A continuum‐discrete model using Darcy's law: formulation and verification

This paper presents a numerical scheme for fluid‐particle coupled discrete element method (DEM), which is based on poro‐elasticity. The motion of the particles is resolved by means of DEM. While within the proposition of Darcian regime, the fluid is assumed as a continuum phase on a Eulerian mesh, and the continuity equation on the fluid mesh for a compressible fluid is solved using the FEM. Analytical solutions of traditional soil mechanics examples, such as the isotropic compression and one‐dimensional upward seepage flow, were used to validate the proposed algorithm quantitatively. The numerical results showed very good agreement with the analytical solutions, which show the correctness of this algorithm. Sensitivity studies on the effect of some influential factors of the coupling scheme such as pore fluid bulk modulus, volumetric strain calculation, and fluid mesh size were performed to display the accuracy, efficiency, and robustness of the numerical algorithm. It is revealed that the pore fluid bulk modulus is a critical parameter that can affect the accuracy of the results. Because of the iterative coupling scheme of these algorithms, high value of fluid bulk modulus can result in instability and consequently reduction in the maximum possible time‐step. Furthermore, the increase of the fluid mesh size reduces the accuracy of the calculated pore pressure. This study enhances our current understanding of the capacity of fluid‐particle coupled DEM to simulate the mechanical behavior of saturated granular materials. Copyright © 2014 John Wiley & Sons, Ltd.     

A unified CFD‐DEM approach for modeling of debris flow impacts on flexible barriers

This paper presents a unified modeling framework to investigate the impacts of debris flow on flexible barriers, based on coupled computational fluid dynamics and discrete element method (CFD‐DEM). We consider a debris flow as a mixture of fluid and particles where the fluid and particle phases are modeled by the CFD and the DEM, respectively. The fluid‐particle coupling is considered by the exchange of interaction forces between CFD and DEM calculations. The flexible barrier is simulated by the DEM as a network of bonded particles with remote interactions. The proposed coupled CFD‐DEM approach enables us to conveniently handle the complicated three‐way interactions among the fluid, the particles, and the flexible barrier structure for debris flow impact simulations. The proposed approach is first used to investigate the influences of channel inclination and the volumetric solid fraction in a debris mixture on the impact force, the resultant deformation, and the retained mass in a flexible barrier. The predictions agree well with existing experimental and numerical studies. We further examine the possible failure modes of a flexible barrier under debris flow impact and their underlying mechanisms. The performance of different components in a flexible barrier system, including single wires, double twists and cables, and their load sharing mechanisms, are carefully evaluated. The proposed unified framework offers a novel, promising pathway towards physically based, quantitative analysis and design of flexible barriers for debris flow mitigation.     

Numerical study of two‐phase fluid distributions in fractured porous media

Two‐phase fluid distributions in fractured porous media were studied using a single‐component multiphase (SCMP) lattice Boltzmann method (LBM), which was selected among three commonly used numerical approaches through a comparison against the available results of micro X‐ray computed tomography. The influence of the initial configuration and the periodic boundary conditions in the SCMP LBM for the fluid distribution analysis were investigated as well. It was revealed that regular porous media are sensitive to the initial distribution, whereas irregular porous media are insensitive. Moreover, to eliminate the influence of boundaries, the model's buffer size of an SCMP LBM simulation was suggested to be taken as approximately 12.5 times the average particle size. Then, the two‐phase fluid distribution of a porous medium was numerically studied using the SCMP LBM. Both detailed distribution patterns and macroscopic morphology parameters were reasonably well captured. Finally, the two‐phase fluid distributions in a fractured porous media were investigated. The influence of the degree of saturation, fracture length, and fracture width on the fluid distributions and migration was explored. Copyright © 2015 John Wiley & Sons, Ltd.     

LBM–DEM modeling of fluid–solid interaction in porous media

Three porous media flow problems, in which the fluid mechanical interactions are critical, are studied in a mesoscopic–microscopic coupling system. In this system, fluid flow in the pore space is explicitly modeled at mesoscopic level by the lattice Boltzmann method, the geometrical representation and the mechanical behavior of the solid skeleton are modeled at microscopic level by the particulate distinct element method (DEM), and the interfacial interaction between the fluid and the solids is resolved by an immersed boundary scheme. In the first benchmark problem, the well‐known and frequently utilized Ergun equation is validated in periodic particle and periodic pore models. In the second problem, the upward seepage problem is simulated over three stages: The settlement of the column of sphere under gravity loading is measured to illustrate the accuracy of the DEM scheme; the system is solved to hydrostatic state with pore space filled with fluid, showing that the buoyancy effect is captured correctly in the mesoscopic–microscopic coupling system; then, the flow with constant rate is supplied at the bottom of the column; the swelling of the ground surface and pore pressure development from the numerical simulation are compared with the predictions of the macroscopic consolidation theory. In the third problem, the fluid‐flow‐induced collapse of a sand arch inside a perforation cavity is tested to illustrate a more practical application of the developed system. Through comparing simulation results with analytical solutions, empirical law and physical laboratory observations, it is demonstrated that the developed lattice Boltzmann–distinct element coupling system is a powerful fundamental research tool for investigating hydromechanical physics in porous media flow. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical modeling of strongly coupled microscale multiphase flow and solid deformation

When fluid flows in porous media under subsurface conditions, significant deformation can occur. Such deformation is dependent on structural and phase characteristics. In this paper, we investigate the effect of multiphase flow on the deformation of porous media at the pore scale by implementing a strongly coupled partitioned solver discretized with finite volume (FV) technique. Specifically, the role of capillary forces on grain deformation in porous media is investigated. The fluid and solid subdomains are meshed using unstructured independent grids. The model is applied for solving multiphase coupled equations and is capable of capturing pore scale physics during primary drainage by solving the Navier-Stokes equation and advecting fluid indicator function using volume of fluid (VOF) while the fluid is interacting with a nonlinear elastic solid matrix. The convergence of the coupled solver is accelerated by Aitken underrelaxation. We also reproduce geomechanical stress conditions, at the pore scale, by applying uniaxial stress on the solid while simultaneously solving the multiphase fluid-solid interaction problem to investigate the effect of external stress on fluid occupancy, velocity-field distribution, and relative permeability. We observe that the solid matrix exhibits elasto-capillary behavior during the drainage sequence. Relative permeability endpoints are shifted on the basis of the external stress exerted.     

Modelling hydraulic and capillary-driven two-phase fluid flow in unsaturated concretes at the meso-scale with a unique coupled DEM-CFD technique

The goal of the research was to demonstrate the impact of thin porous interfacial transition zones (ITZs) between aggregates and cement matrix on fluid flow in unsaturated concrete caused by hydraulic/capillary pressure. To demonstrate this impact, a novel coupled approach to simulate the two-phase (water and moist air) flow of hydraulically and capillary-driven fluid in unsaturated concrete was developed. By merging the discrete element method (DEM) with computational fluid dynamics (CFD) under isothermal settings, the process was numerically studied at the meso-scale in two-dimensional conditions. A flow network was used to describe fluid behaviour in a continuous domain between particles. Small concrete specimens of a simplified particle mesostructure were subjected to fully coupled hydro-mechanical simulation tests. A simple uniaxial compression test was used to calibrate the pure DEM represented by bonded spheres, while a permeability and sorptivity test for an assembly of spheres was used to calibrate the pure CFD. For simplified specimens of the pure cement matrix, cement matrix with aggregate, and cement matrix with aggregate and ITZ of a given thickness, DEM/CFD simulations were performed sequentially. The numerical results of permeability and sorptivity were directly compared to the data found in the literature. A satisfactory agreement was achieved. Porous ITZs in concrete were found to reduce sorption by slowing the capillary-driven fluid flow, and to speed the full saturation of pores when sufficiently high hydraulic water pressures were dominant.     

A four‐node plane parametric element based on quadrilateral area coordinate and its application to coupled solid‐deformation/fluid‐flow simulation for porous geomaterials

A four‐node plane parametric element AQGβ6‐I is constructed on the basis of the quadrilateral area coordinate, the generalized conforming principle and the projection technique with a penalty factor β within an interval of 0–1. When β = 0, the element has excellent bending performance. When β = 1, the element can pass patch test strictly; its performance is as good as many famous elements. When β value is between 0 and 1, such as β = 0.5, the element can arrive at a compromise between (relatively) low sensitivity to mesh distortion and perfect convergence. The work provides an illuminating method to alleviate a difficult problem in finite element modelling using the four‐node quadrilateral element, which can pass the strict patch test, but has poor performance in bending dominated problem; on the contrary, it has excellent performance in bending dominated problem but cannot pass the strong patch test. The AQGβ6‐I with the convergence formulation (β = 1) is then applied to coupled solid‐deformation/fluid‐flow simulation for porous geomaterials. The computational examples are carried out to demonstrate that the AQGβ6‐I (β = 1) element is not only stable, reliable and efficient but also of high accuracy. The present study provides a good applicable element for finite element simulations of solid‐deformation/fluid‐flow for porous geomaterials. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical stability for modelling of dynamic two‐phase interaction

Dynamic two‐phase interaction of soil can be modelled by a displacement‐based, two‐phase formulation. The finite element method together with a semi‐implicit Euler–Cromer time‐stepping scheme renders a discrete equation that can be solved by recursion. By experience, it is found that the CFL stability condition for undrained wave propagation is not sufficient for the considered two‐phase formulation to be numerically stable at low values of permeability. Because the stability analysis of the two‐phase formulation is onerous, an analysis is performed on a simplified two‐phase formulation that is derived by assuming an incompressible pore fluid. The deformation of saturated porous media is now captured in a single, second‐order partial differential equation, where the energy dissipation associated with the flow of the fluid relative to the soil skeleton is represented by a damping term. The paper focuses on the different options to discretize the damping term and its effect on the stability criterion. Based on the eigenvalue analyses of a single element, it is observed that in addition to the CFL stability condition, the influence of the permeability must be included. This paper introduces a permeability‐dependent stability criterion. The findings are illustrated and validated with an example for the dynamic response of a sand deposit. Copyright © 2015 John Wiley & Sons, Ltd.     

Three‐dimensional nonlinear finite element analysis of pile groups in saturated porous media using a new transmitting boundary

The dynamic behaviour of pile groups subjected to an earthquake base shaking is analysed. An analysis is formulated in the time domain and the effects of material nonlinearity of soil, pile–soil–pile kinematic interaction and the superstructure–foundation inertial interaction on seismic response are investigated. Prediction of response of pile group–soil system during a large earthquake requires consideration of various aspects such as the nonlinear and elasto‐plastic behaviour of soil, pore water pressure generation in soil, radiation of energy away from the pile, etc. A fully explicit dynamic finite element scheme is developed for saturated porous media, based on the extension of the original formulation by Biot having solid displacement (u) and relative fluid displacement (w) as primary variables (u–w formulation). All linear relative fluid acceleration terms are included in this formulation. A new three‐dimensional transmitting boundary that was developed in cartesian co‐ordinate system for dynamic response analysis of fluid‐saturated porous media is implemented to avoid wave reflections towards the structure. In contrast to traditional methods, this boundary is able to absorb surface waves as well as body waves. The pile–soil interaction problem is analysed and it is shown that the results from the fully coupled procedure, using the advanced transmitting boundary, compare reasonably well with centrifuge data. Copyright © 2007 John Wiley & Sons, Ltd.     

High‐resolution geochemical record of fluid–rock interaction in a mid‐crustal shear zone: a comparative study of major element and oxygen isotope transport in garnet

Garnet grains from an intensely metasomatized mid‐crustal shear zone in the Reynolds Range, central Australia, exhibit a diverse assortment of textural and compositional characteristics that provide important insights into the geochemical effects of fluid–rock interaction. Electron microprobe X‐ray maps and major element profiles, in situ secondary ion mass spectrometry oxygen isotope analyses, and U–Pb and Sm–Nd geochronology are used to reconstruct their thermal, temporal and fluid evolution. These techniques reveal a detailed sequence of garnet growth, re‐equilibration and dissolution during intracontinental reworking associated with the Ordovician–Carboniferous (450–300 Ma) Alice Springs Orogeny. A euhedral garnet porphyroblast displays bell‐shaped major element profiles diagnostic of prograde growth zoning during shear zone burial. Coexisting granulitic garnet porphyroclasts inherited from precursor wall rocks show extensive cation re‐equilibration assisted by fracturing and fragmentation. Oxygen isotope variations in the former are inversely correlated with the molar proportion of grossular, suggesting that isotopic fractionation is linked to Ca substitution. The latter generally show close correspondence to the isotopic composition of their precursor, indicating slow intergranular diffusion of O relative to Fe²⁺, Mg and Mn. Peak metamorphism associated with shearing (～550 °C; 5.0–6.5 kbar) occurred at c. 360 Ma, followed by rapid exhumation and cooling. Progressive Mn enrichment in rim domains indicates that the retrograde evolution caused partial garnet dissolution. Accompanying intra‐mineral porosity production then stimulated limited oxygen isotope exchange between relict granulitic garnet grains and adjacent metasomatic biotite, resulting in increased garnet δ¹⁸O values over length scales <200 μm. Spatially restricted oxygen interdiffusion was thus facilitated by increased fluid access to reaction interfaces. The concentration of Ca in channelled fracture networks suggests that its mobility was enhanced by a similar mechanism. In contrast, the intergranular diffusion of Fe²⁺, Mg and Mn was rock‐wide under the same P–T regime, as demonstrated by a lack of local spatial variations in the re‐equilibration of these components. The extraction of detailed reaction histories from garnet must therefore take into account the variable length‐ and time‐scales of elemental and isotopic exchange, particularly where the involvement of a fluid phase enhances the possibility of measureable resetting profiles being generated for slowly diffusing components such as Ca and O, even at low ambient temperatures and relatively fast cooling rates.     

Pore‐scale modeling of surface erosion in a particle bed

A fully coupled transient two‐dimensional model was employed to study fundamentals of flood‐induced surface erosion in a particle bed. The interaction of the liquid and solid phases is the key mechanism related to surface erosion. The solid phase was idealized at a particle scale by using the discrete element method. The fluid phase was modeled at a mesoscale level and solved using the lattice Boltzmann method. The fluid forces applied on the particles were calculated on the basis of the momentum the fluid exchanges with the particle. The proposed approach was used to model both single particles and particle beds subjected to Couette flow conditions. The behavior of both the single particle and the particle bed depended on particle diameter and surface shear fluid velocity. The conducted simulations show that the fluid flow profile penetrates the bed for a small distance. This penetration initiates sheet‐flow and surface erosion as the fluid interacts with particles. The effect of suppressing particle rotation on the fluid‐induced forces on the particle was also examined. Suppressing particle spinning may lead to underestimated erosion rate. Results of fluid and particle velocities were compared against experimental results and appeared to agree with the observed trends.Copyright © 2013 John Wiley & Sons, Ltd.     

General coupling extended multiscale FEM for elasto‐plastic consolidation analysis of heterogeneous saturated porous media

This paper presents a general coupling extended multiscale FEM (GCEMs) for solving the coupling problem of elasto‐plastic consolidation of heterogeneous saturated porous media. In the GCEMs, the numerical multiscale base functions for the solid skeleton and fluid phase of the coupling system are all constructed on the basis of the equivalent stiffness matrix of the unit cell, which not only contain the interaction between the solid and fluid phases but also consider the time effect. Furthermore, in order to improve the computational accuracy for two‐dimensional problems, a multi‐node coarse element strategy for the GCEMs is proposed, and a two‐scale iteration algorithm for the elasto‐plastic consolidation analysis is developed. Some one‐dimensional and two‐dimensional homogeneous and heterogeneous numerical examples are carried out to validate the proposed method through the comparison with the coupling multiscale FEM and standard FEM. Numerical results show that the newly developed GCEMs can almost preserve the same convergent property as the standard FEM and also possesses the advantages of high computational efficiency. In addition, the GCEMs can be easily applied to other coupling multifield and multiphase transient problems. Copyright © 2014 John Wiley & Sons, Ltd.     

A model for pore‐fluid‐sensitive rock behavior using a weathering state parameter

Chalk and other porous rocks are known to behave differently when saturated with different pore fluids. The behavior of these rocks varies with different pore fluids and additional deformation occurs when the pore fluid composition changes. In this article, we review the evidence that behavior in porous rocks is pore‐fluid‐dependent, present a constitutive model for pore‐fluid‐dependent porous rocks, and present a compilation of previously published data to develop quantitative relationships between various pore fluids and mechanical behavior. The model proposed here is based on a state parameter approach for weathering and has similarities to models previously proposed for weathering‐sensitive rocks in that the values for parameters that characterize material behavior vary as a function of weathering. Comparisons with published experimental data indicate that the model is capable of reproducing observed behavior of chalk under a variety of loading conditions and changes in pore fluid composition. Copyright © 2008 John Wiley & Sons, Ltd.     

Phase equilibria modelling constraints on P–T conditions during fluid catalysed conversion of granulite to eclogite in the Bergen Arcs,Norway

Exhumed eclogitic crust is rare and exposures that preserve both protoliths and altered domains are limited around the world. Nominally anhydrous Neoproterozoic anorthositic granulites exposed on the island of Holsnøy, in the Bergen Arcs in western Norway, preserve different stages of progressive prograde deformation, together with the corresponding fluid‐assisted metamorphism, which record the conversion to eclogite during the Ordovician–Silurian Caledonian Orogeny. Four stages of deformation can be identified: (1) brittle deformation resulting in the formation of fractures and the generation of pseudotachylites in the granulite; (2) development of mesoscale shear zones associated with increased fluid–rock interaction; (3) the complete large‐scale replacement of granulite by hydrous eclogite with blocks of granulite sitting in an eclogitic “matrix”; and (4) the break‐up of completely eclogitized granulite by continued fluid influx, resulting in the formation of coarse‐grained phengite‐dominated mineral assemblages. P–T constraints derived from phase equilibria forward modelling of mineral assemblages of the early and later stages of the conversion to eclogite document burial and partial exhumation path with peak metamorphic conditions of ~21–22 kbar and 670–690°C. The P–T models, in combination with existing T–t constraints, imply that the Lindås Nappe underwent extremely rapid retrogressive pressure change. Fluid infiltration began on the prograde burial path and continued throughout the recorded P–T evolution, implying a fluid source that underwent progressive dehydration during subduction of the granulites. However, in places limited fluid availability on the prograde path resulted in assemblages largely consuming the available fluid, essentially freezing in snapshots of the prograde evolution. These were carried metastably deeper into the mantle with strain and metamorphic recrystallization partitioned into areas where ongoing fluid infiltration was concentrated.     

Fluid generation and evolution during exhumation of deeply subducted UHP continental crust: Petrogenesis of composite granite–quartz veins in the Sulu belt,China

Composite granite–quartz veins occur in retrogressed ultrahigh pressure (UHP) eclogite enclosed in gneiss at General's Hill in the central Sulu belt, eastern China. The granite in the veins has a high‐pressure (HP) mineral assemblage of dominantly quartz+phengite+allanite/epidote+garnet that yields pressures of 2.5–2.1 GPa (Si‐in‐phengite barometry) and temperatures of 850–780°C (Ti‐in‐zircon thermometry) at 2.5 GPa (~20°C lower at 2.1 GPa). Zircon overgrowths on inherited cores and new grains of zircon from both components of the composite veins crystallized at c. 221 Ma. This age overlaps the timing of HP retrograde recrystallization dated at 225–215 Ma from multiple localities in the Sulu belt, consistent with the HP conditions retrieved from the granite. The ε_Hf(t) values of new zircon from both components of the composite veins and the Sr–Nd isotope compositions of the granite consistently lie between values for gneiss and eclogite, whereas δ¹⁸O values of new zircon are similar in the veins and the crustal rocks. These data are consistent with zircon growth from a blended fluid generated internally within the gneiss and the eclogite, without any ingress of fluid from an external source. However, at the peak metamorphic pressure, which could have reached 7 GPa, the rocks were likely fluid absent. During initial exhumation under UHP conditions, exsolution of H₂O from nominally anhydrous minerals generated a grain boundary supercritical fluid in both gneiss and eclogite. As exhumation progressed, the volume of fluid increased allowing it to migrate by diffusing porous flow from grain boundaries into channels and drain from the dominant gneiss through the subordinate eclogite. This produced a blended fluid intermediate in its isotope composition between the two end‐members, as recorded by the composite veins. During exhumation from UHP (coesite) eclogite to HP (quartz) eclogite facies conditions, the supercritical fluid evolved by dissolution of the silicate mineral matrix, becoming increasingly solute‐rich, more ‘granitic’ and more viscous until it became trapped. As crystallization began by diffusive loss of H₂O to the host eclogite concomitant with ongoing exhumation of the crust, the trapped supercritical fluid intersected the solvus for the granite–H₂O system, allowing phase separation and formation of the composite granite–quartz veins. Subsequently, during the transition from HP eclogite to amphibolite facies conditions, minor phengite breakdown melting is recorded in both the granite and the gneiss by K‐feldspar+plagioclase+biotite aggregates located around phengite and by K‐feldspar veinlets along grain boundaries. Phase equilibria modelling of the granite indicates that this late‐stage melting records P–T conditions towards the end of the exhumation, with the subsolidus assemblage yielding 0.7–1.1 GPa at <670°C. Thus, the composite granite–quartz veins represent a rare example of a natural system recording how the fluid phase evolved during exhumation of continental crust. The successive availability of different fluid phases attending retrograde metamorphism from UHP eclogite to amphibolite facies conditions will affect the transport of trace elements through the continental crust and the role of these fluids as metasomatic agents interacting with the mantle wedge in the subduction channel.     

He–Ar Isotopic Tracing of Pyrite from Ore-forming Fluids of the Sanshandao Au Deposit, Jiaodong Area

The Sanshandao Au deposit is located in the famous Sanshandao metallogenic belt, Jiaodong area. To date, accumulative Au resources of 1000 t have been identified from the belt. Sanshandao is a world-class gold deposit with Au mineralization hosted in Early Cretaceous Guojialing-type granites. Thus, studies on the genesis and ore-forming element sources of the Sanshandao Au deposit are crucial. He and Ar isotopic analyses of fluid inclusions from pyrite(the carrier of Au) indicate that the fluid inclusions have 3 He/4 He=0.043–0.21 Ra with an average of 0.096 Ra and 40 Ar/36 Ar=488–664 with an average of 570.8. These values represent the initial He and Ar isotopic compositions of ore-forming fluids for trapped fluid inclusions. The comparison of H–O isotopic characteristics combined with deposit geology and wall rock alteration reveals that the ore-forming fluids of the Sanshandao Au deposit show mixed crust–mantle origin characteristics, and they mainly comprise crust-derived fluid mixed with minor mantle-derived fluid and meteoric water during the uprising process. The ore-forming elements were generally sourced from pre-Cambrian meta-basement rocks formed by Mesozoic reactivation and mixed with minor shallow crustal and mantle components.     

Nb–Ta fractionation induced by fluid‐rock interaction in subduction‐zones: constraints from UHP eclogite‐ and vein‐hosted rutile from the Dabie orogen,Central‐Eastern China

Niobium and Ta concentrations in ultrahigh‐pressure (UHP) eclogites and rutile from these eclogites and associated high pressure (HP) veins were used to study the behaviour of Nb–Ta during dehydration and fluid‐rock interaction. Samples were collected through a ～2 km profile at the Bixiling complex in the Dabie orogenic belt, Central‐Eastern China. All but one eclogite away from veins (EAVs) display nearly constant Nb/Ta ratios ranging from 16.1 to 19.2, with an average of 16.9 ± 0.8 (2 SE), similar to that of their gabbroic protolith from the Yangtze Block. Nb/Ta ratios of rutile from the EAVs range from 12.7 to 25.3 among different individual grains, with the average values close to those of the corresponding bulk rocks. These observations show that Nb and Ta were not significantly fractionated by prograde metamorphism up to eclogite facies when no significant fluid‐rock interaction occurs. In contrast, Nb/Ta ratios of rutile from eclogites close to veins (ECVs) are highly variable from 17.8 to 49.8, which are systematically higher (by up to 17) than those of rutile from the veins. These observations demonstrate that Nb and Ta were mobilized and fractionated during localized fluid flow and intensive fluid‐rock interaction. This is strongly supported by Nb/Ta zoning patterns in single rutile grains revealed by in situ LA‐ICP‐MS analysis. Ratios of Nb/Ta in the ECV‐hosted rutile decrease gradually from cores towards rims, whereas those in the EAV‐hosted rutile are nearly invariable. Furthermore, the vein rutile shows Nb/Ta zoning patterns that are complementary to those in rutile from their immediate hosts (ECVs), suggesting an internal origin for the vein‐forming fluids. The Nb/Ta ratios of such fluids evolved from low values at the early stage of subduction to higher values at later supercritical conditions with increased temperature and pressure. Quantitative modelling was conducted to constrain the compositional evolution of metamorphic fluids during dehydration and fluid‐rock interaction focusing on Nb–Ta distribution. The modelling results based on our proposed multistage fluid phase evolution path can essentially reproduce the natural observations reported in the present study.     

Large eddy simulation of hydrocyclone—prediction of air-core diameter and shape

Hydrocyclones are widely used in the mining and chemical industries. An attempt has been made in this study, to develop a CFD (computational fluid dynamics) model, which is capable of predicting the flow patterns inside the hydrocyclone, including accurate prediction of flow split as well as the size of the air-core. The flow velocities and air-core diameters are predicted by DRSM (differential Reynolds stress model) and LES (large eddy simulations) models were compared to experimental results. The predicted water splits and air-core diameter with LES and RSM turbulence models along with VOF (volume of fluid) model for the air phase, through the outlets for various inlet pressures were also analyzed. The LES turbulence model led to an improved turbulence field prediction and thereby to more accurate prediction of pressure and velocity fields. This improvement was distinctive for the axial profile of pressure, indicating that air-core development is principally a transport effect rather than a pressure effect.     

A finite element algorithm for parameter identification of material models for fluid saturated porous media

In this contribution an algorithm for parameter identification of geometrically linear Terzaghi–Biot‐type fluid‐saturated porous media is proposed, in which non‐uniform distributions of the state variables such as stresses, strains and fluid pore pressure are taken into account. To this end a least‐squares functional consisting of experimental data and simulated data is minimized, whereby the latter are obtained with the finite element method. This strategy allows parameter identification based on in situ experiments. In order to improve the efficiency of the minimization process, a gradient‐based optimization algorithm is applied, and therefore the corresponding sensitivity analysis for the coupled two‐phase problem is described in a systematic manner. For illustrative purpose, the performance of the algorithm is demonstrated for a slope stability problem, in which a quadratic Drucker–Prager plasticity model for the solid and a linear Darcy law for the fluid are combined. Copyright © 2001 John Wiley & Sons, Ltd.