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PPT – PETROLEUM ENGINEERING 689 Special Topics in Unconventional Resource Reserves Lecture 11 Applied Prob PowerPoint presentation | free to view - id: 1dac18-ZDc1Z

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PETROLEUM ENGINEERING 689Special Topics

inUnconventional Resource ReservesLecture 11

Applied Probabilistic Reserves Texas AM

University - Spring 2007

Outline

- 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

method - 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

summing - 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

Proved.

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

Locations - Assume the reserves distribution on the following

slide - 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

sample - 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

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

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

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

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

Method.

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

forecasts

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

Data? - Reservoir pay, perm, porosity, OGIP, etc.
- Reserves
- Economic Inputs product prices, operating

costs, etc. - Some Data Tend To Follows A Certain Distribution

Type

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

outcomes.

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

End Lecture 11 Applied Probabilistic Reserves