an integrated partial least square -monte carlo model for risk assessment of petroleum development

7/31/2019 An Integrated Partial Least Square -Monte Carlo Model for Risk Assessment of Petroleum Development

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Lecturer: Wang Zhong

Chengdu University of Technology, Chengdu, China

An Integrated Partial

Least Square -Monte

Carlo Model for Risk

Assessment of Petroleum

Development


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Outline


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Highinvestment

HighProfits

3H 1L

A B

Longperiod

D

Highrisk

C

1. Features of Oil & Gas development projects

Risk analysisplays animportant rolein projectsfeasibilityevaluation

How to assessrisk scientifically

and enhanceeconomic benefithas become abottleneck ofChinas oil & gas

industry


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2. Simply review of the methods

Grey theory

Risk probability analysis

Fuzzy Comprehensive Evaluation

Artificial neural network (ANN) Sensibility analysis

Expert System (AHP, Delphi)

Monte Carlo simulation

Stochastically simulate

the dynamic relationship

between variables

Rapid development of

computer science and

technology

MC becomes the most

popular approachby

major oil companies


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3 Shortages of MC in practice

As far as I know, MC was used to assess risk ofpetroleum exploration and development, mostlybased on NPV formula.

0

( ) (1 )n t

t

t

NPV CI CO i

CIcash in every year COcash out every year ttime idiscount rate

NPV is the total present value of a time series. Each cash flow is discounted back

to its present value, and then they are summed. NPV compares the value of dollar

today to the value of that same dollar in the future, taking inflation and returnsinto account. if NPV>0, that means this project is profitable, and also it should be

accepted.

In risk analysis, assuming NPV is a variable, and the probability of NPV>0 is an

important index. If the probability is small, that means this project is highly likely

to loss. So the lager the P value, the lower risk.


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3 Shortages of MC in practice

By using the NPV formula, CI and CO need to beestimated. However, due to the features of Long

period and many uncertain variableshardly toestimate the accurate value of cash flow every year.

NPV formula can not directly reflect some important

qualitative factors, such as the management level,adaptability of technology.


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4. Regression in risk assessment

Feasibility of using regression in risk analysisof petroleum development projects.

Professor Chen(2004)demonstrated the theoreticfoundation of using regression analysis to engineering

projects risk assessment.

Zhan(2007), Sun(2008)proved that in the techno-

economic evaluation to oil & gas exploration anddevelopment projects, NPV is commonly used as the

evaluation criteria, and the relation between NPV andrisk factors is linear or approximately linear.



4. Regression in risk assessment

Defects of Ordinary Least Square (OLS )regression

Hardly to deal with correlation between independent variables:

Ignore the positive correlation: minify the risk

conduct the failure of investment

Ignore the negative correlation: magnify the risk

conduct to abandon some feasible programs

Number of independent variablesmust smaller thansamples: Due to the big difference of geologic setting between oil (gas) fields,

in petroleum development, it is extremely difficulty to find enough

samples, sometimes the number of independent variables is

comparable to or even greater than the number of samples



Outline



1. Introduction of PLSR

General principles of PLSR

PLSR is based on linear transition from a large number of original

independent variables into a new variable spacebased on latentcomponents. In other words, theses latent components are mutually

independent linear combination of original variables.

Advantages of PLSR

simplicity and robustness

Highly predicted precision, clearly qualitative explanation

Can be used to explore data and cope with multicollinearity

Particularly powerful when the number of predictor variables is large

and the sample size is small



2. Monte Carlo simulation

Theoretical foundations of MC

Law of large numbers

Central limit theorem

General principles of MC By letting computer recalculate the model over and over again, and each

time using different randomly selected sets of values from input probability

distribution, the computerused all valid combinations of possible input to

simulate all possible outcomes. If the times of simulation are enough, the

results can take place the real situation.

introduction of MC

A method foranalyzing uncertainty problems. Its goal is to determine how

random variation affects the sensitivity, performance, or reliability of the

system in the condition of lack of knowledge or error



3. The PLS-MC model

Feasibility of using regressionin risk analysis

Superiority of MC in dealingwith uncertainty problems

Defects of ordinary LeastSquare regression

Tried to combinethe advantages

of PLS and MC

toproposed an

PLS-MC model



Build a PLS regression model

Determine distribution of inputs Uniform Distribution

Lognormal Distribution

Triangle Distribution

Normal Distribution

Calculate the through the

regression model and store the

result

Analyze the results

m

simulation

1 2( , , , )nNPV f x x x

iNPV

Generate a set of random inputs

1 2( , , )i i inx x x

Key and difficulty

By experts (geologists,engineers, economists)

By historical data

Shape of distribution

Variance

Confidence intervals

Probability of NPV>0

The simulation can

be accomplished by

EXCEL



Outline



1. Basic information of example

Xinchang gas-field located in Sichuan Basin, it is one

of the biggest gas-field in China.

Now there are some new prospects have been

explored and need to be developed immediately. In

order to assess the risk of the development projects,

ten prospects in this gas-field that have been

developed before were chosen as the samples.


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2. Parameters selection

Giving consideration to the actual situation of Xinchanggas-field and according to early studies, 9 risk variableswere selected as predictors and NPV was selected asresponse:

X1technical difficulty and adaptability (quantified by experts) X2operation management level (quantified by experts)

X3investment (million Yuan)

X4gas price(Yuan/m3)

X5gas production volume(108m3 )

X6interests (million Yuan)

X7operation cost (million Yuan)

X8floating capital (million Yuan)

X9taxes and fees (million Yuan)

Y NPV (million Yuan).


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3. Original data of 10 developed projects

Program

No.X1 X2 X3 X4 X5 X6 X7 X8 X9 Y

1 8 7.5 4776 6.19 4.3 293.7 364.1 70.7 709.5 1506.2

2 8 8 6868 6.16 4.4 422.3 786.2 141 916 2729.7

3 8.5 8.5 8888 6.41 5.5 432.2 1015.8 143 1817.8 4174.2

4 9 9 7018 6.06 4.5 431.5 1119.2 152 2119.8 3725.3

5 8 8.5 7169 6.34 4.2 440 1036.2 149 1656.2 2987.3

6 8.5 8 7318 6.94 4 450 1902.8 146 1453.1 2650.33

7 8 7 15190 6.82 4.5 934 467.9 61 526.5 3490.5

8 8 7.5 10850 6.69 4.2 667.1 499.8 47 1109.2 2876

9 7.5 7 12100 6.76 4 744 511.7 58 2963.1 2371.2

10 7.5 7 12000 6.91 4.2 723 510.3 55 2867.4 2280.4


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3. Distribution

Type ofdistribution

Maximum Minimum The mostlikely

value

Expectationvalue

Variance

X1 triangle 7 8 9.5

X2 triangle 6 7 9

X3 normal 9000 2000

X4 normal 6.4 0.5

X5 triangle 4 4.5 6

X6 normal 0.06 X3 100

X7 normal 700 200

X8 normal 0.01 X3 20

X9 normal 0.15 X3 500

Lack of enough historical data, these

distributions were determined by experts


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4. Build PLS regression equation

987654321

1.0

0.9

0.8

0.7

0.6

optimal

response is NPV

87654321

1.0

0.8

0.6

0.4

0.2

0.0

optimal

Fitted

Crossval

Variables

response is NPV

1 2 3

4 5 6

7 8 9

107.1 946.9 0.1

69.7 661.9 1.5

0.1 1.5 0.1 10798.3

Y x x x

x x x

x x x

1 2 3

4 5 6

7 8 9

3697.1 1711.1 2.4

4865 5898.4 44.7

7.2 58.4 0.1 22876.7

Y x x x

x x x

x x x

Made a mistake: did not use the

cross validation, 9 components were

selected as the best model

Tried again with Cross-Validation,

7 components were selected as the

best model

Another point is amazing, the equation

fitted by PLS without Cross-Validation is

identical with the equation fitted by OLS.

Nevertheless, it give me a chance to

compare these two methods in risk

assessment

By using the PLS toolbox of MINITAB


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5. Fitting results Comparison

4500400035003000250020001500

4500

4000

3500

3000

2500

2000

1500

response is NPV

9 components

4500400035003000250020001500

4500

4000

3500

3000

2500

2000

response is NPV

52612 1254Y x

4500400035003000250020001500

4500

4000

3500

3000

2500

2000

1500

response is NPV

7 components

included only one variable,

can not reflect the risk

comprehensively; and the fitting

results is not so good.

So chose the first two models

to compare.


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6. Results of MC simulation

20000150001000050000-5000-10000

80

70

60

50

40

30

20

10

0

Mean 4721

StDev 5637

N 1000

N orm al

5600480040003200240016008000

90

80

70

60

50

40

30

20

10

0

Mean 2696

StDev 1015

N 1000

N orm al

0.0004

0.0003

0.0002

0.0001

0.0000

0.9

2696

Normal, Mean=2696, StDev=1015

0.00008

0.00007

0.00006

0.00005

0.00004

0.00003

0.00002

0.00001

0.00000

0.9

4721

Noramd, Mean=4721, StDev=5637

At the level of 90%, Confidence interval:

NPV(I)[-4551, 13993]; NPV(II)[1026, 4366]In contrast with samples[1506 4174], the range of

NPV(II) is maybe more rational and more reasonable.

NPV(I)

OLS model

NPV(II)

PLS model

From the shape of the NPVs possible outcome, the

NPV(I) is more scattered, and the NPV(II) is more

concentrated.


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7. Risk curve

-12000

-10500

-9000

-7500

-6000

-4500

-3000

-1500 0

1500

3000

4500

6000

7500

9000

10500

12000

13500

15000

16500

18000

19500

NPV

Accumulated

Pr

obability

The probability of NPV>0

NPV(I): P>80%

NPV(II): P>96%


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8. Conclusion

OLS PLS

Range[-11915 19675] [-12 5912]

Mean 4721 2696

Standard Deviation5637 1015

Confidence Interval (90%)[-4551 13993] [1026 4366]

Probability of NPV>0>80% >96%

>>

>>

0 are two criteria

In the light of this statement, we get the conclusions: By using OLS risk level is higher, by PLS risk level is lower OLS or PLS (without cross-validation) magnify the risk.


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Outline


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1. Significance of PLS-MC model

Take some qualitative risk factors into consideration

Solve the problems of multicollinearity and number of

samples is less than number of variables in regression

Maintain all the original variables, most adequately used

the information

Compared with the NPV formula

Compared with the Ordinary Least Square Regression

Compared with the Stepwise Regression


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2. Shortages of this paper

further study

If we can use PLS related methods

to make sure the inputs of MCsimulation are independent.

How to scientifically determine thedistributions of uncertain variablesis a big challenge


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Id highly appreciate your valuable comment and guidance!

an integrated partial least square -monte carlo model for risk assessment of petroleum development

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