A dual‐porosity scheme for fluid/solid substitution

Glubokovskikh, Stanislav; Gurevich, Boris; Saxena, Nishank

doi:10.1111/1365-2478.12389

Cited by 25 publications

(32 citation statements)

References 35 publications

(94 reference statements)

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“…Even with these effects taken into account, the dual pore structure scheme by Glubokovskikh et al . () model (red stars), give predictions very close to the values given by the lower embedded bound theory (magenta solid line), which defines the smallest change upon solid substitution that occurs in equilibrated pore space. This implies that only compliant and stiff pores might not fully describe the solid squirt effects.…”

Section: Discussionsupporting

confidence: 64%

“…Our experiments, reported later in this paper, show that the dual porosity scheme of Glubokovskikh et al . () is not sufficient to explain the data. When studying dispersion in a large number of fluid‐saturated sandstones, De Paula et al .…”

Section: Introductionmentioning

confidence: 81%

“…We extend the Glubokovskikh et al . () model to a more general case containing stiff, compliant and the so‐called intermediate pores. Intermediate pores tend to deform to a greater extent than do stiff pores but much less than do compliant pores.…”

Section: Discussionmentioning

confidence: 99%

“…In this work, we employed the solution of Tsai and Lee () suggested by Glubokovskikh et al . (). The effective compression stiffness of a circular interlayer can be expressed as

M_{f} = K_{f} + \frac{4}{3} μ_{f} - \frac{{((), K_{f} - \frac{2}{3} μ_{f})}^{2}}{(K_{f} + \frac{4}{3} μ_{f}) \frac{α γ_{f} I_{0} false(α γ_{f} false)}{2 I_{1} false(α γ_{f} false)}},

where

γ_{f} = \sqrt{\frac{36 μ_{f}}{3 K_{f} + 4 μ_{f}}}

, α = r / h is an inverse aspect ratio of compliant or intermediate pores and I k refers to a modified Bessel function of the first kind of the order k .…”

Section: Theoretical Modelmentioning

confidence: 97%

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A triple porosity scheme for fluid/solid substitution: theory and experiment

Sun

Gurevich

Lebedev

et al. 2018

Geophysical Prospecting

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Quantifying the effects of pore‐filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid‐octadecane‐saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so‐called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of the elastic moduli of the sandstone saturated with liquid or solid octadecane. Comparison of the predictions by the new model to other solid substitution schemes implied that accounting for the combined effects of compliant and intermediate pores is necessary to explain the solid squirt effects.

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Section: Discussionsupporting

confidence: 64%

Section: Introductionmentioning

confidence: 81%

Section: Discussionmentioning

confidence: 99%

“…In this work, we employed the solution of Tsai and Lee () suggested by Glubokovskikh et al . (). The effective compression stiffness of a circular interlayer can be expressed as

M_{f} = K_{f} + \frac{4}{3} μ_{f} - \frac{{((), K_{f} - \frac{2}{3} μ_{f})}^{2}}{(K_{f} + \frac{4}{3} μ_{f}) \frac{α γ_{f} I_{0} false(α γ_{f} false)}{2 I_{1} false(α γ_{f} false)}},

where

γ_{f} = \sqrt{\frac{36 μ_{f}}{3 K_{f} + 4 μ_{f}}}

, α = r / h is an inverse aspect ratio of compliant or intermediate pores and I k refers to a modified Bessel function of the first kind of the order k .…”

Section: Theoretical Modelmentioning

confidence: 97%

See 2 more Smart Citations

A triple porosity scheme for fluid/solid substitution: theory and experiment

Sun

Gurevich

Lebedev

et al. 2018

Geophysical Prospecting

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“…Saxena and Mavko () used the embedded‐bound method to obtain the generalized “Gassmann‐like” solutions for the elastic moduli of a rock filled with fluid or solid when the stress is nonuniformly distributed in the pore space. Saxena and Mavko (), Gurevich and Saxena (), and Glubokovskikh et al () extended this approach to include effects of shear resistance of a solid‐like high‐viscosity fluid saturating stiff and compliant pores of a rock.…”

Section: Introductionmentioning

confidence: 99%

A Seismic‐Frequency Laboratory Study of Solid Substitution in Bentheim Sandstone

et al. 2019

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Studying the effects of the solid pore fills on the elastic properties of rocks is of significant importance for a range of applications, such as, for example, monitoring of heavy oil reservoirs or modeling the transport properties of the rocks affected by salt precipitation or cementation. We present the results of the laboratory solid‐substitution experiments carried out on Bentheim sandstone at a seismic frequency of 2 Hz. The experiments were performed when the pore space of the tested sample was filled sequentially with solid (23°C) and liquid (40°C) octadecane. Previously, ultrasonic measurements on the same octadecane‐filled sandstone showed significant discrepancy from the predictions of Ciz‐Shapiro theory, which was explained by the effect of stiffening of compliant pores at the grain contacts. However, the present results show good agreement with the predictions of the Ciz‐Shapiro theory and suggest that the effect of stiffening of the compliant pores in presence of solid is negligible at low frequency.

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An accurate analytical model for squirt flow in anisotropic porous rocks -Part 1: Classical geometry

Alkhimenkov

Quintal

2021

Preprint

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Seismic wave propagation in porous rocks that are saturated with a liquid exhibits significant dispersion and attenuation due to fluid flow at the pore scale, so-called squirt flow. This phenomenon takes place in compliant flat pores such as microcracks and grain contacts that are connected to stiffer isometric pores. Accurate quantitative description is crucial for inverting rock and fluid properties from seismic attributes such as attenuation. Up to now, many analytical models for squirt flow were proposed based on simplified geometries of the pore space. These models were either not compared with a numerical solution or showed poor accuracy. We have developed a new analytical model for squirt flow, which is validated against a 3D numerical solution for a simple pore geometry that has been classically used to explain squirt flow; that is why we refer to it as classical geometry. The pore space is represented by a flat cylindrical (penny-shaped) pore whose curved edge is fully connected to a toroidal (stiff) pore. Compared with correct numerical solutions, our analytical model provides very accurate predictions for the attenuation and dispersion across the whole frequency range. This includes correct low-and high-frequency limits of the stiffness modulus, the characteristic frequency, and the shape of the dispersion and attenuation curves. In a companion paper (part 2), we extend our analytical model to more complex pore geometries. We provide as supplemental information MATLAB and symbolic Maple routines to reproduce our main results.

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A dual‐porosity scheme for fluid/solid substitution

Cited by 25 publications

References 35 publications

A triple porosity scheme for fluid/solid substitution: theory and experiment

A triple porosity scheme for fluid/solid substitution: theory and experiment

A Seismic‐Frequency Laboratory Study of Solid Substitution in Bentheim Sandstone

An accurate analytical model for squirt flow in anisotropic porous rocks -Part 1: Classical geometry

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