Formation Factors of Unconsolidated Porous Media: Influence of Particle Shape and Effect of Cementation
Authors: Wyllie M.R.J. , Gregory A.R. 
Published: April 2012

Abstract
The literature reveals that scant attention has been paid to the systematic experimental determination of the formation factors of unconsolidated porous media. No experiments appear to have been made on the effect of increasing cementation on the formation factor of an initially unconsolidated porous medium.
Measurements have accordingly been made of formation factors as a function of porosity for aggregates of spheres in the porosity range 12–56 per cent and of cubes, cylinders, discs and triangular prisms in the porosity range 30–45 per cent. The results are examined in the light of the theoretical equations of Clerk Maxwell, Fricke and Slawinski.
Aggregates of unconsolidated spheres and beach sands have been artificially cemented with silica and the formation factor-porosity relationships determined. A theory is outlined which seeks to explain the results obtained and which postulates that formation factor and porosity data for consolidated sandstones may be used to determine the original porosity of the unconsolidated sands from which the consolidated sandstones were derived.

Introduction
All schemes of electric log interpretation implicitly or explicitly require the use of formation resistivity factors or, as they are now generally called, formation factors. The originator both of the concept of formation factor and of the use of formation factor data in electric log interpretation was Archie. More recently it has been suggested that formation factors are of value in describing fluid flow in porous media. A full discussion of this problem together with adequate references has given by Wyllie and Spangler.
In spite of the theoretical and practical importance of the subject, there appear to be remarkably few basic formation factor data in the petroleum literature. A wider search reveals that this situation is not confined to the literature of the petroleum industry.
At various times over the last century, attempts have been made to compute the theoretical relationship between the formation factor and porosity of simple systems of unconsolidated particles. However, the formulae derived are not all identical and the experimental evidence adduced in support of each is not wholly convincing. Most of the experimental work has been carried out on systems of unconsolidated spheres, although some attention has been given to systems of spheroids and cylinders. Other simple shapes have received neither theoretical nor experimental investigation. The writers feel that a better understanding of the formation factors of complex systems of practical importance requires a firm foundation of reliable experimental data applicable to simple systems. Accordingly, they have reviewed the relevant literature and have determined experimentally the relationship between the formation factor and porosity of unconsolidated aggregates of particles of regular geometrical shapes. Some experiments have also been carried out to investigate the effect of cementation on the formation factor-porosity relationship.