Tahmasebi and Jef Caers Updating joint uncertainty in trend and depositional models for exploration and early appraisal stage Only 1 well no production yet Low quality 3D seismic How to model properly uncertainty in ID: 777181
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Slide1
Céline Scheidt, Pejman Tahmasebi and Jef Caers
Updating joint uncertainty in trend and depositional models for exploration and early appraisal stage
Slide2Only 1 well, no production yetLow quality 3D seismicHow to model properly uncertainty in trend and proportions? Considerable uncertainty in:Geological continuity, architecture,
geobody
dimensions
Trends, target proportions
Real,
turbidite reservoir in appraisal stage
MPS: focus on the depositional scenario little attention on the trend or proportions
w
1
Courtesy of ENI
Slide3w1Courtesy of ENILocation of next well to be drilled
The company is planning to drill a new well
How can information from a new well be used to
jointly
update uncertainties?
New well:
may provide information on the uncertain parameters
Slide4Uncertainty in depositional scenario: levee and channel complexTI1
TI2
TI3
Use of 3 different Training Images (TIs)
Training case 1
:
base case
Training case 2
:
Only one channel and lower sand percentages.
Training case 3
:
In some zones levees are missing
Back Shale
Thin-bed
Bedded sand
Massive sand
Slide53D seismic data: Inverted into facies probability maps
Background
shales
Thin beds
Bedded sand
Massive sand
Low quality geophysical data: uncertainty in trend
Width of the belt
?
Fixed probability maps : unrealistic model of uncertainty
?
w
1
w
2
Slide6Uncertainty in trend: use of auxiliary variables
w = 7km
w = 3.5km
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
AXD
Narrow belt
AXD
Wide belt
Sub-grid used for the modeling
w
1
w
2
Slide7What about proportions?Proportion is defined by:Well data: only 1 wellSeismic data: low qualityTraining Image: expresses patterns, proportion is only implicitly definedIncomplete information: Uncertainty on the proportions
Proportion becomes an output: p = p(w, TI, well)
Auxiliary variable with varying width w accounts for uncertainty in proportion
Proposed workflow additionally updates the uncertainty on the
proportions
Slide8Prior distribution of uncertain parametersPrior Uncertainties: uniformly distributedTI: training images: tik = {1,2,3}TR: trend (width of auxiliary variable) w = U([3.5,7])km
Slide9Construction of a set of prior modelsw = 3.5w = 7300 prior models for uncertainty modelingWidthShale proportion
TI3
CCSIM
Tahmasebi
et al. 2014
TI1
TI2
Slide10Updating the prior uncertainties with new well dataPrior Uncertainties:
uniformly distributed
TI: training images:
ti
k = {1,2,3}
TR: trend (width of auxiliary variable) w = U([3.5,7])km
Probability of
Trend
given
d
obs
and TI
Probability of
TI
given
d
obs
Updated Uncertainties:
distributed according to
d
obs
1
2
Slide11Updating the prior uncertainties with new well dataPrior Uncertainties: uniformly distributedTI: training images: tik = {1,2,3}TR: trend (width of auxiliary variable) w = U([3.5,7])km
Updated Uncertainties:
distributed according to
d
obs
Update Proportion
Slide12Distance-based scenario modeling to update probabilitiesPark H. et al. (2013) Density of points in metric space at the data location: f(data|TIk)
for TI
1
for TI
2
for TI
3
Water rate data
Production data
TI1 responses
TI2 responses
TI3 responses
1
Slide13Distance: difference of patterns at the well locationSyntheticwell valuesExtraction of well data at the well locationWell location
Multi-Point Histogram (MPH):
Analyze difference in patterns
Observed
well values
MDS
d
r
TI3
TI1
TI1
TI2
TI3
P(
TI
k
|d
obs
)
0.2
0
0.8
TI2
Training Image
d
r
1
d
r
2
1
Slide14Updating probability of TR given TI and dobs2
Probability of
Trend
given
d
obs
and TI
Updated Uncertainties:
distributed according to
1
2
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
TI1
TI2
TI3
P(
TI
k
|d
obs
)
0.2
00.8
Slide15dr1Distance is difference in proportionNarrow w mostly shale
Large w
mostly sand
Proportion at the well is a good indication of w
w = 3.5km
w = 7km
Definition of the distance
Multi-dimensional scaling
d
r
Well location
d
r
obs
Training Image
width
width
f
TI
(
w|d
obs
)
2
Training Image
Slide16Obtaining the final probability
1
TI1
TI2
TI3
P(
TI|d
)
0.2
00.8
2
w
f(
w,
ti
|d
obs
)
TI
TI
w
f
TI
(
w|d
obs
)
Slide17TI1TI2TI3P(TI|d)0.30.30.4
1.
2.
d
obs
TI
w
TI
w
f(
w,
ti
|d
obs
)
f
TI
(
w|d
obs
)
Updated joint probability
Actual well:
all in shale
Updating joint probability of TI and trend given actual well
Slide18dobsTIwf(w,ti|dobs)
Updated joint probability
Actual well:
all in shale
Updating joint probability of TI and trend given actual well
6.5km
w
1
w
2
Probability map from seismic
Slide19Updating joint probability of TI and proportions given actual wellTI1TI2TI3P(TI|d)0.30.30.4
1.
2.
TI
p
f
TI
(
p
|d
obs
)
Updated joint probability
TI
p
f(
p
,
ti
|d
obs
)
d
obs
Actual well:
all in shale
Slide20What are the updated probabilities telling us?Small w and p are most likely For TI1 and TI2:Larger values of w possibleLow proportions are most likely For TI3:
Narrower channel belt
Larger proportion possible
New well not very informative on the TIs
Proportions p
Belt width wTI
w
TIp
f(w,ti|dobs)
f(p,
ti
|d
obs
)
Slide21Rejection sampling yields similar distributions Rejection sampling (1000s models)Draw a TI and w from the priorGenerate a model m with TI and wExtract the well data If dry well, accept the modelRejection Sampling
TI
w
f(
w,
ti
|dobs)
Proposed
Approach (100s models)TIw
frequency
Slide22Conclusionsd
Uncertainty in trend: use auxiliary variable
Variation of the channel belt width
Proportion: output and not input
Useful for green fields with considerable uncertainty in depositional system, trend and proportion
AXD
Methodology to update probabilities on uncertain parameters given new well data
Fully automated
Validated using a resampling procedure
Slide23Resampling procedure for validation
Draw TI
Draw w
d =
sample
Repeat procedure many times
Similar distribution?
In theory:
Slide24Kernel density to estimate
d
r
obs
2
d
r