probabilistic seismic inversion using pseudo-wells · 2019-08-25 · patrick connolly*, pca ltd...
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![Page 1: Probabilistic seismic inversion using pseudo-wells · 2019-08-25 · Patrick Connolly*, PCA Ltd geophysics for integration. Patrick Connolly Associates Ltd. Probabilistic seismic](https://reader030.vdocuments.us/reader030/viewer/2022040905/5e79e852521db97be41ea6b7/html5/thumbnails/1.jpg)
Patrick Connolly*, PCA Ltd
geophysics for integration
Patrick Connolly Associates Ltd.
Probabilistic seismic inversion using pseudo-wells
Seismic Rock Physics Seminar
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Outline
ODiSI: probabilistic inversion algorithm for the estimation of lithofacies and reservoir properties
• Context
• Algorithm
• Uncertainty
• Examples
ODiSI: • developed by BP• re-engineered by Cegal
Stochastic inversion by matching to large numbers of pseudo-wells, 2016,Patrick Connolly and Matthew Hughes, Geophysics
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Reservoir Geological Model
Elastic Properties Ideal Seismic Real Seismic
Geology & petrophysics
Rock Physics Modelling & Inversion
Acquisition & processing
inversion to elastic props.
inversion to reservoir properties
rock physics models
geological models
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Rocks Geological Model
Elastic Properties Ideal Seismic Real Seismic
prior likelihood
posteriorintegration
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X =Prior Likelihood Posterior
1) Analytic
2) Monte Carlo rejection sampling
3) Markov chain Monte Carlo
Solving Bayes
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Samples
Vertical stratigraphic profiles
pseudo-wells
lithofacies shale volume
porosity shear modulus
dry-frame modulus
Vp Vs bulk density
50m
seismic
rock physics models
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One Dimensional Stochastic Inversion (ODiSI)
Thousands of pseudo-wells for each trace
match & accept/reject
cssh-sshss
net-to-gross
Best-match synthetics
Corresponding lith columns
Probabilities
Input seismicLithofacies probabilities
Mean net sand fraction
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Bed thickness statistics
Bed thicknesses
Straight line on log-linear plot implies an
exponential distribution.
Very similar distributions for any clastic
depositional system
sand
shale
𝜆𝜆 = 0.15mean bed thickness = 6.6ms
𝜆𝜆 = 0.18mean bed thickness = 5.5ms
proportion of beds > x(complementary cumulative distribution function - CCDF)
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Lithofacies columnss sh-ss cs sh
clean sand 0 0.9 0.1 0
shaley-sand 0.5 0 0 0.5
cem. sand 0 0 0 1
shale 0 1 0 0
deterministic macro-layers
Overburden
Sheet sand
Intra-reservoir
Channel sand
Basal lag
Underburden
‘Continuous time Markov chain’
stochastic micro-layers
Transition probabilities Lith column
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Prior net-to-grossSheet sand: high net-to-
gross
Intra-reservoir: low net-to-gross
Channel sand: mostly high net-to-gross,
some cemented sands
Basal lag: high net-to-gross, a lot of
cemented sands
Prior expectation of net-to-gross for each macro-layer
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Lithofacies proportions
Lownet-to-
gross
parameterisation
Clean sand
Shaley sand
Shale
Cemented sand
Nor
mal
ised
pr
obab
ility
& c
ount
Nor
mal
ised
pr
obab
ility
& c
ount
Proportion (%) Proportion (%)
Coun
t
Net-to-gross distribution
Highnet-to-
gross
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Lithofacies modelling - sands
porosity
TWT
belo
w d
atum
(ms)
porosity
shea
r mod
ulus
shea
r mod
ulus
dry frame modulus
Porosity/depth trend
Porosity/moduli relationships
Fluid substitution
lithofacies shale volume
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Lithofacies modelling - shales
Vp
TWT
belo
w d
atum
(ms)
Vp/depth trend
Vp
bulk
den
sity
Vs
Vp
Vp / Vs and Vp / ρ correlations
Shaley sand mixing laws & other lithologies
lithofacies shale volume
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Pseudo-wells
50m
real wellpseudo-well
lithofacies shale volume
porosity shear modulus
dry-frame modulus
Vp Vs bulk density
50m
lithofacies shale volume
porosity shear modulus
dry-frame modulus
Vp Vs bulk density
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Matching
• The process is 1D.
• Thousands of pseudo-wells are created for each trace.
• EEI synthetics are generated with consistent wavelet and chi-angle.
• ~1% of pseudo-wells with lowest residual energy are selected.
thousands of pseudo-wells for
each trace
Best-match
synthetics
Corresponding lith columns
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Back to Bayes
Prior information
Data PosteriorSpecific prior
Mean VSh of all pseudo-wells
Mean VSh ofbest-match
pseudo-wellsaccept/reject
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Algorithm stability
200 500 1000 2000
5000
pseudo-wells per trace
• Stability; lateral continuity• Better results with more pseudo-wells
10000 20000 50000
BMPWs = PWs/100
Chi 15
Chi 90
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Most likely lithofacies
Mean net sand fraction
MatchingSimultaneous inversion
CI gradient (lithology)
CI chi 15 (fluid)
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CI gradient (lithology)
CI chi 15 (fluid)
MatchingSimultaneous inversion
synthetic residual
QC
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Validation
Blind well ties: offshore Angola
• Red: well data.
• Blue: ODiSI prediction
estimate overlay well datasmoothed well data
seism
ic n
et p
ay
well net pay
245
macro-layer
blind well tieblind wellscalibration
well
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Percentiles Usually the best-match pseudo-wells are averaged to obtain a mean and standard
deviation of the property to be estimated.But if we sort the BMPWs…
Decreasing match quality
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Percentiles
20 BMPWs centred around the P10 trace
P10
By selecting a number of traces around a selected percentile, different cases with
approximate percentiles can then be calculated.
Increasing net-to-gross
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Percentiles By selecting a number of traces around a selected percentile, different cases with
approximate percentiles can then be calculated.
20 BMPWs centred around the P50 trace
P50
Increasing net-to-gross
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Percentiles By selecting a number of traces around a selected percentile, different cases with
approximate percentiles can then be calculated.
20 BMPWs centred around the P90 trace
P90
Increasing net-to-gross
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UncertaintyP5 P25 P50 P75 P95
Mean net sand
fraction
lithofacies(most likely)
Percentiles
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Uncertainty quantification
Shale: Vp - depth
Measured uncertainties:• Is the relationship linear or higher order?
• How many components; 1 shale or 2?
• Is the data noisy? Should we decrease the variance?
• Is the data representative of the entire reservoir? Should we increase the variance?
The measured variance will depend on the model we choose.
Vp
dept
h
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Quantitative Interpretation Geological model: facies proportions
Rock physics model:
• Bayesian methods require uncertainties to be quantified.
• Uncertainty values determine the results; mean & variance
• But, all uncertainties are subjective.
• Your inversion result is an interpretation.
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Nile Delta example
0
0.5
1.0
ODiSI prediction 0.40Actual 0.41
Layer 1 net-to-gross
ODiSI prediction 0.54Actual 0.54
Layer 2 net-to-gross
Layer 1net-to-gross
Layer 2net-to-gross
ntg
Stochastic Inversion by Trace Matching -Reservoir Property Prediction Case Studies, EAGE 2016,S.R. Grant (BP) & B.J. Dutton (Cegal Ltd)
Blue: ODiSI predictionRed: well data.
50ms
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North Sea example Full stack CI
Upper Jurassic Fulmar reservoir flanked by Triassic shales and
underlain by Triassic shales and Zechstein evaporites.
Most likely lithofacies
Central North Sea, Upper Jurassic Fulmar Inversion Case Study. Utilising Blueback ODiSI, 2016L. Casteleyn1, P. Ashton2, A. D’ Alessandria2, P. Connolly3 and J. Sayer1.
1. Cegal Limited, Aberdeen UK.2. Repsol-Sinopec Resources UK Limited, Aberdeen UK.3. Cegal Limited, Aberdeen and PCA Limited.
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North Sea example
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Performance
Full probabilistic 106 trace inversion~ 2,000 pseudo-wells per trace
= 2 x 109 pseudo-wells
• ~8 hours on a standard workstation
• 25 mins on the cloud
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Transparency
Best-match synthetics
Corresponding lith columns
Monte Carlo rejection sampling• conceptually simple• easy to understand• highly transparent
“Algorithms, when they are not transparent, can lead to a distortion of our perception.”
― Angela Merkel
Inversion QC
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ODiSI Summary
• Full probabilistic inversion to facies probabilities and reservoir properties.
• Efficient, stable, transparent algorithm with results validated on multiple fields.
• Posterior uncertainties are captured.
• Uncertainty quantification is inherently subjective; any inversion is an interpretation.