Gravel-Sand-Clay Mixture Model for Predictions of Permeability and Velocity of Unconsolidated Sediments
Abstract:Gravel-sand-clay mixture model is proposed particularly for unconsolidated sediments to predict permeability and velocity from volume fractions of the three components (i.e. gravel, sand, and clay). A well-known sand-clay mixture model or bimodal mixture model treats clay contents as volume fraction of the small particle and the rest of the volume is considered as that of the large particle. This simple approach has been commonly accepted and has validated by many studies before. However, a collection of laboratory measurements of permeability and grain size distribution for unconsolidated samples show an impact of presence of another large particle; i.e. only a few percent of gravel particles increases the permeability of the sample significantly. This observation cannot be explained by the bimodal mixture model and it suggests the necessity of considering the gravel-sand-clay mixture model.
In the proposed model, I consider the three volume fractions of each component instead of using only the clay contents. Sand becomes either larger or smaller particles in the three component mixture model, whereas it is always the large particle in the bimodal mixture model. The total porosity of the two cases, one is the case that the sand is smaller particle and the other is the case that the sand is larger particle, can be modeled independently from sand volume fraction by the same fashion in the bimodal model. However, the two cases can co-exist in one sample; thus, the total porosity of the mixed sample is calculated by weighted average of the two cases by the volume fractions of gravel and clay. The effective porosity is distinguished from the total porosity assuming that the porosity associated with clay is zero effective porosity. In addition, effective grain size can be computed from the volume fractions and representative grain sizes for each component. Using the effective porosity and the effective grain size, the permeability is predicted by Kozeny-Carman equation. Furthermore, elastic properties are obtainable by general Hashin-Shtrikman-Walpole bounds. The predicted results by this new mixture model are qualitatively consistent with laboratory measurements and well log obtained for unconsolidated sediments.
Acknowledgement: A part of this study was accomplished with a subsidy of River Environment Fund of Japan.