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The mean stress tensor is essential to investigate the dynamics of granular material. In this paper, we use Hamilton's principle of least action to derive the averaged stress tensor of discrete granular assemblies subjected to hydraulic force fields, as well as rigorous conditions for a proper definition of the Representative Volume Element (RVE). The main goal behind our efforts is to upscale particle physics into a sound stress tensor for systems involving the complex interaction between grains and water. We identify the contributions from the unbalanced forces, hydraulic forces, gravity, external forces, and particle fluctuation to the mean stress tensor. In doing so, it is convenient to separate the influence of different force fields when the granular system is subjected to complex environments, e.g., subaqueous conditions. The obtained formula is then validated by triaxial test simulations of dry and saturated granular systems using the Discrete Element Method (DEM) and the Lattice-Boltzmann Method (LBM). The results show that the deduced formula can accurately calculate the stress tensor of discrete assemblies with various body-force fields. We used validated DEM-LBM simulations of submerged granular column collapses to explore the physics happening at the grain scale with this mathematical formalism and showcase its potential. We provide a new perspective based on the granular assembly scale to pursue the fluid-solid interaction. Due to the importance of stress analysis in the constitutive modelling of granular materials, this work could help to better obtain the stress-strain relationship of saturated or submerged granular systems.

Discrete element method (DEM) has achieved considerable success on simulating complex granular material behaviours. One of the key challenges of DEM simulations is how to describe particles with realistic geometries. Many shape description methods have been developed including sphere-clustering, polyhedrons, sphero-polyhedrons, superquadric particles to name a few. However, to model general shaped particles with round features , these techniques are either introducing artificial surface roughness or are limited to a few regular shapes. Here we proposed a metaball based DEM where the metaball equation is used to describe particle shapes. Because of its flexibility on choosing control points in the metaball equation, many complex shaped particles can be modelled within this framework. The particle collision is handled by solving an optimization problem. A Newton–Raphson method based algorithm of finding the closest points for metaball DEM is developed accordingly. Using 3D printed particles, the proposed scheme is validated by comparing the simulated ran-out distance with granular column collapses experimental results. The model is further applied to study shape effects on vibration induced segregations. It is shown that the proposed metaball DEM can capture shape influence which may crucial in many engineering and science applications.

The Lattice Boltzmann method has been widely adopted to simulate flow in porous media. The choice of appropriate boundary schemes is essential to achieve simulation accuracy; however, the criteria for the most suitable boundary treatment in the simulation of flow in porous media flow remain unresolved. Here, three types of the most commonly used boundary conditions are tested: interpolation bounce back (IBB), partial saturated method (PSM), and immersed boundary method (IBM). The dimensionless drag of face-centered cubic (FCC) sphere array and the dimensionless permeability of a random closely packed (RCP) sphere array are calculated and compared at different viscosities and resolutions. In the FCC sphere array case where spheres are not contacted, the IBB and PSM exhibit the same accuracy and both are of the second-order convergence rate. The IBM is less accurate and is of the first-order convergence rate. In the RCP sphere array case where the spheres are contacted, the IBB shows finer results and a second-order convergence rate. PSM underestimates the dimensionless permeability and increases resolution only slightly improved the results of PSM. The IBM overestimates the dimensionless permeability. These results indicate that among the three methods, the IBB is the most accurate. The PSM has the same accuracy as the IBB when sediments are not contacted; however, it loses its accuracy in the simulation of flow in closely packed porous media. This work could serve as a benchmark for further research in choosing the most appropriate method in the simulation of flow in porous media.

Both intra-pore hydrate morphology and inter-pore hydrate distribution influence the physical properties of hydrate-bearing sediments, yet there has been no pore-scale observations of hydrate habit under pressure in preserved pressure core samples so far. We present for the first time a pore-scale micro-CT study of natural hydrate-bearing cores that were acquired from Green Canyon Block 955 in UT-GOM2-1 Expedition and preserved within hydrate pressure–temperature stability conditions throughout sub-sampling and imaging processes. Measured hydrate saturation in the sub-samples, taken from units expected to have in-situ saturation of 80% or more, ranges from 3 ± 1% to 56 ± 11% as interpreted from micro-CT images. Pore-scale observations of gas hydrate in the sub-samples suggest that hydrate in silty sediments at the Gulf of Mexico is pore-invasive rather than particle displacive, and hydrate particles in these natural water-saturated samples are pore-filling with no evidence of grain-coating. Hydrate can form a connected 3D network and provide mechanical support for the sediments even without cementation. The technical breakthrough to directly visualize particle-level hydrate pore habits in natural sediments reported here sheds light on future investigations of pressure- and temperature-sensitive processes including hydrate-bearing sediments, dissolved gases, and other biochemical processes in the deep-sea environment.

Many experiments have shown large flow-enhancement ratios (up to ${10}^{5}$) in carbon nanotubes (CNTs) with diameters larger than 5 nm. However, molecular-dynamics simulations have never replicated these results maintaining a 3-orders-of-magnitude gap with measurements. Our study provides a generic model of nanofluidics for continuum slip flow ($\mathrm{diameter}g3$ nm) that fills this significant gap and sheds light on its origin. Compared to 140 literature cases, the model explains the entire range of experimental flow enhancements by changes of nanotube diameters and finite variations of interfacial energies. Despite large variations of flow-enhancement ratios spanning 5 orders of magnitude in experimental results, the ratio between these data and corresponding model predictions approaches unity for the majority of experiments. The role of viscous entrance effects is discussed. The model provides insight into puzzling observations such as differences of CNTs and boron-nitride nanotubes, the slip on low-contact-angle surfaces and massive functionalization effects. This study could advance our understanding of nanoscale transport mechanisms and aid the design of tailored nanomembranes.

In recent years, CO2 has been utilized to be injected into natural and induced fracture reservoirs with the purpose of enhanced natural energy resources recovery. In this study, the influence of liquid and supercritical CO2 properties under different pressure and temperature conditions on flow behaviors through a 3D self-affine fracture with rough surfaces is investigated with the application of Lattice Boltzmann method (LBM). CO2 has properties highly dependent on pressure and temperature and this study focuses on the liquid and supercritical CO2 properties because it is very common for CO2 to maintain liquid and supercritical states in deep reservoirs. LBM was used to simulate liquid and supercritical CO2 flow through a single fracture with rough surfaces. In addition to CO2 properties, the effects of pressure differences between the injecting and discharging surfaces of the fracture were also considered. The density and dynamic viscosity of CO2 display similar trends in responses to changes in pressure and temperature. Simulation results show that the average velocity of CO2 flow changes considerably with temperatures and pressures. The streamlines distributions revealed the changes of tortuosity under different temperature and pressure conditions, which follows a similar trend to that of the average velocity. A detailed analysis of the effects of the temperature, pressure and upscaling velocity on tortuosity was conducted based on the relevant curves and streamlines distributions. It was found that the values of tortuosity have a close relationship with the kinematic viscosity, which depends on temperature and pressure conditions.

The dynamics of simultaneous flow of immiscible two-phase fluids at the steady state in the capillary force-dominated regime were investigated. It was described by the key state variables, including interfacial area between fluids, capillary pressure and relative permeability, as functions of fluid saturation. Based on the two-dimensional pore-scale simulations using the Shan-Chen multi-component lattice Boltzmann model (SCMC-LBM), the steady-state interfacial area, capillary pressure and relative permeability versus saturation relationships subjected to flow conditions, such as initial fluid distribution, saturation history and magnitude of hydraulic gradient, were examined. Also, the intrinsic differences in the interfacial area and capillary pressure versus saturation curves between at dynamic equilibrium in the steady-state infiltration and at quasi-static equilibrium in the transient displacement were explored. As the SCMC-LBM simulations revealed, the relative permeabilities of both fluids were insensitive to initial fluid distribution or saturation history because of the simultaneous steady-state flow dynamics, but dependent on the magnitude of hydraulic gradient due to the existence of a threshold hydraulic gradient. The hysteresis behaviours of interfacial area-saturation and capillary pressure–saturation curves were captured in the transient displacement but absent in the steady-state infiltration, and the unique interfacial area-capillary pressure–saturation surface at dynamic equilibrium did not tend to overlap with the one at quasi-static equilibrium. The hysteretic capillary pressure behaviour for these two flow patterns was of great theoretical and practical significances.

In this paper, we have used a simulation software to show and characterize the phenomenology associated with airblast events in 3D when the block caving method is used in underground mining. The code couples the Lattice Boltzmann Method (LBM) and the Discrete Element Method (DEM) to simulate in an realistic way the interaction between rocks and the compressed air inside the mine. An underground mine model in 3D has been implemented to quantify simultaneously the air-velocity at the drawpoints and at the observation duct, when an airblast event occurs without warning due to the sudden fall of stuck rocks. The set of numerical simulations include several combinations of the physical properties of the muckpile as the height, angle and, permeability of the fractured zone. As well as, the air-gap size and the position of the observation duct in the mine. Using scaling arguments, a novel mathematical expression formed by the Darcy number is proposed to explain the maximum velocity of the air at the drawpoints. The results presented in this paper can be applied to design hazard and risk matrices in the mining industry, and therefore mitigate the possible damages to the personnel of the mine as well as to the equipment.

In order to improve the accuracy of existing immersed moving boundary method (IMBM) for the coupled discrete element lattice Boltzmann method, a novel weighting function for the fluid-particle interfacial interactions in IMBM is presented in this work. The flow is solved by the three-dimensional lattice Boltzmann method (LBM) D3Q15. The motions of particles are simulated by the discrete element method (DEM). The immersed moving boundary method is applied to resolve the momentum exchange between moving particles and fluids. The solid volume fraction of the fluid cell is calculated by the sphero-polyhedra method. The coupled IMBM-LBM-DEM is programmed based on the open source library Mechsys. The proposed method is validated by simulating flow past a stationary sphere, settling of a sphere and rebound of a spherical particle. These validations demonstrate the accuracy and reliability of this proposed method, which also has a good improvement over the original IMBM. Finally, effects of different parameters in the proposed weighting function are discussed and the suggested values a = 50, b = 0.01 are determined. This paper has implications for improving the ability to capture the fluid-particle interactions for a multiphase flow system. (C) 2018 Elsevier Ltd. All rights reserved.

We investigated the liquid slip in a planar confined flow channel by proposing an exponentially decaying interaction force between fluid particles and two flat walls in the mesoscopic lattice Boltzmann model framework. In this way, we can explicitly link density profile, velocity profile, and apparent slip length with the mesoscale interaction parameters (force strength and decay length), and formulate the permeability-enhancement ratio as a function of two dimensionless numbers that indicate the role of interaction strength and interaction distance (relative to gap size of flow channel) in the slip-flow system.

The collapse of granular columns, which sheds light on the kinematics, dynamics, and deposition morphology of mass-driven flows, is crucial for understanding complex flows in both natural and engineering systems, such as debris flows and landslides. However, our research shows that a strong size effect and cross-section shape influence exist in this test. Thus, it is essential to better understand these effects. In this study, we explore the influence of both relative column sizes and cross-section shapes on the run-out behavior of collapsed granular columns and analyze their influence on the deposition morphology with the discrete element method (DEM) with Voronoi-based spheropolyhedron particles. We link the size effect that occurs in granular column collapse problems to the finite-size scaling functions and investigate the characteristic correlation length associated with the granular column collapses. The collapsing behavior of granular columns with different cross-section shapes is also studied, and we find that particles tend to accumulate in the direction normal to the edge of the cross-section instead of the vertex of it. The differences in the run-out behavior in different directions when the cross-section is no longer a circle can also be explained by the finite-size analysis we have performed in this study. We believe that such a study is crucial for us to better understand how granular material flows, how it deposits, and how to consider the size effect in the rheology of granular flows.

Debris flows are natural events with a high potential of damage due to the materials, volume, and velocity they can reach once the flows were triggered. Mathematical models and numerical schemes constitute a transcendental way to get a deeper comprehension of these natural phenomena. Thus, the coupling of numerical methods is becoming more relevant to describe the behaviour of debris flows. The coupling of Smooth Particle Hydrodynamics (SPH) and Discrete Element Method (DEM) is presented in this work to show the capability to represent the interaction of several materials simultaneously. SPH is employed to represent the fluid and soil by using different constitutive models, from a continuum approach. On the other hand, DEM describes immersed objects to represent large boulders and unmoveable boundary conditions. Thus, it is possible to couple the behaviour occurring at very different scales, fines and water through the continuum approach, and boulders with the discrete one. A hypothetical case here presented shows the potential of our coupling method for simulating debris flows.

Debris flows have been widely researched during the last decades since they are catastrophic events with significant infrastructure and environmental impacts. Typically, they are composed of various materials which interactions are worth for studying, to improve the prediction of some variables, such as velocities, forces and affected areas. Constitutive models and numerical methods are fundamental in broadening the knowledge of the behaviour of these phenomena. Thus, the coupling of numerical techniques, for the different constituents of debris flow is becoming indispensable to describe the behaviour of these natural events. The coupling of Smooth Particle Hydrodynamics (SPH) and Discrete Element Method (DEM) is presented in this paper to show the capacity to represent the interaction of several materials at the same time. SPH is employed to represent the fluid and soil by using different constitutive models from a continuum approach. In contrast, DEM is used to represent immersed objects such as boulders and boundary conditions. In this sense, we can couple the behaviour that occurs at very different scales in a unified framework more suitable to describe the heterogeneity of debris flows. Benchmark cases were solved to validate this new approach. The simulations show good agreement with analytical solutions, experimental results and field data.

Higher-order lattice Boltzmann (LB) pseudopotential models have great potential for solving complex fluid dynamics in various areas of modern science. The discreteness of the lattice discretization makes these models an attractive choice due to their flexibility, capacity to capture hydrodynamic details, and inherent adaptability to parallel computations. Despite those advantages, the discreteness makes high-order LB models difficult to apply due to the larger lattice structure, for which basic fundamental properties, namely diffusion coefficient and contact angle, remain unknown. This work addresses this by providing general continuum solutions for those two basic properties and demonstrating these solutions to compare favorably against known theory. Various high-order LB models are shown to reproduce the sinusoidal decay of a binary miscible mixture accurately and consistently. Furthermore, these models are shown to reproduce neutral, hydrophobic, and hydrophilic contact angles. Discrete differences are shown to exist, which are captured at the discrete level and confirmed through droplet shape analysis. This work provides practical tools that allow for high-order LB pseudopotential models to be used to simulate multicomponent flows.

Granular column collapses result in an array of flow phenomena and deposition morphologies, the understanding of which brings insights into studying granular flows in both natural and engineering systems. Guided by experiments, we carried out computational studies with the discrete element method (DEM) to identify fundamental links between the macro-scale behavior and micro-scale properties of granular columns. A dimensionless number combining particle and bulk properties of the column, $$\alpha _{\text {eff}}$$ , was found from dimensional analysis to determine three collapse regimes (quasi-static, inertial, and liquid-like), revealing universal trends of flow regimes and deposition morphologies under different conditions. This dimensionless number may represent physically the competing inertial and frictional effects that govern the behavior of the granular column collapse, including energy conversion and dissipation. The finding is important for understanding quantitatively the flow of granular materials and their deposits.

In this study, the heat extraction from geothermal reservoirs with the application of CO2 and N2 miscible flow as the novel working fluids has been investigated based on the discrete fracture network model. The miscible flow with different CO2 and N2 proportions and highly pressure and temperature dependent properties have been integrated into reservoir simulations. The heat production processes for CO2 and N2 miscible flow have been simulated with two different discrete fracture networks, which also take the thermal-hydraulic-mechanical (THM) coupling mechanisms into consideration. Based on simulation results, it is revealed that the heat extraction efficiencies show an irregular trend with the increasing proportions of N2 in the mixture. It is found that the miscible flow with two different N2 proportions (20% and 40%) can be a more efficient working fluid than the one with larger N2 proportions. Based on simulation results, cumulative heat production curves that represent ten CO2 and N2 proportions can be divided into three categories. Evaluations of relevant permeabilities and effective normal stresses at sample points were made, which contributed to the comprehensive analysis of the heat transfer processes. It is also found that there are reasonable ranges for the miscible flow with different CO2 and N2 proportions as working fluids that allows higher heat extraction efficiencies, which are validated by a series of comparisons. Thus, in order to define the humps on the heat extraction efficiency curves, a new concept of the optimized heat extraction efficiency range is proposed and validated. It is proved that fluid properties of the miscible flow with different CO2 and N2 proportions and the reservoir temperature determine the optimized heat extraction efficiency range directly. This study proposes the miscible flow of CO2 and N2 as the working fluid, which provides a new alternative for geothermal energy production.

Simulations of simultaneous steady-state two-phase flow in the capillary force-dominated regime were conducted using the state-of-the-art Shan–Chen multi-component lattice Boltzmann model (SCMC-LBM) based on two-dimensional porous media. We focused on analyzing the fluid distribution (i.e., WP fluid-solid, NP fluid-solid and fluid-fluid interfacial areas) as well as the capillary pressure versus saturation curve which was affected by fluid and geometrical properties (i.e., wettability, adhesive strength, pore size distribution and specific surface area). How these properties influenced the relative permeability versus saturation relation through apparent effective permeability and threshold pressure gradient was also explored. The SCMC-LBM simulations showed that, a thin WP fluid film formed around the solid surface due to the adhesive fluid-solid interaction, resulting in discrete WP fluid distributions and reduction of the WP fluid mobility. Also, the adhesive interaction provided another source of capillary pressure in addition to capillary force, which, however, did not affect the mobility of the NP fluid. The film fluid effect could be enhanced by large adhesive strength and fine pores in heterogeneous porous media. In the steady-state infiltration, not only the NP fluid but also the WP fluid were subjected to the capillary resistance. The capillary pressure effect could be alleviated by decreased wettability, large average pore radius and improved fluid connectivity in heterogeneous porous media. The present work based on the SCMC-LBM investigations elucidated the role of film fluid as well as capillary pressure in the two-phase flow system. The findings have implications for ways to improve the macroscopic flow equation based on balance of force for the steady-state infiltration.

We introduce an analytical study of the links between macroscopic strength and the grain-to-grain interactions in two-dimensional frictional granular packings. This study consists of two main parts...

The mechanical behaviour of rocks can be conveniently studied using physical model tests under controlled conditions. Most of the physical models reported in the literature use natural rock samples. Being natural materials, rock samples can show widely varying mechanical and hydraulic responses. The varying responses make the interpretation of testing results difficult and even hinder the study of a selected phenomenon. On the other hand, the use of synthetic materials with customised mechanical properties can favourably reduce the influence of heterogeneities on the material behaviour, while maintaining fundamental mechanical behaviour of natural materials. In addition, randomness can be later included in synthetic materials to mimic natural materials. This paper presents two new synthetic materials and their carefully designed fabrication procedures to obtain reproducible samples. The design aims for low-strength brittle materials that can reduce the complexity and even the cost of experimental set-ups where the loading machine with lower stiffness can be used. Two types of materials are developed: (1) permeable-brittle; and (2) transparent-impermeable-brittle. These materials can help with experiments such as hydraulic fracturing. Standard tests are performed with these synthetic materials. Results demonstrate great advantage of the proposed synthetic materials.

Fluid–structure interactions (FSI) are very common in many natural processes and engineering applications. However, modeling FSI with large structural deformations and turbulence flows under high Reynolds number ( R e ) is still a challenging task. Here, we present a hybrid 3D model that combines the advantages of Lattice Boltzmann Method (LBM) in solving complex flow problems and the capability of Material Point Method (MPM) in handling large structural deformations. A sharp interface coupling scheme is presented in detail and a LES sub-grid model is adapted for turbulent flows. The structure solver is validated by comparing with Euler beam theory and the fluid solver is tested for fluid round circle and cube obstacles under a large range of R e . The coupled model is validated by simulations of a flexible plate deformation in shear flows. Good agreements are found comparing with experimental results. Finally some applications of importing realistic geometries from Computer Assisted Design (CAD) software, are shown to demonstrate the future applications of the method.

The thermal cone dissipation test is a newly-developed method for determining thermal conductivity in situ based on temperature dissipation over time. The standard cone penetration test with pore pressure measurement (CPTu) is used. The cone heats up as it is pushed through the soil, due to the build-up of friction on the cone and rods. The dissipation of this heat can then be measured when penetration of the cone is stopped at intervals, and the thermal conductivity of the soil over that test interval determined. Three thermal cone dissipation tests (TCT) were conducted, the first test in soft clay with a high moisture content, and the second and third tests in clay containing a stiff sandy clay layer. The stiff sandy clay layer showed the more significant temperature increase on cone penetration. Using a previously developed correlation, the thermal conductivity was then calculated for each TCT. The temperature increase of the cone for the duration of each CPTu test was also recorded. While the TCT is a promising new test, it is suggested that further research is necessary to develop and refine the method.

Simulations of two-dimensional (2D) flow past a circular cylinder with the smoothed particle hydrodynamics (SPH) method were conducted in order to accurately determine the drag coefficient. The fluid was modeled as a viscous liquid with weak compressibility. Boundary conditions, such as a no-slip solid wall, inflow and outflow, and periodic boundaries, were employed to resemble the physical problem. A sensitivity analysis, which has been rarely addressed in previous studies, was conducted on several SPH parameters. Hence, the effects of distinct parameters, such as the kernel choices and the domain dimensions, were investigated with the goal of obtaining highly accurate results. A range of Reynolds numbers (1–500) was simulated, and the results were compared with existing experimental data. It was observed that the domain dimensions and the resolution of SPH particles, in comparison to the obstacle size, affected the obtained drag coefficient significantly. Other parameters, such as the background pressure, influenced the transient condition, but did not influence the steady state at which the drag coefficient was determined.

Consequences of submarine landslides include both their direct impact on offshore infrastructure, such as subsea electric cables and gas/oil pipelines, and their indirect impact via the generated tsunami. The simulation of submarine landslides and their consequences has been a long-standing challenge majorly due to the strong coupling among sliding sediments, seawater and infrastructure as well as the induced extreme material deformation during the complete process. In this paper, we propose a unified finite element formulation for solid and fluid dynamics based on a generalised Hellinger–Reissner variational principle so that the coupling of fluid and solid can be achieved naturally in a monolithic fashion. In order to tackle extreme deformation problems, the resulting formulation is implemented within the framework of the particle finite element method. The correctness and robustness of the proposed unified formulation for single-phase problems (e.g. fluid dynamics problems involving Newtonian/Non-Newtonian flows and solid dynamics problems) as well as for multi-phase problems (e.g. two-phase flows) are verified against benchmarks. Comparisons are carried out against numerical and analytical solutions or experimental data that are available in the literature. Last but not least, the possibility of the proposed approach for modelling submarine landslides and their consequences is demonstrated via a numerical experiment of an underwater slope stability problem. It is shown that the failure and post-failure processes of the underwater slope can be predicted in a single simulation with its direct threat to a nearby pipeline and indirect threat by generating tsunami being estimated as well. The authors wish to acknowledge the support of European Commission H2020 Marie Sklodowska-Curie actions individual fellowship (Reference 744281; Proposal title “Towards Submarine Landslides and Their Consequences”).

The observation of structural changes inside geo-materials during testing is still uncommon in geotechnical engineering. New developments in imaging techniques and improved analysis methods allow us for the first time to observe structural changes inside geo-materials and to provide us with the required information for developing new knowledge and constitutive relationships. The presented paper introduces three approaches for observing structural changes in porous media: (1) Particle Imaging Velocimetry (PIV) in combination with transparent hydro-gel beads, (2) Spatial Time Domain Reflectometry (Spatial TDR) for observing porosity distributions during contact erosion testing, and (3) Ultra High Speed Camera (UHSC) imaging in combination with a brittle, low strength rock like material for investigating hydraulic fracturing.

A discrete element method (DEM) implementation is developed to study the micromechanics of liquefaction in granular materials. In a liquefaction event, the pore water acts as a cushion between the grains, reducing the contact and friction forces and the overall soil strength. The proposed model reproduces this phenomenon by introducing the effect of pore water as a constraint over the DEM particles' mechanics. The DEM particles will suffer resistance to any displacement changing the pore volume, which takes into account the very small compressibility of water. It is found that this constraint is enough to simulate soil liquefaction under quasistatic deformation. Finally, it is shown that the initial density of the granular skeleton, defined by the number of contacts between grains, plays a critical role in determining if the soil will liquefy or not. This critical value opens the possibility of treating liquefaction in soils as a bifurcation problem.

In this work we address the application of pseudopotentials directly on high-order lattice Boltzmann models. We derive a general expression for the pressure tensor on high-order lattices considering all nonideal interactions, including intra- and intermolecular interactions, following the discrete lattice theory introduced by X. Shan [Phys. Rev. E 77, 066702 (2008)PLEEE81539-375510.1103/PhysRevE.77.066702]. From the derived expression, a generalized continuum approximation, truncated at fourth-order isotropy, is obtained that is readily applicable to high-order lattices. With this, we demonstrate that high-order lattice models with pseudopotentials can satisfy thermodynamic consistency. The derived generalized expression and continuum approximation are validated for the case of a flat interface and compared against the standard definition available from the literature. The generalized expression is also shown to accurately reproduce the Laplace experiment for a variety of high-order lattice structures. This work sets the preliminary steps towards the application of high-order lattice models for simulating nonideal fluid mixtures.

The liquid slippage behavior due to molecular interactions at fluid-solid (F-S) interfaces is of great importance to the transport of shale oil and clay water. A mesoscopic single-phase lattice Boltzmann method (LBM), based on a continuous and exponentially decaying F-S interaction force and a midgrid bounce-back boundary condition, is proposed to be responsible for the apparent liquid slippage. The F-S interaction force is established at the particle level and thus can be readily extended to porous media. When it is repulsive (attractive), the phenomena of positive (negative) slip lengths and fluid slip (damping) are successfully recovered. This model is validated by the velocity profiles on hydrophobic and hydrophilic surfaces in a benchmark microchannel flow experiment. The slip length is found to be independent of shear rate (its constituents including body force, pore diameter, and kinematic viscosity), but dependent on pore geometry (smaller in porous media than in capillary tubes). Both slip length and permeability ratio follow a power law relationship with interaction parameters (strength and decay length) in capillary tubes and porous media. The permeability ratio estimated analytically with the slip length considered agrees well with that calculated from the LBM simulations, except for the fluid slip in porous media with a significant overestimation. The estimated permeability ratio indicates that it increases (decreases) nonlinearly as the pore diameter decreases, suggesting the great importance of the F-S interaction particularly for thin capillary tubes and microporous media.

Slip flow in ducts and porous media is simulated using lattice-Boltzmann method incorporated with interfacial force models. The dependence of the results on the viscosity, LBM scheme (D3Q15 and D3Q19) and the relaxation time model (single- or multirelaxation time) is investigated. The severity of spurious velocities (arisen from classic and advanced interfacial force models) is discussed that leads to entirely nonphysical results for whole flow rates (0.027 (kappa/kappa(NS))square ducts > (kappa/kappa(NS))porous media (where kappa is the permeability and NS denotes no-slip).

Pore-scale simulations using a Lattice Boltzmann Method (LBM)-based numerical model were conducted to examine how the capillary pressure ( P c ) and saturation (S) evolve within a virtual porous medium subjected to drainage and imbibition cycles. The results show the presence of a sharp front (interface separating the wetting and non-wetting fluids) across the cell during the test, which expectably moves up and down as the controlling non-wetting fluid pressure at the upper boundary varies to simulate different P c levels over the drainage and imbibition cycle. This phenomenon, representing inhomogeneity at the simulated scale, is in conflict with the homogenization applied to the pressure cell for deriving the constitutive P c – S relationship. Different boundary conditions, adopted to achieve more homogeneous states in the virtual soil, resulted in different P c – S curves. No unique relationship between P c and S, even with the interfacial area ( A nw ) included, could be found. This study shows dependence of the LBM-predicted P c – S relation on the chosen boundary conditions. This effect should be taken into account in future numerical studies of multiphase flow within porous media.

Discrete modeling of particle-fluid interaction was of great importance for its wide applications in chemical, petroleum and geotechnical engineering. Using Immersed Boundary Method (IBM) to couple Discrete Element Method (DEM) with Lattice Boltzmann Method (LBM) was adopted by many researchers to study particle-fluid systems. However, to accurately simulate the behavior of a large number of particles in the fluid, a huge computational power wasrequired to fully resolved the motion of each particle and an intensive search of particles’ contacts was needed to account for the collision between particles. In this paper, a periodic boundary was proposed for coupling DEM with LBM using IBM and an efficient particle contact detection algorithm was developed to further reduce the computation cost. The model was validated by several well-defined benchmark including: a single particle settling in a box, particle spinning in a channel and the well-known ‘Drafting, Kissing and Tumbling’ (DKT) effect of two settling disks. The model's applicability was exhibited in the simulation of sediments movement in a channel, which agreed well with previous experiments. These results showed the potential usage of present numerical model to investigate in particle-fluid interaction systems.

The flow conditions influencing the onset of contact erosion have been investigated physically using a novel setup based on the Particle Imaging Velocimetry (PIV) and numerically using a coupled DEM-LBM (Discrete Element Method-Lattice Boltzmann Method) approach. The flow conditions at the transition from base to filter material were experimentally quantified and computationally simulated resulting in a satisfactorily good agreement. An interesting and important outcome of these investigations is that the maximum flow velocity is not appearing in the base material, but in the constriction of the filter material in the transition zone from base to filter just above the surface of the base material. A generalised relationship between flow velocity and geometrical conditions at the transition zone was developed based on the Froude number. The characteristic evolution of the curve clearly shows the competition between hydraulic and geometric/mechanical conditions influencing the onset of contact erosion.

The Enhanced Geothermal Systems (EGS) has been developed to enhance geothermal energy extraction efficiency from geothermal reservoirs by generating effective fracture network. The fracture effective network that are comprised by rough-walled fractures can provide a more realistic reflection of natural reservoir conditions. This study focuses on the construction of a rough-walled discrete fracture model to simulate mass and heat transfer in a geothermal reservoir by using water and CO2 as the working fluid. The thermal-hydraulic-mechanical (THM) coupling process was integrated into the rough-walled discrete fracture network model. The heat mining processes with two working fluids (water and CO2) were simulated with the parallel-plate and rough-walled discrete facture network models. The influences of the parallel and rough-walled discrete fracture network models on flow behaviours, heat transfer and corresponding mechanical responses for water and CO2 were presented and analysed. What’s more, the heat extraction efficiency based on the combination of rough-walled discrete fracture network and the THM method were calculated and analysed in details. The influences of pressure, temperature, fluids and reservoir rock properties on heat extraction rates were also considered. It is found that CO2 leads to faster pressure changes compared with water in both parallel-plate and rough-walled discrete fracture network models. The influences of the pressure and temperature distributions on the permeability and normal stress were also evaluated, which contribute to the investigation of the deforming mechanisms of the rock matrix and fractures. In addition, there are certain differences in the heat production rate between the parallel-plate and rough-walled discrete fracture networks, which reflects that the rough-walled discrete fracture network used in this study has a better conductivity. It is also found that water can be a more efficient working fluid for heat extraction from geothermal reservoirs compared with CO2 during certain production durations in this study. The results of this study present that the rough-walled discrete network model has a great significance in the simulation of the real conditions and processes in geothermal reservoirs during the heat mining process.

Lattice-Boltzmann numerical simulations are conducted to explore the pore-scale flow behavior inside modeled porous media over the Darcy regime. We use static (fixed) and dynamic (rotating) particles to form the porous media. The pore flow behavior (tortuosity) is found to be constant in the static medium within the Darcy range. However, the study reveals distinctively different flow structures in the dynamic case depending on the macroscopic Darcy flow rate and the level of internal energy imposed to the system (via the angular velocity of particles). With small Darcy flow rates, tortuous flow develops with vortices occupying a large portion of the pore space but contributing little to the net flow. The formation of the vortices is linked to spatial fluctuations of local pore fluid pressure. As the Darcy flow rate (and, hence, the global fluid pressure gradient across the medium) increases, the effect of local pressure fluctuations diminishes, and the flow becomes more channelized. Despite the large variations of the pore-scale flow characteristics in the dynamic porous media, the macroscopic flow satisfies Darcy's law with an invariant permeability. The applicability of Darcy's law is proven for an internally disturbed flow through porous media. The results raise questions concerning the generality of the models describing the Darcy flow as being channelized with constant (structure-dependent) tortuosity and how the internal sources of energy imposed to the porous media flow are considered.

Extreme weather events, such as floods, are becoming more frequent in future with all consequences concerning the safety especially of water retaining structures, in particular, levees used as technical flood protection. The knowledge and correct consideration of coupled hydro-mechanical processes influencing the failure and post-failure behaviour of water saturated soils are of paramount significance for the assessment of hydraulically loaded geotechnical structures. This study focuses on the modelling of the processes governing the behaviour of water saturated soils using Smoothed Particle Hydrodynamics (SPH) on the example of a homogeneous embankment under different loading conditions. This paper aims to improve available SPH framework in order to enhance soil-water interaction in this method for geotechnical engineering investigations. To achieve this goal, the suggested approach is validated intensively by various well-known problems. Finally, the verified tool is used to investigate the hydro-mechanical behaviour of homogeneous embankments under simultaneous hydraulic and mechanical loading. The simulation results prove that the suggested approach is capable of simulating relevant hydraulic and mechanical processes governing the deformation behaviour of hydraulically loaded structures beyond the failure point allowing the detailed analysis of the post-failure behaviour characterised by large deformations.