Two-dimensional Transport Model Research Articles

On the nanoparticle transport and release in layered heterogeneous porous media under transient chemical conditions

The rapid increase in production and application of nanoparticles (NPs) across a wide range of commercial and industrial processes has resulted in the extensive invasion of NPs into subsurface environments. Accurately predicting the transport and release of NPs in subsurface environments is important for assessing a wide range of environmental and human health risks. In this study, a two-dimensional NP transport and release model was proposed to investigate the behavior of NPs in a layered heterogeneous medium with transient ionic strength (IS). The layered heterogeneous porous medium comprised a slow flow domain (SFD) and a fast flow domain (FFD). The transport of NPs in the two layers was described by two coupled advection–dispersion equations (ADEs). The NP deposition and release were related to the IS of the electrolyte solution (ES) in the medium and were represented by reversible and irreversible deposition terms in the ADEs. The results indicated that heterogeneity has a significant impact on the transport and release of NPs. When NPs pass through the two‐layer medium, initially part of the NPs in the FFD will migrate into the SFD. A larger amount of NPs are deposited in the SFD than the FFD owing to the higher filtration capacity of the SFD. The retained NPs in both the SFD and FFD will be released when the IS declines. The release of the retained NPs in the FFD is faster than that in the SFD because the FFD has a higher intrinsic release rate and lower IS owing to the more rapid transport of ES in the FFD. The proposed model was applied to laboratory experiments and compared to the double-region model. The proposed model fitted the experimental breakthrough curves better than the double-region model, and it is capable of fitting the release of NPs, which cannot be accomplished with the double-region model.

Optimization Design of Groundwater Pollution Monitoring Scheme and Inverse Identification of Pollution Source Parameters Using Bayes’ Theorem

In the process of identifying groundwater pollution sources, in order to solve the problem that the monitoring data of monitoring wells was insufficient or the correlation between monitoring data and model parameters was weak, a monitoring well optimization method based on Bayesian formula and information entropy was proposed. Two-dimensional phreatic groundwater solute transport model was built and solved by using GMS software. To reduce the computational load of calling the numerical model repeatedly in the optimization design of the monitoring schemes and the identification process of the pollution sources, the Kriging method was used to establish the surrogate model of the numerical model. Under the condition of single well monitoring and determined monitoring frequency, with the target of optimization of monitoring position number D and monitoring time interval ∆t, both the single-objective monitoring scheme with the minimum information entropy of the model parameter posterior distribution and the multi-objective monitoring scheme with the minimum information entropy and the shortest monitoring time were optimized respectively. According to the above-optimized monitoring schemes, the delayed rejection adaptive Metropolis algorithm was used to identify the pollution source parameters. The case study results showed that under the condition of pre-set single well monitoring with monitoring frequency of 10 times, the single-objective optimized monitoring scheme was D = 37 and Δt = 20 days. Under this monitoring scheme, the mean errors of inversion pollution source parameters α = (XS, YS, T1, T2, QS) were 0.09%, 0.4%, 4.72%, 2.43%, and 9.29%, respectively. The multi-objective optimized monitoring scheme was D = 37 and Δt = 2 days. Under this monitoring scheme, the mean errors of the inversion parameters α = (XS, YS, T1, T2, QS) were 12.76%, 3.77%, 5.13%, 1.36%, and 7.68%, respectively. Compared with the monitoring scheme based on the single-objective optimization, although the inversion mean error of the five parameters based on the multi-objective optimized monitoring scheme increased by 2.75%, the monitoring time significantly reduced from 180 to 18 days.

Unsteady numerical simulations considering effects of thermal stress and heavy doping on the behavior of intrinsic point defects in large-diameter Si crystal growing by Czochralski method

Abstract We conducted unsteady simulations of intrinsic point defect dynamics considering the effects of the thermal stress and dopant concentration in a large-diameter silicon crystal growing by the Czochralski (Cz) method. The thermal equilibrium concentration of the intrinsic point defects (vacancy, V, and self-interstitial Si atom, I) was simulated as a function of the thermal stress and the incorporated dopant concentration in a growing Si crystal, which was obtained through ab-initio calculations. Furthermore, point defect dynamics in the crystal were solved within a two-dimensional axisymmetric unsteady global heat and mass transport model by considering the thermal stress and the incorporation of a dopant using segregation for dynamically pulling Si crystal by the Cz method. The unsteady numerical simulations showed that the formation and the distribution of intrinsic point defects depend on the temporal variation of the thermal stress and the incorporated dopant concentration in a growing Si crystal.

Simulation Study on the Mass Transport Based on the Ciliated Dynamic System of the Respiratory Tract

To study the mass transport of mucociliary clearance of the human upper respiratory tract, a two-dimensional mass transport model based on the ciliated movement was established by using the immersed boundary-lattice Boltzmann method (IB-LBM). In this model, different characteristics of the mucus layer (ML) and the periciliary liquid (PCL) were taken into account. A virtual elastic membrane was introduced to divide the two layers dynamically. All moving boundaries that were involved in the present simulation were modeled with the immersed boundary. The Newtonian fluid was used to model the flow in PCL, and the viscoelastic fluid based on the Oldroyd-B model was used for the flow in ML; the two types of flow were both solved by the LBM framework. Based on the model, the ML thickness, the cilia density, and the phase difference of adjacent cilia were regulated, respectively, to study the transport velocity of the ML. In addition, the motion law of solid particles in PCL was also studied. According to the results, four primary conclusions were drawn. (1) At a given beating pattern, the increase of the ML thickness will decrease its transport velocity. (2) Increasing the cilia density can promote the mean transport velocity of the ML. (3) By raising the phase difference of adjacent cilia to a certain scope, the transport of ML can be accelerated. (4) In PCL, particles initially located on the upper part of the cilia tend to migrate upward and then get close to the ML. The above study can provide some reasonable explanations for the mechanism of the mucociliary clearance system, which is also helpful to the further understanding of the mass transport principle of the human upper respiratory tract.

Numerical Study of Remote Sensed Dredging Impacts on the Suspended Sediment Transport in China’s Largest Freshwater Lake

As the largest freshwater lake in China, Poyang Lake plays an important role in the ecosystem of the Yangtze River watershed. The high suspended sediment concentration (SSC) has been an increasingly significant problem under the influence of extensive sand dredging. In this study, a hydrodynamic model integrated with the two-dimensional sediment transport model was built for Poyang Lake, considering sand dredging activities detected from satellite images. The sediment transport model was set with point sources of sand dredging, and fully calibrated and validated by observed hydrological data and remote sensing results. Simulations under different dredging intensities were implemented to investigate the impacts of the spatiotemporal variation of the SSC. The results indicated that areas significantly affected by sand dredging were located in the north of the lake and along the waterway, with a total affected area of about 730 km2, and this was one of the main factors causing high turbidity in the northern part of the lake. The SSC in the northern area increased, showing a spatial pattern in which the SSC varied from high to low from south to north along the main channel, which indicated close agreement with the results captured by remote sensing. In summary, this study quantified the influence of human induced activities on sediment transport for the lake aquatic ecosystem, which could help us to better understand the water quality and manage water resources.

Numerical analysis of effect of thermal stress depending on pulling rate on behavior of intrinsic point defects in large-diameter Si crystal grown by Czochralski method

We analyzed the effects of thermal stress and pulling rate on the behavior of intrinsic point defects in a silicon (Si) single crystal grown by the Czochralski (Cz) method using a numerical approach. The thermal equilibrium concentration of the intrinsic point defects (vacancy, V, and self-interstitial Si atom, I) was simulated as a function of thermal stress, which was obtained via ab -initio calculations. Furthermore, the point defect dynamics in the crystal were solved within a framework of a two-dimensional (2D) axisymmetric steady-state global heat and mass transport model of Si crystal growth by the Cz method. The numerical simulations revealed that both magnitude and distribution of the thermal stress depend on the pulling rate. Moreover, they impact the formation and distribution of intrinsic point defects in a growing Si single crystal.

Probabilistic solution to two-dimensional stochastic solute transport model by the Fokker-Planck equation approach

The study of solute transport in rivers is of environmental significance, since solute transported in river flows may affect the river water quality conditions. Solute transport in natural flows is a challenging process to be investigated, given natural flows usually indicate uncertainty in space and time. Two-dimensional models are more preferable to one-dimensional models, especially when the underlying flow field is complex. In this study, a stochastic horizontally two-dimensional solute transport model is developed. The proposed model can account for the effect of uncertain two-dimensional flow field and solute loading conditions on the uncertainty of the solute transport. The governing equation of the proposed model is in the form of Fokker-Planck equation, which characterizes the spatiotemporal evolution of the probability density function of the state variables of the solute transport process. Consequently, the mean and standard deviation behavior of the ensemble solute transport under uncertain conditions can be quantified. The numerical solutions of the proposed model are validated with the Monte Carlo simulations under uncertain flow fields. The comparison of the results by the two methods indicate the developed two-dimensional stochastic solute transport model can sufficiently express the spatial variability of the solute transport process and adequately capture the ensemble solute transport behavior by the complete probabilistic description of the solute transport process under uncertain conditions.

Feasibility of Velocity-Based Method for Transverse Mixing Coefficients in River Mixing Analysis

AbstractThe feasibility of using the velocity-based method for calculating the transverse mixing coefficient of the two-dimensional contaminant transport model was studied to substitute the concent...

Analysis of permeability change in dissolving rough fractures using depth-averaged flow and reactive transport models

Many geophysical problems and engineering applications involve fluid flow through evolving faults and fractures. These situations are typical in CO2 injection scenarios where supercritical CO2 or CO2–saturated fluids are able to dissolve the solid matrix. Dissolution or precipitation within a fracture could lead to self-reinforcing or self-limiting behavior due to feedbacks from changes in permeability (k). There is limited predictive understanding of this phenomenon. Here, we investigated the case of fracture dissolution using a two-dimensional depth-averaged reactive transport model. The model simulated an acidic fluid dissolving a three-dimensional rough fracture. We observed different dissolution patterns across a wide range of geometric properties and different Peclet and Damkohler numbers (960 cases total). Despite this variation, a persistent linear increase in k with time (t) roughly manifested once the dissolution front advanced through the fracture. The time rate of change of k (k/t) is roughly constant for all simulations. The modeled rate is consistent with a theoretical value based on the parallel plates model and with experimentally derived values. The results confirm the common presence of linear time-dependence of fracture k due to self-reinforcement.

Dynamics of Sediment Transport and Erosion-Deposition Patterns in the Locality of a Detached Low-Crested Breakwater on a Cohesive Coast

Understanding the dynamics of sediment transport and erosion-deposition patterns in the locality of a coastal structure is vital to evaluating the performance of coastal structures and predicting the changes in coastal dynamics caused by a specific structure. The nearshore hydro-morphodynamic responses to coastal structures vary widely, as these responses are complex functions with numerous parameters, including structural design, sediment and wave dynamics, angle of approach, slope of the coast and the materials making up the beach and structures. This study investigated the sediment transport and erosion-deposition patterns in the locality of a detached low-crested breakwater protecting the cohesive shore of Carey Island, Malaysia. The data used for this study were collected from field measurements and secondary sources from 2014 to 2015. Sea-bed elevations were monitored every two months starting from December 2014 to October 2015, in order to quantify the sea-bed changes and investigate the erosion-deposition patterns of the cohesive sediment due to the existence of the breakwater. In addition, numerical modelling was also performed to understand the impacts of the breakwater on the nearshore hydrodynamics and investigate the dynamics of fine sediment transport around the breakwater structure. A coupled two-dimensional hydrodynamics-sediment transport model based on Reynolds averaged Navier-Stokes (RANS) equations and cell-centered finite volume method with flexible meshing approach was adopted for this study. Analysis of the results showed that the detached breakwater reduced both current speed and wave height behind the structure by an average of 0.12 m/s and 0.1 m, respectively. Also, the breakwater made it possible for trapped suspended sediment to settle in a sheltered area by approximately 8 cm in height near to the first main segment of the breakwater, from 1 year after its construction. The numerical results were in line with the field measurements, where sediment accumulations were concentrated in the landward area behind the breakwater. In particular, sediment accumulations were concentrated along the main segments of the breakwater structure during the Northeast (NE) season, while concentration near the first main segment of the breakwater were recorded during the Southwest (SW) season. The assessment illustrated that the depositional patterns were influenced strongly by the variations in seasonal hydrodynamic conditions, sediment type, sediment supply and the structural design. Detached breakwaters are rarely considered for cohesive shores; hence, this study provides new, significant benefits for engineers, scientists and coastal management authorities with regard to seasonal dynamic changes affected by a detached breakwater and its performance on a cohesive coast.

Dynamic conductivity of polymer dielectrics under time-varying temperature field

We succeeded in putting forward a two-dimensional electric transport model based on the first-order kinetic charge trapping/detrapping model. The dynamic conductivity under thermal cycle of polyimide is analyzed from numerical calculations and experimental tests. The conductivity characteristics of polymer dielectric under temperature cycling was found to be dominated by temperature and time, because of filled traps and rapid changes in temperature. The present study contributes in providing an accurate conductivity calculation model for polymer dielectrics under temperature-varying fields.

Roles of fault structures and regional formations on CO2 migration and distribution in shallow saline aquifer in Green River, Utah

Understanding CO2 migration and distribution in fault systems is essential to evaluate long-term secure CO2 storage and prevent hazardous effects caused by CO2 leakage. To elucidate the role of the fault system on subsurface CO2 migration and leakage processes, a two-dimensional multi-phase transport model was constructed to represent Little Grand Wash (LGW) and Salt Wash (SW) faults, where naturally originating CO2 is being leaked to the surface. According to simulation results, buoyant CO2 leaked through various pathways including the faults themselves, fault offsets, and damaged caprock. Because of both fault systems and caprocks serving as barriers, multiple trapped CO2 plumes were developed in this region. Presence of trapped CO2 plumes in the subsurface is supported by multiple field-observations (e.g., elevated soil CO2 fluxes, travertines, and CO2-driven cold-water geysers/CO2 springs) adjacent to both LGW and SW faults. Sensitivity studies were conducted with different permeabilities for faults and caprock, various CO2 source locations, and differing fault parameters (e.g., fault throw and cutoff angle), which affected subsurface CO2 distribution including size, shape, and location of trapped CO2 plumes. Finally, such trapped CO2 plumes have played a key role in the development of CO2-driven cold-water geysers in these regions.

Salt dissolution potential estimated from two-dimensional vertical thermohaline flow and transport modeling along a Transylvanian salt diapir, Romania

The presented study explores the salt dissolution potential of fluids around a salt diapir in the Transylvanian town of Ocna Mures, Romania, which is facing land-collapse hazards related to salt mining activities. A structural three-dimensional (3D) model of the salt diapir, the adjacent basin sediments, and the mining galleries was developed based on existing maps, borehole data, own field observations, and geological publications of the Transylvanian Basin. The salt dissolution potential was estimated from 2D vertical thermohaline flow and transport model scenarios along the southeastern flank of the diapir. Results showed that the following factors increase the salt dissolution capacity along the upper 180 m of the diapir: (1) the presence of more permeable Quaternary alluvial sediments in connection with a fault zone of higher permeability along the diapir, and (2) the presence of more permeable sandstone units within the Miocene sediments in the east of the diapir, which provide freshwater access to the upper parts of the diapir. Thermohaline simulation with viscosity variation of the fluid, instead of a constant viscosity, influences the resulting salt fluxes by up to 50% within studied temperature ranges of 10–60 °C in the model domain. The range of theoretical dissolution rates along the upper 180 m of the diapir supports the hypothesis that cavern collapse is more likely to occur where cavern side walls have already been mined to almost no remaining side walls of rock salt, which is the case in the southeastern part of the diapir.

Forecasting commercial-scale CO2 storage capacity in deep saline reservoirs: Case study of Buzzard's bench, Central Utah

Successful implementation of Geological Carbon Sequestration (GCS) projects requires long-term storage capacity and security at selected fields. The purpose of this work is to evaluate and quantify potential storage capacity, trapping mechanisms and potential risks associated with commercial-scale (at least 50 MT CO2) injection and storage of CO2 in the subsurface. The specific case study evaluated is the Navajo Sandstone formation, a target GCS reservoir in Buzzard's Bench, Central Utah. Two-dimensional reactive transport models are designed for 1000-year simulations, with 50 MT CO2 injection. An uncertainty analysis with different reservoir porosity and permeability are conducted, because only a few samples of the reservoir and caprock near the proposed reservoir were collected. Specific objectives include forecasting the extent of an injected CO2 plume, competing roles of different trapping mechanisms, trapping capacity changes due to porosity changes, and forecasts of CO2 migration into adjacent caprock (the Carmel formation in this case). Resultssuggest that the Navajo formation may be a reliable CO2 sequestration reservoir, capable of trapping commercial volumes. The Jurassic Kayenta and Wingate formations may also store some injected CO2, with these and other clastic formations forming a “stacked storage” system. Storage efficiency decreases with distance away from an injection well, and the estimated storage efficiency for the case study simulations (Navajo storage only) are 2.3 ± 1% within the area of review (AoR) calculated by National Risk Assessment Partnership (NRAP) toolset. After 1000 years, about half of the injected CO2 may be sequestered in safe phases including residually-trapped CO2 via surface tension, aqueous and mineral phases. A small amount of total injected CO2 (∼3%) tends to migrate into the caprock, but is mostly stored in the sandstone reservoir. Simulated porosity enhancement caused by mineral alteration is negligible within 1000 years of the start of injection, with only ∼0.6% added to the total pore volume by the end of simulations. Future studies of detailed reservoir and caprock characteristics with in-situ samples may be helpful for further determining reservoir sequestration capacity and reliability.

Water Sorption and Diffusivity in [C2C1im][BF4], [C4C1im][OAc], and [C4C1im][Cl

Measurements of in situ atmospheric water absorption and desorption in ionic liquids (ILs) (1-ethyl-3-methylimidazolium tetrafluoroborate [C2C1im][BF4], 1-butyl-3-methylimidazolium acetate [C4C1im][OAc], and 1-butyl-3-methylimidazolium chloride [C4C1im][Cl]) were made using a gravimetric microbalance at temperatures ranging from 283.15 to 315.15 K and relative humidity (RH) 0–70% at 101 kPa. Solubility data were well correlated using the nonrandom two-liquid (NRTL) activity model, and time dependent concentration data were used to determine the binary diffusion coefficients using one- and two-dimensional transport models of water in the IL–water systems. The solubility of water was highest in [C4C1im][OAc] (77.5 mol %), followed by [C4C1im][Cl] (68.6 mol %), and [C2C1im][BF4] (19.5 mol %) at equivalent conditions (303.15 K and 25.00% RH). The diffusion coefficients in order of increasing relative humidity ranged from 1.3 × 10–10 to 2.8 × 10–11 m2/s for [C2C1im][BF4], from 8.8 × 10–12 to 3.9 × 10–11 m2/s f...

Reactive Transport Simulation of Fracture Channelization and Transmissivity Evolution.

Underground fractures serve as flow conduits, and they may produce unwanted migration of water and other fluids in the subsurface. An example is the migration and leakage of greenhouse gases in the context of geologic carbon sequestration. This study has generated new understanding about how acids erode carbonate fracture surfaces and the positive feedback between reaction and flow. A two-dimensional reactive transport model was developed and used to investigate the extent to which geochemical factors influence fracture permeability and transmissivity evolution in carbonate rocks. The only mineral modeled as reactive is calcite, a fast-reacting mineral that is abundant in subsurface formations. The X-ray computed tomography dataset from a previous experimental study of fractured cores exposed to carbonic acid served as a testbed to benchmark the model simulation results. The model was able to capture not only erosion of fracture surfaces but also the specific phenomenon of channelization, which produces accelerating transmissivity increase. Results corroborated experimental findings that higher reactivity of the influent solution leads to strong channelization without substantial mineral dissolution. Simulations using mineral maps of calcite in a specimen of Amherstburg limestone demonstrated that mineral heterogeneity can either facilitate or suppress the development of flow channels depending on the spatial patterns of reactive mineral. In these cases, fracture transmissivity may increase rapidly, increase slowly, or stay constant, and for all these possibilities, the calcite mineral continues to dissolve. Collectively, these results illustrate that fluid chemistry and mineral spatial patterns need to be considered in predictions of reaction-induced fracture alteration and risks of fluid migration.

Effect of Nonuniform Vertical Grid on the Accuracy of Two-Dimensional Transport Model

Effect of Nonuniform Vertical Grid on the Accuracy of Two-Dimensional Transport Model

Modeling water temperature effect in diatom (Stephanodiscus hantzschii) prediction in eutrophic rivers using a 2D contaminant transport model

In many eutrophic rivers, the diatom dynamics mainly depends on change of water temperature rather than nutrient concentration because phosphorus and nitrogen loadings are usually sufficient to saturate the diatom growth. In this study, a two-dimensional contaminant transport model was developed in which diatom growth was predicted by incorporating the dynamics of water temperature, dissolved inorganic phosphorus and dissolved inorganic nitrogen as well as the hydrodynamics of river flow. In this study, in order to accurately model the effect of the water temperature on the diatom growth, a new form of the water temperature limitation function, f(T) was proposed, using the field data obtained from water quality monitoring stations at the Nakdong River, one of the eutrophic rivers in South Korea. Fitting the water quality data, the skewed Gaussian function was empirically derived for f(T) with parameter estimation to calculate the growth rate of the centric diatom, Stephanodiscus hantzschii (S. hantzschii) for which the optimal water temperature was found to be 8.7 °C from winter to spring seasons. The calibration of the two-dimensional contaminant transport model with the proposed f(T) showed that the Nash Sutcliffe Efficiency (NSE) of the simulation with the observed data at each monitoring station was 0.63 and 0.85. The validation of the calibrated model also showed that the simulation results were in good agreement with the observed data with NSE larger than 0.74. The results of the parametric sensitivity analysis revealed that the optimal water temperature, Topt most influenced the temporal variation in the diatom abundance. According to results of the scenario simulation using the calibrated and validated model, the thermal effluents introduced from the tributary as well as dispersion coefficients, DL and DT significantly affected the spatial distribution of the diatom concentration in the study site of the Nakdong River.

Application of a weakly compressible smoothed particle hydrodynamics multi-phase model to non-cohesive embankment breaching due to flow overtopping

The subject of present study is the application of mesh free Lagrangian two-dimensional non-cohesive sediment transport model applied to a two-phase flow over an initially trapezoidal-shaped sediment embankment. The governing equations of the present model are the Navier-Stocks equations solved using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method. To simulate the movement of sediment particles, the model considers a powerful two-part technique; when the sediment phase has rigid behavior, only the force term due to shear stress in the Navier-Stokes equations is used for simulation of sediment particles’ movement. Otherwise, all the Navier-Stokes force terms are used for transport simulation of sediment particles. In the present model, the interactions between different phases are calculated automatically, even with considerable difference between the density and viscosity of phases. Validation of the model is performed using simulation of available laboratory experiments, and the comparison between computational results and experimental data shows that the model generally predicts well the flow propagation over movable beds, the induced sediment transport and bed changes, and temporal evolution of embankment breaching.

An improved and fully implicit multi-group non-local electron transport model and its validations

The combined effect of thermal flux inhibition and non-local electron heat flux in the radiation hydrodynamics (RHD) simulation of laser-driven systems can be accurately predicted by using non-local electron transport (NLET) models. These models can avoid commonly used space and time-independent ad-hoc flux-limiting procedures. However, the use of classical electron collision frequency in these models is rigorously valid for high temperature non-degenerate plasmas. In laser-driven systems, the electron thermal energy transport is important in regions between the critical density and ablation surface where the plasma is partially degenerate. Therefore, an improved model for electron collision frequency in this regime is required to accurately predict the thermal energy transport. Previously, we have reported an improved single group non-local electron transport model by using a wide-range electron collision frequency model valid from warm-dense matter (WDM) to fully ionized plasmas. In this work, we have extended this idea into a two-dimensional multi-group non-local electron transport (MG-NLET) model. Moreover, we have used a fully implicit numerical integration scheme in which the models for multi-group thermal radiation transport, laser absorption, electron-ion thermal energy relaxation and ion heat conduction are included in a single step. The performance of this improved MG-NLET model has been assessed by comparing the simulated foil trajectories with the reported experimental data for laser-driven plastic foils. The results indicate that the improved model yields results that are in better agreement with the experimental data.