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Paper   IPM / P / 14625
School of Physics
  Title:   Assessment of petrophysical quantities inspired by joint multifractal approach
1.  Z. Koohi Lai
2.  S.M.S. Movahed
3.  G.R. Jafari
  Status:   Preprint
  Year:  2016
  Supported by:  IPM
In this paper joint multifractal random walk approach is carried out to analyze some petrophysical quantities for characterizing the petroleum reservoir. These quantities include Gamma emission (GR), sonic transient time (DT) and Neutron porosity (NPHI) which are collected from four wells of a reservoir. To quantify mutual interaction of petrophysical quantities, joint multifractal random walk is implemented. This approach is based on the mutual multiplicative cascade notion in the multifractal formalism and in this approach L0 represents a benchmark to describe the nature of cross-correlation between two series. The analysis of the petrophysical quantities revealed that GR for all wells has strongly multifractal nature due to the considerable abundance of large fluctuations in various scales. The variance of probability distribution function, λl2, at scale l and its intercept determine the multifractal properties of the data sets sourced by probability density function. The value of λ0 2 for NPHI data set is less than GR's, however, DT shows a nearly monofractal behavior, namely λ0 2→0, so we find that λ02(GR) > λ02(NPHI) >> λ02(DT). While, the value of Hurst exponents can not discriminate between series GR, NPHI and DT. Joint analysis of the petrophysical quantities for considered wells demonstrates that L0 has negative value for GR-NPHI confirming that finding shaly layers is in competition with finding porous medium while it takes positive value for GR-DT determining that continuum medium can be detectable by evaluating the statistical properties of GR and its cross-correlation to DT signal.

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