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


The variance decreases (spread between the P10 & P90 reserves ... The P90 reserves decrease ... P10, P50 & P90 for the remaining life of a single existing well ... – PowerPoint PPT presentation

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

inUnconventional Resource ReservesLecture 11
Applied Probabilistic Reserves Texas AM
University - Spring 2007
  • Summing Reserves
  • Bootstrap Method
  • Choosing A Distribution Type
  • Scoping Analysis

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.

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

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
  • Read SPE Paper 73828

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
  • The proper technique is not hard as long as the
    threshold probabilities were computed using
    actual statistical methods.

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

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.

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)).

Summing Reserves
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

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).

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

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!
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

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

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
  • Assume the reserves distribution on the following
  • Assume a certain number of locations are
    available for drilling

Summing Reserves
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

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
  • Treat the two-well average reserves as a new
    random variable
  • Monte Carlo the two-well average variable

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

Summing Reserves
  • For A 10-Well Program

Summing Reserves
  • For A 100-Well Program

Summing Reserves
Summing Reserves
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

Summing Reserves - Implications
  • If Two Companies Have Similar Acreage In The Same
  • 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

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
  • Shows the need for conveying the entire reserves
    distribution rather than just this one small piece

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
  • Either requires you to generate probability

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

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

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

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.

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

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

Bootstrap Example
Bootstrap Example
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

Bootstrap Example
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

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

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

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

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

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

Distribution Types
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

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

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

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
  • Know what distribution type to choose
  • Set up a probabilistic scoping analysis

End Lecture 11 Applied Probabilistic Reserves