A Poroelasticity Model Using a Network-Inspired Porosity-Permeability Relation

M. Rahrah; F.J. Vermolen; L.A. Lopez Pena; B.J. Meulenbroek

doi:10.1007/978-3-030-27550-1_11

A Poroelasticity Model Using a Network-Inspired Porosity-Permeability Relation

M. Rahrah, F.J. Vermolen, L.A. Lopez Pena, B.J. Meulenbroek

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

Abstract

Compressing a porous material or injecting fluid into a porous material can induce changes in the pore space, leading to a change in porosity and permeability. In a continuum scale PDE model, such as Biot’s theory of linear poroelasticity, the Kozeny–Carman equation is commonly used to determine the permeability of the porous medium from the porosity. The Kozeny–Carman relation assumes that there will be flow through the porous medium at a certain location as long as the porosity is larger than zero at this location. In contrast, from discrete network models it is known that percolation thresholds larger than zero exist, indicating that the fluid will stop flowing if the average porosity becomes smaller than a certain value dictated by these thresholds. In this study, the difference between the Kozeny–Carman equation and the equation based on the percolation theory, is investigated.

Original language	English
Title of host publication	Progress in Industrial Mathematics at ECMI 2018
Editors	István Faragó, Ferenc Izsák, Péter L. Simon
Place of Publication	Cham
Publisher	Springer
Pages	83 - 88
Number of pages	6
Volume	30
ISBN (Electronic)	978-3-030-27550-1
ISBN (Print)	978-3-030-27549-5
DOIs	https://doi.org/10.1007/978-3-030-27550-1_11
Publication status	Published - 2019
Event	20th European Conference on Mathematics for Industry - Budapest, Hungary Duration: 18 Jun 2018 → 22 Jun 2018 Conference number: 20

Publication series

Name	Mathematics in Industry
Volume	30
ISSN (Print)	1612-3956
ISSN (Electronic)	2198-3283

Conference

Conference	20th European Conference on Mathematics for Industry
Abbreviated title	ECMI 2018
Country/Territory	Hungary
City	Budapest
Period	18/06/18 → 22/06/18

Access to Document

10.1007/978-3-030-27550-1_11

Cite this

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title = "A Poroelasticity Model Using a Network-Inspired Porosity-Permeability Relation",

abstract = "Compressing a porous material or injecting fluid into a porous material can induce changes in the pore space, leading to a change in porosity and permeability. In a continuum scale PDE model, such as Biot{\textquoteright}s theory of linear poroelasticity, the Kozeny–Carman equation is commonly used to determine the permeability of the porous medium from the porosity. The Kozeny–Carman relation assumes that there will be flow through the porous medium at a certain location as long as the porosity is larger than zero at this location. In contrast, from discrete network models it is known that percolation thresholds larger than zero exist, indicating that the fluid will stop flowing if the average porosity becomes smaller than a certain value dictated by these thresholds. In this study, the difference between the Kozeny–Carman equation and the equation based on the percolation theory, is investigated.",

author = "M. Rahrah and F.J. Vermolen and {Lopez Pena}, L.A. and B.J. Meulenbroek",

year = "2019",

doi = "10.1007/978-3-030-27550-1_11",

language = "English",

isbn = "978-3-030-27549-5",

volume = "30",

series = "Mathematics in Industry",

publisher = "Springer",

pages = "83 -- 88",

editor = "Istv{\'a}n Farag{\'o} and Ferenc Izs{\'a}k and Simon, {P{\'e}ter L.}",

booktitle = "Progress in Industrial Mathematics at ECMI 2018",

note = "20th European Conference on Mathematics for Industry, ECMI 2018 ; Conference date: 18-06-2018 Through 22-06-2018",

}

Rahrah, M, Vermolen, FJ, Lopez Pena, LA & Meulenbroek, BJ 2019, A Poroelasticity Model Using a Network-Inspired Porosity-Permeability Relation. in I Faragó, F Izsák & PL Simon (eds), Progress in Industrial Mathematics at ECMI 2018. vol. 30, Mathematics in Industry, vol. 30, Springer, Cham, pp. 83 - 88, 20th European Conference on Mathematics for Industry, Budapest, Hungary, 18/06/18. https://doi.org/10.1007/978-3-030-27550-1_11

A Poroelasticity Model Using a Network-Inspired Porosity-Permeability Relation. / Rahrah, M.; Vermolen, F.J.; Lopez Pena, L.A. et al.
Progress in Industrial Mathematics at ECMI 2018. ed. / István Faragó; Ferenc Izsák; Péter L. Simon. Vol. 30 Cham: Springer, 2019. p. 83 - 88 (Mathematics in Industry; Vol. 30).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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T1 - A Poroelasticity Model Using a Network-Inspired Porosity-Permeability Relation

AU - Rahrah, M.

AU - Vermolen, F.J.

AU - Lopez Pena, L.A.

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N1 - Conference code: 20

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N2 - Compressing a porous material or injecting fluid into a porous material can induce changes in the pore space, leading to a change in porosity and permeability. In a continuum scale PDE model, such as Biot’s theory of linear poroelasticity, the Kozeny–Carman equation is commonly used to determine the permeability of the porous medium from the porosity. The Kozeny–Carman relation assumes that there will be flow through the porous medium at a certain location as long as the porosity is larger than zero at this location. In contrast, from discrete network models it is known that percolation thresholds larger than zero exist, indicating that the fluid will stop flowing if the average porosity becomes smaller than a certain value dictated by these thresholds. In this study, the difference between the Kozeny–Carman equation and the equation based on the percolation theory, is investigated.

AB - Compressing a porous material or injecting fluid into a porous material can induce changes in the pore space, leading to a change in porosity and permeability. In a continuum scale PDE model, such as Biot’s theory of linear poroelasticity, the Kozeny–Carman equation is commonly used to determine the permeability of the porous medium from the porosity. The Kozeny–Carman relation assumes that there will be flow through the porous medium at a certain location as long as the porosity is larger than zero at this location. In contrast, from discrete network models it is known that percolation thresholds larger than zero exist, indicating that the fluid will stop flowing if the average porosity becomes smaller than a certain value dictated by these thresholds. In this study, the difference between the Kozeny–Carman equation and the equation based on the percolation theory, is investigated.

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BT - Progress in Industrial Mathematics at ECMI 2018

A2 - Faragó, István

A2 - Izsák, Ferenc

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Y2 - 18 June 2018 through 22 June 2018

ER -

A Poroelasticity Model Using a Network-Inspired Porosity-Permeability Relation

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