Hyucksoo Park, Céline Scheidt and Jef Caers Stanford University Scenario Uncertainty from Production Data: Methodology and Case Study

History matching and quantifying uncertainty Geosciences: create multiple complex reservoir models Structure Facies Petrophysical properties History matching: an evolution Focus on matching the data → unrealistic models match data + look realistic → unrealistic uncertainty Only matching data risks understating uncertainty

Uncertainty quantification We can verify Whether our models match the production data Whether our models match any other data Whether our models are geologically realistic We cannot verify whether the uncertainty quantification is realistic All 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 Look at data: make interpretations Depositional model Type of fracture hierarchies Rock Physics model Fault 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 Production Data: Water rate/well

Generate initial ensemble of 180 scoping models TI 1 : 50% TI 2 : 25% TI 3 : 25%

Production data & 180 Scoping runs Water rate Time/Days Well 1 Well 2 Well 3 Well 4

Two modeling questions

Trying to falsify with data MDS: distance = difference in water rate response for all wells 9 dimensions = 99% of variance Production data TI1 responses TI2 responses TI3 responses

f (Data | TI k ) Kernel density estimation in 9D for TI 1 for TI 2 for TI 3

History match for each TI Regional 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 TIs CPU: Average of 24 flow simulations/model

A few history matches Notice the absence of any region artifacts From TI 2 From TI 3

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

Rejection sampler results

Comparison P(TI 1 |D)P(TI 2 |D)P(TI 3 |D) Runs/ model Method1%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 interpretations No history matching needed Software engineering No explicit model parameterization needed Easy integration with any geosciences software Computationally feasible Applicable to any type of scenario uncertainty Rock physics modeling Fracture modeling etc…

Acknowledgement Chevron for data Darryl Fenwick for streamline simulation Alexandre Boucher for MPS support

Conclusion What is the practical appeal of the method ? Reject production data-inconsistent geological interpretations No history matching needed Software engineering No explicit model parameterization needed Easy integration with any geosciences software Computationally feasible Applicable to any type of scenario uncertainty Rock physics modeling Fracture modeling etc…