Modeling squirt dispersion and attenuation in fluid-saturated rocks using pressure dependency of dry ultrasonic velocities

Paula, Osni Bastos de; Pervukhina, Marina; Makarynska, Dina; Gurevich, Boris

doi:10.1190/geo2011-0253.1

Cited by 27 publications

(30 citation statements)

References 34 publications

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“…Following De Paula et al . (), intermediate porosity will exhibit an exponential decay with increasing confining pressure, similar to compliant porosity but at much higher confining pressures. In analogy to equations –, the expressions of unrelaxed rock frame moduli at much higher confining pressures when all compliant pores are closed can be written as

\frac{1}{K_{u f m}} = \frac{1}{K_{h m}} + s B_{N m}

and

\frac{1}{μ_{u f m}} = \frac{1}{μ_{h m}} + \frac{4}{15} s B_{N m} + \frac{2}{5} s B_{T m},

where K hm and μ hm are the dry rock frame moduli of a hypothetical rock with both compliant and intermediate pores closed and stiff porosity equal to the unstressed value.…”

Section: Theoretical Modelmentioning

confidence: 84%

“…This implies that the assumption of De Paula et al . () in his paper that only equant pores left when both compliant and intermediate pores are closed is worth exploring. Meanwhile, predictions with an aspect ratio of stiff pores for 0.22 match well with the ultrasonically measured elastic moduli.…”

Section: Discussionmentioning

confidence: 99%

“…Note that for much higher confining pressures (above 50–100 MPa, suggested by De Paula et al . ), K ufm = K uf and μ ufm = μ uf . As a result, the variation of the pressure‐dependent dry rock moduli due to the combined effect of compliant and intermediate porosity can be written as

K_{d r y} = K_{h m} [1 - θ_{m} φ_{m 0} e^{- \frac{θ_{m} P}{K_{h m}}} - false(1 + φ_{m 0} false) θ_{c} φ_{c 0} e^{- \frac{θ_{c} P}{K_{h c}}}]

μ_{d r y} = μ_{h m} [1 - θ_{m} φ_{m 0} e^{- \frac{θ_{m} P}{K_{h m}}} - false(1 + φ_{m 0} false) θ_{c} φ_{c 0} e^{- \frac{θ_{c} P}{K_{h c}}}] .

…”

Section: Theoretical Modelmentioning

confidence: 99%

“…Hence, De Paula et al . () argued that the squirt effects are caused by the presence of the so‐called intermediate pores, which are softer than stiff pores but much stiffer than compliant pores. This provides a good prospective to better characterize the solid squirt effects.…”

Section: Introductionmentioning

confidence: 99%

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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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\frac{1}{K_{u f m}} = \frac{1}{K_{h m}} + s B_{N m}

and

\frac{1}{μ_{u f m}} = \frac{1}{μ_{h m}} + \frac{4}{15} s B_{N m} + \frac{2}{5} s B_{T m},

where K hm and μ hm are the dry rock frame moduli of a hypothetical rock with both compliant and intermediate pores closed and stiff porosity equal to the unstressed value.…”

Section: Theoretical Modelmentioning

confidence: 84%

Section: Discussionmentioning

confidence: 99%

K_{d r y} = K_{h m} [1 - θ_{m} φ_{m 0} e^{- \frac{θ_{m} P}{K_{h m}}} - false(1 + φ_{m 0} false) θ_{c} φ_{c 0} e^{- \frac{θ_{c} P}{K_{h c}}}]

μ_{d r y} = μ_{h m} [1 - θ_{m} φ_{m 0} e^{- \frac{θ_{m} P}{K_{h m}}} - false(1 + φ_{m 0} false) θ_{c} φ_{c 0} e^{- \frac{θ_{c} P}{K_{h c}}}] .

…”

Section: Theoretical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Sun

Gurevich

Lebedev

et al. 2018

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

show abstract

“…This is expected as quasi‐static poroelasticity fits the viscoelastic framework (e.g., Rubino et al, ). This should theoretically be the case also for the squirt flow effect (e.g., Carcione & Gurevich, ; De Paula et al, ). It is thus of interest to investigate the links between measurements and viscoelasticity for this second transition.…”

Section: Interpretation : Dispersion/attenuation In Sandstones Over Tmentioning

confidence: 84%

Elastic Dispersion and Attenuation in Fully Saturated Sandstones: Role of Mineral Content, Porosity, and Pressures

et al. 2017

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Because measuring the frequency dependence of elastic properties in the laboratory is a technical challenge, not enough experimental data exist to test the existing theories. We report measurements of three fluid‐saturated sandstones over a broad frequency band: Wilkenson, Berea, and Bentheim sandstones. Those sandstones samples, chosen for their variable porosities and mineral content, are saturated by fluids of varying viscosities. The samples elastic response (Young's modulus and Poisson's ratio) and hydraulic response (fluid flow out of the sample) are measured as a function of frequency. Large dispersion and attenuation phenomena are observed over the investigated frequency range. For all samples, the variation at lowest frequency relates to a large fluid flow directly measured out of the rock samples. These are the cause (i.e., fluid flow) and consequence (i.e., dispersion/attenuation) of the transition between drained and undrained regimes. Consistently, the characteristic frequency correlates with permeability for each sandstone. Beyond this frequency, a second variation is observed for all samples, but the rocks behave differently. For Berea sandstone, an onset of dispersion/attenuation is expected from both Young's modulus and Poisson's ratio at highest frequency. For Bentheim and Wilkenson sandstones, however, only Young's modulus shows dispersion/attenuation phenomena. For Wilkenson sandstone, the viscoelastic‐like dispersion/attenuation response is interpreted as squirt flow. For Bentheim sandstone, the second effect does not fully follow such response, which could be due to a lower accuracy in the measured attenuation or to the occurence of another physical effect in this rock sample.

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Experimental Investigation on Static and Dynamic Bulk Moduli of Dry and Fluid-Saturated Porous Sandstones

et al. 2020

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Knowledge of pressure-dependent static and dynamic moduli of porous reservoir rocks is of key importance for evaluating geological setting of a reservoir in geo-energy applications. We examined experimentally the evolution of static and dynamic bulk moduli for porous Bentheim sandstone with increasing confining pressure up to about 190 MPa under dry and water-saturated conditions. The static bulk moduli (Ks) were estimated from stress–volumetric strain curves while dynamic bulk moduli (Kd) were derived from the changes in ultrasonic P- and S- wave velocities (~ 1 MHz) along different traces, which were monitored simultaneously during the entire deformation. In conjunction with published data of other porous sandstones (Berea, Navajo and Weber sandstones), our results reveal that the ratio between dynamic and static bulk moduli (Kd/Ks) reduces rapidly from about 1.5 − 2.0 at ambient pressure to about 1.1 at high pressure under dry conditions and from about 2.0 − 4.0 to about 1.5 under water-saturated conditions, respectively. We interpret such a pressure-dependent reduction by closure of narrow (compliant) cracks, highlighting that Kd/Ks is positively correlated with the amount of narrow cracks. Above the crack closure pressure, where equant (stiff) pores dominate the void space, Kd/Ks is almost constant. The enhanced difference between dynamic and static bulk moduli under water saturation compared to dry conditions is possibly caused by high pore pressure that is locally maintained if measured using high-frequency ultrasonic wave velocities. In our experiments, the pressure dependence of dynamic bulk modulus of water-saturated Bentheim sandstone at effective pressures above 5 MPa can be roughly predicted by both the effective medium theory (Mori–Tanaka scheme) and the squirt-flow model. Static bulk moduli are found to be more sensitive to narrow cracks than dynamic bulk moduli for porous sandstones under dry and water-saturated conditions.

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Modeling squirt dispersion and attenuation in fluid-saturated rocks using pressure dependency of dry ultrasonic velocities

Cited by 27 publications

References 34 publications

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

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

Elastic Dispersion and Attenuation in Fully Saturated Sandstones: Role of Mineral Content, Porosity, and Pressures

Experimental Investigation on Static and Dynamic Bulk Moduli of Dry and Fluid-Saturated Porous Sandstones

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