Heterogeneous Flow Field Research Articles

Intermediate-scale 2D experimental investigation of in situ chemical oxidation using potassium permanganate for remediation of complex DNAPL source zones

In situ chemical oxidation is a technology that has been applied to speed up remediation of a contaminant source zone by inducing increased mass transfer from DNAPL sources into the aqueous phase for subsequent destruction. The DNAPL source zone can consist of one or more individual sources that may be present as an interconnected pool of high saturation, as a region of disconnected ganglia at residual saturation, or as combinations of these two morphologies. Potassium permanganate (KMnO 4) is a commonly employed oxidant that has been shown to rapidly destroy DNAPL compounds like PCE and TCE following second-order kinetics in an aqueous system. During the oxidation of a target DNAPL compound, or naturally occurring reduced species in the subsurface, manganese oxide (MnO 2) solids are produced. Research has shown that these manganese oxide solids may result in permeability reductions in the porous media thus reducing the ability for oxidant to be transported to individual DNAPL sources. It can also occur at the DNAPL–water interface, decreasing contact of the oxidant with the DNAPL. Additionally, MnO 2 formation at the DNAPL–water interface, and/or flow-bypassing as a result of permeability reductions around the source, may alter the mass transfer from the DNAPL into the aqueous phase, potentially diminishing the magnitude of any DNAPL mass depletion rate increase induced by oxidation. An experiment was performed in a two-dimensional (2D) sand-filled tank that included several discrete DNAPL source zones. Spatial and temporal monitoring of aqueous PCE, chloride, and permanganate concentrations was used to relate changes in mass depletion of, and mass flux, from DNAPL residual and pool source zones to chemical oxidation performance and MnO 2 formation. During the experiment, permeability changes were monitored throughout the 2D tank and these were related to MnO 2 deposition as measured through post-oxidation soil coring. Under the conditions of this experiment, MnO 2 formation was found to reduce permeability in and around DNAPL source zones resulting in changes to the overall flow pattern, with the effects depending on source zone configuration. A pool with little or no residual around it, in a relatively homogeneous flow field, appeared to benefit from resulting MnO 2 pore-blocking that substantially reduced mass transfer from the pool even though there was relatively little PCE mass removed from the pool. In contrast, a pool with residual around it (in a more typical heterogeneous flow field) appeared to undergo increased mass transfer as MnO 2 reduced permeability, altering the water flow and increasing the mixing at the DNAPL–water interface. Further, the magnitude of increased PCE mass depletion during oxidation appeared to depend on the PCE source configuration (pool versus ganglia) and decreased as MnO 2 was formed and deposited at the DNAPL–water interface. Overall, the oxidation of PCE mass appeared to be rate-limited by the mass transfer from the DNAPL to aqueous phase.

Numerical analysis of gas emission rule from a goaf of tailing roadway

Abstract Targeting the problem of large amounts of gas emission from the goaf of the No.14201 working face in the Shaqu coal mine of Huajin Coking Coal Co. Ltd., we used a negative exponential function to describe the attenuation process of gas emission in goaf (the stable source) based on the principle of field flow. Equations of two-component flow (gas and air) and seepage-diffusion in a heterogeneous goaf flow field are solved by means of numerical simulation and fluid mechanics principles of air movement and gas distribution during gas emission from goaf. The results indicate that the air diversion volume has a negative, exponential relation with the volume of gas emitted from goaf to the working face and is clearly inversely related to gas concentration. We calculated the minimum amount of air diversion and distributed air volume in the tailing roadway required for safe production.

A multi-fidelity software framework for interactive modeling of advective and diffusive contaminant transport in groundwater

Groundwater currently accounts for over 20% of the daily water usage in the United States. As the contamination of groundwater reserves also continues to increase from a variety of pollutants, remediation becomes necessary. Whether the remediation method involves containing or cleaning, a fundamental understanding of the groundwater flow patterns is necessary. This can now be gained through predictive models due to advances in groundwater simulation research. One such method, the Superblock Analytical Element Method (AEM) is capable of capturing both large-scale trends and small-scale variations in complex, heterogeneous flow fields. These trends and variations are not captured by current numerical solutions, typified by finite difference and finite element formulations. The Superblock AEM, as with many groundwater solvers, has a substantial number of input parameters and produces large amounts of 3D output. Thus, an intuitive, 3D visual framework would greatly enhance the usability of the method. With the Superblock AEM as a core solver, Groundwater TRANsport 3D (GTRAN3D) has been developed to provide a platform for modeling and viewing advective and diffusive contaminant spreading over non-intersecting spheroidal in-homogeneities in groundwater. The developed system allows a user to create an input scenario through an interactive three-dimensional graphical user interface (GUI), send that input to the solver, and then view the results on systems ranging from desktop computers to immersive Virtual Reality (VR) environments. In addition, the software can be used on any operating system or even accessed via a web interface. The development of the software framework is discussed along with the presentation of several test cases.

Adaptive importance sampling with prior information in dynamic process imaging

AbstractThe estimation of cross‐sectional material distributions from non‐stationary sparse tomographic measurement data is a demanding class of ill‐posed inverse problems. In this context, electrical capacitance tomography (ECT) is a well‐established modality that aims at monitoring and controlling dynamic industrial processes arising e.g. in pneumatic conveying or heterogeneous flow fields. By measuring the capacitances between certain electrodes that are arranged around the periphery, the permittivity distribution inside closed objects can be spatially resolved. In this paper, the main focus is on the robust estimation of time‐dependent material distributions given uncertain measurements. The underlying inverse problem is formulated in a Bayesian inferential framework, by specifying a prior parameter distribution, and characterizing the statistics of the measurement noise, to give a posterior distribution conditioned on measured data. Transitions between different material phases are described by means of a Fourier contour model of second order implying a geometric regularization. Sequential importance filtering – particle filtering – is applied to solve the non‐stationary ECT problem. A tracking experiment is presented in order to show the robustness of the Bayesian filtering approach to solve the non‐stationary inverse problem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The effect of aquifer heterogeneity on natural attenuation rate of BTEX

Monitored natural attenuation can be a viable option for remediation of groundwater contamination by BTEX compounds. Under the field conditions, the rate of contaminant mass attenuation through natural processes, such as biodegradation, to a large extent affected by the groundwater flow regime, which is primarily controlled by the aquifer heterogeneity. Numerical simulation techniques were used to describe quantitatively the relationship between biodegradation rate of BTEX and aquifer heterogeneity. Different levels of aquifer heterogeneity were described by random hydraulic conductivity fields (K) having different statistical parameters, the coefficient of variation (CV) and the correlation length (h). The Turning Bands Algorithm was used to generate such K fields. Visual MODFLOW/RT3D was used to simulate the fate and transport of dissolved BTEX plume within heterogeneous aquifers. The multispecies reactive transport approach described BTEX degradation using multiple terminal electron-accepting processes. First-order biodegradation rate constants were calculated from simulated BTEX plumes in heterogeneous flow fields. The results showed that aquifer heterogeneity significantly affected biodegradation rate; it decreased with increasing CV when h was in the range of up to 12 m, whereas it increased with increasing CV when h was greater than about 12 m. For well characterized aquifers, this finding could be of great value in assessing the effectiveness of natural attenuation during feasibility studies at BTEX contaminated sites.

Upscaling Hydraulic Properties and Soil Water Flow Processes in Heterogeneous Soils: A Review

This review covers, in a comprehensive manner, the approaches available in the literature to upscale soil water processes and hydraulic parameters in the vadose zone. We distinguish two categories of upscaling methods: forward approaches requiring information about the spatial distribution of hydraulic parameters at a small scale, and inverse modeling approaches requiring information about the spatial and temporal variation of state variables at various scales, including so‐called “soft data”. Geostatistical and scaling approaches are crucial to upscale soil water processes and to derive large‐scale effective fluxes and parameters from small‐scale information. Upscaling approaches include stochastic perturbation methods, the scaleway approach, the stream‐tube approach, the aggregation concept, inverse modeling approaches, and data fusion. With all upscaling methods, the estimated effective parameters depend not only on the properties of the heterogeneous flow field but also on boundary conditions. The use of the Richards equation at the field and watershed scale is based more on pragmatism than on a sound physical basis. There are practically no data sets presently available that provide sufficient information to extensively validate existing upscaling approaches. Use of numerical case studies has therefore been most common. More recently and still under development, hydrogeophysical methods combined with ground‐based remote sensing techniques promise significant contributions toward providing high‐quality data sets. Finally, most of the upscaling literature in vadose zone research has dealt with bare soils or deep vadose zones. There is a need to develop upscaling methods for real world soils, considering root water uptake mechanisms and other soil–plant–atmosphere interactions.

Transport properties of sorbing contaminants in a fractured granite under oxidizing conditions

Migration of some sorbing chemical species has been studied in a single rock fracture of 1 m scale in order to understand the transport behavior of contaminants at underground environments. For the tracers, tritium and anions were used as nonsorbing ones and some sorbing cations such as Sr, Co and Cs were used as well. The experimental study was focused on the identification of the retardation and matrix diffusion of the tracer in the fracture. The hydraulic conductivity in the fracture was determined from the pressure differentials between pairs of boreholes. The hydraulic data were used with a variable aperture channel model to characterize the aperture distribution in the fracture. A transport model has been developed to describe the migration of the solutes in the flow field by using a particle tracking method. Results were plotted in the form of elution curves and migration plumes in the fracture. The experimental elution curves have been explored with the transport model which takes into account sorption and diffusion into the rock matrix. This comparison may contribute to further understanding on the heterogeneous flow field and the interactions between rock and chemical species.

Soil Heterogeneity Effects on Solute Breakthrough Sampled with Suction Cups: Numerical Simulations

Porous cups are widely used to extract soil solution for monitoring solute transport; however, it is not always clear how soil heterogeneity influences solute breakthrough sampled by suction cups. The objective of this study was to evaluate the influence of soil heterogeneity on the breakthrough of solute extracted by suction cups. We conducted numerical simulations using the HYDRUS‐2D code. Local‐scale heterogeneity in hydraulic properties was generated using Miller–Miller scaling theory. Results of the simulations show that effective transport parameters derived from the measured breakthrough curves in the suction cups depended on the location of the suction cup in the heterogeneous flow field. Mean pore water velocities obtained from suction cup measurements ranged by a factor of 1.6 and dispersivities by a factor of 1.5 for the different heterogeneous structures. As a consequence, the arrival time (first moment) of the tracer plume derived from suction cup measurements was accelerated or delayed compared with the homogeneous case. Mass recoveries and suction cup sampling areas were also influenced by the underlying structure. The applied suction in the cup as well as the suction cup sampling area were found to have important effects on the mean pore water velocity, dispersivity, and mass recovery. The effect of variation in applied suction was analyzed using reference point data taken from 10 locations in the undisturbed flow field. Contrary to the general assumption that solute spreading measured with suction cups depends only on the mean pore water velocity, our results show that solute spreading is also influenced by (i) the suction cup sampling area and the deformation of streamlines to the cup, and (ii) the flow channels that are sampled. The numerical simulations indicate that the number of suction cups required for calculating a mean breakthrough curve in the chosen heterogeneous flow field must to be >20.

Reconstructing Groundwater Source Release Histories Using Hybrid Optimization Approaches

Reconstructing release histories of contaminant sources in groundwater is an important environmental forensics problem for identifying responsible parties and allocating remediation costs in a contamination incident. Such problems typically require the solution of an inverse problem. This paper investigates and compares several hybrid optimization approaches that combine genetic algorithms with a number of local search approaches for solving these problems. Previous studies in this area have focused on simple two-dimensional and/or single-source release history problems. The problems solved in this article address both single- and multiple-source releases in three-dimensional heterogeneous flow fields. A parallel computing environment is used to handle the heavy computational needs of these problems. The results indicate that hybrid optimization methods, especially those that combine an initial global heuristic approach (e.g., genetic algorithms) with a subsequent gradient-based local search approach (e.g., conjugate gradients) are very effective in solving these problems.

Tracer and reactive transport modelling of the interaction between high-pH fluid and fractured rock: Field and laboratory experiments

In order to understand the interaction of a hyperalkaline solution with a fractured shear zone in granite and its influence on the migration of radionuclides, laboratory and underground field experiments at the Grimsel Test Site (Switzerland) were analysed by means of numerical modelling. Supporting data came from hydrogeological testing, structural and mineralogic characterisation of boreholes and cores and from dye tracer experiments in different dipole geometries within the shear zone. One-dimensional flow and reactive transport models have been applied to reproduce the breakthrough curves measured in a small-scale laboratory experiment (forced infiltration into a drill core containing a fracture with fault gouge). Major ion concentrations and water flow through the system could be fitted using a kinetic approach for mineral dissolution and precipitation. To reproduce the measured reduction of the flow rate over time, a small value for the effective mineral surface area had to be chosen together with an empirical relationship between the hydraulic conductivity of the fracture and the amount of precipitated calcium silicate hydrate. Tracer dipole experiments have been interpreted using different concepts to reconcile transport processes and radionuclide migration within a shear zone at the Grimsel Test Site altered by high-pH fluid. Parameter fits were possible for a multiple fracture-matrix approach, as well as for a two-dimensional heterogeneous medium approach. A discrimination between approaches was not possible, although the extended dipole flow field geometry, the quite dissimilar breakthrough curves measured for experiments with different dipole geometries and the measured lateral spreading of the high-pH plume favoured the heterogeneous porous medium approach. Using a heterogeneous porosity distribution, together with an empirical Kozeny–Carman equation that relates porosity and hydraulic conductivity, a heterogeneous flow field could be calculated for the shear zone. This flow field was used to predict the interaction of the hyperalkaline solution with the shear zone. Calculations were also performed to predict the spreading of Cs, Co and Eu radionuclide tracers within the shear zone altered by high-pH interaction. It has been shown that the calculated Cs, Co and Eu breakthroughs and their concentration distributions depend on the assumptions on sorption behaviour. In addition, the observed decrease in hydraulic conductivity of the system, which is observed both in the field and in small-scale core infiltration experiments, and the related changes in the flow field, which are linked to mineral alteration, will strongly influence the migration of radionuclides.

Assessing impacts of partial mass depletion in DNAPL source zones: II. Coupling source strength functions to plume evolution

Analytical solutions, describing the time-dependent DNAPL source-zone mass and contaminant discharge rate, derived previously in Part I [Falta, R.W., Rao, P.S., Basu, N., this issue. Assessing the impacts of partial mass depletion in DNAPL source zones: I. Analytical modeling of source strength functions and plume response. J. Contam. Hydrol.] are used as a flux-boundary condition in a semi-analytical contaminant transport model. These analytical solutions assume a power relationship between the flow-averaged source concentration, and the source DNAPL mass; the empirical exponent ( Γ) is a function of the flow field heterogeneity, DNAPL architecture, and the correlation between them. The DNAPL source strength terms can account for partial source remediation, either at time zero, or at some later time after the DNAPL release. The transport model considers advection, retardation, three-dimensional dispersion, and sequential first-order decay/production of several species. A separate solution is used to compute the time-dependent mass of each contaminant in the plume. A series of examples using different values of Γ shows how the benefits of partial DNAPL source remediation can vary with site conditions. In general, when Γ > 1, relatively large short-term reductions in the plume concentrations and mass occur, but the source longevity is not strongly affected. Conversely, when Γ < 1, the short-term reductions in the plume concentrations and mass are smaller, but the source longevity can be greatly reduced. In either case, the source remediation effort is much more effective if it is undertaken at an early time, before much contaminant mass has entered the plume. If the remediation effort is significantly delayed, the leading parts of the plume are not affected by the source remediation, and additional control or remediation of the plume itself is required.

A finite analytic method for solving the 2-D time-dependent advection–diffusion equation with time-invariant coefficients

Difficulty in solving the transient advection–diffusion equation (ADE) stems from the relationship between the advection derivatives and the time derivative. For a solution method to be viable, it must account for this relationship by being accurate in both space and time. This research presents a unique method for solving the time-dependent ADE that does not discretize the derivative terms but rather solves the equation analytically in the space–time domain. The method is computationally efficient and numerically accurate and addresses the common limitations of numerical dispersion and spurious oscillations that can be prevalent in other solution methods. The method is based on the improved finite analytic (IFA) solution method [Lowry TS, Li S-G. A characteristic based finite analytic method for solving the two-dimensional steady-state advection–diffusion equation. Water Resour Res 38 (7), 10.1029/2001WR000518] in space coupled with a Laplace transformation in time. In this way, the method has no Courant condition and maintains accuracy in space and time, performing well even at high Peclet numbers. The method is compared to a hybrid method of characteristics, a random walk particle tracking method, and an Eulerian–Lagrangian Localized Adjoint Method using various degrees of flow-field heterogeneity across multiple Peclet numbers. Results show the IFALT method to be computationally more efficient while producing similar or better accuracy than the other methods.

Modeling expected solute concentration in randomly heterogeneous flow systems with multicomponent reactions.

Many environmental problems require assessment of extensive reaction systems within natural subsurface flow systems exhibiting large physical and biogeochemical heterogeneity. We present an approach to couple stochastic advective-reactive modeling of physical solute transport (LaSAR) with the geochemical model PHREEQC for modeling solute concentrations in systems with variable flow velocity and multicomponent reactions. PHREEQC allows for general and flexible quantification of a multitude of linear and nonlinear geochemical processes, while LaSAR efficiently handles field-scale solute spreading in stochastic heterogeneous flow fields. The combined LaSAR-PHREEQC approach requires very modest computational efforts, thereby allowing a large number of reactive transport problems to be readily assessed and facilitating handling of quantifiable uncertainty in environmental model applications. Computational efficiency and explicit handling of field-scale dispersion without introduction of excessive fluid mixing that may impair model results are general advantages of the LaSAR compared with alternative solute transport modeling approaches. The LaSAR-PHREEQC approach is restricted to steady or unidirectional flow fields, and our specific application examples are limited to homogeneous reaction systems without local or transverse dispersion-diffusion, although these are not general methodological limitations. As a comprehensive application example, we simulate the spreading of acid mine drainage in a groundwater focusing on Zn2+ and including relevant, major-component geochemistry. Model results show that Zn2+ may be substantially attenuated by both sorption and precipitation, with flow heterogeneity greatly affecting expected solute concentrations downstream of the mine waste deposit in both cases.

The effect of multicomponent diffusion on NAPL dissolution from spherical ternary mixtures

This paper investigates the dissolution characteristics of ternary nonaqueous phase liquid (NAPL) mixtures with the goal of comparing the relative contributions of multicomponent (intra-NAPL) diffusion, film transfer and thermodynamic nonideality. These contributions are compared at the pore scale and intermediate scale (several centimeters downstream from the source). Trichloroethene (TCE), tetrachloroethene (PCE) and 1,1,1-trichloroethane (TCA) were selected to model a reasonably ideal mixture; TCE, PCE and octanol were selected as a relevant nonideal mixture. A multicomponent diffusion-based dissolution model incorporating hydrodynamic theory was formulated to estimate intra-NAPL concentration gradients and associated aqueous interfacial concentrations for ideally shaped (spherical) NAPL blobs. Pore scale dissolution times for this model were compared to those generated using the conventional well-mixed NAPL dissolution model, applying the same film transfer boundary condition in both cases. Activity coefficients (spatially and temporally variable for the diffusion model, temporally variable for the well-mixed model) were estimated using UNIFAC. NAPL interfacial concentration histories generated using the pore scale models were used as input in a three-dimensional groundwater transport model (MT3DMS) to compare downstream concentration distributions. For the relatively large NAPL bodies simulated ( r=0.6 cm), intra-NAPL diffusion effects were found to be significant at the pore scale and were strongly impacted by the mixture's thermodynamic ideality. At the intermediate scale, and for the conditions tested, modest differences in the simulations suggested that intra-NAPL diffusion effects would be negligible compared to those associated with mixture composition uncertainty, dissolution rate processes related to NAPL-induced permeability effects and hydrodynamic issues associated with flow field heterogeneity.

ANALYSIS OF UNSATURATED WATER FLOW IN A LARGE SAND TANK

A realistic, physically based simulation of water and solute movement in the unsaturated soil zone requires reasonable estimates of the water retention and unsaturated hydraulic conductivity functions. A variety of studies have revealed the importance of how these unsaturated soil parameters are assessed and subsequently distributed over the numerical mesh on modeling outcome. This study was initiated to acquire experimental data about the water flow characteristics of sandy soils to serve as a base for numerical analyses. Specific objectives were to clarify the effects of (i) the invoked procedure for estimating the soil hydraulic parameters and (ii) using increasingly refined spatial definitions of the hydraulic properties on simulated two dimensional water content and flow velocity distributions. Water flow in and drainage from a large sand tank (approximately 5 × 3 m 2 at the base, 6 × 5.6 m 2 at the top) was investigated using soil hydrologic and geophysical methods. Numerical analyses of variably saturated flow along a two-dimensional cross-section were carried out in attempts to describe the heterogeneous flow fields using the Richards equation-based HYDRUS-2D code. The unsaturated soil hydraulic properties were described using van Genuchten-Mualem type expressions. Information from both in situ and laboratory measurements was employed to obtain parameter estimates. The observed variability in discharge rate with time was reproduced best when an average water retention curve was used and the saturated water content was set equal to the porosity, whereas cumulative outflow was predicted best when all van Genuchten hydraulic parameters were fitted to the retention data. Using heterogeneously distributed hydraulic parameters (assuming a layered profile or a random distribution of the saturated hydraulic conductivity) improve neither predictions of the cumulative discharge rate nor the variability in the outflow rate when compared with the homogeneous case. Efforts to construct or numerically simulate heterogeneous flow experiments may, therefore, not always be justified when water flow in sandy substrates is studied.

Influence of stagnant zones on transient and asymptotic dispersion in macroscopically homogeneous porous media.

The role of stagnant zones in hydrodynamic dispersion is studied for creeping flow through a fixed bed of spherical permeable particles, covering several orders of characteristic time and length scales associated with fluid transport. Numerical simulations employ a hierarchical model to cope with the different temporal and spatial scales, showing good agreement with our experimental results on diffusion-limited mass transfer, transient, and asymptotic longitudinal dispersion. These data demonstrate that intraparticle liquid holdup in macroscopically homogeneous porous media clearly dominates over contributions caused by the intrinsic flow field heterogeneity and boundary-layer mass transfer.

Modeling Sorption and Exchange Processes in Column Experiments and Large Scale Field Studies

This paper demonstrates the possibilities of reactive transport modeling in predicting contaminant transport processes of laboratory and field scales. Basic approaches of reactive transport modeling are discussed, focusing on the incorporation of a thermodynamic description of chemical interactions into the convection-dispersion equation (CDE). Both equilibrium and kinetic approaches are presented. Chemical reaction parameters can be estimated from 1-D column experiments, by combining the CDE and the thermodynamic description of transport. A 2-D simulation with a heterogeneous flow field and ion exchange parameters obtained from column experiments is presented. The results of the 2-D model are in qualitative agreement with measured field breakthrough curves. Limitations of this approach are discussed, focusing on parameter heterogeneity and scaling effects.

Modeling biodegradation processes in porous media by the finite cell method

In this paper, the finite cell method (FCM) presented by Sun [1999] is extended to the two‐dimensional case and used to simulate complicated biodegradation processes in porous media. FCM is based on the direct simulation of various physical, chemical, and biological phenomena rather than solving advection‐dispersion‐reaction equations. The developed two‐dimensional FCM is able to deal with heterogeneous structures and variable flow fields. Two test problems show that FCM can produce more accurate solutions than other numerical methods. It can keep both local and global mass conservation and avoid numerical dispersion even when the Peclet number becomes infinite. The biodegradation model formulated in this paper consists of five partial differential equations with five unknown concentrations when kinetic mass exchange and rate‐limited attachment of microorganisms are considered. Using FCM to solve this problem, we define two sets of cells, the mobile fluid cells and the immobile solid cells. A mobile fluid cell may contain dissolved substrate, suspended microorganisms, and electron acceptor components, while an immobile solid cell may contain adsorbed substrate and attached biomass. When a mobile cell meets an immobile cell on its way, mass exchanges may occur between them and reactions may occur within them. By directly simulating these processes, all the five unknown concentrations can be obtained explicitly and simultaneously. A numerical example is given that shows the FCM solution of a biodegradation process in a randomly heterogeneous porous media. We expect that the FCM can serve as not only a powerful simulation tool but also a useful tool for mechanism study.

Development of structures under the influence of heterogeneous flow field around rigid inclusions: insights from theoretical and numerical models

Rocks that are mechanically heterogeneous due to the presence of stiff or rigid inclusions floating in a ductile matrix, commonly show a variety of micro- to macro-scale structures developing under the influence of heterogeneous flow field in the neighbourhood of the inclusions. It is of fundamental importance to apprehend the nature of strain heterogeneity around inclusions to understand progressive development of structures associated with rigid inclusions such as strain shadow, foliation drag, porphyroclast mantle, porphyroblast inclusion trails, intragranular fractures, etc. The development of these diverse types of structures can be analyzed with the help of a suitable hydrodynamic theory. In this paper, we review different continuum models that have been proposed to characterize the heterogeneous flow field around rigid inclusions, focusing on recent developments. Recent studies reveal that Jeffery's [Proc. R. Soc. Lond. A 120 (1922) 161.] theory dealing with the motion of ellipsoidal rigid bodies in an infinitely extended viscous medium is more general in nature, and applicable for modeling the heterogeneous flow around both equant and inequant shapes of inclusions and ideal or non-ideal shear deformation of the matrix. The application of this theory, therefore, has advantages over other models, based on Lamb's [Lamb, H., 1932. Hydrodynamics. Cambridge University Press, Cambridge.] theory dealing with spherical inclusions. The review finally illustrates numerical simulations based on hydrodynamic theories, highlighting the controls of physical and kinematic factors on the progressive development of the structures mentioned above.

A novel two-dimensional model for colloid transport in physically and geochemically heterogeneous porous media

A two-dimensional model for colloid transport in geochemically and physically heterogeneous porous media is presented. The model considers patchwise geochemical heterogeneity, which is suitable to describe the chemical variability of many surficial aquifers with ferric oxyhydroxide-coated porous matrix, as well as spatial variability of hydraulic conductivity, which results in heterogeneous flow field. The model is comprised of a transient fluid flow equation, a transient colloid transport equation, and an equation for the dynamics of colloid deposition and release. Numerical simulations were carried out with the model to investigate the colloid transport behavior in layered and randomly heterogeneous porous media. Results demonstrate that physical and geochemical heterogeneities markedly affect the colloid transport behavior. Layered physical or geochemical heterogeneity can result in distinct preferential flow paths of colloidal particles. Furthermore, the combined effect of layered physical and geochemical heterogeneity may result in enhanced or reduced preferential flow of colloids. Random distribution of physical heterogeneity (hydraulic conductivity) results in a random flow field and an irregularly distributed colloid concentration profile in the porous medium. Contrary to random physical heterogeneity, the effect of random patchwise geochemical heterogeneity on colloid transport behavior is not significant. It is mostly the mean value of geochemical heterogeneity rather than its distribution that governs the colloid transport behavior.