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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.

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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

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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.

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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.

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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.

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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.

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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

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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.

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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

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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.

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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.

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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.

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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.

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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

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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.

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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.

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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).

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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.

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