Simple Porous Media Research Articles

A comparison study between the realistic random modeling and simplified porous medium for gamma-gamma well-logging

The accurate determination of formation density and the physical properties of rocks is the most critical logging tasks which can be obtained using gamma-ray transport and detection tools. Though the simulation works published so far have considerably improved the knowledge of the parameters that govern the responses of the detectors in these tools, recent studies have found considerable differences between the results of using a conventional model of a homogeneous mixture of formation and fluid and an inhomogeneous fractured medium. It has increased concerns about the importance of the complexity of the model used for the medium in simulation works. In the present study, we have suggested two various models for the flow of the fluid in porous media and fractured rock to be used for logging purposes. For a typical gamma-gamma logging tool containing a 137Cs source and two NaI detectors, simulated by using the MCNPX code, a simplified porous (SP) model in which the formation is filled with elongated rectangular cubes loaded with either mineral material or oil was investigated. In this model, the oil directly reaches the top of the medium and the connection between the pores is not guaranteed. In the other model, the medium is a large 3-D matrix of 1 cm3 randomly filled cubes. The designed algorithm to fill the matrix sites is so that this realistic random (RR) model provides the continuum growth of oil flow in various disordered directions and, therefore, fulfills the concerns about modeling the rock textures consist of extremely complex pore structures. For an arbitrary set of oil concentrations and various formation materials, the response of the detectors in the logging tool has been considered as a criterion to assess the effect of modeling for the distribution of pores in the formation on simulation studies. The results show that defining a RR model for describing heterogeneities of a porous medium does not effectively improve the prediction of the responses of logging tools. Taking into account the computational cost of the particle transport in the complex geometries in the Monte Carlo method, the SP model can be satisfactory for gamma-gamma logging purposes.

Local Thermodynamic Description of Isothermal Single-Phase Flow in Simple Porous Media

Darcy’s law for porous media transport is given a new local thermodynamic basis in terms of the grand potential of confined fluids. The local effective pressure gradient is determined using non-equilibrium molecular dynamics, and the hydraulic conductivity and permeability are investigated. The transport coefficients are determined for single-phase flow in face-centered cubic lattices of solid spheres. The porosity changed from that in the closest packing of spheres to near unity in a pure fluid, while the fluid mass density varied from that of a dilute gas to a dense liquid. The permeability varied between 5.7 times {10^{-20}} hbox {m}^2 and 5.5 times {10^{-17}} hbox {m}^2, showing a porosity-dependent Klinkenberg effect. Both transport coefficients depended on the average fluid mass density and porosity but in different ways. These results set the stage for a non-equilibrium thermodynamic investigation of coupled transport of multi-phase fluids in complex media.

Three-Dimensional Imaging of Dissolution-Driven Convection in Simple Porous Media Using X-ray CT Scanning

Motivated by geological carbon dioxide (CO2) storage and the associated process of CO2 convective mixing in brine, we present an experimental method to visualize dissolution-driven convection in a three-dimensional porous medium. Owing to the difficulty of imaging the time-dependent convective process within an opaque medium, experiments so far have largely focused on two-dimensional systems. However, this imposes a strong restriction on the lateral spreading of the plumes. To explore the flow pattern within a three-dimensional medium, we present an experimental procedure employing X-ray computed tomography that enables the visualization of the spatial and temporal evolution of the mixing process non-invasively. To mimic the dissolution of CO2 in brine, we use potassium iodide (KI) in water. Here, we show the results with high spatial and temporal resolution for an experiment with a homogeneous packing of glass beads (Ra=5300). We discuss the evolution of the average solute mass fraction, compare it to numerical results of a purely diffusive process and report a strong enhancement of the dissolution process when convection dominates over diffusive mass transfer effects.

Complexity analysis of interconnected pore using hydraulic tortuosity

The complexity of the pore structure has been analysed using hydraulic tortuosity. The hydraulic tortuosity is defined as the ratio between the total curvature angles of the fluid flowpath to the distance between two facing sides of the sample. The fluid flowpaths in the connected pore are represented by streamlines which are calculated from the velocity map obtained from fluid flow simulation by means of Lattice Boltzmann Method. The streamline that is calculated with Euler Methods produce coordinates of the flowpath in the connected pore which are then used to calculate the tortuosity. The streamline are verified in a simple porous medium. The complexity analysis is verified on three simple models showing significant differences in complexity levels. The streamline generated using euler methods is suitable for the porous medium. The relation of the tortuosity and the permeability is tested in two porous medium that the permeability is known. It is found that the more complex the pore structure, the greater the tortuosity value. The hydraulic tortuosity is also inversely proportional to the permeability.

Ubiquity of anomalous transport in porous media: Numerical evidence, continuous time random walk modelling, and hydrodynamic interpretation

Anomalous transport in porous media is commonly believed to be induced by the highly complex pore space geometry. However, this phenomenon is also observed in porous media with rather simple pore structure. In order to answer how ubiquitous can anomalous transport be in porous media, we in this work systematically investigate the solute transport process in a simple porous medium model with minimal structural randomness. The porosities we consider range widely from 0.30 up to 0.85, and we find by lattice Boltzmann simulations that the solute transport process can be anomalous in all cases at high Péclet numbers. We use the continuous time random walk theory to quantitatively explain the observed scaling relations of the process. A plausible hydrodynamic origin of anomalous transport in simple porous media is proposed as a complement to its widely accepted geometric origin in complex porous media. Our results, together with previous findings, provide evidence that anomalous transport is indeed ubiquitous in porous media. Consequently, attentions should be paid when modelling solute transport by the classical advection-diffusion equation, which could lead to systematic error.

Cell-to-cell bacterial interactions promoted by drier conditions on soil surfaces

Bacterial cell-to-cell interactions are in the core of evolutionary and ecological processes in soil and other environments. Under most conditions, natural soils are unsaturated where the fragmented aqueous habitats and thin liquid films confine bacterial cells within small volumes and close proximity for prolonged periods. We report effects of a range of hydration conditions on bacterial cell-level interactions that are marked by plasmid transfer between donor and recipient cells within populations of the soil bacterium Pseudomonas putida Using hydration-controlled sand microcosms, we demonstrate that the frequency of cell-to-cell contacts under prescribed hydration increases with lowering water potential values (i.e., under drier conditions where the aqueous phase shrinks and fragments). These observations were supported using a mechanistic individual-based model for linking macroscopic soil water potential to microscopic distribution of liquid phase and explicit bacterial cell interactions in a simplified porous medium. Model results are in good agreement with observations and inspire confidence in the underlying mechanisms. The study highlights important physical factors that control short-range bacterial cell interactions in soil and on surfaces, specifically, the central role of the aqueous phase in mediating bacterial interactions and conditions that promote genetic information transfer in support of soil microbial diversity.

The effects of grain geometry on waterflooding and viscous fingering in micro-fractures and porous media from a lattice Boltzmann method study

The study of fluid fronts formed in porous media is important for enhanced oil recovery. The purposes of this study are to simulate waterflooding and to investigate influential factors on the fluid front movement through a micro-fracture and through simple porous media with different grain geometries. This study used the Shan–Chen form of the Lattice Boltzmann Method (LBM). An increase in the velocity is found to result in viscous fingering, whereas an increase in the wettability of the displacing fluid and the dynamic viscosity ratio creates a piston form of the fluid front. In porous media with the same porosities, various geometries act differently as obstacles against fluid flow from the inlet to the outlet. By enlarging the cross-sectional area of grains in the fluid paths and making them more tortuous, narrower and more twisted films of viscous fingering are formed. The sweep efficiency was also determined under various conditions: with a fixed capillary number, neutral wettability and different viscosity ratios; and with a fixed capillary number, viscosity ratio of (1/3) and wet or non-wet conditions. In all cases, the best sweep efficiency was obtained with grains of diamond geometry. Generally, the least sweep efficiency occurs with grains of star geometry. Simulation results verified the strength and accuracy of LBM predictions.

Prediction of the low-velocity distribution from the pore structure in simple porous media

Prediction of the low-velocity distribution from the pore structure in simple porous media

Implementation of a parallel ADI algorithm on a finite volume GPU-based elementary porous media flow computation

In this work we present flow simulations in laminar and turbulent regime within a representative elementary volume of a simplified porous media by solving the Navier–Stokes equations and a Low-Re turbulence $$k{-}\epsilon$$ model. Numerical solution was achieved with an implementation of the SIMPLE algorithm for pressure velocity coupling of variables, and the solution of the tridiagonal systems of algebraic equations was accomplished by a parallelized ADI scheme based on the Thomas algorithm. Implementation of the numerical solution was done with an in-house C code which combined OMP and CUDA technologies for computations based on CPU and GPU, respectively. Exponential structured grids were employed in the wall vicinity to capture the turbulence behavior. Results indicate that similar profiles for velocity, pressure, turbulent kinetic energy and its dissipation were found. Several CUDA grids were tested and their performances measured over two GPUs: GTX 680 and GTX TITAN. Considerable speedup was achieved by the GPUs over the CPU schemes even without the use of the device shared memory which was not explored due to the nature of the algorithm.

Computational fluid dynamics of cerebral aneurysm coiling using high-resolution and high-energy synchrotron X-ray microtomography: comparison with the homogeneous porous medium approach

BackgroundComputational modeling of intracranial aneurysms provides insights into the influence of hemodynamics on aneurysm growth, rupture, and treatment outcome. Standard modeling of coiled aneurysms simplifies the complex geometry of the...

Lattice Boltzmann simulations of heat transfer in flow past a cylinder and in simple porous media

The Lattice Boltzmann method has been further developed for flow and heat transfer computations in terms of two distribution functions. A modified boundary scheme for heat transfer has been proposed for curvilinear fluid–solid interfaces, based on a weighted relaxation time. Weight coefficients depend on the interface location with respect to the regular lattice. The approach has been validated for two cases in a simple and more complex geometry: a non-isothermal flow past a single circular cylinder and in simple porous (granular) media. Computations have been performed with the use of the new boundary scheme for curvilinear interfaces and compared to a standard scheme known from the literature. For the circular cylinder case, results for the local and averaged Nusselt numbers are validated with the outcome of other numerical methods and with experimental data. For the more complex geometry, two configurations are considered: a regular array of square cylinders and a random arrangement of circular cylinders to simulate a granular medium. The results for the Nusselt number are compared, after a suitable volume averaging, with available semi-empirical correlations.

Development of a Thermal-Hydraulic Analysis Code and Transient Analysis for a Fluoride-Salt-Cooled High-Temperature Test Reactor

The fluoride-salt-cooled high-temperature reactor (FHR) is an advanced reactor concept that uses high-temperature tristructural isotropic (TRISO) fuel with a low-pressure liquid salt coolant. Design of the fluoride-salt-cooled high-temperature test reactor (FHTR) is a key step in the development of the FHR technology and is currently in progress both in China and the United States. An FHTR based on pebble-bed core design with a coolant temperature of 600–700°C is being planned for construction by the Chinese Academy of Sciences’ (CAS) Thorium Molten Salt Reactor (TMSR) Research Center, Shanghai Institute of Applied Physics (SINAP). This paper provides preliminary thermal-hydraulic transient analyses of an FHTR using SINAP’s pebble-bed core design as a reference case. A point kinetic model is implemented using computer code by coupling with a simplified porous medium heat transfer model in the core. The founded models and developed code are applied to analyze the safety characteristics of the FHTR by simulating several transient conditions including the unprotected loss of flow, unprotected overcooling, and unprotected transient overpower accidents. The results show that SINAP’s pebble-bed core is a very safe reactor design.

Lattice Boltzmann simulations of flow past a circular cylinder and in simple porous media

The single relaxation time variant of the Lattice-Boltzmann Method (LBM) is applied to the two–dimensional simulations of viscous fluids. Two flow geometries are considered: a single obstacle (circular cylinder) and a system of obstacles making up a simple, computer-created porous medium. A comparative study of two boundary schemes at the fluid–solid interface is performed. Although reasonable results can be achieved with the usage of (non-equilibrium) half-way bounce–back conditions, the interpolation-free scheme is recommended because of its better accuracy and stability. For flow past a circular cylinder, the lift and drag coefficients are computed together with the Strouhal numbers for periodically shedding vortices and validated against empirical relationships for a wide range of Reynolds numbers. The single cylinder case was also used for a novel comparison of two outlet schemes. Next, the system of obstacles that makes up a porous medium is created in two ways: by a regular arrangement of identical obstacles and by a simple randomization of cylinder centres and radii. The pressure loss in function of volumetric flow rate is compared with empirical relationships: the Darcy–Forchheimer law and the Ergun correlation. The impact of the LBM boundary schemes and the Reynolds number on the permeability and Forchheimer coefficients is studied for the two arrangements.

Effect of the Darcy number on the energy flow and operating conditions of a thermoacoustic porous-medium system

In this paper, a simplified porous medium thermoacoustic system is modeled to observe its energy interaction characteristics and identify its operating conditions mainly as a function of porous medium Darcy number. The governing Darcy–Brinkman momentum equation and energy equation are simplified and linearized by using a first order perturbation analysis. Similar perturbation analysis is usually used to solve the linear thermoacoustic problem in the low Mach number limit. Simplified momentum and energy equations are solved, in the frequency domain, in order to obtain the expressions of the fluctuating velocity ( u 1) and temperature ( T 1). Time averaged and space averaged heat fluxes and work fluxes are calculated using the expressions of fluctuating velocity and temperature. The effects of the drive ratio (DR), Darcy number ( Da δ ), temperature gradient (∇ T m ), and frequency ( f) on the heat flux, work flux, and operating conditions are discussed and graphically presented.

Does pore water velocity affect the reaction rates of adsorptive solute transport in soils? Demonstration with pore-scale modelling

Modelling adsorptive solute transport in soils needs a number of parameters to describe its reaction kinetics and the values of these parameters are usually determined from batch and displacement experiments. Some experimental results reveal that when describing the adsorption as first-order kinetics, its associated reaction rates are not constants but vary with pore water velocity. Explanation of this varies but an independent verification of each explanation is difficult because simultaneously measuring the spatiotemporal distributions of dissolved and adsorbed solutes in soils is formidable. Pore-scale modelling could play an important role to address this gap and has received increased attention over the past few years. This paper investigated the transport of adsorptive solute in a simple porous medium using pore-scale modelling. Fluid flow through the void space of the medium was assumed to be laminar and in saturated condition, and solute transport consisted of advection and molecular diffusion; the sorption and desorption occurring at the fluid–solid interface were modelled as linear first-order kinetics. Based on the simulated spatiotemporal distribution of dissolved and adsorbed solutes at pore scale, volumetric-average reaction kinetics at macroscopic scale and its associated reactive parameters were measured. Both homogeneous adsorption where the reaction rates at microscopic scale are constant, and heterogeneous adsorption where the reaction rates vary from site to site, were investigated. The results indicate that, in contrast to previously thought, the macroscopic reaction rates directly measured from the pore-scale simulations do not change with pore velocity under both homogeneous and heterogeneous adsorptions. In particular, we found that for the homogeneous adsorption, the macroscopic adsorption remains first-order kinetic and can be described by constant reaction rates, regardless of flow rate; whilst for the heterogeneous adsorption, the macroscopic adsorption kinetics continues not to be affected by flow rate but is no longer first-order kinetics that can be described by constant reaction rates. We discuss how these findings could help explain some contrary literature reports over the dependence of reaction rates on pore water velocity.

Soot accumulation and combustion in porous media

Although diesel engines have an advantage of low fuel consumption compared with gasoline engines, several problems must be solved. One of the major concerns is that diesel exhaust gas has more particulate matters (PM) including soot, which are suspected to be linked to human carcinogen. As one of the key technologies, a diesel particulate filter (DPF) has been developed to reduce PM in the post-treatment of exhaust gas. In this study, the authors simulate soot accumulation and combustion in simplified porous media by the lattice Boltzmann method (LBM). Results show that the flow pattern is largely changed when the soot is accumulated. In combustion simulation, the reaction is well simulated to observe the reduction of accumulated soot with increasing temperature near the porous wall. The authors' approach can be used to capture the dynamics of soot behaviours in porous media flow for a better design of DPF.

Velocity fluctuations and dispersion in a simple porous medium.

We model a fluid-filled disordered porous medium by a lattice-Boltzmann system with randomly broken links. The broken links exert a friction on the fluid without excluding volume. Such a model closely mimics the idealized picture of a porous medium, which is often used in the theoretical analysis of hydrodynamic dispersion. We find that the Brinkman equation describes both the mean flow characteristics and the spatial decay of velocity fluctuations in the system. However, the temporal decay of the velocity correlations (that a particle experiences as it moves with the fluid), cannot be simply related to the spatial decay. It is this temporal decay that determines the dispersivity. Thus, hydrodynamic dispersion is generally greater than theories based on spatial correlations would imply. This is particularly true at high densities, where such theories considerably underestimate both the magnitude and transient time scale for dispersion. Nonetheless, temporal velocity correlations are still ultimately screened and the hydrodynamic dispersion coefficient converges exponentially. The long-lived transients reported for more realistic systems must therefore be due explicitly to the presence of excluded volume.

Prediction of interfacial areas during imbibition in simple porous media

The interfacial area between wetting (W-) and non-wetting (NW-) phases is one of the crucial parameters in several flow and transport processes in porous media. This paper gives predictions of such areas during imbibition (displacement of NW-phase by W) in simple porous media. The total interfacial area includes contributions from thin films of W-phase around soil particles, from trapped volumes of NW-phase, and from the meniscus between bulk NW- and W-phases. Imbibition was simulated with simple but physically representative pore-scale calculations in a geometrically predetermined random sphere packing. This approach allows the prediction of interfacial areas for different initial conditions (arising from different drainage endpoints, for example) and the investigation of the influence of phenomena such as “snap-off” of NW-phase due to coalescence of pendular rings. We find that the trend of interfacial area as a function of saturation is not sensitive to these considerations. These predictions were compared to different experimental data and were consistent with most of them. The predictions are also consistent with the conditions imposed by thermodynamics.

Numerical investigations of the steady state relative permeability of a simplified porous medium

The purpose of this paper is to investigate, by flow simulations in a uniform pore-space geometry, how the co and countercurrent steady state relative permeabilities depend on the following parameters: phase saturation, wettability, driving force and viscosity ratio. The main results are as follows: (i) with few exceptions, relative permeabilities are convex functions of saturation; (ii) the cocurrent relative permeabilities increase while the countercurrent ones decrease with the driving force; (iii) with one exception, phase 2 relative permeabilities decrease and phase 1 relative permeabilities increase with the viscosity ratio M = μ1/μ2; (iv) the countercurrent relative permeabilities are always less than the cocurrent ones, the difference being partly due to the opposing effect of the viscous coupling, and partly to different levels of capillary forces; (v) the pore-level saturation distribution, and hence the size of the viscous coupling, can be very different between the cocurrent and the countercurrent cases so that it is in general incorrect to estimate the full mobility tensor from cocurrent and countercurrent steady state experiments, as suggested by Bentsen and Manai (1993).

Prediction of relative permeability in simple porous media.

We present a predictive calculation of two-phase relative permeabilities in granular porous media formed from a dense random packing of equal spheres. The spatial coordinates of every sphere in the pack have been measured, enabling the microstructure of the medium to be completely determined. From these data we extract a network model that replicates the pore space. By compacting the packing or swelling individual spheres, we may generate model porous media of different porosities whose microstructure is also completely determined. We simulate both viscous- and capillary-dominated invasion of a nonwetting fluid into a wetting fluid contained in these media. During invasion we calculate the average hydraulic conductance of each phase to obtain the relative permeabilities as a function of fluid saturation. Because the microstructure is known, the calculations do not involve any adjustable parameters or supplementary measurements of pore structure. The computed relative permeabilities are successfully compared with experimental values previously measured on sand packs, bead packs, and a simple sandstone.