Reservoir Modeling
SPE-CSPG Joint Luncheon Talk – February 9, 2016 Advances in Multivariate Property Modeling and Applications to Uncertainty in Reservoir Forecasting
Dr. Clayton V. Deutsch, P.Eng., Professor Alberta Chamber of Resources Industry Chair in Mining Engineering Canada Research Chair in Natural Resources Uncertainty Assessment
Reservoir Modeling
Lec 01 – page 1
Reservoir Modeling A good model can advance fashion by ten years. Yves Saint Laurent
• A quantitative numerical representation of aspects of the subsurface. Often gridded, but increasingly grid free • Categorical and continuous properties: – Structure, facies, porosity (total and effective), saturations, grain size distributions (Vsh), permeability and other rate constants, acoustic properties, elastic moduli,… – In general, not the flow response itself – Different models at different scales for different purposes
Different Scales of Modeling • Millimeter to 100s of kilometers
Secondary Variables (26)
Primary Variables (39)
Lec 01 – page 2
Some Principles • Geostatistical Simulation: Zkl u , k 1,...,K;l 1,..., L,u A
• Realizations represent our state of incomplete knowledge:
Developments in Reservoir Modeling 1. Data integration is more powerful – Data is not left out for post processing / history matching
2. Multivariate modeling is more straightforward – Tens of variables with complex relationships are modeled simultaneously
3. Decisions are optimized over all realizations – All realizations all the time – as required
4. Uncertainty is modeled better – Parameter and data uncertainty are considered
5. Risk is actively managed and not just passively observed – May choose to trade off some expected value for reduced risk
Lec 01 – page 3
Data Integration
Consider 4-D Seismic • • •
Map the presence of local anomalies based on interpretation Local improvement in the estimation of steam chamber geometry Learnings can be captured in a new set of realizations Producer
Injector
Flow Barrier Flow Conduits
Z (m)
X (m)
Lec 01 – page 4
Anomaly Enforcement • Steam chamber propagation and geometry controls oil production and steam requirements • Anomalies in steam chamber propagation are related to flow barriers or conduits • Unlikely to reproduce anomalies by chance, so they are enforced
Demonstration
Lec 01 – page 5
Effect on Steam Chamber Z (m)
Z (m)
After
X (m)
Z (m)
Before
Y (m)
Data Integration • Some practical techniques (like the one shown) including – Cokriging based techniques – Probability combination – Experimental sensitivity coefficients and optimization
• There are increasingly sophisticated techniques – Couple the forward model with an optimization engine – Ensemble based techniques with experimental covariances
• All data is considered in reservoir modeling by construction – Leaving data out for checking is done for sensitivity analysis – Data should not be left out in final model construction
Lec 01 – page 6
Y (m)
Multivariate Modeling
Multivariate Modeling • Structure and Facies are modeled first in high resolution 3-D models • Simultaneously modeling many continuous variables is common – Directly in 2-D regional models – Within facies and structure in 3-D
• Legacy techniques are not appropriate: – Limited to few variables at a time – Strong assumption of multivariate Gaussian – Bivariate cloud reproduction limited by spatial correlation and number of variables
• Common to have 10s of variables with complex relationships
Lec 01 – page 7
Example with KH and KV • Trimodal Kh-Kv distribution • Explained by percolation
PCA and Data Sphereing • Principal component analysis is standard for: – Understanding essential characteristics – Reducing dimensions – Decorrelating
• Sphereing makes all components have the same variance • Rotate the frame of reference of a sphere – Sphere-R minimizes variable mixing – MAF considers spatial correlation
Zs
Xs
Ws
Lec 01 – page 8
Multivariate Transformation (PPMT) • Geological data are complex beyond what PCA/sphereing can handle, so • PCA, Sphere, then consider projection pursuit iterations
Normal Score Transformed
PPMT Transformed
Projection Pursuit Iterations
Lec 01 – page 9
Modern Multivariate Modeling Workflow • Assemble all variables to model (impute missing values if required) • Pass variables through PPMT transform and assemble variograms (one for each) • Simulate each variable independently using established techniques (consider secondary data as a constraint in sampling) • Back transform by reversing all PPMT iterations… • Assemble realizations, check, post process (calculate any response of interest)
Optimize Decisions Over All Realizations
Lec 01 – page 10
Global versus Local Optimization
X
Multiple Realizations 5m Above Realization 1 Realization 2 Realization 3 Realization 4 Realization 5 Realization 6 Realization 7 Realization 8
Optimal
Realization 9 Realization 10 Mean Pen. Vol.
5m Below
Lec 01 – page 11
Surface Pad / Drainage Area Layout • General optimization of layout and sequencing – – – – – – – – –
Formulate an objective function Complex surface constraints Well length, number of wells, Drilling constraints Pipeline constraints Areal conformance Vertical conformance Pressure in old DAs …
Well Trajectory Optimization • Well elevation is optimized to maximize recovery – Horizontal and deviated are permitted – Executed during DA optimization process
• Updates are tied into the objective function – – – –
Improved accuracy of volume estimates Accounting for steam chamber geometry Steam-oil interface angle for trapped oil Influence of thief zones
n
R (ri cwi ) BIP cs n cwc cc i 1
n number of well pairs ri recovery of a well pair cwi cost for too short/long of wells cs supply cost (barrels / barrel) cwc capital cost of a well pair cc capital cost for a drainage area / surface pad
Lec 01 – page 12
Structural Uncertainty • Assess probability of effectiveness (effective well length) • Couple with facies uncertainty: probability of drilling through mud…
Ranking for Calibration • • • •
There is no P50 model There is no P10 model There is no P90 model Ranking should be avoided if at all possible; if required, done late • Set of realizations should be treated together
wd
1 k j ,iw wk QS V j j 1 S w, j d iw1 j 1 j ,iw nw niw
• Ranking is useful for calibration (for fixed geometry and flow conditions) • Rerank for any change
Lec 01 – page 13
Proxy or SemiAnalytical Flow Models • Fast flow simulation required to help optimization and transfer of uncertainty • Full physics simulation required in most situations and for calibration
Steps
Angles
Cumulative ,
: %4 ↑
,
: %1 ↑
CSOR
rates
Steam pressure
: %3 ↓
Uncertainty Modeled Better
Lec 01 – page 14
Some Principles • • • •
Consider scenario uncertainty if required Realizations represent our state of incomplete knowledge There is uncertainty in all modeling parameters and the data Important to consider a “shift” as well as local fluctuations
Uncertainty Modeling 1.00 0.90 0.80 Actual Fraction in Interval
• Check that uncertainty is fair: • Easier to check uncertainty than a single estimate • We also desire narrow uncertainty
0.70
This example is from a real case where 67 new wells were drilled
0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Width of Probability Interval
• Look at the uncertainty in each input parameters and assess how this translates through the modeling process
Lec 01 – page 15
Managing Uncertainty
Manage Uncertainty and Risk • Choose a design on the efficient frontier – maximize value and minimize risk • Consider different decisions (including decision to get data)
Lec 01 – page 16
Concluding Remarks • Reservoir modeling has changed and needs more change • Principles emphasized in this talk: – – – – –
Integrate all data by construction Model all variables simultaneously Build in parameter and data uncertainty Optimize over all realizations all the time Actively manage risk
• Now is a good time to change
Bob Dylan, 1963, 1964
Lec 01 – page 17
Dr. Clayton V. Deutsch, P.Eng., Professor Alberta Chamber of Resources Industry Chair in Mining Engineering Canada Research Chair in Natural Resources Uncertainty Assessment
Reservoir Modeling
Lec 01 – page 1
Reservoir Modeling A good model can advance fashion by ten years. Yves Saint Laurent
• A quantitative numerical representation of aspects of the subsurface. Often gridded, but increasingly grid free • Categorical and continuous properties: – Structure, facies, porosity (total and effective), saturations, grain size distributions (Vsh), permeability and other rate constants, acoustic properties, elastic moduli,… – In general, not the flow response itself – Different models at different scales for different purposes
Different Scales of Modeling • Millimeter to 100s of kilometers
Secondary Variables (26)
Primary Variables (39)
Lec 01 – page 2
Some Principles • Geostatistical Simulation: Zkl u , k 1,...,K;l 1,..., L,u A
• Realizations represent our state of incomplete knowledge:
Developments in Reservoir Modeling 1. Data integration is more powerful – Data is not left out for post processing / history matching
2. Multivariate modeling is more straightforward – Tens of variables with complex relationships are modeled simultaneously
3. Decisions are optimized over all realizations – All realizations all the time – as required
4. Uncertainty is modeled better – Parameter and data uncertainty are considered
5. Risk is actively managed and not just passively observed – May choose to trade off some expected value for reduced risk
Lec 01 – page 3
Data Integration
Consider 4-D Seismic • • •
Map the presence of local anomalies based on interpretation Local improvement in the estimation of steam chamber geometry Learnings can be captured in a new set of realizations Producer
Injector
Flow Barrier Flow Conduits
Z (m)
X (m)
Lec 01 – page 4
Anomaly Enforcement • Steam chamber propagation and geometry controls oil production and steam requirements • Anomalies in steam chamber propagation are related to flow barriers or conduits • Unlikely to reproduce anomalies by chance, so they are enforced
Demonstration
Lec 01 – page 5
Effect on Steam Chamber Z (m)
Z (m)
After
X (m)
Z (m)
Before
Y (m)
Data Integration • Some practical techniques (like the one shown) including – Cokriging based techniques – Probability combination – Experimental sensitivity coefficients and optimization
• There are increasingly sophisticated techniques – Couple the forward model with an optimization engine – Ensemble based techniques with experimental covariances
• All data is considered in reservoir modeling by construction – Leaving data out for checking is done for sensitivity analysis – Data should not be left out in final model construction
Lec 01 – page 6
Y (m)
Multivariate Modeling
Multivariate Modeling • Structure and Facies are modeled first in high resolution 3-D models • Simultaneously modeling many continuous variables is common – Directly in 2-D regional models – Within facies and structure in 3-D
• Legacy techniques are not appropriate: – Limited to few variables at a time – Strong assumption of multivariate Gaussian – Bivariate cloud reproduction limited by spatial correlation and number of variables
• Common to have 10s of variables with complex relationships
Lec 01 – page 7
Example with KH and KV • Trimodal Kh-Kv distribution • Explained by percolation
PCA and Data Sphereing • Principal component analysis is standard for: – Understanding essential characteristics – Reducing dimensions – Decorrelating
• Sphereing makes all components have the same variance • Rotate the frame of reference of a sphere – Sphere-R minimizes variable mixing – MAF considers spatial correlation
Zs
Xs
Ws
Lec 01 – page 8
Multivariate Transformation (PPMT) • Geological data are complex beyond what PCA/sphereing can handle, so • PCA, Sphere, then consider projection pursuit iterations
Normal Score Transformed
PPMT Transformed
Projection Pursuit Iterations
Lec 01 – page 9
Modern Multivariate Modeling Workflow • Assemble all variables to model (impute missing values if required) • Pass variables through PPMT transform and assemble variograms (one for each) • Simulate each variable independently using established techniques (consider secondary data as a constraint in sampling) • Back transform by reversing all PPMT iterations… • Assemble realizations, check, post process (calculate any response of interest)
Optimize Decisions Over All Realizations
Lec 01 – page 10
Global versus Local Optimization
X
Multiple Realizations 5m Above Realization 1 Realization 2 Realization 3 Realization 4 Realization 5 Realization 6 Realization 7 Realization 8
Optimal
Realization 9 Realization 10 Mean Pen. Vol.
5m Below
Lec 01 – page 11
Surface Pad / Drainage Area Layout • General optimization of layout and sequencing – – – – – – – – –
Formulate an objective function Complex surface constraints Well length, number of wells, Drilling constraints Pipeline constraints Areal conformance Vertical conformance Pressure in old DAs …
Well Trajectory Optimization • Well elevation is optimized to maximize recovery – Horizontal and deviated are permitted – Executed during DA optimization process
• Updates are tied into the objective function – – – –
Improved accuracy of volume estimates Accounting for steam chamber geometry Steam-oil interface angle for trapped oil Influence of thief zones
n
R (ri cwi ) BIP cs n cwc cc i 1
n number of well pairs ri recovery of a well pair cwi cost for too short/long of wells cs supply cost (barrels / barrel) cwc capital cost of a well pair cc capital cost for a drainage area / surface pad
Lec 01 – page 12
Structural Uncertainty • Assess probability of effectiveness (effective well length) • Couple with facies uncertainty: probability of drilling through mud…
Ranking for Calibration • • • •
There is no P50 model There is no P10 model There is no P90 model Ranking should be avoided if at all possible; if required, done late • Set of realizations should be treated together
wd
1 k j ,iw wk QS V j j 1 S w, j d iw1 j 1 j ,iw nw niw
• Ranking is useful for calibration (for fixed geometry and flow conditions) • Rerank for any change
Lec 01 – page 13
Proxy or SemiAnalytical Flow Models • Fast flow simulation required to help optimization and transfer of uncertainty • Full physics simulation required in most situations and for calibration
Steps
Angles
Cumulative ,
: %4 ↑
,
: %1 ↑
CSOR
rates
Steam pressure
: %3 ↓
Uncertainty Modeled Better
Lec 01 – page 14
Some Principles • • • •
Consider scenario uncertainty if required Realizations represent our state of incomplete knowledge There is uncertainty in all modeling parameters and the data Important to consider a “shift” as well as local fluctuations
Uncertainty Modeling 1.00 0.90 0.80 Actual Fraction in Interval
• Check that uncertainty is fair: • Easier to check uncertainty than a single estimate • We also desire narrow uncertainty
0.70
This example is from a real case where 67 new wells were drilled
0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Width of Probability Interval
• Look at the uncertainty in each input parameters and assess how this translates through the modeling process
Lec 01 – page 15
Managing Uncertainty
Manage Uncertainty and Risk • Choose a design on the efficient frontier – maximize value and minimize risk • Consider different decisions (including decision to get data)
Lec 01 – page 16
Concluding Remarks • Reservoir modeling has changed and needs more change • Principles emphasized in this talk: – – – – –
Integrate all data by construction Model all variables simultaneously Build in parameter and data uncertainty Optimize over all realizations all the time Actively manage risk
• Now is a good time to change
Bob Dylan, 1963, 1964
Lec 01 – page 17
