. Thereafter the reservoir volumes are
discretized using a corner point grid as shown in Figure 3. This is a structured grid where the horizontal distance between the
grid block corners may vary.
A consequence of representing heavily faulted reservoirs with a structured grid is concave blocks along the fault surfaces.These blocks are easily identified in Figure 3 as all concave blocks are split into two wedge elements before visualization in
Abaqus/viewer. In addition the pinchout of layers will generate problems in the finite element representation of the faulted
reservoir grid.
Figure 3: Irap RMS corner point grid visualized in Abaqus/Viewer. Note that concave blocks along the faults are split into two wedgeelements.
Merge grid blocks
RMS2ABA must be able to merge grid blocks. There are two reasons for that: (1) pinch-out of layers in the geological model
and (2) necessary reduction of the number of reservoir grid blocks for the stress simulator.
Layers that pinch-out create problems. Block being neighbors to undefined blocks with zero thickness due to the pinch-out ofthe layer can not be represented by a hexahedral element. This is solved by merging of layers. The total number of reservoir
grid blocks is reduced effectively by merging layers, which may be necessary keeping in mind that the volume of the
surrounding shale is much larger than the reservoir volume.
7/26/2019 Bostrom 2009
4/19
4 SPE 124307
Some restrictions must be set to the merging process: (1) Layers that are merged should have the same pressure depletion
history and material properties and (2) Merging is restricted to vertical blocks only.
An example is shown in Figure 4. The three layers seen in the geological model to the top is reduced to two layers is the
Abaqus simulation model shown in the bottom figure. This merging process is handled in RMS2ABA by picking the
top/bottom reservoir horizons and user defined layer interfaces. Horizons and layer interfaces are numbered from 1 to NZ+1,
starting at top reservoir. NZ is the number of layers in the geological model.
layer 1
layer 2
layer 3 pinch-out
layer 1
layer2+3
layer 1
layer 2
layer 3 pinch-out
layer 1
layer2+3
Figure 4: Block merging shown in a cross sectional view. (a) Pinch-out of layer 2 in the geological model (top figure) and (b) Mergingof grid blocks in layers 2 and 3 (bottom figure).
Connect grid blocks
RMS2ABA must be able to smooth faults, i.e. connect FW/HW grid blocks. Three alternatives are sketched in Figure 5.These are: (1) Move HW nodes, (2) Move FW nodes, and (3) Move both FW/HW nodes. RMS2ABA use the last option.
FW
HW
FW
HW
Figure 5: Connection of two grid blocks shown in a cross sectional view. (a) Move HW nodes, (b) Move FW nodes, and (c) Move bothFW/HW nodes.
Open grid
RMS2ABA must be able to open up the grid along the fault surfaces and introduce the geometry of the fault fill material
when a detailed fault model is wanted in Abaqus/CAE. A parametric representation of the cell sides along the fault is useddeciding the blocks shrinkage normal to the fault surface as indicated in Figure 6. In addition blocks with only a corner
touching the fault surface must be handled according to the shrinkage of its neighboring blocks.
7/26/2019 Bostrom 2009
5/19
SPE 124307 5
fault fill material
bounded fault
fault tip
fault tip
fault fill material
bounded fault
fault tip
fault tip
Figure 6: Grid opening and placement of the fault fill material (map view). (a) Irap RMS grid that includes a bounded fault and (b)
Abaqus/CAE representation of the faulted reservoir geometry.
Unique material properties will be given for the fault fill material.
Geometry for surrounding shale
RMS2ABA must add over-, under- and side-burden geometries to the reservoir geometry. This is obtained by a simple CUToperation between the global box (solid) and the surface representation of the reservoir geometry (Boolean operation). The
global box includes the reservoir and the surrounding formations up to seabed, possibly down to base rock and some
reservoir width to each side in order to limit the effects of the imposed displacement boundary conditions on the global box.
This implies that modelled volumes outside the reservoir are far larger than the volume of reservoir represented in IrapRMS/ECLIPSE.
Overburden horizons may be included if interpreted, either from Irap RMS or other seismic software. These can be imported
into Abaqus/CAE as a surface (shell representation using Abaqus terminology).
Tool programming
RMS2ABA is programmed in Python(trademark for the Python Software Foundation).
Abaqus scripting language
An automated generation of a triangulated surface (shell geometry in Abaqus/CAE) representation of the Irap RMS reservoir
geometry is obtained utilizing the scripting interface in Abaqus. The flowchart for the script RMS2ABA is given in Figure 7.
7/26/2019 Bostrom 2009
6/19
6 SPE 124307
RMS/VIP
RMS/MULT
Faulted model
Generate reservoir shell geometry
Yes No
Merge layers
Close faultsOpen grid
Repair geometry
RMS2ABA
stop
RMS/VIP
RMS/MULT
Faulted model
Generate reservoir shell geometry
Yes No
Merge layers
Close faultsOpen grid
Repair geometry
RMS2ABA
stop
Figure 7: RMS2ABA flowchart.
RMS2ABA is started in Abaqus/CAE. After initialization, block geometry and fault definition are read from the Irap RMS
ASCII files VIP and MULT respectively. The merging of grid blocks, fault opening and closing are discussed above. Grid
repair is restricted to repairing gaps in the Irap RMS grid. Finally a reservoir surface (shell using Abaqus terminology)
representation of the reservoir geometry in within Abaqus/CAE is generated utilizing the geometry creation tools: Datumgeometry, wire feature and shell feature. Interpreted horizons in the overburden may be constructed in Abaqus/CAE using the
same geometry creation tools.
Interface against Irap RMS
Irap RMS can export 3D grids to several commercial available reservoir simulators. Amongst these are the reservoir
simulator VIP(trademark of Landmark). The file format for this simulator, named VIP CORP format, uses the corner pointdescription. Corner point coordinates (X,Y,Z) for each grid block (number given by its indices I, J and K) are grouped
together as shown in Table 1. Grid blocks are ordered with I index cycling fastest, followed by the J and K indices.
Undefined blocks are inactive grid blocks in the simulation model.
7/26/2019 Bostrom 2009
7/19
SPE 124307 7
Table 1. Irap RMS grid block coordinates.
CC GRID BLOCK: I = 2 , J = 7 , K = 1
C UNDEFINED BLOCKC
4842.64 -6240.09 4274.01 4929.84 -6327.09 4224.115004.11 -6253.06 4231.87 4918.62 -6168.40 4274.01
4842.64 -6240.09 4274.01 4929.84 -6327.09 4224.11
5004.11 -6253.06 4231.87 4918.62 -6168.40 4274.01C
C GRID BLOCK: I = 3 , J = 7 , K = 1C
4929.84 -6327.09 4224.11 4994.99 -6397.25 4219.055069.00 -6324.16 4226.38 5004.11 -6253.06 4231.87
4926.37 -6323.62 4237.74 4991.42 -6393.40 4233.48
5066.17 -6320.62 4240.66 5001.16 -6249.80 4245.45
1 2
5 6
7
4 3
I
J
K
The fault model generated in Irap RMS is based on a fault network, and consists of a set of gridded fault surfaces, withcorresponding fault lines along the intersections between the selected horizons and the fault surfaces. Table 2 gives the
syntax used in the MULT file that defines the fault location within the simulation grid. I1 and I2 are lower and upper I-
coordinate of cells along the fault. J1, J2, K1 and K2 are defined in a similar manner. The face of the block that is part of the
fault surface is either TX MINUS or TY MINUS (see sketch in Table 2). This implies that the fault surfaces description given
in the MULT file typically are made up of both block faces from the HW and FW side. An algorithm has been made thattransform this definition to either a FW or HW description of the fault surface before a shrinkage of the blocks can be
performed.
Table 2. Irap RMS fault description.
MULT TX ALL MINUS MULT
FNAME Acw_SE1
-- I1 I2 J1 J2 K1 K2
51 51 50 51 1 28 1.000
50 50 52 54 1 28 1.000
49 49 55 56 1 28 1.000
48 48 57 57 1 28 1.000
47 47 58 64 1 28 1.000
48 48 65 71 1 28 1.00049 49 72 73 1 28 1.000
MULT TY ALL MINUS MULT
FNAME Acw_SE1
50 50 52 52 1 28 1.000
49 49 55 55 1 28 1.000
48 48 57 57 1 28 1.000
47 47 58 58 1 28 1.000
47 47 65 65 1 28 1.000
48 48 72 72 1 28 1.000
49 49 74 74 1 28 1.000
C
C next fault
CMULT TX ALL MINUS MULT
FNAME Pw1_NE3
30 30 8 9 1 28 1.000
29 29 10 24 1 28 1.000
MULT TY ALL MINUS MULT
FNAME Pw1_NE3
29 29 10 10 1 28 1.000
I
J
K
Tx MINUS
TY MINUS
7/26/2019 Bostrom 2009
8/19
8 SPE 124307
Link between ECLIPSE and AbaqusA link between Abaqus and ECLIPSE is developed transferring reservoir pore pressure data and initial porosity between
ECLIPSE and Abaqus through the file system. This transfer of data requires special considerations as different meshes arerequired. Abaqus use non-structured meshing, while structured gridding is used in ECLIPSE. Non-structured meshing is
required to handle fault details, to handle the necessary coarsening of the mesh moving away from the reservoir and to be
able to catch possible depletion induced localization of deformations. The mapping technique chosen here is the weighted
least square approximation. This scheme which is written in FORTRAN gives improved mapping for discontinuous
functions.
The Weighted Least Squares Functional () for point (j) is defined as
( )[ ]21
ij
n
i
ij ffxw ==
(1)
Where nis the number of points on the original mesh used in the mapping operation, w(xi)are weighting functions for each
node of the original mesh and fiis the value of the function at each node of the original mesh. For each node (j) the function
is defined in terms a set of unknowns jrelated to a polynomial function; i.e.
( ) jj xpf = (2)
p(x)is a polynomial and iis an unknown coefficient vector. The Weighted Least Squares Functional may then be written as
( ) ( )[ ]21
ijj
n
i
ij fxpxw ==
(3)
Minimisation of this functional leads to
FA = (4)
Where in 3D with ( ) iiii dzcybxaxp +++=
( )=
=n
i
iiiiii
iiiiii
iiiiiii
iii
i
zyzxzz
zyyxyy
zxyxxxx
zyx
xwA1
2
2
1
(5)
( )
=
ii
ii
ii
i
i
fz
fy
fx
f
xwF (6)
An illustration of the mapping process is shown in Figure 8.
7/26/2019 Bostrom 2009
9/19
SPE 124307 9
Figure 8: Illustration of the search algorithm.
Geomechanical evaluation of KvitebjrnVerification and demonstration of capabilities of the developed workflow is done using the faulted North Sea HPHT gas-
condensate field Kvitebjrn as a pilot case. Background data abouth the field may be found in a companion paper (Hettema,
Bostrm and Pedersen 2009), which focuses on the calibration and verification of the full-field Kvitebjrn geomechanical
model.
Geometry
The first step was to regenerate the reservoir geometry within Abaqus/CAE, taking into account both active and inactive cells
in the geomodel. An example of this is shown in Figure 9.
Figure 9: Bottom view of the Kvitebjrn un-faulted reservoir geometry consisting of 41040 triangles.
Point on the new mesh
Original points (i) used in mapping
Original points (i) not used in mapping
Point on the new mesh
Original points (i) used in mapping
Original points (i) not used in mapping
7/26/2019 Bostrom 2009
10/19
10 SPE 124307
Here the top and bottom reservoir horizon is represented as triangulated surfaces (shell geometry). The rug is the Assembly
of 100 Parts, each consisting of 400 triangles. A total of 41040 triangles are needed to represent the contour of the reservoir
geometry. Traces of the fault network are still seen after connecting HW/FW blocks. A water-tight (closed volume)structure is obtained adding triangulated reservoir edge surfaces. This process is fully automated creating valid and precise
shell geometry that must be converted to a solid geometry before meshing.
The process of creating a CAD representation of the reservoir geometry could certainly be done in any commercial CAD
tool. Here we have choosen ABAQUS/CAE, a tool that is fully integrated with the FEM tool Abaqus. In this way haveavoided issues related to the import of CAD geometries from third party software: Geometry repair tool.
In Figure 10, a top view of the reservoir is shown displaying the depth coordinate. The top reservoir is at deph 3933 m
TVDSS, while the lower most part is at depth 4610 TVDSS. Note that Z coordinates are scaled with a factor of 5.
Figure 10: Top view of the reservoir displaying the depth coordinate m TVDSS. Note that Z coordinates are scaled with a factor of 5.
Reservoir geometry is next expanded to include the overburden up to seabed, the sideburden and underburden as shown in
Figure 11. The dimensions of this box like geometry will typically be: Width - 3 times the reservoir width, height - At least
twice the reservoir depth (maximum down to solid rock). This is done in order to avoid boundary effects on the calculated
values of interest like reservoir compaction, reservoir stress changes, movements along plane of weakness, overburden stresschanges, seabed subsidence etc. The current Kvitebjrn model includes volumes that are 3500 times as large as the reservoir
volume.
7/26/2019 Bostrom 2009
11/19
SPE 124307 11
Seabed
7km
40km
40km
Seabed
7km
40km
40km
Figure 11: Global box that includes the reservoir and the surrounding formations.
Material data
Kvitebjrn geomechanical reservoir mesh must be populated with material properties. This will not be a topic here as this iscovered in some extend in the companion paper (Hettema, Bostrm and Pedersen 2009). This paper emphasizes the
importance of including transversal anisotrophy for the reservoir surrounding shale. This model may be extended into the
elasto-plastic regime using the Cam clay model as a reference frame. See Crook, Yu and Wilson 2002 and Sreide, Bostrmand Horsrud 2009 for details.
Some general comments will however be given here. Geomechanical materials are characterized as pressure sensitivematerials so it is of importance to test the materials over the range of hydrostatic pressure of interest. Typical tests performed
are hydrostatic (or isotropic compression tests), oedometer (or uniaxial strain) tests, triaxial compression and extension tests;
drained CID tests for the sandstone and undrained CIU tests for the shale, uniaxial compression tests (special case of triaxial
compression tests), shear tests and Brazilian tests (should be standard).
Information generated by these standard tests is enough to calibrate the constitutive model chosen to represent the sandstone
and shale matrix in the present study. The list below summarizes the model parameters that should be identified
Elastic secant drained Youngs modulus, E
Poissons ratio, Bulk modulus of pore water, Kw
Shear strength
Tensile strength
Compression strength
Biot Cofficient (or bulk modulus of the solid particles)Porosity, n
Permeability
Undrained effective stress analysis
A technique to handle displacement undrained effective stress analyses in commercial software that do not support the Kw-
formulation according to Naylor 1974 is developed. This technique makes use of two overlapping elements: (1) the firstelement represents the matrix and (2) the second element represents the fluid. The overlapping elements have different
element numbers, however identical node numbers, thus deforming together.
The apparent compressibility of the pore water,Ka, is given as
wa
KK = (7)
HereKwis the bulk modulus of the pore water and is the porosity.
7/26/2019 Bostrom 2009
12/19
12 SPE 124307
Geostatic procedureAll geomechanical analyses where pressure depend material models are used (Mohr Coulomb plasticity etc.) need to begin
from a geostatic state, which is a steady-state equilibrium configuration of the undisturbed rock body under geostatic loading.It is important to establish these initial conditions correctly so that the problem begins from an equilibrium state.
Vertical equilibrium in the model is obtained introducing the submerged unit weight of the matrix corresponding to the v.The excess pore pressure is set to zero.
Mesh
Meshing will be done in Abaqus as a consequence of the chosen geometry based strategy. Non-structured gridding will be
applied in order to mesh these complex geometries consisting of reservoir horizons, calculated layer interfaces and fault
geometries as shown in Figures 12 and 13. A model with more than 400 thousand 10-noded modified tetrahedron elementshas been created. Corresponding number of variables are more than 3 million. The mesh resolution will be high in the
reservoir and in the reservoir surrounding formations, i.e. where large straining is expected.
Figure 12: Wavy cross sectional view through the model showing vertical displacements. Note that the reservoir elements are notdisplayed.
7/26/2019 Bostrom 2009
13/19
SPE 124307 13
Figure 13: Horizontal view at reservoir level showing horizontal mesh resolution. Note that the reservoir elements are not displayed.
Pore pressure loading
A link between ECLIPSE and Abaqus is established reading amongst other pressure data. The pore pressure depletionhistory is used as loading in the geomechanical model. Values displayed in Figure 14 for the year 2025 show that the pressure
depletion is relative constant within different zones.
Bottom viewBottom view
Figure 14: Bottom view of the pore pressure change 1 of January 2025. Finite elements representing inactive cells in the geomodelhave zero pressure change and are coloured red in the contour plot.
Results
Reservoir deformations
The companion paper focuses amongst other on seabed subsindence and reservoir compaction early in the production historyfor model calibration purposes. Here we present the estimated top reservoir subsidence in the year 2025 as shown in Figure
15. The found subsidence reflects to some degree the varation in the reservoir thickness. Peak value is less than 0.41 m.
7/26/2019 Bostrom 2009
14/19
14 SPE 124307
Top viewTop view
Figure 15: Reservoir compaction, top view.
Reservoi r str ess path
Knowledge of the stress path during depletion is essential in order to estimate the no drill date using conventional drillingequipments. A convenient scalar expression for the reservoir stress path is the depletion coefficient given by Equation 8. This
coefficient is defined as the ratio of the horizontal stress and pore pressure change.
(8)
An estimate of this scalar is obtained assuming uniaxial compaction (see Fjr et al 2008 for more details)
(9)
Where is the Biot coefficient,is the Poissons ratio and n is the porosity of the Kvitebjrn reservoir sandstone. Usingtriaxial test based data for the Kvitebjrn sandstone, this value is found to vary between 0.56 and 0.66.
This property may also be evaluated from the finite element results taking into account both non-uniaxial compaction,
arching effects and non-linear material behaviour. Figure 16 displays this property at the top of the reservoir. The finite
element results indicate a broader variation range for the depletion coefficient than found using the simple uniaxial strain
model. The depletion coefficient in the blue area is below, green area is equal, while in the yellow/red area exceed the valuesfound using an uniaxial assumption. This knowledge may be used to optimize the placement of the infill well at the reservoir
level. Finally, note that the stress path is not defined outside the depleted reservoir segments, i.e. white areas in the contour
plot.
p
h
=
==
===
=
%21,17.0,66.0
%12,22.0,56.0
1
21
n
n
7/26/2019 Bostrom 2009
15/19
SPE 124307 15
Top viewTop view
Figure 16: Stress path map showing different zones red, yellow and green with respect to infill drilling.
Dri lli ng window change
Wellbore stability calculation for the infill well can conveniently utilize the finite element results for the overburden. For thegiven well trajectory as shown in Figure 17, we have calculated the total stress changes along the path as shown in Figure 18.
The vertical stress is reduced in the overburden as a consequence of the overburden swelling that take place during depletion,
while the two horizontal stresses increase in value. These can be transformed to s.g units and added to the initial stress field
before doing a standard wellbore stability calculation.
Advanced finite element wellbore stability analyses may conveniently be done at critical depth as found from the stardardwellbore stability calculations above. These are local models that are initialized by the global full-field model.
Figure 17: Infill well trajectory.
7/26/2019 Bostrom 2009
16/19
16 SPE 124307
0
1000
2000
3000
4000
5000
6000
7000
8000
-3 -2 -1 0 1 2
Change in total stresses, MPa
mTVDSS S11
S22
S33
Figure 18: Overburden total stress changes along the well path. Compressive stresses are positive.
Submodelling
Regional models or submodels driven by the full-field geomechanical model will be used to obtain an accurate, detailed
solution in a local region from an initial, relative coarse, global mesh. Typically there will be two levels of models; (1)
Reservoir scale models and (2) wellbore scale model. Even reservoir scale models with fault details may be run as asubmodel to the global un-faulted full field model in order to keep the geomechanical models at a convenient size. A
submodel can be a global model for a more refined submodel.
Here we will show an application of a wellbore stability model using a node based submodelling technique, i.e the nodes at
the boundary of the wellbore stability model is driven from the global model. The mesh of the model that is shown in Figure
19 will have an orientation with respect to the global coordinate system according to the well path at the depth of interest.
The plot indicates that the displacement degree of freedoms at the periphery of the model is prescribed.
7/26/2019 Bostrom 2009
17/19
SPE 124307 17
Figure 19: Finite element mesh and boundary conditions of wellbore stability model.
The finite element wellbore stability model will be run in four steps: (1) Geostatic; (2) Reservoir depletion, (3) Drillout and
(4) Open hole. The model is initialized in the geostatic step. Initial effective Terzaghi stresses are read, while the excess pore
pressure is set to zero. All nodes at the periphery of the model are fixed. In the reservoir depletion step, the wellbore stabilitymodel is driven by the global reservoir geomechanical model. Using a node based submodelling technique, all displacement
nodes at the boundary of the wellbore stability model is driven by the global model. After this step we have the correct
state of stress at the time of the infill drilling. In the drillout step, the borehole is excavated by removing elements. A normal
pressure equal the mud pressure is applied at the borehole wall pW-p0(excess pore pressure calculations). Pore pressureequalization will take place in the open hole step. This implies that we will have different type of elements representing the
shale in the global and the submodel: Displacement elements are conveniently used in the full-field model to capture the
undrained (no pore fluid flow) shale response using a Kw-formulation, while poro-elastic elements are utilized in the
wellbore stability model in order to capture both the undrained shale response immediately after drillout and the pore
pressure equalization taking place with time.
Figure 20 show a result from running the model. The excess pore pressure contours immediately after drillout varies with the
local hoop direction as a consequence of the anisotropic stress situation. The cross section picked is in the middle of themodel in order to reduce the effect of the fixed top and bottom boundary.
Figure 20: Contour plot of the excess pore pressure build up immediately after drillout (undrained shale response).
7/26/2019 Bostrom 2009
18/19
18 SPE 124307
A tool box with submodel is under development. In addition to the wellbore stability model outlined above, we will have
casing integrity models and sand prediction models. Simple GUIs will be developed that ease the use of these submodels
that are created using the Abaqus scripting interface (i.e. programmed in Python).
Geomechanical model deliveries
To sum up, deliveries from the above simulation model are deformations and the evolution of stresses across the entire field:
Subsidence, overburden effects, compaction prognoses and fault behaviour Drilling (Stress path map, drilling window)
This has provided a basis for dividing the reservoir into different zones of red, yellow and green with respect to infill drilling.
The above results may be used further in related studies:
Well collapse
Sand prediction
Casing integrity
Geomechanical effects on reservoir flow properties (two-way coupling with ECLIPSE)
Geomechanical effects on 4D seismics
Conclusions
The established workflow has successfully been applied to model the coupled hydro-mechanical behaviour of the faulted
Kvitebjrn reservoir. A model with more than 400 thousand 10-noded modified tetrahedron elements has been created.
Corresponding number of variables are more than 3 million. A wellbore stability model has also been successfully applied
showing the versatility of the established workflow.
The most challenging part of the work has been to establish a valid geomechanical model based on the geomodel. A
geometry based strategy has been chosen. First the reservoir geometry is recreated within the CAD, meshing and
visualization program Abaqus/CAE. Second the geometry of over-, side- and under-burden is added. In other words all
developments are geometry based which is believed to be a unique feature of the developed workflow. Meshing will be donein Abaqus/CAE as a consequence of the chosen geometry based strategy. Non-structured meshing must be applied to mesh
these complex geometries consisting of reservoir horizons, calculated layer interfaces and fault geometries.
A technique to handle displacement undrained effective stress analyses in commercial software that do not support the Kw-
formulation according to Naylor 1974 is also developed. This technique makes use of two overlapping elements: (1) the first
element represents the matrix and (2) the second element represents the fluid. The overlapping elements have different
element numbers, however identical node numbers, thus deforming together.
The link between Abaqus and ECLIPSE requires special considerations as used in the geomechanical simulator differs from
the geogrid. Abaqus use non-structured meshing, while structured gridding is used in ECLIPSE. Non-structured meshing isrequired to handle fault details, to handle the necessary coarsening of the mesh moving away from the reservoir and to be
able to catch possible depletion induced localization of deformations. The mapping technique chosen here is the weighted
least square approximation.
AcknowledgmentsThe author would like to thank the Kvitebjrn Unit license owners; Enterprise Oil Norge, Petoro, Total Norge and
StatoilHydro, for permission to publish this paper. The author would also like to thank Eiliv Skomedal and Per Horsrud for
their valuable contribution to the discussions.
ReferencesBostrm, B. and Skomedal, E. 2007. A Geomechanical Reservoir Modelling Tool. Abaqus Users conference.
Crook, A.J.L., Yu, J.G., Wilson, S.M, 2002. SPE/ISRM 78238. Development of an Orthotropic 3D Elastoplastic Material Model for Shale.Rock Mechanics Conference, 20-23 October, Irving, Texas.
Fjr, E., Holt, R.M., Horsrud, P., Raaen, A.M, and Risnes, R., 2008.Petroleum Related Rock Mechanics 2nd
edition. Elsevier B.V.
Hettema, M. H. H., Bostrm, B. and Pedersen, E. S., 2009. SPE 124713. Depletion-induced Stress Changes in a HPHT Reservoir:
Calibration and Verification of a full-field Geomechanical Model. To be presented at the ATCE conference in New Orleans, Oct. 4-7.
7/26/2019 Bostrom 2009
19/19
SPE 124307 19
Kristiansen, T.G., Barkved, O.I., Buer, K. and Bakke, R., 2005. IPTC 10818. Production-Induced Deformation Outside the Reservoir andTheir Impact on 4D Seismic. IPTC, Doha, Qatar, 21-23 November.
Li., X., Zienkiewicz, O.C., 1992. Multiphase Flow in Deforming Porous Media and finite Element Solutions. Comp Struct;45(2):211-27.
Marchina, P. and Onaisi, A., 2006. SPE/IADC 92546. Reservoir-Geomechanics Coupled Simulations: A Powerful Tool for Well Design
and Operation in HP-HT Environment. SPE/IADC Drilling Conference, Amsterdam, The Netherlands, 23-25 February.
Naylor, D.J., 1974. Stresses in Nearly Incompressible Materials by Finite Elements with Application to the Calculation of Excess PorePressure, I.J.N.M.E., Vol. 8, pp. 443-460.
Samier, P.S. and De Gennaro, S., 2007. SPE 107077. A Practical Iterative Scheme for Coupling Geomechanics with Reservoir Simulation.SPE Europec/EAGE Annual Conference and exhibition, Oct. 11-14 June.
Stone. T., Bowen, G, Papanastasiou, P., Fuller, J., 2000. SPE European Petroleum Conference, 24-25 October, Paris, France.
Sreide, O. K., Bostrm, B. and Horsrud, P., 2009. Borehole Stability Simulations of an HPHT Field using Anisotropic Shale Modeling.The 43rd US Rock Mechanics Symposium and 4
thU.S.-Canada Rock Mechanics Symposium, held in Asheville, NC June 28
th July
1.