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Lattice Boltzmann (LB) models can be used to simulate flow in porous media at scales much larger than pore size. LB-based models for such macroscopic scale porous media flow simulations are an extension of standard LB models. There are at least two alternative approaches for implementing such models. In the first approach the local velocity is altered during the collision step by incorporating an external force, F, equivalent to the damping effect of solid particles in porous media. The porous media can be permeable or impermeable depending upon the external forcing term. A sink term is introduced in the LB model to simulate a pumping well and this model is further applied to solve transient ground water well problems for confined aquifers.Directly solving the ground water flow equation with an LB model by exploiting its ability to solve the diffusion equation is another strategy. The second order transient ground water flow equation is analogous to the diffusion equation and mass diffusivity is analogous to hydraulic diffusivity. This diffusion model is used to solve transient ground water problems. Simulated results accurately match analytical solutions of the transient ground water flow equation.

This work reports a new and accurate way of theoretical and numerical description of the extended 3D fluid (electromagnetic and flow) driven crack progression in co-seismic slip under P- and S-waves. First, based on the viscous fluid flow reciprocal work theorem, the hybrid hypersingular integral equation (HIE) method proposed by the author was defined by combined with the coupled extended wave time-domain HIE and the extended diffused interface phase field method. The general extended 3D fluid flow velocity wave solutions are obtained by the extended wave time-domains Green’s function method. The 3D extended dynamic fluid driven crack modeling under fully coupled electromagnetothermoelastic P- and S-wave and flow field was established. Then, the problem is reduced to solving a set of extended hybrid HIEs coupled with nonlinear boundary domain integral equations, in which the unknown functions are the general extended flow velocity discontinuity waves. The behavior of the general extended singular stress indices around the crack front terminating is analyzed by hybrid time-domain main-part analysis. The general extended singular pore stress waves (SPSWs) and the extended dynamic stress intensity factors (DSIFs) on the fluid driven crack surface are obtained from closed-form solutions. In addition, a numerical method for the problem is proposed, in which the extended velocity discontinuity waves are approximated by the product of time-domain density functions and polynomials. The extended DSIFs and general extended SPSWs are calculated, and the results are presented toward demonstrating the applicability of the proposed method.

This contribution presents an extended hypersingular intergro-differential equation (E-HIDE) method for modeling the 3D interface crack problem in fully coupled electromagnetothermoelastic anisotropic multiphase composites under extended electro-magneto-thermo-elastic coupled loads through theoretical analysis and numerical simulations. First, based on the extended boundary element method, the 3D interface crack problem is reduced to solving a set of E-HIDEs coupled with extended boundary integral equations, in which the unknown functions are the extended displacement discontinuities. Then, the behavior of the extended singular stress indices around the interface crack front terminating at the interface is analyzed by the extended main-part analysis. The extended stress intensity factors near the crack front are defined. In addition, a numerical method for a 3D interface crack problem subjected to extended loads is proposed, in which the extended displacement discontinuities are approximated by the product of basic density functions and polynomials. Finally, the radiation distribution of extended stress intensity factors at the interface crack surface are calculated, and the results are presented toward demonstrating the applicability of the proposed method.

AU›o®ƒa®EAÝ : LBM, lattice Boltzmann method; MPA, Marshall’s probabilistic approach; PCC, probabilistic capillary connectivity. SO›‘®ƒ½ S›‘a®EA : FUƒ‘aƒ½Ý We derived two new expressions for the intrinsic permeability (k) of fractal porous media. The fi rst approach, the probabilisƟ c capillary connecƟ vity (PCC) model, is based on evaluaƟ ng the expected value of the cross-secƟ onal area of pores connected along various fl ow paths in the direcƟ on in which the permeability is sought. The other model is a modifi ed version of Marshall’s probabilisƟ c approach (MPA) applied to random cross matching of pores present on two parallel slices through a fractal porous medium. The Menger sponge is a three-dimensional mass fractal that represents the complicated pore space geometry of soil and rock. PredicƟ ons based on the analyƟ cal models were compared with esƟ mates of k derived from laƫ ce Boltzmann method (LBM) simulaƟ ons of saturated fl ow in virtual representaƟ ons of Menger sponges. Overall, the analyƟ cally predicted k values matched the k values from the LBM simulaƟ ons with

Addition of granular materials to floating crude oil slicks can be effective in capturing and densifying the floating hydrophobic phase, which settles by gravity. Interaction of light hydrophobic liquids (LHL) with quartz sand was investigated in LHL-salt water systems. The LHLs studied were decane, tetradecane, hexadecane, benzene, toluene, ethylbenzene, m-xylene, and 2-cholorotoluene. Experiments were conducted with fine quartz sand (passing sieve No. 40 with openings 0.425 mm). Each LHL was dyed with few crystals of Sudan IV dye for ease of visual observation. A volume of 0.5 mL of each LHL was added to 100 mL salt water (34 g/L). Addition of one gram of quartz sand to the floating hydrophobic liquid layer resulted in formation of sand-encapsulated globules, which settled due to increased density. All LHLs (except for a few globules of decane) formed globules covered with fine sand particles that were heavy enough to settle by gravity. The encapsulated globules were stable and retained their shape upon settling. Polarity of hydrophobic liquids as the main factor of aggregation with minerals was found to be insufficient to explain LHL aggregation with sand. Contact angle measurements were made by submerging a large quartz crystal with the LHL drop on its surface into salt water. A positive correlation was observed between the wetting angle of LHL and the LHL volume captured (r = 0.75). The dependence of the globule density on globule radius was analyzed in relation to the coverage (%) of globule surface (LHL-salt water interface) by fine quartz particles.

Recent analyses of field data suggest that saturated hydraulic conductivity, K, distributions of rocks and soils are multifractal in nature. Most previous attempts at generating multifractal K fields for flow and transport simulations have focused on stochastic approaches. Geometrical multifractals, in contrast, are grid-based and thus better able to simulate distinct facies or horizons. We present a theoretical framework for generating two-dimensional geometrical multifractal K fields. Construction of monofractal Sierpinski carpets using the homogenous and heterogeneous algorithms is recalled. Averaging multiple, non-spatially randomized, heterogeneous Sierpinski carpet generators yields a new generator with variable mass fractions determined by the truncated binomial probability distribution. Repeated application of this generator onto itself results in a multiplicative cascade of mass fractions or multifractal. The generalized moments, Mi(q), of these structures scale as Mi(q)=(1/b i ) (q−1)Dq , where b is the scale factor, i is the iteration level and Dq is the q−th order generalized dimension, with q being any integer between −∞and ∞. This theoretical approach is applied to the problem of aquifer heterogeneity by equating the mass fractions with K. An approximate analytical expression is derived for the effective hydraulic conductivity, Keff, of multifractal K fields, and Keff is shown to increase as a function of increasing length scale in power law fashion, with an exponent determined by Dq→∞. Numerical simulations of flow in b=3,Dq→∞=1.878 and i=1 though 5 multifractal K fields produced similar increases in Keff with increasing length scale. Extension of this approach to three dimensions appears to be relatively straightforward.

Application of the lattice Boltzmann method (LBM) to invasion percolation of single component multiphase fluids in porous media offers an opportunity for more realistic modeling of the configurations and dynamics of liquid/vapor and liquid/solid interfaces. The complex geometry of connected paths in standard invasion percolation models arises solely from the spatial arrangement of simple elements on a lattice. In reality, fluid interfaces and connectivity in porous media are naturally controlled by the details of the pore geometry, its dynamic interaction with the fluid, and the ambient fluid potential. The multiphase LBM approach admits realistic pore geometry derived from imaging techniques and incorporation of realistic hydrodynamics into invasion percolation models.

Considerable effort has been directed towards the application of percolation theory and fractal modeling to porous media. We combine these areas of research to investigate percolation in prefractal porous media. We estimated percolation thresholds in the pore space of homogeneous random 2-dimensional prefractals as a function of the fractal scale invariance ratio b and iteration level i. The percolation thresholds for these simulations were found to increase beyond the 0.5927l... porosity expected in Bernoulli (uncorrelated) percolation networks. Percolation in prefractals occurs through large pores connected by small pores. The thresholds increase with both b (a finite size effect) and i. The results allow the prediction of the onset of percolation in models of prefractal porous media and can be used to bound modeling efforts. More fundamental applications are also possible. Only a limited range of parameters has been explored empirically but extrapolations allow the critical fractal dimension to be estimated for a large combination of b and i values. Extrapolation to infinite iterations suggests that there may be a critical fractal dimension of the solid at which the pore space percolates. The extrapolated value is close to 1.89 – the well-known fractal dimension of percolation clusters in 2-dimensional Bernoulli networks.

Quantification of the character and spatial distribution of porosity in carbonate aquifers is important as input into computer models used in the calculation of intrinsic permeability and for next-generation, high-resolution groundwater flow simulations. Digital, optical, borehole-wall image data from three closely spaced boreholes in the karst-carbonate Biscayne aquifer in southeastern Florida are used in geostatistical experiments to assess the capabilities of various methods to create realistic two-dimensional models of vuggy megaporosity and matrix-porosity distribution in the limestone that composes the aquifer. When the borehole image data alone were used as the model training image, multiple-point geostatistics failed to detect the known spatial autocorrelation of vuggy megaporosity and matrix porosity among the three boreholes, which were only 10 m apart. Variogram analysis and subsequent Gaussian simulation produced results that showed a realistic conceptualization of horizontal continuity of strata dominated by vuggy megaporosity and matrix porosity among the three boreholes.

Fractal models of porous media are of interest in numerous scientific disciplines, including hydrology and soil science. This interest arises in part from the ability of these models to parsimoniously produce highly complex and richly structured geometries. Examination of the soil hydrology literature suggests that there are at least two different ways these models are being constructed. We review the two primary algorithms and compare the computed water retention behavior of the different media. Water retention is computed using a method that explicitly considers the connections between pores and to the atmosphere. The distributions of simulated water saturations (for 1000 realizations) around their median values as a function of applied tension were complex and multimodal for both homogeneous and heterogeneous prefractals. The range between the first and third quartiles for the water retention in heterogeneous prefractal structures was, on average, more than twice as large as that for the homogeneous prefractals. This suggests that relations between fractal parameters used to construct the porous media and the water retention behavior of the media can be more readily determined for homogeneous prefractals.

A method of computing the vertical distributions of solute concentrations in aquifer strata penetrated by an existing well or borehole can be developed from a simple solute mass/water balance approach. This approach allows refinement of site characterization without the cost of drilling additional wells or using other site characterization methods. This method also allows pre-diction of the water quality impacts of different well construction and screening options when the vertical distribution of flows from an aquifer and the aquifer water concentrations are known or can be estimated. Data requirements and methods of data collection for use of the technique are reviewed. Flowmeter or spinner logging surveys indicate the flow contribution of each portion of the well. When depth-specific samples are collected under the same pumping conditions as the spinner logging, a solute mass/water balance approach allows vertical concentration distributions in the aquifer to be estimated. Application to a well containing arsenic concentrations that approach the maximum contaminant level (MCL) of 50 μ/L indicates that water with arsenic concentrations of nearly 100 μ/L enters the well from a particular stratum.

This study evaluated the ability to improve Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) chl-a retrieval from optically shallow coastal waters by applying algorithms specific to the pixels’ benthic class. The form of the Ocean Color (OC) algorithm was assumed for this study. The operational atmospheric correction producing Level 2 SeaWiFS data was retained since the focus of this study was on establishing the benefit from the alternative specification of the bio-optical algorithm. Benthic class was determined through satellite image-based classification methods. Accuracy of the chl-a algorithms evaluated was determined through comparison with coincident in situ measurements of chl-a. The regionally-tuned models that were allowed to vary by benthic class produced more accurate estimates of chl-a than the single, unified regionally-tuned model. Mean absolute percent difference was approximately 70% for the regionally-tuned, benthic class-specific algorithms. Evaluation of the residuals indicated the potential for further improvement to chl-a estimation through finer characterization of benthic environments. Atmospheric correction procedures specialized to coastal environments were recognized as areas for future improvement as these procedures would improve both classification and algorithm tuning.

Only limited hydrogeological research has been conducted using ichnology in carbonate aquifer characterization. Regardless, important applications of ichnology to carbonate aquifer characterization include its use to distinguish and delineate depositional cycles, correlate mappable biogenically altered surfaces, identify zones of preferential groundwater flow and paleogroundwater flow, and better understand the origin of ichnofabric-related karst features. Three case studies, which include Pleistocene carbonate rocks of the Biscayne aquifer in southern Florida and Cretaceous carbonate strata of the Edwards–Trinity aquifer system in central Texas, demonstrate that (1) there can be a strong relation between ichnofabrics and groundwater flow in carbonate aquifers and (2) ichnology can offer a useful methodology for carbonate aquifer characterization. In these examples, zones of extremely permeable, ichnofabric-related macroporosity are mappable stratiform geobodies and as such can be represented in groundwater flow and transport simulations.

The present study demonstrates a methodology for optimization of environmental data acquisition. Based on the premise that the worth of data increases in proportion to its ability to reduce the uncertainty of key model predictions, the methodology can be used to compare the worth of different data types, gathered at different locations within study areas of arbitrary complexity. The method is applied to a hypothetical nonlinear, variable density numerical model of salt and heat transport. The relative utilities of temperature and concentration measurements at different locations within the model domain are assessed in terms of their ability to reduce the uncertainty associated with predictions of movement of the salt water interface in response to a decrease in fresh water recharge. In order to test the sensitivity of the method to nonlinear model behavior, analyses were repeated for multiple realizations of system properties. Rankings of observation worth were similar for all realizations, indicating robust performance of the methodology when employed in conjunction with a highly nonlinear model. The analysis showed that while concentration and temperature measurements can both aid in the prediction of interface movement, concentration measurements, especially when taken in proximity to the interface at locations where the interface is expected to move, are of greater worth than temperature measurements. Nevertheless, it was also demonstrated that pairs of temperature measurements, taken in strategic locations with respect to the interface, can also lead to more precise predictions of interface movement.

This study was conducted to examine adsorption and the utility of Koc for the pesticides carbofuran (2,3‐dihydro‐2,2‐dimethyl‐7‐benzofuranyl methylcarbamate), metalaxyl (N‐(2,6‐dimethylphenyl)‐N‐(2‐methoxyacetyl) alanine methyl ester), and simazine (6 chloro‐?,?'‐diethyl‐1,3,5‐triazine‐2,4‐diamine). Adsorption parameters for these pesticides were measured in the laboratory on samples from 12 western Washington soil layers. Predicted transport of the 3 pesticides using Koc values from the literature and from this study as model inputs were compared with field observations. Carbofuran was the least strongly adsorbed of the three pesticides. Carbofuran adsorption correlated well with soil organic carbon content. Koc values calculated for carbofuran were similar over a range of soils from both this study and other literature. Metalaxyl appeared to be preferentially adsorbed on soil mineral surfaces, and meaningful Koc estimates could not be obtained. Simazine behavior was intermediate between carbofu...

SEAWAT is a coupled version of MODFLOW and MT3DMS designed to simulate variable-density ground water flow and solute transport. The most recent version of SEAWAT, called SEAWAT Version 4, includes new capabilities to represent simultaneous multispecies solute and heat transport. To test the new features in SEAWAT, the laboratory experiment of Henry and Hilleke (1972) was simulated. Henry and Hilleke used warm fresh water to recharge a large sand-filled glass tank. A cold salt water boundary was represented on one side. Adjustable heating pads were used to heat the bottom and left sides of the tank. In the laboratory experiment, Henry and Hilleke observed both salt water and fresh water flow systems separated by a narrow transition zone. After minor tuning of several input parameters with a parameter estimation program, results from the SEAWAT simulation show good agreement with the experiment. SEAWAT results suggest that heat loss to the room was more than expected by Henry and Hilleke, and that multiple thermal convection cells are the likely cause of the widened transition zone near the hot end of the tank. Other computer programs with similar capabilities may benefit from benchmark testing with the Henry and Hilleke laboratory experiment.

Lattice Boltzmann method (LBM) and direct simulation Monte Carlo (DSMC) method are used for analysis of moderate Knudsen number phenomena. Simulation results are presented for pressure-driven isothermal rarefied channel flow at various pressure ratios. Analytical equations for non-linear pressure distribution and velocity profiles along the channel axis are used to verify the present LBM and DSMC results. We conclude that the LBM method can be used as an alternative model to DSMC simulations.Copyright © 2009 by ASME

Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcy's law-based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions.

A parallel implementation of the three-dimensional Shan-and-Chen multicomponent, multiphase lattice Boltzmann method (LBM) was used to simulate the equilibrium distributions of two immiscible fluids in porous media. The simulations were successfully validated against cone-beam x-ray microtomographic data on the distribution of oil (decane), water, and air phases in a 5-mm cube of porous medium composed of packed quartz sand grains. The results confirm that LBM models allow for the straightforward incorporation of complex pore space geometry determined from x-ray microtomography measurements and that simulated wetting and nonwetting phase distributions are consistent with x-ray observations on both macroscopic and microscopic scales.

We propose a method for approximating the adhesion parameters in the Shan and Chen multicomponent, multiphase lattice Boltzmann model that leads to the desired fluid-solid contact angle. The method is a straightforward application of Young's equation with substitution of the Shan and Chen cohesion parameter and a density factor for the fluid-fluid interfacial tension, and the adhesion parameters for the corresponding fluid-solid interfacial tensions.

This study describes the behavior of bubbles rising under gravity using the Shan and Chen-type multicomponent multiphase lattice Boltzmann method (LBM) [X. Shan and H. Chen, Phys. Rev. E47, 1815 (1993)]. Two-dimensional (2D) single bubble motions were simulated, considering the buoyancy effect for which the topology of the bubble was characterized by the nondimensional Eötvös (Eo), and Morton (M) numbers. In this study, a new approach based on the "effective buoyancy" was adopted and proven to be consistent with the expected bubble shape deformation. This approach expands the range of effective density differences between the bubble and the liquid that can be simulated. Based on the balance of forces acting on the bubble, it can deform from spherical to ellipsoidal shape with skirts appearing at high Eo number. A benchmark computational case for qualitative and quantitative validation was performed using COMSOL Multiphysics based on the level set method. Simulations were conducted for 1 ≤ Eo ≤ 100 and 3 × 10-6≤ M ≤ 2.73 × 10-3. Interfacial tension was checked through simulations without gravity, where Laplace's law was satisfied. Finally, quantitative analyses based on the terminal rise velocity and the degree of circularity was performed for various Eo and M values. Our results were compared with both the theoretical shape regimes given in literature and available simulation results.

Liquid distributions in unsaturated porous media under different gravitational accelerations and corresponding macroscopic gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. We used a single-component, multiphase lattice Boltzmann code to simulate liquid configurations in two-dimensional porous media at varying water contents for different gravity conditions and measured gas diffusion through the media using a multicomponent lattice Boltzmann code. The relative diffusion coefficients (D rel) for simulations with and without gravity as functions of air-filled porosity were in good agreement with measured data and established models. We found significant differences in liquid configuration in porous media, leading to reductions in D rel of up to 25% under zero gravity. The study highlights potential applications of the lattice Boltzmann method for rapid and cost-effective evaluation of alternative plant growth media designs under variable gravity.

The Shan and Chen single component multiphase lattice Boltzmann model is used to simulate homogeneous and heterogeneous cavitation. The simulations show excellent agreement with the equation of state for homogeneous cavitation and with energy considerations based on interface formation and bubble expansion for heterogeneous cavitation.

[1] The lattice Boltzmann method (LBM) has emerged as a powerful tool for simulating the behavior of multiphase fluid systems in complex pore networks. Specifically, the single component multiphase LBM can simulate the interfacial phenomena of surface tension and adsorption and thus be used for modeling fluids such as water and its vapor in porous media. This paper provides an introduction to LBM applications to interface configurations in partially saturated porous media. Key elements of this LBM application are fluid-fluid and fluid-solid interactions that successfully mimic the Young-Laplace equation and liquid film adsorption. LBM simulations of liquid behavior in simple pore geometry considering capillarity and adsorption are in good agreement with analytical solutions and serve as critical first steps toward validating this approach. We demonstrate the usefulness of LBM in constructing virtual liquid retention measurements based on porous media imagery. Results of this study provide a basis for application of LBM to understanding liquid configurations in more complex geometries and clear a path for applications involving interface migration, flow, and transport in partially saturated porous media.

A. Hunt and R. Ewing. Springer, Berlin Heidelberg. 2009. 319 pp. US$99.00. ISBN 978-3-540-89789-7. The second edition of Percolation Theory for Flow in Porous Media , by Alan Hunt and Robert Ewing, begins with a nice foreword by Bob Horton contrasting traditional methods of porous media analysis

VLEACH is a simple one-dimensional vadose zone leaching model capable of simulating volatile chemical transport. There is no explicit dispersion coefficient in VLEACH. Solutions computed with it show dispersion due to diffusion in the gaseous phase and its interaction with the liquid phase and also due to the discretization of the problem domain. By turning off gaseous diffusion and comparing VLEACH results to the standard convection dispersion equation, this Computer Note illustrates that the effective dispersivity due to the discretization is equal to half of the model cell size.

After seeing an announcement of the publication of Randomnicity , and reading its description in January 2009, I immediately requested that our library purchase a copy. Then I was pleased to receive, and eager to accept, the invitation to review it for Vadose Zone Journal . The experience reminded

Transport phenomena for different boundary conditions in finite and effectively semi-infinite domains were successfully simulated using the lattice Boltzmann method (LBM). We verified an LBM solute transport algorithm and its boundary conditions by comparing simulation results with analytical solutions for four different one-dimensional solute transport problems. Zero-diffusion analytical breakthrough curves were derived for parallel plate and pipe flow, and LBM simulations with small diffusion coefficients matched these well. Simulations of solute transport in one-dimensional finite and semi-infinite domains were performed at a low column Peclet number (Pe = 1) for first- and third-type inlet boundary conditions; these followed the analytical solutions closely. A series of transport simulations were performed to demonstrate the impact of diffusion and dispersion on the solute front. Taylor dispersion coefficients for the simulated range of Peclet numbers were estimated using moment analysis of the concentration obtained from transport simulation by the LBM. The simulation results showed good agreement with theoretical predictions and thus verified the robustness of LBM-based transport models.

Originally, the color-gradient model proposed by Rothman and Keller (R–K) was unable to simulate immiscible two-phase flows with different densities. Later, a revised version of the R–K model was proposed by Grunau et al. [D. Grunau, S. Chen and K. Eggert, Phys. Fluids A: Fluid Dyn. 5, 2557 (1993).] and claimed it was able to simulate two-phase flows with high-density contrast. Some studies investigate high-density contrast two-phase flows using this revised R–K model but they are mainly focused on the stationary spherical droplet and bubble cases. Through theoretical analysis of the model, we found that in the recovered Navier–Stokes (N–S) equations which are derived from the R–K model, there are unwanted extra terms. These terms disappear for simulations of two-phase flows with identical densities, so the correct N–S equations are fully recovered. Hence, the R–K model is able to give accurate results for flows with identical densities. However, the unwanted terms may affect the accuracy of simulations significantly when the densities of the two fluids are different. For the simulations of spherical bubbles and droplets immersed in another fluid (where the densities of the two fluids are different), the extra terms may not be important and hence, in terms of surface tension, accurate results can be obtained. However, generally speaking, the unwanted term may be significant in many flows and the R–K model is unable to obtain the correct results due to the effect of the extra terms. Through numerical simulations of parallel two-phase flows in a channel, we confirm that the R–K model is not appropriate for general two-phase flows with different densities. A scheme to eliminate the unwanted terms is also proposed and the scheme works well for cases of density ratios less than 10.

Numerous lattice Boltzmann (LB) methods have been proposed for solution of the convection?diffusion equations (CDE). For the 2D problem, D2Q9, D2Q5 or D2Q4 velocity models are usually used. When LB convection?diffusion models are used to solve a CDE coupled with Navier?Stokes equations, boundary conditions are found to be critically important for accurately solving the coupled simulations. Following the idea of a regularized scheme (Latt et al 2008 Phys.?Rev.?E 77 056703), a regularized boundary condition for solving a CDE is proposed. A simple extrapolation scheme is also proposed for the Neumann boundary condition. Spatial accuracies of three existing and the proposed boundary conditions are discussed in details. The numerical evaluations are based on simulations of steady and unsteady natural convection flows in a cavity and an unsteady Taylor?Couette flow. Our studies show that the simplest D2Q4 model with terms of O(u) in the equilibrium distribution function is capable of obtaining results of equal accuracy as D2Q5 or D2Q9 models for the CDE. A slightly revised LB equation for solving a CDE that is used to cancel some unwanted terms does not seem to be necessary for incompressible flows. The regularized boundary condition for solving the CDE has second-order spatial accuracy and it is the best one in terms of the spatial accuracy. The regularized scheme and non-equilibrium extrapolation scheme are applicable to handle both the Dirichlet and Neumann boundary conditions. For the Neumann boundary condition with zero flux, all the five boundary conditions are applicable to give accurate results and the bounce-back scheme is the simplest one.

A combination of cyclostratigraphic, ichnologic, and borehole geophysical analyses of continuous core holes; tracer-test analyses; and lattice Boltzmann fl ow simulations was used to quantify biogenic macroporosity and permeability of the Biscayne aquifer, southeastern Florida. Biogenic macroporosity largely manifests as: (1) ichnogenic macroporosity primarily related to postdepositional burrowing activity by callianassid shrimp and fossilization of components of their complex burrow systems (Ophiomorpha); and (2) biomoldic macroporosity originating from dissolution of fossil hard parts, principally mollusk shells. Ophiomorpha-dominated ichnofabric provides the greatest contribution to hydrologic characteristics in the Biscayne aquifer in a 345 km 2 study area. Stratiform tabular-shaped units of thalassinidean-associated macroporosity are commonly confi ned to the lower part of upward-shallowing highfrequency cycles, throughout aggradational cycles, and, in one case, they stack vertically within the lower part of a high-frequency cycle set. Broad continuity of many of the macroporous units concentrates groundwater fl ow in extremely permeable passageways, thus making the aquifer vulnerable to long-distance transport of contaminants. Ichnogenic macroporosity represents an alternative pathway for concentrated groundwater fl ow that differs considerably from standard karst fl ow-system paradigms, which describe groundwater movement through fractures and cavernous dissolution features. Permeabilities were calculated using lattice Boltzmann methods (LBMs) applied to computer renderings assembled from X-ray computed tomography scans of various biogenic macroporous limestone samples. The highest simulated LBM permeabilities were about fi ve orders of magnitude greater than standard laboratory measurements using air-permeability methods, which are limited in their application to extremely permeable macroporous rock samples. Based on their close conformance to analytical solutions for pipe fl ow, LBMs offer a new means of obtaining accurate permeability values for such materials. We suggest that the stratiform ichnogenic groundwater fl ow zones have permeabilities even more extreme (~2‐5 orders of magnitude higher) than the Jurassic “super-K” zones of the giant Ghawar oil fi eld. The fl ow zones of the Pleistocene Biscayne aquifer provide examples of ichnogenic macroporosity for comparative analysis of origin and evolution in other carbonate aquifers, as well as petroleum reservoirs.

Dispersivity (a) is a required input parameter in solute-transport models based on the advection-dispersion equation (ADE). Normally a is obtained from miscible-displacement experiments. This dependency on inverse procedures imposes a severe limitation on our predictive capability. If solute breakthrough curves and soil hydraulic properties were measured simultaneously, pedotransfer functions could be developed to predict a from independent measurements. In this study, short (6 cm long) undisturbed columns were employed to investigate the relationship between a and the water-retention curve as parameterized by the air-entry value (ψ a ) and Campbell exponent (b ). We worked with 69 columns from six soil types ranging in texture from loamy sand to silty clay, conventional-till and no-till management practices, steady-state saturated flow conditions, and a step decrease in CaCl 2 concentration from 0.009 to 0.001 M. Breakthrough curves were measured by monitoring changes in effluent electrical conductivity using a computerized data acquisition system. Estimates of a (calculated using the method of moments) ranged from 1 to 192 mm for the six soil types. Stepwise multiple-regression analysis explained ∼50% of the total variation in a, and indicated that dispersion increased as ψ a and b increased. Since both ψ a and b increase with increasing day content, a also increases moving from coarse- to fine-textured soils. Our regression equation can be used as a pedotransfer function to predict a from existing databases of soil hydraulic properties. Further research is needed to independently validate its predictive capability, and to develop strategies for upscaling the model predictions.