1. Céline Scheidt, Pejman Tahmasebi and Jef Caers
Updating joint uncertainty in trend and depositional models for exploration and early appraisal stage
Céline Scheidt, Pejman Tahmasebi and Jef Caers

2. Real, turbidite reservoir in appraisal stage
Courtesy of ENI
Only 1 well, no production yet
Low quality 3D seismic w1
Considerable uncertainty in:
Geological continuity, architecture, geobody dimensions
Trends, target proportions
MPS: focus on the depositional scenario
 little attention on the trend or proportions
How to model properly uncertainty in trend and proportions?

3. Location of next well to be drilled
The company is planning to drill a new well
Courtesy of ENI w1
Location of next well to be drilled
New well: may provide information on the uncertain parameters
How can information from a new well be used to jointly update uncertainties?

4. Uncertainty in depositional scenario: levee and channel complex
Use of 3 different Training Images (TIs)
Back Shale
Thin-bed
Bedded sand
Massive sand
TI2
TI3
Training case 1:
base case
Training case 2:
Only one channel and lower sand percentages.
Training case 3:
In some zones levees are missing

5. Fixed probability maps : unrealistic model of uncertainty
Low quality geophysical data: uncertainty in trend
3D seismic data: Inverted into facies probability maps
Background
shales
Thin beds
Bedded sand
Massive sand w2 ? w1
Fixed probability maps : unrealistic model of uncertainty
Width of the belt?

6. Sub-grid used for the modeling
Uncertainty in trend: use of auxiliary variables
Channel belt: use simple auxiliary variable
Easily parameterized: w defines the width of the belt
Uncertainty in the belt width accounted by varying the width of the auxiliary variable
Sub-grid used for the modeling w2
w = 3.5km
w = 7km w1
AXD
Narrow belt
AXD
Wide belt

7. Incomplete information: Uncertainty on the proportions
What about proportions?
Proportion is defined by:
Well data: only 1 well
Seismic data: low quality
Training Image: expresses patterns, proportion is only implicitly defined
Incomplete information: Uncertainty on the proportions
Auxiliary variable with varying width w accounts for uncertainty in proportion
Proportion becomes an output: p = p(w, TI, well)
Proposed workflow additionally updates the uncertainty on the proportions

8. Prior distribution of uncertain parameters
Prior Uncertainties: uniformly distributed
TI: training images: tik = {1,2,3}
TR: trend (width of auxiliary variable)
w = U([3.5,7])km

9. Construction of a set of prior models
CCSIM
Tahmasebi et al. 2014
w = 3.5
w = 7
TI1
TI2
300 prior models for uncertainty modeling
Shale proportion
Width
TI3

10. Probability of TI given dobs
Updating the prior uncertainties with new well data
Prior Uncertainties: uniformly distributed
TI: training images: tik = {1,2,3}
TR: trend (width of auxiliary variable)
w = U([3.5,7])km
dobs
Updated Uncertainties: distributed according to 2 1
Probability of Trend
given dobs and TI
Probability of TI given dobs

11. Updating the prior uncertainties with new well data
Prior Uncertainties: uniformly distributed
TI: training images: tik = {1,2,3}
TR: trend (width of auxiliary variable)
w = U([3.5,7])km
dobs
Updated Uncertainties: distributed according to
Update Proportion

12. Distance-based scenario modeling to update probabilities1
Park H. et al. (2013)
Density of points in metric space at the data location: f(data|TIk)
for TI1
for TI2
for TI3
Water rate data
Production data
TI1 responses
TI2 responses
TI3 responses

13. Distance: difference of patterns at the well location1
Distance: difference of patterns at the well location
Extraction of well data at the well location
Synthetic
well values
Observed
well values
Well location
TI3
TI1
MDS  dr
Multi-Point Histogram (MPH):
Analyze difference in patterns
TI2
dr2
Training Image
dr1
TI1
TI2
TI3
P(TIk|dobs)
0.2
0.8

14. Updating probability of TR given TI and dobs2
Updating probability of TR given TI and dobs
Updated Uncertainties: distributed according to 2 1
Probability of Trend
given dobs and TI
TI1
TI2
TI3
P(TIk|dobs)
0.2
0.8
Challenges:
TR is a continuous variable  density instead of probability
Joint uncertainty in TR and TI  additional dimension to the problem
Distance for distinguishing trends  difference in facies proportion at the well

15. Distance is difference in proportion2
Distance is difference in proportion
Definition of the distance
w = 3.5km
w = 7km
Narrow w  mostly shale
Large w  mostly sand
 Proportion at the well is a good indication of w
Well location
Multi-dimensional scaling  dr
fTI(w|dobs)
width
Training Image
Training Image
drobs
dr1
width

16. Obtaining the final probability2 1
TI1
TI2
TI3
P(TI|d)
0.2
0.8
fTI(w|dobs) TI w
f(w,ti|dobs) TI w

17. Updating joint probability of TI and trend given actual well
Updated joint probability 1.
Actual well:
all in shale
TI1
TI2
TI3
P(TI|d)
0.3
0.4 2.
dobs
f(w,ti|dobs) w TI
fTI(w|dobs) TI w

18. Updating joint probability of TI and trend given actual well
Updated joint probability
Probability map from seismic
6.5km w1 w2
Actual well:
all in shale
dobs
f(w,ti|dobs) w TI

19. Updating joint probability of TI and proportions given actual well
Updated joint probability 1.
Actual well:
all in shale
TI1
TI2
TI3
P(TI|d)
0.3
0.4 2.
dobs
f(p,ti|dobs) TI
fTI(p|dobs) p TI p

20. What are the updated probabilities telling us?
Belt width w
Small w and p are most likely
For TI1 and TI2:
Larger values of w possible
Low proportions are most likely
For TI3:
Narrower channel belt
Larger proportion possible
New well not very informative on the TIs
f(w,ti|dobs) TI w
Proportions p
f(p,ti|dobs) TI p

21. Rejection sampling yields similar distributions
Rejection sampling (1000s models)
Proposed Approach (100s models)
frequency
f(w,ti|dobs) w TI w TI
Rejection Sampling
Draw a TI and w from the prior
Generate a model m with TI and w
Extract the well data
If dry well, accept the model

22. Conclusions Uncertainty in trend: use auxiliary variable
AXD
Uncertainty in trend: use auxiliary variable
Variation of the channel belt width
Proportion: output and not input
Methodology to update probabilities on uncertain parameters given new well data
Fully automated
Validated using a resampling procedure d
Useful for green fields with considerable uncertainty in depositional system, trend and proportion