1. Yongduk Shin and Tapan Mukerji May 8th, 2014
Uncertainty Quantification with Multiple Scenarios on the Deformation of Reservoir Structure and Evolution of Reservoir Properties
Recent SCRF research -> more focuses on uncertainty of reservoir structure.
My talk is also a part in that movement.
Yongduk Shin and Tapan Mukerji
May 8th, 2014

2. Motivation: Sources of geological deformation uncertainty
1. Deformation style
Uncertainty on how the structure has been deformed
2. Accommodation style
Uncertainty on how the rock has accommodated deformation
 Brittle accommodation vs. ductile accommodation
Deformation
Restoration
Depositional domain
Structural domain
Extension
Contraction
Having high porosity vs. having fractures
Huge uncertainty to define current structural shape. -> lewis
Even we figure out the current structural shape, uncertainty on how the structured has been deformed.
Let’s call it uncertainty on deformation style
Rock may accommodate the given deformation differently. It can break down, or it can changes its pore volume
Let’s call it uncertainty on accommodation style.
Different deformation style and accommodation styles will surely impacts on reservoir properties. and reservoir responses.
Dilatation from
interpretation #1
Dilatation from
Interpretation #2
Deformation style
Accommodation style
Reservoir properties
Reservoir responses

3. Motivation: why deformation and accommodation styles matter?
Early stage of field life: no knowledge of fractures  Huge delay on development decision
Linking fracture modeling with structural deformation
 Applied in matured field
 Different deformation analysis gives different fracture estimations
 Effects on matrix properties are not tested
Early stage with limited number of wells, especially vertical wells, no knowedege of fractures.
May delay decision on field development. So uncertainty on accommodation styles can be important.
There is many attempts on linking fractures and structural deformation. Limited but meaningful results. Deformation style matters.
No link btw. Deformation style with matrix properties. + previous works are conducted in matured field.
If deformation styles matters, let’s link it for both fracture properties and matrix properties.
It would be good if we can screen more appropriate scenario on deformation/accommodation style in early stage of field life cycle

4. Objectives
Develop workflow that accounts for: - deformation style - accommodation style - for both fractures and matrix properties Test the effects of different scenarios of deformation and accommodation on reservoir responses
From motivation,
Objectives of this work is
Develop workflow acconts for deformation stlye- how the reservoir has been deformed – and accommodation style – whether the rock was broken, or changed volume – on reservoir properties – for both fracture and matrix.
Then, using the workflow, test the effect of different scenarios on reservoir responses.

5. Geostatistical simulations Simulated Values*(S*)
Main idea: Link structural deformation and reservoir property evolution
Structural domain
Depositional domain
Observed Values(O)
Restored Values*(O*)
Backward Transformation
Reservoir property restoration to syn-depositional condition
Well paths
Geostatistical simulations
Deformed Values (S)
Simulated Values*(S*)
When we do the geostatistical simulation, it is done on Cartesian box, which represent depositonal domain. If we do a porosity modeling, porosity values along the wells will be copy and pasted into depositonal grid by mapping two different coordinates. It normally done internally in commercial S/W such as petrel, and gocad.
We only change spatial coordinate during the transformation btween two domains. No changes on the values themselves.
The main idea is let’s changes to values by considering the accommodation style and deformation styles.
Forward Transformation
Reservoir property deformation to current condition
* Shin and Mukerji, 2013 SCRF annual meeting
(Figure modified from Caers, 2005)

6. Scenarios of deformation and accommodation styles
Deformation style
Flexural deformation
Minimal deformation
Accommodation style
Brittle : having fractures
Ductile : having pore rearrangement
Flexural deformation
Minimal deformation
Brittle
Matrix & fractures
Ductile
Matrix
Brittle
Matrix & fractures
Ductile
Matrix
To test the idea, I made two alternative scenarios on each deformation style and accommodation style.
Flexural deformation – deformations are discontinued across faults. More localized strain distribution
Minimal deformation principal – deformation is distiributed as much evenly as possible
For the accommodation style
brittle: having fractures
Ductile: having pore volume changes
Different scenario need to be linked with different reservoir property.
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Need to have different reservoir property evolution for each scenario

7. Information form deformation/restoration analysis
Depositional Grid
Structural Grid
Deformation 𝒖 𝒓
Restoration
Get Displacement (Restoration) Vector Map from Deformation analysis
𝒙 [𝑝𝑎𝑠𝑡] ← 𝒙 [𝑐𝑢𝑟𝑟𝑒𝑛𝑡] +𝒓( 𝒙 [𝑐𝑢𝑟𝑟𝑒𝑛𝑡] )
𝒖 =-𝒓
Deformation attributes: principal strains and their directions
Once the deformation style is chosen, we have deformation vector, which is merely a difference between two coordiantes of each grid.
From that vector, we can extract out strain tensors. In many previous works, direction of principal strain is used to estimate fracture orientation, and strain or stress magnitudes for fracture intensity.
In this talk, we are going to use strain information for both matrix and matrix property
Direction and magnitudes of principal strain
𝒘 𝑖 ,
𝜀 𝑖
Use principal strain on reservoir property evolution
𝒅𝒊𝒍𝒂𝒕𝒂𝒕𝒊𝒐𝒏=𝒕𝒓𝒂𝒄𝒆(𝒔𝒕𝒓𝒂𝒊𝒏 𝒕𝒆𝒏𝒔𝒐𝒓)
Use strain tensors for both brittle (fractures) and ductile (pore volume change) accommodations

8. Modeling reservoir properties evolution by accommodation style
Simplify the geological history into
limited number of geological events and the order they occurred
- Timing of cementation vs. the timing of deformation
Syn-depositional
𝝓, k, elastic properties
Diagenesis
Deformation
Brittle
Accommodation
Ductile
Accommodation
cemented
properties
Deformed
properties
Deformation on stiff rock
fractures
Deformation on soft rock
 pore volume changes
Deformation
Diagenesis
Reservoir rock may react differently to the given deformation.
Here, I simplified the geological events is deformation, cementation, and the order of two.
For the case when cementing occurred 1st, we have stiff rock. And the applied deformation is accommodated by having fractures.
For the case cementing occurred later, deformation is applied on soft rock. This is modeled as pore volume changes.
Deformed
properties
Cemented
properties
Post-depositional
𝝓, k, elastic properties

9. Modeling reservoir properties evolution: ductile accommodation
Porosity
evolution
Permeability
evolution
Elastic property
evolution
strain tensors from structural deformation
𝝓 𝒔𝒚𝒏−𝒅𝒆𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏
∆𝝓 by deformation
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏
mineral composition
amount of cementation
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏
𝝓 𝒅𝒆𝒇𝒐𝒓𝒎𝒆𝒅
Rock physics
Model*
Rock physics
Model**
∆𝝓 by cementing
For the ductile accommodation case,
Porosity is the key parameter. Porosity is changes twice – by deformation and by cementation.
Strain from structural deformation is used on porosity changes of rock matrix.
Elastic properties of cemented rock is only used to calculate seismic properties
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒌
Elastic properties
For flow simulation
For seismic attributes
* Kozeny-Carman relation, Carman, 1961
** Constant cement model from Avseth et al., 2000

10. Modeling reservoir properties evolution: Brittle accommodation
Porosity
evolution
Permeability
evolution
Elastic property
evolution
𝝓 𝒄𝒆𝒎𝒆𝒏𝒕𝒆𝒅
𝝓 𝒔𝒚𝒏−𝒅𝒆𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏
mineral composition
amount of cementation
𝝓 𝒄𝒆𝒎𝒆𝒏𝒕𝒆𝒅
∆𝝓 by cementing
Rock physics
Model
Rock physics
Model
𝝓 𝒄𝒆𝒎𝒆𝒏𝒕𝒆𝒅
strain tensors from structural deformation 𝒌
Elastic properties
Brittle accommodation case,
Matrix porosity changes only once – by cementation.
Strain tensors from deformation is used for fracture modeling.
With elastic properties of cemented rock, we can calculated deformation induced stress, we know the principal strain orientations
Permeability and porosity of fractures are derived from DFN modeling and elastic stiffness tensors of fractured medium can be calculated by using rock physics model.
Now, we have all scenarios and the way to generate reservoir properties under each scenarios.
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏
fracturing
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒎𝒂𝒕𝒓𝒊𝒙
𝒌 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒎𝒂𝒕𝒓𝒊𝒙
Elastic stiffness tensors*
of fractured medium
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒇𝒓𝒂𝒄𝒕𝒖𝒓𝒆
𝒌 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒇𝒓𝒂𝒄𝒕𝒖𝒓𝒆
𝑪 𝑖𝑗𝑘𝑙
For flow simulation
For seismic attributes
* Hudson’s model, Hudson, 1980

11. Example case: a synthetic fractured reservoir
Production area
Flexural deformation
Minimal deformation
Structural model
Brittle
Matrix & fractures
Ductile
Matrix
Brittle
Matrix & fractures
Ductile
Matrix
wells
We choose scenario 1 as the true history. Given strucuture on upper left side will be created in depositional domain and all the forward transformation to the current time will be conducted.
Observations from 6 wells will be used on proposed workflows with each scenario.
No fractures observed from the wells
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Ref.: True history

12. Generating true reservoir properties: foreword transformation from past to current condition
Syn-depositional
Reservoir properties
Cemented
Reservoir properties
Flexural deformation
With brittle accommodation
Tensile stress from structural deformation
Porosity at syn-depositional condition
(unconditional SGSim)
Cemented porosity
0.15
0.35
1.5 GPa
Strain from structural deformation
On generating true reservoir under scenario 1,
1st, porosity field in depositonal grid was greated.
Then the porosity is reduced by amount of cementation.
Elastic properties of cemented rock is calculated by rock physics model.
Then, deformation is applied. Since we know the point by point elastic properties and strain distirbuiton, we can calculate deformation induced stress using Hooke’s law.
For similification, we assume the open mode fractures. + 10
30 GPa
-0.1
0.1
Bulk modulus of cemented rock
From rock physics model

13. Generating true reservoir properties: for flow response
Properties for flow responses
Intensity of fractures
Fracture intensity from principal stress
Production area
DFN realization
0.08/m +
Strain from structural deformation
Now, we have fracture orientation, which is direction vector of the most tensile strain,
And fracture intensity is scaled from stress concentration.
Area inside of the rectangle is assumed as the early development region. So, explicit DFN modeling is only conducted in that region.
We can extract permeability tensors of fracture and fracture porosity from DFN realization.
-0.1
0.1
Direction of fractures

14. Generating true reservoir properties: for seismic attributes
Elastic properties of un-fractured rock
Direction of fractures
Intensity of fractures
Strain from structural deformation
Bulk modulus of cemented rock
Fracture intensity from principal stress + +
-0.1
0.1 10
30 GPa
0.08/m
Elastic stiffness tensors
of fractured medium*
𝑪 𝑖𝑗𝑘𝑙
By using orientation, intensity, and unfractured matrix elastic properties, we created elastic stiffness tensors for whole field.
Now, we have all the required reservoir properties to create reservoir responses.
Seismic velocity of true reservoir
* Hudson’s model, Hudson, 1980
3.5
5.0 km/s

15. Applying proposed workflow for each scenarios
Structural domain
Depositional domain
Observed Values(O)
Restored Values*(O*)
Backward Transformation
Reservoir property restoration to syn-depositional condition
Well paths
Geostatistical simulations
Deformed Values (S)
Simulated Values*(S*)
Now, realizaitons using the proposed workflow will be populated.
Under each scenario, observed values will be back transfored – restored, and each realizations on deposional domain will be forward transfored – deformed into current structural domain.
Forward Transformation
Reservoir property deformation to current condition

16. Geostatistical simulations
wells
Restored porosity
Realization 1 of
fractured reservoirs from S1
Restoration
(Un-cementing)
Geostatistical simulations
Let’s see the 1st realization under scenario 1.
1st, porosity values on wells are restored by un-cementing. Since it share the same assumption with the reference reservoir, restored porosity along the wells are also identical with the true case.
Simulated porosity is deformed back into the current condition by cementation.
The fracture modeling parts for flow ans seismic is identical with true case except the individual values.
True condition
0.15
0.35
Deformation
(cementing)
𝜙 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛
𝜙 𝑠𝑦𝑛−𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛𝑎𝑙

17. Geostatistical simulations Strain from deformation
wells
Restored porosity
Realization 1 of
unfractured reservoirs from S2
Restoration
Un-cementing
Un-deforming
Geostatistical simulations
With scenario 2, which shares the true deformation style but the different accommodation style,
Porosity is restored twices by un-cementing and un-deforming. thus, restored porosity along the wells are nomore same with the true porosity in syn-depositional condition.
Strain from deformation
True condition
0.15
0.35
Deformation
Re-deforming
Cementing
𝜙 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛
𝜙 𝑠𝑦𝑛−𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛𝑎𝑙

18. Geostatistical simulations
Realization 1 of
Unfractured reservoirs from Conventional approach
wells
Geostatistical simulations
Conventionalworkflow, just uses what we observed.
True condition
0.15
0.35
𝜙 𝑐𝑢𝑟𝑟𝑒𝑛𝑡−𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛

19. Fracture intensity (1/m)
Oil saturation
@ 900 days
Ductile
Accommodation
Porosity
Kxx (mD)
Reference P1 I1 P2
Cv.-R1 I2
S2-R1
Producers
comparison of flow properties and saturation distribution of realizations from ductile accommodation.
Deformation style of s4 makes more high porosity and permeability btw injector and producer in the upper parts. So it shows higher sweep efficiency. Realizations in S4 may gives higher production for both oil and water. Remember S4.
Injectors
S4-R1
0.08
0.15
0.25
1000
0.15
0.85

20. Fracture intensity (1/m)
Oil saturation
@ 900 days
Brittle
Accommodation
Porosity
Kxx (mD)
Reference P1 I1 P2 I2
S1-R1
Producers
Let’s see the results from brittle accommodation.
Reference and realization from S1 has high perm conduit from bottom injector to producer at the center. In fractured reservoir, linking producer and injector like this may not be a good idea. For S3, similar thing happen for the upper parts, but less strong connectivity.
We may guess that realizations from S1 may gives earlier water breakthrough.
Injectors
S3-R1
0.08
0.15
0.25
1000
0.15
0.85

21. Reference S1-R1 S3-R1 Brittle Accommodation 0.08 0.15 0.25 3.5 5.0 0⁰
Fracture intensity (1/m)
P-wave
velocity (km/s)
Fracture dip
from deformation strain
Brittle
Accommodation
Porosity
Reference P1 I1 P2 I2
S1-R1
Producers
When we see the p-wave distribution,
Reference model, and realization from S1 show good agreements on fracture intensity with slow seismic velocity.
But in S3, eventhough it must have even denser fractures, velocity is remained relatively high. Maybe the low matrix porosity can be the reason but it may be very challenging to define fractured region from seismic data. If we see the fracture dip driven from the strain,
It start make sense. Fracture dip under scenario 1 is relatively shallow and it makes bigger velocity changes.
S3, which have vertical fractures, effects of fractures are just masked by their orientation.
By applying the propsed workflow, the reservoir properties and reservoir responses for both flow and seismic attributes are connected by sharing the same scenario on deformation and accommodation styles.
Injectors
S3-R1
0.08
0.15
0.25
3.5
5.0 0⁰
90⁰

22. Results: flow responses
Ref.
Ref. S3 S4 S3 Cv S2
Cumulative water production, STB
Cumulative oil production, STB S4 Cv S2
As you can see, the major differences of flow responses comes from accommodation style.
But if you see the S1 and S3, S1 shows smaller oil production while have higher water production. It is because S1 have a fractured conduits between injector and producer. These differences comes from deformation style.
If you see S4 results, it has higher production for both oil and water than other scenarios with ductile accommodation.
Realizations under S4 have slightly higher perm between the producer and injector into upper parts.
Time from production starts, in days
Time from production starts, in days
Accommodation style – fracturing vs. matrix rearrangement – leads the most differences
Deformation style impacts on flow responses for realizations with ductile accommodations (See S4)
Connectivity btw. Injector and producer works differently in different scenarios

23. Results in MDS: distance by flow responses
Distance by Cum. Oil production
Distance by watercut
Ductile S1 Cv Cv
Flexural
deformation
Brittle
Accommodation
Ref. S4 S3 S1 S2 S3 S2
Ref. S4
Here we see the same results by MDS plot.
Again, accommodation styles give the most distinctive differences.
Deformation style gives in between differences for scenarios under different accommodation style.
If we managed to figure out more appropriate scenario in early stage, we may have different development plans.
But in reality, knowing the true reservoir responses is not available in the early stage.
Accommodation style and deformation style impact on flow responses
Deformation style impacts on flow responses even on NO fractured cases
May give different development strategy

24. Results: Seismic Attributes
Distance by Acoustic Impedance
Distance by P-wave velocity S2 S1 S2 S1
Ref. Cv Cv S4
Ref. S3 S4 S3
Let’s see MDS plot by seismic responses. Seismic attributes from different scenarios shows good similarities within the same scenarios and dissimilarities between other scenarios.
Since seismic data is available in early stage of project life, we may screen scenario in early stage.
Screening multiple scenario in early stage by seismic attributes

25. Strains from deformation
Discussions
Proposed workflow may work well in some situations
When strain distribution is highly heterogeneous
Field B
Field A
May works well
May not necessary
Strains from deformation
The proposed workflow and idea worked nicely in the synthetic example. It is obvious since the problem is made exactly that I intended.
In real field case, it may works and may not. Let’s think about a certain case when it works.
When deformation is distributed out evenly through the area of interest, like the field A in the figure, the difference will be gone between the proposed workflow and the conventional approach.
Limitations of the example case
Porosity dependent
One accommodation style in a single realization

26. Distance by reservoir responses
Conclusions
Workflow accounting for deformation style and accommodation style
- Reservoir property evolution
- Link structural deformation with matrix properties
- Differences both flow and seismic responses
Multiple scenario may can be screened in early stage
- Different development decision by different scenario
Consistency among reservoir properties for
geostat./flow forecasting/seismic attribute
- May gives better understandings & decisions in time
Distance by reservoir responses S2
Developed a workflow that accounts for deformation style and accommodation style
- Different results
Receiving questions and comments S1 Cv
Ref. S4 S3

27. Back-up slices

28. Modeling reservoir properties evolution: ductile accommodation
Porosity
evolution
Permeability
evolution
Elastic property
evolution
Syn-depostional
Reservoir properties
𝝓 𝒔𝒚𝒏−𝒅𝒆𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏
strain tensors from structural deformation
Structural
deformation
Structural
restoration
∆𝝓 by deformation
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏
mineral composition
amount of cementation
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏
deformed
Reservoir properties
𝝓 𝒅𝒆𝒇𝒐𝒓𝒎𝒆𝒅
Rock physics
Model*
Rock physics
Model**
Cementation
Un-cementing
∆𝝓 by cementing
For the ductile accommodation case,
Porosity is the key parameter. Porosity is changes twice – by deformation and by cementation.
Strain from structural deformation is used on porosity changes of rock matrix.
Elastic properties of cemented rock is only used to calculate seismic properties
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏
Cemented
Reservoir properties 𝒌
Elastic properties
For flow simulation
For seismic attributes
* Kozeny-Carman relation, Carman, 1961
** Constant cement model from Avseth et al., 2000

29. Modeling reservoir properties evolution: ductile accommodation
Porosity
evolution
Permeability
evolution
Elastic property
evolution
strain tensors from structural deformation
𝝓 𝒔𝒚𝒏−𝒅𝒆𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏
∆𝝓 by deformation
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏
mineral composition
amount of cementation
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏
𝝓 𝒅𝒆𝒇𝒐𝒓𝒎𝒆𝒅
Rock physics
Model*
Rock physics
Model**
∆𝝓 by cementing
For the ductile accommodation case,
Porosity is the key parameter. Porosity is changes twice – by deformation and by cementation.
Strain from structural deformation is used on porosity changes of rock matrix.
Elastic properties of cemented rock is only used to calculate seismic properties
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒌
Elastic properties
For flow simulation
For seismic attributes
* Kozeny-Carman relation, Carman, 1961
** Constant cement model from Avseth et al., 2000

30. Modeling reservoir properties evolution: Brittle accommodation
Porosity
evolution
Permeability
evolution
Elastic property
evolution
𝝓 𝒄𝒆𝒎𝒆𝒏𝒕𝒆𝒅
𝝓 𝒔𝒚𝒏−𝒅𝒆𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏
mineral composition
amount of cementation
𝝓 𝒄𝒆𝒎𝒆𝒏𝒕𝒆𝒅
∆𝝓 by cementing
Rock physics
Model
Rock physics
Model
𝝓 𝒄𝒆𝒎𝒆𝒏𝒕𝒆𝒅
strain tensors from structural deformation 𝒌
Elastic properties
Brittle accommodation case,
Matrix porosity changes only once – by cementation.
Strain tensors from deformation is used for fracture modeling.
With elastic properties of cemented rock, we can calculated deformation induced stress, we know the principal strain orientations
Permeability and porosity of fractures are derived from DFN modeling and elastic stiffness tensors of fractured medium can be calculated by using rock physics model.
Now, we have all scenarios and the way to generate reservoir properties under each scenarios.
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏
fracturing
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒎𝒂𝒕𝒓𝒊𝒙
𝒌 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒎𝒂𝒕𝒓𝒊𝒙
Elastic stiffness tensors*
of fractured medium
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒇𝒓𝒂𝒄𝒕𝒖𝒓𝒆
𝒌 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒇𝒓𝒂𝒄𝒕𝒖𝒓𝒆
𝑪 𝑖𝑗𝑘𝑙
For flow simulation
For seismic attributes
* Hudson’s model, Hudson, 1980

31. Possibility on field applications
Link between porosity model and empirical rock physics model*
Field specific transfer relation can be made
More reliable link btw.
geostatistical models and seismic simulations
* Cuu Long basin, offshore Vietnam (Binh et al., 2008; Ngoc and Quan, 2010)

32. Modeling reservoir properties evolution: Brittle accommodation
Porosity
evolution
Permeability
evolution
Elastic property
evolution
Syn-depostional
Reservoir properties
𝝓 𝒄𝒆𝒎𝒆𝒏𝒕𝒆𝒅
𝝓 𝒔𝒚𝒏−𝒅𝒆𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏
mineral composition
amount of cementation
𝝓 𝒄𝒆𝒎𝒆𝒏𝒕𝒆𝒅
Cementation
Un-cementing
∆𝝓 by cementing
Rock physics
Model
Rock physics
Model
Cemented
Reservoir properties
𝝓 𝒄𝒆𝒎𝒆𝒏𝒕𝒆𝒅
Structural
deformation
strain tensors from structural deformation
Structural
restoration 𝒌
Elastic properties
Brittle accommodation case,
Matrix porosity changes only once – by cementation.
Strain tensors from deformation is used for fracture modeling.
With elastic properties of cemented rock, we can calculated deformation induced stress, we know the principal strain orientations
Permeability and porosity of fractures are derived from DFN modeling and elastic stiffness tensors of fractured medium can be calculated by using rock physics model.
Now, we have all scenarios and the way to generate reservoir properties under each scenarios.
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏
Deformed
Reservoir properties
fracturing
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒎𝒂𝒕𝒓𝒊𝒙
𝒌 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒎𝒂𝒕𝒓𝒊𝒙
Elastic stiffness tensors*
of fractured medium
𝝓 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒇𝒓𝒂𝒄𝒕𝒖𝒓𝒆
𝒌 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏 𝒇𝒓𝒂𝒄𝒕𝒖𝒓𝒆
𝑪 𝑖𝑗𝑘𝑙
For flow simulation
For seismic attributes
* Hudson’s model, Hudson, 1980

33. Possibility on field applications
Link between structural deformation and fracture density*
Field specific transfer relation can be made
Quality of structural analysis can be tested
* North West German basin (Lohr et al., 2008)