Quantifying the effects of temperature and concentration on variable-density flow in numerical modeling of groundwater systems: Implications for predictive uncertainty and data collection

Groundwater systems of different densities are often mathematically modeled to understand and predict environmental behavior such as seawater intrusion or submarine groundwater discharge. Additional data collection may be justified if it will cost-effectively aid in reducing the uncertainty of a model's prediction. The collection of salinity, as well as, temperature data could aid in reducing predictive uncertainty in a variable-density model. However, before numerical models can be created, rigorous testing of the modeling code needs to be completed. This research documents the benchmark testing of a new modeling code, SEAWAT Version 4. The benchmark problems include various combinations of density-dependent flow resulting from variations in concentration and temperature. The verified code, SEAWAT, was then applied to two different hydrological analyses to explore the capacity of a variable-density model to guide data collection. ^ The first analysis tested a linear method to guide data collection by quantifying the contribution of different data types and locations toward reducing predictive uncertainty in a nonlinear variable-density flow and transport model. The relative contributions of temperature and concentration measurements, at different locations within a simulated carbonate platform, for predicting movement of the saltwater interface were assessed. Results from the method showed that concentration data had greater worth than temperature data in reducing predictive uncertainty in this case. Results also indicated that a linear method could be used to quantify data worth in a nonlinear model. ^ The second hydrological analysis utilized a model to identify the transient response of the salinity, temperature, age, and amount of submarine groundwater discharge to changes in tidal ocean stage, seasonal temperature variations, and different types of geology. The model was compared to multiple kinds of data to (1) calibrate and verify the model, and (2) explore the potential for the model to be used to guide the collection of data using techniques such as electromagnetic resistivity, thermal imagery, and seepage meters. Results indicated that the model can be used to give insight to submarine groundwater discharge and be used to guide data collection. ^

Three-dimensional model for multi-component reactive transport with variable density groundwater flow

PHWAT is a new model that couples a geochemical reaction model (PHREEQC-2) with a density-dependent groundwater flow and solute transport model (SEAWAT) using the split-operator approach. PHWAT was developed to simulate multi-component reactive transport in variable density groundwater flow. Fluid density in PHWAT depends not on only the concentration of a single species as in SEAWAT, but also the concentrations of other dissolved chemicals that can be subject to reactive processes. Simulation results of PHWAT and PHREEQC-2 were compared in their predictions of effluent concentration from a column experiment. Both models produced identical results, showing that PHWAT has correctly coupled the sub-packages. PHWAT was then applied to the simulation of a tank experiment in which seawater intrusion was accompanied by cation exchange. The density dependence of the intrusion and the snow-plough effect in the breakthrough curves were reflected in the model simulations, which were in good agreement with the measured breakthrough data. Comparison simulations that, in turn, excluded density effects and reactions allowed us to quantify the marked effect of ignoring these processes. Next, we explored numerical issues involved in the practical application of PHWAT using the example of a dense plume flowing into a tank containing fresh water. It was shown that PHWAT could model physically unstable flow and that numerical instabilities were suppressed. Physical instability developed in the model in accordance with the increase of the modified Rayleigh number for density-dependent flow, in agreement with previous research. (c) 2004 Elsevier Ltd. All rights reserved.

Variable-density jet flows induced by concentrated sources of momentum and energy

The planar and axisymmetric variable-density flows induced in a quiescent gas by a concentrated source of momentum that is simultaneously either a source or a sink of energy are investigated for application to the description of the velocity and temperature far fields in laminar gaseous jets with either large or small values of the initial jet-to-ambient temperature ratio. The source fluxes of momentum and heat are used to construct the characteristic scales of velocity and length in the region where the density differences are of the order of the ambient density, which is slender for the large values of the Reynolds number considered herein. The problem reduces to the integration of the dimensionless boundary-layer conservation equations, giving a solution that depends on the gas transport properties but is otherwise free of parameters. The boundary conditions at the jet exit for integration are obtained by analysing the self-similar flow that appears near the heat source in planar and axisymmetric configurations and also near the heat sink in the planar case. Numerical integrations of the boundary-layer equations with these conditions give solutions that describe accurately the velocity and temperature fields of very hot planar and round jets and also of very cold plane jets in the far field region where the density and temperature differences are comparable to the ambient values. Simple scaling arguments indicate that the point source description does not apply, however, to cold round jets, whose far field region is not large compared with the jet development region, as verified by numerical integrations

EM optimization of latent-variable density models

There is currently considerable interest in developing general non-linear density models based on latent, or hidden, variables. Such models have the ability to discover the presence of a relatively small number of underlying `causes' which, acting in combination, give rise to the apparent complexity of the observed data set. Unfortunately, to train such models generally requires large computational effort. In this paper we introduce a novel latent variable algorithm which retains the general non-linear capabilities of previous models but which uses a training procedure based on the EM algorithm. We demonstrate the performance of the model on a toy problem and on data from flow diagnostics for a multi-phase oil pipeline.

LEAST ACTION PRINCIPLE and THE INCOMPRESSIBLE EULER EQUATIONS WITH VARIABLE DENSITY

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the regularity of the pressure field of relaxed solutions to Euler equations with variable density

In this paper we improve the regularity in time of the gradient of the pressure field in the solution of relaxed version of variational formulation proposed by V. I. Arnold and by Y. Brenier, for the incompressible Euler equations with variable density. We obtain that the pressure field is not only a measure, but a function in Lloc2((0,T);BVloc(D)) as an extension of the work of Ambrosio and Figalli (2008) in [1] to the variable density case. © 2013 Elsevier Ltd.

Influence of seaward boundary condition on contaminant transport in unconfined coastal aquifers

Contaminant transport in coastal aquifers is complicated partly due to the conditions at the seaward boundary including seawater intrusion and tidal variations of sea level. Their inclusion in modelling this system will be computationally expensive. Therefore, it will be instructive to investigate the consequence of simplifying the seaward boundary condition by neglecting the seawater density and tidal variations in numerical predictions of contaminant transport in this zone. This paper presents a comparison of numerical predictions for a simplified seaward boundary condition with experimental results for a corresponding realistic one including a saltwater interface and tidal variations. Different densities for contaminants are considered. The comparison suggests that the neglect of the seawater intrusion and tidal variations does not affect noticeably the overall migration rate of the plume before it reaches the saltwater interface. However, numerical prediction shows that a more dense contaminant travels further seaward and part of the solute mass exits under the sea if the seawater density is not included. This is not consistent with the experimental result, which shows that the contaminant travels upwards to the shoreline along the saltwater interface. Neglect of seawater density, therefore, will result in an underestimation of the exit rate of solute mass around the coastline and fictitious migration paths under the seabed. For a less dense contaminant, neglect of seawater density has little effect on numerical prediction of migration paths. (C) 2001 Elsevier Science B.V. All rights reserved.

Numerical modelling of contaminant transport in coastal aquifers

This paper employs a two-dimensional variable density flow and transport model to investigate the transport of a dense contaminant plume in an unconfined coastal aquifer. Experimental results are also presented to show the contaminant plume in a freshwater-seawater flow system. Both the numerical and experimental results suggest that the neglect of the seawater interface does not noticeably affect the horizontal migration rate of the plume before it reaches the interface. However, the contaminant will travel further seaward and part of the solute mass will exit under the sea if the higher seawater density is not included. If the seawater density is included, the contaminant will travel upwards towards the beach along the freshwater-saltwater interface as shown experimentally. Neglect of seawater density, therefore, will result in an underestimate of solute mass rate exiting around the coastline. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.

Numerical investigation of seawater intrusion at Gooburrum, Bundaberg, Queensland, Australia

Seawater intrusion in coastal agricultural areas due to groundwater abstraction is a major environmental problem along the northeastern coast of Australia. Management options are being explored using numerical modelling, however, questions remain concerning the appropriate level of sophistication in models, choice of seaward boundary conditions, and how to accommodate heterogeneity and data uncertainty. The choice of seaward boundary condition is important since it affects the amount of salt transported into the aquifers and forms the focus of the present study. The impact of this boundary condition is illustrated for the seawater-intrusion problem in the Gooburrum aquifers, which occur within Tertiary sedimentary strata. A two-dimensional variable-density groundwater and solute-transport model was constructed using the computer code 2DFEMFAT (Cheng et al. 1998). The code was tested against an experiment for a steady-state freshwater-saltwater interface and against the Elder (Elder 1967) free-convection problem. Numerical simulations show that the imposition of the commonly-used equivalent hydrostatic freshwater heads, combined with a constant salt concentration at the seaward boundary, results in overestimated seawater intrusion in the lower Gooburrum aquifer. Since the imposition of this boundary condition allows water flow across the boundary, which subsequently takes salt into the aquifer, a careful check is essential to estimate whether too much mass of salt is introduced.

Characterisation of sea-water intrusion in the Pioneer Valley, Australia using hydrochemistry and three-dimensional numerical modelling

Sea-water intrusion is actively contaminating fresh groundwater reserves in the coastal aquifers of the Pioneer Valley,north-eastern Australia. A three-dimensional sea-water intrusion model has been developed using the MODHMS code to explore regional-scale processes and to aid assessment of management strategies for the system. A sea-water intrusion potential map, produced through analyses of the hydrochemistry, hydrology and hydrogeology, offsets model limitations by providing an alternative appraisal of susceptibility. Sea-water intrusion in the Pioneer Valley is not in equilibrium, and a potential exists for further landward shifts in the extent of saline groundwater. The model required consideration of tidal over-height (the additional hydraulic head at the coast produced by the action of tides), with over-height values in the range 0.5-0.9 m giving improved water-table predictions. The effect of the initial water-table condition dominated the sensitivity of the model to changes in the coastal hydraulic boundary condition. Several salination processes are probably occurring in the Pioneer Valley, rather than just simple landward sea-water advancement from modern sources of marine salts. The method of vertical discretisation (i.e. model-layer subdivision) was shown to introduce some errors in the prediction of watertable behaviour.

Investigation of the flow field of a highly heated jet of air

Measurements of mean and fluctuating velocity and temperature and their self- and cross-products to the third-order are presented for a heated axisymmetric air jet. Froude numbers in the range of 3500 13,190, Reynolds numbers in the range of 3470-8500 and non-dimensional streamwise distances. X*, from 0.27 to 1.98 are covered by the data. It was found that turbulence intensity decreases for the heated jet in the region between the inertia dominated and the buoyancy dominated regions which is contrary to findings with helium jets mixing with ambient air to produce density fluctuations. The effects of heating on the turbulent kinetic energy budget and the temperature variance budget show small differences for the inertia dominated region and the intermediate region which help to explain the transition process to the far field plume region. Constants are evaluated for the isotropic eddy diffusivity and generalised gradient hypothesis models as well as the scalar variance model. No significant effect of heating on the dissipation time-scale ratio was found. A novel wire array with an inclined cold wire was used. Measurements obtained with this probe are found to lead to asymmetries in some of the higher-order products. Further investigation suggested that the asymmetries are attributable to an as yet unreported interference effect produced by the leading prong of the inclined temperature wire, The effect may also have implications for inclined velocity wires which contain a temperature component when used in heated flows. (C) 2002 Elsevier Science Inc. All rights reserved.

Tidal effects on sea water intrusion in unconfined aquifers

A variable-density groundwater model is used to analyse the effects of tidal fluctuations on sea-water intrusion in an unconfined aquifer. It is shown that the tidal activity forces the sea-water to intrude further inland and it also creates a thicker interface than would occur without tidal effects. Moreover, the configuration of the interface is radically changed when the tidal fluctuations are included. This is because of the dramatic changes in the flow pattern and velocity of the groundwater near the shoreline. For aquifer depths much larger than tidal amplitudes, the tidal fluctuation does not have much effect on how far the sea-water intrudes into the aquifer; nevertheless, a significant change in the configuration of concentration contours because of the effect of tidal fluctuations is observed. This change is more noticeable at the top of the aquifer, near the water table, than at the bottom of the aquifer, and is caused by the infiltration of salt water into the top of the aquifer at higher tidal levels. A flatter beach slope, therefore, intensifies this phenomenon. The interface configurations do not change noticeably over the course of a tidal cycle. Neglecting tidal fluctuation effects results in an inaccurate evaluation of the water table elevation at the land end of the aquifer, although no distinguishable difference is seen between the water tables near the shoreline. Where the landward boundary condition is a constant head, the effects of tidal fluctuations on sea-water intrusion are more pronounced than for cases where the landward boundary condition is a specified flux. Also it is shown that the effects of tidal fluctuations are more significant for a sloping beach than for a vertical shoreline and the salt water intrudes further inland for the sloping case. (C) 1999 Elsevier Science B.V. All rights reserved.

Geochemistry of Miocene "blue tuff" samples

Distinctive, massive to stratified, pale blue volcaniclastics, initially referred to as the "blue tuff," were encountered at all four sites drilled during ODP Leg 127 in the Japan Sea. Detailed vertical sequence analysis, plagioclase chemistry, plagioclase 87Sr/86Sr isotopic composition, and 40Ar/39Ar age dating indicate that thick sequences of the blue tuff are not genetically related. Blue tuffs at Hole 794B were apparently deposited by density flows at ambient temperature. Deposition was penecontemporaneous with a large submarine phreatomagmatic eruption at 14.9 Ma in bathyal or deeper water depths. The blue tuffs at this location comprise mostly reworked hydroclastic glass shards and lesser amounts of plagioclase crystals. Pyrogenic plagioclase has an average An mole% of 18±3. Comparison of blue tuff plagioclase compositions with the composition of plagioclase from acoustic basement at Site 794 suggests that these rocks are not genetically related. As such, the extrapolation of sediment accumulation rate data in conjunction with this more precise age for the blue tuff corroborates previous minimum age estimates of 16.2 Ma for acoustic basement at Site 794. Blue tuffs at Hole 796B were probably deposited at ambient temperatures by downslope slumping and density flow of reworked pyrogenic debris. This debris includes abundant bubble wall glass shards and plagioclase crystals, with variable admixture of volcanic lithic and intrabasinal fragments. Pyrogenic fragments were produced by subaerial or shallow submarine, magmatic eruptions dated at 7.6 Ma. Blue tuffs contain a heterogeneous mixture of unrelated fragments including a mixed population of plagioclase crystals. The average An mole% of the predominant, probable comagmatic, plagioclase population is 30±4. The two sequences of blue tuff studied are distinct in age, mineral composition, and the eruptive origin of pyroclastic fragments. Preliminary 87Sr/86Sr isotopic compositions of plagioclase, however, indicates that blue tuffs at both locations are the product of typical, subduction-related island arc magmatism. Based on the results of this study, there is no justification for stratigraphic correlation of widespread, Miocene, blue to blue-gray bentonitic tuff and tuffaceous sandstones nor the interpretation that these strata are indicative of regional, explosive submarine volcanism genetically related to rifting and formation of the Japan Sea. Rather, these reworked pyroclastic strata of intermediate composition were deposited over a protracted 6-8 m.y. period in association with widespread, subduction-related submarine to subaerial volcanism in the Japan Sea backarc basin.

The use of non-standard CT conversion ramps for Monte Carlo verification of 6 MV prostate IMRT plans

Monte Carlo (MC) dose calculation algorithms have been widely used to verify the accuracy of intensity-modulated radiotherapy (IMRT) dose distributions computed by conventional algorithms due to the ability to precisely account for the effects of tissue inhomogeneities and multileaf collimator characteristics. Both algorithms present, however, a particular difference in terms of dose calculation and report. Whereas dose from conventional methods is traditionally computed and reported as the water-equivalent dose (Dw), MC dose algorithms calculate and report dose to medium (Dm). In order to compare consistently both methods, the conversion of MC Dm into Dw is therefore necessary. This study aims to assess the effect of applying the conversion of MC-based Dm distributions to Dw for prostate IMRT plans generated for 6 MV photon beams. MC phantoms were created from the patient CT images using three different ramps to convert CT numbers into material and mass density: a conventional four material ramp (CTCREATE) and two simplified CT conversion ramps: (1) air and water with variable densities and (2) air and water with unit density. MC simulations were performed using the BEAMnrc code for the treatment head simulation and the DOSXYZnrc code for the patient dose calculation. The conversion of Dm to Dw by scaling with the stopping power ratios of water to medium was also performed in a post-MC calculation process. The comparison of MC dose distributions calculated in conventional and simplified (water with variable densities) phantoms showed that the effect of material composition on dose-volume histograms (DVH) was less than 1% for soft tissue and about 2.5% near and inside bone structures. The effect of material density on DVH was less than 1% for all tissues through the comparison of MC distributions performed in the two simplified phantoms considering water. Additionally, MC dose distributions were compared with the predictions from an Eclipse treatment planning system (TPS), which employed a pencil beam convolution (PBC) algorithm with Modified Batho Power Law heterogeneity correction. Eclipse PBC and MC calculations (conventional and simplified phantoms) agreed well (<1%) for soft tissues. For femoral heads, differences up to 3% were observed between the DVH for Eclipse PBC and MC calculated in conventional phantoms. The use of the CT conversion ramp of water with variable densities for MC simulations showed no dose discrepancies (0.5%) with the PBC algorithm. Moreover, converting Dm to Dw using mass stopping power ratios resulted in a significant shift (up to 6%) in the DVH for the femoral heads compared to the Eclipse PBC one. Our results show that, for prostate IMRT plans delivered with 6 MV photon beams, no conversion of MC dose from medium to water using stopping power ratio is needed. In contrast, MC dose calculations using water with variable density may be a simple way to solve the problem found using the dose conversion method based on the stopping power ratio.