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This study aims to address the harmful effects of excessive nitrogen fertilizer by investigating the mobility retardance effect of zeolite on nitrate movement in loam soil columns. Disturbed and undisturbed soil columns, treated with zeolite, as well as control soil columns, were analysed over a span of three years. Breakthrough curves generated from the experiments were evaluated using the HYDRUS1D code with mobile–immobile water (MIM) and dual-permeability (DP) models. Our findings highlight that zeolite application significantly reduced nitrate mobility, with recovery rates decreasing by 8% in disturbed and 11% in undisturbed columns. The DP model, which accurately reflects real soil water flow conditions, outperformed the MIM model in predictive accuracy. This research offers a novel long-term perspective on the benefits of zeolite in enhancing soil properties and mitigating nitrate leaching, recommending the DP model for superior prediction of contaminant transport in structured soils within the vadose zone. [ABSTRACT FROM AUTHOR]

This paper gives the construction and analysis of a new numerical method to solve variable order time fractional mobile-immobile transport model. The proposed numerical method is based on Crank-Nicolson approach with fourth order accurate compact exponential scheme for spatial discretization. We prove that the new scheme is uniquely solvable and unconditionally stable. Furthermore, some numerical results are presented to check the effectiveness of the proposed scheme and consistency of computational results with the theoretical findings. [ABSTRACT FROM AUTHOR]

This work is focused on the derivation and analysis of a novel numerical technique for solving time fractional mobile-immobile advection-dispersion equation which models many complex systems in engineering and science. The scheme is derived using the effective combination of Euler and Caputo numerical techniques for approximating the integer and fractional time derivatives respectively, and a fourth order exponential compact scheme for spatial derivatives. The Fourier analysis technique is used to prove that the proposed numerical scheme is unconditionally stable and perform convergence analysis. To assess the viability and accuracy of the proposed scheme, some numerical examples are demonstrated with constant as well as variable order time fractional derivatives for this model. [ABSTRACT FROM AUTHOR]

Mobile-immobile transport models can be effective in reproducing heavily tailed breakthrough curves of concentration. However, such models may not adequately describe transport along multiple flow paths with intermediate velocity contrasts in connected fields. We propose using the mobile-mobile model for simulating subsurface flow and associated mixing-controlled reactive transport in connected fields. This model includes two local concentrations, one in the fast- and the other in the slow-flow domain, which predict both the concentration mean and variance. The normalized total concentration variance within the flux is found to be a non-monotonic function of the discharge ratio with a maximum concentration variance at intermediate values of the discharge ratio. We test the mobile-mobile model for mixing-controlled reactive transport with an instantaneous, irreversible bimolecular reaction in structured and connected random heterogeneous domains, and compare the performance of the mobile-mobile to the mobile-immobile model. The results indicate that the mobile-mobile model generally predicts the concentration breakthrough curves (BTCs) of the reactive compound better. Particularly, for cases of an elliptical inclusion with intermediate hydraulic-conductivity contrasts, where the travel-time distribution shows bimodal behavior, the prediction of both the BTCs and maximum product concentration is significantly improved. Our results exemplify that the conceptual model of two mobile domains with diffusive mass transfer in between is in general good for predicting mixing-controlled reactive transport, and particularly so in cases where the transfer in the low-conductivity zones is by slow advection rather than diffusion. [ABSTRACT FROM AUTHOR]

In this article, we proposed a new numerical method to obtain the approximation solution for the time variable fractional order mobile–immobile advection–dispersion model based on reproducing kernel theory and collocation method. The equation is obtained from the standard advection–dispersion equation (ADE) by adding the Coimbra's variable fractional derivative in time of order γ ( x , t ) ∈ [ 0 , 1 ] . In order to solve this kind of equation, we discuss and derive the ε -approximate solution in the form of series with easily computable terms in the bivariate spline space. At the same time, the stability and convergence of the approximation are investigated. Finally, numerical examples are provided to show the accuracy and effectiveness. [ABSTRACT FROM AUTHOR]

Contaminants in groundwater may experience a broad spectrum of velocities and multiple rates of mass transfer between mobile and immobile zones during transport. These conditions may lead to non-Fickian plume evolution which is not well described by the advection–dispersion equation (ADE). Simultaneously, many groundwater contaminants are degraded by processes that may be modeled as first-order decay. It is now known that non-Fickian transport and reaction are intimately coupled, with reaction affecting the transport operator. However, closed-form solutions for these important scenarios have not been published for use in applications. In this paper, we present four new Green's function analytic solutions in the uncoupled, uncorrelated continuous time random walk (CTRW) framework for reactive non-Fickian transport, corresponding to the quartet of conservative tracer solutions presented by Kreft and Zuber (1978) for Fickian transport. These consider pulse injection for both resident and flux concentration combined with detection in both resident and flux concentration. A pair of solutions for resident concentration temporal pulses with detection in both flux and resident concentration is also presented. We also derive the relationship between flux and resident concentration for non-Fickian transport with first-order reaction for this CTRW formulation. An explicit discussion of employment of the new solutions to model transport with arbitrary upgradient boundary conditions as well as mobile–immobile mass transfer is then presented. Using the new solutions, we show that first-order reaction has no effect on the anomalous spatial spreading rate of concentration profiles, but produces breakthrough curves at fixed locations that appear to have been generated by Fickian transport. Under the assumption of a Pareto CTRW transition distribution, we present a variety of numerical simulations including results showing coherence of our analytic solutions and CTRW particle tracking. [ABSTRACT FROM AUTHOR]

In this work, laboratory experiments and numerical simulations were used to investigate the transport of solute through stratified porous media. Experiments were performed using nonreactive solute transport through an experimental model of stratified porous media of different lengths. The aim of conducting the experiments was to evaluate the effect of the length of mobile-immobile domain on estimation of first-order mass transfer coefficient. The velocity was also changed for different lengths of stratification for understanding the behavior of mass transfer coefficient. The estimated values of mass transfer coefficient were analyzed for interdependency with length, velocity, and dispersion coefficient. It was found that mass transfer coefficient has an inverse relation with dispersion coefficient and also varies with the length of the mobile-immobile region and velocity. Finally, the variable behavior of mass transfer coefficient is obtained when the transport media are under the influence of physical nonequilibrium. [ABSTRACT FROM AUTHOR]

We assess the possibility to use conservative transport information, such as that contained in transit time distributions, breakthrough curves and tracer tests, to predict nonlinear fluid-rock interactions in fracture/matrix or mobile/immobile conditions. Reference simulated data are given by conservative and reactive transport simulations in several diffusive porosity structures differing by their topological organization. Reactions includes nonlinear kinetically controlled dissolution and desorption. Effective Multi-Rate Mass Transfer models (MRMT) are calibrated solely on conservative transport information without pore topology information and provide concentration distributions on which effective reaction rates are estimated. Reference simulated reaction rates and effective reaction rates evaluated by MRMT are compared, as well as characteristic desorption and dissolution times. Although not exactly equal, these indicators remain very close whatever the porous structure, differing at most by 0.6% and 10% for desorption and dissolution. At early times, this close agreement arises from the fine characterization of the diffusive porosity close to the mobile zone that controls fast mobile-diffusive exchanges. At intermediate to late times, concentration gradients are strongly reduced by diffusion, and reactivity can be captured by a very limited number of rates. We conclude that effective models calibrated solely on conservative transport information like MRMT can accurately estimate monocomponent kinetically controlled nonlinear fluid-rock interactions. Their relevance might extend to more advanced biogeochemical reactions because of the good characterization of conservative concentration distributions, even by parsimonious models (e.g., MRMT with 3-5 rates). We propose a methodology to estimate reactive transport from conservative transport in mobile-immobile conditions. [ABSTRACT FROM AUTHOR]

• Mass loss of nanoparticles occurred in the streambed. • The presence of biofilms significantly increased mass loss of nanoparticles. • Nanoparticles were irreversibly trapped in biofilms. • Nanoparticle trapping was reversible in the presence of dissolved organic matter. • The mobile-immobile model predicted the transport of nanoparticles in stream. The fate and transport of nanoparticles (NPs) in streams is critical for understanding their overall environmental impact. Using a unique field-scale stream at the Notre Dame-Linked Experimental Ecosystem Facility, we investigated the impact of biofilms and the presence of dissolved organic matter (DOM) on the transport of titanium dioxide (TiO 2) NPs. Experimental breakthrough curves were analyzed using temporal moments and fit using a mobile-immobile model. The presence of biofilms in the stream severely reduced the transport of the TiO 2 NPs, but this was mitigated by the presence of DOM. Under minimal biofilm conditions, the presence of DOM increased the mass recovery of TiO 2 from 4.2% to 32% for samples taken 50 m downstream. For thriving biofilm conditions only 0.5% of the TiO 2 mass was recovered (50 m), but the presence of DOM improved the mass recovery TiO 2 to 36%. The model was suitable for predicting early, peak, tail, and truncation time portions of the breakthrough curves, which attests to its ability to capture a range of processes in the mobile and immobile domains of the stream. The model outcomes supported the hypothesis that DOM changed the interaction of NP-biofilm from an irreversible to a reversible process. Collectively, these outcomes stress the importance of considering biogeological complexity when predicting the transport of NPs in streams. [ABSTRACT FROM AUTHOR]

Quasi-1D mobile–immobile transport processes which have exponentially distributed random waiting times in both mobile and immobile states are common in hydrologic models (for example, of transport subject to kinetic sorption). The central limit theorem implies that eventually such transport will be expressible with an effective ADE (i.e. a generalization of the common retardation factor approach with an added Fickian dispersion coefficient accounting for the effect of trapping). Previous works have determined formulae for the value of this coefficient based on the transport properties. However, the time until convergence to Gaussian behavior has not previously been quantified. To this end, exact Green’s functions characterizing the transport at all times are derived for the case of pure advection. The Green’s functions are expressed in terms of three dimensionless parameters, representing location, time, and capacity coefficient. In the pre-Gaussian regime, a parametric study characterizing concentration profile asymmetry as a function of the capacity coefficient is performed. Next, heuristics are presented in terms of the dimensionless parameters for the time until the effective ADE adequately reflects reality. For strongly retarded solute, the time until effective ADE validity is found inversely proportional to release (e.g., desorption) rate. The nature of the effective dispersion coefficient is examined, and the possibility of large trapping-driven dispersion even in cases where batch experiments would detect negligible trapping is demonstrated. Collectively, these results call into question reliance on retardation factors derived from batch experiments for many practical transport modeling efforts; knowledge of both the trapping and release kinetics appears essential. [ABSTRACT FROM AUTHOR]

Characterization of preferential flow and transport is still a major challenge but may be improved employing noninvasive, tomographic methods. In this study, 3-D time lapse electrical resistivity tomography (ERT) was employed during infiltration on an undisturbed, unsaturated soil core in a laboratory lysimeter. A tracer breakthrough was conducted during transient conditions by applying a series of short-term infiltrations, simulating natural precipitation events. The electrical response was quantitatively validated using data from a multicompartment suction sampler. Water content probes were also installed for ground-truthing of ERT responses. Water content variations associated with an infiltration front dominated the electrical response observed during individual short-term infiltration events, permitting analysis of water content dynamics from ERT data. We found that, instead of the application of an uncertain petrophysical function, shape measures of the electrical conductivity response might be used for constraining hydrological models. Considering tracer breakthroughs, the ERT observed voxel responses from time lapse tomograms at constant water contents in between infiltration events were used to quantitatively characterize the breakthrough curve. Shape parameters of the breakthrough derived from ERT, such as average velocity, were highly correlated with the shape parameters derived from local tracer breakthrough curves observed in the compartments of the suction plate. The study demonstrates that ERT can provide reliable quantitative information on both, tracer breakthroughs and water content variations under the challenging conditions of variable background electrical conductivity of the pore solution and non steady-state infiltration. [ABSTRACT FROM AUTHOR]

In the area of simulating pesticide transportation in soil profile, the majority of models adhere to simplification techniques and due to this, the simulation achieved does not reflect the reality. One such commonly used model in this regard is PRZM3. In the present research, to ensure improved results, in addition to a general software update, modified equations concerning water movement in soil were applied. To achieve this, one of the most exact numerical solutions (MC-Cormack method) was selected for solving water movement equation (Richard's equation). This equation was then rewritten in the form of mobile-immobile (MIM), and the Shuffled Complex Evaluation (SCE) method for calculating mobile-immobile coefficients was also added to the model. Following model modification, this was used to simulate 2,4-D concentration, and the results were then compared with the results of the main model and measured data (Noshadi et al., 2011) in two different treatments (normal irrigation and deficit irrigation). Considering the statistics, in the normal irrigation treatment for PRZM3, the figure for NRMSE (normalized root mean square error), CRM (coefficient of residual mass) and d (index of agreement) accounted for 0.58, 0.78 and -0.47, respectively while the figures reported in the modified model using MC-Cormack method (PRZM3-MC) were 0.79, 0.28 and -0.04, and in the modified model using MIM form (PRZM3-MC-MIM) they were 0.86, 0.23 and -0.06. Regarding deficit irrigation treatment, for PRZM3, the figure for NRMSE, CRM and d accounted for 0.65, 0.52 and 0.08, respectively while the figures reported in the modified model using PRZM3-MC were 0.77, 0.38 and -0.24 and in PRZM3-MC-MIM they were 0.73, 0.36 and -0.24, respectively. Simulation results reveal that compared to PRZM3, results were more accurate after model modification using PRZM3-MC and PRZM3-MC-MIM. [ABSTRACT FROM AUTHOR]

Abstract: Push–pull tests are a popular technique to investigate various aquifer properties and microbial reaction kinetics in situ. Most previous studies have interpreted push–pull test data using approximate analytical solutions to estimate (generally first-order) reaction rate coefficients. Though useful, these analytical solutions may not be able to describe important complexities in rate data. This paper reports the development of a multi-species, radial coordinate numerical model (PPTEST) that includes the effects of sorption, reaction lag time and arbitrary reaction order kinetics to estimate rates in the presence of mixing interfaces such as those created between injected “push” water and native aquifer water. The model has the ability to describe an arbitrary number of species and user-defined reaction rate expressions including Monod/Michelis–Menten kinetics. The FORTRAN code uses a finite-difference numerical model based on the advection-dispersion-reaction equation and was developed to describe the radial flow and transport during a push–pull test. The accuracy of the numerical solutions was assessed by comparing numerical results with analytical solutions and field data available in the literature. The model described the observed breakthrough data for tracers (chloride and iodide-131) and reactive components (sulfate and strontium-85) well and was found to be useful for testing hypotheses related to the complex set of processes operating near mixing interfaces. [Copyright &y& Elsevier]

Abstract: The success of transient storage (TS) modeling for natural streams depends, in part, on the ability to describe the dispersion process accurately. Evidence based on stream tracer data shows that solute transport processes often do not follow the classical second-order dispersion model (e.g., early breakthrough and faster than Fickian travel times were observed). While models based on space-fractional dispersion are a promising alternative, different definitions of fractional derivatives exist in the literature. Unlike integer-order derivatives, fractional derivatives represent convolutions of concentration with long-range spatial correlation and numerical approximations can produce dense matrices. Therefore issues of both accuracy and computational efficiency need to be examined to successfully identify model parameters for natural streams. In this paper, we first compare the performance of several numerical approaches for solving the space-fractional dispersion equation. We examine three different numerical approaches to approximate the space-fractional derivatives including: (a) a fully-implicit scheme based on the shifted Grünwald–Letnikov (GL) approximation (b) a three-point implicit representation based on the GL formula and (c) a three-point implicit scheme based on mass conservation and the Caputo definition of the fractional derivative. We then use an operator-splitting technique to evaluate a TS model based on space-fractional dispersion (the FSTS model) and test the model against analytical solutions and stream tracer data. A sequence acceleration method (Richardson extrapolation) significantly improves the performance of all schemes examined. Results indicate that the fully-implicit GL method with Richardson extrapolation produces the most accurate solutions while the three-point implicit GL scheme has a stringent time-step restriction to produce acceptable solutions. The three-point implicit scheme based on the Caputo derivative produces accurate solutions in a fraction of the time taken by the fully-implicit GL method and represents the best trade-off between accuracy and computational efficiency for practical applications. The scheme is suitable for parameter estimation and is used to successfully describe tracer data in a natural stream. [Copyright &y& Elsevier]

Abstract: Lignitic mine soils represent a typical two-scale dual-porosity medium consisting of a technogenic mixture of overburden sediments that include lignitic components as dust and as porous fragments embedded within a mostly coarse-textured matrix. Flow and transport processes in such soils are not sufficiently understood to predict the course of soil reclamation or of mine drainage. The objective of this contribution is to identify the most appropriate conceptual model for describing small-scale heterogeneity effects on flow on the basis of the physical structure of the system. Multistep flow experiments on soil cores are analyzed using either mobile–immobile or mobile–mobile type 1D dual-porosity models, and a 3D numerical model that considers a local-scale distribution of fragments. Simulations are compared with time series'' of upward infiltration and matric potential heads measured at two depths using miniature tensiometers. The 3D and the 1D dual-permeability models yielded comparable results as long as pressure heads are in local equilibrium; however, could describe either the upward infiltration or the matric potential curves but not both at the same time. The mobile–immobile type dual-porosity model failed to describe the data. A simultaneous match with pressure heads and upward infiltration data could only be obtained with the 1D dual-permeability model (i.e., mobile–mobile) by assuming an additional restriction of the inter-domain water transfer. These results indicate that for unsaturated flow conditions at higher matric potential heads (i.e., here >−40 hPa), water in a restricted part of the fragment domain must be more mobile as compared to water in the sandy matrix domain. Closer inspections of the pore system and first neutron radiographic imaging support the hypothesis that a more continuous pore region exists at these pressure heads in the vicinity of the lignitic fragments possibly formed by fragment contacts and a lignitic dust interface-region between the two domains. The results suggest that the small-scale structure is too complex as to be represented by weighted contributions of individual components alone. [Copyright &y& Elsevier]

Abstract: In this work we compare the recently developed two-region mass transfer theory reported by Ahmadi et al. [A. Ahmadi, M. Quintard, S. Whitaker (1998), Transport in chemically and mechanically heterogeneous porous media, V, two-equation model for solute transport with adsorption, Adv. Water Resour. 1998;22:59–86] with experimental results reported by Zinn et al. [Zinn, B., L. C. Meigs, C. F. Harvey, R. Haggerty, W. J. Peplinski, C. F. Von Schwerin. Experimental visualization of solute transport and mass transfer processes in two-dimensional conductivity fields with connected regions of high conductivity. Environ Sci Technol 2004;38:3916–3926]. We find that the constant mass transfer coefficient predicted by the steady-state closure to the theory, when used with the macroscale transport equation, provides a reasonable prediction of the observed breakthrough curve. However, the use of a constant mass transfer coefficient does not allow good representation of the tailing that is observed in the data. We show that the mass transfer coefficient can be represented in terms of the eigenvalue expansion of a Green’s function. For a steady solution to the closure problem, this expansion leads to the effective mass transfer coefficient being defined in terms of the harmonic average of the eigenvalues of the expansion; this is consistent with previous work on this topic. To further investigate the influence of using a single, constant value for the mass transfer coefficient, we examine the solution to the mass transfer problem in terms of a mixed model, where the eigenvalues of one region (the inclusions) are kept, while the second region (the matrix) is treated as a homogenized material. The results from this comparison indicate that the mass transfer coefficient predicted via volume averaging using a quasi-steady closure could potentially be improved upon by development of new methods that retain more of the eigenvalues of the system. [Copyright &y& Elsevier]

Solute transfer between regions of high and low permeability will limit rates of aquifer remediation in the field and can also affect solute transport through laboratory columns. Transport in systems with such rate limitations is often modeled by assuming that advective transport occurs only in the high-permeability region (mobile domain) and that solute movement within the lower-permeability region (immobile domain) is via diffusion only. The validity of such models was explored by experimentally observing the influence of pore water velocity on the apparent rates of transfer within a geometrically well defined, two-domain system. Tritiated water tracer (3H2O) experiments were conducted in a 7-cm soil column with a central cylindrical zone of highly permeable material surrounded by an annulus of relatively impermeable finer-grained sediment. Experimental pore water velocities spanned over two orders of magnitude and included 'long' and 'short' solute input pulse lengths. The breakthrough data were interpreted using a first-order mass transfer model (FOM) and a Fickian pore-diffusion model (PDM). As expected, the rate parameters fitted to the PDM were less sensitive to pore water velocity than those estimated using the FOM. Nonetheless, parameters for the PDM exhibited a negative correlation with pore water velocity. Reestimated parameters from experiments of Young and Ball (1998) showed similar scaling. The velocity dependency indicates deficiencies in inherent model assumptions of both the FOM and the PDM. For the PDM, reasons for the velocity dependency may include mass transfer limitations in the mobile domain and/or heterogeneity of diffusion rates within the immobile domain. [ABSTRACT FROM AUTHOR]

Bromide breakthrough curves from push-pull tests were obtained at two wells before, during, and after citrate injections to assess how citrate-induced colloid mobilization affected physical aquifer transport properties. Tailing and incomplete bromide recoveries (67-95%) could not be fit with a conservative advection/dispersion model, and the results of batch tests using aquifer solids implied bromide was not significantly sorbing. Thus we modeled the bromide returns considering advection, dispersion, and rate-limited diffusive mass transfer between mobile and immobile regions by fitting α r, the radial dispersivity; α, the rate-limited mass transfer coefficient; and β, the volumetric ratio of immobile-to-mobile domains. Statistical t-tests indicated that the changes in aquifer transport parameters at a well where colloid mobilization was limited were not significant at a 95% percent confidence level. However, the substantial colloid mobilization at a second well corresponded to significantly decreased α r and β, while increasing α between premobilization and both mobilization and postmobilization. The changes in aquifer parameters and their correlation to the recovered colloidal mass are consistent with the idea that pore-clogging colloids were mobilized and/or reorganized during citrate injections. The results suggest that flushing a site under the right conditions with citrate could open up immobile regions and substantially reduce remediation time and costs by liberating contaminants whose transport would otherwise be diffusion limited. [ABSTRACT FROM AUTHOR]