Continuous Porous Media Research Articles

Comprehensive CFD modelling of reduction behaviour inside coal-based composite pellets

ABSTRACT The direct reduction process of coal-based composite pellet involves a series of physicochemical reactions. This paper reports a 3D unsteady mathematical model for simulation of heat transfer, mass transfer and chemical reactions inside the pellets. In this model, the pellets are assumed to be continuous porous medium composed of fine spherical particles. User-defined functions (UDFs) program in C language are developed to define chemical reactions, parameters and linked to FLUENT. The results predicted by the model are good agreement with experimental data. In addition, temperature, concentration, pressure and flow field inside the pellets are investigated by the model. Finally, the effects of furnace temperature and pellet diameter on the average pellet temperature, average molar concentration of reducing gases and degree of metallization have been simulated. The results show that the reduction rate is influenced more by the average pellet temperature than by average molar concentration of reducing gases.

Elastoplastic analysis of anchored tunnel under seepage

In order to study the stress and displacement distribution of surrounding rock of full-length bonded anchor support tunnel under seepage. The surrounding rock is regarded as a uniform and continuous porous medium. The supporting reaction force and seepage force of the surrounding rock are converted into the axisymmetric radial volume force of the circular tunnel and act on the stress field. Considering the reinforcement of the surrounding rock parameters by the bolt, the mechanical model is established. The elastoplastic analysis method is used to derive the analytical solution of the stress and displacement elasticity of the surrounding rock and plastic analytical solution based on Mohr-Coulomb yield criterion, which can be used to obtain the expression of the radius of the plastic zone of the tunnel and the displacement of the wall. Finally, the calculation results of this paper are compared with the numerical simulation analysis. The results show that the influence of the seepage on the plastic zone range and the wall displacement is more serious. The length and pretension of the bolt are inversely related to the plastic zone range and the displacement of the wall. The bolt row spacing is positively correlated with the plastic zone range and the displacement of the wall. Under the same conditions, considering the seepage requires the anchor to provide greater support. In order to avoid the instability of tunnel caused by seepage, the length of the bolt can be reasonably increased, the bolt spacing can be reduced, and the bolt pretension can be increased.

Numerical analysis and modeling of multiscale Forchheimer–Forchheimer coupled model for compressible fluid flow in fractured media aquifer system

A multiscale coupled model is developed to simulate the compressible fluid flow in fractured media aquifer system, where the flow is governed by Forchheimer’s law in the fracture and continuum porous medium. Due to the fact that the thickness of fracture is much smaller than characteristic diameters of surrounding porous medium, the fracture is reduced to a lower dimensional interface and a more complicated transmission condition is derived on the fracture-interface. The coupled model is numerically solved by the finite difference method with an implicit iteration procedure. The fewest nodal points are used to construct the optimal scheme for approximating the multiscale Forchheimer–Forchheimer coupled model. Different degrees of freedom are located on both sides of fracture-interface in order to capture the jump of velocity. Second-order error estimates in discrete norms are derived on nonuniform staggered grids for both pressure and velocity. The proposed scheme can also be extended to high dimensional model without loss of accuracy. Numerical experiments are performed to demonstrate the efficiency and accuracy of the numerical method.

Effective Elastic and Hydraulic Properties of Fractured Rock Masses with High Contrast of Permeability: Numerical Calculation by an Embedded Fracture Continuum Approach

In this work, the hydromechanical modeling of the fractured rock masses was conducted based on a new numerical simulation method named as embedded fracture continuum (EFC) approach. As the principal advantage, this approach allows to simplify the meshing procedure by using the simple Cartesian meshes to model the fractures that can be explicitly introduced in the porous medium based on the notion of fracture cells. These last elements represent the grid cells intersected by at least one fracture in the medium. Each fracture cell in the EFC approach present a continuum porous medium whose hydromechanical properties are calculated from ones of the matrix and ones of the intersected fractures, thanks for using the well‐known solution of the joint model. The determination of the hydromechanical properties of the fracture cells as presented in this work allows to provide the theoretical base and to complete some simple approximations introduced in the literature. Through different verification tests, the capability of the developed EFC approach to model the hydromechanical behavior of fractured rock was highlighted. An analysis of different parameters notably the influence of the fracture cell size on the precision of the proposed approach was also conducted. This novel approach was then applied to investigate the effective permeability and elastic compliance tensor of a fractured rock masses taken from a real field, the Sellafield site. The comparison of the results calculated from this approach with ones conducted in the literature based on the distinct element code (UDEC) presents a good agreement. However, unlike the previous studies using UDEC, which limits only in the case of fractured rock masses without dead‐end fractures, our approach allows accounting for this kind of fractures in the medium. The numerical simulations show that the dead‐end fractures could have a considerable contribution on the effective compliance moduli, while their effect can be neglected to calculate the overall permeability of the of fractured rock masses.

Enriched mixed finite element models for dynamic analysis of continuous and fractured porous media

Enriched Finite Element Models are presented to more accurately investigate the transient and wave propagation responses of continuous and fractured porous media based on mixture theory. Firstly, the Generalized Finite Element Method (GFEM) trigonometric enrichments are introduced to suppress the spurious oscillations that may appear in dynamic analysis with the regular Finite Element Method (FEM) due to numerical dispersion/Gibbs phenomenon. Secondly, the Phantom Node Method (PNM) is employed to model multiple arbitrary fractures independently of the mesh topology. Thirdly, frictional contact behavior is simulated using an Augmented Lagrange Multiplier technique. Mixed Lagrangian interpolants, bi-quadratic for displacements and bi-linear for pore pressure, are used for the underlying FEM basis functions. Transient (non-wave propagation) response of fractured porous media is effectively modeled using the PNM. Wave propagation in continuous porous media is effectively modeled using the mixed GFEM. Wave propagation in fractured porous media is simulated using a mixed GFEM-enriched Phantom Node Method (PNM-GFEM-M). The developed mixed GFEM portion of the model is verified through a transient consolidation problem. Subsequently, the ability of the enriched FEM models to capture the dynamic response of fractured fully-saturated porous media under mechanical and hydraulic stimulations is illustrated. The superior ability of the PNM-GFEM-M in inhibiting spurious oscillations is shown in comparison against the regular finite element solutions of some impact problems. It is demonstrated that by embedding appropriate enrichment basis functions in both displacement and pore pressure fields the results obtained are more accurate than those obtained using standard finite element approximations or approximations in which only the displacement is enriched.

A hydromechanical approach for anisotropic elasto-viscoplastic geomaterials: Application to underground excavations in sedimentary rocks

To better describe excavation operations in deep geological formations, several aspects should be considered, especially the material anisotropy, time-dependent behavior, and hydromechanical coupling. In the present paper, a hydromechanical model based on the framework of continuous porous media was proposed. The mechanical elasto-viscoplastic constitutive model accounted for the material elastic and non-elastic anisotropies, using a transformation between the real transversely isotropic material and a fictitious isotropic material. Considering the hydraulic behavior, the permeability was expressed as a function of the volumetric viscoplastic strain. The model was applied to a case study of two tunnel excavations in an anisotropic rock under an initial anisotropic stress state. The results of the numerical simulations using a finite element code were in good agreement with the field convergence and permeability data.

Hydrodynamic dispersion in thin channels with micro-structured porous walls

Flow and transport within porous- and microtextured-walled channels is relevant to a number of natural and industrial processes. Designing and optimizing the topology of the pores and/or microstructure to achieve target performance at the system scale (or macroscale) is still an open question. In this work, we study whether hydrodynamic dispersion in microfluidic channels with walls structured by obstacles can be modeled by dispersion in channels with porous walls described as continuous porous media of zero or finite permeability. We perform single phase microfluidic non-reactive flow experiments in channels embedded in micropatterns with different topologies. Specifically, we focus on transverse riblets and arrays of pillars as examples of impermeable and permeable obstructions, respectively. We compare the experimental results with three models: 3D pore-scale simulations which resolve the micropattern geometry explicitly and two upscaled models which treat the micropattern as a continuum of zero or finite permeability. This study demonstrates that polydimethylsiloxane micromodels with appropriately patterned surfaces can be successfully employed to validate various continuum-scale modeling approximations in different physical regimes, identified by the order of magnitude of the Péclet number and the obstruction permeability.

Scaling and critical behavior of lattice and continuum porous media with different connectivity configurations

Determination of the connectivity and conductivity of porous media is of great importance in evaluation of fluid transport in different systems including petroleum formations, ground water hydrology, and contaminant transport. Among the conventional methods for connectivity forecasting, the percolation approach is an efficient method that can provide an estimate for both connectivity and conductivity of a porous medium as well as their uncertainties. In the classic percolation approach, connectivity is considered between two lines at the opposite sides of a 2-D porous medium (i.e., injectors and producers in the petroleum terminology). While in reality, the connectivity can be between point-shaped locations (e.g., point-to-point connection in a 2-D areal cross sectional map of a 3-D porous medium containing vertical wells). In this study, by implementing an object-based Monte Carlo simulations algorithm, the connectivity and conductivity behavior of a system with the point-shaped connectivity model is compared with that in the conventional line-shaped models. The focus of the research is on the evaluation of scaling and critical percolation properties of both lattice and continuum systems with different connectivity configurations. Having calculated the percolation threshold values as well as universal percolation exponents in both percolation systems, the scaling functions of connectivity and conductivity will be evaluated for both connectivity models. These scaling functions can be used to predict the connectivity and conductivity behavior of a system with any size by simple algebraic calculations. The results show that the point-to-point connection behavior of the site and continuum percolation is similar to each other but is different from that in the conventional line-to-line connectivity model.

Experimental and CFD analysis of the effects of debris deposition across the fuel assemblies

During a loss of coolant accident (LOCA) or a main steam line break accident (MSLB) in a pressurize water reactor (PWR), debris of different sorts like particulate, latent fiber or chemical nature might be generated due to jet impingement or ensuing, hot, pressurized steam leaking from the site of damage. This debris gets transported to the emergency core cooling system (ECCS) or the containment recirculation system (CRS) and might get deposited on the sump screens and causes a head loss. Some of these debris particles escape the sump screens and get access to the primary system through the bypass and thereafter challenge the core flow path and cause the head-loss across the fuel assemblies. The deposition of these debris particles in the fuel assemblies generates the possibility of hindering the long term core cooling (LTCC) of the nuclear power plant. The US Nuclear Regulation Commission (NRC) regulates the possibility of a commercial nuclear power plant to be able to maintain long term core cooling in case of a LOCA based event. In light of the aforementioned reasons the study of the debris particles inside the fuel assembly under different conditions becomes necessary to investigate the deposition of these debris particles in the assembly. This paper consists of two parts. The first part reports the experimental results carried out on an actual 15 × 15 experimental fuel assembly for the study of the effects of debris deposition on the pressure drop observed due to it. The second part reports CFD study of debris particles deposited on the spacer grid in the form of a continuous porous medium under different conditions. The study involves steady state (pseudo-transient) analysis of a scaled model of the fuel assembly with the variation of thickness of the porous debris bed, the inlet flow-rate of the fluid and the void fraction of the porous medium against the pressure drop observed.

Development of a discrete‐continuum VDFST‐CFP numerical model for simulating seawater intrusion to a coastal karst aquifer with a conduit system

AbstractA hybrid discrete‐continuum numerical model, Variable‐Density Flow and Solute Transport—Conduit Flow Process (VDFST‐CFP), is developed to simulate seawater intrusion to a coastal karst aquifer with a conduit network. The Darcy‐Weisbach equation is applied to simulate the nonlaminar groundwater flow in the conduit system that is conceptualized as pipes, while the Darcy equation is used for laminar groundwater flow in the continuum porous medium. Density‐dependent groundwater flow with appropriate additional density terms in the conduit is analytically derived. The flow and transport equations are coupled, and numerically solved by the finite difference method with an implicit iteration procedure. Two synthetic benchmarks are developed to compare the VDFST‐CFP model results with other numerical models, such as the variable‐density SEAWAT, constant‐density continuum MODFLOW/MT3DMS, and constant‐density discrete‐continuum CFPv2/UMT3D models. The VDFST‐CFP model compares reasonably well with the other model results in both conduit and porous medium domains, and well describes water and salt exchange between the two systems. Under turbulent flow conditions within the conduit, the Darcy‐Weisbach equation calculates the flow rate more accurately without overestimation by the Darcy equation. Sensitivity analysis indicates that conduit diameter, friction factor, matrix hydraulic conductivity, and effective medium porosity are important parameters in the VDFST‐CFP model. The pros and cons of the VDFST‐CFP model are discussed, including the model assumptions and simplifications, limitations of the discrete‐continuum modeling method, and the convergence criteria. In general, the newly developed VDFST‐CFP model provides a new numerical modeling method for simulating seawater intrusion in a coastal karst aquifer with conduits.

Linking hydraulic traits to tropical forest function in a size-structured and trait-driven model (TFS v.1-Hydro)

Abstract. Forest ecosystem models based on heuristic water stress functions poorly predict tropical forest response to drought partly because they do not capture the diversity of hydraulic traits (including variation in tree size) observed in tropical forests. We developed a continuous porous media approach to modeling plant hydraulics in which all parameters of the constitutive equations are biologically interpretable and measurable plant hydraulic traits (e.g., turgor loss point πtlp, bulk elastic modulus ε, hydraulic capacitance Cft, xylem hydraulic conductivity ks,max, water potential at 50 % loss of conductivity for both xylem (P50,x) and stomata (P50,gs), and the leaf : sapwood area ratio Al : As). We embedded this plant hydraulics model within a trait forest simulator (TFS) that models light environments of individual trees and their upper boundary conditions (transpiration), as well as providing a means for parameterizing variation in hydraulic traits among individuals. We synthesized literature and existing databases to parameterize all hydraulic traits as a function of stem and leaf traits, including wood density (WD), leaf mass per area (LMA), and photosynthetic capacity (Amax), and evaluated the coupled model (called TFS v.1-Hydro) predictions, against observed diurnal and seasonal variability in stem and leaf water potential as well as stand-scaled sap flux. Our hydraulic trait synthesis revealed coordination among leaf and xylem hydraulic traits and statistically significant relationships of most hydraulic traits with more easily measured plant traits. Using the most informative empirical trait–trait relationships derived from this synthesis, TFS v.1-Hydro successfully captured individual variation in leaf and stem water potential due to increasing tree size and light environment, with model representation of hydraulic architecture and plant traits exerting primary and secondary controls, respectively, on the fidelity of model predictions. The plant hydraulics model made substantial improvements to simulations of total ecosystem transpiration. Remaining uncertainties and limitations of the trait paradigm for plant hydraulics modeling are highlighted.

A fully coupled geomechanics and fluid flow model for proppant pack failure and fracture conductivity damage analysis

One reason for observed reductions in the conductivity of hydraulic fractures is failure of the proppant pack. Proppant deformation, crushing, or embedment can decrease the fracture width and conductivity. In this paper, the continuity and momentum balance equations were fully coupled to simulate the transient phenomena involving fluid flow through a deformable porous proppant pack. Porous media displacement, water pressure, and gas pressure were derived as primary unknowns. The governing equation was discretized using the finite element method and solved numerically. In this model, the proppant pack and formation rocks were treated as two different types of continuous porous media (Biot type). Proppant deformation, crushing, and embedment could be identified through the geomechanical model, while the damage effects on gas/oil production would be studied through the fluid-flow model. Analysis of proppant deformation and crushing was based on the proppant pack stress–strain behavior. The displacement of the fracture-formation interface represented both the deformation of proppant and rock solids around fracture surface. Mohr–Coulomb failure was used as the criterion for proppant crushing. Effects of proppant damage were evaluated on proppant pack porosity and permeability. The model can be applied generally in hydraulically fractured reservoirs with proper inputs. In this paper, we used a fractured tight sand gas reservoir as a study case. The pressure distribution as well as proppant pack deformation are illustrated in the paper. Proppant pack mechanical behavior was found to be sensitive to the fluid flow pressure. Proppant near the wellbore has a higher likelihood of being crushed.

Continuous and discrete microstructured materials with null Poisson's ratio

In this paper we propose different classes of isotropic microstructured media with tunable Poisson's ratio. The elastic periodic systems are continuous porous media and two- and three-dimensional lattices. The microstructural parameters can be tuned in order to have an effective Poisson's ratio equal to zero. The connection between microstructural parameters and effective properties is shown in detail both analytically and numerically.

A Mathematical Thermal Hydraulic-Mechanical Coupling Model for Unsaturated Porous Media

s: Temperature, seepage and deformation are the important parts of the engineering geological mechanics both in water conservancy and hydropower engineering since there are highly nonlinear complex coupling effect between each other. In this paper, the earth and rock mass are classified as continuous porous media. The thermal constitutive relation of porous media and motion regularity of pore fluid are deduced from the basic theory of solid mechanics, hydraulics, and thermodynamics. Based on momentum, mass and energy conservation equations, the multi-field controlling equations of unsaturated porous media are given, in which the unknown variables include displacements, pore liquid pressure, pore gas pressure, temperature, and porosity.

Seepage Field-Strain Field Coupling Analysis for Rock Masses of Coal Seam Floor during Mining Based on COMSOL

Based on the fluid-solid coupling theory, The fractured rock mass was described as a continuous porous medium, and consider the rock mass permeability coefficient has a relationship with the stress and strain. The dynamic change of permeability coefficient was achieved using the multi-physics coupling analysis software COMSOL, and found that the stress and strain of surrounding rocks changes a lot due to mining. The maximum stress and strain in the mudstone area reaches 2-3 times of the original one, which happened at the immediate roof of mined-out area. According to the analysis of seepage field, mining does not destroy water resistance of floor aquifer. Mining fissures do not connect limestone aquifers, and water in the limestone is less likely to flow into stop to cause damage.

Multi-scale groundwater flow modeling during temperate climate conditions for the safety assessment of the proposed high-level nuclear waste repository site at Forsmark, Sweden

Forsmark in Sweden has been proposed as the site of a geological repository for spent high-level nuclear fuel, to be located at a depth of approximately 470 m in fractured crystalline rock. The safety assessment for the repository has required a multi-disciplinary approach to evaluate the impact of hydrogeological and hydrogeochemical conditions close to the repository and in a wider regional context. Assessing the consequences of potential radionuclide releases requires quantitative site-specific information concerning the details of groundwater flow on the scale of individual waste canister locations (1–10 m) as well as details of groundwater flow and composition on the scale of groundwater pathways between the facility and the surface (500 m to 5 km). The purpose of this article is to provide an illustration of multi-scale modeling techniques and the results obtained when combining aspects of local-scale flows in fractures around a potential contaminant source with regional-scale groundwater flow and transport subject to natural evolution of the system. The approach set out is novel, as it incorporates both different scales of model and different levels of detail, combining discrete fracture network and equivalent continuous porous medium representations of fractured bedrock.

Influence of artificial ecological floating beds on river hydraulic characteristics

The artificial ecological floating bed is widely used in rivers and lakes to repair and purify polluted water. However, the water flow pattern and the water level distribution are significantly changed by the floating beds, and the influence on the water flow is different from that of aquatic plants. In this paper, based on the continuous porous media model, a moveable two-layer combination model is built to describe the floating bed. The influences of the floating beds on the water flow characteristics are studied by numerical simulations and experiments using an experimental water channel. The variations of the water level distribution are discussed under conditions of different flow velocities (v=0.1 m/s, 0.2 m/s, 0.30 m/s, 0.4 m/s), floating bed coverage rates (20%, 40%, 60%) and arrangement positions away from the channel wall (D = 0 m, 0.1 m, 0.2 m). The results indicate that the flow velocity increases under the floating beds, and the water level rises significantly under high flow velocity conditions in the upstream region and the floating bed region. In addition, the average rising water level value (ARWLV) increases significantly with the increase of the floating bed coverage rate, and the arrangement position of floating beds in the river can also greatly influence the water level distribution under a high-flow velocity condition (v ≥ 0.2 m/s).

Coupled chemical and mechanical processes in concrete structures with respect to aging

Accurate prognoses of the durability of concrete structures require a detailed description of the continuously running aging processes and a consideration of the complete load history. Therefore, in the framework of continuous porous media mechanics a model is developed, which allows a detailed analysis of the most important aging processes of concrete as well as a flexible coupling of different processes. An overview of the prediction model and the balance equations is given. The material dependent model equations, the consequences of coupling different processes and the solution scheme are discussed. In two case studies the aging of concrete due to hydration and chloride penetration are presented, which illustrate the capabilities and the characteristics of the developed model.

Modeling of coupled THMC processes in porous media

For landfill monitoring and aftercare, long-term prognoses of emission and deformation behaviour are required. Landfills may be considered as heterogeneous porous soil-like structures, in which flow and transport processes of gases and liquids interact with local material degradation and mechanical deformation of the solid skeleton. Therefore, in the framework of continuous porous media mechanics a model is developed that permits the investigation of coupled mechanical, hydraulical and biochemical processes in municipal solid waste landfills.

A methodology to constrain the parameters of a hydrogeological discrete fracture network model for sparsely fractured crystalline rock, exemplified by data from the proposed high-level nuclear waste repository site at Forsmark, Sweden

The large-scale geological structure of the crystalline rock at the proposed high-level nuclear waste repository site at Forsmark, Sweden, has been classified in terms of deformation zones of elevated fracture frequency. The rock between deformation zones was divided into fracture domains according to fracture frequency. A methodology to constrain the geometric and hydraulic parameters that define a discrete fracture network (DFN) model for each fracture domain is presented. The methodology is based on flow logging and down-hole imaging in cored boreholes in combination with DFN realizations, fracture connectivity analysis and pumping test simulations. The simulations suggest that a good match could be obtained for a power law size distribution where the value of the location parameter equals the borehole radius but with different values for the shape parameter, depending on fracture domain and fracture set. Fractures around 10–100 m in size are the ones that typically form the connected network, giving inflows in the simulations. The report also addresses the issue of up-scaling of DFN properties to equivalent continuous porous medium (ECPM) bulk flow properties. Comparisons with double-packer injection tests provide confidence that the derived DFN formulation of detailed flows within individual fractures is also suited to simulating mean bulk flow properties and their spatial variability.