MIM Model Research Articles

Zeolite intervention in soil nitrate dynamics: insights from column experiments and modelling

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 HYDRUS-1D 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.

Formation of convective roll patterns over a longitudinal throughflow in an active inhomogeneous porous medium with weak clogging

The convective stability of a plane-parallel longitudinal throughflow in a system consisting of two porous sublayers with distinct permeability is studied taking into account the weak pore clogging effect and given a finite difference in concentration between the upper and lower boundaries of the system. A system of differential equations for convection is derived within the framework of the continuum approach and the nonlinear MIM model. A linear stability analysis of the basic longitudinal flow is carried out. The boundary value problem is solved using the numerical technique for constructing a fundamental system of solutions. The neutral stability curves of the basic flow with respect to the disturbances in the form of rolls with different wavelength are obtained. For the absence of pore clogging, the convective stability maps of the critical solutal Rayleigh-Darcy number versus the permeability ratio for the initial uncontaminated sublayers, as well as the plots of the critical disturbance frequency and wave number versus the permeability ratio for some values of the Peclet number, are constructed. It is shown that these results have symmetry with respect to the solution for equal initial permeability of sublayers. The clogging effect associated with the solute adsorption and desorption in a porous medium is studied in the two-layered systems with the values 0.1 and 10 of the ratio of initial permeabilities of the sublayers; convection localization occurs in distinct sublayers. It was found that clogging increases the stability of the longitudinal basic flow relative to solutal inhomogeneity and breaks the symmetry of solutions with respect to the case when the two-layered system is reduced to a single layer with the same filtration properties of the porous medium throughout its volume. The influence of sorption effects on the critical parameters of oscillatory convection is investigated by plotting the critical solutal Rayleigh-Darcy number, disturbance frequency and wave number against the adsorption coefficient at fixed values of the desorption coefficient. The isolines of the stream function are constructed to analyze convective flow patterns. It was established that there is a weak relationship between the typical size of local convective roll patterns and the clogging parameters. It is shown that the sorption processes, which can lead to clogging, have a significant impact on the velocity of convective rolls moving along the two-layered system at a slight variation in their sizes.

Cadmium and copper transport in alluvial soils in the Brazilian semiarid region: column percolation and modeling

ABSTRACT Regarding the Brazilian textile industry, part of the northeast region stands out as the second-largest textile manufacturing hub in the country. Despite its importance, this industrial activity has been bringing relevant environmental concerns regarding the disposal of textile effluents, especially from industrial laundries. This waste contains many chemicals and among them are various types of heavy metals. To assess environmental risks associated with heavy metals, pollutant transfer needs to be investigated. This study evaluated the retention and mobility of heavy metals Cd and Cu in alluvial soil, through soil column tests. The up-flow column percolation tests were performed using a nonreactive tracer (KBr) at a concentration of 0.3 mol L -1 and injecting a metallic solution containing Cu and Cd at 100 and 60 mg L -1 , respectively. The injection flow rate was 0.75 mL min -1 . The hydro-dispersive parameters were obtained by modeling the observed breakthrough curves with the convection-dispersion equation (CDE) and the two-region model, also referred to as the MIM (Mobile-IMmobile waters) model. The transport parameters were obtained from the two-site model (TSS). All elution curves were fitted to the models with the CXTFIT 2.0 program. The Two-Site Sorption Model was the best for the case studied, with R 2 of 0.985 and 0.995 for Cu and Cd, respectively. The values of R were considerably higher than the unit, presenting an average of 2.138 for Cu and 1.907 for Cd. This indicates a delay of these contaminants when leaving the column, which is caused by the interaction of these chemical compounds with the soil. The values obtained for parameter D were 3.469 for Cu and 5.205 for Cd. Thus, the metals in this study present a risk of groundwater contamination for the local alluvial aquifers. The main reason for that is the physicochemical features of the soil, such as high sand content (85 %) and low OM content (2.1 %). The results also indicated greater retention and less mobility for Cu than for Cd, pointing to a greater risk for Cd.

Precipitation forecasting with radar echo maps based on interactive spatiotemporal context with self-attention and the MIM model

ABSTRACT A sequence of radar echo maps can visually show the motion and variation trends of the echo area, making it a common tool for precipitation forecasting. The spatiotemporal context reveals the correlations of variation trends among different parts within the echo area. This paper proposes a novel precipitation forecasting model, ISTC-SA-MIM (Interactive Spatiotemporal Context Learning with Self-Attention and Memory in Memory), based on the MIM. Leveraging the spatiotemporal interactions and self-attention mechanism of the ISTC-SA structure, the proposed model effectively captures both long-term and short-term spatiotemporal contexts. By memorizing the spatiotemporal context and non-stationary information, ISTC-SA-MIM can accurately predict the motion and variation trends of the echo area. Radar echo data from the Qingdao station are collected as the dataset to evaluate the commonly used spatiotemporal models and ISTC-SA-MIM. The experiments demonstrate that ISTC-SA-MIM can predict the variation trends of the echo area more accurately by learning the spatiotemporal context.

Уточнение модели концентрационной конвекции в пористой среде с учетом иммобилизации примеси и слабой закупорки

The influence of weak clogging on the process of a heavy impurity transport through a horizontal layer of a porous medium is studied. A constant concentration drop is set at the boundaries of the layer, the flow along the layer is maintained by a constant pressure drop. The present problem is a concentration analog of the well-known Horton-Rogers-Lapwood (HRL) problem. The equations describing the transport of the impurity taking into account the deposition (immobilization) of the impurity particles on the porous skeleton are obtained. The deposition process is described in the framework of the well-known linear sorption model (linear MIM model). Clogging is assumed to be weak in the sense that the influence of deposited particles on porosity is considered to be negli-gible and is taken into account only with respect to the reduction of the permeability of the medi-um. It is found that the basic solution to this system admits the regime of stationary filtration along the layer. In this case, the impurity distribution is linear, which coincides with the known HRL so-lution. The stability of the basic state is analyzed numerically. Neutral curves as well as minimum values of critical parameters (Rayleigh-Darcy number, wave number, and frequency) depending on the system parameters are obtained and analyzed. It is shown that the arising instability, as in the HRL problem, is oscillatory by nature. Taking into account the clogging (along with taking into ac-count the deposition) leads to an increase in the stability of the stationary filtration flow and attenu-ation of the oscillations. The study determines the limits of applicability of the linear MIM model, widespread in the literature, that does not taking into account the clogging.

Mass Transfer from Mobile to Immobile Regions in Irregularly Shaped Micro-Channels at Low Reynolds Number.

Transient mass transfer in rough-walled micro-channels was investigated experimentally. We conducted experiments using rough-walled channels with various irregularities at small Reynolds number conditions. Mass transfer in the mainstream (mobile region) and dead water region (immobile region) were quantified using an image analysis technique based on absorption photometry. The experimental results showed that the solute dispersion in the mobile region was influenced by the irregular shape of the channel wall complicatedly. In contrast, mass transfer in the immobile region occurred by molecular diffusion independently on the wall roughness in our experimental conditions. The irregular shape of channel wall may enhance the mass transfer in mobile region by distorting the velocity distribution (Togi et al., 2020), while the solute redistribution to immobile region may suppress it in streamwise direction, just on a longer time scale. We developed a mass transfer model analogous to Mobile-Immobile model (MIM model) proposed by previous studies. The concept of the model is the same as the previous study (Zhou et al., 2019) and the coefficients of the model describing mass transfer in each region were quantified from the experimental results as functions of geometric characteristics of the rough-walled channel. In addition, mass transfer coefficient from mobile to immobile regions were derived mathematically based on the experimental results. The MIM model with the coefficients derived in this study well describes solute dispersion in variously shaped irregular channels quantitatively.

Numerical modeling of solute convection in the system of two porous layers with different permeabilities

The numerical simulation of the dynamics of a liquid with solute of high concentration in two horizontal layers of a porous medium with different permeability coefficients is carried out. The dynamics of the solute is modeled within the framework of a nonlinear MIM model that takes into account the adhesion and separation process at the skeleton of a porous medium. The modeling was carried out in a two-dimensional setting. The mobile (moving together with the carrier fluid) and immobile (deposited on the skeleton) phases are modeled by the finite volume method with adaptive mesh refinement algorithm. At each point in space, functions of volumetric saturation are set, and a kinematic equation is solved that describes the dynamics of adhesion and separation. The effective permeability of a porous medium depends on the saturation function of the immobile phase and is calculated using the Kozeny-Karman formula. The obtained numerical data are compared with the results of a linear analysis of stability, and the nonlinear regimes of concentration convection and the distribution of impurities at high supercriticalities are studied. In the case of high ratio of permeability coefficients of upper and lower layers, convection occurs locally in a more permeable sublayer, even with a decrease in its thickness. With an increase in supercriticality the penetration of the convective flow into the poorly permeable sublayer and the transition from local convection to large-scale convection are observed.

Onset of solutal convection in layered sorbing porous media with clogging

The effect of pore clogging on the onset of solute-driven convection in a layered sorbing porous medium consisting of two sublayers with distinct permeabilities is investigated. Solute transport in the medium is described by the nonlinear MIM model involving the Langmuir equation. The solute is divided into two phases. The first one is a mobile phase that drifts with flow and the second one is an immobile phase captured by porous matrix and reducing the total pore space. The model takes into account the saturation concentration, which is a maximal possible amount of solute adsorbed by a unit volume of porous medium. The degree of pore clogging is determined through a clogging coefficient proportional to the saturation concentration. Another coefficient is a sorption parameter including the ratio of adsorption and desorption rates. By varying these coefficients, we obtain the threshold solutal Rayleigh–Darcy number for the onset of convection in the following three types of layered sorbing systems: (1) system with the upper thin highly permeable sublayer, (2) system with the lower thin highly permeable sublayer, and (3) system with equal thick sublayers. The results show that convection onset delays due to the enhancement of clogging effect in all of the three systems. It is more difficult to induce convection here because the pore plugging together with an increase in adsorption rate as compared to desorption rate reduces the mean porosity and permeability of porous matrix. Forward and reverse transitions between the critical convective rolls with different wavelengths are found to occur in the systems 1 and 2 containing the upper or lower thin highly permeable sublayers as the sorption parameter increases. A sequence of “local convection – large-scale convection – local convection” transitions is observed in system 1. There is an opposite sequence of “large-scale convection – local convection – large-scale convection” transitions in system 2. The preferred convective roll width at the onset of convection changes by almost fifth times at the described forward and reverse transitions. It roughly corresponds to the ratio of the total thickness of porous system to that of the thin highly permeable sublayer where local convection generates.

Numerical Simulation for a Fractal MIM Model for Solute Transport in Porous Media

A fractal mobile-immobile (MIM in short) model for solute transport in heterogeneous porous media is investigated from numerics. An implicit finite difference scheme is set forth for solving the coupled system, and stability and convergence of the scheme are proved based on the estimate of the spectral radius of the coefficient matrix. Numerical simulations with different parameters are presented to reveal the solute transport behaviors in the fractal case.

Solutal convection in a horizontal porous layer with clogging at a high solute concentration

The authors study the transport of solute particles in a horizontal layer of a porous medium taking into account the clogging process for a wide range of solute concentrations. On the basis of the most popular and experimentally confirmed MIM model with saturation of the immobile phase, a closed equation system describing such transport is derived. The concentration dependence of porosity is described within the Kozeny-Carman model. The criteria for the transition to the popular model of weak clogging, when the solute concentration is significantly lower than the porosity of the medium, are considered. It is shown that the basic state for the model does not correspond to the classical linear distribution of mobile solute. The convective instability of horizontal seepage with respect to two dimensional perturbations is studied. The critical curves in the space of problem parameters are obtained.

Transport through the array of vortices: from microscopic model to macroscopic transport with immobilization

The paper is devoted to the study of longitudinal solute transport through an array of vortices, bounded by rigid walls. Since the fluid velocity in such system is very heterogeneous, the transfer of solute particles has non-trivial properties. Some particles can flow into the vortex driving by diffusion. These particles do not move in a longitudinal direction. As a result, the observed transport process is similar to the transport with immobilisation. It allows dividing the full solute concentration to mobile and immobile by analogy to the MIM approach. Mobile solute transports with the mean flow in a longitudinal direction. The immobile solute is immobilized by the vortices. The solute transition between these two phases is provided by the diffusion and determines by the concentrations in both phases. The MIM approach is used very often for modelling the transport in porous media. Usually, the particle immobilisation in porous media is explained by the interaction of solute particles with a solid matrix of porous media. However, the flow through porous media is complex and vortices are formed by the interaction of flow with the solid matrix of media. We model the transport of initially heterogeneous distributed solute through the channel by the flow with vortices. The modelling is performed into the terms of special flow by the microscopic methods. The distribution of passage time is compared for the same distribution obtained by standard linear macroscopic MIM model. The comparison is performed by the solution of the inverse problem with minimization the difference between these two distributions. As a result, the parameters of the linear MIM model is defined and its dependence on the vortices structure and the molecular diffusivity is obtained.

Modelling of Transportation Process in Plane Flows with Stagnation Points

We study transport of passive tracers by plane laminar flows with stagnation points. This setup serves as a simple model of transport in porous media. Close to stagnation points, the flow velocity is much lower than on the average. Many experimental data disclose that transport through porous media is slower than predictions of the standard advection-diffusion model. Commonly, in descriptions of flows through porous media the heterogeneity of flow is disregarded, and some average velocity is adopted. To model regular arrays of flow patterns with stagnation points, we employ the construction of special flow: a combination of mapping and a sort of ceiling function with singularity. We show that, depending on the type of stagnation points, many experimentally established effects can be reproduced. This includes the linear sorption, usually described by the standard MIM model, as well as subdiffusion, described by the fractional MIM model. We also show that slow molecular diffusion does not eliminate the effects of the transport slowdown.

Нелинейные сорбционные эффекты при прокачке наножидкости через пористую среду

Filtration process of a nanofluid with particles size less than 100 nm through a porous medium is analyzed theoretically on the base of direct numerical simulation. Mathematical description of this process is fulfilled using the MIM model and Darcy's law, which are modified to take into account the nonlinear reverse reaction of sorption properties of the material on the intensity of pore velocity. A new parameter, which characterizes this nonlinearity, is introduced into the model. In fact, it represents the value of critical velocity for particle separation from the pore walls by the flow. The values of permeability and porosity decrease in dependence on time during the saturation of porous medium with nanoparticles. These parameters are related with each other by the Kozeny–Carman equation. The results of calculations show that the variation of the critical velocity for particle separation significantly affects on the dynamics of redistribution of the mobile and immobile impurity in porous material.

The motion of the concentration front and adsorption of impurity during pumping of a nanofluid through a porous medium

The direct numerical simulation of the process of filtering a nanofluid through a porous medium of artificial origin is performed. The phenomenon of pore plugging due to the adsorption of nanoparticles on the walls of the channels is investigated. The theoretical study was initiated by the necessity to improve the technological process of saturation of porous materials by powdery media with desired properties. The description of the filtration process is based on Darcy's law with consideration for the variability of porosity and permeability of the medium, which are related by the Kozeny-Carman formula. The model takes into account the non-linear effect of the backward response to pore plugging, which lies in the fact that the filtration rate essentially decreases causing thereby the enhancement of impurity absorption. Based on the method of finite differences, an algorithm for solving the problem is constructed, and a program code for describing the process of penetration of the suspension into a rectangular sample is developed. The results of numerical simulation are used to plot the fields of velocity, pressure, porosity, permeability, and concentrations of mobile and immobile impurities, which make it possible to trace the dynamics of the filtration process. The obtained numerical results support the observation that the main factor contributing to the flow pattern and pore plugging is the nonlinear interaction between the nanofluid flow and porous material. It is shown that the change in the distribution of immobile impurity in a porous medium is determined by the dynamics of the concentration front, the steepness and speed of which depends on the ratio of the problem parameters (parameters of adsorption-desorption, diffusion coefficient, permeability and pressure difference at the inlet and outlet of the porous material. The results of problem solution obtained within the framework of the advanced MIM model from the beginning of the process to complete pore plugging are used to estimate the time of the technological process, which is found to be in good agreement with experimental data on the saturation of artificial porous materials.

Roles of PIP2 in the membrane binding of MIM I-BAR: insights from molecular dynamics simulations.

In order to probe the roles of PIP2 in the interactions between MIM I-BAR and model membranes, we performed a series of 10 μs-scale coarse-grained molecular dynamics simulations. Our results indicate that PIP2 plays predominant roles in the membrane binding of MIM I-BAR in a concentration-dependent manner and via electrostatic interactions. Besides, we find that the occurrence of the membrane curvature may induce the re-distribution of lipids in the membrane and result in the local enrichment of PIP2 at negatively curved membrane areas. Combining these roles of PIP2 in the membrane binding of MIM I-BAR helps explain how MIM I-BAR senses negative curvature and, thus, contributes to maintaining membrane protrusions.

Estimación de parámetros hidrodinámicos en un acuífero volcánico libre fracturado en Cosa Rica. Parte II. Modelo de doble porosidad

En este trabajo se aplicó el modelo de transporte MIM 1D para simular de manera satisfactoria el comportamiento asimétrico observado en las curvas de llegada de tres ensayos de trazador en condición de gradiente natural realizados en un acuífero libre desarrollado en lavas fracturadas. Los parámetros de transporte obtenidos a partir del empleo de un programa de computador (que permitió ajustar los datos de campo con una curva teórica), sugieren que solamente el 50% de la porosidad total contribuyó efectivamente al transporte advectivo-dispersivo (fracción móvil), y que el otro 50% se comportó como un reservorio transitorio para el trazador (fracción inmóvil), siendo liberado o transferido hacia la fracción móvil de manera gradual. Los valores de los parámetros representativos del modelo MIM obtenidos en este trabajo, así como las propiedades hidráulicas estimadas para el acuífero se encuentran dentro del rango de valores reportados por otros autores. Esto es, a pesar de las limitaciones en la cantidad y calidad de información de campo disponible fue posible establecer un marco conceptual y numérico para explicar la asimetría observada en los tres ensayos.

A Non-Linear Model for Solute Transport, Accounting for Sub-diffusive Concentration Decline and Sorption Saturation

Solute transport in porous media is very often complicated by solute immobilization on a solid matrix of porous media. Usually, immobilization is accounted by the mobile/immobile media approach (MIM). However, solute immobilization is very complicated phenomena with a variety of specific features. Therefore, in the literature there have been a lot of specific MIM-type models. Usually each model is constructed for to account one specific feature. Examples are the power decline of concentration in the large time limit at small concentration and the limitation of the immobilization process at high concentrations. Both effects have been evidenced by experiments. The present paper develops a hybrid nonlinear fractional MIM model potentially able to describe the above two features. A step-by-step process of constructing the nonlinear fractional MIM model is presented, and the main properties of the new model are discussed. Two limiting cases describe power law decline and sorption saturation have predicted by the new model equations. Numerical simulations illustrate limiting cases and the capabilities of new nonlinear fractional model.

Compost Effect on Diuron Retention and Transport in Structured Vineyard Soils

ABSTRACT Diuron is frequently detected in surface- and groundwater under the vineyards, where organic amendments are often used, in Burgundy of France. Undisturbed column experiments were conducted to study the influence of three composted organic amendments on diuron leaching through columns of two vineyard soils from Vosne-Romanee (VR, calcareous Cambisol) and Beaujolais (Bj, sandy Leptosol), France. Bromide (used as non-reactive tracer) and diuron breakthrough curves (BTCs) were analyzed using convectivedispersive equation (CDE), two-region (mobile-immobile, MIM) and two-site models. No influence of the composts was observed on the bromide recovery rates. The CDE model described well the bromide BTCs for all columns of the Bj soil and seven of the VR soil, suggesting a homogeneous water flow. However, for five VR soil columns, the MIM model fitted better, suggesting a partition of the water flow (15%–50% of matrix flow). The texture, the coarse material content and the tillage of the VR soil could explain this heterogeneity. However, for all columns, diuron leaching was greater through the Bj soil (46%–68%) than the VR soil (28%–39%). The compost addition resulted in a contrasting effect on diuron leaching: no difference or a decrease was observed for the VR soil, probably due to an increase of adsorption sites, whereas no difference or an increase was observed for the Bj soil possibly because of interactions and/or competition of diuron with the compost water-extractable organic matter which could facilitate its transport. All the diuron BTCs were best described using the two-site model, suggesting a large proportion of time-dependent sorption sites (30%–50%). The soil type and the nature of the amendments had contrasting influences on diuron transport. Composts with a high water-soluble fraction must be avoided in sandy soils to reduce the risk of groundwater contamination.

A reservoir model of tracer transport for karstic flow systems

A reservoir approach to analyzing tracer transport in steady-state karstic groundwater systems is evaluated. Tracer transport is dictated by a central flow system made up of a series of reservoirs or pools. These reservoirs may also have a ‘side capacity’ that represents less integrated hydraulic features that act to delay tracer as it moves through the system. The composite system results in a relatively extended tracer signal following a rapid first arrival, a behavior often observed in tracer experiments performed in karst. The reservoir model is an alternative to the often-used advection-dispersion model augmented with a first-order exchange between mobile and immobile fractions of the flow system (the MIM model). A well-known field tracer test is revisited using both the reservoir and MIM approach. The reservoir model indicates that ‘immobile’ zones actually represent only a small delay in tracer transport, but these delays, in sum, lead to a significant tail on the breakthrough curve. It is suggested that a reservoir analysis of tracer breakthrough in karst systems may be more relevant to physical descriptions of karstic groundwater systems than models such as MIM, which are based upon solute transport in porous media.

Effect of a nonwoven geotextile on solute and colloid transport in porous media under both saturated and unsaturated conditions

Geotextiles are thin polymeric materials widely used in geotechnical, environmental and hydraulic applications. They are employed in infiltration basins designed to collect and improve the quality of storm and runoff waters before their infiltration into the surrounding soil. The introduction of geotextiles in the subsoil of infiltration basins may significantly influence the flow and transfer of pollutants present in storm and runoff waters in solute form or associated with colloidal and particulate phases. The objective of this work was to study the influence of a nonwoven geotextile on conservative solute and colloidal transport through sandy and gravel porous media under both saturated and unsaturated conditions. Solute and colloid transport through columns containing soil amended with a geotextile were characterized by injecting a tracer solution and a suspension of colloidal particles at a constant flow rate under saturated and unsaturated conditions. The flow pattern was described using a MIM model implemented with the HYDRUS 1D code. The results showed that nonwoven geotextiles can increase flow homogeneity. Their effect on flow homogenization depended on soil heterogeneity and the degree of water saturation. Colloidal retention efficiency at column scale was also modified by the presence of geotextiles. By homogenizing flow they increased the filter capacity of the soil, thereby decreasing the pollutant transfer in colloidal form.