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Simulation of seismic wave propagation in poroelastic media using vectorized Biot’s equations: an application to a CO2 sequestration monitoring case

Anthony Emmanuel, Vedanti Nimisha

Acta Geophysica

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2020

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Vol. 68, no. 2

435--444

EN

Wave propagation through porous media allows us to understand the response and interaction that occur between the elastic rock matrix and the fuid. This interaction has been described by Biot in his theory of poroelasticity. Seismic wave simulation using Biot’s formulations is computationally expensive when compared with the acoustic and elastic cases. This computational burden can be reduced by reformulating the numerical derivative operators to improve the efciency. To achieve this, we used a staggered-grid fnite diference operator to discretize 2D velocity stress equations as given by Biot’s theory. A vectorized derivative is applied on the staggered grid by shifting the coordinates. The reformulated equations were applied to compute the seismic response of a reservoir, where CO2 is being injected and the efect of injected CO2 in the formation is clearly seen in the synthetic data generated. The algorithm was coded in Python and to test its efciency, the simulation run-time was compared for both serial and vectorized equations, and the speed-up ratio was calculated. Our results show a decrease in the simulation run-time for the vectorized execution with over a factor of a hundred percent (100%). We further observed that the amplitudes of the events increase with an increase in CO2 saturation in the formation. This matches well with the real data.

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Effects of the microcrack shape, size and direction on the poroelastic behaviors of a single osteon: a finite element study

Cen H-P., Wu X-G., Yu W-L., Liu Q-Z., Yia Y-M.

Acta of Bioengineering and Biomechanics

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2016

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Vol. 18, no. 1

3--10

EN

In this work, a finite element study is proposed by using the Comsol Multiphysics software to evaluate the effects of microcrack shape, size and direction on the poroelastic behaviors of a single osteon. Methods: This finite element model is established by using the Comsol Multiphysics software, and we just focus on the comparison of the influences of those microcrack geometric parameters on the osteonal fluid pressure and velocity. Results: The results show that: (1) microcracks in the osteon wall can induce a release of the fluid pressure, but enlarge the velocity in this region; (2) equal-area microcrack with ellipsoid-like shape produced a larger fluid pressure and velocity fields in the osteon than that of rectangular shape; (3) in the elliptic microcracks, the longer of the length (major semi-axis) induces a smaller fluid pressure and velocity amplitudes, whereas the width (minor axis) has little effect; (4) the direction of the microcracks (major axial direction) has an limited influence area around about 1/15 of the osteon cross-sectional area. Conclusions: This model permits the linking of the external loads and microcracks to the osteonal fluid pressure and velocity, which can be used for other purpose associate microcracks with the mechanotransduction and bone remodeling.

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Biomechanical and fluid flowing characteristics of intervertebral disc of lumbar spine predicted by poroelastic finite element method

Guo L.-X, Li R., Zhang M.

Acta of Bioengineering and Biomechanics

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2016

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Vol. 18, no. 2

19--29

EN

Purpose: This study is to reveal the deformation of intervertebral disc (IVD), the stress distribution of solid phase and liquid phase, the variation of fluid flux and flow velocity in lumbar spine and the influence of different permeability parameters on them under intermittent compressive loading. Methods: A poroelastic FEM of L4-L5 is assigned with different permeability parameters to analyze the deformation, stress distribution and fluid convection under intermittent compressive loads. Results: The results show that the pore pressure of IVD decreases with time, but the effective stress increases under intermittent compressive loads. The axial and radial strain will increase and fluid loss will recover at a more rapid rate if the permeability of endplate increases during unloading period. The velocity vectors show that most of the liquid in the disc flows into vertebrae through endplates and only a small quantity of liquid flows through the annulus fibrosus at the loading step, however, at the unloading step, almost all the liquid flowing into IVD is through the endplates. Conclusions: The changing rate of pore pressure and effective stresses of nucleus pulposus and annulus fibrosus with higher permeability is smaller than that with smaller permeability. The degenerated endplate (with low permeability) yields high flow velocity decreasing gradient, which might impede liquid inflowing/outflowing smoothly through the endplates. The fluid flowing velocity in loading phase is faster than that in unloading phase, so a short resting time can relieve fatigue, but could not recover to the original liquid condition in IVDs.