Uniform Random Field Morphing for Reservoir History Matching
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Solution Overview
Problem
Existing history matching methods for geostatistical reservoir models are complex and limited, particularly due to the need for Gaussian score transformations and the restriction on combination coefficients when combining uniform random fields, which complicates the preservation of geological features and statistical integrity.
Innovation Solution
A method that modifies uniform random number fields by linear combination without Gaussian score transformations, using uniform score transformations to derive a modified uniform field, allowing for a wider range of combination coefficients and applicable to various geostatistical models, including multiple point statistics models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Gaussian score transformations are used to combine uniform random fields, then the statistical integrity is preserved, but the device complexity increases and the combination coefficients are restricted
Solution Approach 1:
The patent extracts and eliminates the Gaussian score transformation step from the history matching process. By working directly with uniform random fields and their cumulative distribution functions, the method removes the complex Gaussian transformation layer while preserving the ability to combine fields linearly with unrestricted coefficients, thereby simplifying the overall process.
Solution Approach 2:
The patent changes the parameter space from Gaussian-distributed fields to uniform-distributed fields. This parameter transformation allows linear combination of random fields without requiring the coefficients to satisfy specific constraints (such as sum of squares equal to 1), thereby increasing flexibility and reducing computational complexity.
2Measurement precision
If Gaussian score transformations are applied to uniform fields, then the model predictions are accurate, but the ease of operation decreases due to restricted combination coefficients
Solution Approach 1:
Instead of transforming uniform fields to Gaussian fields and then combining them (as in conventional methods), the patent inverts the approach by combining uniform fields directly and then transforming the result. This inversion eliminates the need for coefficient restrictions and simplifies the operational process while maintaining prediction accuracy.
3Adaptability or versatility
If uniform random fields are combined with unrestricted coefficients, then the space of possible solutions increases, but the preservation of geological features becomes challenging
Solution Approach 1:
The patent employs feedback through the cumulative distribution function transformation. After linearly combining uniform random fields with unrestricted coefficients, the method applies a feedback transformation using the empirical cumulative distribution function to normalize the result back into a uniform field. This feedback mechanism ensures that geological features and statistical properties are preserved while allowing unrestricted coefficient flexibility.
Data Source
AI summary
A method for creating a modified realization of a geostatistical model of a subterranean hydrocarbon reservoir is described, which may be used in a history matching process. The modified realization is based on a current realization which is a function of a first uniform random number field. At least one further uniform random number field Ui is created and a linear combination made of the first uniform random number field and the further uniform random number field or fields Ui, together with combination coefficients ri, to derive a modified non-uniform random number field V. A uniform score transformation procedure is then performed, e.g. using an empirical cumulative distribution function, on the modified non-uniform number field V, to derive a modified uniform random number field Umod. A modified realization of the model can then be derived from the uniform random number field Umod.