Evaluation of drying shrinkage effects on the elastic properties of porous sandstones using a modified micromechanical model

Abstract

SUMMARY The effects of pore fluids on the elastic properties of sedimentary rocks can be broadly categorized into two mechanisms: variations in pore compressibility due to the physical properties of the fluids and alterations in the stiffness of the rock frame resulting from rock–fluid interactions. Particularly, as rock–fluid interactions alter the stiffness of contacts between mineral grains, changes in the fluid properties around grain contacts can induce volumetric deformation of the rock as well as in variations of the associated elastic coefficients. Even though many previous studies have explored the influence of swelling of clay minerals, the relationships between changes in elastic moduli and deformation in rocks, which hardly contain swellable minerals, remain to date enigmatic. In this paper, to evaluate quantitatively these effects, drying rates, strains and ultrasonic velocities of small cylindrical Berea sandstone samples were measured as their water saturation was decreased by evaporative drying. The measurements clearly showed drying shrinkage and drastic increases in shear and compressional moduli for all the samples under an almost fully dried condition. Previous studies considered that the alteration in surface energy of grain minerals between wet and dry states affected the contact stiffness between them. Some of them used micromechanical model, uniting the Digby grain contact model with the effective medium theory, to interpret the changes in elastic moduli observed in the non-swellable sandstones during water adsorption on the grain surface. The conventional micromechanical model assumes that a mineral grain is a pure sphere and that the number of contacts between the grains is one. However, grains in a sedimentary rock are generally not purely spherical, and the contact surface is composed of several adhesive asperities. We therefore modified the conventional model by introducing the curvature radius and the number of asperities per contact surface. The modified model well reproduced the shear moduli under wet conditions using the strain and moduli measured under dry conditions. On the other hand, the predictions of the compressional moduli using the model were partially in agreement with the experimental results. Therefore, we attempted to qualitatively interpret the relationship by combining the model with the viscoelastic effect associated with wave-induced fluid flow. The deformation and changes in the elastic moduli of rocks resulting from multiple pore fluids within them can be better understood by the present combined model.