考虑非等温环境下污染物在黏土中的运移解析模型

利用广义积分变换法推导了非等温条件下污染物在压实黏土衬垫中的运移解析解。所提出的解析解考虑了分子扩散、对流、吸附和热扩散的耦合效应,并考虑了压实黏土的渗透系数、分布系数和有效扩散系数3个参数随温度的变化。通过与热扩散试验结果、已有的解析解和基于COMSOL软件的数值模型的对比,验证了所提出的解析解。利用经过验证的解析解,研究了非等温环境以及压实黏土的渗透系数、有效扩散系数和分布系数3个参数随温度的变化对甲苯在压实黏土衬垫系统中迁移的影响。结果表明,非等温环境以及压实黏土的渗透系数、有效扩散系数和分布系数随温度的变化均对甲苯在压实黏土衬垫中迁移有着显著的影响。不考虑非等温环境的影响将极大低估污染物的溢出量和污染物的击穿时间。既有解析解忽略压实黏土的渗透系数和有效扩散系数随温度的变化会极大低估甲苯的流出速率,而忽略压实黏土分布系数随温度的变化会极大高估甲苯击穿衬垫系统的时间和达到稳态的时间。所提出的解析解能够考虑热扩散作用,同时考虑了压实黏土的渗透系数、分布系数和有效扩散系数3个参数随温度的变化,较既有解析解更贴近工程实际,能够为压实黏土衬垫系统的设计和服役性能评价提供指导和借鉴。     

Diffusion and sorption experiments using a DKS permeameter

The analysis of contaminant transport through clay liner is a relevant aspect in the design of industrial, urban and mining waste disposal systems, since these areas must be designed and operated to prevent contaminating substances from reaching underground water systems in unacceptable concentrations. The design requires an estimate of the potential contaminant transport rate. However, before any attempt at quantification can be made, values for transport mechanism control parameters must be established. Clayey materials are frequently used as contaminant barriers. In these materials, which have low hydraulic conductivity, the main contaminant transport mechanism is molecular diffusion. Parameters controlling transport for these conditions are the diffusion coefficient and sorption parameters. These parameters depend on soil constituents and characteristics as well as on the chemical constitution of the contaminant. The great complexity of the factors involved makes it necessary to determine the parameters of each type of soil. This paper discusses an equipment called DKS permeameter (diffusion, convection, sorption), for the study of soil-contaminant transport mechanisms, designed at the Institute for Soil Mechanics of the Ruhr-University Bochum, and some results obtained from its use at COPPE/Federal University of Rio de Janeiro (UFRJ), Brazil. This equipment determines the effective diffusion coefficient and sorption parameter with a better reflection of field conditions. The soil under study is a mix of sodium–bentonite that has low hydraulic conductivity (k=10⁻⁹ cm/s) with adequate liner characteristics. The result indicated the relevance of determining sorption parameters for structured soils, since the sorption perceived from batch test results using pulverised soil represents maximum soil capacity. Designs based on this parameter would overestimate the attenuation capacity of the liner.     

Analytic solutions to the advective contaminant transport equation with non-linear sorption

This paper considers advective transport of a soluble contaminant through saturated soil with non-linear sorption of the contaminant onto a stationary porous media. The non-linear sorption isotherms considered in the transport analysis are the Langmuir and Freundlich sorption isotherms. A special case of the Freundlich sorption isotherm is the linear sorption isotherm, and it is shown that in this case transport through a homogeneous soil results in the initial concentration profile simply being translated in the direction of the groundwater flow. However, when the sorption isotherm is non-linear the initial concentration profile distorts as it is translated with the groundwater flow, leading to the development of concentration shock fronts and rarefactions. Analytic solutions to the non-linear first-order hyperbolic equations are developed for a number of contaminant transport problems of practical significance. It is shown that in the case of the Langmuir sorption isotherms, shock fronts develop at the leading edge of the concentration profile while for the Freundlich sorption isotherm shock fronts may develop at either the leading or trailing edge of the concentration profile. Copyright © 1999 John Wiley & Sons Ltd.     

Gas sorption and transport in coals: A poroelastic medium approach

In this paper, single-component gas sorption and transient diffusion processes are described within coal matrix exhibiting bimodal pore structure. The coal matrix is treated as a poroelastic medium manifesting swelling and shrinkage effects due to the sorption of gas under effective overburden stress. Gas transport is considered Fickian with molecular (bulk) and surface diffusion processes simultaneously taking place in the macro- and micropores of coal, respectively. The numerical formulation is intended to be explicit in nature to investigate the influences of sorption phenomena on the macropore volumes and on the overall gas transport for the cases of gas uptake by and release from coal.Results of the study show the presence of hysteresis during a sorption–desorption cycle of the gas. It is also found that the overall gas transport takes place at a rate significantly less than that in the macropores only. Thus the existence of a retardation effect in the overall gas transport is concluded. This retardation effect is primarily due to the micropore resistances, in particular gas adsorption, and is independent of the changes in the macropore volumes. It is shown that macroporosity of the coal matrix may change during gas transport due to combined effects of pressure and sorption-induced swelling or shrinkage of the coal. It is estimated that the macroporosity variation is non-uniform in space and time, as it is expected in reality, and typically taking values less than ± 10 percent of the initial porosity.     

Contaminant transport with non‐equilibrium processes in unsaturated soils and implicit characteristic Galerkin scheme

A non‐equilibrium sorption—advection—diffusion model to simulate miscible pollutant transport in saturated–unsaturated soils is presented. The governing phenomena modelled in the present simulation are: convection, molecular diffusion, mechanical dispersion, sorption, immobile water effect and degradation, including both physical and chemical non‐equilibrium processes. A finite element procedure, based on the characteristic Galerkin method with an implicit algorithm is developed to numerically solve the model equations. The implicit algorithm is formulated by means of a combination of both the precise and the traditional numerical integration procedures. The stability analysis of the algorithm shows that the unconditional stability of the present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results illustrate good performance of the present algorithm in stability and accuracy, and in simulating the effects of all the mentioned phenomena governing the contaminant transport and the concentration distribution. Copyright © 2000 John Wiley & Sons, Ltd.     

Interpretation of carbon dioxide diffusion behavior in coals

Storage of carbon dioxide in geological formations is for many countries one of the options to reduce greenhouse gas emissions and thus to satisfy the Kyoto agreements. The CO₂ storage in unminable coal seams has the advantage that it stores CO₂ emissions from industrial processes and can be used to enhance coalbed methane recovery (CO₂-ECBM). For this purpose, the storage capacity of coal is an important reservoir parameter. While the amount of CO₂ sorption data on various natural coals has increased in recent years, only few measurements have been performed to estimate the rate of CO₂ sorption under reservoir conditions. An understanding of gas transport is crucial for processes associated with CO₂ injection, storage and enhanced coalbed methane (ECBM) production.A volumetric experimental set-up has been used to determine the rate of sorption of carbon dioxide in coal particles at various pressures and various grain size fractions. The pressure history during each pressure step was measured. The measurements are interpreted in terms of temperature relaxation and transport/sorption processes within the coal particles. The characteristic times of sorption increase with increasing pressure. No clear dependence of the characteristic time with respect to the particle size was found. At low pressures (below 1 MPa) fast gas diffusion is the prevailing mechanism for sorption, whereas at higher pressures, the slow diffusion process controls the gas uptake by the coal.     

Understanding the effect of single-fracture heterogeneity from single-well injection-withdrawal (SWIW) tests

The single-well injection-withdrawal (SWIW) tracer test is a method used to estimate the tracer retardation properties of a fracture or fracture zone. The effects of single-fracture aperture heterogeneity on SWIW-test tracer breakthrough curves are examined by numerical modelling. The effects of the matrix diffusion and sorption are accounted for by using a particle tracking method through the addition of a time delay added to the advective transport time. For a given diffusion and sorption property (P _m) value and for a heterogeneous fracture, the peak concentration is larger compared to a homogeneous fracture. The cumulative breakthrough curve for a heterogeneous fracture is similar to that for a homogeneous fracture and a less sorptive/diffusive tracer. It is demonstrated that the fracture area that meets the flowing water, the specific flow-wetted surface (sFWS) of the fracture, can be determined by matching the observed breakthrough curve for a heterogeneous fracture to that for a homogeneous fracture with an equivalent property parameter. SWIW tests are also simulated with a regional pressure gradient present. The results point to the possibility of distinguishing the effect of the regional pressure gradient from that of diffusion through the use of multiple tracers with different P _m values.     

Numerical modeling of stress effects on solute transport in fractured rocks

The effects of stress/deformation on fluid flow and contaminant transport in fractured rocks is one of the major concerns for performance and safety assessments of many subsurface engineering problems, especially radioactive waste disposal and oil/gas reservoir fields. However, very little progress has been made to study this issue due to difficulties in both experiments and numerical modeling. The objective of this study is to systematically investigate the influence of stress on solute transport in fractured rocks for the first time, considering different stress and hydraulic pressure conditions. A hybrid approach combining discrete element method (DEM) for stress-flow simulations and a particle tracking algorithm is developed. The impact of matrix diffusion (diffusion of molecular size solutes in and out of the rock matrix, and sorption onto the surface of micropores in rock matrix) is also included. The numerical results show that stress not only significantly changes the solute residence time through the fracture networks, but also changes the solute travel paths. Matrix diffusion plays a dominant role in solute transport when the hydraulic gradient is small, which is often encountered in practice.     

Numerical Modeling and Spatial Moment Analysis of Solute Mobility and Spreading in a Coupled Fracture-Skin-Matrix System

This study deals with transport of solutes through a saturated sub-surface rock formation with well-defined horizontal parallel fractures. For this purpose, a simplified conceptual model consisting of a single fracture and its associated rock-matrix is considered in the presence of a fracture-skin in order to study the mobility and mixing of solutes along the fracture. In this paper, a coupled fracture-skin-matrix system is modeled numerically using finite difference method in a pseudo two-dimensional domain with a constant continuous source at fracture inlet. Flow and transport processes are considered parallel to the fracture axis, while the transport processes in fracture-skin as well as in rock-matrix are considered perpendicular to the fracture axis. Having obtained the concentration distribution along the fracture, method of spatial moments is employed to study the mobility and spreading of solutes. Sensitivity analyses have been done to understand the effect of various fracture-skin parameters like porosity, thickness, and diffusion coefficient. Further, the influence of non-linear sorption and radioactive decaying of solutes are carried out for different sorption intensities and decay constants. Results suggest that the presence of fracture-skin significantly influences the mobility and spreading of solutes along the fracture in comparison with a coupled fracture-matrix system without fracture-skin.     

The kinetic studies of the cobalt ion removal from aqueous solutions by dolomite-based sorbent

The kinetics of Co(II) ions adsorption on thermally activated dolomite was studied with respect to the calcination temperature of natural dolomite. The sorption of Co(II) onto all samples is reasonably fast: The first 30–35 min accounts for approximately 70–80 % of Co(II) removal from feed solutions. In order to select the main rate-determining step in the overall uptake mechanism, a series of experiments were performed and data obtained were interpreted in terms of film diffusion control, intraparticle diffusion, pseudo-first-order and pseudo-second-order models. From the modeling of kinetic data, it can be concluded that adsorption of Co(II) ions from aqueous solution by heat-treated dolomite is a complex phenomenon and occurs in a mixed diffusion mode—the kinetic data are well described by the pseudo-second-order equation. The possible multistage sorption mechanism involving film diffusion and intraparticle diffusion control steps as well as chemical interaction between Co(II) ions and calcined dolomite is proposed.     

Evaluation of retention properties of a semi-synthetic fractured block from modelling at performance assessment time scales (Äspö Hard Rock Laboratory, Sweden)

Modelling of radionuclide transport in fractured media is a primary task for safety evaluation of a deep nuclear waste repository. A performance assessment (PA) model has been derived from site characterization data with the aim of improving confidence for quantifying transport of sorbing radionuclides at a safety time scale of 10⁶ y. The study was conducted on a 200?×?200?×?200 m semi-synthetic fractured block, providing a realistic system derived from the Äspö Hard Rock Laboratory (Sweden) dataset. The block includes 5,632 fractures ranging from 0.5 to 100 m in length and a heterogeneous matrix structure (fracture coating, gouge, mylonite, altered and non-altered diorite). The PA model integrates steady-state flow conditions and transport of released radionuclides during the safety time scale. An original simulation method was developed involving Eulerian flow and transport within fracture planes with a mixed hybrid finite element scheme and a semi-analytical source term to account for heterogeneous matrix diffusion. Total mass flux of radionuclides (conservative to strongly sorbing) was computed. A method to simplify the system was demonstrated, leading to a major path of 12 fractures. This is mainly due to the low connectivity of the fracture network. Matrix diffusion and sorption proved to have major impact on block retention properties for PA conditions.     

Fate and transport of zinc in a sand tank model: monitoring of 2-D plume using TDR method

Sorption is a well-known phenomenon that may cause the retardation effect of zinc in the subsurface environment. In this study, the governing process for zinc sorption during transport was investigated by conducting 2-D plume tests in a laboratory scale sand tank model using the time domain reflectometry (TDR) method. Tracer solutions of NaNO₃ and ZnSO₄ were applied at a constant flow rate as a pulse type to capture the plumes of both solutes based on TDR-measured resistance. It was revealed that the observed zinc sulfate plume showed no retardation relative to sodium nitrate with a retardation factor of R ≈ 1. Instead of retardation, a prominent reduction of zinc sulfate mass occurred during transport through the tank model due to the irreversible sorption as well as longitudinal dispersion. This indicates that the controlling factor for the sorption process of zinc sulfate in the sand tank model is kinetic rather than equilibrium. These hydrogeological parameters would provide valuable information on the prediction of the fate of zinc in sandy aquifer materials.     

Investigations on Diffusion Characteristics of Granite and Chalk Rock Mass

Contaminant transport through fractured rock mass is predominated by diffusion. This is due to the continuous interaction of the mobile water present in the fracture network and relatively immobile pore water, which is adsorbed on the surface and in the rock matrix itself. Even though the advective flow through the fracture network is high, besides sorption of rock mass, the diffusive exchange into the rock mass leads to significant retardation of contaminant transport. Hence, for describing contaminant transport in fractured rock mass, more precisely, the effect of retardation attributed to the matrix diffusion must be taken in account. With this in view, a methodology, which can be employed for determination of the diffusion characteristics of the rock mass, has been developed and its details are presented in this paper. Validation of the methodology has been demonstrated with the help of Archie’s law.     

Diffusion of uranium in compacted sodium bentonite

Sorption and diffusion of uranium in sodium bentonite MX-80 were measured in aerobic conditions. The batch method was used for the sorption measurements and the steady state method for the diffusion measurements. Clear sorption was noticed only when high uranium concentrations were used so that the pH of the solution decreased.

The diffusivities of uranium were strongly dependent on the compaction of bentonite so that in the highly compacted samples the diffusion was very restricted. Uranium shows both features of ion-exclusion and sorption. Further studies are, however, needed to explain the diffusion mechanisms of uranium.     

http://www.sciencedirect.com/science/article/pii/S1674987112000369

A numerical model is developed for describing the transport of virus in a fracture-matrix coupled system with fracture-skin.An advective dispersive virus transport equation,including firstorder sorption and inactivation constant is used for simulating the movement of viruses.Implicit finite-difference numerical technique is used to solve the coupled non-linear governing equations for the triple continuum model consisting of fracture,fracture-skin and the rock-matrix.A varying grid is adopted at the fracture and fracture-skin interface to capture the mass transfer.Sensitivity analysis was performed to investigate the effect of various properties of the fracture-skin as well as viruses on the virus concentration in the fractured formation with fracture-skin.Simulation results suggest that the virus concentration in the fracture decreases with increment in the fracture-skin porosity,fracture-skin diffusion coefficient,mass transfer coefficient,inactivation constant and sorption distribution coefficient, and with reduction in the fracture aperture.     

EXPERIMENTAL DATA ON SORPTION OF COPPER BY VARIOUS MINERALS AND ORGANIC SORBING AGENTS

Experimental data on copper sorption by organic and mineral sorbing agents have shown that sorption can take place from very dilute solutions. The degree of sorption depends on the total amount of dissolved copper in solution, the velocity of the circulating solution, on the duration of contact between the sorbent and fresh solutions, and on the degree of diffusion of the solution within the sorbent. Organic matter, namely pine loam, peat, lignite, and humic acid, absorbs copper from very dilute solutions (from 2x10^-4 to 2x10^-5 grams per liter copper concentrations, 2.5 to 4.5 percent); other sorbents, namely; sand, kaolin, feldspar, and quartz, absorb one-tenth as much as the organic sorbents. Desorption is very slight in organic material; it is almost complete in mineral sorbents. It is believed that sorption plays a very significant part in the formation of sedimentary copper deposits, particularly in the copper sandstones of the Urals.     

Analytical solutions of tracer transport in fractured rock associated with precipitation-dissolution reactions

Precipitation-dissolution reactions are important for a number of applications such as isotopic tracer transport in the subsurface. Analytical solutions have been developed for tracer transport in both single-fracture and multiple-fracture systems associated with these reactions under transient and steady-state transport conditions. These solutions also take into account advective transport in fractures and molecular diffusion in the rock matrix. For studying distributions of disturbed tracer concentration (the difference between actual concentration and its equilibrium value), effects of precipitation-dissolution reactions are mathematically equivalent to a “decay” process with a decay constant proportional to the corresponding bulk reaction rate. This important feature significantly simplifies the derivation procedure by taking advantage of the existence of analytical solutions for tracer transport associated with radioactive decay in fractured rock. It is also useful for interpreting tracer breakthrough curves, because the impact of a decay process is relatively easy to analyze. Several illustrative examples are presented, which show that the results are sensitive to fracture spacing, matrix diffusion coefficient (fracture surface area), and bulk reaction rate (or “decay” constant), indicating that the relevant flow and transport parameters may be estimated by analyzing tracer signals.     

一种用于突发性场地污染模拟的解析模型

为了及时有效地应对各种突发性环境污染事故,有必要开发一种简单实用、适于各类型污染物的场地污染数学模型。通过污染事故发生后污染物在包气带、饱和带迁移转化的概化,建立了污染物运移的自由入渗模型以及降雨入渗模型并给出各自相应的解析解。无降雨时,考虑污染物在重力作用下随包气带向下渗透的作用,建立一维垂直入渗模型。有降雨时,考虑污染场地（包气带）中污染物迁移和转化的对流作用、扩散作用及挥发、生物降解、吸附、根系吸收等作用,建立包气带剖面二维溶质运移模型和饱和带平面二维溶质运移数学模型。建模过程中,假定降雨量的平均分布及土壤质地、水力参数以及有机物成分、种类均相同,同时假定污染物与多孔介质间的作用为线性吸附,植物根系对污染物的吸附遵循一级动力学。基于模型的解析解,实现案例的模拟计算。模拟结果表明：该模型具有适用范围广、模拟高效快捷等优点,能够较准确预测污染发生后污染物在土壤中的动向、到达饱和带的时间以及饱和带中污染物的迁移情况。     

A particle tracking transport method for the simulation of resident and flux-averaged concentration of solute plumes in groundwater models

A new numerical technique called the convolution-based particle tracking (CBPT) method is developed to simulate resident or flux-averaged solute concentrations in groundwater models. The method is valid for steady-state flow and linear transport processes such as sorption with a linear sorption isotherm and first-order decay. The CBPT method uses particle tracking to take advantage of the ability of particle-based approaches to maintain sharp fronts for advection-dominated transport problems common in groundwater modeling and because of the flexibility of the random walk method to simulate a wide range of possible forms of the dispersion tensor. Furthermore, the algorithm for carrying out the convolution and superposition calculation from particle tracking results is very efficient. We show that from a single particle tracking run, source term variability, sorption, and decay can all be simulated rapidly without rerunning the underlying transport model unless the flow field or dispersion parameters are changed. A series of verification simulations are presented to demonstrate the accuracy and efficiency of the CBPT method compared to more conventional particle tracking approaches.