TY - CHAP

T1 - Entropic bounds for multi-scale and multi-physics coupling in earth sciences

AU - Regenauer-Lieb, Klaus

AU - Karrech, Ali

AU - Chua, Hui Tong

AU - Poulet, Thomas

AU - Veveakis, Manolis

AU - Wellmann, Florian

AU - Liu, Jie

AU - Schrank, Christoph Eckart

AU - Gaede, Oliver

AU - Trefry, Michael G

AU - Ord, Alison

AU - Hobbs, Bruce E

AU - Metcalfe, Guy

AU - Lester, Daniel Robert

PY - 2014

Y1 - 2014

N2 - The ability to understand and predict how thermal, hydrological, mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal–Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties, stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.

AB - The ability to understand and predict how thermal, hydrological, mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal–Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties, stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.

KW - Thermodynamics

KW - Multi-scaling

KW - THMC coupling

KW - Numerical simulations

KW - Dissipative structures

KW - Finite time thermodynamics

KW - Maximum entropy production

KW - Minimum entropy production

KW - Thermodynamic homogenization methods

U2 - 10.1007/978-3-642-40154-1_17

DO - 10.1007/978-3-642-40154-1_17

M3 - Chapter (Report)

SN - 9783642401534

T3 - Understanding Complex Systems

SP - 323

EP - 335

BT - Beyond the Second Law

A2 - Dewar, Roderick C

A2 - Lineweaver, Charles H

A2 - Niven, Robert K

A2 - Regenauer-Lieb, Klaus

PB - Springer

CY - Heidelberg Germany

ER -