Error estimates of elastic components in stress-dependent VTI media

Knowledge of anisotropic elastic properties of shales is important for understanding of shale compaction trends, improved seismic to well tie, nonhyperbolic moveout correction as well as for establishing a baseline for predicting properties of organic-rich shales. So far, however, building a predictive model of elastic properties of shales remains a difficult task. This might be explained by the multiparametric character of such modeling and the fact that the effects of some parameters cannot be measured and are thus poorly understood. The significant number of parameters required for prediction of the elastic properties of shale stems from its multicomponent nature. Shales are nanocomposite materials that comprise phyllosilicate clay particles with a substantial part of their grain size distribution smaller than 2 μm in radius and typically silt particles of quartz and feldspar with grain sizes between 2 and 60 μm (Mitchell & Soga, 2005). The complexity of the system is complemented by pores of micrometer to nanometer scale, whose shape and orientation are seldom characterized (Desbois, 2009). In the smallest of these pores, the filling water contributes to the stiffness and rigidity of the composite via electrostatic and van der Waals interactions (Holt & Kolsto, 2017). Attempts to model elastic properties of shales began with the classic work of Hornby et al. (1994) who modeled shale as a composite material that comprises anisotropic water-saturated clay blocks with a preferred orientation, silt inclusions, and free water. The orientation distribution function (ODF) of the clay crystals was estimated from scanning electron microscopy and the silt fraction from X-ray diffraction analysis or microtomographic images. The other unknown parameters, namely, elastic moduli of the clay blocks, aspect ratio of pores, and the fractions of free water and bound water in the clay blocks became fitting parameters.

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“…The VTI elastic properties of the clay particles

C_{i j}^{0}

are subjected to a set of physical constraints summarized, for example, in Spikes (2014):

C_{44} \geq 0,

C_{11} > | C_{12} |,

(C_{11} + C_{12}) C_{33} \geq 2 C_{13}^{2},

(C_{13} + C_{44}) > 0,

δ \geq - \frac{1}{2} (1 - \frac{C_{44}}{C_{33}}),

δ \leq \frac{2}{C_{33} / C_{44} - 1},

ε - δ > 0,

γ \geq 0,

C_{44} < C_{66},

where ε , γ , and δ are the Thomsen's (1986) anisotropy parameters:

ε = \frac{C_{11} - C_{33}}{2 C_{33}},

γ = C_{66} - C_{44}

…”

Section: Methodsmentioning

confidence: 99%

Modeling of Compaction Trends of Anisotropic Elastic Properties of Shales

et al. 2021

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“…The anisotropy parameter δ is subject to a set of physical constraints (e.g. Berryman, Grechka and Berge 1999;Tsvankin 2001;Spikes 2014). In the preserved Opalinus shale, the upper bound of δ is 0.36.…”

Section: The Fluid Substitution Effectmentioning

confidence: 99%

Water retention effects on elastic properties of Opalinus shale

Yurikov

Lebedev

Pervukhina

et al. 2018

Geophysical Prospecting

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Shales play an important role in many engineering applications such as nuclear waste, CO2 storage and oil or gas production. Shales are often utilized as an impermeable seal or an unconventional reservoir. For both situations, shales are often studied using seismic waves. Elastic properties of shales strongly depend on their hydration, which can lead to substantial structural changes. Thus, in order to explore shaly formations with seismic methods, it is necessary to understand the dependency of shale elastic properties on variations in hydration. In this work, we investigate structural changes in Opalinus shale at different hydration states using laboratory measurements and X‐ray micro‐computed tomography. We show that the shale swells with hydration and shrinks with drying with no visible damage. The pore space of the shale deforms, exhibiting a reduction in the total porosity with drying and an increase in the total porosity with hydration. We study the elastic properties of the shale at different hydration states using ultrasonic velocities measurements. The elastic moduli of the shale show substantial changes with variations in hydration, which cannot be explained with a single driving mechanism. We suggest that changes of the elastic moduli with variations in hydration are driven by multiple competing factors: (1) variations in total porosity, (2) substitution of pore‐filling fluid, (3) change in stiffness of contacts between clay particles and (4) chemical hardening/softening of clay particles. We qualitatively and quantitatively analyse and discuss the influence of each of these factors on the elastic moduli. We conclude that depending on the microstructure and composition of a particular shale, some of the factors dominate over the others, resulting in different dependencies of the elastic moduli on hydration.

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“…The described model has two parameters: a) the aspect ratio of pores , and b) the anisotropy parameter (Thomsen, 1986), which is used to calculate the 13 (Mavko et al, 2009), the only not measured component of the stiffness tensor of the VTI Opalinus shale samples. The anisotropy parameter is subjected to physical constraints reported, for instance, by Spikes (2014). According to these constraints must be less then 0.36 for the preserved Opalinus shale, which is used as the initial state for the modelling.…”

Section: Fluid Substitution and Reduction Of Porositymentioning

confidence: 99%

Experimental and Theoretical Study of Water Retention Effects on Elastic Properties of Opalinus Shale

Yurikov¹,

Lebedev²,

Pervukhina³

et al. 2018

ASEG Extended Abstracts

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Understanding of shales elastic properties behaviour with saturation changes is important for geological storage of nuclear waste, CO2 sequestration as well as for development of conventional and unconventional shale oil and gas reservoirs. Existing data describing effects of saturation on elastic properties of shales are sparse and contradictory. To improve understanding of the effects of changing water content on elastic properties in shales, we conduct an experimental study on Opalinus shale samples. We measure vertical and horizontal ultrasonic P-and S-wave velocities of the same set of samples with controlled water content. The measured velocities are used to calculate components of elastic stiffness tensor in the shale at different saturations assuming its vertical transverse isotropy. Obtained results show increasing C11 and decreasing C33 with drying of the samples. Moreover, we observe 80% and 60% increase of shear moduli C44 and C66, respectively, with reduction of the water content from 5.5% weight in the preserved state to 0.3%. Conventional rock physics models are not designed to explain the observed dynamics. Here we perform a theoretical investigation of the influence on the shale moduli of following factors: (1) mechanical softening of the rock with the decrease of water saturation; (2) shrinkage of clay leading to reduction of porosity; (3) chemical hardening of clay particles; and (4) enhancing stiffness of contacts due to removing of water between clay particles.

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Error estimates of elastic components in stress-dependent VTI media

Cited by 10 publications

References 35 publications

Modeling of Compaction Trends of Anisotropic Elastic Properties of Shales

Modeling of Compaction Trends of Anisotropic Elastic Properties of Shales

Water retention effects on elastic properties of Opalinus shale

Experimental and Theoretical Study of Water Retention Effects on Elastic Properties of Opalinus Shale

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