Hysteresis effects studied by numerical simulations: Cyclic loading-unloading of a realistic sand model

García, Xavier; Medina, Ernesto

doi:10.1190/1.2181309

Cited by 56 publications

(28 citation statements)

References 18 publications

(33 reference statements)

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“…() confirm the HM model prediction of bulk modulus of glass beads with experimental data using an empirical dependence of coordination number, that is, the average number of grains in contact, and porosity on pressure from numerical simulations (Zhang and Makse ). Garcia and Medina () confirm the dependence of coordination number and porosity to the hydrostatic pressure and thus validate the HM model. Zimmer et al .…”

Section: Introductionsupporting

confidence: 57%

“…Garcia and Medina () have shown that this power law fits coordination and porosity results in their relationship for glass beads:

C false(P false) = C_{0} + 9.7 {(φ_{0} - φ false(P false))}^{0.48} .

These geometrical parameters are empirically estimated from the simulation of random spherical packs. Zimmer et al .…”

Section: Theorymentioning

confidence: 95%

“…() have predicted the bulk modulus of glass beads, based on the empirical equation of coordination number, with good agreement with experimental data, although their empirical equation of coordination number is different from Makse et al . () and Garcia and Medina (). By assuming their empirical expression for the coordination number, they found the stress dependency of moduli varies from the fourth root to the sixth root of pressure.…”

Section: Introductionmentioning

confidence: 97%

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Estimation of grain elasticity properties from ultrasonic measurements on dry granular pack

Madadi

Ahmed

Bóna

et al. 2018

Geophysical Prospecting

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The elastic properties of crystalline rocks can be estimated from ultrasonic measurements on the powders of crushed rocks produced by the drilling process. To determine the elastic properties of grains from properties of powder packs, we study the dependence of their ultrasonic wave velocities on pressure. From this dependency, using the Hertz–Mindlin theory, we can calculate the effective ratio of the grain shear modulus to one minus the Poisson ratio. The Hertz–Mindlin theory requires the knowledge of grain coordination number as a function of pressure, which can be obtained using an empirical relation based on published numerical simulations. Previous work has shown that this approach gives an accurate prediction of the effective bulk modulus of glass beads but produces a significant discrepancy for sand. This discrepancy may be attributed to the angularity of sand grains. To overcome this problem, we introduce a shape factor into the empirical relation for the coordination number. This new shape factor allows us to reconcile the rock physics model with laboratory measurements. We show that the shape factor varies from 1 to 2.5 for different grain shape angularity and sorting (grain size distributions). The modified theory allows us to estimate a combination of elasticity parameters of the grains from the measured dependence of P‐wave velocity in the pack on the pressure.

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Section: Introductionsupporting

confidence: 57%

“…Garcia and Medina () have shown that this power law fits coordination and porosity results in their relationship for glass beads:

C false(P false) = C_{0} + 9.7 {(φ_{0} - φ false(P false))}^{0.48} .

These geometrical parameters are empirically estimated from the simulation of random spherical packs. Zimmer et al .…”

Section: Theorymentioning

confidence: 95%

Section: Introductionmentioning

confidence: 97%

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Estimation of grain elasticity properties from ultrasonic measurements on dry granular pack

Madadi

Ahmed

Bóna

et al. 2018

Geophysical Prospecting

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“…The coordination number n' is reduced for the static loading condition (Takahashi and Tanaka 2010) and is modeled using the power-law relation by Garcia and Medina (2006):…”

Section: Analytical Evaluationmentioning

confidence: 99%

Rock Mechanical Properties of Shallow Unconsolidated Sandstone Formations

Ramcharitar

Hosein

2016

All Days

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Rock mechanical properties, such as the Poisson's ratio, Bulk, Shear and Young's moduli are required for various oilfield operations such as seismic processing, reservoir simulation studies, and hydraulic fracturing for sand control. These properties are usually determined from compressional (P) and shear (S) wave velocities which can be captured by the dipole sonic logging tool. For unconsolidated rocks (shallower than 6000 ft), the P and S-wave velocities are difficult to predict due to the dispersive nature of these rocks. Also, the available correlations in the open literature to determine these parameters should be used with caution since these were developed mainly for deeper formations.In this study, we compared the sonic wave velocities empirically predicted by Castagna et al., Eberhart-Phillips and Han with the logged sonic wave velocities across the Cruse Formation for eight onshore wells in South-Western Trinidad. We also investigated more suitable methods of matching the logged velocities across the Cruse, by developing new empirical models and an analytical method (Hertz-Mindlin contact model) to account for the unconsolidated rocks. The basic input data required for predicting the sonic velocities and dynamic rock mechanical properties were porosity, clay content and bulk density which were taken from the log data. The models for obtaining the static rock mechanical properties were tested against the results of Mini-Frac tests in two offset wells in the Cruse.The Artificial Neural Network (ANN) empirical method was shown to be best suited for predicting the dynamic rock mechanical properties for the Cruse Formation, since Average Absolute Errors (AAE) of 3 and 6 % were obtained in matching the P and S-wave velocities respectively. Similarly, the AAE obtained from applying the three empirical correlations were worse than 17 and 30 %. This error was generally observed to lessen for wells which encountered the Cruse at greater depths. While AAE of 6 and 12 % were obtained from applying the analytical method, reservoir depletion was found to significantly affect the results of the modeling due to the implied presence of hard-to-predict free gas saturations. Also, it was found that the analytical method is the only viable procedure to predict the static rock mechanical properties in lieu of laboratory core tests. The analytical method has been tuned in this study using True Vertical Depth (TVD) as a correlation parameter for the first time, and it can generally be used to estimate both the dynamic and static rock mechanical properties of the Cruse Formation for future oilfield operations.

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“…Makse et al (2005) obtained CN as a function of pressure for both two and three dimensional cases from simulation results and found a critical minimal value of 4 and 6 respectively. Garcia and Medina (2006) used numerical simulation and got different CN in loading and unloading cycles as a function of pressure and porosity. Zimmer et al (2007a) rewrote the trend of CN as a function of porosity from the data compiled by Murphy (1982).…”

Section: Introductionmentioning

confidence: 99%

Inverting Dynamic Elastic Moduli of a Granular Pack to Get Shear Modulus of the Grain

Ahmed¹,

Lebedev²,

Madadi³

et al. 2016

ASEG Extended Abstracts

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SUMMARYElastic moduli of rocks derived from its powder is a new concept and can be applied in practical geophysics studies. To develop this concept, we make ultrasonic velocity measurement on granular packs of quartz sand. We calculate dynamic elastic moduli from that measurement and invert afterwards to find the shear modulus of quartz. The inversion technique follows Extended Walton Model that relies on the grain's contact surface condition between infinitely rough and perfectly smooth. We use different coordination numbers from previous studies (for different samples) in the process of forward modelling and inversion. Forward models have good match with the laboratory measurements both in bulk and shear moduli of the granular pack. Our overall inverted results for the shear modulus are stable and close to actual shear modulus of quartz. However, the coordination numbers that has better match in forward modelling a little bit overestimates shear modulus. On the contrary, the coordination numbers that predicts the higher effective moduli of the pack is giving closest result. As the experiment set up and procedure are simple and robust, this technique can be extended and run in very rigorous situation such as at hard rock drilling rig site to get the elastic properties of the penetrated rocks in real time, where the effective elastic moduli of a grain can be represented as a statistical averaging of elastic moduli of hard rock minerals. This information can be helpful for planning and monitoring the ongoing drilling procedure. It can also be a replacement of solid cores that are missing or damaged for elasticity study.

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Hysteresis effects studied by numerical simulations: Cyclic loading-unloading of a realistic sand model

Cited by 56 publications

References 18 publications

Estimation of grain elasticity properties from ultrasonic measurements on dry granular pack

Estimation of grain elasticity properties from ultrasonic measurements on dry granular pack

Rock Mechanical Properties of Shallow Unconsolidated Sandstone Formations

Inverting Dynamic Elastic Moduli of a Granular Pack to Get Shear Modulus of the Grain

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