Boolean Spectral Analysis in Categorical Reservoir Modeling

Niyaz Ismagilov, Viacheslav Borovitskiy, Mikhail Lifshits, Mariia Platonova

Research output: Contribution to journalArticlepeer-review

Abstract

This work introduces a new method for simulating facies distribution with two categories based on Fourier analysis of Boolean functions. According to this method, two categories of facies distributed along vertical wells are encoded as Boolean functions taking two values. The subsequent simulation process is divided into three consecutive steps. First, Boolean functions of the well data are decomposed into a binary version of a Fourier series. Decomposition coefficients are then simulated over the two-dimensional area as stationary random fields. Finally, synthetic data in the interwell space are reconstructed from simulated coefficients. The described method was implemented experimentally in software and tested on a case of a real oil field and on a case of a synthetic oil field model. Simulations on the synthetic model were used to test the performance of the method for two different bases in the Fourier expansion (Walsh functions and Haar wavelets). The simulation results were compared to those obtained on the same synthetic model via the classical sequential indicator simulation. It was shown that, for both bases, the new method reproduces statistical parameters of the well data better than sequential indicator simulation.

Original languageEnglish
JournalMathematical Geosciences
DOIs
StateE-pub ahead of print - 1 Feb 2021

Scopus subject areas

  • Mathematics (miscellaneous)
  • Earth and Planetary Sciences(all)

Keywords

  • Boolean functions
  • Categorical simulation
  • Reservoir modeling
  • Spectral analysis

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