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.     

Three-fluid retention in porous media involving water, PCE and air

A classical way to obtain three-fluid retention curves in porous media from measured two-fluid retention curves is based on the Leverett concept, which states that the total volumetric liquid content in a water-wet porous medium, containing water, a nonaqueous-phase liquid (NAPL) and air, is a function of the capillary pressure across the interface between the continuous NAPL and air. This functional relationship results from the assumed condition that in a three-fluid porous medium, the intermediate wetting fluid spreads over the water-air interface. Application of Leverett's concept may not be valid, however, for nonspreading NAPLs like perchloroethylene (PCE). This paper discusses measurements of both PCE-air and water-PCE-air retention curves using a long vertical column in conjunction with a dual-energy gamma radiation system. The data indicate that the Leverett concept was applicable only until a critical PCE saturation had been reached.     

Machine learning-based models for predicting gas breakthrough pressure of porous media with low/ultra-low permeability

Environmental Science and Pollution Research - Gas breakthrough pressure is a significant parameter for the gas exploration and safety evaluation of engineering barrier systems in the carbon...     

Prediction of mass-transfer coefficient for solute transport in porous media

Several previously reported laboratory studies related to transport of solutes through packed columns were utilized to develop predictive relationships for mass-transfer rate coefficient. The data were classified into two groups: those obtained under rate-limited mass transfer between mobile and immobile water regions (physical nonequilibrium conditions), and those derived from rate-limited mass transfer between instantaneous and slow sorption sites (sorption nonequilibrium conditions). The mass-transfer coefficient in all these studies was obtained by fitting breakthrough data to a transport model employing a first-order rate limitations with a "constant" mass-transfer coefficient, independent of flow conditions. This study demonstrated that the mass-transfer coefficient in these models is dependent on system parameters including pore-water velocity, length-scale, retardation coefficient, and particle or aggregate size. Predictive relationships were developed, through regression analysis, relating mass-transfer coefficient to residence time. The developed relationships adequately estimated previously reported field mass-transfer values. Successful simulations of field desorption data reported by Bahr [J. Contam. Hydrol. 4 (1989) 205] further demonstrate the potential applicability of the developed relationships.     

Gel barrier formation in unsaturated porous media

The gel barrier formation by a gelling liquid (Colloidal Silica) injection in an unsaturated porous medium is investigated by developing a mathematical model and conducting numerical simulations. Gelation process is initiated by adding electrolytes such as NaCl, and the gel phase consisting of cross-linked colloidal silica particles grows as the gelation process proceeds. The mathematical model describing the transport and gelation of Colloidal Silica (CS) is based on coupled mass balance equations for the gel mixture (the sol phase plus the gel phase), gel phase (cross-linked colloidal silica particles plus water captured between cross-linked particles), and colloidal silica particles (discrete and cross-linked) and NaCl in the sol (suspension of discrete colloidal silica particles in water) and gel phases. The solutions in terms of volumetric fraction of the gel phase yield the gel mixture viscosity via the dependency on the volumetric fraction of gel phase. This dependency is determined from a kinetic gelation model with time-normalized viscosity curves. The proposed model is verified by comparing experimentally and numerically determined hydraulic conductivities of gel-treated soil columns at different CS injection volumes. The numerical experiments indicate that an impermeable gel layer is formed within the time period twice the gel-point in a one-dimensional flow system. At the same normalized time corresponding to twice the gel-point, the CS solutions with lower NaCl concentrations result in further migration and poor performance in plugging the pore space. The viscosity computation proposed in this study is compared with another method available in the literature. It is observed that the other method estimates the viscosity at the mixing zone higher than the one proposed by the authors. The proposed model can simulate realistic injection scenarios with various combinations of operating parameters such as NaCl concentration and NaCl mixing time, and thus providing guidelines in performing this technology on site.     

一维饱和多孔介质中胡敏酸的运移研究

研究了胡敏酸在不同多孔介质中的运移特征.结果表明:(1)CXTFIT.2.1软件对多孔介质中胡敏酸运移的拟合效果随多孔介质不同而有较大的差异,其对石英砂和河沙中胡敏酸的运移过程拟合较好,对3种土壤(风沙土、黄绵土和黑垆土)中胡敏酸的运移过程拟合较差.(2)胡敏酸溶液在多孔介质中的运移行为与不同多孔介质有关,在石英砂和河沙中运移迅速,而在土壤中运移缓慢;胡敏酸的快速运移对应较低的阻滞因子和吸附系数,而缓慢运移对应较高的阻滞因子和吸附系数.对于石英砂和河沙,胡敏酸的运移在石英砂中较快,在河沙中较慢;对于3种土壤(风沙土、黄绵土和黑垆土),胡敏酸在风沙土中运移最快,在黑垆土中运移最慢.     

A hybrid micro-scale model for transport in connected macro-pores in porous media

This paper presents a hybrid model for transport in connected macro-pores in porous media. A pore-scale model is used to parameterize the hybrid model. The hybrid model explicitly models the advection and diffusion of species in the connected macro-pores and treats the porous media around the connected macro-pores as a continuum with effective transport properties. The pore-scale model is used to calculate the effective transport properties of the porous continuum. This approach negates the need to calibrate the hybrid model against experimental data, which is common for continuum-scale models of porous media, and allows an arbitrary microstructure to be considered. The paper presents the multi-scale modeling approach along with the details of the hybrid and pore-scale models. Validation of the model is also presented along with several case studies investigating the applicability of the multi-scale modeling approach to different geometries and transport conditions. The case studies show that the multi-scale modeling approach is accurate for various connected macro-pore geometries given that the porosity of the porous medium around the connected macro-pores is sufficiently small. The accuracy of the hybrid model decreases with increasing porosity of the matrix.     

Pore-scale modeling of dispersion in disordered porous media

We employ a direct pore-level model of incompressible flow that uses the modified moving particle semi-implicit (MMPS) method. The model is capable of simulating both unsteady- and steady-state flow directly in microtomography images of naturally-occurring porous media. We further develop this model to simulate solute transport in disordered porous media. The governing equations of flow and transport at the pore level, i.e., Navier-Stokes and convection-diffusion, are solved directly in the pore space mapped by microtomography techniques. Three naturally-occurring sandstones are studied in this work. We verify the accuracy of the model by comparing the computed longitudinal dispersion coefficients against the experimental data for a wide range of Peclet numbers, i.e., 5×10(-2)相似文献   

Reactive solute transport in macroscopically homogeneous porous media: analytical solutions for the temporal moments

In this work, we investigate one-dimensional solute transport affected by rate-limited sorption, first-order mass transfer, and first-order transformation. Analytical expressions are obtained for the temporal moments of the solute in the solution phase. The effect of various rate coefficients on the temporal moments is examined. It was found that, in the presence of transformation reactions, the mean arrival time, and the spread and skewness of the breakthrough curves, are not monotonic functions of the rate coefficients. These solutions will be useful as a preliminary analysis tool for ascertaining the relative importance of various processes under given conditions. They may also be used to analyze the accuracy of various numerical techniques used for simulation of reactive transport.     

Immiscible fluid flow in porous media: dielectric properties

The movement and retention of immiscible fluids in porous media was determined using a microwave dielectric measuring technique. The technique was used to monitor the composite dielectric constant of columns containing model soil materials to observe the effect of displacement of various saturating fluids by water and determine the retained immiscible components. Various combinations of displacing fluids, both miscible and immiscible, were studied, yielding time-dependent flow characteristics as well as the total retention factor. The flow circumstances were similar to what would be encountered in an accidental spill of chlorocarbons or crude oil.The retention of chlorocarbons and crude oil was determined for model soils consisting of sand or glass spheres. The storage capacity of the sand for immiscible fluids was dependent on the fluid initially saturating the porous medium. For chlorocarbons, it was increased in water-wet compared to dry sands while the inverse was true for crude oil. The retention of crude oil in the sand was dependent on the water flow velocity and was much larger than that for chlorocarbons. The crude oil could be displaced by solvents such as cyclohexane in the sand but the net volume occupied by the two immiscible fluids after water flushing did not change appreciably, i.e. the crude oil component was replaced by the solvent. Application of a miscible fluid-water mixture or surfactants improved the ability of water to displace the immiscible fluid from the sand column.     

Migration of saline solutions in variably saturated porous media

Migration of concentrated NaNO3 solutions in homogeneous packs of pre-wetted silica sands was investigated using a light transmission system. Solutions of 5 molal NaNO3 were found to migrate downward 24-62% faster than pure water, in an unstable, fingered manner. This behavior was attributed primarily to a surface tension induced, non-zero apparent contact angle between the imbibing and the resident fluids. For saline solutions of similar surface tension to that of pure water (achieved by the addition of 2% methanol), the migration rates and plume shapes were comparable to that of water, demonstrating that density was not the primary source of the observed differences in migration patterns. At depths where resident saturation increased above residual, the migration process appeared to occur via film flow with slight changes in saturation (<4%), rather than in a series of abrupt jumps, as observed at shallower depths. A method for contact angle scaling was used to illustrate the effects of non-zero contact angles on capillary pressure-saturation curves.     

Straining phenomena in bacteria transport through natural porous media

Background, aim, and scope  

Transport of bacteria through natural porous media is an issue of increasing concern arising in several very important environmental processes. These include the percolation of bacteria from fecal waste to drinking water reservoirs, thus leading to a risk for human health, or the bioremediation of contaminated soils in which the bacteria are expected to travel long distances underground in order to reach contaminated areas and degrade chemicals originating from accidental spills. An understanding of bacterial retention and transport mechanisms in porous media would be of great help in the development of models able to predict the distance covered by bacterial suspensions in these situations.     

Entrapment and dissolution of DNAPLs in heterogeneous porous media

Two-dimensional multiphase flow and transport simulators were refined and used to numerically investigate the entrapment and dissolution behavior of tetrachloroethylene (PCE) in heterogeneous porous media containing spatial variations in wettability. Measured hydraulic properties, residual saturations, and dissolution parameters were employed in these simulations. Entrapment was quantified using experimentally verified hydraulic property and residual saturation models that account for hysteresis and wettability variations. The nonequilibrium dissolution of PCE was modeled using independent estimates of the film mass transfer coefficient and interfacial area for entrapped and continuous (PCE pools or films) saturations. Flow simulations demonstrate that the spatial distribution of PCE is highly dependent on subsurface wettability characteristics that create differences in PCE retention mechanisms and the presence of subsurface capillary barriers. For a given soil texture, the maximum and minimum PCE infiltration depth was obtained when the sand had intermediate (an organic-wet mass fraction of 25%) and strong (water- or organic-wet) wettability conditions, respectively. In heterogeneous systems, subsurface wettability variations were also found to enhance or diminish the performance of soil texture-induced capillary barriers. The dissolution behavior of PCE was found to depend on the soil wettability and the spatial PCE distribution. Shorter dissolution times tended to occur when PCE was distributed over large regions due to an increased access of flowing water to the PCE. In heterogeneous systems, capillary barriers that produced high PCE saturations tended to exhibit longer dissolution times.     

An evaluation of contaminant migration patterns at two waste disposal sites on fractured porous media in terms of the equivalent porous medium (EPM) model

Contamination has occurred many non-indurated and bedrock systems wherein the groundwater flows almost exclusively through a network of connected, open fractures. The matrix surrounding the fractures often possesses porosity which allows contaminant diffusion into the matrix. If the diffusion rates are fast relative to the fracture groundwater velocity, transport effects may be predicted by considering the system to be an equivalent porous medium (EPM). The rapidity with which fracture/immobile-matrix equilibrium is established will be determined in part by the: fracture aperture (2b); interfracture spacing (2B); porosity in the immobile matrix (θ_im); and the matrix diffusion coefficient (D′). Two systems which are characterized by very different values of the above parameters have been studied by our laboratories. At Alkali Lake, Oregon, the EPM approach describes contaminant transport well. At Bayview Park, Ontario, the EPM approach is not appropriate. Several features of the two sites are compared to illustrate the different nature of these two sites. These features include: (1) natural characteristics of the groundwater systems; (2) contaminant distributions; (3) observed transport; and (4) computed fracture/immobile-matrix diffusion times.     

On the selection of primary variables in numerical formulation for modeling multiphase flow in porous media

Selecting the proper primary variables is a critical step in efficiently modeling the highly nonlinear problem of multiphase subsurface flow in a heterogeneous porous-fractured media. Current simulation and ground modeling techniques consist of (1) spatial discretization of mass and/or heat conservation equations using finite difference or finite element methods; (2) fully implicit time discretization; (3) solving the nonlinear, discrete algebraic equations using a Newton iterative scheme. Previous modeling efforts indicate that the choice of primary variables for a Newton iteration not only impacts computational performance of a numerical code, but may also determine the feasibility of a numerical modeling study in many field applications. This paper presents an analysis and general recommendations for selecting primary variables in simulating multiphase, subsurface flow for one-active phase (Richards' equation), two-phase (gas and liquid) and three-phase (gas, water and nonaqueous phase liquid or NAPL) conditions. In many cases, a dynamic variable switching or variable substitution scheme may have to be used in order to achieve optimal numerical performance and robustness. The selection of primary variables depends in general on the sensitivity of the system of equations to the variables selected at given phase and flow conditions. We will present a series of numerical tests and large-scale field simulation examples, including modeling one (active)-phase, two-phase and three-phase flow problems in multi-dimensional, porous-fractured subsurface systems.     

A direct passive method for measuring water and contaminant fluxes in porous media

This paper introduces a new direct method for measuring water and contaminant fluxes in porous media. The method uses a passive flux meter (PFM), which is essentially a self-contained permeable unit properly sized to fit tightly in a screened well or boring. The meter is designed to accommodate a mixed medium of hydrophobic and/or hydrophilic permeable sorbents, which retain dissolved organic/inorganic contaminants present in the groundwater flowing passively through the meter. The contaminant mass intercepted and retained on the sorbent is used to quantify cumulative contaminant mass flux. The sorptive matrix is also impregnated with known amounts of one or more water soluble 'resident tracers'. These tracers are displaced from the sorbent at rates proportional to the groundwater flux; hence, in the current meter design, the resident tracers are used to quantify cumulative groundwater flux. Theory is presented and quantitative tools are developed to interpret the water flux from tracers possessing linear and nonlinear elution profiles. The same theory is extended to derive functional relationships useful for quantifying cumulative contaminant mass flux. To validate theory and demonstrate the passive flux meter, results of multiple box-aquifer experiments are presented and discussed. From these experiments, it is seen that accurate water flux measurements are obtained when the tracer used in calculations resides in the meter at levels representing 20 to 70 percent of the initial condition. 2,4-Dimethyl-3-pentanol (DMP) is used as a surrogate groundwater contaminant in the box aquifer experiments. Cumulative DMP fluxes are measured within 5% of known fluxes. The accuracy of these estimates generally increases with the total volume of water intercepted.     

A numerical model for transient-hysteretic flow and solute transport in unsaturated porous media

A two-dimensional flow and transport model was developed for simulating transient water flow and nonreactive solute transport in heterogeneous, unsaturated porous media containing air and water. The model is composed of a unique combination of robust and accurate numerical algorithms for solving the Richards', Darcy flux, and advection-dispersion equations. The mixed form of Richards' equation is solved using a finite-element formulation and a modified Picard iteration scheme. Mass lumping is employed to improve solution convergence and stability behavior. The flow algorithm accounts for hysteresis in the pressure head-water content relationship. Darcy fluxes are approximated with a Galerkin and Petrov-Galerkin finite-element method developed for random heterogeneous porous media. The transport equation is solved using an Eulerian-Lagrangian method. A multi-step, fourth-order Runge-Kutta, reverse particle tracking technique and a quadratic-linear interpolation scheme are shown to be superior for determining the advective concentration. A Galerkin finite-element method is used for approximating the dispersive flux. The unsaturated flow and transport model was applied to a variety of rigorous problems and was found to produce accurate, mass-conserving solutions when compared to analytical solutions and published numerical results.     

Evaluation of simplified mass transfer models to simulate the impacts of source zone architecture on nonaqueous phase liquid dissolution in heterogeneous porous media

Nonaqueous phase liquid (NAPL) dissolution was studied in three-dimensional (3D) heterogeneous experimental aquifers (25.5 cm x 9 cm x 8.5 cm) with two different longitudinal correlation lengths (2.1 cm and 1.1 cm) and initial spill volumes (22.5 ml and 10.5 ml). Spatial and temporal distributions of NAPL during dissolution were measured using magnetic resonance imaging (MRI). At high NAPL spill volume, average effluent concentrations initially increased during dissolution, as NAPL pools transitioned to NAPL ganglia, and then decreased as the total NAPL-water interfacial area decreased over time. Experimental results were used to test six dissolution models: (i and ii) a one-dimensional (1D) model using either specific NAPL-water interfacial area values estimated from MR images at each time step (i.e., 1D quasi-steady state model), or an empirical mass transfer (Sh') correlation (i.e., 1D transient model), (iii and iv) a multiple analytical source superposition technique (MASST) using either the NAPL distribution determined from MR images at each time step (i.e., MASST steady state model), or the NAPL distribution determined from mass balance calculations (i.e., MASST transient model), (v) an equilibrium streamtube model, and (vi) a 3D grid-scale pool dissolution model (PDM) with a dispersive mass flux term. The 1D quasi-steady state model and 3D PDM captured effluent concentration values most closely, including some concentration fluctuations due to changes in the extent of flow reduction. The 1D transient, MASST steady state and transient, and streamtube models all showed a monotonic decrease in effluent concentration values over time, and the streamtube model was the most computationally efficient. Changes during dissolution of the effective NAPL-water interfacial area estimated from imaging data are similar to changes in effluent concentration values. The 1D steady state model incorporates estimates of the effective NAPL-water interfacial area directly at each time point; the 3D PDM does so indirectly through mass balance and a relative permeability function, which causes reduced water flow through high saturation NAPL regions. Hence, when model accuracy is required, the results indicate that a surrogate of this effective interfacial area is required. Approaches to include this surrogate in the MASST and streamtube models are recommended.     

Factors affecting mass transfer limited biodegradation in saturated porous media

Microbial degradation rates in the subsurface are not only limited by the physiological capacity of the organisms, but also by inefficient supply of nutrients to the microbes. Although mass transfer limitation of biodegradation in the subsurface has been postulated for years, experimental evidence is still scarce. In the column experiments described here, diffusive transport of 4-nitroanisole from the bulk solution to cells of Rhodococcus opacus strain AS2 immobilized on glass beads or sand appeared to be responsible for the slow transformation rates observed. Assuming steady state, we applied a coupled transformation/transport equation to these data (Best equation) and apparent bead-related mass transfer coefficients were found to increase in proportion to the surface area covered with bacteria. This implies that mass transfer coefficients for individual cells remained constant. In an idealized oligotrophic environment where cells are only loosely clustered and do not shield each other, we would therefore expect biodegradation rates to be independent from the longitudinal distribution of the total biomass along a given flow path. Moreover, apparent mass transfer coefficients increased with the grain size of the column fillings, but did not change upon varying the flow rate. With a limiting external transport step, overall transformation fluxes do not become saturated at concentrations as low as predicted for Michaelis-Menten-type kinetics. Mass transfer limitation thus offers a justification for the common assumption that biodegradation rates in the subsurface follow first order kinetics in a wide concentration range.