Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation

Aguilar, Gloria; Gaspar, Francisco J.; Lisbona, F. J.; Rodrigo, Carmen

doi:10.1002/nme.2295

Cited by 63 publications

(58 citation statements)

References 24 publications

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“…We assume the porous medium to be linearly elastic, homogeneous, isotropic and saturated by an incompressible Newtonian fluid. According to Biot's theory, the consolidation process satisfies the following system of equations (Aguilar et al 2008;Wang 2000):…”

Section: Biot's Partial Differential Equationsmentioning

confidence: 99%

“…Let P k h ⊂ H 1 (Ω) be a function space of piecewise polynomials on Ω of degree k. Hence, we define finite element approximations for W and Q as (Aguilar et al 2008;Prokharau and Vermolen 2009). Subsequently, we approximate the functions u(t) and p(t) with functions…”

Section: Finite Element Discretisationmentioning

confidence: 99%

“…However, spurious oscillations are diminished but not completely removed for small time steps. To fully remove the non-physical oscillations, one may use the stabilisation techniques as considered by Aguilar et al (2008). The numerical investigations are carried out using the matrix-based software package MATLAB (version R2011b).…”

Section: Finite Element Discretisationmentioning

confidence: 99%

“…The domain is discretised using a 101 by 11 regular triangular grid, which provides sufficient resolution according to a mesh refinement study. The chosen values for the material properties of the porous medium are given in Table 1, where λ and μ are related to the Young's modulus E and the Poisson's ratio ν by (Aguilar et al 2008 1+ν) . The values in Table 1 are chosen based on discussions with experts from engineering and consultancy company Fugro GeoServices B.V. and on the literature (Van Wijngaarden 2015).…”

Section: Numerical Simulationsmentioning

confidence: 99%

See 3 more Smart Citations

Monte Carlo Assessment of the Impact of Oscillatory and Pulsating Boundary Conditions on the Flow Through Porous Media

Rahrah

Vermolen

2018

Transp Porous Med

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Stress and water injection induce deformations and changes in pore pressure in the soil. The interaction between the mechanical deformations and the flow of water induces a change in porosity and permeability, which results in nonlinearity. To investigate this interaction and the impact of mechanical vibrations and pressure pulses on the flow rate through the pores of a porous medium under a pressure gradient, a poroelastic model is proposed. In this paper, a Galerkin finite element method is applied for solving the quasi-static Biot's consolidation problem for poroelasticity, considering nonlinear permeability. Space discretisation using Taylor-Hood elements is considered, and the implicit Euler scheme for time stepping is used. Furthermore, Monte Carlo simulations are performed to quantify the impact of variation in the parameters on the model output. Numerical results show that pressure pulses and soil vibrations in the direction of the flow increase the amount of water that can be injected into a deformable fluid-saturated porous medium.

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Section: Biot's Partial Differential Equationsmentioning

confidence: 99%

Section: Finite Element Discretisationmentioning

confidence: 99%

Section: Finite Element Discretisationmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

See 2 more Smart Citations

Monte Carlo Assessment of the Impact of Oscillatory and Pulsating Boundary Conditions on the Flow Through Porous Media

Rahrah

Vermolen

2018

Transp Porous Med

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“…For the spatial discretization, we use a stabilized linear finite element method [19]. The stabilization proposed in that work was based on adding an artificial Let T h denote a triangulation of Ω satisfying the usual admissibility assumptions.…”

mentioning

confidence: 99%

On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics

Gaspar

Rodrigo

2017

Computer Methods in Applied Mechanics and Engineering

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Please cite this article as: F.J. Gaspar, C. Rodrigo, On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics, Comput. Methods Appl. Mech. Engrg. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics This solver combines the advantages of being a fully coupled method, with the benefit of decoupling the flow and the mechanics part in the smoothing algorithm. Moreover, the fixed-stress split smoother is based on the physics of the problem, and therefore all parameters involved in the relaxation are based on the physical properties of the medium and are given a priori. A local Fourier analysis is applied to study the convergence of the multigrid method and to support the good convergence results obtained. The proposed geometric multigrid algorithm is used to solve several tests in semi-structured triangular grids, in order to show the good behaviour of the method and its practical utility.

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Joint inversion in coupled quasi-static poroelasticity

Hesse

Stadler

2014

J. Geophys. Res. Solid Earth

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[1] Geodetic surveys now provide detailed time series maps of anthropogenic land subsidence and uplift due to injection and withdrawal of pore fluids from the subsurface. A coupled poroelastic model allows the integration of geodetic and hydraulic data in a joint inversion and has therefore the potential to improve the characterization of the subsurface and our ability to monitor pore pressure evolution. We formulate a Bayesian inverse problem to infer the lateral permeability variation in an aquifer from geodetic and hydraulic data and from prior information. We compute the maximum a posteriori (MAP) estimate of the posterior permeability distribution and a Gaussian approximation of the posterior. Computing the MAP estimate requires the solution of a large-scale minimization problem subject to the poroelastic equations, for which we propose an efficient Newton-conjugate gradient optimization algorithm. The covariance matrix of the Gaussian approximation of the posterior is given by the inverse Hessian of the log posterior, which we construct by exploiting low-rank properties of the data misfit Hessian. First and second derivatives are computed using adjoints of the time-dependent poroelastic equations, allowing us to fully exploit transient data. Using three increasingly complex model problems, we find the following general properties of poroelastic inversions: Augmenting standard hydraulic well data by surface deformation data improves the aquifer characterization. Surface deformation contributes the most in shallow aquifers but provides useful information even for the characterization of aquifers down to 1 km. In general, it is more difficult to infer high-permeability regions, and their characterization requires frequent measurement to resolve the associated short-response timescales. In horizontal aquifers, the vertical component of the surface deformation provides a smoothed image of the pressure distribution in the aquifer. Provided that the mechanical properties are known, coupled poroelastic inversion is therefore a promising approach to detect flow barriers and to monitor pore pressure evolution.

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Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation

Cited by 63 publications

References 24 publications

Monte Carlo Assessment of the Impact of Oscillatory and Pulsating Boundary Conditions on the Flow Through Porous Media

Monte Carlo Assessment of the Impact of Oscillatory and Pulsating Boundary Conditions on the Flow Through Porous Media

On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics

Joint inversion in coupled quasi-static poroelasticity

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