Rock-physics models for heterogeneous creeping rocks and viscous fluids

Abstract

Rock-physics models are used to explore how small-scale heterogeneity can affect the larger scale viscoelasticity of rocks. Applications include mixtures of creeping clay and elastic quartz, mixtures of different creeping materials (e.g., clay and kerogen), or viscous fluids containing bubbles or solid fines. We have found that elastic inclusions in a Maxwell viscoelastic background change the effective viscosity and the high-frequency limiting elastic modulus. The viscosity response was similar to that observed for a Newtonian fluid, and the high-frequency elastic modulus varied as predicted by elastic effective media models. The characteristic frequency of the effective medium scales with the ratio of effective modulus and effective viscosity. Inclusions also distribute the relaxation times, converting the Maxwell material to resemble a Cole-Cole material. Elastic inclusions in a creeping background decrease the effective viscoelastic Poisson’s ratio of the composite. As with elastic media, geometric alignment of phases with contrasting properties leads to viscoelastic anisotropy. Our modeling has illustrated how the amount of heterogeneity and the microgeometry of heterogeneity affects anisotropy; for example, aligned oblate elastic inclusions can increase the amount of creep in the symmetry direction while decreasing creep normal to the symmetry direction. We have developed a suggested interpretation template for how creep function parameters vary with the amount and microgeometry of elastic phases. Interpretation also depends strongly on the material properties of the creeping phase in the absence of elastic inclusions. Extrapolating from dynamic to quasi-static viscoelastic response is intrinsically nonunique without knowledge of the material microstructure. Dominant relaxation mechanisms can be different at different measurement scales and at different measurement strain amplitudes. For example, the observed dynamic response can be fit with an infinite number of microgeometries, each of which has a different long-term behavior.