SPE Journal
Volume 14, Number 4, December 2009, pp. 805-810

Summary

The usual practice is to transform intrinsic-permeability data with logarithms to get a linear relation with porosity. Such transformations are known to produce undesired effects in 3D geocellular-models (i.e., smoothing data, elimination of extreme values, and biased estimates). Ideally, logarithms of data may lead to Gaussian distributions, which are easily handled by classical spatial statistics and linear collocated-cokriging. The exponential model from back-transformed linear regression "underestimates" permeability. If the lognormal assumption is not met, a second order correction may "overestimate" permeability. Transformations of permeability data may uncover the fact that a truly non-Gaussian statistical distribution cannot be avoided, and this brings complications to the modeling of permeability. Shortcomings of transforms for non-Gaussian cases may affect the quality of reservoir models for history match forcing to the use of arbitrary multipliers. Systematically biased flow predictions might be avoided by proper modeling of flow parameters including intrinsic permeability. Truly non-Gaussian modeling of permeability is developed in this paper to find a solution to these problems. The analysis starts by linking the exponential model to power transformations from Taylor series. Residual-terms (RTs) are introduced for correct back-transformation of estimates. An advanced result, for the truly non-Gaussian case, is that the RTs take the form of numerical higher order cumulants and not moments. RTs represent the contribution of spatial heterogeneous components that occur when spatial permeability varies beyond a pair-wise covariance or variogram. Results in this paper show that "higher-order cumulants" improve permeability estimates significantly in rocks with large dispersion of values dominated by higher permeabilities (e.g., shaley sands and laminated grainstone carbonates). This study has proposed new ways for spatial modeling of permeability, avoiding under or overestimations, and the proposed approach provides the basis for the use of cumulants for spatial higher-order estimation.

© 2009. Society of Petroleum Engineers

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History

• Original manuscript received: 4 April 2008
• Revised manuscript received: 22 July 2008
• Manuscript approved: 31 July 2008
• Published online: 2 July 2009
• Version of record: 22 December 2009