Effective Matrix Diffusion Research Articles

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

Evidence for Enhanced Matrix Diffusion in Geological Environment

Molecular diffusion in rock matrix, called as matrix diffusion, has been appreciated as a static process for elemental migration in geological environment that has been acknowledged in the context of geological disposal of radioactive waste. However, incomprehensible enhancement of matrix diffusion has been reported at a number of field test sites. Here, the matrix diffusion of saline water at Horonobe, Hokkaido, Japan is highlighted directly probing angstrom-scale pores on a field scale up to 1 km by positron–positronium annihilation spectroscopy. The first application of positron–positronium annihilation spectroscopy to field-scale geophysical research reveals the slight variation of angstrom-scale pores influenced by saline water diffusion with complete accuracy. We found widely interconnected 3 Å pores, which offer the pathway of saline water diffusion with the highly enhanced effective matrix diffusion coefficient of \(4\times 10^{-6}\) cm2 s-1. The present findings provide unambiguous evidence that the angstrom-scale pores enhance effective matrix diffusion on a field scale in geological environment.

Long term infiltration and tracer transport in fractured rocks: Field observations and model analyses

Summary This paper presents modeling analyses of long term infiltration and tracer tests in fractured tuffs at Yucca Mountain, NV, USA. The experiments were conducted on a 20 m thick tuff section in a flyover formed by two exploratory tunnels. The infiltration test last for 870 days. Both measured infiltration and seepage show significant temporal and spatial variations. The tracer test used inorganic tracers (I − , Br − , F − ) and organic tracers (fluorobenzoic acids) released 559 days after the infiltration test started. Leaching from dry salts from fracture walls was found to have affected tracer breakthroughs. The unsaturated flow was evaluated by optimizing 45 parameter values in a three-dimensional model, which accounts for fracture–matrix interaction and heterogeneous hydraulic properties in a column-based scheme. The field data are valuable asset to evaluate the modeling approaches for fractured rocks and the relative importance of the matrix diffusion process. Results show that matrix diffusion is an important process for transport, and that effective matrix-diffusion coefficients at the field-scale are larger than those at the laboratory-scale for the solutes.

Interpretation of the enhancement of field‐scale effective matrix diffusion coefficient in a single fracture using a semi‐analytical power series solution

AbstractA power series solution for convergent radial transport in a single fracture (PCRTSF) is developed. Transport processes considered in PCRTSF include advection and hydrodynamic dispersion in the fracture, molecular diffusion in the matrix, diffusive mass exchange across the fracture‐matrix interface, and mixing effects in the injection and the extraction boreholes. An analytical solution in terms of a power series in Laplace domain is developed first, which is then numerically inverted by de‐Hoog et al.'s algorithm. Four dimensionless parameters determine the behaviour of a breakthrough curve (BTC) calculated by PCRTSF, which are, in the order of decreasing sensitivity, the matrix diffusion factor, two mixing factors, and the Peclet number. The first parameter is lumped from matrix porosity, effective matrix diffusion coefficient, fracture aperture, and retardation factors. Its value increases as the matrix diffusion effect becomes significant. A non‐zero matrix diffusion factor results in a − 3/2 slope of the tail of a log–log BTC, a common property for tracer diffusion into an infinite matrix. Both mixing factors have equal effects on BTC characteristics. However, the Peclet number has virtually no effect on BTC tail. PCRTSF is applied to re‐analyse two published test results that were obtained from convergent radial tracer tests in a discrete, horizontal fracture in Silurian dolomite. PCRTSF is able to fit the field BTCs better than the original channel model does if a large matrix diffusion coefficient is used. Noticeably, the ratio of field‐scale to lab‐scale matrix diffusion coefficients can be as large as 378. This enhancement of the field‐scale matrix diffusion coefficient may be ascribed to the presence of a degraded zone at the fracture‐matrix interface because of karstic effects, or to flow channeling as a result of aperture heterogeneity. Copyright © 2009 John Wiley & Sons, Ltd.

Experimental and numerical modeling of the mass transfer between rock matrix and fracture

Abstract Mass transfer between matrix and fracture is encountered during enhanced oil recovery applications, greenhouse gas sequestration and contaminant transportation in naturally fractured subsurface reservoirs. We used a combination of laboratory scale physical experiments and numerical simulations to evaluate the mass transfer between fracture and matrix and effective diffusion/dispersion in the matrix of naturally fractured subsurface reservoirs. Experiments on artificially fractured porous media showed the influence of various factors such as injection flow rate, matrix–fracture length, solute viscosity and density and matrix porosity/permeability on solvent/solute diffusion into/from the porous matrix media from/into the adjacent fracture. Mass transfer between matrix and fracture was simulated using advection–convection equation governing the system. Experimental results were compared with the results from numerical simulations to evaluate the major contributing parameters, mass transfer rate and effective matrix diffusion coefficient. It was found that effective matrix diffusion coefficient in the matrix is higher than the mutual diffusion coefficient. The mass transfer rate was found to be linearly dependent on velocity and affected by wettability as well as rock properties. These two parameters are correlated with other factors governing the physical process. These correlations would be useful in modeling mass transfer into matrix during solvent flow in fracture.

Scale Dependence of the Effective Matrix Diffusion Coefficient: Some Analytical Results

Matrix diffusion is an important process affecting solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies have indicated that effective matrix diffusion coefficient values obtained from a number of field tracer tests are enhanced in comparison with local values and may increase with test scale. In this communication, we develop analytical expressions for the effective matrix diffusion coefficient for two simple fracture–matrix systems and demonstrate that heterogeneities in the rock matrix at different scales may contribute to the scale dependence of the effective matrix diffusion coefficient.

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.

An interpretation of potential scale dependence of the effective matrix diffusion coefficient

Matrix diffusion is an important process for solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies have indicated that the effective matrix diffusion coefficient values, obtained from a large number of field tracer tests, are enhanced in comparison with local values and may increase with test scale. In this study, we have performed numerical experiments to investigate potential mechanisms behind possible scale-dependent behavior. The focus of the experiments is on solute transport in flow paths having geometries consistent with percolation theories and characterized by multiple local flow loops formed mainly by small-scale fractures. The water velocity distribution through a flow path was determined using discrete fracture network flow simulations, and solute transport was calculated using a previously derived impulse-response function and a particle-tracking scheme. Values for effective (or up-scaled) transport parameters were obtained by matching breakthrough curves from numerical experiments with an analytical solution for solute transport along a single fracture. Results indicate that a combination of local flow loops and the associated matrix diffusion process, together with scaling properties in flow path geometry, seems to be an important mechanism causing the observed scale dependence of the effective matrix diffusion coefficient (at a range of scales).

Effects of diffusive property heterogeneity on effective matrix diffusion coefficient for fractured rock

Heterogeneities of diffusion properties are likely to influence the effective matrix diffusion coefficient determined from tracer breakthrough curves. The objectives of this study are (1) to examine if it is appropriate to use a single, effective matrix diffusion coefficient to predict breakthrough curves in a fractured formation, (2) to examine if a postulated scale dependence of the effective matrix diffusion coefficient is caused by heterogeneity in diffusion properties, and (3) to examine whether multirate diffusion results in the previously observed time dependence of the effective matrix diffusion coefficient. The results show that the use of a single effective matrix diffusion coefficient is appropriate only if the interchannel and intrachannel variability of diffusion properties is small. The scale dependence of the effective matrix diffusion coefficient is not caused by the studied types of heterogeneity. Finally, the multirate diffusion process does not result in the time dependence of the effective matrix diffusion coefficient.

Effective matrix diffusion in kilometer‐scale transport in fractured crystalline rock

Concentrations of tritium (3H) and dichlorodifluoromethane (CFC‐12) in water samples taken from glacial drift and fractured crystalline rock over 4 km2 in central New Hampshire are interpreted to identify a conceptual model of matrix diffusion and the magnitude of the diffusion coefficient. Dispersion and mass transfer to and from fractures has affected the 3H concentration to the extent that the peak 3H concentration of the 1960s is no longer distinguishable. Because of heterogeneity in the bedrock the sparsely distributed chemical data do not warrant a three‐dimensional transport model. Instead, a one‐dimensional model of CFC‐12 and 3H migration along flow lines in the glacial drift and bedrock is used to place bounds on the processes affecting kilometer‐scale transport, arid model parameters are varied to reproduce the measured relation between 3H and CFC‐12, rather than their spatial distributions. A model of mass exchange to and from fractures that is dependent on the time‐varying concentration gradient at fracture surfaces qualitatively reproduces the measured relation between 3H and CFC‐12 with an upper bound for the fracture dispersivity approximately equal to 250 m and a lower bound for the effective matrix diffusion coefficient equal to 1 m2 yr−1. The diffusion coefficient at the kilometer scale is at least 3 orders of magnitude greater than laboratory estimates of diffusion in crystalline rock. The large diffusion coefficient indicates that diffusion into an immobile fluid phase (rock matrix) is masked at the kilometer scale by advective mass exchange between fractures with large contrasts in trarismissivity. The measured transmissivity of fractures in the study area varies over more than 6 orders of magnitude. Advective mass exchange from high‐permeability fractures to low‐permeability fractures results in short migration distances of a chemical constituent in low‐permeability fractures over an extended period of time before reentering high‐permeability fractures; viewed at the kilometer scale, this process is analogous to the chemical constituent diffusing into and out of an immobile fluid phase.

Two-phase flow and transport in a single fracture-porous medium system

The prognosis for the remediation of contaminated fractured media is much worse than that for more homogeneous units. Fractures act as conduits for the flow of dense non-aqueous phase liquids (DNAPLs), while diffusion is responsible for the storage of dissolved mass in the surrounding matrix. A numerical model incorporating aqueous phase transport in a variable-aperture fracture and its surrounding matrix is developed and coupled with an existing two-phase flow model. The processes of transient two-phase flow, non-equilibrium dissolution, advective–dispersive transport in the fracture, and three-dimensional matrix diffusion are included in the model. Results from various investigations show that the DNAPL distribution is very sensitive to variations in aperture within a single fracture. Diffusion-controlled mass removal from both the matrix and from the hydraulically inaccessible zones within the fracture itself result in extremely large time frames for significant mass removal from these systems. Success in aqueous phase mass removal from the matrix is very sensitive to the effective fracture spacing. The hydraulic gradient in the fracture only affects the amount of water removed from the system, and does not greatly affect the amount of time required to remove the contaminant mass from the matrix. The ability to remove mass is somewhat sensitive to the porosity and effective matrix diffusion coefficient over the range of expected values.