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.     

煤层气在非饱和水流阶段的非定常渗流摄动解

煤层甲烷由煤层的割理裂隙系统流入生产井一般经历：单相水流、非饱和流和气、水两相饱和流三个阶段，在非饱和流阶段，储层压力降至临界解吸压力之后，储存在煤基质中的吸附气体少量被解吸出来形成互不连续的气泡并阻止水的流动，含气量尚未达到饱和程度。同时煤层甲烷运移包含渗流场、变形场和应力场的动态耦合过程。本文考虑渗流过程中水-气两相不溶混流体与固体耦合作用，建立了非饱和水流阶段非定常渗流问题的流固耦合数学模型，对该强非线性一维数学模型采用摄动法和积分变换法进行解析求解，并讨论了其压力动态特性，分析了压力随饱和度S及时间t变化的规律和气相及耦合作用的影响，这些研究对煤层气、石油和天然气的开采等地下工程领域具有一定的指导意义。     

GAS-WATER TWO-PHASE DIFFUSION MODEL FOR UNSATURATED LAYERED COVER SYSTEMS

为了研究垃圾填埋场内部生物降解产生的气体(以甲烷为主) 和氧气等在非饱和覆盖层中的运移规律,建立了气体在成层非饱和覆盖层中的一维扩散模型. 该模型考虑了覆盖层含水量瞬态变化和气体扩散的耦合作用. 采用有限元多物理场耦合分析软件COMSOL Multiphysics 4.3进行求解. 其计算结果与前人实验结果能符合得很好. 研究结果表明,对典型垃圾填埋场中厚度为1m的非饱和黏土覆盖层,含水量变化对覆盖层中气体污染物的扩散运移有显著影响. 与含水量稳态变化情况相比,20 d到100 d的运移时间内同一覆盖层深度处耦合含水量作用下,气体相对浓度可以相差接近8倍. 含水量是气体在非饱和覆盖层中不稳定运移的重要影响因素.     

Influence of root resistivity on plant water uptake mechanism,Part II: analytical solutions for low/moderate soil-root conductivity ratio

A one-dimensional approximate analytical model, which preserves the main features of soil-crop-atmospheric hydrodynamics, has been suggested for plant roots of low soil-root conductivity ratio (SRCR). The proposed approach involves physically based concepts, such as mass balance equation, Darcy’s law, and related water uptake and plant transpiration functions. Two main assumptions have been made to derive the analytical solution: (1) gravitational flow is adopted and (2) the uniform soil moisture distribution within the root water activity zone is supposed. The mass balance equation in its integral form is solved by the method of characteristics. This leads to the two functional equations for soil pressure head and root potential, which can be solved simultaneously by using common software. The model has been further verified against the numerical one. The model represents a reasonable compromise between the complicated mechanism of unsaturated water flow with root water uptake (RWU) and still insufficient knowledge of the soil-plant-atmospheric continuum. It is able to account for temporal fluctuations in root activity zone and provides a relatively simple algorithm for investigation of RWU-mechanism. Besides the theoretical and applicative importance, this flow model yields water and velocity distributions within soil profile, and, thereby, constitutes a preliminary step toward solution of contaminant transport problems in vadose zone. Deceased     

Numerical and experimental investigation of convective drying in unsaturated porous media with bound water

The heat and mass transfer in an unsaturated wet cylindrical porous bed packed with quartz particles was investigated theoretically for relatively low convective drying rates. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi-phase flow in the unsaturated porous media using the energy and mass conservation equations to describe the heat and mass transfer during the drying. The drying model included convection and capillary transport of the free water, diffusion of bound water, and convection and diffusion of the gas. The numerical results indicated that the drying process could be divided into three periods, the temperature rise period, the constant drying rate period and the decreasing drying rate period. The numerical results agreed well with the experimental data verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. The effects of drying conditions such as the ambient temperature, the relative humidity, and the velocity of the drying air, on the drying process were evaluated by numerical solution.     

A Benchmark Solution for Infiltration and Adsorption of Polluted Water Into Unsaturated–Saturated Porous Media

We discuss the numerical modeling of the infiltration of contaminated water into unsaturated porous media. A system with contaminant transport, dispersion, and adsorption is considered. The mathematical model for unsaturated flow is based on Richards nonlinear and degenerate equation. Nonlinear adsorption is represented by adsorption isotherms and kinetic rates. An accurate numerical method is constructed in 1D which can be a good candidate for the solution of inverse problems to determine model parameters in the adsorption part of the model. Our numerical solution is based on the method of lines (MOL method) where space discretization leads to the corresponding system of ODEs. We substantially use the numerical modeling of interfaces, separating fully saturated, partially saturated, and dry zones in the underground. Finally, in a series of numerical experiments and in comparisons with HYDRUS (?imunek et al., The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably/saturated media, version 2.0, Rep. IGWMC-TPS-70, 202 pp., Int. Groundwater Model. Cent., Colo. Sch of Mines, Golden, Colo), we demonstrate the effectiveness of our method.     

Laboratory Investigation of Variable-Density Flow and Solute Transport in Unsaturated–Saturated Porous Media

In many groundwater systems, fluid density and viscosity may vary in space and time as a function of changes in concentration and temperature of the fluid. When dense groundwater plumes interact with less dense ambient groundwater, these density variations can significantly affect flow and transport processes. Under certain conditions, gravitational instabilities in the form of lobe-shaped fingers can occur. This process is significant because it can lead to more rapid and spatially extensive solute transport. This paper presents new experiments carried out in a sand filled glass flow container under both fully saturated and variably-saturated conditions and focuses upon the processes that occur at the capillary fringe and below the water table, as affected by a dense contaminant plumes migration through the unsaturated zone. Source fluids stained with Rhodamine-WT were introduced at the upper boundary of the tank at a range of low and high densities. In addition to the fluid density gradients and porous medium permeability that determine the onset conditions for instabilities in fully saturated experiments, volumetric water content appears critical in the variably-saturated laboratory runs. Plume behaviour at the water table appears dependent upon the density of the fluid that accumulates there. For neutral and low density fluids, plumes accumulate at the water table and then spread laterally above it and the water table forms a barrier to further vertical flow as pore water velocities reduce with increasing water content. For medium and high density fluids, vertical movement continues as instabilities form at the capillary fringe and fingers begin to grow at the water table boundary and move downwards into the saturated zone. In these cases, lateral spreading of the plume is small. Despite these more qualitative observations, the exact nature of the relevant stability criteria for the onset and growth of instabilities in variably-saturated porous media presently remain unclear. All experimental results suggest, however, that the unsaturated zone and position of the water table must be considered in contaminant studies in order to predict the migration pathways, rates and ultimate fate of dense contaminant plumes. It is possible that the results of experiments presented in this paper could form a useful basis for the testing of variable-density (and variably-saturated) groundwater flow and solute transport numerical codes because they offer controlled physical laboratory analogs for comparison. They also provide a strong basis for the development of more rigorous mathematical formulations that are likely to be either developed or tested using numerical flow and solute transport simulators.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain,water andgas.In this paper,the consolidation problem of unsaturated soil is investigated basedon the theory of mixture.A theoretical formula of effective stress on anisotropicporous media and unsaturated soil is derived.The principle of effective stress and theprinciple of Curie symmetry are taken as two fundamental constitutive principles ofunsaturated soil.A mathematical model of consolidation of unsaturated soil isproposed,which consists of25 partial differenfial equations with25 unknowns.Withthe help of increament linearizing method,the model is reduced to5 governingequations with5 unknowns,i.e.,the three displacement components of solid phase,thepore water pressure and the pore gas pressure.7 material parameters are involved inthe model and all of them can be measured using soil tests.It is convenient to use themodel to engineering practice.The well known Biot’s theory is a special case of themodel.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain, water and gas. In this paper, the consolidation problem of unsaturated soil is investigated based on the theory of mixture. A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived. The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil. A mathematical model of consolidation of unsaturated soil is proposed, which consists of 25 partial differenfial equations with 25 unknowns. With the help of increament linearizing method, the model is reduced to 5 governing equations with 5 unknowns, i.e., the three displacement components of solid phase, the pore water pressure and the pore gas pressure. 7 material parameters are involved in the model and all of them can he measured using soil tests. It is convenient to use the model to engineering practice. The well known Biot’s theory is a special case of the model.     

Migration of salts in the unsaturated zone caused by heating

Heat-transfer phenomena as well as moisture movement in unsaturated soils due to thermal gradients, have been extensively studied during the last four decades. Less attention has been devoted to the transport and redistribution of solutes caused by heating.Solar radiation, radioactive waste repositories, underground energy storage, buried electric cables and steam pipes, disposal of waste heat from power plants are examples of heat sources in the soil.Soil-water properties, such as surface tension, viscosity, density, as well as the equilibrium composition of phases, depend on temperature. Hence, nonuniform heating of a soil partially saturated by saline water has an effect on such processes as water flow under capillary and gravitational forces, evaporation, condensation and diffusion of vapor and transport and precipitation of salts.A mathematical model is presented for the migration of salts in the vadoze zone in the soil under nonisothermal conditions, taking into account the above-mentioned phenomena. The physical assumptions underlying the model are briefly discussed.The study of a particular case shows that under certain conditions, a heat source may attract dissolved salts, and cause their precipitation in the hot area.     

填埋气体迁移气-热-力耦合动力学模型的研究

基于连续介质力学—势弹性力学原理，运用多场耦合理论建立了填理场中可压缩垃圾气体迁移耦合的动力学模型，并采用摄动法及积分变换法对该强非线性数学模型进行拟解析求解。通过算例对比分析，探讨了耦侵动力场中气压、温度和应力变化对可压缩气体迁移的影响，得出了垃圾气体迁移过程中的孔隙压力分布规律。结果表明，三场耦合作用与非耦合作用相对差别较大，耦合效应不能忽略。这为定量化研究垃圾气体在填埋场中的扩散状况以及污染气体的排放和收集、防止二次污染提供了可靠的理论依据。     

Analytical Solutions for Reactive Transport of Multiple Volatile Contaminants in the Vadose Zone

Groundwater contamination usually originates from surface contamination. Contaminants then move downward through the vadose zone and finally reach the groundwater table. To date, however, analytical solutions of multi-species reactive transport are limited to transport only in the saturated zone. The motivation of this work is to utilize analytical solutions, which were previously derived for single-phase transport, to describe the reactive transport of multiple volatile contaminants in the unsaturated zone. A mathematical model is derived for describing transport with phase partitioning of sequentially reactive species in the vadose zone with constant flow velocity. Linear reaction kinetics and linear equilibrium partitioning between vapor, liquid, and solid phases are assumed in this model.     

Effect of sorption hysteresis on the spatial distribution of contaminants in soils

A mathematical model of the combined transport of water and a dissolved contaminant in a peaty soil which takes hysteresis of the sorption and desorption processes into account is developed. The solvability of the initial and boundary value problems and the stability of the solutions are investigated. A series of problems characterizing the features of the contaminant distribution over peaty masses is solved numerically. A physical mechanism leading to the frequently observed effect of localization of the equilibrium sorbent distribution over the upper layer of soil is proposed. The effect of both the medium parameters and the regime of water and contaminant supply to the system is analyzed numerically.     

2D numerical simulation for simultaneous heat, water and gas migration in soil bed under different environmental conditions

A general mathematical model for investigating simultaneous heat, water and gas (air plus vapor) transfer in unsaturated porous soil under different environmental conditions is presented based on the volume-averaging method. Two-dimensional numerical simulation in steady state is conducted for obtaining accurate images of field characteristics in a confined soil bed, which might be useful to provide necessary information for agricultural applications. Various effects of environmental parameters, such as ambient temperature, relative humidity, radiative heat flux and wind speed, on transport processes in soil without plant roots are analyzed through the calculating results in the present paper. Received on 13 January 1998     

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.     

A hyperbolic mathematical modeling for describing the transition saturated/unsaturated in a rigid porous medium

This work proposes a mathematical model to study the filling up of an unsaturated porous medium by a liquid identifying the transition from unsaturated to saturated flow and allowing a small super saturation. As a consequence the problem remains hyperbolic even when saturation is reached. This important feature enables obtaining numerical solution for any initial value problem and allows employing Glimm’s scheme associated with an operator splitting technique for treating drag and viscous effects. A mixture theory approach is used to build the mechanical model, considering a mixture of three overlapping continuous constituents: a solid (porous medium), a liquid (Newtonian fluid) and a very low-density gas (to account for the mixture compressibility). The constitutive assumption proposed for the pressure gives rise to a continuous function of the fluid fraction. The complete solution of the Riemann problem associated with the system of conservation laws, as well as four examples, considering all the four possible connections, namely, 1-shock/2-shock, 1-rarefaction/2-rarefaction, 1-rarefaction/2-shock and 1-shock/2-rarefaction are presented.     

页岩基质解吸-扩散-渗流耦合实验及数学模型

采用川南地区龙马溪组页岩样品,设计了页岩基质解吸-扩散-渗流耦合物理模拟实验,揭示了页岩基质气体流动特征以及压力传播规律.推导了页岩气解吸-扩散-渗流耦合数学模型并且利用有限差分法对数学模型进行数值求解,与实验结果相比较表明该数学模型能够很好地描述气体在页岩基质中的流动规律.同时对页岩基质气体流动的影响因素进行了分析,认为页岩基质的渗透率、扩散系数、解吸附常数等因素均能影响页岩基质气体的流量和压力传播规律,在页岩气藏的开发过程中需要考虑这些参数的影响,该数学模型为页岩气井产能计算提供了更准确的计算方法.      

Electromagnetic Sounding of Oil and Gas Formations

A mathematical model is proposed that describes electrical conductivity variation in the near-well zone during drilling formations containing three immiscible phases: oil, gas, and a small amount of native salt water. It is assumed that borehole drilling is performed using a clay–water solution, the mass-exchange process between the moving mud filtrate and immovable native water is infinitely fast, and displacement of the gas phase occurs by piston flow. The redistribution of the immiscible phases is described by the conventional Buckley–Leverett equations. The electromagnetic response of the medium is interpreted using the earlier proposed method of probabilistic convolutions.     

A linearization technique for multi-species transport problems

We study a one-dimensional multi-species system of dispersive-advective contaminant transport equations coupled by nonlinear biological (kinetic reactions) and physical (adsorption) processes. To deal with the nonlinearities and the coupling, and to avoid additional computational costs, we propose a linearization technique based on first-order Taylor’s series expansions. A stabilized finite element in space, combined with an Euler implicit finite difference discretization in time, is used to approximate the dispersive-advective transport problem. Three computational tests are performed with different boundary conditions, retardation factors and kinetic parameters for a nonlinear reactive multi-species transport model. The proposed methodology is shown to be accurate and decrease computational costs in the numerical implementation of nonlinear reactive transport problems.     

3D contaminant migration model with consolidation dependent transport coefficients

Soil consolidation would induce variations of its transport coefficients such as hydraulic conductivity and diffusion coefficient. This paper presents a study of the influence of barrier consolidation on transport coefficients, and a 3D transport model based on mixture theory is proposed for describing the liners that involve circular defects in the geomembrane. The elastoplastic ALPHA model is revised by using the spatially mobilized plane (SMP) criterion for simulating the deformation of the soils. Then, the 3D model coupling the nonlinear consolidation and contaminant advection-diffusion is solved using the finite element software ABAQUS. The results show that the importance of reducing the defect size in the geomembrane and the liner porosity to control the contaminant concentration increase.