Numerical Mass Transport Model Research Articles

Degradation of the Lunar Surface by Small Impacts

The surfaces of airless bodies like the Moon are bombarded by a steady stream of small impactors that lead to erosion of the topography over time. However, the rate of degradation from small impacts, a key parameter in interpreting the ages of present-day lunar surface features, is not well constrained. Here we demonstrate, using a numerical mass transport model, that impact erosion is a nonlinear diffusion process, in contrast to past studies of crater degradation that have assumed that the downslope mass flux of ejecta is linearly proportional to hillslope gradient. Nonlinearity is a consequence of the asymmetric shape of ejecta blankets on sloped surfaces, and as a result, the degradation rate on steep slopes is over 40% greater than on nearly flat surfaces. Using measurements of the morphology and formation rate of small primary and secondary craters, the kilometer-scale lunar landscape diffusivity is computed and compared to the value inferred from topographic profiles of degraded craters. We show that the abundance of decameter-scale craters forming on the Moon over the past decade is consistent with small impacts dominating the erosion of the lunar landscape, but only if the primary size−frequency distribution remains steep down to the submillimeter scale.

Low‐Capacity Well Pairs for Treating Contaminated Groundwater in Homogeneous and Heterogeneous Aquifers

Groundwater remediation alternatives were simulated for homogeneous and heterogeneous aquifers with a numerical mass transport model. Low‐energy alternatives involved an injection–extraction well pair positioned along a downgradient linear transect. This transect was located 5 m from the contaminant plume and oriented perpendicular to the regional hydraulic gradient. Through numerous trials, for one homogeneous and three heterogeneous settings, the model identified an optimal spacing and minimum pumping rate for a well pair: (1) centered on the downgradient tip of the plume (best centered), and (2) anywhere along the downgradient transect (best overall). Results suggest that low‐energy well pairs are an effective means for containing and removing some contaminant plumes, and best‐performing configurations are generally not centered on the downgradient tip of the initial contaminant plume. ©2015 Wiley Periodicals, Inc.

Relative efficiency of multi-transect, non-pumped, reactive well networks for removing contaminated groundwater

Alternative networks of non-pumped wells filled with reactive media were evaluated for groundwater remediation capability. Wells were screened across the saturated zone of a simulated, unconfined aquifer with a heterogeneous hydraulic conductivity. A numerical mass transport model generated an initial contaminant plume and then simulated its movement through different networks of non-pumped wells. Two cases were investigated: (1) a linear transect of wells downgradient of the plume; and (2) a downgradient linear transect combined with a second linear transect crossing the plume's interior. Several simulations were conducted for each case to determine the smallest number of wells necessary to prevent the plume from traveling offsite. Case 2 required 11% more wells, but reduced cleanup time by 21%.

Natural attenuation with varying degrees of aquifer heterogeneity: Implications for groundwater monitoring

AbstractThis study evaluated the effect of heterogeneity in hydraulic conductivity on the tendency for contaminant plumes to attenuate via dilution, hydrodynamic dispersion, and molecular diffusion in simulated aquifers. Simulations included one homogeneous and four increasingly heterogeneous hydraulic conductivity fields. A numerical mass transport model generated an initial contaminant plume for each case; all initial plumes had the same mass. Next, the model simulated plume migrations through the simulated aquifers. Results suggest that highly heterogeneous settings are potentially effective at plume attenuation. Low‐velocity zones in heterogeneous settings delay plume travel, enabling more time for natural processes to lower contaminant concentrations in groundwater. © 2012 Wiley Periodicals, Inc.

Numerical modeling of mass transport in microfluidic biomolecule-capturing devices equipped with reactive surfaces

This paper presents and compares three different designs including open-channel, circular-pillar and screen-plate microreactors for capturing and detection of biomolecules in a buffer liquid. In general, these capturing/detection devices consist of a flow cell containing one or several reactive surfaces loaded with ligand molecules. The critical issue in the design of an efficient device is the proximity of the biomolecules to the ligands in the capturing stage since the latter is immobilized on the reactive surface and the former is freely moving in the flow. The flow pattern and the geometry of the device are the key factors in this regard. The presented designs are numerically modeled and compared in terms of capture efficiency. Immersed biomolecules are assumed to behave like a continuum medium. The Navier-Stokes and convection–diffusion equations are solved in two dimensions and the concentration profile is obtained after a certain sampling period. The chemical reaction between the ligand and the biomolecule is included in the model through solving the reversible kinetic equation at the boundaries. Considering the level of performance, and ease of implementation, the screen plates are found to be the favourable option for the purpose of biomolecule removal. The effects of the change in the geometric parameters (i.e., the number of plates and reactive side preference) and physicochemical parameters (i.e., the diffusion constant, ligand surface density, and forward and backward reaction rates all combined in non-dimensional numbers) on the capture efficiency of the screen plates are thoroughly inspected and the corresponding results are plotted.

Containment of groundwater pollution (methyl tertiary butyl ether and benzene) to protect a drinking-water production site in Belgium

The subsurface migration of methyl tertiary butyl ether (MTBE) and benzene towards a drinking-water production site in Belgium was monitored for 9 years. A large gasoline spill at a nearby fuel station had caused a 500-m long and 50-m-wide pollution plume of MTBE (10−30 mg/L) and benzene (2−10 mg/L). In order to prevent any intrusion of pollutants into the drinking-water supply, a conceptual model was used to design a pump-and-treat system that intercepted the gasoline-contaminated groundwater emanating from the spill. The contaminated soil in the spill zone was excavated. A numerical mass transport model was developed to evaluate the ongoing plume containment. The model describes the subsurface MTBE migration and was regularly updated, based on groundwater monitoring data and the measured mass of MTBE extracted with the pump-and-treat system. With continued interception pumping, the MTBE plume can be remediated in 14 years. Without it, MTBE and benzene concentrations up to 600 μg/L could have reached the drinking-water production site and the plume would persist for 9 years longer. Source zone treatment combined with plume interception pumping is a suitable risk-based remediation strategy for the containment of MTBE and benzene groundwater pollution.

Configuring passive wells with reactive media for treating contaminated groundwater

AbstractPassive (nonpumped) wells filled with reactive media may be an effective alternative to permeable reactive barriers for treating contaminated groundwater in deep aquifers. This study's objective was to evaluate alternative passive well configurations for treating contaminated groundwater in a simulated aquifer. Six configurations of 17 wells were tested, each well screened across the saturated zone. Passive wells occupied various locations on monitoring transects. Five configurations involved one or more monitoring transects perpendicular to regional groundwater flow, positioned downgradient of a contaminant plume. In a sixth configuration, monitoring transects were ±45° to groundwater flow, joined downgradient of the contaminant plume. A numerical mass transport model, accounting for advection and hydrodynamic dispersion, tested the ability of each passive well configuration to reduce contaminant concentrations and prevent offsite contaminant migration. For a fixed number of wells, relatively effective strategies include: (a) spanning the lateral width of a contaminant plume; (b) multiple monitoring transects, with relatively close well spacing along upgradient transects; and (c) 45° monitoring transects. Overall, the 45° structure was most effective. © 2008 American Institute of Chemical Engineers Environ Prog, 2008

Performance assessment of hanging funnel‐and‐gate structures designed by reverse particle tracking for capturing polluted groundwater

AbstractThe objective of this study was to evaluate the capability of partially penetrating (hanging) funnel‐and‐gate structures, designed using reverse flow trajectories, for capturing plumes of contaminated groundwater. Linear capture structures, comprised of two slurry cutoff walls on either side of a permeable gate, were positioned perpendicular to regional groundwater flow in a hypothetical unconfined aquifer. A four‐step approach was used for each of two simulated settings: (1) a numerical mass transport model generated a contaminant plume originating from a source area; (2) a particle‐tracking model projected groundwater flow paths upstream from a treatment gate; (3) the structure was widened and deepened until bounding path lines contained the plume; and (4) mass transport simulation tested the ability of the structure to capture the plume. Results of this study suggest that designing funnel‐and‐gate structures using reverse particle tracking may result in too small a structure to capture a contaminant plume. This practice generally ignores effects of hydrodynamic dispersion, which may enlarge plumes such that contaminants move beneath or around a capture structure. This bypassing effect may be considerable even for low values of dispersivity. Particle‐tracking approaches may also underestimate the amount of time required to reduce contaminant concentrations to acceptable levels. © 2007 Wiley Periodicals, Inc.

A Boltzmann-based mesoscopic model for contaminant transport in flow systems

The objective of this paper is to demonstrate the formulation of a numerical model for mass transport based on the Bhatnagar–Gross–Krook (BGK) Boltzmann equation. To this end, the classical chemical transport equation is derived as the zeroth moment of the BGK Boltzmann differential equation. The relationship between the mass transport equation and the BGK Boltzmann equation allows an alternative approach to numerical modeling of mass transport, wherein mass fluxes are formulated indirectly from the zeroth moment of a difference model for the BGK Boltzmann equation rather than directly from the transport equation. In particular, a second-order numerical solution for the transport equation based on the discrete BGK Boltzmann equation is developed. The numerical discretization of the first-order BGK Boltzmann differential equation is straightforward and leads to diffusion effects being accounted for algebraically rather than through a second-order Fickian term. The resultant model satisfies the entropy condition, thus preventing the emergence of non-physically realizable solutions including oscillations in the vicinity of the front. Integration of the BGK Boltzmann difference equation into the particle velocity space provides the mass fluxes from the control volume and thus the difference equation for mass concentration. The difference model is a local approximation and thus may be easily included in a parallel model or in accounting for complex geometry. Numerical tests for a range of advection–diffusion transport problems, including one- and two-dimensional pure advection transport and advection–diffusion transport show the accuracy of the proposed model in comparison to analytical solutions and solutions obtained by other schemes.

Realistic numerical simulation of chlorine decay in pipes

The objective of the present study is to develop a numerical mass transport model that can simulate chlorine disappearance mechanisms under low flow conditions. The model accounts for axial convection and radial diffusion in a pipe under turbulent, transitional and laminar flow regimes and uses realistic velocity profiles. The bulk decay coefficient assumed to be constant in previous models is taken to be a function of residence time of water in pipes based on the findings of the experiments by laboratory tests. Furthermore, a methodology is introduced to convert simple one dimensional model solutions into refined results as if they were calculated by a much more precise two dimensional model.

Evaluation of a capture zone overlay method for designing groundwater remediation systems

Simplified approaches are often used to model the removal of groundwater contamination. These approaches can yield poor remediation schemes because they incorrectly portray the effects of multiple pumping wells. In this study, a pumping configuration designed by graphically overlaying capture zones having an identical, quasi-elliptical shape was evaluated with a numerical mass transport model. After a 3-year period (within which the hypothetical aquifer was to be remediated) the contaminant mass had been reduced by 77%. Due to stagnation zones which developed between extraction wells, approximately 15 years of pumping was required to remediate the aquifer with the overlay configuration. An alternative design, consisting of an extraction well between two injection wells along the long axis of the plume, removed the contaminant within the 3-year design period.

Plasma enhanced deposition of a-Si-H: comparison of two reactor arrangements

Plasma deposition processes involve complex phenomena which render the design and optimization of industrial equipment difficult to perform. In the particular case of silane plasmas used to produce amorphous silicon, two flow arrangements were studied by numerical modeling of mass transport. The modeling of the first geometry, using inlet slit gas feed, showed a decrease of both silane concentration and deposition rate from inlet to outlet. The modeling of the second geometry, using a distributed gas feed by means of a porous electrode, showed more uniform concentration profiles and deposition rate. In large industrial plasma enhanced chemical vapor deposition machines, the choice of gas flow arrangement plays a particularly important role. However, this subject has seldom been treated in the literature [1,2], probably because an experimental approach would involve a high level of investment to build the necessary equipment. This paper suggests an alternative theoretical treatment, using modeling and numerical simulation. First, the principles and methods of a recently developed model [3,4] will be recalled. Then, numerical simulation will be used to compare two different gas flow arrangements and their consequences on the deposition rate profile.