Computational poroelasticity — A review

Carcione, José M.; Morency, C.; Santos, Juan E.

doi:10.1190/1.3474602

Cited by 174 publications

(90 citation statements)

References 124 publications

(115 reference statements)

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“…A time-splitting method and a fourth-order Runge-Kutta algorithm are used to solve the differential equations 33, 34, 35, and 36 (Carcione and Quiroga-Goode, 1995;Carcione, 1998Carcione, , 2007Carcione et al, 2010). These equations of motion can be recast asv ¼ M · v þ s, where v is the vector of unknown variables, M is the evolution matrix and s is the source vector.…”

Section: Methodsmentioning

confidence: 99%

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

Carcione

Gurevich

2011

GEOPHYSICS

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The squirt-flow wave attenuation mechanism is implemented in Biot's theory of poroelasticity in the form of differential equations. All the stiffnesses involved in the stress-strain relation become complex and frequency dependent, which can exactly be expressed in terms of kernels based on the Zener mechanical model. In the time domain, this approach implies time convolutions, which are circumvented by introducing memory variables. The differential equations are consistent with Gassmann's and Mavko-Jizba equations at low and high frequencies, respectively. All the coefficients in the poro-viscoelastic differential equations have a clear physical meaning and can be obtained or estimated from independent measurements. The key additional parameters are the dry-rock bulk modulus at a confining pressure where all the compliant pores are closed, i.e., a hypothetical rock without the soft porosity, the grain-contact aspect ratio and the compliant porosity. We recasted the wave equation in the particle-velocity/stress formulation and solved it by using a time-splitting technique and the Fourier pseudospectral method to compute the spatial derivatives. The algorithm can be used to obtain synthetic wave fields in inhomogeneous media.

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Section: Methodsmentioning

confidence: 99%

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

Carcione

Gurevich

2011

GEOPHYSICS

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“…with r k > 0 and p k ∈ (a, b) for k = 1, · · · , n. It will be made clear later in the paper that this property can be used for generating efficient quadrature rules for dealing with the memory term in the dynamic Darcy's law (18) in time domain.…”

Section: Definition 31mentioning

confidence: 99%

On reconstruction of dynamic permeability and tortuosity from data at distinct frequencies

2014

Inverse Problems

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This article focuses on the mathematical problem of reconstructing the dynamic permeability K(ω) and dynamic tortuosity of poroelastic composites from permeability data at different frequencies, utilizing the analytic structure of the Stieltjes function representation of K(ω) derived by Avellaneda and Tortquato in [7], which is valid for all pore space geometry. The integral representation formula (IRF) for dynamic tortuosity is derived and its analytic structure exploited for reconstructing the function from a finite data set. All information of pore-space microstructure is contained in the measure of the IRF. The theory of multipoint Padé approximates for Stieltjes functions guarantees the existence of relaxation kernels that can approximate the dynamic permeability function and the dynamic tortuosity function with high accuracy. In this paper, a numerical algorithm is proposed for computing the relaxation time and the corresponding strength for each element in the relaxation kernels. In the frequency domain, this approximation can be regarded as approximating the Stieltjes function by rational functions with simple poles and positive residues. The main difference between this approach and the curve fitting approach is that the relaxation times and the strengths are computed from the partial fraction decomposition of the multipoint Padé approximates, which is the main subject of the proposed approximation scheme.With the idea from dehomogenization, we also established the exact relations between the moments of the positive measures in the IRFs of permeability and tortuosity with two important parameters in the theory of poroelasticity: the infinite-frequency tortuosity α ∞ for the general case and the weighted volume-to-surface ratio Λ for the JKD model, which is regarded as a special case of the general model. From these relations, we suggest a new way for evaluating these two microstructure-dependent parameters from a finite data set of permeability at different frequencies, without assuming any specific forms of the functions except the fact that they satisfies the IRFs. Numerical results for JKD permeability and tortuosity are presented.

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“…Numerical modeling studies have been published by e.g. Castagna et al (2003), Carcione et al (2010), Silin and and Goloshubin (2010), Chen et al (2012), Lefeuve-Mesgouez et al (2012) and Huang et al (2015). Several authors have observed low-frequency anomalies associated with hydrocarbon reservoirs in reflection-seismic exploration data, e.g.…”

Section: List Of Tablesmentioning

confidence: 99%