Reservoir Geostatistics
Let’s Use All The Information!
Beth Rees
July 27, 2020
Outline
Geostatistical Inversion– Why and How
– Components of Information
Examples
– Reservoir Properties in Depth (West Africa)
– Understanding Pressure Depletion (Nile Delta)
– Predicting Production (Western Siberia)
– Predicting Porosity (Alberta Canada)
Summary
2
Rodina O. et al., Detailed Geological Model of Carbonate
Reservoir Based on Geostatistical AVA Inversion – A
Case Study, EAGE Ann. Mtg., 2008
Timan Pechora Carbonate
Why Geostatistical Inversion? Seismic vs Geomodel Grids
Technical Objectives– Well Planning
o Reservoir delineation
o Facies connectivity
o Efficiency – few wells, maximum production
– Reservoir Modelling
o Connectivity of the reservoir
o Flow simulation
o History Matching
– Uncertainty Assessment for Risk Management
o Multi-realization analysis: Facies, Properties
o Ranking (P10, P50, P90)
Business Objectives – Maximizing value
o Optimizing development plan
o Predicting reservoir performance
o Maximize Return On Investment (ROI)
Reservoir Geostatistics Deliverables– Details beyond seismic resolution
o Relax the restrictions of Deterministic Inversion
– Tightly integrated data for reservoir modeling
o Joint use of data with different scales
o 3D models of both facies and reservoir properties
– Uncertainty assessment
o Generate and rank multiple plausible realizations
Geostatistical Inversion – An Integration of Techniques
Geostatistical reservoir modeling
– Interpolates between wells
o Accurate near wells
o Multiple realizations with plausible details
o Not elsewhere
Deterministic inversion
– Estimates elastic properties to match the seismic
o Accurate within seismic bandwidth
o Unrealistically smooth
o Only one possibility
Geostatistical inversion
– Combines geostatistical modeling & deterministic
inversion, simultaneously in a statistically rigorous way
o Multiple plausible realizations at high detail (eg 1ms x 25m)
o Geological interpretations of the seismic away from wells
4
Modern Bayesian Geostatistics – How It Works
5
Plausible Reservoir Models
Well Logs
DATA (New Information)
Seismic Data & WaveletBAYESIAN INFERENCE
MCMC SAMPLING
Geology
PRIOR INFORMATION (Hypotheses)
Fluid Contacts
Stratigraphic
Grid
Rock Physics Heterogeneity
Seismic S/N
Facies Proportions
Multivariate PDFs
Facies Priors
Transfer
to
Reservoir
Model
(CPG)
Facies
Porosity
Vp/Vs
Saturation
Facies
Porosity
Vp/Vs
Saturation
Facies
Porosity
Vp/Vs
Saturation
Time /
Depth
1a 1b
2
3
4
6
Components of Information
Engineering
Geostatistical Inversion Components: Facies Type
Geophysics
Vo
lum
e C
lay
Porosity
Vp
/Vs
P Impedance
Co
re P
erm
eab
ilit
y (
mD
)
Core Porosity %
Geology
Petrophysics
Meaningful Facies in Multiple Domains
7
Facies
• Facies type
• Prior Probabilities
• Associations
Reservoir properties per facies
• Stratigraphic depth trends
• Multivariate PDFs
• Heterogeneity
• Saturation functions
• Rock physics models
Per Geological Layer
Inverted Ip + Well Facies
Inverted FaciesInverted Ip + Well Facies
Why Joint Inversion of Properties and Facies?
P-imp
Joint inversion
of P-Impedance
and Facies
Inversion of
P-Impedance
onlyP-imp
Less continuity of large-
scale features
Body edges are not as
sharp
Less values from the
extremes of the distributionSeismic
8
Geostatistical Inversion Components: Prior Probabilities
9
Facies
• Facies type
• Prior Probabilities
• Associations
Reservoir properties per facies
• Stratigraphic depth trends
• Multivariate PDFs
• Heterogeneity
• Saturation functions
• Rock physics models
Per Geological Layer
3D Prior ProbabilitiesFacies
LogsVertical
Trends
Constant
Proportions
Geostatistical Inversion Components: Hierarchical Relations
10
Level 1
Channel & Overbank always
separated by Levee
Level 2
Overbank is Shale and Muck
Level 2
Levee consists of Tight and
Loose
Level 2
Channel can be Oil, Gas or
Water. Water does not contact
gas
Level 3
Oil in Channel is Light or
Heavy
Facies
• Facies type
• Prior Probabilities
• Facies Associations
Reservoir properties per facies
• Stratigraphic depth trends
• Multivariate PDFs
• Heterogeneity
• Saturation functions
• Rock physics models
Per Geological Layer
Geostatistical Inversion Components: Depth Trends
11
Facies
• Facies type
• Prior Probabilities
• Associations
Reservoir properties per facies
• Stratigraphic depth trends
• Multivariate PDFs
• Heterogeneity
• Saturation height functions
• Rock physics models
Per Geological Layer
Engineering properties and elastic
properties do not behave alike
Geostatistical Inversion Components: Distributions
Effective Porosity
Volu
me o
f cla
y
Shale
Channel sand
Cemented sand
12
Facies
• Facies type
• Prior Probabilities
• Associations
Reservoir properties per facies
• Stratigraphic depth trends
• Multivariate PDFs
• Heterogeneity
• Saturation functions
• Rock physics models
Per Geological Layer
Probability
Data from…• Logs
• Rock Physics models
• Monte Carlo simulations
• Analogues
Geostatistical Inversion Components: Heterogeneity
Shale
Channel sand
Cemented sand
100 m
13
Facies
• Facies type
• Prior Probabilities
• Associations
Reservoir properties per facies
• Stratigraphic depth trends
• Multivariate PDFs
• Heterogeneity
• Saturation functions
• Rock physics models
Per Geological Layer
3D VariogramsVariogram Features
• Per layer
• Per facies
• Per property
• Azimuth-Aligned
o aka anisotropic
Geostatistical Inversion Components: Saturation & Fluid Contacts
0.1
103.14
38.21
log
shale
K
eff
sand
Sw
Sw
14
Porosity
Oil Saturation
Facies
• Facies type
• Prior Probabilities
• Associations
Reservoir properties per facies
• Stratigraphic depth trends
• Multivariate PDFs
• Heterogeneity
• Saturation functions
• Rock physics models
Per Geological Layer
Facies based model of Sw as a
function of porosity and permeability.
OWC
Geostatistical Inversion Components: Rock Physics Models
15
Facies
• Facies type
• Prior Probabilities
• Associations
Reservoir properties per facies
• Stratigraphic depth trends
• Multivariate PDFs
• Heterogeneity
• Saturation height functions
• Rock physics models
Per Geological Layer
Geostatistical Inversion Components: Seismic
Seismic Data
• Offset or angle stacks
• Time or depth migrated
• 4D, PP-PS, WAZ
• Known trends in wavelets
and noise
15-25 degrees
25-35 degrees
5-15 degrees
16
Facies
• Facies type
• Prior Probabilities
• Associations
Reservoir properties per facies
• Stratigraphic depth trends
• Multivariate PDFs
• Heterogeneity
• Saturation functions
• Rock physics models
Per Geological Layer
Well log data
Geostatistical Inversion Components: Logs
Porosity Vclay P Vel. Vp/VsFacies
De
pth
Log Constraints• Hard
• Soft
• Blind
Seismic Data
• Offset or angle stacks
• Time or depth migrated
• 4D, PP-PS, WAZ
• Known trends in wavelets
and noise
17
Facies
• Facies type
• Prior Probabilities
• Associations
Reservoir properties per facies
• Stratigraphic depth trends
• Multivariate PDFs
• Heterogeneity
• Saturation functions
• Rock physics models
Per Geological Layer
Well log data
18
Examples – Reservoir Properties in Depth (West Africa)
– Understanding Pressure Depletion (Nile Delta)
– Updating the Geologic Model(Western Siberia)
– Determining Probability of Porosity (Alberta Canada)
Example 1 – Inverting for Reservoir Properties in Depth
Offshore West Africa
– Passive shelf
– Main play is a Miocene/Oligocene turbidite
channel system
Objective: Evaluate potential around a
proposed well location
Five wells
– Good rock physics model
Four partial stacks
Brownfield, M.E., and Charpentier, R.R., 2006, U.S.G.S. Bulletin 2207-B, p. 52
Jimenez, J., Marquez, D., Saussus, D. and Bornard, R. [2013]
Incorporating Rock Physics into Geostatistical Seismic Inversion -
A Case Study. 75th EAGE Conference & Exhibition, Extended
Abstracts, We 07 01.
Geostatistical Inversion Workflow
Key challenge: High degree of
variation in quality of reservoir sands
Solution: Incorporating multi-level
facies modeling
Workflow
1. Stratigraphic modeling in depth
2. Facies definition
3. Geological trend modeling
4. Geostatistical inversion
5. Analysis of realizations
20
Stratigraphic Model
Five lithofacies identified
– Shale
– Brine Sand
– Oil Sand
o Low Quality
o Medium Quality
o High Quality
Reasonable separation between
shale, brine sands and oil sands
– Oil sand quality levels were not
separable
Facies Definition
21
Brine Sands
Petrophysical
Brine SandsElastic
Facies Definition: Associations, Ordering & Prior Probabilities
22
Shale Sand
25
75
Constant Proportions
MedLow High
Mic
rola
ye
r
1D Proportion TrendOil
SandBrine
Sand
3D Proportion Trend
Probability of Oil Sand
Probability of Brine Sand
Rock Physics Model
Rock physics is the link between seismic elastic and engineering properties
Different facies (shale, sandstone) will be modeled with different parameters
23
r, Vp, Vs
Elastic Properties
of Saturated Rock
Empirical relation
per faciesK
P
Capillary Pressure
Derived
Sw
Vclay
Hertz-Mindlin + modified
Hashin-Shtrikman
lower bound
Gassmann
Fluid Substitution
Dry Elastic Moduli
• Sandstone
• Shale
Simulated properties
Calculated properties
Inverted Facies Inverted Porosity
Inverted Vclay Inverted Sw
TV
D
OWC
OWC
0.5
0.3
0.4
0.6
0.2
0.1
0.0
0.8
0.4
0.6
1.0
0.2
0.20
0.10
0.15
0.25
0.05
Geostatistical Depth Inversion – Single Realization
24
TV
D
TV
DT
VD
OWC
OWC
Sand Shale
42%
44%
40%
High Scenario
Medium Scenario
Low Scenario
NTG Ranking for 3 Scenarios
P10
P50
P90
Uncertainty Analysis
P10
P50
P90
P10
P50
P90
P10
P50
P90
P10
P50
P90
Pay Volume
Nile Delta
– Abu Madi Formation
– Upper Miocene
– Fluviomarine
– Sandstone intercalated with
siltstone and shale
– Intraformational shale baffles
Data
– Six wells
– Six partial stacks
Sulistiono, et al., Integrating Seismic and Well data into
Highly Detailed Reservoir Model through AVA
Geostatistical Inversion, SPE 2015 (SPE-177963-MS)
Example 2 - Understanding Unexpected Pressure Depletion
Abdel-Fatah,
2015
Objective
– Understand the unexpected pressure depletion observed
in the field.
Original
Pressure
Depleted
Pressure
Key Question: What is the level of connectivity between north and south?
Solution: Flow simulation of multiple realizations
Geostatistical Inversion Workflow
27
Shale
Tim
e (
ms)
Facies from Deterministic Inversion Workflow
1. Stratigraphic modeling
2. Facies definition
3. Geostatistical inversion
4. Vclay and porosity cosimulation
5. Permeability and saturation modeling
6. Ranking of realizations
7. Upscaling P10, P50 and P90 realizations
8. Dynamic simulation
Sand
Lithotypes
28
Facies from Deterministic and Geostatistical Inversions
Comparison of Facies from Deterministic and Geostatistical Inversion
Tim
e (
ms)
Tim
e (
ms)
Deterministic Inversion
Geostatistical Inversion – Realization #1
Deterministic results
– Results at seismic BW
– Sands in lower reservoir
– No connection to south
Geostatistical results
– Modeled at 0.5 ms
– Thin sands throughout
– Connection possible
Shale
Sand
Lithotypes
29
Further Modeling, Ranking, Upscaling and Flow Simulation
P50 Properties Upscaled and Transferred to the Corner Point
Grid
Realization ranking based on net pore volume at proposed wells
Vertical dimension is Depth
Vclay Vclay
Lithotype Lithotype
Reservoir Grid CPG Grid
Realization upscaling to CPG
Co-Simulated reservoir properties of Vclay and Effective porosity
Permeability and saturation modelled from porosity
Flow simulation and history matching of realizations
Pressure simulation shows connectivity
between northern and southern area
30
Pressure from Dynamic Flow Simulation Using RockMod P50 Model
Pressure Changes: 2007-2012
Pressure
Sulistiono, et al., Integrating Seismic and Well data
into Highly Detailed Reservoir Model through AVA
Geostatistical Inversion, SPE 2015 (SPE-177963-MS)History matching done to observed well pressures
Feb. 2007
Apr. 2010
Dec. 2008 Dec. 2012
Sept. 2011
Example 3 – Updating the Geologic Model
Western Siberia
Clastic Reservoir
– Neokomian interval
– Net pay: 5 to 18 meters
– Porosity: 15% to 17%
Field under production for 10 years
– 10 exploration wells
– 30 production wells
– Variable OWC across the field
Objective: Update the geologic model to
incorporate the observed compartmentalization
Fillipova et al., Geostatistical Inversion as a Tool for the Accurate Updates
of the Hydrodynamic Models – Case Study, EAGE Ann. Mtg., 2013
Top Reservoir
Map
OWC -2523m
OWC -2485m
Elastic Properties
P Impedance
Vp
/Vs
Fre
quen
cyAddressing the Compartmentalization
Key challenge: Update the geologic model to incorporate the
observed compartmentalization
Solution: Use the seismic for mapping reservoir compartments
But: Poor separation between reservoir and non-reservoir
Solution 2: Analysis of the reservoir frequency volume
OWC -2523m
OWC -2485m
Reservoir Non-reservoir
P Impedance
Reservoir Frequency from Geostatistical Inversion
33
Tiled Stratigraphy
Analysis of reservoir frequency volume showed
four compartments, two of which have not been
drilled.
Comparison of Two Geological Models
Model1: No Seismic
Model 2: Geostatistical Inversion
Reservoir Non-Reservoir
Reservoir Non-Reservoir
34
Original geologic model
Built using only wells and
seismic horizons
More continuity
Updated geologic model
Built based on geostatistical
inversion results
Less continuity
History Match and Prediction at Newly Drilled Well
Net-to-Gross
• Predicted: 0.92
• Actual: 0.88
Production Rate
• Observed
• No Seismic
• Geostatistical
Inversion
2008 2009 2010 2011 2012 2013
35
Regional Platform
Platform Facies
LagoonReef Margin
EmbaymentLower
Foreslope
Reef Facies
FSL
Sand
ForeslopeReef Flat
Example 4 – Determining Porosity Probability
Swan Hills Reef– Devonian, Alberta, Canada
– Beaverhill Lake Group
Environment– 2810 m
– 65 wells – Producers & Injectors
– Up to 85 m Limestone
– Limestone Porosity to 18%
– Continuous pay up to 25 m
– Fluid: Oil
Van der Laan, J., Pendrel, J., Geostatistical Simulation of Porosity and Risk in a Swan Hills
Reef, CSEG Nat. Conv. Abs., 2001
Tim
e (
s)
1.72
1.74
1.76
1.78
1.80
1.82
1.84
Geostatistical Probability Analysis
Objective: Quantify and map areas with high
likelihood of porosity above the required threshold
Solution: Analyze the porosity probabilities from a
set of porosity realizations
Analysis Workflow
– Analyze porosity values of each cell across multiple
realizations to find porosity distributions for each cell.
– Select porosity threshold and create volume of
probabilities for that value from the porosity
distributions.
– Analyze volume of probabilities relative to that porosity
value.
Porosity
Pro
b. D
en
sit
y
0 5 10
Pro
b. D
en
sit
y
0 5 10
Prob. = 0.63Prob. = 0.15
Results of Geostatistical Probability Analysis
Geostatistical inversion is the best basis for
reservoir models
– Integrates a broad range of data
– Provides geologically realistic models
• Highly detailed from well information
• Laterally accurate from seismic information
• Distinct features from simultaneous property and
facies modeing
– Creates basis for range and uncertainty estimations
These reservoir models provide
– Rapid history matches to flow simulation
– Accurate predictions for future wells
Incorporating All of the Data
Reservoir properties
Shale
Sand
Tight
sand
Facies
Flow Simulator
Porosity,
Permeability,
Saturation and
others
Geostatistical inversion can help you meet technical
and business objectives
39
Thank You!Acknowledgements
• John Pendrel
• Leonardo Quevedo
• Rong Zeng
• Anton Ephanov
• Harry Debeye
• Irina Yakovleva
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