SPE Distinguished Lecture

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SPE DISTINGUISHED LECTURER SERIES is funded
principally through a grant of the SPE
FOUNDATION The Society gratefully
acknowledges those companies that support the
program by allowing their professionals to
participate as Lecturers. And special thanks to
The American Institute of Mining,
Metallurgical, and Petroleum Engineers (AIME) for
their contribution to the program.
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Assessing Dynamic Reservoir UncertaintyIntegrati
ng Experimental Design with Field Development
PlanningMark WilliamsChevron Energy Technology
Company
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Points I Would Like To Reinforce

• Experimental Design structures assessments of
  reservoir performance
• Uncertainties are not decisions
• Assess reservoir uncertainty and decisions
  sequentially
• OHIP, rates, and recovery are outputs not
  uncertainties
• Use the unconstrained development scenario (UDS)
  for the initial Experimental Design assessment
• Use unbiased models for development alternatives
  analysis

Best Practices tips will be highlighted in
Green.
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Assessing Dynamic Uncertainty 6-Step Process Flow

• Define Subsurface Uncertainties and Their Ranges

2. Make ED Runs with an
Unconstrained Scenario
3. Create Proxy Equation for the Simulation Model
4. Create S-Curve of Recovery Using Proxy Equation
5. Build Deterministic P10-P50-P90 Base Models
6. Use Base Models toAssess Alternatives
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Assessing Dynamic Uncertainty What are the
end-products of this process?

• A set of P10, P50, P90 base models
• These P10-50-90 recoveries are minimally
  affected by decisions
• These base models will be used to test
  development alternatives

P10
P50
P90
P90 P50 P10
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Assessing Dynamic Uncertainty What are the
end-products of this process?

• A field development plan with a high chance of
  economic success.
• Decisions are evaluated using the 3 base models
• Economic and/or Decision Analysis models used to
  select the optimum plan
• Plans are usually flexible (narrow/widen scope
  as data comes in

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Step 1 Define SS Uncertainties Their
RangesUncertainties vs. Decisions

• Dont confuse uncertainties with decisions
• Uncertainties drive decisions decisions manage
  uncertainties
• Difficult to assess them concurrently
• Typical decisions
• Number and location of wells
• Recovery process
• Artificial lift method
• Well configuration and type
• Pattern type and spacing
• Subsea vs. Platform development
• Facility capacity

We will assess these after we build our base
models
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Step 1 Define SS Uncertainties Their
RangesSimple vs. Complex Uncertainties

• Simple The uncertainty can be directly measured.
• Examples include
• Structure Top
• Porosity and Swir
• Net and Gross Thickness
• Oil and Water Viscosity
• Permeability
• Sorw and Sorg
• Krw and Krg

• Complex The uncertainty is
• the product of multiple simple uncertainties, or
• the result of the interaction of multiple simple
  uncertainties
• Examples include
• Connectivity
• Transition height
• Mobility ratio

• Areal sweep
• Decline rate
• Well EUR

Simple uncertainties are easier to communicate
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Step 1 Define SS Uncertainties Their
RangesStatic vs. Dynamic Uncertainties

• Static uncertainties affect the OHIP
• Structure top and OWC/GOC
• Porosity and Swir
• Net and Gross thickness
• Boi and Bgi
• Dynamic uncertainties affect rate and recovery
• Horizontal permeability
• Relative permeability
• Residual oil saturation
• Oil and water viscosity
• Fault sealing
• Productivity index

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Step 1 Define SS Uncertainties Their
RangesMinimums and Maximums

• Typical projects assess 12 to 20 uncertainties
• ½ static and ½ dynamic
• Many are common to all projects
• Uncertainty ranges come from
• in-field data, analogues, history matching, and
  expert opinion
• The Minimum and Maximum values are not P10 and
  P90 values!
• The Midpoint values are not Most-Likely!

Try to keep all of your uncertainties SIMPLE
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Step 2 Make ED Runs with an Unconstrained
ScenarioSetting Up the ED Table

• The ED table can structure the analysis
• Plackett-Burman ED is popular since it is the
  simplest

• Plackett-Burman is used to screen large numbers
  of uncertainties.
• Parameter combinations (-1, 0, 1) are prescribed
  for each run.
• The centerpoint run uses all midpoints (0 values)
  to test for curvature
• Curvature (e.g. a poor linear fit) requires
  D-Optimal Design or some other 3-level method
• More runs can be made to increase the degrees of
  freedom, if desired
• Better estimates of the error

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Step 2 Make ED Runs with an Unconstrained
Scenario Normal vs. Actual Uncertainty Values

• Normal Value Parameters
• Geologic framework (structure and layers)
• Geobody configurations
• Porosity arrays
• Permeability arrays
• Saturation arrays (Swir, Sorw, Sorg)
• Fault sealing

Normal parameters does not mean they are
normally distributed. They are arrays
represented by -1, 0, and 1

• Actual Value Parameters
• Oil-in-Place
• Pore volume
• Any array multipliers (perm, NTG, pore volume)
• OOWC
• Relative Permeability (Krw, Krg)
• Skin factors
• PI Multipliers
• Kv/Kh ratio

-1
Worst
1
Best
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Step 2 Make ED Runs with an Unconstrained
Scenario Normal and Actual Uncertainty Values

• The Plackett-Burman table with actual values
  replacing the normal values
• 0, 1, and -1 denote min, mid, and max values.
• Normal and actual values can be mixed
• Actual values give you more flexibility in Step
  5
• This is when you create your P10-50-90 base
  models

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Step 2 Make ED Runs with an Unconstrained
Scenario What is the Unconstrained Development
Scenario?

• A development that is not constrained by
• The number of wells
• Facilities capacity
• Well hydraulics (no flow tables or networks)
• Economic limits
• Drilling schedule
• Different recovery processes require a separate
  UDS (e.g. water vs. gas injection)
• Dont use too many wells

5-Spot UDS Model
The main point Let the differences in recovery
be attributable to subsurface uncertainty
alone!
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Step 2 Make ED Runs with an Unconstrained
ScenarioPlackett-Burman ED Table with Run Results

• These are the simulator recoveries under the UDS
• The same UDS was used for all runs
• Convert to Net Present Production
• captures the impact of uncertainties that affect
  rate (e.g. perm)

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Step 3 Create Proxy Equation for the Simulation
ModelPlackett-Burman ED Table with Run Results
The uncertainty values (independent) and oil
recoveries (dependent) are regressed into a proxy
equation.
Oil Rec 52.765 0.161(OOIP) - 82.5(KRW) -
4.167(XPERM) 151.515(KVKH) - 85.0(SORW)
0.917(SKIN)
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Step 3 Create Proxy Equation for the Simulation
ModelPlackett-Burman ED Table with Run Results

• Cross-plot the model-calculated vs.
  proxy-calculated recoveries
• The coefficient of determination (R2) does not
  tell the whole story
• See if the proxy equation is a suitable
  substitute for the models

Proxy-Calculated Oil Recovery
Model-Calculated Oil Recovery
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Step 4 Create S-Curve of Recovery Using Proxy
EquationUsing the Proxy Equation Instead of the
Models

• Use the proxy equation from Step 3
• Assign distributions to each uncertainty
• Run Monte Carlo to generate an S-curve for oil
  recovery.

Oil Recovery 52.808 0.161(OOIP) - 82.5(KRW)
- 4.167(XPERM) 151.515(KVKH) - 85.0(SORW)
0.917(SKIN)
CDF Curve from Monte Carlo
Monte Carlo Simulator
0.9
0.5
0.1
P10
P50
P90
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Step 4 Create S-Curve of Recovery Using Proxy
EquationTips for Uncertainty Distribution
Functions

• Typical uncertainty distributions
• Uniform
• Normal
• Log normal
• Triangular
• Discrete
• Range is more important than distribution shape
• If you arent sure run Monte Carlo using
  different shapes
• If you dont know the most-likely use a uniform
  distribution
• Continuous distributions are most popular and
  logical
• Truncate normal and log-normal distributions
• define the minimum and maximum
• avoids extreme or unreasonable outcomes

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Step 4 Create S-Curve of Recovery Using Proxy
EquationUsing the Proxy Equation Instead of the
Models
Uncertainty Distribution Functions
Oil Rec 52.765 0.161(OOIP) - 82.5(KRW) -
4.167(XPERM) 151.515(KVKH) - 85.0(SORW)
0.917(SKIN)
Monte Carlo Simulation Result
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Step 4 Create S-Curve of Recovery Using Proxy
EquationSensitivity to Distribution Shape

• Uncertainty distribution shapes will affect the
  S-curve range
• Distribution shape may be dictated when there is
  ample in-field data
• In most cases the shape is assumed due to limited
  data
• Using uniform distributions gives you a wider
  S-curve

Oil Recovery S-Curve
Cumulative Distribution
Proxy-Calculated Oil Recovery
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Step 5 Build Deterministic P10-50-90 Base
ModelsChoosing Uncertainty Combinations that
Make Sense

• Select parameter combinations that will create
  P10, P50, and P90 predictive models.
• This is where engineering judgment comes in
• These base models will be used to assess the
  different development alternatives

Structure
Chan
OWC
NTG
Porosity
Krw
Perm
Sorw
Kv/Kh
Visc
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Step 5 Build Deterministic P10-50-90 Base Models
Validating Proxy Equation Accuracy

• Ensure the deterministic simulation models yield
  P10-50-90 results
• Adjust big-hitter uncertainty values to match
  P10-50-90 recoveries

P90 P50 P10
Run the models
Do the model results match the proxy equation?
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Step 5 Build Deterministic P10-50-90 Base Models
Selecting the Big-Hitter Uncertainties to Adjust
Oil Recovery Tornado Chart
Oil-in-Place
Sorw
Krw
Kv/Kh
Skin Factor
Permeability
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Step 5 Build Deterministic P10-50-90 Base Models
Building Deterministic Models that Make Sense
The P10-50-90 oil recoveries from Monte Carlo

• The P10-50-90 oil recoveries from the proxy
  equation
• The recoveries calculated by the simulation
  model
• P10 OOIP used in the P10 recovery model (same
  with P50 and P90)
• Sorw and Krw adjustments have most impact in
  this example
• Logical progression of parameter values (getting
  better P10 -gt P90)

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Step 5 Build Deterministic P10-50-90 Base Models
Some Issues to Overcome

• What are appropriate uncertainty values for the
  P10, P50, and P90 models?
• An infinite number of combinations are possible
• Random Monte Carlo combinations are possibly not
  desirable
• Most are comfortable selecting their own
  parameter combinations
• P10 OHIP -gt P10 recovery, etc.
• Ensure a logical progression of the uncertainty
  values
• Avoid being too deterministic!
• You still dont know whats down there!

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Step 6 Use Base Models to Assess Alternatives
Addressing the Decisions

• The P10-50-90 Base Models are used to assess
  design decisions
• Flood pattern type and spacing
• Number of producers and injectors
• Optimum well locations
• Well configurations and type
• Artificial lift method
• Facility capacity
• Injection rates
• Operating pressures

This is where the design decisions are tested
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Step 6 Use Base Models to Assess
AlternativesTest Alternatives with the Base Model

• In this example, we used the P50 base model to
  assess these scenarios
• 5-Spot Pattern Flood, 400-m well spacing
• 9-Spot Pattern Flood, 400-m well spacing
• Line Drive Flood, 500-m well spacing
• Staggered Line Drive Flood, 500-m well spacing
• The numbers of producers and injectors for each
  plan are

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Step 6 Use Base Models to Assess
AlternativesTest Alternatives with the Base Model
LINE DRIVE
5-SPOT
STAGGERED LINE DRIVE
9-SPOT
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Step 6 Use Base Models to Assess
AlternativesTest Alternatives with the Base Model

• An economic screening model or DA model is needed
  to choose the best alternative
• You now have unbiased physical models to test any
  alternative

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Step 6 Use Base Models to Assess
AlternativesTest Alternatives with the Base Model
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Step 6 Use Base Models to Assess
AlternativesTest Alternatives with the Base Model
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Step 6 Use Base Models to Assess
AlternativesSelecting the Preferred Scenario
The 9-Spot appears to be the most promising
alternative
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Step 6 Use Base Models to Assess
AlternativesOptimizing the Unconstrained
Development Scenario
Eliminating potentially poor wells

• A good starting point for optimizing the
  development alternative.
• Easy to remove redundant wells
• Easy to identify good vs. bad areas
• Add flow tables and nodal networks at this time

• Add other constraints and limits
• facilities capacity
• WOR GOR
• economic minimums
• Drilling schedule

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Step 6 Use Base Models to Assess
AlternativesOptimizing the 9-Spot Preferred
Alternative
Oil Recovery S-Curve

• Subsequent runs were made in which poor wells
  were removed from the plan
• The oil recovery S-curves at right show that 18
  flank wells can be removed from the 9-spot
  pattern with little impact on oil recovery

Most project teams and decision makers never know
how their preferred alternative compares to a
theoretical maximum.
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Step 6 Use Base Models to Assess
AlternativesOptimizing the 9-Spot Preferred
Alternative
Removing 18 marginal producers has a low impact
on oil rates
A drilling schedule has also been applied that
has stretched out the production profiles.
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Step 6 Use Base Models to Assess
AlternativesOptimizing the Preferred Scenario
Removing 18 marginal producers has a big impact
on NPV
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Step 6 Use Base Models to Assess
AlternativesPlanning for Downside and Upside
Outcomes

• P10 model used to assess possible downside
  mitigation actions
• e.g., drill fewer wells, install gas lift, add
  water injection, etc.
• P90 model used to assess possible upside capture
  actions
• e.g. drill more wells, delay water injection,
  etc.
• Typical development plan flexibility
• P10 24 wells (reservoir is smaller)
• P50 33 wells (reservoir is as expected)
• P90 40 wells (reservoir is larger)

P90 --- P50 --- P10 ---
P10 --- P10 w/mitigation ---
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Step 6 Use Base Models to Assess
AlternativesReserves vs. Contingent Resources
Oil Recovery S-Curve

• Re-run the ED models with the preferred
  alternative
• create another S-curve
• Show how much oil your plan will give up due to
  economic constraints
• The blue S-curve defines your P1-P2-P3 reserves
• The green S-curve defines your P4-P5-P6
  contingent resources

This method is gaining acceptance within Chevron
as a way to quantify reserves vs. contingent
resources.
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Assessing Dynamic Performance Using Experimental
DesignSummary

• Experimental Design adds structure and efficiency
  to subsurface assessments
• Uncertainties drive Decisions Decisions manage
  Uncertainties
• Dont get them confused
• The unconstrained development scenario (UDS)
  allows you to assess reservoir uncertainty prior
  to assessing alternatives
• Minimizes the impact of decisions you arent
  ready to make
• Deterministic models can be built that
• Are unbiased
• Span the range of reservoir outcomes
• The UDS is a good starting point to optimize the
  preferred alternative
• Easier to remove wells than to add them by trial
  and error
• Helps you quantify your preferred alternatives
  limitations
• Can quantify reserves vs. contingent resources