Single and Dual-Domain Models to Evaluate the Effects of Preferential Flow Paths in Alluvial Sediments

Typical features of preferential flow paths were evidenced by numerical tests of convective transport of conservative solutes performed in three blocks of alluvial sediments at the scale of depositional elements. The numerical experiments are analysed with standard single-domain models (SDMs) and with dual-domain models (DDMs): the model parameters are identified by minimisation of the misfit between the ??experimental?? and the modelled cumulative breakthrough curves (BTCs) and between the ??experimental?? and the modelled temporal moments of the BTCs. The results for the SDMs show different behaviours for the three model blocks and for the different flow directions, in good agreement with their hydrostratigraphic characteristics. The results for the DDMs sometimes correspond to cases for which one of the two domains is dominant and its values of diffusivity and average velocity are close to those obtained for the SDM; in some cases the DDM performs much better than the SDM and correctly represents the effects of preferential flow paths. Finally the relevance of the DDM is analysed in the framework of multi-objective optimisation: a proper choice of the objective-functions yields Pareto sets whose geometries are different for single- and dual-domain media.     

Seismic responses of a hemispherical alluvial valley to SV waves： a three-dimensional analytical approximation

An analytical solution to the three-dimensional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier–Bessel series expansion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot’s dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn: (1) there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; (2) the normalized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; (3) with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.The project was supported by the National Natural Science Foundation of China (50478062 and 10532070) and Open Fund at the Key Laboratory of Urban Security and Disaster Engineering (Beijing University of Technology), Chinese Ministry of Education. The English text was polished by Keren Wang.     

Experiments on Solute Transport in Aggregated Porous Media: Are Diffusions Within Aggregates and Hydrodynamic Dispersion Independent?

Two region models for solute transport in porous media assume that hydrodynamic dispersion in mobile water and solute diffusion within immobile water regions are independent. Experimental and theoretical results for transport through a macropore indicate that hydrodynamic dispersion and solute exchange are interdependent. Experiments were carried out to investigate this problem for a column packed with spherical porous aggregates. The effective diffusion coefficient of a tracer within the agreggates was determined from specific experiments. The dispersivity of the bed was determined from experiments carried out with a column filled with nonporous beads. We took advantage of the dependence of hydrodynamic dispersion on density ratios between the invading and displaced solutions to obtain a set of breakthrough curves corresponding to situations where the diffusion coefficient remains constant, whereas the dispersivity varies. Simulations reproduce correctly the experiments. Small discrepancies are noted that can be corrected either by increasing the dispersion coefficient or by fitting the external mass transfer coefficient. Increased dispersion coefficients probably reveal a modification of Taylor dispersion due to solute exchange. The fitted external mass transfer coefficients are close to the values obtained with classical correlations of the chemical engineering literature.     

Role of Molecular Diffusion in Contaminant Migration and Recovery in an Alluvial Aquifer System

Highly-resolved simulations and flow and transport in an alluvial system at the Lawrence Livermore National Laboratory (LLNL) site explore the role of diffusion in the migration and recovery of a conservative solute. Heterogeneity is resolved to the hydrofacies scale with a discretization of 10.0, 5.0 and 0.5m in the strike, dip and vertical directions of the alluvial-fan system. Transport simulations rely on recently developed random-walk techniques that accurately account for local dispersion processes at interfaces between materials with contrasting hydraulic and transport properties. Solute migration and recovery by pump and treat are shown to be highly sensitive to magnitude of effective diffusion coefficient. Further, transport appears significantly more sensitive to the diffusion coefficient than to local-scale dispersion processes represented by a dispersivity coefficient. Predicted hold back of solute mass near source locations during ambient migration and pump-and-treat remediation is consistent with observations at LLNL, and reminiscent of observations at the MADE site of Columbus Air Force Base, Mississippi. Results confirm the important role of diffusion in low-conductivity materials and, consequently, its impact on efficacy of pump-and-treat and other remedial technologies. In a typical alluvial system on a decadal time scale this process is, in part, fundamentally nonreversible because the average thickness of low-K hydrofacies is considerably greater than the mean-square length of penetration of the solute plume.     

Effects of geometric modulation and surface potential heterogeneity on electrokinetic flow and solute transport in a microchannel

A numerical investigation is performed on the electroosmotic flow (EOF) in a surface-modulated microchannel to induce enhanced solute mixing. The channel wall is modulated by placing surface-mounted obstacles of trigonometric shape along which the surface potential is considered to be different from the surface potential of the homogeneous part of the wall. The characteristics of the electrokinetic flow are governed by the Laplace equation for the distribution of external electric potential; the Poisson equation for the distribution of induced electric potential; the Nernst–Planck equations for the distribution of ions; and the Navier–Stokes equations for fluid flow simultaneously. These nonlinear coupled set of governing equations are solved numerically by a control volume method over the staggered system. The influence of the geometric modulation of the surface, surface potential heterogeneity and the bulk ionic concentration on the EOF is analyzed. Vortical flow develops near a surface modulation, and it becomes stronger when the surface potential of the modulated region is in opposite sign to the surface potential of the homogeneous part of the channel walls. Vortical flow also depends on the Debye length when the Debye length is in the order of the channel height. Pressure drop along the channel length is higher for a ribbed wall channel compared to the grooved wall case. The pressure drop decreases with the increase in the amplitude for a grooved channel, but increases for a ribbed channel. The mixing index is quantified through the standard deviation of the solute distribution. Our results show that mixing index is higher for the ribbed channel compared to the grooved channel with heterogeneous surface potential. The increase in potential heterogeneity in the modulated region also increases the mixing index in both grooved and ribbed channels. However, the mixing performance, which is the ratio of the mixing index to pressure drop, reduces with the rise in the surface potential heterogeneity.     

Experimental investigation of characteristic length scale in periodic heterogeneous porous media

An experimental investigation of scale-dependent dispersion in periodic heterogeneous porous media was conducted. Models with two-, three- and four-layer periodic heterogeneities were constructed to investigate the effect of heterogeneity size on the scale-dependence of dispersion. Longitudinal dispersion coefficients were determined as a function of column length by measuring the breakthrough of a continuous injection of potassium chloride tracer solution. Chloride ion concentration was monitored by recording the millivolt potential of silver/silver chloride electrodes placed at intervals along the length of the column. In all three models, dispersion appeared to be scale dependent up to a distance of approximately 20–30 times the size of the repeated heterogeneity group (hydraulic unit). Because all three models suggested a similar dependence, it was concluded that a medium with periodic heterogeneity may likely be characterized by the scale of its hydraulic unit.     

Long-wavelength dispersion of acoustic waves in transversely inhomogeneous anisotropic plates

Long-wavelength onset of the fundamental branches is described for a free anisotropic plate with arbitrary through-plate variation of material properties. Main attention is given to the flexural branch. Closed-form expressions for the leading-order dispersion coefficient of the velocity and displacement are derived for a generic case and exemplified for the various types of either continuous, or discrete, or periodic inhomogeneity and for the monoclinic symmetry. The relevance of the static averaging is examined in detail. The bounds for the slope of the flexural velocity branch are established. The upper fundamental branches are considered for the case when these are uncoupled inplane and shear horizontal ones.     

Diffusion of Tracer in Altered Tonalite: Experiments and Simulations with Heterogeneous Distribution of Porosity

Numerical time-domain-diffusion simulations were used for studying the diffusion behavior of tracer molecules in rock matrix with homogeneous and heterogeneous porosity. As the heterogeneous sample in these simulations, a 3D tomographic image of altered tonalite was used, in which the mineral components and the pores resolved by X-ray microtomography were represented by their respective intragranular porosities determined previously by the ¹⁴C-PMMA method. The apparent diffusion coefficient of a tracer in altered tonalite was determined experimentally, and was then used in the simulations. In the altered tonalite analyzed, inclusion of heterogeneity in the porosity increased the diffusion coefficient by 16 %. Altered and pristine feldspar was the main mineral component in the sample (72 %), and it also provided the dominant contribution to tracer diffusion, explaining alone 52 % of the diffusion coefficient. The large pores resolved by microtomography (6 %) and altered and pristine mica (22 %) gave an equal contribution to the diffusion coefficient. The simulation method applied was also validated by comparing the results to both an analytical and a numerical solution to the diffusion equation in a homogenous medium. In addition, the method was compared to discrete-time random-walk simulations in the case of randomly placed overlapping spheres.     

Methods of Quantum Field Theory in the Physics of Subsurface Solute Transport

The stochastic theory of subsurface solute transport has received stimulus recently from modeling techniques originating in quantum field theory (QFT), resulting in new calculations of the solute macrodispersion tensor that derive from the solving Dyson equation with a subsequent renormalization group analysis. In this paper, we offer a critical evaluation of these techniques as they relate specifically to the derivation of a field-scale advection–dispersion equation. An approximate Dyson equation satisfied by the ensemble-average solute concentration for tracer movement in a heterogeneous porous medium is derived and shown to be equivalent to a truncated cumulant expansion of the standard stochastic partial differential equation which describes the same phenomenon. The full Dyson equation formalism, although exact, is of no importance to the derivation of an improved field-scale advection–dispersion equation. Similarly, renormalization group analysis of the macrodispersion tensor has not yet provided results that go beyond what is available currently from the cumulant expansion approach.     

Non-linear normal modes and their bifurcation of a two DOF system with quadratic and cubic non-linearity

The non-linear normal modes (NNMs) and their bifurcation of a complex two DOF system are investigated systematically in this paper. The coupling and ground springs have both quadratic and cubic non-linearity simultaneously. The cases of ω₁:ω₂=1:1, 1:2 and 1:3 are discussed, respectively, as well as the case of no internal resonance. Approximate solutions for NNMs are computed by applying the method of multiple scales, which ensures that NNM solutions can asymtote to linear normal modes as the non-linearity disappears. According to the procedure, NNMs can be classified into coupled and uncoupled modes. It is found that coupled NNMs exist for systems with any kind of internal resonance, but uncoupled modes may appear or not appear, depending on the type of internal resonance. For systems with 1:1 internal resonance, uncoupled NNMs exist only when coefficients of cubic non-linear terms describing the ground springs are identical. For systems with 1:2 or 1:3 internal resonance, in additional to one uncoupled NNM, there exists one more uncoupled NNM when the coefficients of quadratic or cubic non-linear terms describing the ground springs are identical. The results for the case of internal resonance are consistent with ones for no internal resonance. For the case of 1:2 internal resonance, the bifurcation of the coupled NNM is not only affected by cubic but also by quadratic non-linearity besides detuning parameter although for the cases of 1:1 and 1:3 internal resonance, only cubic non-linearity operate. As a check of the analytical results, direct numerical integrations of the equations of motion are carried out.     

Identification methodology and comparison of phenomenological ductile damage models via hybrid numerical–experimental analysis of fracture experiments conducted on a zirconium alloy

The present study details the methodology of the identification process of uncoupled damage formulations proposed by Bai and Wierzbicki (B&W model – Bai and Wierzbicki (2008) and Modified Mohr–Coulomb – Bai and Wierzbicki (2010)) as well as the Lemaitre and enhanced Lemaitre coupled damage models. These uncoupled models were first implemented in the Finite Element (FE) software Forge2009®, then their parameters identifications were carried out. These identifications involve two steps: identification of hardening law parameters and identification of damage parameters. In the first step, the method to obtain the coefficient of a non-linear friction law in compression test is also presented. The second step differs between the above-mentioned models: the identification of uncoupled models is carried out through the experimental fracture strains of different loading paths, while the identification of Lemaitre’s model is based on the softening effect of damage. The latter model is enhanced by accounting for the influence of the Lode parameter to improve its ability to predict fracture in shear loading. The results show that, among the studied models, the proposed enhanced Lemaitre model gives overall best results in terms of fracture prediction for all the tests. The proportionality of studied loading paths is also discussed. It is shown that the compression is not suitable to identify the parameters of the studied uncoupled damage models.     

The Effect of Magnetic Field Dependent Viscosity on Thermosolutal Convection in a Ferromagnetic Fluid Saturating a Porous Medium

The effect of magnetic field dependent viscosity on thermosolutal convection in a ferromagnetic fluid saturating a porous medium is considered for a fluid layer heated and soluted from below in the presence of uniform magnetic field. Using linearized stability theory and normal mode analysis, an exact solution is obtained for the case of two free boundaries. For case of stationary convection, medium permeability has a destabilizing effect, whereas a stable solute gradient and magnetic field dependent viscosity have a stabilizing effect on the system. In the absence of magnetic field dependent viscosity, the destabilizing effect of non-buoyancy magnetization is depicted but in the presence of magnetic field dependent viscosity non-buoyancy magnetization may have a destabilizing or stabilizing effect on the onset of instability. The critical wave number and the critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of buoyancy magnetization parameter M₁ and the results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid saturating a porous medium heated from below in the absence of stable solute gradient. The oscillatory modes are introduced due to the presence of the stable solute gradient, which were non-existent in its absence. A sufficient condition for the non-existence of overstability is also obtained. The paper also reaffirms the qualitative findings of earlier investigations which are, in fact, limiting cases of the present study.     

Connectivity in Vuggy Carbonates, New Experimental Methods and Applications

The length and spatial distribution of the touching-vugs channels affect the degree of permeability variations and is the main contributor to heterogeneity in vuggy carbonates. Hence, this article focuses on vug connectivity characterization and its impact on fluid flow. A whole core sample was scanned by X-ray computed tomography (CT). Image segmentation was used to obtain a binarized three-dimensional (3D) model of the vuggy pore space. Analysis of the binarized 3D model is used to calculate the correlation function and correlation length for the vuggy pore space. Connectivity analysis of the binarized 3D model shows that 79% of the vugs connected network spanning along the sample. The remaining 21% vug porosity exists in a large number of isolated vugs. The correlation length for the connected vug network is found to be larger than for vugs in general. NMR T ₂ measurements at increasing capillary pressure is tested on the vuggy material and used to investigate the amount of connected- and isolated vugs. The results verify the large fraction of connected vugs. Application of NMR T ₂ measurements in combination with capillary pressure experiments can also reveal matrix properties that play an important role in recovery processes. The transition between non-Fickian and Fickian regimes for tracer/solute transport is studied by laboratory experiments performed at various sample lengths, from cm to m scale. For the largest sample measured in our experiments show that effluent concentration curve conform to the CDE solution, suggesting that the Fickian regime has been established.     

Computation of cascade flutter by uncoupled and coupled methods

A computational method for flutter prediction of turbomachinery cascades is presented. The flow through multiple blade passages is calculated using a time-domain approach with coupled aerodynamic and structural models. The unsteady Euler/Navier-Stokes equations are solved in quasi-three-dimensions using a second-order implicit scheme with dual time-stepping and a multigrid method. A structural model for the blades with bending and torsion degrees of freedom is integrated in time together with the flow field. Information between structural and aerodynamic models is exchanged until convergence in each real-time step. Computational results for a cascade are presented and compared with those obtained by the conventional energy method and with experimental and numerical data by other authors. Significant differences are found between the coupled and uncoupled methods at low mass ratios. A transonic test case with strong nonlinear phenomena is investigated with the fluid-structure coupled method. Results for inviscid flow are compared with results of Navier-Stokes computations.     

Ductile fracture: Experiments and computations

Numerous criteria have been developed for ductile fracture (DF) prediction in metal plastic deformation. Finding a way to select these DF criteria (DFCs) and identify their applicability and reliability, however, is a non-trivial issue that still needs to be addressed in greater depth. In this study, several criteria under the categories of ‘uncoupled damage criterion’ and the ‘coupled damage criterion’, including the continuum damage mechanics (CDM)-based Lemaitre model and the Gurson-Tvergaard-Needleman (GTN) model, are investigated to determine their reliability in ductile failure prediction. To create diverse stress and strain states and fracture modes, different deformation scenarios are generated using tensile and compression tests of Al-alloy 6061 (T6) with different sample geometries and dimensions. The two categories of criteria are coded into finite element (FE) models based on the unconditional stress integration algorithm in the VUMAT/ABAQUS platform. Through physical experiments, computations and three industrial case studies, the entire correlation panorama of the DFCs, deformation modes and DF mechanisms is established and articulated. The experimental and simulation results show the following. (1) The mixed DF mode exists in every deformation of concern in this study, even in the tensile test of the round bar sample with the smallest notch radius. A decrease of stress triaxiality (η-value) leads to a reduction in the accuracy of DF prediction by the two DFC categories of DFCs, due to the interplay between the principal stress dominant fracture and the shear-stress dominant factor. (2) For deformations with a higher η-value, both categories of DFCs predict the fracture location reasonably well. For those with a lower or even negative η-value, the GTN and CDM-based criteria and some of the uncoupled criteria, including the C&L, Ayada and Oyane models, provide relatively better predictions. Only the Tresca and Freudenthal models can properly predict the shear dominant fracture. The reliability sequence of fracture moment prediction is thus the GTN model, followed by the CDM-based model and the uncoupled models. (3) The applicability of the DFCs depends on the use of suitable damage evolution rules (void nucleation/growth/coalescence and shear band) and consideration of several influential factors, including pressure stress, stress triaxiality, the Lode parameter, and the equivalent plastic strain or shear stress. These parameters determine the deformation mode (shear dominant or maximum principal stress dominant deformation) and, further, the DF mechanism (dimple fracture/shear fracture/mixed fracture).     

Modeling of Solute Transport in a 3D Rough-Walled Fracture–Matrix System

Fluid flow and solute transport in a 3D rough-walled fracture–matrix system were simulated by directly solving the Navier–Stokes equations for fracture flow and solving the transport equation for the whole domain of fracture and matrix with considering matrix diffusion. The rough-walled fracture–matrix model was built from laser-scanned surface tomography of a real rock sample, by considering realistic features of surfaces roughness and asperity contacts. The numerical modeling results were compared with both analytical solutions based on simplified fracture surface geometry and numerical results by particle tracking based on the Reynolds equation. The aim is to investigate impacts of surface roughness on solute transport in natural fracture–matrix systems and to quantify the uncertainties in application of simplified models. The results show that fracture surface roughness significantly increases heterogeneity of velocity field in the rough-walled fractures, which consequently cause complex transport behavior, especially the dispersive distributions of solute concentration in the fracture and complex concentration profiles in the matrix. Such complex transport behaviors caused by surface roughness are important sources of uncertainty that needs to be considered for modeling of solute transport processes in fractured rocks. The presented direct numerical simulations of fluid flow and solute transport serve as efficient numerical experiments that provide reliable results for the analysis of effective transmissivity as well as effective dispersion coefficient in rough-walled fracture–matrix systems. Such analysis is helpful in model verifications, uncertainty quantifications and design of laboratorial experiments.     

Mathematical Analysis of the Effect of Sedimentation and Compaction on Steady Transport Profiles in Sediments

Based on fundamental principles transport equations are derived for components in sediment layers. These differ from the usual formulation by the fact that compaction of sediments is explicitly considered. Compaction without doubt plays a significant role in the processes of early diagenesis. As an effect of compaction changing porosity can be observed in sediment profiles. In the paper analytical solutions are derived for cases in which porosity logs show an exponential shape. Comparison with those solutions, which are obtained for the constant porosity (i.e., no compaction) situation, show the relevance of the theoretically rigorous formulation, which is therefore recommended for implementation in computational models.