PETROLEUM ENGINEERING 689 Special Topics in Unconventional Resource Reserves Lecture 11 Applied Prob

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PETROLEUM ENGINEERING 689Special Topics
inUnconventional Resource ReservesLecture 11
Applied Probabilistic Reserves Texas AM
University - Spring 2007
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Outline

• Summing Reserves
• Bootstrap Method
• Choosing A Distribution Type
• Scoping Analysis

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Learning Objectives

• How to sum reserves classes at the well, field
  and company level
• Be able to generate reserves classes from DCA
• Know when to choose a log-normal distribution or
  something else
• How to set up a probabilistic scoping analysis.

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Summing Reserves

• One cannot add proved reserves for zones to get
  well proved reserves. Nor can one add well
  reserves to get field reserves. Mathematically
  incorrect. Leads to the wrong answer.
• - E.C. Capen, SPE paper 73828

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Summing Reserves

• In practice, the vast majority of reserves
  analysts will add reserves per well to get field
  reserves regardless of the reserves class
• This works only if the mean reserves per well are
  being added to get the mean reserves for the
  field (or Zone ? Well or Field ? Company)
• The reserve class thresholds of Proved (P10),
  Probable (P50) and Possible (P90) are not equal
  to the Mean and have to be summed by a different
  method
• Read SPE Paper 73828

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Summing Reserves

• Very few reserves analysts actually apply a true
  probabilistic approach to generate P10, P50 P90
  reserves, further complicating the issue
• Without a proper approach to compute P10, P50 and
  P90 reserves, there is no proper technique for
  summing
• The proper technique is not hard as long as the
  threshold probabilities were computed using
  actual statistical methods.

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Summing Reserves

• In Practice, Many Reserves Analysts Use Something
  Close To The Mean When Assigning Proved Reserves
• Producing Wells Mean is probably assigned as
  Proved more often than not
• Proved Undeveloped Locations / Behind Pipe
  Probably still some Mean assignments

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Summing Reserves

• Lets Start With Definitions
• Proved Definitions vary, but words such as
  reasonable certainty or confident are often
  used. In practice, industry claims it is moving
  to assigning reserves to the proved class if
  there is a 90 probability that the reserves
  level will be met or exceeded.
• Applying the 90 probability that reserves will
  exceed a certain threshold should correspond
  statistically to P10 on a probability plot.
• Proved P10 90 chance that reality will be
  above the proved value.

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Summing Reserves

• Lets Start With Definitions
• Probable Now generally defined as meeting or
  exceeding a P50 threshold
• Possible New generally defined as meeting or
  exceeding a P90 threshold (P90 means only a 10
  chance that reality will be at or above the
  threshold ? 90th percentile on a cumulative
  probability plot (ascending)).

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Summing Reserves
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Summing Reserves

• Why Cant You Add Two P10 Proved Reserves Cases
  to Get a Combined P10 Proved Case?
• If you sample the distribution only one time, you
  will get the P10 value or less 10 of the time,
  but if you sample the distribution more than one
  time the chances of getting all the samples at
  the P10 value or less become exceedingly small
• Adding P10 proved reserves will underestimate the
  combined proved reserves

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Rolling the Dice Example

• With One Die
• Assume Proved Reserves a one in six chance
• Hurdle corresponds to a One on the die (P16.7)
• With Two Dice
• Chance of rolling a one on each die is 1/6 1/6
  1/36 ? much smaller chance of happening than
  when rolling only one die.
• If Proved meant it had a 1/6 chance of
  happening, then using the One on a die as the
  test for Proved only works if only one die is
  rolled (i.e. only one well is drilled).

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Outcomes of rolling two dice

• If Proved lowest 1/6 of outcomes, then any
  two-dice combination equaling 4 or less would be
  Proved.

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Outcomes of rolling six dice

• For Six Dice, Proved Could Be a Large Number of
  Dice Combinations, With Some Individual Dice With
  Numbers Well Above One.

The chance that a roll of six dice produces six
ones is 1 in 46,000!
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Outcomes of rolling six dice

• Possible Totals From 6 to 36
• Proved With Six Dice
• Lowest 1/6 of all possible outcomes
• Any combination of dice totaling 17 or less
• Average value per die of 2.8, or 280 the
  Proved value when rolling only one die
• Some individual dice could have the highest
  possible value of 6

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Summing Reserves

• How Do We Add Reserves?
• Reserves are added by maintaining the uncertainty
  in the combined population of outcomes.
• Statistically, this can be accomplished by adding
  the Means and the Variances.
• See SPE 73828 for formulas

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Summing Reserves

• Another Way To Add Reserves is to Sample The
  Overall Distribution From The Perspective Of An
  Entire Drilling Project.
• Example Reserves For Undeveloped Drilling
  Locations
• Assume the reserves distribution on the following
  slide
• Assume a certain number of locations are
  available for drilling

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Summing Reserves
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Summing Reserves

• If We have One Drilling Location
• P10 Proved Reserves 0.046 Bcf
• P50 Probable Reserves 0.222 Bcf
• P90 Possible Reserves 1.321 Bcf
• What if We Have Two Drilling Locations?
• We have to determine P10, P50 P90 outcomes for
  two-well pairs

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Summing Reserves

• We Can Perform A Monte Carlo Simulation of
  Two-Well Outcomes
• Randomly sample the distribution twice
• Compute the average reserves from this two-well
  sample
• Treat the two-well average reserves as a new
  random variable
• Monte Carlo the two-well average variable

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Summing Reserves
This Distribution is Defined As RiskLognorm(0.5,
1, RiskTruncate(0.01, 5))
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Summing Reserves
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Summing Reserves

• Now The Proved Reserves Per Well Have Increased!
• 0.091 vs. 0.046 Bcf
• But The P90 (Possible) Reserves Have Decreased
• 0.914 vs. 1.32

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Summing Reserves

• For A 10-Well Program

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Summing Reserves

• For A 100-Well Program

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Summing Reserves
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Summing Reserves
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Summing Reserves

• As The Size Of The Drilling Program Increases
• The variance decreases (spread between the P10
  P90 reserves
• The Mean expectation remains unchanged
• The per-well P10 P50 reserves increase, with
  the P50 reserves nearing the Mean reserves
• The P90 reserves decrease
• The average per-well reserves distribution
  approaches a normal distribution for large
  drilling programs

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Summing Reserves - Implications

• If Two Companies Have Similar Acreage In The Same
  Play
• The company with more drilling locations, can
  book higher per-well proved reserves (P10)
• Both companies would have the same expected value
  per-well since the Mean is used to determine the
  value of the wells

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Summing Reserves - Implications

• Current Industry Practice of Using P10 as a
  Criteria for Proved Reserves
• Creates a large gap between Proved reserves (P10)
  and Asset Value (Mean), especially in
  Unconventional Resources
• Makes Proved reserves of little business value
  other than as a floor to corporate value
• Does not reflect the Expected Value of the
  reserves
• Shows the need for conveying the entire reserves
  distribution rather than just this one small piece

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Summing Reserves

• To Sum Reserves, Do One Of Two Things
• Model the combined process and/or distributions
  using Monte Carlo techniques
• Add the Means and Variances using statistical
  equations
• Either requires you to generate probability
  distributions

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Summing Reserves

• The Prior Examples Are For Assigning Reserves To
  Wells Before They Are Drilled
• To Apply This To Producing Wells, The Concept Is
  The Same, But You Must Have A Method To Determine
  P10, P50 P90 Production Forecasts

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Bootstrap Method

• One Method For Determining Probabilistic Reserves
  For Production Data Is The Bootstrap Method
• Outlined in Lecture 9

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Bootstrap Method For DCA Analysis

• Single-Well Forecast Confidence Levels
• P10, P50 P90 for the remaining life of a single
  existing well
• Deals Effectively With Noise in Production Data
• More noise greater range between P10 P90
• Does Not Require Any a priori Knowledge about DCA
  Parameters (Qi, Di, b) But it Generates Them
  for You!!!
• Repeatable No Matter Who Does The Analysis

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Bootstrap Method For DCA Analysis

• See SPE Papers 36633 95974
• Randomly Samples Historic Production Data To
  Create a Synthetic Production Curve
• Uses Sampling With Replacement
• If you have 50 historic data points, perform 50
  random samples with replacement
• Some historic data points will be duplicated,
  some omitted
• Regression-Fit the synthetic curve to find DCA
  parameters (Qi, Di, b)
• Repeat until a large number of synthetic
  production curves are generated Now you have a
  Qi, Di, b distribution set to work from.

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Bootstrap Method For DCA Analysis

• Much Improved Forecasts May Be Possible If You
  Use Subsets of Your Production Data (i.e. recent
  data) And If You Use the Modified Bootstrap
  Method.

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DCA Forecast Using All Historical Data
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DCA Forecast Using Last 4 Years of Data
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DCA Forecast Using Last 2 Years of Data
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Bootstrap Example
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Bootstrap Example

• 100 Iterations Of Generating Copies of The
  Production Data Using The Bootstrap Method
• Used Excel Solver to regress on each copy to
  generate Qi, Di b
• Ranked each iteration by EUR
• Picked P10, P50 P90 curves based on ranking

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Bootstrap Example
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Bootstrap Example
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Bootstrap Example

• The Distribution of The Bootstrap Outcomes is a
  Normal Distribution
• Therefore P50 Mean
• This may not be the case for all Bootstrap
  outcomes on other data sets

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Bootstrap Example
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Bootstrap Example

• A Least Squares Regression Of The Raw Data Gives
  Us Essentially The Same Curve As The P50 Case
• The Least Squares Fit Is The Usual Way Reserves
  Auditors Make Decline Curve Projections For
  Proved Reserves
• Proved Least Squares P50
• If normally distributed, then Least Squares
  Mean Proved reserves can be added.
• These Proved reserves ARE NOT P10 reserves

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Bootstrap Example

• What Does This Mean?
• In practice, Proved Developed Producing Reserves
  may in fact be similar to a P50 or Mean case, and
  if so then can be added
• Industry is not prepared to apply a more
  sophisticated probabilistic approach to generate
  a true P10, P50, P90 distribution of production
  forecasts

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Bootstrap Example

• This Example Only Addresses Uncertainty In The
  Production Data
• Deals with how to weight individual data points
• Could be tied to a reservoir simulator for
  forecasting rather than regressing on a decline
  curve equation
• Does not address uncertainty in reservoir
  description of reservoir model

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Distribution Types

• How Do You Choose A Distribution Type For Various
  Data?
• Reservoir pay, perm, porosity, OGIP, etc.
• Reserves
• Economic Inputs product prices, operating
  costs, etc.
• Some Data Tend To Follows A Certain Distribution
  Type

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Distribution Types

• The Central Limit Theorem (CLT)
• Adding or subtracting distributions will tend
  towards a normal distribution
• Multiplying or dividing distributions will tend
  towards a log-normal distribution

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Distribution Types

• Triangular Distributions From SPE 73828
• Distributions Added/Multiplied etc. As Shown Below

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Distribution Types
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Distribution Types

• Recommend Uniform, Triangular, Normal
  Log-Normal Distributions Unless You Have Good
  Reason To Use Something Different
• Per-Well Reserves, Permeability, Drainage Area
• Log-Normal
• Porosity, Drilling Package Reserves
• Normal to Log-Normal
• Decide For Yourself If You Have Sufficient Data

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Distribution Types

• Correct Distribution Will Be A Straight Line On A
  Probability Scale

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Scoping Analysis

• Scoping Analysis Example
• Use spreadsheet Scoping.xls
• We will build a scoping analysis in class,
  complete a matrix of outcomes and show how to
  make business decisions from this matrix of
  outcomes.

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Learning Objectives/Accomplishments

• Now You Should Be Able To
• Sum reserves classes at the well, field and
  company level
• Generate reserves classes from Decline Curve
  Analysis
• Know what distribution type to choose
• Set up a probabilistic scoping analysis

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End Lecture 11 Applied Probabilistic Reserves