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**Harvard**

Janicke, R., Larsson, F., Runesson, K. och Steeb, H. (2016) *Numerical identification of a viscoelastic substitute model for heterogeneous poroelastic media by a reduced order homogenization approach*.

** BibTeX **

@article{

Janicke2016,

author={Janicke, R. and Larsson, Fredrik and Runesson, Kenneth and Steeb, H.},

title={Numerical identification of a viscoelastic substitute model for heterogeneous poroelastic media by a reduced order homogenization approach},

journal={Computer Methods in Applied Mechanics and Engineering},

issn={0045-7825},

volume={298},

pages={108-120},

abstract={The paper deals with the computational homogenization of pressure diffusion processes in a poroelastic medium. The underlying physical phenomena are of interest for the interpretation of seismic data with applications in hydrocarbon production and geothermal energy. Pressure diffusion is assumed to take place on a length scale much smaller than the observer scale. Thus, the macroscopic observer is not able to measure the properties of the poroelastic medium directly but notices an intrinsic viscous attenuation. Under these circumstances, the macro-scale can be interpreted as a single-phase solid with (apparent) viscoelastic properties. In this paper, we establish a numerical upscaling procedure based on a volume averaging concept. This enables us to identify the material properties of the viscoelastic substitute model in a numerically efficient manner. For this purpose, the poroelastic medium on the small scale is modelled in terms of the momentum balance of the biphasic mixture and a coupled diffusion equation. We approximate the poroelastic pressure field on the small scale by a linear combination of pressure modes forming a reduced orthogonal basis and being identified by a Proper Orthogonal Decomposition (POD) technique. From the superposition principle, the evaluation of the poroelastic continuity equation results in a proper identification of the evolution equations defining the apparent viscoelastic model. In comparison to the nested FE2 solution schemes, the reduced order approach only requires a small amount of "off-line" precomputations and, therefore, causes very low numerical costs. The proposed method is validated for the simple setup of a layered porous rock with alternating water-and gas-saturated zones. },

year={2016},

keywords={Computational homogenization, Poroelasticity, Order reduction, },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 231009

A1 Janicke, R.

A1 Larsson, Fredrik

A1 Runesson, Kenneth

A1 Steeb, H.

T1 Numerical identification of a viscoelastic substitute model for heterogeneous poroelastic media by a reduced order homogenization approach

YR 2016

JF Computer Methods in Applied Mechanics and Engineering

SN 0045-7825

VO 298

SP 108

OP 120

AB The paper deals with the computational homogenization of pressure diffusion processes in a poroelastic medium. The underlying physical phenomena are of interest for the interpretation of seismic data with applications in hydrocarbon production and geothermal energy. Pressure diffusion is assumed to take place on a length scale much smaller than the observer scale. Thus, the macroscopic observer is not able to measure the properties of the poroelastic medium directly but notices an intrinsic viscous attenuation. Under these circumstances, the macro-scale can be interpreted as a single-phase solid with (apparent) viscoelastic properties. In this paper, we establish a numerical upscaling procedure based on a volume averaging concept. This enables us to identify the material properties of the viscoelastic substitute model in a numerically efficient manner. For this purpose, the poroelastic medium on the small scale is modelled in terms of the momentum balance of the biphasic mixture and a coupled diffusion equation. We approximate the poroelastic pressure field on the small scale by a linear combination of pressure modes forming a reduced orthogonal basis and being identified by a Proper Orthogonal Decomposition (POD) technique. From the superposition principle, the evaluation of the poroelastic continuity equation results in a proper identification of the evolution equations defining the apparent viscoelastic model. In comparison to the nested FE2 solution schemes, the reduced order approach only requires a small amount of "off-line" precomputations and, therefore, causes very low numerical costs. The proposed method is validated for the simple setup of a layered porous rock with alternating water-and gas-saturated zones.

LA eng

DO 10.1016/j.cma.2015.09.024

LK http://dx.doi.org/10.1016/j.cma.2015.09.024

OL 30