Вероятно Вы говорите о стать в SPWLA R Agillera, у него было несколько работ посвященных поведению "м" на Пикетте для разных типов пористости. В частности математически выводилось, что для системы вертикальных трещин "М"-->1

Paper 2003 v44n1a1

Improved Models for Petrophysical Analysis of Dual Porosity Reservoirs

Maria Silvia Aguilera
Servipetrol Ltd.
Roberto Aguilera
Servipetrol Ltd.

ABSTRACT: The analysis of vuggy and fractured reservoirs has been an area of significant interest in the past few past years. Several researchers have studied the characterization of these reservoirs and have looked for means of estimating values of the porosity exponent m for use in calculations of water saturation. We have found that some of the models for nonconnected vugs fail for certain combinations of matrix and non-connected vug porosities. The reason for the failures is an improper scaling of the matrix porosity. The same scaling problem is present in some of the models to analyze naturally fractured reservoirs but the magnitude of the error in the calculation of m is very small for most cases of practical importance. We present an improved model for reservoirs with non-connected vugs that is shown to hold for all combinations of matrix and non-connected vug porosities. The model is validated with data for carbonate reservoirs published previously in landmark works by Lucia (1983, 1995). We also present an improved model for reservoirs with natural fractures and/or connected vugs.

Paper 2004 v45n2a4

A Triple Porosity Model for Petrophysical Analysis of Naturally Fractured Reservoirs

Roberto F. Aguilera
Servipetrol Ltd.
Roberto Aguilera
Servipetrol Ltd.

ABSTRACT The analysis of vuggy and fractured reservoirs has been an area of significant interest in the past few years. Several researchers have studied the characterization of these reservoirs using dual porosity models and have looked for means of estimating values of the dual porosity exponent m for use in calculations of water saturation. There are instances where the reservoir is composed mainly of matrix, fractures and non-connected vugs. In these cases a triple porosity model appears more suitable for petrophysical evaluation of the reservoir. A new technique is presented for these types of reservoirs that is shown to hold for all combinations of matrix, fracture, and non-connected vug porosities. At low porosities, the fractures dominate and the m values of the composite system tend to be smaller than the porosity exponent of the matrix (mb). As the total porosity increases, however, the effect of the non-connected vugs becomes more important and m of the triple porosity system can become larger than mb. To the best of our knowledge a solution to the problem associated with the triple porosity exponent has not been addressed previously in the petrophysical literature. This research is inspired by the availability of modern magnetic resonance, micro-resistivity and sonic image tools that permit reasonable characterization of complex reservoirs. The use of the triple porosity model is illustrated with an example.