Modeling Nonlinear Beta Probability Fields

Khan, K. Daniel; Vargas-Guzmán, JA

doi:10.1007/978-94-007-4153-9_7

Geostatistics Oslo 2012

2012

DOI: 10.1007/978-94-007-4153-9_7

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Modeling Nonlinear Beta Probability Fields

K. Daniel Khan¹,

JA Vargas-Guzmán²

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2013

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Facies Proportions From the Inference of Nonlinear Conditional Beta-Field Parameters

Khan

Vargas-Guzmán

2013

SPE Journal

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Summary Conditional beta distributions are proposed with examples to evaluate the probability of intercepting specific proportions of target rocks in well planning. Geological facies or rock-type proportions are random variables pk(x) at each location, x. This paper recalls and further demonstrates that facies proportions can be modeled by local beta distributions. However, the highly variable shapes of the conditional probability-density functions (PDFs) for the random variables in the field lead to complex nonstationarity and nonlinearity issues. A practical and robust approach is to transform the proportion random variables to Gaussian variables, thus enabling the use of classical geostatistics. Although a direct relationship between Gaussian and beta random variables appears intractable, a suitable transformation that involves second-order expectations of proportions is proposed. The conditional parameters of the beta variables are recovered from kriging estimates after back transformation to proportions through Riemann sums.

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Facies Proportions From the Inference of Nonlinear Conditional Beta-Field Parameters

Khan

Vargas-Guzmán

2013

SPE Journal

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show abstract

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Modeling Nonlinear Beta Probability Fields

Cited by 1 publication

References 9 publications

Facies Proportions From the Inference of Nonlinear Conditional Beta-Field Parameters

Facies Proportions From the Inference of Nonlinear Conditional Beta-Field Parameters

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