Investigating the effects of intersection flow localization in equivalent-continuum-based upscaling of flow in discrete fracture networks

Predicting effective permeabilities of fractured rock masses is a crucial component of reservoir modeling. Its often realized with the discrete fracture network (DFN) method, whereby single-phase incompressible fluid flow is modeled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in high computational costs. Equivalent continuum models (ECMs) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While continuum methods have the advantage of lower computational costs and the possibility of including matrix properties, choosing the right cell size to discretize the fracture network into an ECM is crucial to provide accurate flow results and conserve anisotropic flow properties. Whereas several techniques exist to map a fracture network onto a grid of continuum cells, the complexity related to flow in fracture intersections is often ignored. Here, numerical simulations of Stokes flow in simple fracture intersections are utilized to analyze their effect on permeability. It is demonstrated that intersection lineaments oriented parallel to the principal direction of flow increase permeability in a process we term intersection flow localization (IFL). We propose a new method to generate ECMs that includes this effect with a directional pipe flow parameterization: the fracture-and-pipe model. Our approach is compared against an ECM method that does not take IFL into account by performing ECM-based upscaling with a massively parallelized Darcy flow solver capable of representing permeability anisotropy for individual grid cells. While IFL results in an increase in permeability at the local scale of the ECM cell (fracture scale), its effects on network-scale flow are minor. We investigated the effects of IFL for test cases with orthogonal fracture formations for various scales, fracture lengths, hydraulic apertures, and fracture densities. Only for global fracture porosities above 30 % does IFL start to increase the systems permeability. For lower fracture densities, the effects of IFL are smeared out in the upscaling process. However, we noticed a strong dependency of ECM-based upscaling on its grid resolution. Resolution tests suggests that, as long as the cell size is smaller than the minimal fracture length and larger than the maximal hydraulic aperture of the considered fracture network, the resulting effective permeabilities and anisotropies are resolution-independent. Within that range, ECMs are applicable to upscale flow in fracture networks.

Effect of a High Mg Solute Content on the Hot Workability of Al–Mg Alloys

The workability of Al–xMg alloys with a high Mg content (Al–6Mg, Al–8Mg, Al–9Mg) was evaluated by investigating the microstructure and processing map. Hot torsion tests were conducted in the range of 350–500 °C between 0.1 and 1 s−1. Constitutive equations were derived from various effective stress–strain curves, and the thermal activation energies for deformation obtained were 171 kJ/mol at Al–6Mg, 195 kJ/mol at Al–8Mg, and 220 kJ/mol at Al–9Mg. In the case of the processing map, the instability region, which widened with increasing Mg content, was due mainly to the influence of the Mg solute, which activated grain boundary cracking and flow localization.

Plasticity: from Crystal Lattice to Macroscopic Phenomena

New representations concerning plasticity physics in crystals are discussed. The model of plastic flow is suggested, which can describe its main regularities. With the use of the experimental investigation, it is shown that the plastic flow localization plays the role in the evolution of plastic deformation. Obtained data are explained with the application of the principles of nonequilibrium-systems’ theory. The quasi-particle is introduced for the description of plasticity phenomenon. It is established the relation between plasticity characteristics of metals and their position in Periodic table of the elements. A new model is elaborated to address localized plastic-flow evolution in solids. The basic assumption of the proposed model is that the elementary plasticity acts evolving in the deforming of medium would generate acoustic emission pulses, which interact with the plasticity carriers and initiate new elementary shears. As found experimentally, the macrolocalization of plastic flow involves a variety of autowave processes. To address the phenomenon of localized plastic-flow autowaves, a new quasi-particle called ‘autolocalizon’ is introduced; the criterion of validity of the concept is assessed.

Localization in Flow of Non-Newtonian Fluids Through Disordered Porous Media

We combine results of high-resolution microfluidic experiments with extensive numerical simulations to show how the flow patterns inside a “swiss-cheese” type of pore geometry can be systematically controlled through the intrinsic rheological properties of the fluid. Precisely, our analysis reveals that the velocity field in the interstitial pore space tends to display enhanced channeling under certain flow conditions. This observed flow “localization”, quantified by the spatial distribution of kinetic energy, can then be explained in terms of the strong interplay between the disordered geometry of the pore space and the nonlinear rheology of the fluid. Our results disclose the possibility that the constitutive properties of the fluid can enhance the performance of chemical reactors and chromatographic devices through control of the channeling patterns inside disordered porous media.

Autowave Mechanics of Plastic Flow

The notions of plastic flow localization are reviewed here. It have been shown that each type of localized plasticity pattern corresponds to a given stage of deformation hardening. In the course of plastic flow development a changeover in the types of localization patterns occurs. The types of localization patterns are limited to a total of four pattern types. A correspondence has been set up between the emergent localization pattern and the respective flow stage. It is found that the localization patterns are manifestations of the autowave nature of plastic flow localization process, with each pattern type corresponding to a definite type of autowave. Propagation velocity, dispersion and grain size dependence of wavelength have been determined experimentally for the phase autowave. An elastic-plastic strain invariant has also been introduced to relate the elastic and plastic properties of the deforming medium. It is found that the autowave’s characteristics follow directly from the latter invariant. A hypothetic quasi-particle has been introduced which correlates with the localized plasticity autowave; the probable properties of the quasi-particle have been estimated. Taking the quasi-particle approach, the characteristics of the plastic flow localization process are considered herein.

Quasi-Particle Approach to the Autowave Physics of Metal Plasticity

This paper is the first attempt to use the quasi-particle representations in plasticity physics. The de Broglie equation is applied to the analysis of autowave processes of localized plastic flow in various metals. The possibilities and perspectives of such approach are discussed. It is found that the localization of plastic deformation can be conveniently addressed by invoking a hypothetical quasi-particle conjugated with the autowave process of flow localization. The mass of the quasi-particle and the area of its localization have been defined. The probable properties of the quasi-particle have been estimated. Taking the quasi-particle approach, the characteristics of the plastic flow localization process are considered herein.

Constitutive Relationship for Hot Deformation of TB18 Titanium Alloy

In the present work, the hot deformation behavior of TB18 titanium alloy was investigated by isothermal hot compression tests with temperatures from 650 to 880°C and strain rates from 0.001 to 10 s−1. The flow curves after friction and temperature correction show that the peak stress decreased with the temperature increase and the strain rate decrease. Three typical characteristics of flow behavior indicate the dynamic softening behavior during hot deformation. At a strain rate of 0.001∼0.01 s−1, the flow stress continues to decrease as the strain rate increases after the flow stress reaches the peak stress; the flow softening mechanism is dynamic recovery and dynamic recrystallization at a lower temperature and dynamic recrystallization at a higher temperature. The discontinuous yielding phenomenon could be seen at a strain rate of 1 s−1, dynamic recrystallization took place in the β single-phase zone, and flow localization bands were observed in the α + β two-phase zone. At a higher strain rate of 10 s−1, the flow instabilities were referred to as the occurrence of flow localization by adiabatic heat. Constitutive equation considering the compensation of strain was also established, and the results show high accuracy to predict the flow stress with the correlation coefficient of 99.2% and the AARE of 6.1%, respectively.