Predicting Resistivity and Permeability of Porous Media Using Minkowski Functionals

Per Arne Slotte,Hamid Hosseinzade Khanamiri,Carl Fredrik Berg

doi:10.1007/s11242-019-01363-2

Per Arne Slotte, Hamid Hosseinzade Khanamiri + Show 1 more

Open Access

https://doi.org/10.1007/s11242-019-01363-2

Copy DOI

Abstract

Permeability and formation factor are important properties of a porous medium that only depend on pore space geometry, and it has been proposed that these transport properties may be predicted in terms of a set of geometric measures known as Minkowski functionals. The well-known Kozeny–Carman and Archie equations depend on porosity and surface area, which are closely related to two of these measures. The possibility of generalizations including the remaining Minkowski functionals is investigated in this paper. To this end, two-dimensional computer-generated pore spaces covering a wide range of Minkowski functional value combinations are generated. In general, due to Hadwiger’s theorem, any correlation based on any additive measurements cannot be expected to have more predictive power than those based on the Minkowski functionals. We conclude that the permeability and formation factor are not uniquely determined by the Minkowski functionals. Good correlations in terms of appropriately evaluated Minkowski functionals, where microporosity and surface roughness are ignored, can, however, be found. For a large class of random systems, these correlations predict permeability and formation factor with an accuracy of 40% and 20%, respectively.

Highlights

Permeability is the most important parameter for fluid transport through porous rocks and soils, such as aquifers and hydrocarbon reservoirs
We have first generated a number of two-dimensional pore spaces by varying the allowed shapes and sizes of sub-grains and the parameters a and b in (16) without enforcing the Minkowski functionals (weights wn = 0 in (15))
Since the permeability cannot be fully determined using the Minkowski functionals, we have investigated whether a better predictor might be found using τe as an alternative to the dimensionless number λ

Summary

Introduction

Permeability is the most important parameter for fluid transport through porous rocks and soils, such as aquifers and hydrocarbon reservoirs. Tying all measured data to a set of underlying parameters will improve the credibility of these permeability estimates, and the effort to try to express the permeability in terms of a small number of underlying geometric properties goes back several decades, at least to the work of Kozeny (1927) and Carman (1937). The so-called Kozeny–Carman equation remains to this day the most popular formulation. How this equation is expressed varies somewhat throughout the literature depending on which geometric parameters are considered known and how they are expressed in terms of each other.

Objectives

Results

Conclusion