Differential form and numerical implementation of Biot’s poroelasticity equations with squirt dissipation

Carcione, José M.; Gurevich, Boris

doi:10.1190/geo2010-0169.1

Cited by 79 publications

(27 citation statements)

References 34 publications

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“…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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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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“…Please note that in the following we shall refer to h / R as the aspect ratio of the compliant pores. In addition, it is important to take into account that is based on the assumption that the fluid bulk modulus satisfies which in turn implies that the fluid must actually be a liquid (Carcione and Gurevich 2011).…”

Section: Methodological Backgroundmentioning

confidence: 99%

Research note: Seismic attenuation due to wave‐induced fluid flow at microscopic and mesoscopic scales

Rubino

Holliger

2013

Geophysical Prospecting

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A B S T R A C TWave-induced fluid flow at microscopic and mesoscopic scales arguably constitutes the major cause of intrinsic seismic attenuation throughout the exploration seismic and sonic frequency ranges. The quantitative analysis of these phenomena is, however, complicated by the fact that the governing physical processes may be dependent. The reason for this is that the presence of microscopic heterogeneities, such as microcracks or broken grain contacts, causes the stiffness of the so-called modified dry frame to be complex-valued and frequency-dependent, which in turn may affect the viscoelastic behaviour in response to fluid flow at mesoscopic scales. In this work, we propose a simple but effective procedure to estimate the seismic attenuation and velocity dispersion behaviour associated with wave-induced fluid flow due to both microscopic and mesoscopic heterogeneities and discuss the results obtained for a range of pertinent scenarios.

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“…Between these limits, the moduli are complex and frequency dependent, and thus the corresponding elastic waves exhibit attenuation and dispersion. Furthermore, at frequencies where viscoinertial relaxation becomes important, these equations can be combined with Biot's (1962) equations of poroelasticity to account for squirt and local and Biot's global flow dissipation mechanisms (Carcione and Gurevich, 2011).…”

Section: Wa158mentioning

confidence: 99%

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

et al. 2012

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Modeling dispersion and attenuation of elastic waves in fluidsaturated rocks due to squirt flow requires the knowledge of a number of geometrical parameters of the pore space, in particular, the characteristic aspect ratio of the pores. These parameters are usually inferred by fitting measurements on saturated rocks to model predictions. To eliminate such fitting and thus make the model more predictive, we propose to recover the geometrical parameters of the pore space from the pressure dependency of elastic moduli on dry samples. Our analysis showed that the pressure dependency of elastic properties of rocks (and their deviation from Gassmann's prediction) at ultrasonic frequencies is controlled by the squirt flow between equant, stiff, and so-called intermediate pores (with aspect ratios between 10 −3 -2 × 10 −1 ). Such intermediate porosity is expected to close at confining pressures of between 200 and 2000 MPa, and thus cannot be directly obtained from ultrasonic experiments performed at pressures below 50 MPa. However, the presence of this intermediate porosity is inferred from the significant linear trend in the pressure dependency of elastic properties of the dry rock and the difference between the bulk modulus of the dry rock computed for spherical pores and the measured modulus at 50 MPa. Moreover, we can infer the magnitude of the intermediate porosity and its characteristic aspect ratio. Substituting these parameters into the squirt model, we have computed elastic moduli and velocities of the water-saturated rock and compared these predictions against laboratory measurements of these velocities. The agreement is good for a number of clean sandstones, but not unexpectedly worse for a broad range of shaley sandstones. Our predictions showed that dispersion and attenuation caused by the squirt flow between compliant and stiff pores may occur in the seismic frequency band. Confirmation of this prediction requires laboratory measurements of elastic properties at these frequencies.

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Differential form and numerical implementation of Biot’s poroelasticity equations with squirt dissipation

Cited by 79 publications

References 34 publications

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

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

Research note: Seismic attenuation due to wave‐induced fluid flow at microscopic and mesoscopic scales

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

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