Advective Transport Model Research Articles

Predicting the Timing of the Solar Cycle 25 Polar Field Reversal

The process of the Sun’s polar field cancellation reversal commences with the emergence of new cycle Hale’s polarity active regions. Once the Sun undergoes polarity reversal, typically occurring near the peak of solar activity, it begins the process of accumulating the seed field for the forthcoming solar cycle. In recent years, the advective flux transport (AFT) model has proven highly effective in forecasting the progression of polar fields by leveraging observations of surface flows and magnetic flux emergence. In this study, we make use of the predictive capability of the AFT model to simulate the evolution of the polar fields and estimate the timing of the Solar Cycle 25 polarity reversal in both hemispheres of the Sun. We use the statistical properties of active regions along with Solar Cycle 13, which closely resembles the current solar cycle (Cycle 25), to generate synthetic active regions in order to simulate future magnetic flux emergence in AFT to predict the evolution of the polar field. Based on our simulations, we anticipate that the northern hemisphere of the Sun will undergo a polarity reversal between 2024 June and November, with the center of our distribution at 2024 August. In the southern hemisphere, we anticipate a polarity reversal between 2024 November and 2025 July, centered around 2025 February. Additionally, assuming that the reversal of the axial dipole moment coincides with the peak of the solar cycle, our findings indicate that Cycle 25 is expected to peak in 2024 (likely between 2024 April and August).

A 3D diffusive and advective model of electron transport applied to the pulsar wind nebula HESS J1825 − 137

ABSTRACT HESS J1825 − 137 is one of the most powerful and luminous TeV gamma-ray pulsar wind nebulae, making it an excellent laboratory to study particle transportation around pulsars. We present a model of the (diffusive and advective) transport and radiative losses of electrons from the pulsar PSR J1826 − 1334 powering HESS J1825 − 137 using interstellar medium gas (ISM) data, soft photon fields, and a spatially varying magnetic field. We find that for the characteristic age of $21\, \mathrm{k}\mathrm{yr}$, PSR J1826 − 1334 is unable to meet the energy requirements to match the observed X-ray and gamma-ray emission. An older age of $40\, \mathrm{k}\mathrm{yr}$, together with an electron conversion efficiency of 0.14 and advective flow of v = 0.002c, can reproduce the observed multiwavelength emission towards HESS J1825 − 137. A turbulent ISM with magnetic field of $B=20 \,{\rm to}\, 60 \,\mathrm{\mu }{\rm G}$ to the north of HESS J1825 − 137 (as suggested by ISM observations) is required to prevent significant gamma-ray contamination towards the northern $\mathrm{T}\mathrm{e\mathrm{V}}$ source HESS J1826 − 130.

Impact of velocity correlations on longitudinal dispersion in space-Lagrangian advective transport models

Space-Lagrangian random walk models conceptualize advective transport in heterogeneous media in terms of collections of particles undergoing fixed-length steps along flow streamlines. We study the impact of velocity correlation structure on longitudinal dispersion for different point velocity statistics. We find that asymptotic equivalence requires the step length of an uncorrelated continuous time random walk to be higher than the correlation length when velocity correlations decay exponentially with distance. We characterize the conditions for equivalence for broad classes of velocity distributions.

Groundwater heat transfer and thermal outflow plume modelling in the Alps

Thermal water discharge within the gravity-driven groundwater flow system in the Alps and other similar areas around the world may be hidden in Quaternary deposits which, in these regions, often cover the regional aquifer. When thermal water drains into Quaternary deposits, the mixing of the deep thermal component and the cold shallow groundwater forms a thermal plume that extends parallel to the main groundwater flow in shallow system. In the Bled case study in Slovenia, the thermal water discharges from carbonate rocks into Quaternary glaciofluvial sediments, and as the Toplice spring at a rate of 5 l/s at an average temperature of 21.5 °C. Knowing the spatial extent and intensity of thermal outflow is essential to decision making related to the development and protection of this renewable resource. By approximating the thermal water outflow from a discharge zone as a planar source, a planar advective heat transport model can be used to evaluate its geometry and quantify rates. An analytical procedure follows rough assumptions leading to conservative results. Moreover, a numerical model using the FEFLOW code was applied for comparison with the simulations of the analytical model. The heat transport model was based on measured hydraulic parameters (e.g. groundwater levels) and borehole temperatures as well as on-site and international literature (e.g. dispersivity, thermal conductivity). Nine scenarios were applied accounting for different dimensions of the heat source and compared to the results of numerical simulations. Each scenario was verified by calculating the relative error between the analytical models and the measured borehole temperatures. The results confirm that the main outflow of thermal water can be determined using planar geometry, and is 200–300 m wide. The height of the thermal outflow zone is approximately 25 m, corresponding to the expected thickness of the direct contact between the fractured dolomite and the shallower Quaternary aquifer. Using the proposed widths and depths, the hidden natural thermal outflow rates are estimated at 57–86 l/s.

Quantification of a subsea CO2 release with lab-on-chip sensors measuring benthic gradients

We present a novel approach to detecting and quantifying a subsea release of CO2 from within North Sea sediments, which mimicked a leak from a subsea CO2 reservoir. Autonomous lab-on-chip sensors performed in situ measurements of pH at two heights above the seafloor. During the 11 day experiment the rate of CO2 release was gradually increased. Whenever the currents carried the CO2-enriched water towards the sensors, the sensors measured a decrease in pH, with a strong vertical gradient within a metre of the seafloor. At the highest release rate, a decrease of over 0.6 pH units was observed 17 cm above the seafloor compared to background measurements. The sensor data was combined with hydrodynamic measurements to quantify the amount of CO2 escaping the sediments using an advective mass transport model. On average, we directly detected 43 ± 8% of the released CO2 in the water column. Accounting for the incomplete carbonate equilibration process increases this estimate to up to 61 ± 10%. This technique can provide long-term in situ monitoring of offshore CO2 reservoirs and hence provides a tool to support climate change mitigation activities. It could also be applied to characterising plumes and quantifying other natural or anthropogenic fluxes of dissolved solutes.

New perspectives on the use of 224Ra/228Ra and 222Rn/226Ra activity ratios in groundwater studies

The naturally occurring Ra isotopes (223Ra; T1/2 = 11.4 d, 224Ra; T1/2 = 3.66 d, 226Ra; T1/2 = 1,600 y, and 228Ra; T1/2 = 5.7 y) and Rn (222Rn; T1/2 = 3.82 d) have been widely applied as environmental tracers. The application of these radioactive tracers has mainly been restricted to the evaluation of oceanographic and land-ocean interaction processes, although in recent years their use has also been extended to the study of groundwater systems. In this context, the activity ratios of 224Ra/228Ra and 222Rn/226Ra can be instrumental in providing key information on groundwater transit times in aquifers and those processes governing groundwater discharge into the coastal sea (often referred to as Submarine Groundwater Discharge or SGD). This work evaluates the potential use of these activity ratios as proxies for investigating groundwater systems through an advective transport model that integrates the radionuclides involved in these activity ratios (224Ra, 228Ra, 226Ra, and 222Rn) and their immediate parents into a single formulation. The results provided by the transport model indicate that the main factors controlling the 224Ra/228Ra and 222Rn/226Ra activity ratios are the alpha recoil supply, the retardation factor of Ra, and the groundwater transit times. The advective transport model and the activity ratios are used to present novel applications that interrelate the disciplines of hydrogeology and coastal oceanography. The main applications include the determination of groundwater transit times and the assessment of pathways and end-members related to submarine groundwater discharge processes. These applications were tested in a Mediterranean coastal aquifer.

Hydrogeological characterization and parameters estimation of the aquifer close to the Adige River (Verona, Italy) for the design of deep excavations

In the framework of the final design of a new hydroelectric plant close to the existing dam on the Adige River in the municipality of San Giovanni Lupatoto (VR, Italy), the design of deep excavations in loose sediments below groundwater level, and the connected risks of piping and excavation bottom heave required a detailed study of hydrogeological characterization, aimed to an accurate aquifer parameterization and so a confident design of excavation supports and dewatering systems. Particularly a three-dimensional analysis of the problem was necessary, because the hydrogeological system was complicated by many “artificial” boundary conditions (dam on the river, deep foundations of the existing and new engineering works) causing vertical not negligible flow paths. The conceptual model has been developed applying, in parallel, different prospecting tools: a preliminary Step Drawdown Test, a long duration Constant Rate Test, a multiple tracing test and the implementation of a three-dimensional numerical model of groundwater flow (MODFLOW-2005 code) and advective transport (MODPATH code). The modeling has allowed a good estimate of the aquifer parameters such as hydraulic conductivity and effective porosity through calibration of the pumping/tracing tests under transient conditions. Moreover, the simulation of post operam conditions and the comparison with ante operam, in terms of flow paths length and filtration velocity, showed that the construction of the new works foundations would have determined a sensitive reduction of groundwater velocities closed to the existing dam.

Estimation of effective porosity in large-scale groundwater models by combining particle tracking, auto-calibration and <sup>14</sup>C dating

Abstract. Effective porosity plays an important role in contaminant management. However, the effective porosity is often assumed to be constant in space and hence heterogeneity is either neglected or simplified in transport model calibration. Based on a calibrated highly parametrized flow model, a three-dimensional advective transport model (MODPATH) of a 1300 km2 coastal area of southern Denmark and northern Germany is presented. A detailed voxel model represents the highly heterogeneous geological composition of the area. Inverse modelling of advective transport is used to estimate the effective porosity of 7 spatially distributed units based on apparent groundwater ages inferred from 11 14C measurements in Pleistocene and Miocene aquifers, corrected for the effects of diffusion and geochemical reactions. By calibration of the seven effective porosity units, the match between the observed and simulated ages is improved significantly, resulting in a reduction of ME of 99 % and RMS of 82 % compared to a uniform porosity approach. Groundwater ages range from a few hundred years in the Pleistocene to several thousand years in Miocene aquifers. The advective age distributions derived from particle tracking at each sampling well show unimodal (for younger ages) to multimodal (for older ages) shapes and thus reflect the heterogeneity that particles encounter along their travel path. The estimated effective porosity field, with values ranging between 4.3 % in clay and 45 % in sand formations, is used in a direct simulation of distributed mean groundwater ages. Although the absolute ages are affected by various uncertainties, a unique insight into the complex three-dimensional age distribution pattern and potential advance of young contaminated groundwater in the investigated regional aquifer system is provided, highlighting the importance of estimating effective porosity in groundwater transport modelling and the implications for groundwater quantity and quality assessment and management.

Regionalization of Groundwater Residence Time Using Metamodeling

AbstractGroundwater residence‐time distributions (RTDs) are critical for assessing susceptibility of water resources to degradation. A novel combination of numerical modeling and statistical methods allows estimation of regional RTDs with unprecedented speed. In this method, particle RTDs are generated in 30 type locales in the northeastern glaciated U.S. by using automated generalized finite‐difference groundwater flow and advective transport models. Targets for statistical learning were created from particle RTDs by fitting Weibull, gamma, and inverse Gaussian distributions. Whole‐basin flux‐weighted RTDs were well fit by one‐component Weibull distributions. Flux‐weighted RTDs at stressed receptors such as wells often produced more complicated RTDs that required a two‐component mixture to fit. A Multitask LASSO regression was trained on the parametric RTDs using hydrogeographic features of the modeled areas as explanatory features. In this way, RTDs are regionalized with mappable physical features such as recharge and aquifer volume. The shape, location, and scale parameters of the parametric RTDs are strongly related to the mean exponential age. The shape parameter of the distribution, which controls deviation from exponential, is additionally a function of aquifer heterogeneity and hydrologic features. Regionalized RTDs provide useful metrics with respect to groundwater lag times and solute loading to streams. The lag time between input and output contained in the RTD is critical to understanding the relation between the land surface and human and ecological receptors.

An Updated Solar Cycle 25 Prediction With AFT: The Modern Minimum

AbstractOver the last decade there has been mounting evidence that the strength of the Sun's polar magnetic fields during a solar cycle minimum is the best predictor of the amplitude of the next solar cycle. Surface flux transport models can be used to extend these predictions by evolving the Sun's surface magnetic field to obtain an earlier prediction for the strength of the polar fields, and thus the amplitude of the next cycle. In 2016, our Advective Flux Transport (AFT) model was used to do this, producing an early prediction for Solar Cycle 25. At that time, AFT predicted that Cycle 25 will be similar in strength to the Cycle 24, with an uncertainty of about 15%. AFT also predicted that the polar fields in the southern hemisphere would weaken in late 2016 and into 2017 before recovering. That AFT prediction was based on the magnetic field configuration at the end of January 2016. We now have two more years of observations. We examine the accuracy of the 2016 AFT prediction and find that the new observations track well with AFT's predictions for the last 2 years. We show that the southern relapse did in fact occur, though the timing was off by several months. We propose a possible cause for the southern relapse and discuss the reason for the offset in timing. Finally, we provide an updated AFT prediction for Solar Cycle 25 that includes solar observations through January of 2018.

Analytical solutions for predicting thermal plumes of groundwater heat pump systems

Groundwater heat pump (GWHP) systems have gained attention for space heating and cooling due to their efficiency and low installation costs. Their number is growing in many countries, and therefore in some areas, dense installations are expected. This might lead to thermal interferences between neighbouring groundwater wells and a decrease in efficiency. In the presented study, three analytical formulations are inspected for the prediction of the thermal plume around such open-loop systems under various hydrogeological conditions. A thermal radial transport scenario without background groundwater flow and two advective scenarios with moderate to significant ambient flow velocities (1 and 10 m d−1) are analytically simulated and compared with numerical simulations. Two-dimensional (2D) numerical models are used to estimate the validity of analytical results for a homogeneous confined aquifer, without considering heat transfer in upper and lower layers of the aquifer. In order to represent more realistic aquifer conditions of limited vertical extension, an additional three-dimensional numerical model (3D) is deployed to account for vertical heat losses. The estimated relative errors indicate that the analytical solution of the radial heat transport is in good agreement with both numerical model results. For the advective scenarios, the suitability of the linear and planar advective heat transport models strongly depend on ambient groundwater flow velocity and well injection rate. For low groundwater velocities (1 m d−1), the planar model fits both numerical model results better than the linear advective model. However, the planar model's ability to estimate thermal plumes considerably decreases for high injection rates (>0.6 l s−1). In contrast, the linear advective model shows a good agreement with the two-dimensional numerical results for high groundwater flow conditions (≥10 m d−1). The comparison with the three-dimensional numerical models indicates that the vertical heat transfer is challenging for all of the selected analytical solutions. Despite this, there is a wide range of applicability for the provided analytical solutions in studying the thermal impact of GWHP systems. Hence, the inspected solutions prove to be useful candidates for first-tier impact assessment in crowded areas with potential thermal interferences.

Investigation of pore water residence times and drainage velocities in salt marshes using short-lived radium isotopes

Abstract Pore water residence times and drainage velocities were investigated in Jamaica Bay (NY, USA), a highly urbanized estuary in New York City where salt marsh degradation and loss has accelerated in recent years. Five different marshes were sampled for shallow (25 cm) and deep (≥ 50 cm) dissolved 224 Ra over a several year period. Pore water residence times were estimated using a one-dimensional advective transport model, assuming that the pore water 224 Ra grows into an equilibrium 224 Ra activity, and that flow is vertical. Equilibrium between dissolved 224 Ra and the marsh sediment was assessed with respect to solid-phase 228 Th, 228 Ra, reactive solid-phase Fe and Mn, all of which except Mn scaled as a function of grain size. Pore water 224 Ra and estimated residence times did not display any seasonality between the marshes. The shortest residence times were estimated for the highest elevation, fine-grained-sand marsh (1.4 ± 0.9 d at 25 cm), which has the highest percent vegetation cover. We hypothesize that the faster drainage velocity (25.9 ± 17.8 cm d − 1 at 25 cm) of this marsh, combined with a higher mean elevation above sea-level, together limit exposure of the marsh plants to the build-up of H 2 S, a phytotoxin, in the pore fluid from the spring through summer. In contrast, shallow pore water residence times were greater for marshes with a lower elevation above sea-level, from (3.9 ± 1.8) d to (9.2 ± 3.6) d, where sediments were finer-grained, and throughput fluxes of Fe and H 2 S were higher throughout spring and summer seasons. This work demonstrates the utility of 224 Ra as a tracer of salt marsh flow dynamics, and highlights the importance of sediment heterogeneity and marsh platform elevation on the dynamic geochemistry of salt marshes.

Application of 224Ra and 222Rn for evaluating seawater residence times in a tidal subterranean estuary

The length of time in which seawater circulates through the beach face and mixes with terrestrial groundwater will have a profound influence on the geochemical cycling of nutrient deliveries to surface waters through submarine groundwater discharge. The goal of this work is to utilize pore water measurements of 222Rn and Ra isotopes to evaluate the time-scale of tidal seawater circulation in a coastal bluff and a barrier beach subterranean estuary (STE) on Long Island, NY. Intertidal pore water profiles sampled monthly between 2014 and 2015 revealed distinct geochemical differences between the two sites that were driven by the primary hydrogeologic forcing mechanisms. The coastal bluff site was dominated by a large hydraulic gradient that drove terrestrial groundwater discharge, while the barrier beach site had saline pore waters and was physically controlled by tidal forcing mechanisms. These mechanisms resulted in notably different pore water radionuclide (222Rn, 223,224,226,228Ra) and trace metal (Fe, Mn, Ba) distributions in the STE. A one-dimensional advective transport model was applied to estimate the residence time of circulated seawater within the STE using measured radionuclide activities. There are inherent uncertainties within the model, set by the activity of deep groundwater that has mixed with the circulated seawater, the initial activity of seawater that infiltrated the coastal aquifer and the radionuclide production rates. Residence times generally increased with depth from 0.1 to ≥15d and were greater in the low tide well of the barrier beach (4.9±3.4d) compared to the coastal bluff (1.1±0.4d). Residence times were fairly constant over time within the coastal bluff STE but varied seasonally in the barrier beach STE, suggesting that the barrier beach may have not been in “steady-state.” Variable pore water residence times within the STE may have a profound effect on the cycling of carbon, nutrient and trace metal fluxes to the coastal ocean.

A travel time‐based approach to model kinetic sorption in highly heterogeneous porous media via reactive hydrofacies

AbstractWe present a semianalytical model for the transport of solutes being subject to sorption in porous aquifers. We couple a travel time‐based model of advective transport with a spherical diffusion model of kinetic sorption in nonuniform material mixtures. The model is formulated in the Laplace domain and transformed to the time domain by numerical inversion. By this, three‐dimensional transport of solutes undergoing mass transfer between aqueous and solid phases can be simulated very efficiently. The model addresses both hydraulic and reactive heterogeneity of porous aquifers by means of hydrofacies, which function as homogeneous but nonuniform subunits. The total exposure time to each of these subunits controls the magnitude of sorption effects, whereas the particular sequence of facies through which the solute passes is irrelevant. We apply the model to simulate the transport of phenanthrene in a fluvio‐glacial aquifer, for which the hydrofacies distribution is known at high resolution, the lithological composition of each facies has been analyzed, and sorption properties of the lithological components are available. Taking the fully resolved hydrofacies model as reference, we evaluate different approximations referring to lower information levels, reflecting shortcomings in typical modeling projects. The most important feature for a good description of both the main breakthrough and tailing of phenanthrene is the nonuniformity of the porous medium. While spatial heterogeneity of chemical properties might be neglected without introducing a large error, an approximation of the facies' composition in terms of a uniform substitute material considerably compromises the quality of the modeling result.

Mass-conservative reconstruction of Galerkin velocity fields for transport simulations

Accurate calculation of mass-conservative velocity fields from numerical solutions of Richards’ equation is central to reliable surface–subsurface flow and transport modeling, for example in long-term tracer simulations to determine catchment residence time distributions. In this study we assess the performance of a local Larson-Niklasson (LN) post-processing procedure for reconstructing mass-conservative velocities from a linear (P1) Galerkin finite element solution of Richards’ equation. This approach, originally proposed for a-posteriori error estimation, modifies the standard finite element velocities by imposing local conservation on element patches. The resulting reconstructed flow field is characterized by continuous fluxes on element edges that can be efficiently used to drive a second order finite volume advective transport model. Through a series of tests of increasing complexity that compare results from the LN scheme to those using velocity fields derived directly from the P1 Galerkin solution, we show that a locally mass-conservative velocity field is necessary to obtain accurate transport results. We also show that the accuracy of the LN reconstruction procedure is comparable to that of the inherently conservative mixed finite element approach, taken as a reference solution, but that the LN scheme has much lower computational costs. The numerical tests examine steady and unsteady, saturated and variably saturated, and homogeneous and heterogeneous cases along with initial and boundary conditions that include dry soil infiltration, alternating solute and water injection, and seepage face outflow. Typical problems that arise with velocities derived from P1 Galerkin solutions include outgoing solute flux from no-flow boundaries, solute entrapment in zones of low hydraulic conductivity, and occurrences of anomalous sources and sinks. In addition to inducing significant mass balance errors, such manifestations often lead to oscillations in concentration values that can moreover cause the numerical solution to explode. These problems do not occur when using LN post-processed velocities.

MAGNETIC FLUX TRANSPORT AND THE LONG-TERM EVOLUTION OF SOLAR ACTIVE REGIONS

With multiple vantage points around the Sun, STEREO and SDO imaging observations provide a unique opportunity to view the solar surface continuously. We use He II 304 A data from these observatories to isolate and track ten active regions and study their long-term evolution. We find that active regions typically follow a standard pattern of emergence over several days followed by a slower decay that is proportional in time to the peak intensity in the region. Since STEREO does not make direct observations of the magnetic field, we employ a flux-luminosity relationship to infer the total unsigned magnetic flux evolution. To investigate this magnetic flux decay over several rotations we use a surface flux transport model, the Advective Flux Transport (AFT) model, that simulates convective flows using a time-varying velocity field and find that the model provides realistic predictions when information about the active region's magnetic field strength and distribution at peak flux is available. Finally, we illustrate how 304 \AA\ images can be used as a proxy for magnetic flux measurements when magnetic field data is not accessible.

The major ion, 87Sr/86Sr, and δ11B geochemistry of groundwater in the Wyodak-Anderson coal bed aquifer (Powder River Basin, Wyoming, USA)

We developed a multicomponent, 1D advective transport model that describes the downgradient evolution of solute concentrations, 87Sr/86Sr ratios, and δ11B values in the Wyodak-Anderson Coal Bed (WACB) aquifer located in the Powder River Basin, Wyoming, USA. The purpose of the study was to evaluate the chemical vulnerability of groundwater to potential environmental change stemming from the extraction of coal bed methane and shale gas. Model calculations demonstrate that coupling between microbial activity and the dissolved carbonate system controls major ion transport in the WACB aquifer. The analysis of 87Sr/86Sr ratios further reveals the importance of ion-exchange reactions. Similarly, δ11B data emphasize the significance of pH-dependent surface reactions and demonstrate the vulnerability of the aquifer to the long-term acidification of recharge water.

Chemistry of groundwater discharge inferred from longitudinal river sampling

We present an approach for identifying groundwater discharge chemistry and quantifying spatially distributed groundwater discharge into rivers based on longitudinal synoptic sampling and flow gauging of a river. The method is demonstrated using a 450 km reach of a tropical river in Australia. Results obtained from sampling for environmental tracers, major ions, and selected trace element chemistry were used to calibrate a steady state one-dimensional advective transport model of tracer distribution along the river. The model closely reproduced river discharge and environmental tracer and chemistry composition along the study length. It provided a detailed longitudinal profile of groundwater inflow chemistry and discharge rates, revealing that regional fractured mudstones in the central part of the catchment contributed up to 40% of all groundwater discharge. Detailed analysis of model calibration errors and modeled/measured groundwater ion ratios elucidated that groundwater discharging in the top of the catchment is a mixture of local groundwater and bank storage return flow, making the method potentially useful to differentiate between local and regional sourced groundwater discharge. As the error in tracer concentration induced by a flow event applies equally to any conservative tracer, we show that major ion ratios can still be resolved with minimal error when river samples are collected during transient flow conditions. The ability of the method to infer groundwater inflow chemistry from longitudinal river sampling is particularly attractive in remote areas where access to groundwater is limited or not possible, and for identification of actual fluxes of salts and/or specific contaminant sources.

Analysis and Computation of the Pressure Field of Preatherosclerotic Transport in the Artery Wall

Prerequisite to atherogenesis is low-density lipoprotein (LDL) cholesterol transport from the blood into the artery wall across its endothelial cell (EC) lining. Whereas most EC junctions are tight enough to preclude LDL passage, some $({\approx}1/2000-6000)$ rare ECs have temporarily-widened junctions (typically ${\approx}10^{-5}$ of the problem's radial scale) that allow passage of large molecular aggregates like LDL. In a purely diffusive transport model, Laplace's equation describes the steady tracer profile throughout the two major subendothelial wall layers, connected by matching conditions. In a diffusive and transmural-pressure-driven advective transport model, Laplace’s equation describes the steady pressure distribution in the wall, whose gradient is proportional to the advecting velocity. Both problems yield the same boundary value problem that has mixed Dirichlet/ Robin boundary conditions. We construct a linear system of integral equations that approximates the series expansion coefficients o...

Field scale longitudinal dispersivities estimation in a karstic aquifer

To simulate contaminant advective transport it is required to provide dispersivity values to the models, values that are unknown in many cases. In this paper a methodology is presented to estimate longitudinal dispersivities at field scale, based on the monitoring of groundwater quality at an unconfined aquifer that is below a waste disposal site with no liners for groundwater protection, and by applying a one-dimensional advective transport model. Chloride was used as a tracer, which is known to be present in dump site leachates. As part of the results, an equation was obtained that relates longitudinal dispersivity against the observation scale for the unconfined karstic aquifer of Yucatan, Mexico. Some scenarios were employed for the longitudinal dispersivity estimation and for the solute transport simulation. In this way, a sensitivity analysis was performed to calculate the longitudinal dispersivities by varying the hydraulic conductivity and the hydraulic gradient. As a simulation exercise, a sensitivity analysis was also carried out to calculate the travel time that a particle would require to reach a certain distance depending on the longitudinal dispersivity value.