Modeling of in-situ biorestoration of organic compounds in groundwater

A convergent numerical method for modeling in situ biorestoration of contaminated groundwater is outlined. This method treats systems of transport-biodegradation equations by operator splitting in time. Transport is approximated by a finite element modified method of characteristics. The biodegradation terms are split from the transport terms and treated as a system of ordinary differential equations. Numerical results for vertical cross-sectional flow are presented. The effects of variable hydraulic conductivity and variable linear adsorption are studied.     

Modeling Biogeochemical Processes in Leachate-Contaminated Soils: A Review

During subsurface transport, reactive solutes are subject to a variety of hydrological, physical and biochemical processes. The major hydrological and physical processes include advection, diffusion and hydrodynamic dispersion, and key biochemical processes are aqueous complexation, precipitation/dissolution, adsorption/desorption, microbial reactions, and redox transformations. The addition of strongly reduced landfill leachate to an aquifer may lead to the development of different redox environments depending on factors such as the redox capacities and reactivities of the reduced and oxidised compounds in the leachate and the aquifer. The prevailing redox environment is key to understanding the fate of pollutants in the aquifer. The local hydrogeologic conditions such as hydraulic conductivity, ion exchange capacity, and buffering capacity of the soil are also important in assessing the potential for groundwater pollution. Attenuating processes such as bacterial growth and metal precipitation, which alter soil characteristics, must be considered to correctly assess environmental impact. A multicomponent reactive solute transport model coupled to kinetic biodegradation and precipitation/dissolution model, and geochemical equilibrium model can be used to assess the impact of contaminants leaking from landfills on groundwater quality. The fluid flow model can also be coupled to the transport model to simulate the clogging of soils using a relationship between permeability and change in soil porosity. This paper discusses the different biogeochemical processes occurring in leachate-contaminated soils and the modeling of the transport and fate of organic and inorganic contaminants under such conditions.     

An operator splitting algorithm for the three-dimensional advection–diffusion equation

Operator splitting algorithms are frequently used for solving the advection–diffusion equation, especially to deal with advection dominated transport problems. In this paper an operator splitting algorithm for the three-dimensional advection–diffusion equation is presented. The algorithm represents a second-order-accurate adaptation of the Holly and Preissmann scheme for three-dimensional problems. The governing equation is split into an advection equation and a diffusion equation, and they are solved by a backward method of characteristics and a finite element method, respectively. The Hermite interpolation function is used for interpolation of concentration in the advection step. The spatial gradients of concentration in the Hermite interpolation are obtained by solving equations for concentration gradients in the advection step. To make the composite algorithm efficient, only three equations for first-order concentration derivatives are solved in the diffusion step of computation. The higher-order spatial concentration gradients, necessary to advance the solution in a computational cycle, are obtained by numerical differentiations based on the available information. The simulation characteristics and accuracy of the proposed algorithm are demonstrated by several advection dominated transport problems. © 1998 John Wiley & Sons, Ltd.     

The Role of Biofilm Growth in Bacteria-Facilitated Contaminant Transport in Porous Media

Groundwater contaminants adhered to colloid surfaces may migrate to greater distances than predicted by using the conventional advective-dispersive transport equation. Introduction of exogenous bacteria in a bioremediation operation or mobilization of indigenous bacteria in groundwater aquifers can enhance the transport of contaminants in groundwater by reducing the retardation effects. Because of their colloidal size and favorable surface conditions, bacteria can be efficient contaminant carriers. In cases where contaminants have low mobility because of their high partition with aquifer solids, facilitated contaminant transport by mobile bacteria can create high contaminant fluxes. In this paper, we developed a methodology to describe the bacteria-facilitated contaminant transport in a subsurface environment using the biofilm theory. The model is based on mass balance equations for bacteria and contaminant. The contaminant is utilized as a substrate for bacterial growth. Bacteria are attached to solid surfaces as a biofilm. We investigate the role of the contaminant adsorption on both biofilm and mobile bacteria on groundwater contaminant transport. Also, the effect of bacterial injection on the contaminant transport is evaluated in the presence of indigenous bacteria in porous media. The model was solved numerically and validated by experimental data reported in the literature. Sensitivity analyses were conducted to deduce the effect of critical model parameters. Results show that biofilm grows rapidly near the top of the column where the bacteria and contaminant are injected, and is detached by increasing fluid shear stress and re-attach downstream. The adsorption of contaminant on bacterial surfaces reduces contaminant mobility remarkably in the presence of a biofilm. The contaminant concentration decreases significantly along the biofilm when contaminant partition into bacteria. Bacterial injection and migration in subsurface environments can be important in bioremediation operations regardless of the presence of indigenous bacteria.     

Modeling the Enhanced Bioremediation of Organic Contaminants in Pyrite-containing Aquifers

The bioremediation of organic contaminants in the subsurface is strongly influenced by the existing geochemical environment. In this study a coupled reactive transport and geochemical model is developed for the simulation of enhanced bioremediation of organic contamination in the presence of pyrite. The two-dimensional model allows for the simulation of both kinetically defined as well as geochemical equilibrium reactions. The model is applied to a hypothetical pyrite-containing aquifer contaminated with petroleum hydrocarbons. Oxygen injected into the aquifer to enhance contaminant biodegradation reacts with pyrite resulting in reduced oxygen availability, acidification of the subsurface environment and, subsequently, the inadvertent inhibition of the microbial activity. The reactive transport and geochemical model is used to quantify these processes. The dominance of the various chemical reactions and the sensitivity of the biodegradation on pyrite content are evaluated. Through groundwater pH manipulation, the interference of pyrite with the intended remedial action is partially mitigated. It is shown that when oxygen availability is a limiting factor, the optimal pH that would maximize hydrocarbon degradation may significantly differ from the pH value that maximizes bacterial activity.     

Singular Value Decomposition Method for Multi-species First-order Reactive Transport with Identical Decay Rates

A new decomposition method for solution of multi-component advection- dispersion-reaction equations coupled by first-order reactions is developed. This new method overcomes some of the limitations that were implicit in previously published algorithms. The approach is based on the Singular Value Decomposition (SVD) method. We derived analytical solution formulas, which can also be applied to systems with identical reaction rates. The proposed approach is flexible for solving one-, two- or three-dimensional advection-dispersion-reaction networks. The methodology is demonstrated on the reductive biodegradation of chlorinated solvents.     

Articular cartilage with intra- and extrafibrillar waters – mass transfer and generalized diffusion

The present analysis complements the chemo-mechanical model of articular cartilage developed in Loret and Simões [Loret, B., Simões, F.M.F., 2004. Articular cartilage with intra- and extrafibrillar waters. A chemo-mechanical model. Mech. Mater. 36 (5–6), 511–541; Loret, B., Simões, F.M.F., 2005a. Mechanical effects of ionic replacements in articular cartilage. Part I – The constitutive model. Biomech. Model. Mechanobiol. 4 (2–3), 63–80. Part II – Simulations of successive substitutions of NaCl and CaCl₂, 81–99], where only equilibria were considered, and therefore time was absent. The focus here is, first, to present how transport phenomena are aggregated to the porous media framework, and, second, to detail the constitutive equations of these transports. Indeed, these equations are developed in the context of a three-phase multi-species electro-chemo-mechanical model that accounts for the effects of two water compartments, namely intrafibrillar water stored between collagen fibrils and extrafibrillar water covering the negatively charged proteoglycans. The electrolyte circulating the two fluid phases contains ions sodium Na⁺, calcium Ca²⁺ and chloride Cl⁻.Species diffuse within their phase. They transfer from one fluid phase to the other. The various sources of dissipation are built in a thermodynamic framework, segregated and decoupled via the Clausius–Duhem inequality.Linear and non-linear equations of mass transfer are proposed along an onsagerist approach.The generalized diffusion in the extrafibrillar compartment accounts for Darcy's law of seepage through the porous solid skeleton, Fick's law of ionic diffusion, and Ohm's law of electric flow. An original derivation of the constitutive equations of generalized diffusion is proposed. Indeed, the dissipation inequality is written in two forms, which are required to be equivalent. This approach has the advantage of delivering the general structure of the diffusion matrix. It also displays in explicit form the degrees of freedom for possible refinements. Simple assumptions, phrased in terms of entities that are standard in transport of porous media, allow to recover arrowhead diffusion matrices. Comparison with an earlier proposal is detailed.An osmotic coefficient is found to be hidden in the equations, and anomalous negative osmosis is observed to take place for both sodium chloride and calcium chloride electrolytes.Finally, an experimental setup to measure transport properties is analyzed. The model describes correctly the increase and leveling of the experimental diffusion coefficient, and no additional ad hoc constitutive assumptions are needed in contrast to some suggestions in the literature.The results are presented for sodium chloride NaCl and calcium chloride CaCl₂.     

Integration of linear and some model non-linear equations of motion of incompressible fluids

We suggest a new exact method that allows one to construct solutions to a wide class of linear and some model non-linear hydrodynamic-type systems. The method is based on splitting a system into a few simpler equations; two different representations of solutions (non-symmetric and symmetric) are given. We derive formulas that connect solutions to linear three-dimensional stationary and non-stationary systems (corresponding to different models of incompressible fluids in the absence of mass forces) with solutions to two independent equations, one of which being the Laplace equation and the other following from the equation of motion for any velocity component at zero pressure. To illustrate the potentials of the method, we consider the Stokes equations, describing slow flows of viscous incompressible fluids, as well as linearized equations corresponding to Maxwell's and some other viscoelastic models. We also suggest and analyze a differential-difference fluid model with a constant relaxation time. We give examples of integrable non-linear hydrodynamic-type systems. The results obtained can be suitable for the integration of linear hydrodynamic equations and for testing numerical methods designed to solve non-linear equations of continuum mechanics.     

饱和-非饱和土壤中污染物运移过程的数值模拟

本文提出了一个模拟饱和 非饱和土壤中溶和污染物运移过程的数值模型．模拟的控制污染物运移的物理 化学现象包括：对流，机械逸散，分子弥散，吸附，蜕变，不动水效应．发展了一个修正的特征线Ｇａｌｅｒｋｉｎ方法以离散污染物运移过程的控制方程并导出了一个用于有限元方程求解的显式算法．数值例题结果表明所提出模型和算法的功能     

Monte Carlo Simulation of Contaminant Transport: I. Long-range Correlations in Fracture Conductivity

We develop a network model of fractures, and use the model to study transport of contaminants by groundwater through natural geological media. The fractures are narrow rectangular channels between large flat parallel plates, which are embedded in the surrounding rock matrix. The fracture-permeabilities and the fracture-widths are obtained from both uniform and fBm distributions. The pressure distribution in the network, and subsequently the velocity of groundwater in each channel, is obtained. The transport problem in an individual fracture is solved in Laplace space using the realized groundwater velocities and network mass conservation. The transform space solutions are then inverted to real time using a fast and efficient inversion algorithm. Monte Carlo simulations are then carried out by repeating the above procedure for a large number of realizations. The main focus of this study is to explore the effects correlated fracture-permeabilities and fracture-widths have on the transport of contaminants. While the primary transport mechanism is convection, we also study such processes as adsorption onto the fracture surface, and radioactive decay. We show how these phenomena, individually and in combination with one another, affect the overall transport process. In addition, we investigate the nature of the mixing zone, and discuss how these results can be helpful in developing remediation techniques for a contaminated site.     

Investigation of Transport- and Sorption-Related Factors on the Removal of Hydrophobic Organic Compounds in Heterogeneous Soils Using a Hierarchical Modeling Approach

Hydrophobic organic compounds (HOCs) represent a class of generally highly persistent contaminants in groundwater. Factors influencing the transport of HOCs are evaluated through a hierarchical modeling approach, which incorporates particle scale sorption/diffusion with pore scale flow and transport models. The relative contributions of transport- and sorption-related factors on HOCs transport are first elucidated in a simplified single particle system. The comparative roles of different soil organic matter contents and compositions on the fate and transport of HOCs are further investigated by simulation of phenanthrene transport in porous media. This effort represents a proof-of-concept demonstration of bridging comprehensive representations of fluid-flow with mechanistic sorption/desorption processes.     

Density-driven Transport of Volatile Organic Compounds and its Impact on Contaminated Groundwater Plume Evolution

Density-driven advection of gas phase due to vaporization of chlorinated volatile organic compounds (VOCs) has a significant effect on fate and transport of contaminants. In this study, we investigated the effects of density-driven advection, infiltration, and permeability on contaminant plume evolution and natural attenuation of VOCs in the subsurface system. To analyze these effects, multiphase flow and contaminant transport processes were simulated using a three-dimensional Galerkin-finite-element-based model. Trichloroethylene (TCE) is selected as a target contaminant. Density-driven advection of gas phase elevated the potential of groundwater pollution in the saturated zone by accelerating downward migration of vaporized contaminant in the unsaturated zone. The advection contributed to increased removal rates of non-aqueous phase liquid (NAPL) TCE source and reduced dissolved TCE plume development in the downstream area. Infiltration reduced the velocity of the density-driven advection and its influence zone, but raised TCE transfer from the unsaturated to the saturated zone. The variation in soil permeability showed greater impact on contaminant migration within water phase in the saturated zone than within gas phase in the unsaturated zone. Temporal variations of TCE mass within two-dimensional (2D) and three-dimensional (3D) domains under several modeling conditions were compared. These results are important in evaluation of natural attenuation processes, and should be considered to effectively design monitored natural attenuation as a remedial option.     

Exact analytic solutions of the porous media and the gas pressure diffusion ODEs in non-linear mechanics

Two kinds of second-order non-linear ordinary differential equations (ODEs) appearing in mathematical physics and non-linear mechanics are analyzed in this paper. The one concerns the Kidder equation in porous media and the second the gas pressure diffusion equation. Both these equations are strongly non-linear including quadratic first-order derivatives (damping terms). By a series of admissible functional transformations we reduce the prescribed equations to Abel's equations of the second kind of the normal form that they do not admit exact analytic solutions in terms of known (tabulated) functions. According to a mathematical methodology recently developed concerning the construction of exact analytic solutions of the above class of Abel's equations, we succeed in performing the exact analytic solutions of both Kidder's and gas pressure diffusion equations. The boundary and initial data being used in the above constructions are in accordance with each specific problem under considerations.     

Transport Through a Clay Barrier with the Contaminant Concentration Dependent Permeability

Transport of contaminants through clays is characterized by a very low dispersivity, but depends on the sensitivity of its intrinsic permeability to the contaminant's concentration. An additional constitutive relationship for a variable intrinsic permeability is thus adopted leading to a coupled system of equations for diffusive–advective transport in multicomponent liquid. A one-dimensional transport problem is solved using finite difference and Newton–Raphson procedure for nonlinear algebraic equations. The results indicate that although diffusion contributes to an increase of transport with respect to pure advection, the flux ultimately depends on end boundary conditions for concentration which, if low, may actually slow down the evolution of concentration and thus of permeability. Indeed, the advective component of flux may still remain secondary if the end portion of the layer remains unaffected by high concentrations. With no constraints on concentration at the bottom (zero concentration gradient boundary condition) and high concentration applied at the top, a significant shortening of the breakthrough time occurs.     

Finite volume solution to integrated shallow surface–saturated groundwater flow

This paper describes development of an integrated shallow surface and saturated groundwater model (GSHAW5). The surface flow motion is described by the 2‐D shallow water equations and groundwater movement is described by the 2‐D groundwater equations. The numerical solution of these equations is based on the finite volume method where the surface water fluxes are estimated using the Roe shock‐capturing scheme, and the groundwater fluxes are computed by application of Darcy's law. Use of a shock‐capturing scheme ensures ability to simulate steady and unsteady, continuous and discontinuous, subcritical and supercritical surface water flow conditions. Ground and surface water interaction is achieved by the introduction of source‐sink terms into the continuity equations. Two solutions are tightly coupled in a single code. The numerical solutions and coupling algorithms are explained. The model has been applied to 1‐D and 2‐D test scenarios. The results have shown that the model can produce very accurate results and can be used for simulation of situations involving interaction between shallow surface and saturated groundwater flows. Copyright © 2005 John Wiley & Sons, Ltd.     

A Two-Dimensional Areal Model for Density Dependent Flow Regime

A two-dimensional (2D) plane model of saltwater intrusion was developed, for the simulation of groundwater level and the average solute concentration in a 2D horizontal plane, together with the estimation of the saltwater depth. The proposed approach is of particular interest when assessing the effect of different regional pumping scenarios on groundwater level and its quality. The corresponding MEL2DSLT code was developed on the basis of the Modified Eulerian–Lagrangian (MEL) method to overcome difficulties arising from hyperbolic behavior of flow and transport equations, due to the advective nature of solute transport and heterogeneity of the soil characteristics (permeabilities and dispersivities). The code was verified against the 2D cross sectional model SUTRA and the three-dimensional (3D) model SWICHA. Simulation was conducted concerning the problem of saltwater intrusion in the Khan Yunis portion of the phreatic coastal aquifer of Gaza Strip. After calibrating the model for the aquifer parameters, we investigated its predictions resulting from various regional pumping scenarios using the actual pumping intensity from the year 1985 and extrapolating on the basis of 3.8% annual population growth. Results show a considerable depletion of groundwater level and intrusion of seawater due to excessive pumping.     

Effects of chemical reaction on mixed convection flow of a polar fluid through a porous medium in the presence of internal heat generation

This paper reports a detailed numerical investigation on mixed convection flow of a polar fluid through a porous medium due to the combined effects of thermal and mass diffusion. The energy equation accounts for heat generation or absorption, while the nth order homogeneous chemical reaction between the fluid and the diffusing species is included in the mass diffusion equation. The governing equations of the linear momentum, angular momentum, energy and concentration are obtained in a non-similar form by introducing a suitable group of transformations. The final set of non-similar coupled non-linear partial differential equations is solved using an implicit finite-difference scheme in combination with quasi-linearization technique. The effects of various parameters on the velocity, angular velocity, temperature and concentration fields are investigated. Numerical results for the skin friction coefficient, wall stress of angular velocity, Nusselt number and Sherwood number are also presented.     

Nodal operator splitting adaptive finite element algorithms for the Navier–Stokes equations

Solution algorithms for solving the Navier–Stokes equations without storing equation matrices are developed. The algorithms operate on a nodal basis, where the finite element information is stored as the co-ordinates of the nodes and the nodes in each element. Temporary storage is needed, such as the search vectors, correction vectors and right hand side vectors in the conjugate gradient algorithms which are limited to one-dimensional vectors. The nodal solution algorithms consist of splitting the Navier–Stokes equations into equation systems which are solved sequencially. In the pressure split algorithm, the velocities are found from the diffusion–convection equation and the pressure is computed from these velocities. The computed velocities are then corrected with the pressure gradient. In the velocity–pressure split algorithm, a velocity approximation is first found from the diffusion equation. This velocity is corrected by solving the convection equation. The pressure is then found from these velocities. Finally, the velocities are corrected by the pressure gradient. The nodal algorithms are compared by solving the original Navier–Stokes equations. The pressure split and velocity–pressure split equation systems are solved using ILU preconditioned conjugate gradient methods where the equation matrices are stored, and by using diagonal preconditioned conjugate gradient methods without storing the equation matrices. © 1998 John Wiley & Sons, Ltd.