Formation factor logging by electrical methods. Comparison of formation factor logs obtained in situ and in the laboratory

In this paper, a new in situ method for obtaining the formation factor, which is essential for the matrix diffusion, is described and tested in intrusive igneous rock. The method is based on electrical resistivity measurements in rock where the pore water and rock resistivities are essential parameters. The method is based on electromigration instead of diffusion as in traditional diffusion experiments. In previous works, quantitative formation factors of rock have been obtained by electrical methods in the laboratory. Here, a similar approach is used in situ. An in situ logging campaign was performed by SKB during 2000 in the 1700-m-deep borehole KLX02 in Laxemar, Sweden. The rock resistivity was measured with the slimhole Dual Laterolog from Antares. The groundwater resistivity was measured with the Difference Flow Meter from Posiva. A formation factor log was obtained with the maximum vertical resolution of 10 cm. In order to validate the log, 100 rock samples were taken from the bore core, and a formation factor log was obtained by using electrical methods in the laboratory. Both direct current (DC) and alternating current (AC) were used. The measurements on the core confirmed that the in situ log was quantitative, but with a possible systematic error. The in situ formation factors were on average about 1/3 to 1/5 of the laboratory formation factors, depending on depth.     

The effects of scale and spatial heterogeneities on diffusion in volcanic breccias and basalts: Amchitka Island, Alaska

Knowledge of the factors that influence the diffusion of contaminants, such as the diffusivity and the connected porosity, is crucial to modeling the long-term fate and transport of contaminants in subsurface systems with small or negligible advective flow, such as in fractured crystalline rock. Fractured rock is naturally heterogeneous, and hence, understanding the diffusivity of a molecule through this material (or the formation factor of the medium) becomes a complex problem, with critical concerns about the scale of laboratory measurements and about the spatial variability of these measurements relative to the scale needed for fate and transport modeling. This study employed both electrical and tracer-based laboratory methods to investigate the effects of scale and pore system connectivity on the diffusivity for volcanic matrix rock derived from the study site, a former underground nuclear test site at Amchitka Island, Alaska. The results of these investigations indicate a relatively well-connected pore system with scale effects generally limited to approximately 6 cm lengths and well-correlated to observed heterogeneous features. An important conclusion resulting from this study, however, is that there is a potential for the estimated diffusivity to be misrepresented by an order of magnitude if multiple samples or longer sample lengths are not used. Given the relatively large number of measurements resulting from these investigations, an analysis of the probability density function (PDF) of the diffusivity was possible. The PDF of the diffusivity was shown to generally follow a normal distribution for individual geologic layers. However, when all of the geologic layers are considered together, the distribution of the subsurface as a whole was shown to follow a lognormal distribution due to the order of magnitude differences amongst the layers. An understanding of these distributions is essential for future stochastic modeling efforts.     

A laboratory experiment for determining both the hydraulic and diffusive properties and the initial pore-water composition of an argillaceous rock sample: a test with the Opalinus clay (Mont Terri, Switzerland)

Argillaceous formations are thought to be suitable natural barriers to the release of radionuclides from a radioactive waste repository. However, the safety assessment of a waste repository hosted by an argillaceous rock requires knowledge of several properties of the host rock such as the hydraulic conductivity, diffusion properties and the pore water composition. This paper presents an experimental design that allows the determination of these three types of parameters on the same cylindrical rock sample. The reliability of this method was evaluated using a core sample from a well-investigated indurated argillaceous formation, the Opalinus Clay from the Mont Terri Underground Research Laboratory (URL) (Switzerland). In this test, deuterium- and oxygen-18-depleted water, bromide and caesium were injected as tracer pulses in a reservoir drilled in the centre of a cylindrical core sample. The evolution of these tracers was monitored by means of samplers included in a circulation circuit for a period of 204 days. Then, a hydraulic test (pulse-test type) was performed. Finally, the core sample was dismantled and analysed to determine tracer profiles. Diffusion parameters determined for the four tracers are consistent with those previously obtained from laboratory through-diffusion and in-situ diffusion experiments. The reconstructed initial pore-water composition (chloride and water stable-isotope concentrations) was also consistent with those previously reported. In addition, the hydraulic test led to an estimate of hydraulic conductivity in good agreement with that obtained from in-situ tests.     

Through-electromigration: a new method of investigating pore connectivity and obtaining formation factors

The retardation of radionuclides and other contaminants in fractured crystalline rock is strongly associated with the diffusive properties of the rock matrix. At present, the scientific community is divided concerning the question of long-range pore connectivity in intrusive igneous rock. This paper presents a fast new method, called the through-electromigration method, of obtaining formation factors and investigating pore connectivity. The method involves the migration of an ionic tracer through a rock sample with an electrical potential gradient as the main driving force. The method is analogous to the through-diffusion method but the experimental time is reduced by orders of magnitude. This enables investigations of pore connectivity, as measurements can be made on longer samples. In a preliminary investigation, the new method is compared to the traditional through-diffusion method as well as to rock resistivity methods. The diffusive properties of nine granitic rock samples from Laxemar in Sweden, ranging from 15 to 121 mm in length, have been investigated and the results are compared.     

Prediction of some in situ tracer tests with sorbing tracers using independent data

Some recent converging tracer tests with sorbing tracers at the Asp? Hard Rock Laboratory in Sweden, the TRUE tests, have been predicted using only laboratory data and hydraulic data from borehole measurements. No model parameters were adjusted to obtain a better fit with the experiments. The independent data were fracture frequency and transmissivity data obtained in the field and laboratory data on sorption and matrix diffusion. Transmissivity measurements in five boreholes in the rock volume containing the region surrounding the injection and collection points show that there is a high frequency of water conducting fractures. Of 162 packed off sections with 0.5 m packer distances, 112 were found to have a transmissivity above the detection limit. The specific flow-wetted surface (FWS) of the rock mass could be estimated from these data. The transmissivities were found to be reasonably well described by a lognormal distribution. Laboratory data on diffusion and sorption properties together with the hydraulic data were used to "predict" the residence time distribution (RTD) of the sorbing tracers. The results were compared with the experimental breakthrough curves. In these experiments, the water residence time is very small compared to the residence time of the sorbing tracers due to their diffusion and sorption within the rock matrix. We thus could neglect the influence of the water residence time in our predictions. Therefore, no information on water residence times or on "dispersion" was needed. The dispersion of the sorbing tracers is caused by the different sorbing tracer residence times in different pathways. The sorbing tracer residence time is determined by the ratio of flowrate to the flow-wetted surface in the different pathways and not by the water residence time. Assuming a three-dimensional flow pattern and using the observed fracture frequency and flowrate distribution, breakthrough curves for three strongly sorbing tracers were predicted. Only the laboratory data, the transmissivity measurements and the pumping flowrate were used in the predictions. No information on the water residence time as obtained by the nonsorbing tracers was used. The predictions were surprisingly accurate.     

Determination of the flow-wetted surface in fractured media

Diffusion and sorption in the rock matrix are important retardation mechanisms for radionuclide transport in fractured media. For the conditions existing in a deep repository in crystalline rock, interaction with the rock matrix is controlled by the water flowrate in the fractures and the surface area in contact with the flowing water (the so-called "flow-wetted surface" (FWS)). The flow-wetted surface may be determined from the frequency of open fractures intersecting a borehole. The choice of packer distance used in these hydraulic measurements is crucial, however, since several open fractures may be found in one packer interval. The use of a packer distance that is too large may result in a considerable underestimation of the flow-wetted surface. This is especially important in zones with a high frequency of open fractures (fracture zones) where a small packer distance is a fundamental requirement. A large volume of hydraulic data has been compiled in Sweden from measurements using quite small packer distances. Over the last decade, the most common packer distance used for the hydraulic tests has been 3 m, although some new measurements using a shorter packer distance have also been performed. In several cases, the resolution of these measurements has been less than 0.5 m. All these data have been analysed in detail. From these data, the flow-wetted surface has been calculated and compared with the flow-wetted surface estimated in earlier studies. The results show the importance of using a small packer distance for carrying out borehole transmissivity measurements.     

A model of oscillatory transport in granular soils, with application to barometric pumping and earth tides

A simple algebraic model is proposed to estimate the transport of a volatile or soluble chemical caused by oscillatory flow of fluid in a porous medium. The model is applied to the barometric pumping of vapors in the vadose zone, and to the transport of dissolved species by earth tides in an aquifer. In the model, the fluid moves sinusoidally with time in the porosity of the soil. The chemical concentration in the mobile fluid is considered to equilibrate with the concentration in the surrounding matrix according to a characteristic time governed by diffusion, sorption, or other rate processes. The model provides a closed form solution, to which barometric pressure data are applied in an example of pore gas motion in the vadose zone. The model predicts that the additional diffusivity due barometric pumping in an unfractured vadose zone would be comparable to the diffusivity in stagnant pore gas if the equilibration time is 1 day or longer. Water motion due to the M2 lunar tide is examined as an example of oscillatory transport in an aquifer. It is shown that the tidal motion of the water in an aquifer might significantly increase the vertical diffusivity of dissolved species when compared to diffusion in an absolutely stagnant aquifer, but the hydrodynamic dispersivity due to tidal motion or gravitational flow would probably exceed the diffusivity due to oscillatory advection.     

Characterisation of HTO diffusion properties by an in situ tracer experiment in Opalinus clay at Mont Terri

A long-term single borehole diffusion experiment using tritiated water as tracer was carried out in Opalinus clay, an argillaceous rock formation that is accessible at the Mont Terri Underground Research Laboratory, situated in the Swiss Jura. The tracer was diluted in reconstituted formation water and introduced into a packed-off section of a borehole located in saturated rock. Pressure in this interval was maintained equal to the pore pressure of the surrounding rock in order to prevent any hydraulic gradient around the borehole and to avoid advective transport processes. The evolution of the tracer concentration in the injection system was monitored over time. After 1 year of diffusion, the claystone surrounding the interval was retrieved by overcoring the whole borehole and packer system, and by an adjacent oblique borehole. Compressed air was used as drilling fluid to reduce rock disturbances. The recovered overcore was sampled along profiles perpendicular to the borehole wall with a view to determining the tracer-concentration profiles in the rock. To avoid further evaporation of tritiated water, subsamples were immediately transferred into polyethylene bottles and disaggregated by adding a known amount of tracer-free water. Fifteen profiles were determined and showed a decreasing tracer concentration with distance into the rock. The pore-water contents were constant along those profiles, confirming that only very little water was lost during overcoring operations. The evolution of tritium-tracer concentration in the injection system over time and in situ profiles were interpreted with a 3-D numerical simulation of the experiment. That allowed for the identification of the transport parameters (orthotropic diffusion tensor and porosity) by minimising the relative quadratic error between the experimental and simulated data. The fitting is good and the results are consistent with data obtained on drill-core samples. The result of tritiated water is discussed regarding (1) the potential effect of mechanical and/or chemical disturbances around the injection borehole and (2) the specific behaviour of tritiated water.     

In situ diffusion experiment in granite: phase I

A program of in situ experiments, supported by laboratory studies, was initiated to study diffusion in sparsely fractured rock (SFR), with a goal of developing an understanding of diffusion processes within intact crystalline rock. Phase I of the in situ diffusion experiment was started in 1996, with the purpose of developing a methodology for estimating diffusion parameter values. Four in situ diffusion experiments, using a conservative iodide tracer, were performed in highly stressed SFR at a depth of 450 m in the Underground Research Laboratory (URL). The experiments, performed over a 2 year period, yielded rock permeability estimates of 2 x 10(-21) m(2) and effective diffusion coefficients varying from 2.1 x 10(-14) to 1.9 x 10(-13) m(2)/s, which were estimated using the MOTIF code. The in situ diffusion profiles reveal a characteristic "dog leg" pattern, with iodide concentrations decreasing rapidly within a centimeter of the open borehole wall. It is hypothesized that this is an artifact of local stress redistribution and creation of a zone of increased constrictivity close to the borehole wall. A comparison of estimated in situ and laboratory diffusivities and permeabilities provides evidence that the physical properties of rock samples removed from high-stress regimes change. As a result of the lessons learnt during Phase I, a Phase II in situ program has been initiated to improve our general understanding of diffusion in SFR.     

Obtaining the porewater composition of a clay rock by modeling the in- and out-diffusion of anions and cations from an in-situ experiment

A borehole in the Callovo–Oxfordian clay rock in ANDRA's underground research facility was sampled during 1 year and chemically analyzed. Diffusion between porewater and the borehole solution resulted in concentration changes which were modeled with PHREEQC's multicomponent diffusion module. In the model, the clay rock's pore space is divided in free porewater (electrically neutral) and diffuse double layer water (devoid of anions). Diffusion is calculated separately for the two domains, and individually for all the solute species while a zero-charge flux is maintained. We explain how the finite difference formulas for radial diffusion can be translated into mixing factors for solutions. Operator splitting is used to calculate advective flow and chemical reactions such as ion exchange and calcite dissolution and precipitation. The ion exchange reaction is formulated in the form of surface complexation, which allows distributing charge over the fixed sites and the diffuse double layer. The charge distribution affects pH when calcite dissolves, and modeling of the experimental data shows that about 7% of the cation exchange capacity resides in the diffuse double layer. The model calculates the observed concentration changes very well and provides an estimate of the pristine porewater composition in the clay rock.     

In situ anion diffusion experiments using radiotracers

Diffusion experiments in compacted bentonite have been carried out in situ using the borehole laboratory CHEMLAB. The "ordinary" anion iodide and the redox-sensitive pertechnetate ion have been investigated. In spite of strongly reducing groundwater conditions, technetium was found to diffuse mostly unreduced as TcO4-, although in some spots in the compacted clay, the activity was significantly higher, which may be explained by reduction of some TcO4- by iron-containing minerals in the bentonite. The measured concentration profiles in the clay cannot be accommodated by assuming one single diffusion process. The experimental data are modeled assuming two diffusion paths, intralamellar diffusion and diffusion in external water. The apparent diffusivity for the intralamellar diffusion was found to be 8.6 x 10(-11) m2 s(-1) for iodide with a capacity factor of 0.1, while the apparent diffusivity for the diffusion in external water was found to be 5 x 10(-14) m2 s(-1) with alpha=2.26. The corresponding values for Tc were found to be Da= 6 x 10(-11) m2 s(-1), alpha=0.1 and Da= 1 x 10(-13) m2 s(-1), alpha=0.46, respectively. The diffusion constants and capacity factors obtained in this study are in accordance with data from laboratory experiments.     

Modeling the Reduction of Vapor Phase Emissions from Surface Soils Due to Soil Matrix Effects: Porosity/Tortuosity Concepts

ABSTRACT

A major route for transport of volatile organic compounds within porous media is vapor phase diffusion. The diffusion rate through a porous medium is less than that through free-air due to the decreased cross-sectional area available for gas movement and the increased path length due to pore tortuosity. Numerous empirical expressions have been published that relate the diffusion coefficient in porous media to the diffusion coefficient in free-air (unobstructed gas phase). Published measurements of relative diffusivity and air-filled porosity were combined into a database. Empirical expressions available in the literature, including the popular Millington-Quirk equation, were evaluated along with a fourth-degree polynomial expression developed by the authors to determine the best type of equation to predict relative diffusivity as a function of air-filled porosity over the domain of values for porosity ranging from 0.071 to 1 for different types of materials. Mean square deviations were used as the statistical test to compare equations. The polynomial expression developed in this project produced a significantly different effective diffusion coefficient (1.3 x 10^-6 m²/sec) compared to values of 9.2 x 10^-6 m²/sec and 3.1 x 10^-6 m²/ sec predicted by forms of the Millington-Quirk equation for a specific case.     

Interpretation of injection-withdrawal tracer experiments conducted between two wells in a large single fracture

Tracer experiments conducted using a flow field established by injecting water into one borehole and withdrawing water from another are often used to establish connections and investigate dispersion in fractured rock. As a result of uncertainty in the uniqueness of existing models used for interpretation, this method has not been widely used to investigate more general transport processes including matrix diffusion or advective solute exchange between mobile and immobile zones of fluid. To explore the utility of the injection-withdrawal method as a general investigative tool and with the intent to resolve the transport processes in a discrete fracture, two tracer experiments were conducted using the injection-withdrawal configuration. The experiments were conducted in a fracture which has a large aperture (>500 microm) and horizontally pervades a dolostone formation. One experiment was conducted in the direction of the hydraulic gradient and the other in the direction opposite to the natural gradient. Two tracers having significantly different values of the free-water diffusion coefficient were used. To interpret the experiments, a hybrid numerical-analytical model was developed which accounts for the arcuate shape of the flow field, advection-dispersion in the fracture, diffusion into the matrix adjacent to the fracture, and the presence of natural flow in the fracture. The model was verified by comparison to a fully analytical solution and to a well-known finite-element model. Interpretation of the tracer experiments showed that when only one tracer, advection-dispersion, and matrix diffusion are considered, non-unique results were obtained. However, by using multiple tracers and by accounting for the presence of natural flow in the fracture, unique interpretations were obtained in which a single value of matrix porosity was estimated from the results of both experiments. The estimate of porosity agrees well with independent measurements of porosity obtained from core samples. This suggests that: (i) the injection-withdrawal method is a viable tool for the investigation of general transport processes provided all relevant experimental conditions are considered and multiple conservative tracers are used; and (ii) for the conditions of the experiments conducted in this study, the dominant mechanism for exchange of solute between the fracture and surrounding medium is matrix diffusion.     

The effect of a biofilm on solute diffusion in fractured porous media

At sites in fractured rock where contamination has been exposed to the rock matrix for extended periods of time, the amount of contaminant mass residing in the matrix can be considerable. Even though it may be possible to diminish concentrations by the advection of clean water through the fracture features, back diffusion from mass held in the matrix will lead to a continuing source of contamination. In such an event, the development of a biofilm (a thin film of microbial mass) on the wall of the fractures may act to limit or prevent the back diffusion process. The objective of this preliminary study is to explore the influence imparted by the presence of a biofilm on the process of matrix diffusion. The investigation was conducted using radial diffusion cells constructed from rock core in which biofilm growth was stimulated in a central reservoir. Once biofilms were developed, forward diffusion experiments were conducted in which a conservative solute migrated from the central reservoir into the intact rock sample. Diffusion experiments were performed in a total of 11 diffusion cell pairs where biofilm growth was stimulated in one member of the pair and inhibited in the other. The effect of the presence of a biofilm on tracer diffusion was determined by comparison of the diffusion curves produced by each cell pair. A semi-analytical model that accounts for the presence of a biofilm was used to investigate the effect of the biofilm on mass transfer due to changes in the effective porosity, effective diffusion coefficient, and the depth of penetration of the biofilm into the intact rock. The results show that the biofilm acted to plug the rock matrix, rather than forming a discrete layer on the reservoir surface. The reduction in effective porosity due to the biofilm ranged from 6% to 52% with the majority of the samples in the 30% to 50% range. Based on the present results, with more efficient biofilm stimulation, it is reasonable to assume that a more complete plugging of the microcrack porosity might be possible, leaving a much thicker and efficient barrier than could be achieved via a surface biofilm.     

Modeling tracer diffusion in fractured and unfractured, unsaturated, porous media

A proposed tracer diffusion test for the Exploratory Shaft Facility at Yucca Mountain, NV, is modeled. For the proposed test, a solution containing conservative tracers will be introduced into a borehole in the geologic medium of interest. The tracers will diffuse and advect from the saturated source region into the unsaturated matrix in the surrounding tuff. After some time, the borehole is to be overcored, and tracer concentrations in the fluid will be measured in the core as a function of distance from emplacement. The data will be used to evaluate diffusive behavior and to derive effective diffusion coefficients for the tracers in the specific tuff. Numerical simulations are used to study the effects of effective diffusion coefficient, porosity, saturation, and fracturing on tracer transport. Results are reported for numerical simulations of tests in the Topopah Spring Member and the Tuff of Calico Hills, which have significantly different porosities and saturations. The simulations make the following predictions: The spread of tracer during the test will be sensitive to the effective diffusion coefficient of the tracer. Tracer will diffuse farther in the Topopah Spring Member than in the Tuff of Calico Hills because of the former's lower porosity and saturation. Tracer transport by advection into the Topopah Spring Member will be greater than that into the Tuff of Calico Hills because of capillary effects. While advection will be a significant mechanism for tracer penetration into the Topopah Spring tuff, it will be less significant for tracer penetration into the Calico Hills tuff. The proximity of a single vertical fracture to the source region determines its effects on tracer transport, especially if the fracture diverts fluid flowing from the source region into the matrix.     

Influence of the mode of matrix porosity determination on matrix diffusion calculations

The theoretical basis for matrix diffusion in fractured rocks and the methodology for the determination of diffusion coefficients in the laboratory are well established. One significant problem, however, remains in that it is difficult to quantify the degree of sample disturbance affecting the geometrical, geophysical and hydraulic properties of the rock matrix. A new technique, with in situ rock impregnation with resin, for examining the diffusion-accessible rock matrix has been developed and successfully adopted to the rock matrix behind a water-conducting fracture in host crystalline rocks at Nagra's Grimsel Test Site in Switzerland and JNC's Kamaishi In Situ Test Site in Japan. In line with the results of a large number of natural analogue and laboratory studies, the existence of an in situ interconnected pore network was substantiated. Matrix porosities determined on the laboratory samples from both the sites are 1.5-3 times higher than in situ values, irrespective of the technique applied. On the Grimsel granodiorite matrix, matrix porosity existing in situ and artefacts of stress release and physical disturbance, induced by sampling and sample preparation, were clearly distinguished, allowing in situ porosity to be quantified. Laboratory work with conventional techniques tends to overestimate the porosity of the rock matrix, hence leading to an overestimation of in situ matrix diffusion. The implications of these differences to a repository performance assessment are assessed with a couple of examples from existing assessments, and recommendations for future approaches to the examination of in situ matrix porosity are made.     

Field-scale effective matrix diffusion coefficient for fractured rock: results from literature survey

Matrix diffusion is an important mechanism for solute transport in fractured rock. We recently conducted a literature survey on the effective matrix diffusion coefficient, D_m^e, a key parameter for describing matrix diffusion processes at the field scale. Forty field tracer tests at 15 fractured geologic sites were surveyed and selected for the study, based on data availability and quality. Field-scale D_m^e values were calculated, either directly using data reported in the literature, or by reanalyzing the corresponding field tracer tests. The reanalysis was conducted for the selected tracer tests using analytic or semi-analytic solutions for tracer transport in linear, radial, or interwell flow fields. Surveyed data show that the scale factor of the effective matrix diffusion coefficient (defined as the ratio of D_m^e to the lab-scale matrix diffusion coefficient, D_m, of the same tracer) is generally larger than one, indicating that the effective matrix diffusion coefficient in the field is comparatively larger than the matrix diffusion coefficient at the rock-core scale. This larger value can be attributed to the many mass-transfer processes at different scales in naturally heterogeneous, fractured rock systems.Furthermore, we observed a moderate, on average trend toward systematic increase in the scale factor with observation scale. This trend suggests that the effective matrix diffusion coefficient is likely to be statistically scale-dependent. The scale-factor value ranges from 0.5 to 884 for observation scales from 5 to 2000 m. At a given scale, the scale factor varies by two orders of magnitude, reflecting the influence of differing degrees of fractured rock heterogeneity at different geologic sites. In addition, the surveyed data indicate that field-scale longitudinal dispersivity generally increases with observation scale, which is consistent with previous studies. The scale-dependent field-scale matrix diffusion coefficient (and dispersivity) may have significant implications for assessing long-term, large-scale radionuclide and contaminant transport events in fractured rock, both for nuclear waste disposal and contaminant remediation.     

Modelling radionuclide transport for time varying flow in a channel network

Water flowrates and flow directions may change over time in the subsurface for a number of reasons. In fractured rocks flow takes place in channels within fractures. Solutes are carried by the advective flow. In addition, solutes may diffuse in and out of stagnant waters in the rock matrix and other stagnant water regions. Sorbing species may sorb on fracture surfaces and on the micropore surfaces in the rock matrix. We present a method by which solute particles can be traced in flowing water undergoing changes in flowrate and direction in a complex channel network where the solutes can also interact with the rock by diffusion in the rock matrix. The novelty of this paper is handling of diffusion in the rock matrix under transient flow conditions. The diffusive processes are stochastic and it is not possible to follow a particle deterministically. The method therefore utilises the properties of a probability distribution function for a tracer moving in a fracture where matrix diffusion is active. The method is incorporated in a three dimensional channel network model. Particle tracking is used to trace out a multitude of flowpaths, each of which consists of a large number of channels within fractures. Along each channel the aperture and velocity as well as the matrix sorption properties can vary. An efficient method is presented whereby a particle can be followed along the variable property flowpath. For stationary flow conditions and a network of channels with advective flow and matrix diffusion, a simple analytical solution for the residence time distribution along each pathway can be used. Only two parameter groups need to be integrated along each path. For transient flow conditions, a time stepping procedure that incorporates a stochastic Monte-Carlo like method to follow the particles along the paths when flow conditions change is used. The method is fast and an example is used for illustrative purposes. It is exemplified by a case where land rises due to glacial rebound. It is shown that the effects of changing flowrates and directions can be considerable and that the diffusive migration in the matrix can have a dominating effect on the results.     

Fixed bed adsorption of acid dyes onto activated carbon

The context of the study here is the adsorption of acid dyes from wastewater arising from a nylon carpet printing plant which currently receives no treatment. Since nylon is a particularly difficult fibre to dye, acid dyes are required for successful coloration. However, their presence, in high concentrations, in aqueous effluent arising from the plant can create major problems with respect to disposal. A treatment method based on adsorption onto granular activated carbon (GAC F400) in a fixed column configuration is described and breakthrough data of the dyes determined. The breakthrough data were correlated using a model based on liquid and pore diffusion with a good fit of experimental results obtained. Trends in the effective diffusivity used in the model correlated with other authors. A slight decrease in effective diffusivity was found with decrease in particle size and was attributed to interactions between the relatively large molecular sized dye and the microspore structure found in granular activated carbon.