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.     

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.     

Transport of Pseudomonas putida in a 3-D Bench Scale Experimental Aquifer

This study is focused on the transport of Pseudomonas (P.) putida bacterial cells in a 3-D model aquifer. The pilot-scale aquifer consisted of a rectangular glass tank with internal dimensions: 120?cm length, 48?cm width, and 50?cm height, carefully packed with well-characterized quartz sand. The P. putida decay was adequately represented by a first-order model. Transport experiments with a conservative tracer and P. putida were conducted to characterize the aquifer and to investigate the bacterial behavior during transport in water saturated porous media. A 3-D, finite-difference numerical model for bacterial transport in saturated, homogeneous porous media was developed and was used to successfully fit the experimental data. Furthermore, theoretical interaction energy calculations suggested that the extended-DLVO theory seems to predict bacteria attachment onto the aquifer sand better than the classical DLVO theory.     

Transient Heat and Moisture Flow Around Heat Source Buried in an Unsaturated Half Space

This article presents solutions for the transient heat and moisture transport due to both disk heat source and cylindrical heat source buried in an unsaturated half space. The solutions are presented in Hankel–Laplace transform domain and in dimensionless style. Coupled effect of thermally driven moisture transport is especially investigated because of its importance to alter the flow field in low-permeability medium. Parametric study has been performed to assess the effects of five independent dimensionless parameters on flow field. The stability and accuracy of the present solutions are demonstrated from the comparison between the results obtained from these solutions and those by using a well-established finite element code CODE_BRIGHT. Despite the simplified assumptions required in order to obtain analytical solutions in Hankel–Laplace transform domain, the results incorporate the main mechanisms involved in the coupled thermo-hydraulic (T-H) problem, and they may be eventually used for validation purposes.     

基于渗透率连续变化的低渗透多孔介质非线性渗流模型

基于低渗透多孔介质渗透率的渐变理论,确定了能精确描述低渗透多孔介质渗流特征的非线性运动方程,并通过实验数据拟合．验证了非线性运动方程的有效性。非线性渗流速度关于压力梯度具有连续-阶导数,方便于工程计算;由此建立了低渗透多孔介质的单相非线性径向渗流数学模型,并巧妙采用高效的Douglas-Jones预估一校正有限差分方法求得了其数值解。数值结果分析表明：非线性渗流模型为介于拟线性渗流模型和达西渗流模型之间的一种中间模型或理想模型,非线性渗流模型和拟线性渗流模型均存在动边界;拟线性渗流高估了启动压力梯度的影响,使得动边界的移动速度比实际情况慢得多;非线性越强,地层压力下降的范围越小,地层压力梯度越陡峭,影响地层压力的敏感性减弱,而影响地层压力梯度的敏感性增强。     

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.     

Analytical model of the linear inflow to a horizontal well with hydraulic fractures in low-permeability reservoirs

At present, increasing attention has been concentrated on low-permeability deposits whose development is tightly related with technologies of horizontal drilling and hydraulic fracturing of the reservoir. However, the simultaneous presence of a horizontal section of the well and hydraulic fractures in the reservoir impedes the process of flow of reservoir liquids and gases through the porous medium and complicates simulation of such flows. In the present study a new analytical model of the linear inflow to a horizontal well with hydraulic fractures in low-permeability reservoirs is proposed. This is a generalizing model which takes into account both situations when there exists a linear flow in the direction perpendicular to the borehole of a horizontal well in the distant sections of the reservoir and when there is a linear flow in the direction parallel to the borehole of a horizontal well. The use of the model is not restricted by the shape of the flow domain. The new model proposed has a wide application field and does not require complex computations.     

Water Injection into a Low-Permeability Rock - 1 Hydrofracture Growth

In this paper, we model water injection through a growing vertical hydrofracture penetrating a low-permeability reservoir. The results are useful in oilfield waterflood applications and in liquid waste disposal through reinjection. Using Duhamel's principle, we extend the Gordeyev and Entov (1997) self-similar 2D solution of pressure diffusion from a growing fracture to the case of variable injection pressure. The flow of water injected into a low-permeability rock is almost perpendicular to the fracture for a time sufficiently long to be of practical interest. We revisit Carter's model of 1D fluid injection (Howard and Fast, 1957) and extend it to the case of variable injection pressure. We express the cumulative injection through the injection pressure and effective fracture area. Maintaining fluid injection above a reasonable minimal value leads inevitably to fracture growth regardless of the injector design and the injection policy. The average rate of fracture growth can be predicted from early injection. A smart injection controller that can prevent rapid fracture growth is needed.     

Solution and its application of transient stream/groundwater model subjected to time-dependent vertical seepage

Based on the first linearized Boussinesq equation,the analytical solution of the transient groundwater model,which is used for describing phreatic flow in a semi- infinite aquifer bounded by a linear stream and subjected to time-dependent vertical seepage,is derived out by Laplace transform and the convolution integral.According to the mathematical characteristics of the solution,different methods for estimating aquifer parameters are constructed to satisfy different hydrological conditions.Then,the equation for estimating water exchange between stream and aquifer is proposed,and a recursion equation or estimating the intensity of phreatic evaporation is also proposed.A phreatic aquifer stream system located in Hualbei Plain,Anhui Province,China,is taken as an example to demonstrate the estimation process of the methods stated herein.     

An Extended-FEM Model for CO2 Leakage Through a Naturally Fractured Cap-Rock During Carbon Dioxide Sequestration

In this paper, a numerical model is developed for the assessment of carbon dioxide transport through naturally fractured cap-rocks during CO₂ sequestration in underground aquifers. The cap-rock contains two types of fracture with different length scales: micro-cracks (fissures) and macro-cracks (faults). The effect of micro-cracks is incorporated implicitly by modifying the intrinsic permeability tensor of porous matrix, while the macro-cracks are modeled explicitly using the extended finite element method (X-FEM). The fractured porous medium is decomposed into the porous matrix and fracture domain, which are occupied with two immiscible fluid phases, water and CO₂. The flow inside the matrix domain is governed by the Darcy law, while the flow within the fracture is modeled using the Poiseuille flow. The mass conservation law is fulfilled for each fluid phase at both porous matrix and fracture domain; moreover, the mass exchange between the matrix and fracture is guaranteed through the integral formulation of mass conservation law. Applying the X-FEM technique, the explicit representation of macro-cracks is modeled by enriching the standard finite element approximation space with an enrichment function. Finally, several numerical examples of CO₂ injection into a brine aquifer below a naturally fractured cap-rock are modeled in order to investigate the effects of cracks’ aperture and orientation as well as the temperature of aquifer and the depth of injection on the leakage pattern of the carbon dioxide through the cap-rock.

     

SLIPPAGE SOLUTION OF GAS PRESSURE DISTRIBUTION IN PROCESS OF LANDFILL GAS SEEPAGE

A mathematical model of landfill gas migration was established under presumption of the effect of gas slippage. The slippage solutions to the nonlinear mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of gas pressure in landfill site was presented under the conditions of considering and neglecting slippage effect. Sensitivity of the model input parameters was analyzed. The model solutions were compared to observation values. Results show that gas slippage effect has a large impact on gas pressure distribution. Landfill gas pressure and pressure gradient considering slippage effect is lower than that neglecting slippage effect, with reasonable agreement between model solution and measured data. It makes clear that the difference between considering and neglecting slippage effect is obvious and the effects of coupling cannot be ignored. The theoretical basis is provided for engineering design of security control and decision making of gas exploitation in landfill site. The solutions give scientific foundation to analyzing well test data in the process of low-permeability oil gas reservoir exploitation.     

Modeling primary substrate controlled biotransformation and transport of halogenated aliphatics in porous media

In situ biorestoration is a groundwater remediation technique in which the indigenous aquifer bacteria are stimulated by injecting compounds to provide carbon source and energy. Stimulated bacteria may transform the target contaminants such as tetrachloroethylene (PCE) and trichloroethylene (TCE) into intermediate products. In this study, we developed a model to simulate the substrate-limited biotransformation of the halogenated solvents present in anoxic groundwater by sequential reductive dehalogenation under methanogenic conditions. The model consists of conservation of mass equations for the primary substrate, immobile indigenous biomass, organic solvents such as PCE and TCE, and their intermediate products trichloroethylene, dichloroethylene, and vinyl chloride. The utilization of primary substrate and the biotransformation of organic solvents are assumed to follow Monod kinetics. The limiting factor on bacterial growth is assumed to be the primary substrate. The microbial yield coefficient is determined from the stoichiometric equation describing the anaerobic process. The model is solved by using a finite difference technique. Results are presented for three different case studies: continuous injection of primary substrate (acetate), single-pulse injection, and double-pulse injection. The single-pulse or double-pulse injection techniques were found to be more effective than continuous injection of primary substrate. Double-pulse technique reduces the clogging of injection wells caused by excessive microbial growth around boreholes and achieves a more uniform distribution of microbial growth in the subsurface. In all cases target compounds were effectively removed. The results, however, indicate substantial levels of intermediate product accumulation. Numerical results of a simplified model which assumes an abundance of primary substrate and a constant population of biomass, compare favorably with experimental data reported in the literature.     

Mass and heat transfer modeling of bio-substrates during packaging

Perishable bio-substrate behavior can be modeled during packaged storage. Local mass and heattransfer have been coupled to respiration rate and microbial growth. Validating measurements have also been performed, and a multi-objective optimization was employed to tune the model. The model is able to simulate gas composition history and local bacteria spoilage in storage modes commonly adopted by the food industry, depending on product features and temperature. Exploitation of this mathematical tool would allow for informed technical and management decisions.     

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.     

低渗透微尺度孔隙气体渗流规律

微尺度条件下气体流动特性的研究是现代渗流力学前沿领域之一．分析了低渗透岩石饱和气体渗流实验结果,探索了微尺度孔隙气体渗流规律,探讨了气体非线性渗流力学机理,发现了低渗透岩石微尺度孔隙气体与液体渗流遵循同一形式的运动定律,建立了气体与液体非线性运动定律统一模型．结果表明：新模型与实验结果吻合很好,为微尺度孔隙气体微流动特性研究提供了新的理论依据,对工程地质环境保护及地下流体资源开发有重要指导意义．     

Pattern Formation in Turing Systems on Domains with Exponentially Growing Structures

Turing reaction–diffusion systems have been used to model pattern formation in several areas of developmental biology. Previous biomathematical Turing system models employed static domains which failed to incorporate the growth that inherently occurs as an organism develops. To address this shortcoming, we incorporate an exponentially growing domain into a Turing system, allowing one to more realistically model biological pattern formation. This Turing system can generate patterns on an exponentially growing domain in any of the eleven coordinate systems in which the Helmholtz equation is separable, making the system incredibly flexible and giving one the capability to mathematically model pattern formation on a geometrically diverse group of domains. Linear stability analysis is employed to generate mathematical conditions which ensure such a system can generate patterns. We apply the exponentially growing Turing system to a prolate spheroidal domain and conduct numerical simulations to investigate the system’s pattern-generating behavior. We find that the addition of growth to a Turing system causes a significant change in the pattern-generating behavior of the system. While a static domain Turing system converges to a final pattern, an exponentially growing domain Turing system produces transient patterns that continually evolve and increase in complexity over time.     

Free vibration analysis of the axially moving Levy-type viscoelastic plate

In this paper, the viscoelastic theory is applied to the axially moving Levy-type plate with two simply supported and two free edges. On the basis of the elastic – viscoelastic equivalence, a linear mathematical model in the form of the equilibrium state equation of the moving plate is derived in the complex frequency domain. Numerical calculations of dynamic stability were conducted for a steel plate. The effects of transport speed and relaxation times modeled with two-parameter Kelvin–Voigt and three-parameter Zener rheological models on the dynamic behavior of the axially moving viscoelastic plate are analyzed.     

Integrating Hydrogeochemical and Geophysical Data for Testing a Finite Volume Based Numerical Model for Saltwater Intrusion

In this paper, hydrogeological and geophysical data are used to validate a numerical model developed to predict seawater intrusion into coastal aquifers. The cell-centered finite volume method is adopted here to solve the set of coupled partial differential equations describing the motion of saltwater and freshwater separated by a sharp interface. These equations are based on the Dupuit approximation and are obtained from integration of 3D flow equations for fresh and salt water zones over the vertical dimension. In order to have flexibility upon complex configurations domain, non structured grid meshing is utilized. To approximate the diffusion fluxes, Green-Gauss type reconstruction, based on diamond-cell and least squares interpolation, is performed. The model is first validated using academic test case studies with known closed form solutions. The mathematical model has been calibrated using hydrogeochemical and geophysical data. The geophysical method applied in this study has been a frequency domain electromagnetic method. In this method the apparent electrical conductivity is measured by induction using two separate hand-held transmitter and receiver coils. During the operation the transmitter coil is energized by a low frequency alternating current that radiates an electromagnetic field and the receiver coil detects the resulting field. Taking into account the relationship between the bulk conductivity of the subsoil and the conductivity of groundwater, EM soundings have been interpreted to provide complementary information to hydrogeochemical data to outline the fresh–saltwater interface. This methodology has been applied to the case of saltwater intrusion into the Llobregat delta aquifer, near Barcelona, Spain.     

Effects of Clay Dispersion on Aquifer Storage and Recovery in Coastal Aquifers

Cyclic injection, storage, and withdrawal of freshwater in brackish aquifers is a form of aquifer storage and recovery (ASR) that can beneficially supplement water supplies in coastal areas. A 1970s field experiment in Norfolk, Virginia, showed that clay dispersion in the unconsolidated sedimentary aquifer occurred because of cation exchange on clay minerals as freshwater displaced brackish formation water. Migration of interstitial clay particles clogged pores, reduced permeability, and decreased recovery efficiency, but a calcium preflush was found to reduce clay dispersion and lead to a higher recovery efficiency. Column experiments were performed in this study to quantify the relations between permeability changes and clay mineralogy, clay content, and initial water salinity. The results of these experiments indicate that dispersion of montmorillonite clay is a primary contributor to formation damage. The reduction in permeability by clay dispersion may be expressed as a linear function of chloride content. Incorporating these simple functions into a radial, cross-sectional, variable-density, ground-water flow and transport model yielded a satisfactory simulation of the Norfolk field test – and represented an improvement over the model that ignored changes in permeability. This type of model offers a useful planning and design tool for ASR operations in coastal clastic aquifer systems.