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1.
We extend the particle-tracking method to simulate general multi-rate mass transfer (MRMT) equations. Previous methods for single-rate equations used two-state Markov chains and found that the time a particle spends in the mobile state between waiting time epochs is random and exponentially distributed. Using Bochner’s subordination technique for Markov processes, we find that the random mobile times are still exponential for the stochastic process that corresponds to the MRMT equations. The random times in the immobile phase have a distribution that is directly related to the memory function of the MRMT equation. This connection allows us to interpret the MRMT memory function as the rate at which particles of a certain age, measured by residence time in the immobile zone, exit to become mobile once again. Because the exact distributions of mobile and immobile times are known from the MRMT equations, they can be simulated very simply and efficiently using random walks. 相似文献
2.
This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile–immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection–dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer tests. 相似文献
3.
We determine the relevance of Multi-Rate Mass Tansfer (MRMT) models (Haggerty and Gorelick, 1995) to general diffusive porosity structures. To this end, we introduce Structured INteracting Continua (SINC) models as the combination of a finite number of diffusion-dominated interconnected immobile zones exchanging with an advection-dominated mobile domain. It directly extends Multiple INteracting Continua framework (Pruess and Narasimhan, 1985) by introducing a structure in the immobile domain, coming for example from the dead-ends of fracture clusters or poorly-connected dissolution patterns. We demonstrate that, whatever their structure, SINC models can be made equivalent in terms of concentration in the mobile zone to a unique MRMT model. We develop effective shape-free numerical methods to identify its few dominant rates, that comply with any distribution of rates and porosities. We show that differences in terms of macrodispersion are not larger than 50% for approximate MRMT models with only one rate (double porosity models), and drop down to less than 0.1% for five rates MRMT models. Low-dimensional MRMT models accurately approach transport in structured diffusive porosities at intermediate and long times and only miss early responses. 相似文献
4.
Analytical approach for sheet flow transport in purely acceleration-skewed oscillatory flow 总被引：1，自引：0，他引：1
An instantaneous analytical approach is developed to predict sheet flow transport in purely acceleration-skewed oscillatory flow. The approach is derived from exponential approximations of velocity and concentration profiles above a mobile seabed, and it particularly considers factors of phase lead; phase lag (i.e. phase residual and phase shift); acceleration modification; and asymmetries in shear stress, roughness height, and boundary layer development. The approach can predict net boundary layer flow above a mobile seabed, and can revert to the classical bedload model. Instantaneous and net sediment transport rates are studied using the approach. The instantaneous sediment transport rate in an onshore flow stage can be approximated by a power function of velocity in which the exponent is confirmed to range between 1 and 5 with a decrease in the phase residual. The net sediment transport rate predicted using the approach is validated using a considerable amount of measured data, and compared with existing instantaneous and half-period type models that consider the phase lag or acceleration modification. For the net sediment transport rate in purely acceleration-skewed oscillatory flow, the phase residual is less important than the acceleration-skewed boundary layer difference between onshore and offshore acceleration stages. 相似文献
5.
Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization 
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下载免费PDF全文 Hydraulic tomography (HT) is a method for resolving the spatial distribution of hydraulic parameters to some extent, but many details important for solute transport usually remain unresolved. We present a methodology to improve solute transport predictions by combining data from HT with the breakthrough curve (BTC) of a single forced‐gradient tracer test. We estimated the three dimensional (3D) hydraulic‐conductivity field in an alluvial aquifer by inverting tomographic pumping tests performed at the Hydrogeological Research Site Lauswiesen close to Tübingen, Germany, using a regularized pilot‐point method. We compared the estimated parameter field to available profiles of hydraulic‐conductivity variations from direct‐push injection logging (DPIL), and validated the hydraulic‐conductivity field with hydraulic‐head measurements of tests not used in the inversion. After validation, spatially uniform parameters for dual‐domain transport were estimated by fitting tracer data collected during a forced‐gradient tracer test. The dual‐domain assumption was used to parameterize effects of the unresolved heterogeneity of the aquifer and deemed necessary to fit the shape of the BTC using reasonable parameter values. The estimated hydraulic‐conductivity field and transport parameters were subsequently used to successfully predict a second independent tracer test. Our work provides an efficient and practical approach to predict solute transport in heterogeneous aquifers without performing elaborate field tracer tests with a tomographic layout. 相似文献
6.
7.
The on–offshore (cross-shore) transport of sand on beaches is highly time-variable, which has made it difficult to model or predict. In this paper, simple energetics modelling is used to compare velocity moment predictions with field observations of suspended sand transport rates. Separate consideration is given to transport associated with the three main frequency-dependent cross-shore transport processes: that associated with the short (incident) waves, that due to the long (infragravity) waves, and transport associated with the mean flow. Direct comparison between the depth-averaged model predictions, and the in-situ point measurements was facilitated by making the first order assumption that the time-averaged suspension profile is exponential and the wave velocity profile is vertically uniform. An appropriate rippled bed roughness was used to provide the drag coefficient in the energetics model and the vertical length scale of the exponential suspension profile. Despite these simple assumptions, comparison of the velocity moment predictions with the field observations of suspended sand fluxes reveals that this approach has the capacity to predict transport magnitudes due to short wave, long wave, and mean flow components to within about one order of magnitude. However, owing to the limitations of the model, the transport direction of the short wave component could not, on occasion, be correctly determined, probably due to ‘reverse’ transport over ripples. © 1998 John Wiley & Sons, Ltd. 相似文献
8.
The method of temporal moments is an efficient approach for analyzing breakthrough curves (BTCs). By matching the moments of the BTCs computed through parametric transfer-function models or one-dimensional transport models to those of the data, one can estimate the parameters characterizing the transfer function or apparent transport parameters. The classical method of moments presumes infinite duration. However, the measurement of BTCs is usually terminated prematurely, before the concentration has reached zero. Unless this truncation of the BTCs has been taken into account, the estimates of the parameters may be in error. Truncated measured BTCs are sometimes extrapolated assuming exponential decay. In this study, we use the concept of moments of the truncated impulse–response function [Jawitz JW. Moments of truncated continuous univariate distributions. Adv Water Res 2004;27:269–81] in the analysis of truncated BTCs corresponding to the commonly encountered step and step-pulse injection modes. The method is straightforward, based on the relation, which we derive, between truncated moments of the impulse–response function and the measured BTC. It is practical to apply and does not require the extrapolation of the measured BTC. The method is also accurate. In a numerical study we discuss how short a step-pulse injection may be so that we can approximate it as instantaneous. Finally, we apply the method to the analysis of a field-scale tracer test. 相似文献
9.
R. Gong C. Lu W.‐M. Wu H. Cheng B. Gu D. Watson P.M. Jardine S.C. Brooks C.S. Criddle P.K. Kitanidis J. Luo 《Ground water》2011,49(2):209-218
A generalized, efficient, and practical approach based on the travel‐time modeling framework is developed to estimate in situ reaction rate coefficients for groundwater remediation in heterogeneous aquifers. The required information for this approach can be obtained by conducting tracer tests with injection of a mixture of conservative and reactive tracers and measurements of both breakthrough curves (BTCs). The conservative BTC is used to infer the travel‐time distribution from the injection point to the observation point. For advection‐dominant reactive transport with well‐mixed reactive species and a constant travel‐time distribution, the reactive BTC is obtained by integrating the solutions to advective‐reactive transport over the entire travel‐time distribution, and then is used in optimization to determine the in situ reaction rate coefficients. By directly working on the conservative and reactive BTCs, this approach avoids costly aquifer characterization and improves the estimation for transport in heterogeneous aquifers which may not be sufficiently described by traditional mechanistic transport models with constant transport parameters. Simplified schemes are proposed for reactive transport with zero‐, first‐, nth‐order, and Michaelis‐Menten reactions. The proposed approach is validated by a reactive transport case in a two‐dimensional synthetic heterogeneous aquifer and a field‐scale bioremediation experiment conducted at Oak Ridge, Tennessee. The field application indicates that ethanol degradation for U(VI)‐bioremediation is better approximated by zero‐order reaction kinetics than first‐order reaction kinetics. 相似文献
10.
A new tracer experiment (referred to as MADE‐5) was conducted at the well‐known Macrodispersion Experiment (MADE) site to investigate the influence of small‐scale mass‐transfer and dispersion processes on well‐to‐well transport. The test was performed under dipole forced‐gradient flow conditions and concentrations were monitored in an extraction well and in two multilevel sampler (MLS) wells located at 6, 1.5, and 3.75 m from the source, respectively. The shape of the breakthrough curve (BTC) measured at the extraction well is strongly asymmetric showing a rapidly arriving peak and an extensive late‐time tail. The BTCs measured at seven different depths in the two MLSs are radically different from one another in terms of shape, arrival times, and magnitude of the concentration peaks. All of these characteristics indicate the presence of a complex network of preferential flow pathways controlling solute transport at the test site. Field‐experimental data were also used to evaluate two transport models: a stochastic advection‐dispersion model (ADM) based on conditional multivariate Gaussian realizations of the hydraulic conductivity field and a dual‐domain single‐rate (DDSR) mass‐transfer model based on a deterministic reconstruction of the aquifer heterogeneity. Unlike the stochastic ADM realizations, the DDSR accurately predicted the magnitude of the concentration peak and its arrival time (within a 1.5% error). For the multilevel BTCs between the injection and extraction wells, neither model reproduced the observed values, indicating that a high‐resolution characterization of the aquifer heterogeneity at the subdecimeter scale would be needed to fully capture 3D transport details. 相似文献
11.
Dam-break flows usually propagate along rivers and floodplains, where the processes of fluid flow, sediment transport and bed evolution are closely linked. However, the majority of existing two-dimensional (2D) models used to simulate dam-break flows are only applicable to fixed beds. Details are given in this paper of the development of a 2D morphodynamic model for predicting dam-break flows over mobile beds. In this model, the common 2D shallow water equations are modified, so that the effects of sediment concentrations and bed evolution on the flood wave propagation can be considered. These equations are used together with the non-equilibrium transport equations for graded sediments and the equation of bed evolution. The governing equations are solved using a matrix method, thus the hydrodynamic, sediment transport and morphological processes can be jointly solved. The model employs an unstructured finite volume algorithm, with an approximate Riemann solver, based on the Roe-MUSCL scheme. A predictor–corrector scheme is used in time stepping, leading to a second-order accurate solution in both time and space. In addition, the model considers the adjustment process of bed material composition during the morphological evolution process. The model was first verified against results from existing numerical models and laboratory experiments. It was then used to simulate dam-break flows over a fixed bed and a mobile bed to examine the differences in the predicted flood wave speed and depth. The effects of bed material size distributions on the flood flow and bed evolution were also investigated. The results indicate that there is a great difference between the dam-break flow predictions made over a fixed bed and a mobile bed. At the initial stage of a dam-break flow, the rate of bed evolution could be comparable to that of water depth change. Therefore, it is often necessary to employ the turbid water governing equations using a coupled approach for simulating dam-break flows. 相似文献
12.
CJN Wilson 《Bulletin of Volcanology》1991,53(8):635-644
Ignimbrite morphology, previously generalised using aspect ratios, is here quantified as the relationships between the various thicknesses of material forming an ignimbrite and the areas and volumes represented by those thicknesses. The morphology can be measured for the deposit in its present-day, eroded condition, or reconstructed for the original deposit. The reconstructed morphology of the 22 500 year BP, ca. 11 500 km2, ca. 300 km3 Oruanui ignimbrite in New Zealand is documented to illustrate the latter approach. The Oruanui ignimbrite is an intermediate aspect ratio deposit and shows broadly linear relationships between (1) In thickness and the cumulative area occupied by that thickness or less of material and (2) thickness and the volume represented by that thickness or less of material. Two theoretical morphologies, one where thicknesses exponentially decay with distance from a maximum and the other of uniform thickness (slab), are compared with the Oruanui data. Limited comparative data suggest that low aspect ratio (violently emplaced) ignimbrites will show upward-concave curves (at one extreme following the exponential decay model) and high aspect ratio (gently emplaced) ignimbrites downward-concave curves (with the slab model as an extreme) when plotted on diagrams where the Oruanui data show linear trends. The effects of erosion on Oruanui and model ignimbrite morphologies are modelled using two theoretical erosion scenarios: (1) material is evenly removed from the land surface, and (2) thinner, non-welded material is preferentially removed. For the Oruanui ignimbrite data, area is lost much more rapidly in the first instance than volume; for example, 5 m of erosion is sufficient to remove 50 area %, whereas 40 m (scenario 1) or 120 m (scenario 2) of erosion is required to remove 50 volume %. In old ignimbrites, volume estimates may be reasonably accurate even after strong erosion, provided the original thicknesses of ponded/landscape-forming material can be inferred, but estimates of original area and aspect ratio will be inaccurate. An envelope enclosing all known outcrops of an ignimbrite will give a better estimate of original area and aspect ratio than simply summing the areas of known outcrops. 相似文献
13.
Atrazine, an herbicide widely used for selective control of grassy weeds in the fields where maize is grown, is a potential ground water contaminant in China and, consequently, there is interest in predicting its mobility in agricultural soils. In this study, we determined the nonequilibrium transport characteristics of atrazine in Shahe soil (Beijing sandy loam) using the advection-dispersion equation, and using a sensitivity analysis, we evaluated the contribution of the uncertainty in a given input parameter to the overall uncertainty in model results. The asymmetrical shape and tailing of the atrazine breakthrough curve (BTC) showed that atrazine was subject to nonequilibrium transport. The observed atrazine BTC was best fitted by the chemical nonequilibrium model with a nonlinear least-squares optimization approach. Results from the sensitivity analysis indicated that the retardation factor was the most sensitive parameter. Considering the reliability of the estimated parameters, the best fit to the atrazine BTC was obtained by fixing the retardation factor based on the linear distribution coefficient, and by calculating the dispersion coefficient from the bromide BTC and the average pore water velocity from the measured data; nonequilibrium parameters were the only unknown parameters that were optimized. Model verification procedures were based on best-fit parameters optimized from one soil column experiment and applied to simulate the transport of atrazine in the duplicate experiment. The results showed there was good agreement between measured and simulated concentrations for atrazine leaching in the soil column. 相似文献
14.
Kuo-Chin Hsu Kuan-Chih Chen 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(7):1053-1065
This paper proposes a multiscale flow and transport model which can be used in three-dimensional fractal random fields. The
fractal random field effectively describes a field with a high degree of variability to satisfy the one-point statistics of
Levy-stable distribution and the two-point statistics of fractional Levy motion (fLm). To overcome the difficulty of using
infinite variance of Levy-stable distribution and to provide the physical meaning of a finite domain in real space, truncated
power variograms are utilized for the fLm fields. The fLm model is general in the sense that both stationary and commonly
used fractional Brownian motion (fBm) models are its special cases. When the upper cutoff of the truncated power variogram
is close to the lower cutoff, the stationary model is well approximated. The commonly used fBm model is recovered when the
Levy index of fLm is 2. Flow and solute transport were analyzed using the first-order perturbation method. Mean velocity,
velocity covariance, and effective hydraulic conductivity in a three-dimensional fractal random field were derived. Analytical
results for particle displacement covariance and macrodispersion coefficients are also presented. The results show that the
plume in an fLm field moves slower at early time and has more significant long-tailing behavior at late time than in fBm or
stationary exponential fields. The proposed fractal transport model has broader applications than those of stationary and
fBm models. Flow and solute transport can be simulated for various scenarios by adjusting the Levy index and cutoffs of fLm
to yield more accurate modeling results. 相似文献
15.
《Advances in water resources》2005,28(11):1217-1229
We present a new method to interpret three-dimensional pressure interference tests, which is based on an asymptotic analysis of late time pressure transient data. The approach yields reliable estimates of equivalent permeability and porosity without resorting to type-curve fitting or numerical inverse models. This is accomplished by analyzing the late-time behavior of type-curve solutions for pressure interference tests. We use our approach to infer the permeability and porosity of fractured tuff from cross-hole pneumatic injection test data. Their values are found to be in good agreement with those inferred from more complicated methods of data analysis. We analyze the statistical properties of the estimated equivalent permeability and porosity and observe a weak correlation between the two. 相似文献
16.
N. Ardjmandpour C. Pain J. Singer J. Saunders E. Aristodemou J. Carter 《Geophysical Prospecting》2011,59(4):721-748
An artificial neural network method is proposed as a computationally economic alternative to numerical simulation by the Biot theory for predicting borehole seismoelectric measurements given a set of formation properties. Borehole seismoelectric measurements are simulated using a finite element forward model, which solves the Biot equations together with an equation for the streaming potential. The results show that the neural network method successfully predicts the streaming potentials at each detector, even when the input pressures are contaminated with 10% Gaussian noise. A fast inversion methodology is subsequently developed in order to predict subsurface material properties such as porosity and permeability from streaming potential measurements. The predicted permeability and porosity results indicate that the method predictions are more accurate for the permeability predictions, with the inverted permeabilities being in excellent agreement with the actual permeabilities. This approach was finally verified by using data from a field experiment. The predicted permeability results seem to predict the basic trends in permeabilities from a packer test. As expected from synthetic results, the predicted porosity is less accurate. Investigations are also carried out to predict the zeta potential. The predicted zeta potentials are in agreement with values obtained through experimental self potential measurements. 相似文献
17.
We propose a new numerical solution to the first‐order linear acoustic/elastic wave equation. This numerical solution is based on the analytic solution of the linear acoustic/elastic wave equation and uses the Lie product formula, where the time evolution operator of the analytic solution is written as a product of exponential matrices where each exponential matrix term is then approximated by Taylor series expansion. Initially, we check the proposed approach numerically and then demonstrate that it is more accurate to apply a Taylor expansion for the exponential function identity rather than the exponential function itself. The numerical solution formulated employs a recursive procedure and also incorporates the split perfectly matched layer boundary condition. Thus, our scheme can be used to extrapolate wavefields in a stable manner with even larger time‐steps than traditional finite‐difference schemes. This new numerical solution is examined through the comparison of the solution of full acoustic wave equation using the Chebyshev expansion approach for the matrix exponential term. Moreover, to demonstrate the efficiency and applicability of our proposed solution, seismic modelling results of three geological models are presented and the processing time for each model is compared with the computing time taking by the Chebyshev expansion method. We also present the result of seismic modelling using the scheme based in Lie product formula and Taylor series expansion for the first‐order linear elastic wave equation in vertical transversely isotropic and tilted transversely isotropic media as well. Finally, a post‐stack migration results are also shown using the proposed method. 相似文献
18.
José E. Capilla J. Rodrigo J. J. Gómez-Hernández 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(3):171-190
A common approach for the performance assessment of radionuclide migration from a nuclear waste repository is by means of
Monte-Carlo techniques. Multiple realizations of the parameters controlling radionuclide transport are generated and each
one of these realizations is used in a numerical model to provide a transport prediction. The statistical analysis of all
transport predictions is then used in performance assessment. In order to reduce the uncertainty on the predictions is necessary
to incorporate as much information as possible in the generation of the parameter fields. In this regard, this paper focuses
in the impact that conditioning the transmissivity fields to geophysical data and/or piezometric head data has on convective
transport predictions in a two-dimensional heterogeneous formation. The Walker Lake data based is used to produce a heterogeneous
log-transmissivity field with distinct non-Gaussian characteristics and a secondary variable that represents some geophysical
attribute. In addition, the piezometric head field resulting from the steady-state solution of the groundwater flow equation
is computed. These three reference fields are sampled to mimic a sampling campaign. Then, a series of Monte-Carlo exercises
using different combinations of sampled data shows the relative worth of secondary data with respect to piezometric head data
for transport predictions. The analysis shows that secondary data allows to reproduce the main spatial patterns of the reference
transmissivity field and improves the mass transport predictions with respect to the case in which only transmissivity data
is used. However, a few piezometric head measurements could be equally effective for the characterization of transport predictions. 相似文献
19.
José E. Capilla J. Rodrigo J. J. Gómez-Hernández 《Stochastic Hydrology and Hydraulics》1998,12(3):171-190
A common approach for the performance assessment of radionuclide migration from a nuclear waste repository is by means of
Monte-Carlo techniques. Multiple realizations of the parameters controlling radionuclide transport are generated and each
one of these realizations is used in a numerical model to provide a transport prediction. The statistical analysis of all
transport predictions is then used in performance assessment. In order to reduce the uncertainty on the predictions is necessary
to incorporate as much information as possible in the generation of the parameter fields. In this regard, this paper focuses
in the impact that conditioning the transmissivity fields to geophysical data and/or piezometric head data has on convective
transport predictions in a two-dimensional heterogeneous formation. The Walker Lake data based is used to produce a heterogeneous
log-transmissivity field with distinct non-Gaussian characteristics and a secondary variable that represents some geophysical
attribute. In addition, the piezometric head field resulting from the steady-state solution of the groundwater flow equation
is computed. These three reference fields are sampled to mimic a sampling campaign. Then, a series of Monte-Carlo exercises
using different combinations of sampled data shows the relative worth of secondary data with respect to piezometric head data
for transport predictions. The analysis shows that secondary data allows to reproduce the main spatial patterns of the reference
transmissivity field and improves the mass transport predictions with respect to the case in which only transmissivity data
is used. However, a few piezometric head measurements could be equally effective for the characterization of transport predictions. 相似文献
20.
1 INTRODUCTION Estuaries and coastal zones have been used as means of navigation, disposal of waste material, fishing and many commercial and economic activities over the centuries. One of the most important phenomena in these regions is the suspended sediment transport, which may cause erosion and deposition, and hence changes in the estuarys morphology. In turn, such changes may lead to problems relating to navigation and estuarine management. When the bed boundary of an estuary change… 相似文献