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April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 1
Reservoir Connectivity and Fluid Uncertainty Analysis using Fast Geostatistical Seismic Inversion
Reservoir Connectivity and Fluid Uncertainty Analysis using Fast Geostatistical Seismic Inversion
Ashley Francis and Graham Hicks*
Earthworks Environment & Resources Ltd
*BG Group plc
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 2
Relative, Deterministic and Stochastic Inversion
• Seismic zero phasing and amplitude spectrum shaping
• Wavelet removal by assuming blocky, layered earth
• Introduce low frequency model to give absolute impedance estimates
• Perturb low and high frequency outside wavelet bandwidth to investigate uncertainty– Inversion is unique within seismic bandwidth
– Constrained by wells and spatial model outside seismic bandwidth
Relative Impedance, Coloured InversionRelative Impedance, Coloured Inversion
Deterministic InversionDeterministic Inversion
Stochastic InversionStochastic Inversion
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 3
Limitations of Deterministic Inversion
• Deterministic inversion works well in thick layered systems– Reservoir interval has strong reflectivity
– Reservoir layering is relatively thick with well defined units close to the seismic resolution limit
– Blocky layering with little vertical variation in reservoir properties so layer average impedance is useful
• Deterministic inversion can work in thinner intervals where tuning occurs if– Well control is good
– Conformal layering with gradual lateral thickness changes
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Deterministic InversionStrong Reflectivity
9300 10600Absolute Impedance
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Deterministic InversionPorosity Mapping
0.20
0.05
0.25
0.05
Porosity - JurassicPorosity - Jurassic Porosity – Rotliegendes/DevonianPorosity – Rotliegendes/Devonian
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Seismic Property Constraints & Reservoir Models
• The use of deterministic seismic inversion as an input to reservoir modelling is becoming common
• Deterministic inversion is unsuitable for this purpose for several reasons– Seismic resolution is at a much coarser scale than the cell
size of reservoir models
– Deterministic seismic inversion contains a low frequency model derived generally from wells
– Reservoir volume may be under or over-estimated, especially for thin intervals
– Deterministic inversion connectivity is exaggerated due to the effective smoothing (resolution limitation)
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 7
Scale of MeasurementsCore Plug to Seismic
Zone C
Zone B
Zone A
20 m20 m
100 m100 m
2 m2 m
(x70)(x70)
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Reservoir Model Support
• Reservoir model Scale-up of well logs is generally vertical correction only– Incomplete correction resulting in too high variance
– Varying cell thickness or deviated geometry will give arbitrary change of support correction across model
• Additional correction for horizontal scale-up– Variogram based support correction by fine-scale
simulation
– Not generally supported by reservoir model packages
• Seismic vertical support ≈ 10 – 20 cells thick
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Reservoir Model Upscaling200 x 200 x 2 m Cell Size
1250 1260 1270 1280 1290 1300 1310 1320 13304000
5000
6000
7000
8000
9000
10000
11000
12000
13000
Log Values for Well10
TWT (ms)
Imp
ed
an
ce (
m/s
*g/c
c)
Original
Vertical Scale-up Only
Correct model Cell Support
1250 1260 1270 1280 1290 1300 1310 1320 13304000
5000
6000
7000
8000
9000
10000
11000
12000
13000
Log Values for Well10
TWT (ms)
Imp
ed
an
ce (
m/s
*g/c
c)
Original
Vertical Scale-up Only
Correct model Cell Support
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 10
Deterministic Inversion4ms Block size (λ/8) @ 60Hz
1250 1260 1270 1280 1290 1300 1310 1320 13304000
5000
6000
7000
8000
9000
10000
11000
12000
13000
Log Values for Well10
TWT (ms)
Imp
ed
an
ce (
m/s
*g/c
c)
Original
Seismic Support
1250 1260 1270 1280 1290 1300 1310 1320 13304000
5000
6000
7000
8000
9000
10000
11000
12000
13000
Log Values for Well10
TWT (ms)
Imp
ed
an
ce (
m/s
*g/c
c)
Original
Seismic Support
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 11
Deterministic Inversion
• The impedance information at low frequencies is simply an interpolation of the well data and so deterministic inversions should not be used to condition reservoir models
Wells
Frequency
Seismic
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Deterministic InversionConstraining Porosity
SGS PorositySGS Porosity
Collocated PorosityCollocated Porosity
Seismic ImpedanceSeismic Impedance
• Seismic property has similar values vertically over zone of reservoir model
• Collocated co-simulation follows low frequency trends of seismic impedance
• Low frequency trends are from wells not seismic
• If trends were valid, constraint should be to vertical average, not cell by cell
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 13
Reservoir Model Conditioning with Seismic Data
• Conditioning a reservoir model to a deterministic inversion is largely equivalent to conditioning to a map of the wells
• If model cell thickness ≈ seismic resolution (eg λ/4) then we can condition a reservoir model to– seismic attributes
– relative or coloured impedances
– deterministic inversion filtered to remove low frequencies
• This makes the assumption of first order stationarity of the mean ie no lateral trends
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 14
Reservoir Modelling with Stochastic Inversion
• Condition model to realisations of impedance generated through stochastic seismic inversion– Incorporates geophysical uncertainty in the reservoir model
– Sample rate closer to required cell thickness
• Stochastic inversion is– Spatially constrained, typically by a variogram
– Mean of 100+ realisations = deterministic inversion
– Each realisation honours the well data
– Forward convolution of each realisation matches seismic
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 15
Stochastic Inversion and Resolution
• Common misconception related to resolution– “It…allows substantially increased resolution, capturing
details well beyond seismic bandwidth”.
• Stochastic seismic inversion can be run at any required output sample rate
• This does not imply a higher resolution– resolution is controlled by the (limited) frequency content and
bandwidth of the seismic conditioning data
• Stochastic seismic inversion simulates the broad band impedance and so properly represents the uncertainty in the seismic inversion
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 16
When Should You Use Stochastic Inversion?
D > /2
D <= /4
Continuous Change
DeterministicInversion
DeterministicInversion
StochasticInversion
StochasticInversion
Continuous andConformal layers
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 17
Stochastic Inversion
• Principal of producing non-unique realisations of impedance rather than an average impedance
• Condition impedance realisations to seismic trace & wells– SGS plus accept/reject (Haas & Dubrule, 1994)
– Other MCMC methods (eg Moyen et al, 2007)
– Good reliable methods but relatively slow
• To be of any use in calculating probabilities and statistics we need to generate many realisations - at least 100+– Computational runtimes long so fast methods required
• MPSI UltraFast FFT direct method used here
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Performance BenchmarkUnderlying Technology
• Moyen & Doyen (2008) IP/IS stochastic inversion– 35 Million cells x 25 Realisations
– 70 Hours on dual CPU 64-bit machine
• MPSI 32-bit pre-stack batch technology– Approximately 2 hours for same problem & hardware
• MPSI recent service project (IP/IS pre-stack)– 240 Million cells x 100 Realisations
– 27 hours on quad CPU PC
– Moyen & Doyen estimated time = 40 days
• MPSI 3-term simultaneous pre-stack stochastic inversion now available (IP/IS/Rho)
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Deterministic Inversion
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Stochastic InversionRealisation 1
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Stochastic InversionRealisation 2
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Stochastic InversionRealisation 3
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Deterministic Inversion
Thick SandThick Sand
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Deterministic InversionThick Sand Geobody
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Stochastic InversionThick Sand Geobody 01
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Stochastic InversionThick Sand Geobody 47
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Stochastic InversionThick Sand Geobody 65
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Thick Sand Volume
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
100000 120000 140000 160000 180000 200000 220000 240000 260000 280000 300000
Volume
Cu
mu
lati
ve P
erce
nta
ge
Deterministic Sand VolumeDeterministic Sand Volume
For a thick sand the deterministicvolume estimate plots close to themean volume from the realisations
For a thick sand the deterministicvolume estimate plots close to themean volume from the realisations
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 29
Deterministic Inversion
Thin SandThin Sand
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Deterministic InversionThin Sand Geobody
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Stochastic InversionThin Sand Geobody 08
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Stochastic InversionThin Sand Geobody 25
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Stochastic InversionThin Sand Geobody 49
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Thin Sand Volume
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000
Volume
Cu
mu
lati
ve P
erce
nta
ge
Deterministic Sand VolumeDeterministic Sand Volume
For a thin sand the deterministicvolume estimate is biased (±)
For a thin sand the deterministicvolume estimate is biased (±)
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 35
Deterministic InversionWell08 Connected Net Pay
Well08
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Stochastic InversionMultiple Realisations
• Multiple realisations from stochastic seismic inversion can be used for– Volumetric uncertainty
– Connectivity Analysis
– Individual realisations reservoir model conditioning
– Net Pay estimation: P90 / P50 / P10
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Stochastic InversionThin Sand Connectivity 08
Well08
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Stochastic InversionThin Sand Connectivity 25
Well08
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Stochastic InversionThin Sand Connectivity 49
Well08
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Stochastic InversionWell08 P90 Connected Net Pay
Well08
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Stochastic InversionWell08 P50 Connected Net Pay
Well08
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Stochastic InversionWell08 P10 Connected Net Pay
Well08
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Probability and Connectivity
• Probability maps by themselves are not always useful as they do not indicate possible connectivity
• Geobody (connectivity) calculations followed by net pay or probability calculation much more useful– Spatial geometry of pay analysed
– Volumetric uncertainty accounted for
– Swept/contacted volume uncertainty
– Evaluation of risk in well planning
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 44
Oil Sand Probability MapMax Below Top Res
0.15
1.0
Pro
ba
bil
ity
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D3 Heel: Maximum Connected Probability
0.02
1.0
Pro
ba
bil
ity
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 46
D3 Heel: Connected Probability Section
W E
0.02
1.0
Pro
ba
bil
ity
Low Chance of ConnectivityLow Chance of Connectivity
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 47
Oil Sand Probability MapMax Below Top Res
0.15
1.0
Pro
ba
bil
ity
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 48
D3: Maximum Connected Probability
0.02
1.0
Pro
ba
bil
ity
Risk of Missed PayRisk of Missed Pay
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 49
Summary 1
• Significant scale changes are not properly accounted for in reservoir modelling software
• Deterministic inversion may be useful when:– Reservoir interval has strong reflectivity
– Lots of wells and good seismic horizon constraints
– Reservoir layering is relatively thick with well defined units close to the seismic resolution limit
– Minimal lateral or vertical trends
April 10, 2023 © Earthworks Environment & Resources Ltd. All rights reserved 50
Summary 2
• Deterministic seismic inversion data is not suitable for conditioning reservoir models– Low frequency model is an artefact of well gridding
– Scale change between seismic and model cells
– Not suitable for connectivity / volumetric computations
• Stochastic inversion benefits– What if Scenario analysis eg well track risks
– Geophysical uncertainty input to reservoir modelling
– Scale change better handled in reservoir models
– Connectivity and volumes more reliable
• Further discussion available at Booth 137
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