Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions

Xu, Congcong; Mudunuru, Maruti K.; Nakshatrala, K. B.

doi:10.1007/s00161-016-0511-4

Cited by 21 publications

(11 citation statements)

References 60 publications

(52 reference statements)

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“…The approach followed in this work to develop the constitutive laws is based on the thermodynamic framework and the consideration of internal variables. However, there exist some other methodologies for the development of constitutive laws such as the principle of the maximization of entropy production [46][47][48]. In this context, one can show that using such a principle with an appropriate definition of the dissipation function, the present constitutive laws are recovered.…”

Section: Remarkmentioning

confidence: 99%

Thermo-Chemo-Poromechanical Modeling of the Anode Mixture During the Baking Process: Constitutive Laws and Governing Equations

Chen

Chaouki

Picard

et al. 2019

Journal of Applied Mechanics

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Aluminum is reduced from alumina by the Hall–Héroult electrolysis process in which the anode is utilized as the positive electrode. The quality of the prebaked anode plays a crucial rule in the efficiency of the aluminum electrolysis process. To produce high-quality anodes in the aluminum industry, the anode baking process calls for a deep understanding of mechanisms that govern the evolution of the anode mixture properties under the high-temperature condition. Therefore, the aim of this paper is to establish a thermo-chemo-poromechanical model for the baking anode by using the theory of reactive porous media based on the theory of mixtures within the thermodynamic framework. For this purpose, an internal state variable called “shrinking index” is defined to characterize the chemical progress of the pitch pyrolysis in the anode skeleton, and the Clausius–Duhem inequality is developed according to the Lagrangian formalism. By introducing a reduced Green–Lagrange strain tensor, a Lagrangian free energy is formulated to found a set of state equations. Then, the thermodynamic dissipation for this pyrolyzing solid–gas mixture is derived, and a constitutive model linking the chemical pyrolysis with the mechanical behavior is achieved. A dissipation potential is consistently defined to ensure the non-negativeness of the thermodynamic dissipation and to obtain the constitutive laws for viscous behaviors. Field equations governing the volatile diffusion and the heat transfer through the draining mixture body are derived from the entropy balance.

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Section: Remarkmentioning

confidence: 99%

Thermo-Chemo-Poromechanical Modeling of the Anode Mixture During the Baking Process: Constitutive Laws and Governing Equations

Chen

Chaouki

Picard

et al. 2019

Journal of Applied Mechanics

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“…Material degradation is a common phenomenon and affects its mechanical parameters [55,56]. Before node failure, the damage variable remains zero and Young's modulus stays constant.…”

Section: Relationship Between Damage and Permeabilitymentioning

confidence: 99%

Numerical Study of Fracture Network Evolution during Nitrogen Fracturing Processes in Shale Reservoirs

et al. 2018

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This paper develops a numerical model to study fracture network evolution during the nitrogen fracturing process in shale reservoirs. This model considers the differences of incompressible and compressible fluids, shear and tensile failure modes, shale heterogeneity, and the strength and permeability of both shale matrix and bedding planes through the coupling of mechanical-seepage-damage during fracturing fluid injection. The results show that nitrogen fracturing has a lower breakdown pressure and larger seepage zone than hydraulic fracturing under the same injection pressure. Tensile failure was identified as the major reason for the initiation and propagation of fractures. Ignoring the effect of bedding planes, the fracture initiation pressure, breakdown pressure, and fracturing effectiveness reached their maxima when the stress ratio is 1. Under the same strength ratio, the propagation path of the fractures was controlled by the stronger effect that was casused by the bedding angle and stress ratio. With increasing the strength ratio, the fracture number and shearing of the bedding plane increased significantly and the failure pattern changed from tensile-only mode to tensile-shear mode. These analyses indicated that the fracture network of bedding shale was typically induced by the combined impacts of stress ratio, bedding angle and strength ratio.Energies 2018, 11, 2503 2 of 22 more effective if N 2 is applied for the hydraulic fracturing [22,23]. Different fracturing fluids lead to the different pore pressure distributions during fluid flow due to the various properties such as viscosity and compressibility. According to the principle of effective stress, the difference in pore pressure distribution induces the difference in the stress distribution in rocks, which plays an important role in fracturing behavior during the fracturing process [24][25][26][27]. Lower breakdown pressure, larger seepage zone and more complex fracture network were observed during nitrogen fracturing [24][25][26][27]. However, these studies were performed on simple rock samples and the influence of other factors during nitrogen fracturing has not been well evaluated. It is essential to investigate fracture network evolution during the nitrogen fracturing process.Several numerical models have been developed to investigate fracture behaviors during the hydraulic fracturing process. These models include the boundary element method [28], finite element method [29][30][31], and discrete element method [32,33]. Wang et al. [29] applied a new mathematical model to investigate fracture network evolution of multi-stranded fractures with pre-existing natural fractures. Shalev and Lyakhovsky [31] studied the damage evolution and seismicity phenomenon in hydraulic fracturing using an improved damage model based on the finite element method. However, there are still only a few studies on a numerical model for nitrogen fracturing and the comparison between water fracturing and nitrogen fracturing. On the other hand, shale reservoirs occur at di...

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“…An attractive feature of this hypothesis is that prescription of two physically meaningful functionals (Helmholtz potential and dissipation functional) provides the constitutive relations even for a phenomenon which involves a multitude of interacting processes [Ziegler and Wehrli, 1987]. Subsequently, this hypothesis has been successfully employed to develop constitutive models for a wide variety of physical phenomena, which include inelasticity [Srinivasa and Srinivasan, 2009], anisotropic fluids [Rajagopal and Srinivasa, 2001], degradation of materials [Xu et al, 2016], and diffusion in viscoelastic polymers [Karra, 2013]. However, this hypothesis has not been utilized to derive constitutive relations for porous media with multiple pore-networks.…”

Section: Proposed Approach To Develop Double Porosity/permeability Momentioning

confidence: 99%

Modeling Flow in Porous Media With Double Porosity/Permeability: Mathematical Model, Properties, and Analytical Solutions

Nakshatrala

Joodat

Ballarini

2018

Journal of Applied Mechanics

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Geo-materials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores with different hydro-mechanical properties. Moreover, these pore-networks are connected through fissures and conduits. Although some models are available in the literature to describe flow in such porous media, they lack a strong theoretical basis. This paper aims to fill this lacuna by providing the much needed theoretical foundations of the flow in porous media that exhibit double porosity/permeability. We first obtain a mathematical model using the maximization of rate of dissipation hypothesis, and thereby providing a firm thermodynamic underpinning. We then present, along with mathematical proofs, several important mathematical properties that the solutions to the model satisfy. We also present several canonical problems and obtain the corresponding analytical solutions, which are used to gain insights into the velocity and pressure profiles, and the mass transfer across the two pore-networks. In particular, we highlight how the solutions under the double porosity/permeability differ from the corresponding ones under Darcy equations.

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Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions

Cited by 21 publications

References 60 publications

Thermo-Chemo-Poromechanical Modeling of the Anode Mixture During the Baking Process: Constitutive Laws and Governing Equations

Thermo-Chemo-Poromechanical Modeling of the Anode Mixture During the Baking Process: Constitutive Laws and Governing Equations

Numerical Study of Fracture Network Evolution during Nitrogen Fracturing Processes in Shale Reservoirs

Modeling Flow in Porous Media With Double Porosity/Permeability: Mathematical Model, Properties, and Analytical Solutions

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