Macrodispersion Coefficient Research Articles

The Pathologically Evolving Aggregation-State of Cells in Cancerous Tissues as Interpreted by Fractal and Multi-Fractal Dispersion Theory in Saturated Porous Formations.

A recent author's fractal fluid-dynamic dispersion theory in porous media has focused on the derivation of the associated nonergodic (or effective) macrodispersion coefficients by a 3-D stochastic Lagrangian approach. As shown by the present study, the Fickian (i.e., the asymptotic constant) component of a properly normalized version of these coefficients exhibits a clearly detectable minimum in correspondence with the same fractal dimension (d ≅ 1.7) that seems to characterize the diffusion-limited aggregation state of cells in advanced stages of cancerous lesion progression. That circumstance suggests that such a critical fractal dimension, which is also reminiscent of the colloidal state of solutions (and may therefore identify the microscale architecture of both living and non-living two-phase systems in state transition conditions) may actually represent a sort of universal nature imprint. Additionally, it suggests that the closed-form analytical solution that was provided for the effective macrodispersion coefficients in fractal porous media may be a reliable candidate as a physically-based descriptor of blood perfusion dynamics in healthy as well as cancerous tissues. In order to evaluate the biological meaningfulness of this specific fluid-dynamic parameter, a preliminary validation is performed by comparison with the results of imaging-based clinical surveys. Moreover, a multifractal extension of the theory is proposed and discussed in view of a perspective interpretative diagnostic utilization.

Theoretical investigation of nonergodic solute dispersion in natural porous formations characterized by persistent and antipersistent power-law log-conductivity correlations

Tracer dispersion within log-conductivity fields represented by power-law semivariograms is investigated by an analytical first-order Lagrangian approach that, in treating subsurface flow and transport, resorts to the superposition principle of an infinite double hierarchy of mutually independent scales of heterogeneity. The results of the investigation, which are corroborated by a preliminary field validation, and also interpreted in terms of probabilistic risk analysis, say that transport anomaly is intrinsically associated with evolving-scale heterogeneous porous formations, regardless of their semivariogram scaling exponent b. In contrast with what was found by previous studies that dealt with this subject in a Lagrangian framework, it is demonstrated that: (1) the magnitude of nonergodic dispersion is nonmonotonically related to b; (2) consistently assuming a characteristic advective-heterogeneity length-scale leads to a universal (and quadratic) dependence of the dimensionless macrodispersion coefficients on the dimensionless time. Additionally, it is demonstrated that, in the presence of fractal heterogeneity, and unlike what happens for short-range correlations, diffusion acts as an antagonist mechanism in terms of Fickian dispersion achievement. Finally, the reinterpretation of antipersistent and persistent correlations as a double hierarchy of oscillatory nonperiodic and periodic fields, respectively, besides allowing for a technical explanation of all the detected trends, envisions a possible alternative methodology for their numerical generation.

Evidence Based Estimation of Macrodispersivity for Groundwater Transport Applications.

The scope of this work is to discuss the proper choice of macrodispersion coefficients in modeling contaminant transport through the advection dispersion equation (ADE). It is common to model solute concentrations in transport by groundwater with the aid of the ADE. Spreading is quantified by macrodispersivity coefficients, which are much larger than the laboratory observed pore-scale dispersivities. In the frame of stochastic theory, longitudinal macrodispersivity is related to the hydraulic conductivity spatial variability via its statistical moments (mean, variance, integral scales), which are generally determined by geostatistical analysis of field measurements. In many cases, especially for preliminary assessment of contaminant spreading, these data are not available and ad hoc values are adopted by practitioners. The present study aims at recommending dispersivity values based on a thorough analysis of tens of field experiments. Aquifers are classified as of weak, medium, and high heterogeneity and for each class a range of macrodispersivity values is recommended. Much less data are available for the transverse macrodispersivities, which are significantly smaller than the longitudinal one. Nevertheless, a few realistic values based on field data, are recommended for applications. Transport models using macrodispersivities can predict mean concentrations, different from the local ones. They can be used for estimation of robust measures, like plumes spatial moments, longitudinal mass distribution and breakthrough curves at control planes.

Macrodispersion in generalized sub-Gaussian randomly heterogeneous porous media

• Features of log-conductivity, Y , fields are captured by a non-Gaussian (GSG) model. • Expressions of flow and transport moments in three-dimensional GSG fields are derived. • Head and velocity fields are more correlated in GSG than in Gaussian Y structures. • Non-Gaussianity of Y heavily influences pre-asymptotic macrodispersion values. • Late time transport exhibits a Fickian behavior also in non-Gaussian Y fields. In this work, we explore the implications of modeling the logarithm of hydraulic conductivity, Y , as a Generalized Sub-Gaussian (GSG) field on the features of conservative solute transport in randomly heterogeneous, three-dimensional porous media. Hydro-geological properties are often viewed as Gaussian random fields. Nevertheless, the GSG model enables us to capture documented non-Gaussian traits that are not explained through classical Gaussian models. Our formulation yields lead- (or first-) order analytical solutions for key statistical moments of flow and transport variables. These include flow velocities, hydraulic head, and macrodispersion coefficients, as obtained across GSG log-conductivity fields. The analytical model is based on a first-order spectral theory, which constrains the rigorous validity of our results to small values of log-conductivity variance ( σ Y 2 < < 1 ). Analytical results are then compared against detailed numerical estimates obtained through a Monte Carlo scheme encompassing various levels of domain heterogeneity. An asymptotic Fickian transport regime is attained at late times in both Gaussian and GSG Y fields. Convergence to such regime is slower for GSG as compared to Gaussian fields. This suggests a strong impact of the heterogeneity structure on non-Fickian pre-asymptotic behaviors of the kind documented in the literature. The quality of the comparison between analytical and numerical results deteriorates with increasing σ Y 2 . Otherwise, our lead-order solutions frame macrodispersion coefficients in appropriate orders of magnitude also for values of σ Y 2 up to approximately 1.7, which are consistent with the spatial variability of Y across a single geological unit. In this sense, our analytical approach enables one to obtain prior information on solute plume evolution and to grasp the effects of non-Gaussian medium heterogeneity while favoring simplicity. Our findings also enhance the current level of understanding of the nature of mass transfer across heterogeneous media characterized by complex variability structures which cannot be reconciled with classical Gaussian scenarios.

GPU implementation of Explicit and Implicit Eulerian methods with TVD schemes for solving 2D solute transport in heterogeneous flows

In this work we present an efficient implementation of Eulerian TVD methods. We apply parallelization strategies based entirely on GPU for the solution of the 2D transport equation in heterogeneous porous media. Additionally, a parallel strategy is proposed for the generation of exponentially correlated lognormally distributed permeability fields in GPU. The programs are developed using C++/CUDA. The implemented methods are used to solve advective dominant problems, in a context of Monte Carlo type simulations to numerically determine the longitudinal and transversal macrodispersion coefficients averaging over 100 simulations for permeability fields for a large range of variances. The following types of transport are considered for testing: pure advection, advection-diffusion and advection-dispersion. The performance in terms of the computation time of explicit and implicit methods are compared. We show that the implemented algorithms allow to efficiently solve problems in computational domains of up to 134.5 million cells in a single GPU.

Macrodispersion and Recovery of Solutes and Heat in Heterogeneous Aquifers

AbstractThe recovery efficiency of aquifer storage systems with radial flow fields are studied for heterogeneous aquifers. Macrodispersion, arising from spatially heterogeneous hydraulic conductivity, is modeled as a scale‐dependent mechanical dispersion process. Approximate solutions for the recovery efficiency as a function of local dispersion and macrodispersion parameters, the injection‐extraction rate and duration , and storage cycle count, are derived and validated against numerical simulations. If macrodispersion dominates and the macrodispersion coefficient scales linearly with distance, the recovery efficiency is independent of both . For sublinear and superlinear scalings, recovery increases and decreases respectively if increases. However, if local dispersion dominates, increasing always increases recovery. As macrodispersion becomes increasingly dominant with scale, the recovery efficiency may be a nonmonotonic function of , with a maximum. In homogeneous aquifers, nonmonotonicity does not occur for 1D and 2D radial flow, but occurs for 3D radial flow fields only as a function of , not . These methods may also be used for fitting local dispersion and macrodispersion parameters with push‐pull tests using recovery data, with advantages in scope of applicability and ease of data acquisition and interpretation, compared to existing push‐pull test methods, which fit to breakthrough curves and do not consider macrodispersion. Furthermore, characterizing macrodispersion with push‐pull tests may be advantageous over methods that use observation wells, as observation well placement may be challenging in highly heterogeneous aquifers. The results show that the macrodispersion parameters are not innate aquifer hydraulic properties, as their values vary with flow field geometry.

Confronting heterogeneous sorption and hydrodynamic dispersion on solute transport in a fracture-skin-matrix system using spatial moment analysis.

Understanding the intricacies of inter-dependency of fluid flow and solute transfer at the scale of a single fracture is limited by various simplifying assumptions employed for computational purposes. In the present study, the fracture-rock matrix interface is assumed to be consisting of a skin layer with sufficient mass transfer properties where non-linear adsorption is considered to be the limiting reaction among the various interfaces. A numerical model has been developed using implicit finite difference method with varying grids at the fracture-skin interface to capture the mass transfer during solute transport in the presence of non-linear Sips adsorption. The model was used to identify the critically influencing parameters on the temporal profiles of fluid velocity, macro-dispersion coefficient and dispersivity using the method of spatial moments. The results indicate that the presence of the skin has enhanced the mixing phenomenon as well as the sorptive mass transfer rates. Summary of the sensitivity analysis provides the critical factors to be considered while employing such comprehensive models for elucidating details at a small scale. The presence of fracture-skin evades the sensitive role played by (a) the fracture adsorption coefficient (with a reduced rate constant for adsorption and an increased rate constant for desorption) at early times, while resulting in an enhanced mixing characteristics at later times, and (b) maximum sorption capacity of fracture as a function of solute velocity; and in turn, it provides an improved control over the transportation of solutes through the fracture.

Impact of the fracture contact area on macro-dispersion in single rough fractures

In the scientific literature, the study of the impact of the fracture contact area on macro-dispersion in single rough fractures is still an open question. In this work, we study numerically the combined effects of the fracture roughness and the fracture contact area on the non-Fickian transport in single rough fractures. In particular, we quantify the contribution of the fracture contact area on macro-dispersion. These objectives are achieved by estimating the macro-dispersion coefficient from Monte Carlo parallel numerical simulations in pure advection and advection–diffusion cases. When the fractional void S O is equal to 1 (i.e., for σ lnb <0.25), the Monte Carlo simulations show that macro-dispersion results of two contributions, dispersion caused by the heterogeneity of fracture apertures that induces a channelization of flow paths and molecular diffusion, as shown by the analytical solution proposed by Gelhar in 1993. When the fraction void S O is different from 1 (i.e., for σ lnb >0.25), a third mechanism plays in macro-dispersion. The presence of contacts or obstacles causes a disruption of flow paths. This mechanism is identical to that induced by the fracture roughness with a lower amplitude. Its amplitude is the function of the fractional void S O .

A Theoretical Study about Ergodicity Issues in Predicting Contaminant Plume Evolution in Aquifers

A large-time Eulerian–Lagrangian stochastic approach is employed to: (1) estimate centroid position uncertainty of contaminant plumes that originate from instantaneous point sources in statistically stationary and isotropic porous formations; (2) assess the time needed for achieving ergodic conditions, which would allow for the evaluation of local concentration values based on the only ensemble mean distribution; (3) derive the concentration coefficient of variation (CV) as a function of asymptotic macro-dispersion coefficients and centroid trajectory variances. The results indicate that the decay time of plume position uncertainty is so large that there is practically no chance for effective ergodicity. The concentration coefficient of variation is zero at the centroid but rapidly increases when moving away from it. The dissipative effect of local dispersion in the presence of relatively high Péclet numbers is considerably exalted by marked flow field heterogeneity, which confirms the previously postulated synergic, non-additive effect of advection and local dispersion in passive solute dilution. A further result from this study is the derivation of the power law that relates dimensionless concentration micro-scale to dimensionless local dispersive area. The exponent of this power law is the same that appears in the relationship between dimensionless Kolmogorov turbulent micro-scale and flow Reynolds number.

Effective flow and transport properties of heterogeneous unsaturated soils

The heterogeneity of field scale soils poses a challenge to predictive large scale flow and transport modeling. The theory of effective macroscale parameters holds good and is applicable in dealing with such problems. But the validity of the analytic stochastic solutions obtained for randomly heterogeneous soils is debatable, as the test cases under which they are validated are of limited scope due to linearization and perturbation approximations. In this study, samples of heterogeneous soils are generated using sets of spatially correlated random field parameters that are either geometrically isotropic, or else, geometrically anisotropic with either horizontal or vertical stratification (perfect or imperfect). Several combinations of ratios of correlation length and capillary dispersion lengths are considered. Numerical simulations of unsaturated flow are performed on each randomly heterogeneous soil sample. The principal components K^ii(Ψ) of the macroscale effective unsaturated conductivity are then obtained as a function of the mean suction Ψ of the sample. They are compared to stochastic spectral perturbation theory, and to a probabilistic semi-empirical Power Average Model (PAM). They are also compared with arithmetic, geometric and harmonic mean conductivity-suction curves. The numerically upscaled principal conductivity curves match quite well the PAM, better than the classical means (Arithmetic, Geometric, Harmonic), and also somewhat better than the curves obtained from stochastic spectral perturbation theory. It is observed that the upscaled principal components Kii(ψ), obtained numerically and with the PAM along directions “i” orthogonal/parallel to perfect stratification coincide with the harmonic/arithmetic mean curves at low suctions (i.e., near saturation), but deviate from it and come closer to the geometric mean at higher suctions. The PAM appears suitable for generation of approximate upscaled conductivity curves, e.g., for obtaining the mesh-scale or block-scale conductivity curves in large scale simulation codes. Transient solute transport simulations are then performed on the detailed random velocity fields obtained from the steady state simulations of unsaturated flow in the randomly heterogeneous soil samples. Snapshots of solute concentration C(x,z,t) are taken at different times. The temporal evolution of spatial moments of concentration is analyzed in order to characterize the macroscale advection and dispersion of the unsaturated concentration plume, and in particular, its macro-dispersion coefficient (D) and dispersivity length scale (A). For the synthetic soil samples considered in this study, the macro-dispersive spreading of the solute is stronger for flow parallel to vertical stratification, compared to flow perpendicular to horizontal stratification, and also, compared to flow in statistically isotropic non-stratified soil.

Ensemble and effective dispersion in three-dimensional isotropic fractal media

We determine the time-dependent behavior of the dispersion coefficient for transport in formations with isotropic log-conductivity fields showing fractal behavior.We consider two different dispersion coefficients for point-like injection: (1) the ensemble dispersion coefficients, defined as half the rate of change of the second central moments of the ensemble-averaged concentration distribution and (2) the effective dispersion, which is half the rate of change of the expected second central moments. Our results show, that the two longitudinal macrodispersion coefficients steadily grow with time and remain different at all times in a fully fractal regime, indicating that no Fickian transport regime is ever reached. The resulting effective longitudinal transport model is consequently a fractional advection–dispersion equation. In the semi-fractal regime, a Gaussian transport regime is reached eventually. However, compared to the case of a classic non-fractal regime, the transient non-Gaussian regime lasts much longer. In the transverse direction, the two dispersion coefficients approach the same large-time limit also in fractal media highlighting the fundamental difference between longitudinal and transverse dispersion.

Seismicity Enhances Macrodispersion in Finite Porous and Fractured Domains: A Pore‐Scale Perspective

AbstractUnderstanding the effects of oscillating flow field induced by seismicity on the transport process is vital for predicting the fate and transport of solute in many dynamic environments. However, there is prominent discrepancy in arguing with the response of dispersion to the oscillating flow field (i.e., the longitudinal dispersion coefficient would decrease, increase, or maintain unchanged). To unravel the underpinning physics about this controversial response, we simulated two‐hundred twenty pore‐scale numerical experiments for the seismicity‐induced oscillating flow field and associated solute transport in the idealized finite porous (i.e., fluidic plate) and fractured (i.e., parallel plates) domains. The numerically obtained breakthrough curves were fitted to the macroscopic advection‐dispersion equation to retrieve the mean velocity and apparent macrodispersion coefficient (DL). We found that DL increases to its maxima when the oscillating flow field resonates with the finite systems, that is, the period (T) of the oscillating flow field or the seismic wave approaches the pore volume (τ) of a finite domain. The resonant effects diminish and DL barely changes when T is much larger or smaller than τ. Moreover, the degree of enhancement in DL increases exponentially with the amplitude of the seismic force. Fundamental understanding of the response of macrodispersion to the oscillating flow field adds value in predicting the fate of solute in transient flow systems via the advection‐dispersion equation.

The scale dependence of dispersivity in multi-facies heterogeneous formations

Dispersivity, a parameter describing dispersive mixing of solutes in aquifers, is scale dependent. Macrodispersion coefficient equations are developed for solute transport in three-dimensional domains based on a general global covariance function of log conductivity in multi-facies heterogeneous formations. The longitudinal dispersivity was then derived to show the scale dependence of this parameter. The time evolution trends and the relative contributions of the auto- and cross-facies transition terms to the macrodispersion were discussed with an example. Sensitivity analysis indicates that the values of the longitudinal dispersion coefficient are positively correlated to facies mean length and the difference of the mean log conductivity between different facies. The longitudinal dispersivity coefficient also shows clearly a linear dependence on the global variance of the log conductivity in the multi-facies sediments.

Direct Breakthrough Curve Prediction From Statistics of Heterogeneous Conductivity Fields

AbstractThis paper presents a methodology to predict the shape of solute breakthrough curves in heterogeneous aquifers at early times and/or under high degrees of heterogeneity, both cases in which the classical macrodispersion theory may not be applicable. The methodology relies on the observation that breakthrough curves in heterogeneous media are generally well described by lognormal distributions, and mean breakthrough times can be predicted analytically. The log‐variance of solute arrival is thus sufficient to completely specify the breakthrough curves, and this is calibrated as a function of aquifer heterogeneity and dimensionless distance from a source plane by means of Monte Carlo analysis and statistical regression. Using the ensemble of simulated groundwater flow and solute transport realizations employed to calibrate the predictive regression, reliability estimates for the prediction are also developed. Additional theoretical contributions include heuristics for the time until an effective macrodispersion coefficient becomes applicable, and also an expression for its magnitude that applies in highly heterogeneous systems. It is seen that the results here represent a way to derive continuous time random walk transition distributions from physical considerations rather than from empirical field calibration.

Semi-analytical solution of land-derived solute transport under tidal fluctuation in a confined aquifer

A one-dimensional semi-analytical solution of land-derived solute transport, subject to tidal fluctuation in a coastal confined aquifer, was derived using the generalized integral-transform technique (GITT). To investigate the plume migration of land-derived contaminants within a tidally influenced aquifer, both spatially and temporally varying expressions of the Darcy velocity and dispersion coefficients obtained from the analytical solution of the groundwater head response, which were subject to sinusoidal boundary conditions due to tidal fluctuation, were considered. This new semi-analytical solution was verified against a numerical solution, as well as the peak location trajectory obtained using the Predictor-Corrector method. Sensitivity analyses of tidal amplitude, hydraulic conductivity, and storage coefficient using the proposed solution were performed to understand plume behavior with regard to plume shape, plume spatial moments, and macrodispersion coefficients to gain a better understanding of the transport mechanisms. As the tidal amplitude, hydraulic conductivity, and storage coefficient were increased, the peaks were travelled faster, and peak concentrations were decreased. In addition, an increase in tidal amplitude, hydraulic conductivity, and storage coefficient caused an increase in variance as well as the macrodispersion coefficient. It was observed that negative macrodispersion appeared when the storage coefficient was largest, as well as when the difference between landward-directed advective velocity at the leading and trailing edges of the plume was greatest. This newly developed semi-analytical solution provides a useful mathematical tool for validating numerical models and understanding the physical mechanism of the migration of plume discharge to the sea or estuaries within a tidally influenced aquifer.

Lagrangian scheme to model subgrid‐scale mixing and spreading in heterogeneous porous media

AbstractSmall‐scale heterogeneity of permeability controls spreading, dilution, and mixing of solute plumes at large scale. However, conventional numerical simulations of solute transport are unable to resolve scales of heterogeneity below the grid scale. We propose a Lagrangian numerical approach to implement closure models to account for subgrid‐scale spreading and mixing in Darcy‐scale numerical simulations of solute transport in mildly heterogeneous porous media. The novelty of the proposed approach is that it considers two different dispersion coefficients to account for advective spreading mechanisms and local‐scale dispersion. Using results of benchmark numerical simulations, we demonstrate that the proposed approach is able to model subgrid‐scale spreading and mixing provided there is a correct choice of block‐scale dispersion coefficient. We also demonstrate that for short travel times it is only possible to account for spreading or mixing using a single block‐scale dispersion coefficient. Moreover, we show that it is necessary to use time‐dependent dispersion coefficients to obtain correct mixing rates. On the contrary, for travel times that are large in comparison to the typical dispersive time scale, it is possible to use a single expression to compute the block‐dispersion coefficient, which is equal to the asymptotic limit of the block‐scale macrodispersion coefficient proposed by Rubin et al. (1999). Our approach provides a flexible and efficient way to model subgrid‐scale mixing in numerical models of large‐scale solute transport in heterogeneous aquifers. We expect that these findings will help to better understand the applicability of the advection‐dispersion‐equation (ADE) to simulate solute transport at the Darcy scale in heterogeneous porous media.

Temporal Moment Analysis of Multi-Species Radionuclide Transport in a Coupled Fracture-Skin-Matrix System with a Variable Fracture Aperture

This paper presents an analysis using temporal moments to study multi-species radionuclide transport along a single fracture with variable fracture aperture in a fracture-skin-matrix system. In the present study, a decay chain having three elements is considered and transport of each member in the decay chain is modeled by solving a coupled system of partial differential equations for fracture, fracture-skin, and rock matrix using explicit finite difference method. Having obtained the concentration distribution, lower order temporal moments of radionuclide distribution are computed to analyze the effective velocity and macro-dispersion coefficient of radionuclides in the fracture. In the present study, effect of varying fracture aperture on transport characteristics of radionuclides is also analyzed. It is found that the fracture aperture variation profile has significant impact on radionuclide distribution along the fracture. Sensitivity analysis is carried out in a fracture-skin-matrix system with sinusoidal fracture aperture to study the effect of various parameters like fracture aperture thickness, fracture-skin porosity, fracture-skin diffusion coefficient, flow rate, radioactive decay constant, and Freundlich sorption isotherm exponent on transport characteristics of radionuclide. The results suggest that the above mentioned parameters significantly influence concentration, distribution, mobility, and effective macro-dispersion coefficient of radionuclides along the fracture.

The Boundaries Influence in Trending Hydraulic Conductivity Fields

We analyze the impact of the boundary conditions on flow and transport solutions for the case of a two-dimensional heterogeneous medium with a linear trend in the mean log-conductivity. The influence of the boundaries is analyzed for different values of the domain size and aspect ratio, and different directions of the trend respect to the mean flow direction. The analysis involving a steady, spatially nonstationary velocity field, is developed by using the stochastic finite element method. Results of this study show that the impact of the trend in finite domains may disagree with that obtained in unbounded domains and it is more complex. The trend alters the result obtained for the medium with stationary conductivity, leading to a larger or smaller value of the macrodispersion coefficients, depending on the size and aspect ratio of the domain, and this effect may vary with the travel distance from the solute source. Moreover in limited domains here analyzed also for particles starting at distance of several integral scales from the boundaries and traveling in the middle of the domain, the behavior of macrodispersion coefficients is affected by the boundary conditions and the influence of the trend on longitudinal and transverse macrodispersion coefficients may vary with the imposed constraints.

Numerical modelling and spatial moment analysis of solute transport with Langmuir sorption in a fracture matrix-coupled system

Sorption is one of the key processes that play a major role in the transport of contaminants in fractured porous media. While Freundlich adsorption isotherm has been studied extensively in fractured porous media, limited studies have been conducted using Langmuir sorption. To address this issue, a numerical model is developed for analysing the influence of sorption intensities on velocity, macro-dispersion coefficient and dispersivity using the method of moments. Implicit finite difference numerical technique has been used to solve the coupled non-linear-governing equations. A varying grid is adopted at the fracture and rock matrix interface to capture the mass transfer at the interface. Results suggest that for relatively higher sorption capacities and distribution coefficients, the effective solute velocity as well as the retardation factor clearly becomes a non-linear function of time. The higher magnitude of second spatial moments for the cases of higher sorption capacities and distribution coefficients clearly conveys that there is an excessive mixing of solutes within the fracture resulting from Langmuir sorption with reference to the classical porous medium mixing. Also, the behaviour of effective macro-dispersion coefficient with time is highly complex for higher maximum sorption capacity.

Spatial moment analysis of solute transport with Langmuir sorption in a fracture–skin–matrix coupled system

Sorption is one of the key processes that plays a major role in the transport of contaminants in fractured porous media. Extensive studies have been conducted on sorption isotherms in fracture matrix coupled system but studies pertaining to sorption in fractured porous media with fracture–skin are very limited. In this study, a numerical model is developed for analysing the influence of sorption intensities on velocity, macro dispersion coefficient and dispersivity using the method of spatial moments. Implicit finite difference numerical technique has been used to solve the coupled non-linear governing equations. A varying grid is adopted at the fracture and skin interface to capture the mass transfer at the interface. Results suggest that the role of non-linear sorption is dominant in comparison with that of advection and dispersion in deciding the final relative concentration within the fracture. The role of sorption partition coefficients is not always enhancing the mixing phenomena which lead to dilution of solutes. Furthermore, the role of sorption partition coefficients is extremely sensitive in the sense that the resultant magnitude of effective dispersivity may either get enhanced or mitigated depending on the magnitude of sorption partition coefficients.