3D Model Uncertainty

Renaud Meunier - November 2013

Model-derived uncertainties or uncertainty about models

Geomodels• A 3D geomodel is a numerical representation of the reality

• It is used to compute uncertainty on global parameters:− Volumes (OOIP)− Production forecast

• It is possible to compute statistics locally (e.g. cell by cell)

• Questions:− What are the values of these statistics?− Could they help to predict properties or forecast production?

o At the global and local scales?

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Geomodeling workflow

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Uncertainty is present at each step

Where is uncertainty coming from?

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• "We deal with one reservoir only, but our knowledge of it is such that several reservoir models are compatible with our priori knowledge and data" (Dubrule, Geo-statistics for Seismic Data Integration in Earth Models, 2003)

• We have several solutions matching the data that we have− Not enough certain data (e.g. well logs)− Uncertain or imprecise data (e.g. seismic)

o A matter of scale

• Consequence:− We cannot predict with exactitude the reality

Global vs local prediction

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• The 3 maps below are different

• But their statistics are the same

• Global uncertainty will be the same but local uncertainty will be different, e.g.:

− volumes (global)− new well location (local)

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Nb Ech : 40000Minimum: 0.10Maximum: 35.00Moyenne: 1.69Ec-Type: 2.34

How is the uncertainty measured?

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• We can simulate by stochastically varying key parameters

• For global uncertainty we can “cumulate” the uncertainty coming from each input parameters

• This approach can be generalized to production data:− By simulating flow in the model with varying dynamic parameters

o If too long, an approximation by experimental design can be used

P90

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1.1e+008 1.1e+008 1.1e+008 1.2e+008 Volumes (m3)

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e.g. <OOIP>=<GRV>*<NtG>*<φ>*(1-<Sw>)/Bo

Quality of uncertainty computation

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• We need to find a minimal uncertainty on variable parameters

• The uncertainty level depends on the degree of heterogeneity of the variable

− Link to the data samplingo Number of observations (should increase with the heterogeneity)o Position in space (better when uniformly sampled)

• Assuming same variable and field (i.e. same heterogeneity)

- uncertainty+ uncertainty

Heterogeneity Examples

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Sylvinite beds in potash mines can be continuous over long distances

Shoal in carbonate environment can be very heterogeneous (less than the typical reservoir cell size)

Consequences: - More heterogeneous our system is less we can predict at the local scale- But the global scale prediction still holds as long as the statistics (i.e. PDF) are accurate

Courtesy Jeffrey Yarus and Richard Chambers

Underwater photograph of a reef front off Discovery Bay, Jamaica. Water depth is ~7 meters. (Noel James, 1983; from AAPG Memoir 33)

Global parameters uncertainty

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GRV N/G Φ Sw

Random number generation

GRV x N/G x Φ x (1-Sw)STOOIP = -----------------------------

Bo

Need to take into account correlation between variables to get the right amount of uncertainty

Knowing the histograms or PDF, global uncertainty quantification can be done by a Monte-Carlo approach

Radical errors

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• Incertitude are computed on a mathematical model− Geostatistical simulation (PDF + Variogram + Data (hard and soft)) [1]− Geostatistical inversion ([1] + physical forward model)

• However it is possible to get radical errors occurring if the model is not realist

− e.g. Presence of a sub-seismic faulto seal problemo structural problem +- 10m below or above target

• This type of error is not captured by uncertainty quantification− Could have a minimum impact on reserves but a strong one on local

parameters (e.g. reservoir top, connection between blocks)

What can be done?

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• A model is not a measure of the reality− It is our numerical approximation of the reality

• To minimize the error we need to integrate data of different natures and of different scales

− Well logs, cores− Seismic, Gravimetric, EM…− Dynamic synthesis (basic reservoir engineering)

o Generally not taken into account in static model building

• The geomodel quality then depends on the amount of information (knowledge) that it incorporates.

− Integrating inputs (knowledge) from various disciplines helps reducing the risk of radical errors.

Consistency with dynamic synthesis• Dynamic synthesis allows defining the hydraulic connection

between wells and/or stratigraphic units

• Geomodels are expected to reproduce these connections− If not, History Match will be very difficult

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Consistency with dynamic synthesis• There is no geostatistical algorithm honoring connections

− Connections can be managed only by workflows linking geostatistical and morphological tools

• Connections can be checked by mean of connected bodies

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Connected wells

• Solving wells connection inconsistencies:− Modify local Vertical Proportion Curves to allow the presence of

connecting facies between the wells or at the contact between units

Consistency with dynamic synthesis

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VPC @ well1 VPC @ well2VPC between wellsConnecting facies in blue

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The null proportion of connectingfacies between wells cuts the hydraulic connection

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The presence of connecting facies between wells allows the hydraulic connection

Conclusion (1)

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• Geomodels are representations of the reality not the reality itself

• Uncertainty is due to lack of precise data (e.g. well control), imprecise data (e.g. seismic), impossibility to conceive with certainty a conceptual model

• Model uncertainty can be accessed by stochastically varying the model parameters and generating equiprobable outcomes

Conclusion (2)

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• Even if uncertainty on a global parameter is low, the prediction capability at local scale may be poor

− Low uncertainty on OOIP may be associated with poor properties distribution prediction at local scale in heterogeneous environments

− Difference between local and global uncertainty− Conceptual uncertainty require a scenario based approach

• Geomodel quality depends on the amount of information (knowledge) that it incorporates.

− Integrating knowledge from various disciplines helps reducing the risk of radical errors