Hyucksoo Park, Céline Scheidt and Jef CaersStanford University

Scenario Uncertainty from Production Data:Methodology and Case Study

History matchingand quantifying uncertainty

Geosciences: create multiple complex reservoir modelsStructureFaciesPetrophysical properties

History matching: an evolutionFocus on matching the data → unrealistic modelsmatch data + look realistic → unrealistic uncertainty

Only matching data risks understating uncertainty

Uncertainty quantification

We can verifyWhether our models match the production dataWhether our models match any other dataWhether our models are geologically realistic

We cannot verify whether the uncertainty quantification is realisticAll such tests rely on assumptions that invalidate them

Let’s try the rejection argument

Karl Popper: physical processes are laws that are only abstract in nature and can never be proven correct, they can only be disproven/falsified with facts or data

Popperism: No model can be proven correct; models can only be falsified

Geosciences as an interpretative science

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: to reject scenarios without

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Look at data: make interpretationsDepositional modelType of fracture hierarchiesRock Physics modelFault Hierarchy

Application to reservoir case study

New well planned

P1

P2

P3

P4

West-Coast Africa (WCA) slope-valley system

Data: geology and production

TI1: 50% TI2: 25% TI3: 25%

Scenario uncertainty:

3 training images

ProductionData:

Water rate/well

Generate initial ensemble of 180 scoping models

TI1: 50% TI2: 25% TI3: 25%

Production data & 180 Scoping runsW

ater

rate

Time/Days

Well 1 Well 2

Well 3 Well 4

Two modeling questions

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P odel, | ata

: reject low probability training images

: create history matches with the remaining on

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Trying to falsify with dataMDS: distance = difference in water rate response for all wells

9 dimensions = 99% of variance

Production data

TI1 responsesTI2 responsesTI3 responses

f (Data | TIk )Kernel density estimation in 9D

| PP |

| Pk k

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f TI TITI

f TI TI

dataData

data

1P | 0.8% TI Data 2P | 38.5% TI Data 2P | 60.7% TI Data

for TI1 for TI2 for TI3

History match for each TIRegional probability perturbation

Why regional PPM? Geological realism Works for facies models Easy optimization with region parameters

Streamline geometry at final time step

Example of region geometry

History match results for all TIsCPU: Average of 24 flow simulations/model

A few history matches

Notice the absence of any region artifacts

From TI2 From TI3

Rejection sampler on TI and facies

1. Draw randomly a TI from the prior

2. Generate a single geo-model m with that TI

3. Run the flow model simulator to obtain a response d=g(m)

4. Accept the model using the following probability

2

RMSE( , ( ))exp

2obs gp

d m

Rejection sampler results

Comparison

P(TI1|D) P(TI2|D) P(TI3|D) Runs/model

Method 1% 38% 61% 24

Rejection Sampler 3% 33% 64% 250

Prediction in newly planned well for next 1 year

Water rate prediction from method

Water rate prediction from Rejection Sampler

P10, P50 and P90 quantiles?

P90

P50

P10

Conclusion

What is the practical appeal of the method ?

Reject production data-inconsistent geological interpretationsNo history matching needed

Software engineeringNo explicit model parameterization neededEasy integration with any geosciences softwareComputationally feasible

Applicable to any type of scenario uncertaintyRock physics modelingFracture modeling etc…

Acknowledgement

Chevron for dataDarryl Fenwick for streamline simulationAlexandre Boucher for MPS support

Conclusion

What is the practical appeal of the method ?

Reject production data-inconsistent geological interpretationsNo history matching needed

Software engineeringNo explicit model parameterization neededEasy integration with any geosciences softwareComputationally feasible

Applicable to any type of scenario uncertaintyRock physics modelingFracture modeling etc…