Solute transport in sand and chalk: a probabilistic approach

A probabilistic approach is used to simulate particle tracking for two types of porous medium. The first is sand grains with a single intergranular porosity. Particle tracking is carried out by advection and dispersion. The second is chalk granulates with intergranular and matrix porosities. Sorption can occur with advection and dispersion during particle tracking. Particle tracking is modelled as the sum of elementary steps with independent random variables in the sand medium. An exponential distribution is obtained for each elementary step and shows that the whole process is Markovian. A Gamma distribution or probability density function is then deduced. The relationships between dispersivity and the elementary step are given using the central limit theorem. Particle tracking in the chalky medium is a non‐Markovian process. The probability density function depends on a power of the distance. Experimental simulations by dye tracer tests on a column have been performed for different distances and discharges. The probabilistic approach computations are in good agreement with the experimental data. The probabilistic computation seems an interesting and complementary approach to simulate transfer phenomena in porous media with respect to the traditional numerical methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Two‐dimensional solute transport for periodic flow in isotropic porous media: an analytical solution

In this article, a mathematical model is presented for the dispersion problem in finite porous media in which the flow is two‐dimensional, the seepage flow velocity is periodic, and dispersion parameter is proportional to the flow velocity. In addition to these, first‐order decay and zero‐order production parameters have also been considered directly proportional to the velocity. Retardation factor is taken into account in the present problem. First‐type boundary condition of periodic nature is considered at the extreme end of the boundary. Mixed‐type boundary condition is assumed at the origin of the domain. A classical mathematical substitution transforms the original advection–dispersion equation into diffusion equation in terms of other dependent and independent variables, with constant coefficients. Laplace transform technique is used to obtain the analytical solution. Copyright © 2011 John Wiley & Sons, Ltd.     

An integrated approach for modeling solute transport in streams and canals with applications

A new modeling approach for solute transport in streams and canals was developed to simulate solute dissolution, transport, and decay with continuously migrating sources. The new approach can efficiently handle complicated solute source feeding schemes and initial conditions. Incorporating the finite volume method (FVM) and the ULTIMATE QUICKEST numerical scheme, the new approach is capable of predicting fate and transport of solute that is added to small streams or canals, typically in a continuous fashion. The approach was tested successfully using a hypothetical case, and then applied to an actual field experiment, where linear anionic polyacrylamide (LA-PAM) was applied to an earthen canal. The field experiment was simulated first as a fixed boundary problem using measured concentration data as the boundary condition to test model parameters and sensitivities. The approach was then applied to a moving boundary problem, which included subsequent LA-PAM dissolution, settling to the canal bottom and transport with the flowing canal water. Simulation results showed that the modeling approach developed in this study performed satisfactorily and can be used to simulate a variety of transport problems in streams and canals.     

Strong seasonality in sand loading and resulting feedbacks on sediment transport,bed texture,and channel planform at Mount Pinatubo,Philippines

Declining sand inputs to a channel with bimodal bed sediment can lead to degradation, armoring, and reduced bedload transport rates. Where sand loading is episodic, channels may alternate between high‐sand and low‐sand conditions, with ensuing responses in bed texture and bedload transport rates. The effects of episodic sand loading are explored through flow, grain size, and bedload transport measurements on the Pasig‐Potrero River, a sediment‐rich channel draining Mount Pinatubo, Philippines. Sand loading on the Pasig‐Potrero River is highly seasonal, and channel adjustments between seasons are dramatic. In the rainy season, inputs from sand‐rich 1991 eruption deposits lead to active, sand‐bedded, braided channels. In the dry season, many precipitation‐driven sand sources are cut off, leading to incision, armoring, and significantly lower bedload transport rates. This seasonal transition offers an excellent opportunity to examine models of degradation, incision, and armoring as well as the effectiveness of sediment transport models that explicitly encapsulate the importance of sand on transport rates. During the fall 2009 seasonal transition, 7·6 km of channel incised and armored, carving a 2–3 m deep channel on the upper alluvial fan. Bedload transport rates measured in the August 2009 rainy season were over four orders of magnitude greater than gravel‐bedded dry‐season channels surveyed in January 2010, despite having similar shear stress and unit discharge conditions. Within dry‐season incised channels, bed armoring is rapid, leading to an abrupt gravel‐sand transition. Bedload transport rates adjust more slowly, creating a lag between armoring and commensurate reductions in transport. Seasonal channel incision occurred in steps, aided by lateral migration into sand‐rich banks. These lateral sand inputs may increase armor layer mobility, renewing incision, and forming terraces within the incised seasonal channel. The seasonal incised channel is currently being reset by precipitation‐driven sand loading during the next rainy season, and the cycle begins again. Copyright © 2012 John Wiley & Sons, Ltd.     

Heuristic numerical and analytical models of the hydrologic controls over vertical solute transport in a domed peat bog,Jura Mountains,Switzerland

We report the results of numerical and analytical simulations to test the hypothesis that downward vertical flow of porewater from the crests of domed alpine and kettle bogs controls vertical porewater distributions of major solutes such as Ca and Mg. The domed Etang de la Gruère bog (EGr), Switzerland, characterized by a vertical downward gradient of 0·04 and stratified layers of peat, is chosen as a field site for the model calibration and evaluation. The middle 4‐m section of the 6·5 m thick bog peat is heavily humified and has a hydraulic conductivity of ～10^?5·6 cm s^?1. Above and below, peat is less humified with a hydraulic conductivity of ～10^?3 cm s^?1. Heuristic finite difference simulations, using Visual MODFLOW, of the bog hydraulics show that the higher conductivity peat at the bog base is critical to create the observed deep, local flow cells that substantively recharge porewater. Model results and Peclet number calculations show that before ～7000 ¹⁴C yr BP diffusion of solutes from underlying mineral soils controlled the vertical distribution of porewater chemistry. From 7000 to ～1250 ¹⁴C BP the porewater chemistry was probably controlled by both upward diffusion and downward advection, and after ～1250 ¹⁴C yr BP porewater chemistry was probably controlled by downward advection. Concentrations of conservative major solutes in the porewaters of alpine, ombrotrophic bogs are the net effect of both downward vertical porewater movement and upward vertical diffusion, the magnitudes of which are delicately poised to the configuration of the bog water table over time and subsurface peat stratigraphy. Copyright © 2002 John Wiley & Sons, Ltd.     

Infiltration and solute transport under a seasonal wetland: bromide tracer experiments in Saskatoon,Canada

In the northern glaciated plain of North America, the duration of surface water in seasonal wetlands is strongly influenced by the rate of infiltration and evaporation. Infiltration also plays important roles in nutrient exchange at the sediment–water interface and groundwater recharge under wetlands. A whole‐wetland bromide tracer experiment was conducted in Saskatchewan, Canada to evaluate infiltration and solute transport processes. Bromide concentrations of surface water, groundwater, sediment pore water and plant tissues were monitored as the pond water‐level gradually dropped until there was no surface water. Hydraulic head gradients showed strong lateral flow from under the wetland to the treed riparian zone during the growing season. The bromide mass balance analysis showed that in early spring, almost 50% of water loss from the wetland was by infiltration, and it increased to about 70% in summer as plants in and around the wetland started to transpire more actively. The infiltration contributed to recharging the shallow, local groundwater under the wetland, but much of it was taken up by trees without recharging the deeper groundwater system. Emergent plants growing in the wetlands incorporated some bromide, but overall uptake of bromide by vegetation was less than 10% of the amount initially released. After one summer, most of the subsurface bromide was found within 40–80 cm of the soil surface. However, some bromide penetrated as deep as 2–3 m, presumably owing to preferential flow pathways provided by root holes or fractures. Copyright © 2004 Crown in the Right of Canada. Published by John Wiley & Sons, Ltd.     

Influence of a cyclic and dynamic loading history on dynamic properties of dry sand, part II: cyclic axial preloading

Initial fabric of a soil induced by its cyclic strain history is an important parameter among others like void ratio, state of stress and amplitude concerning the further accumulation of deformations under cyclic loading. It is of high importance to determine methods in order to estimate the initial fabric of the grain skeleton or the cyclic loading history of the soil. An attempt is made in this paper to correlate small strain stiffness of non-cohesive soil with its cyclic loading history. For this purpose several cyclic triaxial tests with specimens subjected to cyclic axial loading were performed and changes of small strain soil properties due to this cyclic loading were studied. All these tests showed only moderate changes of small strain stiffnesses independently of the different boundary conditions. Thus, a correlation between fabric or strain history and small strain stiffnesses seems not to be possible.     

Formation mechanism and model for sand lens reservoirs in the Jiyang Sub-basin, East China

The Bohai Bay basin comprises some very important and well documented subtle traps known in China, which have been the major exploration focus and have become a major petroleum play since the 1990s. However, recent exploration showed that the oil-bearing properties of some sand lens reservoirs may vary significantly and the accumulation mechanisms for these lithological subtle traps are not well understood. Based on statistical analysis of oil-bearing properties for 123 sand lens reservoirs in the Jiyang Sub-basin and combined with detailed anatomy of typical sand lens reservoirs and NMR experiments, it has been shown that the structural and sedimentary factors, hydrocarbon generation and expulsion conditions of the surrounding source rocks, as well as the petrophysical properties of sand lens reservoirs are the main controlling factors for the formation of sand lens reservoirs. The formation of a sand lens reservoir depends on the interaction between the hydrocarbon accumulation driving force and the resistance force. The driving force is made up of the differential capillary pressure between sandstones and sources rocks and the hydrocarbon diffusion force, and as well as the hydrocarbon expansion force. The resistance force is the friction resistance force for hydrocarbons and water to move through the pore throats of the sand lens. The sedimentary environment, source rock condition and sand reservoir properties can change from unfavorable to favorable depending on the combination of these factors. When these three factors all reach certain thresholds, the sand lens reservoirs may begin to be filled by hydrocarbons. When all of these conditions become favorable for the formation of sand lens reservoirs, the reservoir would have high oil saturation. This approach has been applied to evaluating the potential of petroleum accumulation in the sand lens reservoirs in the third member of the Neogene Shahejie Formation in the Jiyang Sub-basin.     

Influence of a cyclic and dynamic loading history on dynamic properties of dry sand, part I: cyclic and dynamic torsional prestraining

Initial fabric of a soil induced by its cyclic strain history is an important parameter together with the void ratio, state of stress and amplitude in respect to further accumulation of deformations under drained cyclic loading. It is of importance for the further deformation prediction to determine the initial fabric of the grain skeleton or the cyclic loading history of the soil. An attempt is made within this paper to correlate small strain stiffness of non-cohesive soil with its cyclic loading history. The results of performed cyclic and dynamic torsional tests show that small strain shear modulus is only moderately affected by cyclic prestraining even if high amplitudes are applied. A signature of prestraining history is observed in the tests since the sand memorizes its prestraining amplitude and the number of applied cycles.     

Cross‐sectional profiles of sand ripples,megaripples, and dunes: a method for discriminating between formational mechanisms

Cross‐sectional profiles of sand ripples, megaripples, and sand dunes provide a useful tool for discriminating between formation by ripple and dune processes. Feature width, defined as the basal break in slope along the profile to either side of the crest, represents a good standard for comparison of profile attributes across more than three orders of magnitude. Aspect ratio (height/width) as a function of log width separates measurements into clusters representing differing mechanisms of formation. Scaling both height and distance for individual profiles by feature width facilitates comparison of profile shapes across three orders of magnitude in width. The data presented here should prove useful for evaluating possible mechanisms of origin for aeolian features observed remotely, including on planetary bodies. Copyright © 2012 John Wiley & Sons, Ltd.     

Theoretical models and experimental determination methods for equations of state of silicate melts: A review

Silicate melts are very active in the interior of the Earth and other terrestrial planets, and are important carriers for the transport of material and energy. The determination of the equation of state(EOS) for silicate melts and the acquisition of a precise quantitative relationship between molar volume(or density) and temperature, pressure, and composition is essential for simulating the generation, migration, and eruption processes of magmas and the evolution of the magma ocean stage during the early formation of the Earth and other terrestrial planets, for calculating and modeling the phase equilibria involving silicate melts, and for revealing the variation of the microstructure of silicate melts with pressure. However, it is experimentally challenging to determine the volumetric properties of silicate melts and the accumulated density data at high pressure are still very limited due to a series of problems such as: the high liquidus temperature of silicate rocks; proneness for silicate melts to react with sample capsules to change the melt composition; and proneness for melts to flow and leak during the high pressure and high temperature experiments. In recent years, there is rapid progress in the high pressure and high temperature experimental techniques, in terms of not only the extension of temperature and pressure ranges but also the improvement on the accuracy of measurements, and the emergence of new methods for in-situ measurements. Here, we review the widely-used theoretical models of ambient-pressure and high-pressure EOS for silicate melts, and illustrate some problems that need to be solved urgently:(1) the room pressure EOS for iron-and titanium-bearing silicate melts needs to be improved;(2) the partial molar properties of the H2 O and CO2 components in silicate melts containing volatile components may vary markedly with the melt composition, which need to be addressed in high-pressure EOS;(3) how the formulation and applicable range of EOS correspond to changes in melt structure and compression mechanism requires further study. We highlight the basic principle and applicable range of various methods for determining the EOS for silicate melts, and compare the advantages and disadvantages of doublebob Archimedes method, fusion curve analysis, shock compression experiments, sink-float method, X-ray absorption, X-ray diffraction and ultrasonic interferometry. Future trends in this field are to develop experimental techniques for in situ measurements on melt density or sound velocity at high temperature and high pressure and to accumulate more experimental data,and on the other hand, to improve the theoretical models of the EOS for silicate melts by a combination of research on the microstructure and compression mechanisms of silicate melts.     

The role of eddies in solute transport and recovery in rock fractures: Implication for groundwater remediation

A better understanding of solute transport and retention mechanism in rock fractures has been challenging due to difficulty in their direct observations in microscale rough‐walled fractures. Six representative troughs in a rough‐walled fracture were selected for microscale observations of eddy formation with increasing flow velocity and its effect on spatiotemporal changes of solute concentration. This experimental study was enabled by a microscale visualization technique of micro particle image velocimetry. With increasing flow velocity (Re ≤ 2.86), no eddies were generated, and solutes along the main streamlines transported rapidly, whereas those near the wall moved slowly. A larger amount of solutes remained trapped at all troughs at Re = 2.86 than Re < 1. For Re = 8.57, weak eddies started to be developed at the troughs on the lee side, which little contributed to overall solute flushing in the fracture. Accordingly, a large of amount of water was needed for solute flushing. The flow condition of 1 < Re < 10, before a full development of eddies, was least favourable in terms of time and amount of remediation fluid required to reach a target concentration. After large eddies were fully developed at troughs on the lee side for Re = 17.13, solutes were substantially reduced by eddies with less amount of water. Fully developed eddies were found to enhance solute transport and recovery, as opposed to a general consensus that eddies trap and delay solutes. Direct inflow into troughs on the stoss side also made a great contribution to solute flushing out of the troughs. This study indicates that fully developed eddies or strong inflows at troughs are highly possible to form for Re > 10 and this flow range could be favourable for efficient remediation.     

The impact of boundary on the fractional advection–dispersion equation for solute transport in soil: Defining the fractional dispersive flux with the Caputo derivatives

The inherent heterogeneity of geological media often results in anomalous dispersion for solute transport through them, and how to model it has been an interest over the past few decades. One promising approach that has been increasingly used to simulate the anomalous transport in surface and subsurface water is the fractional advection–dispersion equation (FADE), derived as a special case of the more general continuous time random walk or the stochastic continuum model. In FADE, the dispersion is not local and the solutes have appreciable probability to move long distances, and thus reach the boundary faster than predicted by the classical advection–dispersion equation (ADE). How to deal with different boundaries associated with FADE and their consequent impact is an issue that has not been thoroughly explored. In this paper we address this by taking one-dimensional solute movement in soil columns as an example. We show that the commonly used FADE with its fractional derivatives defined by the Riemann–Liouville definition is problematic and could result in unphysical results for solute transport in bounded domains; a modified method with the fractional dispersive flux defined by the Caputo derivatives is presented to overcome this problem. A finite volume approach is given to numerically solve the modified FADE and its associated boundaries. With the numerical model, we analyse the inlet-boundary treatment in displacement experiments in soil columns, and find that, as in ADE, treating the inlet as a prescribed concentration boundary gives rise to mass-balance errors and such errors could be more significant in FADE because of its non-local dispersion. We also discuss a less-documented but important issue in hydrology: how to treat the upstream boundary in analysing the lateral movement of tracer in an aquifer when the tracer is injected as a pulse. It is shown that the use of an infinite domain, as commonly assumed in literature, leads to unphysical backward dispersion, which has a significant impact on data interpretation. To avoid this, the upstream boundary should be flux-prescribed and located at the upstream edge of the injecting point. We apply the model to simulate the movement of Cl⁻ in a tracer experiment conducted in a saturated hillslope, and analyse in details the significance of upstream-boundary treatments in parameter estimation.     

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: One-dimensional soil thaw with conduction and advection

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.     

Preliminary sensitivity study of eruption source parameters for operational volcanic ash cloud transport and dispersion models — A case study of the August 1992 eruption of the Crater Peak vent, Mount Spurr, Alaska

Ash clouds are one of the major hazards that result from volcanic eruptions. Once an eruption is reported, volcanic ash transport and dispersion (VATD) models are used to forecast the location of the ash cloud. These models require source parameters to describe the ash column for initialization. These parameters include: eruption cloud height and vertical distribution, particle size distribution, and start and end time of the eruption. Further, if downwind concentrations are needed, the eruption mass rate and/or volume of ash need to be known. Upon notification of an eruption, few constraints are typically available on many of these source parameters. Recently, scientists have defined classes of eruption types, each with a set of pre-defined eruption source parameters (ESP). We analyze the August 18, 1992 eruption of the Crater Peak vent at Mount Spurr, Alaska, which is the example case for the Medium Silicic eruption type. We have evaluated the sensitivity of two of the ESP – the grain size distribution (GSD) and the vertical distribution of ash – on the modeled ash cloud. HYSPLIT and Puff VATD models are used to simulate the ash clouds from the different sets of source parameters. We use satellite data, processed through the reverse absorption method, as reference for computing statistics that describe the modeled-to-observed comparison. With the grain size distribution, the three options chosen, (1) an estimated distribution based on past eruption studies, (2) a distribution with finer particles and (3) the National Oceanic and Atmospheric Administration HYSPLIT GSD, have little effect on the modeled ash cloud. For the initial vertical distribution, both linear (uniform concentration throughout the vertical column) and umbrella shapes were chosen. For HYSPLIT, the defined umbrella distribution (no ash below the umbrella), apparently underestimates the lower altitude portions of the ash cloud and as a result has a worse agreement with the satellite detected ash cloud compared to that with the linear vertical distribution for this particular eruption. The Puff model, with a Poisson function to represent the umbrella cloud, gave similar results as for a linear distribution, both having reasonable agreement with the satellite detected cloud. Further sensitivity studies of this eruption, as well as studies using the other source parameters, are needed.     

Nitrate fluctuations at the water table: implications for recharge processes and solute transport in the Chalk aquifer

This study investigates fluctuations in nitrate concentration at the water table to improve understanding of unsaturated zone processes in the Chalk aquifer. Sampling was conducted using a novel multi‐level sampler during periods of water table rise over 5 years at a vertical resolution of 0.05 m. Nitrate concentration increased as the water table seasonally recovered, with similar inter‐annual trends with depth. The rising water table activated horizontal fractures facilitating the delivery of water elevated by up to 10 mg/l of nitrate with respect to the adjacent groundwater below. These fractures are considered to activate via piston displacement of water from the adjoining matrix. Hydrograph analysis identified 16 events which significantly perturbed the water table within 24–48 h of rainfall. Consistent nitrate concentrations indicate recharge through persistent fracture flow from the surface was not generally the primary driver of the rapid water table response during these events. Instead, the response was attributed to the piston displacement of porewater immediately above the water table. However, a single event in November 2012 delivered relatively dilute recharge indicating rapid persistent fracture flow following rainfall was possible to a depth of 14–15 m. Decreases in porewater nitrate concentration around fracture horizons and the dilution of many groundwater samples with respect to porewaters indicate a fresher source of water at depth. This was considered most likely to be a result of near surface water bypassing the matrix because of widespread mineralization on fracture surfaces, which retard water and solute exchange. Therefore, persistent fracture flow maybe considered a frequent process, operating independently of the matrix, and is not necessarily event driven. Copyright © 2015 John Wiley & Sons, Ltd.     

Temperature in lowland Danish streams: contemporary patterns,empirical models and future scenarios

Continuous temperature measurements at 11 stream sites in small lowland streams of North Zealand, Denmark over a year showed much higher summer temperatures and lower winter temperatures along the course of the stream with artificial lakes than in the stream without lakes. The influence of lakes was even more prominent in the comparisons of colder lake inlets and warmer outlets and led to the decline of cold‐water and oxygen‐demanding brown trout. Seasonal and daily temperature variations were, as anticipated, dampened by forest cover, groundwater input, input from sewage plants and high downstream discharges. Seasonal variations in daily water temperature could be predicted with high accuracy at all sites by a linear air‐water regression model (r²: 0·903–0·947). The predictions improved in all instances (r²: 0·927–0·964) by a non‐linear logistic regression according to which water temperatures do not fall below freezing and they increase less steeply than air temperatures at high temperatures because of enhanced heat loss from the stream by evaporation and back radiation. The predictions improved slightly (r²: 0·933–0·969) by a multiple regression model which, in addition to air temperature as the main predictor, included solar radiation at un‐shaded sites, relative humidity, precipitation and discharge. Application of the non‐linear logistic model for a warming scenario of 4–5 °C higher air temperatures in Denmark in 2070‐2100 yielded predictions of temperatures rising 1·6–3·0 °C during winter and summer and 4·4–6·0 °C during spring in un‐shaded streams with low groundwater input. Groundwater‐fed springs are expected to follow the increase of mean air temperatures for the region. Great caution should be exercised in these temperature projections because global and regional climate scenarios remain open to discussion. Copyright © 2006 John Wiley & Sons, Ltd.     

Uplift mechanism for a shallow-buried structure in liquefiable sand subjected to seismic load: centrifuge model test and DEM modeling

Based on a centrifuge model test and distinct element method(DEM), this study provides new insights into the uplift response of a shallow-buried structure and the liquefaction mechanism for saturated sand around the structure under seismic action. In the centrifuge test, a high-speed microscopic camera was installed in the structure model, by which the movements of particles around the structure were monitored. Then, a two-dimensional digital image processing technology was used to analyze the microstructure of saturated sand during the shaking event. Herein, a numerical simulation of the centrifuge experiment was conducted using a two-phase(solid and fl uid) fully coupled distinct element code. This code incorporates a particle-fl uid coupling model by means of a "fi xed coarse-grid" fl uid scheme in PFC3D(Particle Flow Code in Three Dimensions), with the modeling parameters partially calibrated based on earlier studies. The physical and numerical models both indicate the uplifts of the shallow-buried structure and the sharp rise in excess pore pressure. The corresponding micro-scale responses and explanations are provided. Overall, the uplift response of an underground structure and the occurrence of liquefaction in saturated sand are predicted successfully by DEM modeling. However, the dynamic responses during the shaking cannot be modeled accurately due to the restricted computer power.