Constantinos V. Chrysikopoulos

Three‐Dimensional Analytical Models of Contaminant Transport From Nonaqueous Phase Liquid Pool Dissolution in Saturated Subsurface Formations

Closed form analytical solutions are derived for three-dimensional transient contaminant transport resulting from dissolution of single-component nonaqueous phase liquid pools in saturated porous media. The solutions are suitable for homogeneous porous media with unidirectional interstitial velocity. The dissolved solute may undergo first-order decay or may sorb under local equilibrium conditions. The solutions are obtained for rectangular and elliptic as well as circular source geometries, assuming that the dissolution process is mass transfer limited, by applying Laplace and Fourier transforms. Although the solutions contain integral expressions, these integrals are easily evaluated numerically. These solutions are useful for verifying the accuracy of numerical solutions to more comprehensive models and for design and interpretation of experiments in laboratory-packed beds and possibly some field studies. The results of several simulations indicate that for short downstream distances, predictions of contaminant concentrations are sensitive to the source structure and orientation with respect to the direction of interstitial flow. 33 refs., 8 figs., 1 tab.

Transport of biocolloids in water saturated columns packed with sand: Effect of grain size and pore water velocity

The main objective of this study was to evaluate the combined effects of grain size and pore water velocity on the transport in water saturated porous media of three waterborne fecal indicator organisms (Escherichia coli, MS2, and ΦX174) in laboratory-scale columns packed with clean quartz sand. Three different grain sizes and three pore water velocities were examined and the attachment behavior of Escherichia coli, MS2, and ΦX174 onto quartz sand was evaluated. The mass recoveries of the biocolloids examined were shown to be highest for Escherichia coli and lowest for MS2. However, no obvious relationships between mass recoveries and water velocity or grain size could be established from the experimental results. The observed mean dispersivity values for each sand grain size were smaller for bacteria than coliphages, but higher for MS2 than ΦX174. The single collector removal and collision efficiencies were quantified using the classical colloid filtration theory. Furthermore, theoretical collision efficiencies were estimated only for E. coli by the Interaction-Force-Boundary-Layer, and Maxwell approximations. Better agreement between the experimental and Maxwell theoretical collision efficiencies were observed.

Attachment of bacteriophages MS2 and ΦX174 onto kaolinite and montmorillonite: Extended-DLVO interactions

This study aims to gain insights into the interaction of virus particles with clay colloids. Bacteriophages MS2 and ΦX174 were used as model viruses and kaolinite (KGa-1b) and montmorillonite (STx-1b) as model colloids. The experimental data obtained from batch experiments of MS2 and ΦX174 attachment onto KGa-1b and STx-1b suggested that virus attachment is adequately described by the Freundlich isotherm equation. Both MS2 and ΦX174 were attached in greater amounts onto KGa-1b than STx-1b with MS2 having greater affinity than ΦX174 for both clays. Furthermore, extended-DLVO interaction energy calculations explained that the attachment of viruses onto model clay colloids was primarily caused by hydrophobic interaction. The theoretical and experimental results of this study were found to be in good agreement with previous findings.

One-dimensional virus transport in homogeneous porous media with time-dependent distribution coefficient

Abstract A stochastic model for one-dimensional virus transport in homogeneous, saturated, semi-infinite porous media is developed. The model accounts for first-order inactivation of liquid-phase and adsorbed viruses with different inactivation rate constants, and time-dependent distribution coefficient. It is hypothesized that the virus adsorption process is described by a local equilibrium expression with a stochastic time-dependent distribution coefficient. A closed form analytical solution is obtained by the method of small perturbation or first-order approximation for a semi-infinite porous medium with a flux-type inlet boundary condition. The results from several simulations indicate that a time-dependent distribution coefficient results in an enhanced spreading of the liquid-phase virus concentration.

Analytical Models for One‐Dimensional Virus Transport in Saturated Porous Media

Analytical solutions to two mathematical models for virus transport in one-dimensional homogeneous, saturated porous media are presented, for constant flux as well as constant concentration boundary conditions, accounting for first-order inactivation of suspended and adsorbed (or filtered) viruses with different inactivation constants. Two processes for virus attachment onto the solid matrix are considered. The first process is the nonequilibrium reversible adsorption, which is applicable to viruses behaving as solutes; whereas, the second is the filtration process, which is suitable for viruses behaving as colloids. Since the governing transport equations corresponding to each physical process have identical mathematical forms, only one generalized closed-form analytical solution is developed by Laplace transform techniques. The impact of the model parameters on virus transport is examined. An empirical relation between inactivation rate and subsurface temperature is employed to investigate the effect of temperature on virus transport. It is shown that the differences between the two boundary conditions are minimized at advection-dominated transport conditions.

Mass transfer correlations for nonaqueous phase liquid pool dissolution in saturated porous media

Local mass transfer correlations are developed to describe the rate of interface mass transfer of single component nonaqueous phase liquid (NAPL) pools in saturated subsurface formations. A three‐dimensional solute transport model is employed to compute local mass transfer coefficients from concentration gradients at the NAPL–water interface, assuming that the aqueous phase concentration along the NAPL–water interface is constant and equal to the solubility concentration. Furthermore, it is assumed that the porous medium is homogeneous, the interstitial fluid velocity steady and the dissolved solute may undergo first‐order decay or may sorb under local equilibrium conditions. Power‐law expressions relating the local Sherwood number to appropriate local Peclet numbers are developed for both rectangular and elliptic/circular source geometries. The proposed power law correlations are fitted to numerically generated data and the correlation coefficients are determined using nonlinear least squares regression. The estimated correlation coefficients are found to be direct functions of the interstitial fluid velocity, pool dimensions, and pool geometry.

Transport of polydisperse colloids in a saturated fracture with spatially variable aperture

A particle tracking model is developed to simulate the transport of variably sized colloids in a fracture with a spatially variable aperture. The aperture of the fracture is treated as a lognormally distributed random variable. The spatial fluctuations of the aperture are described by an exponential autocovariance function. It is assumed that colloids can sorb onto the fracture walls but may not penetrate the rock matrix. Particle advection is governed by the local fracture velocity and diffusion by the Stokes-Einstein equation. Model simulations for various realizations of aperture fluctuations indicate that lognormal colloid size distributions exhibit greater spreading than monodisperse suspensions. Both sorption and spreading of the polydisperse colloids increase with increasing variance in the particle diameter. It is shown that the largest particles are preferentially transported through the fracture leading to early breakthrough while the smallest particles are preferentially sorbed. Increasing the variance of the aperture fluctuations leads to increased tailing for both monodisperse and variably sized colloid suspensions, while increasing the correlation length of the aperture fluctuations leads to increased spreading.

Interaction between viruses and clays in static and dynamic batch systems.

Bacteriophage MS2 and PhiX174 were used as surrogates for human viruses in order to investigate the interaction between viruses and clay particles. The selected phyllosilicate clays were kaolinite and bentonite (>90% montmorillonite). A series of static and dynamic experiments were conducted at two different temperatures (4 and 25 degrees C) to investigate the effect of temperature and agitation (dynamic experiments) on virus adsorption onto clays. Appropriate adsorption isotherms were determined. Electrokinetic features of bacteriophages and clays were quantified at different pH and ionic strength (IS). Moreover, interaction energies between viruses and clays were calculated for the experimental conditions (pH 7 and IS = 2 mM) by applying the DLVO theory. The experimental results shown that virus adsorption increases linearly with suspended virus concentration. The observed distribution coefficient (K(d)) was higher for MS2 than PhiX174. The observed K(d) values were higher for the dynamic than static experiments, and increased with temperature. The results of this study provided basic information for the effectiveness of clays to remove viruses by adsorption from dilute aqueous solutions. No previous study has explored the combined effect of temperature and agitation on virus adsorption onto clays.

Analysis of a model for contaminant transport in fractured media in the presence of colloids

Abstract A mathematical model has been developed to study the cotransport of contaminants with colloids in saturated rock fractures. The contaminant is assumed to decay, and sorb on to fracture surfaces and on to colloidal particles, as well as to diffuse into the rock matrix; whereas, colloids are envisioned to deposit irreversibly on to fracture surfaces without penetration into the rock matrix. The governing one-dimensional equations describing the contaminant and the colloid transport in the fracture, colloid deposition on to fracture surfaces, and contaminant diffusion into the rock matrix are coupled. This coupling is accomplished by assuming that the amount of contaminant mass captured by colloidal particles in solution and the amount captured by deposited colloids on fracture surfaces are described by modified Freundlich reversible equilibrium sorption relationships, and that mass transport by diffusion into the rock matrix is a first-order process. The contaminant sorption on to fracture surfaces is described by a linear equilibrium sorption isotherm, while the deposition of colloids is incorporated into the model as a first-order process. The resulting coupled contaminant transport non-linear equation is solved numerically with the fully implicit finite difference method. The constant concentration as well as the constant flux boundary conditions have been considered. The impact of the presence of colloids on contaminant transport is examined. According to model simulations the results show that, depending on the conditions of the physical system considered, colloids can increase or decrease the mobility of contaminants.

Modeling colloid transport and deposition in saturated fractures

A model is developed to describe the transport of colloids in a saturated fracture with a spatially variable aperture, accounting for colloid deposition onto fracture surfaces under various physicochemical conditions. The fracture plane is partitioned into unit elements with different apertures generated stochastically from a log-normal distribution. The model also accounts for colloid size exclusion from fracture elements with small apertures. Both equilibrium and kinetic colloid deposition onto fracture surfaces are investigated. Colloid surface exclusion is incorporated in the dynamics of kinetic deposition. The impact of deposited colloids on further colloid deposition is described by either a linear or a non-linear blocking function. The resulting system of governing partial differential equations is solved numerically using the fully implicit finite difference method. Model simulations illustrate the presence of preferential colloid transport in the fracture plane. It is shown that size exclusion increases the dispersion of colloids and leads to earlier breakthrough, especially for large-size particles. Furthermore, it is demonstrated that surface exclusion enhances colloid transport, and the assumption of clean-bed media may underestimate liquid-phase colloid concentrations.