### Abstract

The linear theory of multiple-porosity and multiple-permeability poroelasticity is presented; a self-consistent extension to Biot's formulation of a single-porosity, homogenous, isotropic, fluid-saturated, and linearly elastic material is made to obtain the constitutive relations and poroelastic constants of a material with an arbitrary number of N systems or scales of porosity and permeability. Sudden and continued confinement of a spherical sample of porous material while allowing for the pore fluid drainage from the surface boundary is known as Cryer's problem in the poromechanics literature. The closed-form solution to this problem is developed in Laplace transform domain for the general case of N-porosity and N-permeability poroelasticity with full inter-porosity fluid exchange property. Numerical results in the time domain are presented for single-porosity, double-porosity, triple-porosity, quadruple-porosity, and quintuple-porosity poroelastic models of organic-rich shale.

Original language | English (US) |
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Title of host publication | Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics |

Editors | Patrick Dangla, Jean-Michel Pereira, Siavash Ghabezloo, Matthieu Vandamme |

Publisher | American Society of Civil Engineers (ASCE) |

Pages | 262-271 |

Number of pages | 10 |

ISBN (Electronic) | 9780784480779 |

DOIs | |

State | Published - Jan 1 2017 |

Event | 6th Biot Conference on Poromechanics, Poromechanics 2017 - Paris, France Duration: Jul 9 2017 → Jul 13 2017 |

### Publication series

Name | Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics |
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### Other

Other | 6th Biot Conference on Poromechanics, Poromechanics 2017 |
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Country | France |

City | Paris |

Period | 7/9/17 → 7/13/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Acoustics and Ultrasonics

### Cite this

*Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics*(pp. 262-271). (Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics). American Society of Civil Engineers (ASCE). https://doi.org/10.1061/9780784480779.032

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*Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics.*Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics, American Society of Civil Engineers (ASCE), pp. 262-271, 6th Biot Conference on Poromechanics, Poromechanics 2017, Paris, France, 7/9/17. https://doi.org/10.1061/9780784480779.032

**Multiple-Porosity and Multiple-Permeability Poroelasticity : Theory and Benchmark Analytical Solution.** / Mehrabian, Amin; Abousleiman, Younane N.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Multiple-Porosity and Multiple-Permeability Poroelasticity

T2 - Theory and Benchmark Analytical Solution

AU - Mehrabian, Amin

AU - Abousleiman, Younane N.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The linear theory of multiple-porosity and multiple-permeability poroelasticity is presented; a self-consistent extension to Biot's formulation of a single-porosity, homogenous, isotropic, fluid-saturated, and linearly elastic material is made to obtain the constitutive relations and poroelastic constants of a material with an arbitrary number of N systems or scales of porosity and permeability. Sudden and continued confinement of a spherical sample of porous material while allowing for the pore fluid drainage from the surface boundary is known as Cryer's problem in the poromechanics literature. The closed-form solution to this problem is developed in Laplace transform domain for the general case of N-porosity and N-permeability poroelasticity with full inter-porosity fluid exchange property. Numerical results in the time domain are presented for single-porosity, double-porosity, triple-porosity, quadruple-porosity, and quintuple-porosity poroelastic models of organic-rich shale.

AB - The linear theory of multiple-porosity and multiple-permeability poroelasticity is presented; a self-consistent extension to Biot's formulation of a single-porosity, homogenous, isotropic, fluid-saturated, and linearly elastic material is made to obtain the constitutive relations and poroelastic constants of a material with an arbitrary number of N systems or scales of porosity and permeability. Sudden and continued confinement of a spherical sample of porous material while allowing for the pore fluid drainage from the surface boundary is known as Cryer's problem in the poromechanics literature. The closed-form solution to this problem is developed in Laplace transform domain for the general case of N-porosity and N-permeability poroelasticity with full inter-porosity fluid exchange property. Numerical results in the time domain are presented for single-porosity, double-porosity, triple-porosity, quadruple-porosity, and quintuple-porosity poroelastic models of organic-rich shale.

UR - http://www.scopus.com/inward/record.url?scp=85026323611&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85026323611&partnerID=8YFLogxK

U2 - 10.1061/9780784480779.032

DO - 10.1061/9780784480779.032

M3 - Conference contribution

AN - SCOPUS:85026323611

T3 - Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics

SP - 262

EP - 271

BT - Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics

A2 - Dangla, Patrick

A2 - Pereira, Jean-Michel

A2 - Ghabezloo, Siavash

A2 - Vandamme, Matthieu

PB - American Society of Civil Engineers (ASCE)

ER -