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The anelastic properties of porous rocks depend on the pore characteristics, specifically, the pore aspect ratio and the pore fraction (related to the soft porosity). At high frequencies, there is no fluid pressure communication throughout the pore space and the rock becomes stiffer than at low frequencies, where the pore pressure is fully equilibrated. This causes a significant difference between the moduli at low and high frequencies, which is known as seismic dispersion and is commonly explained by the squirt-flow mechanism. In this paper, we consider and contrast three squirt-flow dispersion models: the modified Mavko–Jizba model, valid for a porous medium with arbitrary shapes of the pores and cracks, and two other models, based on idealized geometries of spheres and ellipsoids: the EIAS (equivalent inclusion-average stress) and CPEM (cracks and pores effective medium) models. We first perform analytical comparisons and then compute several numerical examples to demonstrate similarities and differences between the models. The analytical comparison shows that when the stiff pores are spherical and the crack density is small, the theoretical predictions of the three models are very close to each other. However, when the stiff pores are spheroids with an aspect ratio smaller than 1 (say, between 0.2 and 1), the predictions of inclusion based models are not valid at frequencies of ultrasonic measurements on rock samples. In contrast, the predictions of the modified Mavko–Jizba model are valid at ultrasonic frequencies of about 106 Hz, which is a typical frequency of laboratory measurements on core samples. We also introduce Zener-based bulk and shear dispersion indices, which are proportional to the difference between the high- and low-frequency stiffness moduli, and are a measure of the degree of anelasticity, closely related to the quality factors by view of the Kramers–Kronig relations. The results show that the three models yield similar moduli dispersion with very small differences when the crack density is relatively high. The indices versus crack density can be viewed as a template to obtain the crack properties from low- and high-frequency velocity measurements. [ABSTRACT FROM AUTHOR]

Estimating the effects of pore filling material on the elastic moduli or velocities of porous and fractured rocks attracts widespread attention. This effect can be modelled by a recently proposed triple-porosity scheme, which quantifies this effect from parameters of the pressure dependency of the elastic properties of the dry rock. This scheme divides total porosity into three parts: compliant, intermediate and stiff. Each type of pores is assumed to be spheroidal and characterized by a single aspect ratio. However, the implementation of this model requires the asymptotic values of the elastic moduli at much higher pressures where only non-closable pores remain open. Those pressures are beyond the capacity of most rock physics laboratories and can even crush typical sandstone samples. Experimental data at such pressures are usually unavailable. To address this issue, we introduce pore-scale numerical simulations in conjunction with effective medium theories (EMT) to compute the asymptotic values directly from the microtomographic images. This workflow reduces the uncertainty of model predictions on the geometric information of stiff pores and strengthens the predictive power and usefulness of the model without any adjustable parameters. Applying this to a Bentheim sandstone fully filled with liquid and solid octadecane gives a reasonable match between model predictions and laboratory measurements. This success verifies the accuracy and applicability of the model and indicates its potential in further exploitation and characterization of heavy oil reservoirs and other similar reservoirs. [ABSTRACT FROM AUTHOR]