共查询到20条相似文献，搜索用时 22 毫秒
1.
This work is the fourth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are built upon by formulating macroscale models for conservation of mass, momentum, and energy, and the balance of entropy for a species in a phase volume, interface, and common curve. In addition, classical irreversible thermodynamic relations for species in entities are averaged from the microscale to the macroscale. Finally, we comment on alternative approaches that can be used to connect species and entity conservation equations to a constrained system entropy inequality, which is a key component of the TCAT approach. The formulations detailed in this work can be built upon to develop models for species transport and reactions in a variety of multiphase systems. 相似文献
2.
This work is the third in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach to modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works in this series, we demonstrate the TCAT approach for the case of single-fluid-phase flow. The formulated model is based upon conservation equations for mass, momentum, and energy and a general entropy inequality constraint, which is developed to guide model closure. A specific example of a closed model is derived under limiting assumptions using a linearization approach and these results are compared and contrasted with the traditional single-phase-flow model. Potential extensions to this work are discussed. Specific advancements in this work beyond previous averaging theory approaches to single-phase flow include use of macroscale thermodynamics that is averaged from the microscale, the use of derived equilibrium conditions to guide a flux–force pair approach to simplification, use of a general Lagrange multiplier approach to connect conservation equation constraints to the entropy inequality, and a focus on producing complete, closed models that are solvable. 相似文献
3.
《Advances in water resources》2005,28(2):181-202
This paper is the second in a series that details the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in porous medium systems. In this work, we provide the mathematical foundation upon which the theory is based. Elements of this foundation include definitions of mathematical properties of the systems of concern, previously available theorems needed to formulate models, and several theorems and corollaries, introduced and proven here. These tools are of use in producing complete, closed-form TCAT models for single- and multiple-fluid-phase porous medium systems. Future work in this series will rely and build upon the foundation laid in this work to detail the development of sets of closed models. 相似文献
4.
This work is the sixth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works, the limiting case of connected two-fluid-phase flow is considered. A constrained entropy inequality is developed based upon a set of primary restrictions. Formal approximations are introduced to deduce a general simplified entropy inequality (SEI). The SEI is used along with secondary restrictions and closure approximations consistent with the SEI to produce a general functional form of a two-phase-flow model. The general model is in turn simplified to yield a hierarchy of models by neglecting common curves and by neglecting both common curves and interfaces. The simplest case considered corresponds to a traditional two-phase-flow model. The more sophisticated models including interfaces and common curves are more physically realistic than traditional models. All models in the hierarchy are posed in terms of precisely defined variables that allow for a rigorous connection with the microscale. The explicit nature of the restrictions and approximations used in developing this hierarchy of models provides a clear means to both understand the limitations of traditional models and to build upon this work to produce more realistic models. 相似文献
5.
This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches. 相似文献
6.
Advances in Water Resources has been a prime archival source for implementation of averaging theories in changing the scale at which processes of importance in environmental modeling are described. Thus in celebration of the 35th year of this journal, it seems appropriate to assess what has been learned about these theories and about their utility in describing systems of interest. We review advances in understanding and use of averaging theories to describe porous medium flow and transport at the macroscale, an averaged scale that models spatial variability, and at the megascale, an integral scale that only considers time variation of system properties. We detail physical insights gained from the development and application of averaging theory for flow through porous medium systems and for the behavior of solids at the macroscale. We show the relationship between standard models that are typically applied and more rigorous models that are derived using modern averaging theory. We discuss how the results derived from averaging theory that are available can be built upon and applied broadly within the community. We highlight opportunities and needs that exist for collaborations among theorists, numerical analysts, and experimentalists to advance the new classes of models that have been derived. Lastly, we comment on averaging developments for rivers, estuaries, and watersheds. 相似文献
7.
This work is the eighth in a series that develops the fundamental aspects of the thermodynamically constrained averaging theory (TCAT) that allows for a systematic increase in the scale at which multiphase transport phenomena is modeled in porous medium systems. In these systems, the explicit locations of interfaces between phases and common curves, where three or more interfaces meet, are not considered at scales above the microscale. Rather, the densities of these quantities arise as areas per volume or length per volume. Modeling of the dynamics of these measures is an important challenge for robust models of flow and transport phenomena in porous medium systems, as the extent of these regions can have important implications for mass, momentum, and energy transport between and among phases, and formulation of a capillary pressure relation with minimal hysteresis. These densities do not exist at the microscale, where the interfaces and common curves correspond to particular locations. Therefore, it is necessary for a well-developed macroscale theory to provide evolution equations that describe the dynamics of interface and common curve densities. Here we point out the challenges and pitfalls in producing such evolution equations, develop a set of such equations based on averaging theorems, and identify the terms that require particular attention in experimental and computational efforts to parameterize the equations. We use the evolution equations developed to specify a closed two-fluid-phase flow model. 相似文献
8.
River discharges vary strongly through time and space, and quantifying this variability is fundamental to understanding and modelling river processes. The river basin is increasingly being used as the unit for natural resource planning and management; to facilitate this, basin‐scale models of material supply and transport are being developed. For many basin‐scale planning activities, detailed rainfall‐runoff modelling is neither necessary nor tractable, and models that capture spatial patterns of material supply and transport averaged over decades are sufficient. Nevertheless, the data to describe the spatial variability of river discharge across large basins for use in such models are often limited, and hence models to predict river discharge at the basin scale are required. We describe models for predicting mean annual flow and a non‐dimensional measure of daily flow variability for every river reach within a drainage network. The models use sparse river gauging data, modelled grid surfaces of mean annual rainfall and mean annual potential evapotranspiration, and a network accumulation algorithm. We demonstrate the parameterization and application of the models using data for the Murrumbidgee basin, in southeast Australia, and describe the use of these predictions in modelling sediment transport through the river network. The regionalizations described contain less uncertainty, and are more sensitive to observed spatial variations in runoff, than regionalizations based on catchment area and rainfall alone. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
9.
This paper presents the predicted flow dynamics from the application of a Reynolds‐averaged Navier–Stokes model to a series of bifurcation geometries with morphologies measured during previous flume experiments. The topography of the bifurcations consists of either plane or bedform‐dominated beds which may or may not possess discordance between the two bifurcation distributaries. Numerical predictions are compared with experimental results to assess the ability of the numerical model to reproduce the division of flow into the bifurcation distributaries. The hydrodynamic model predicts: (1) diverting fluxes in the upstream channel which direct water into the distributaries; (2) super‐elevation of the free surface induced at the bifurcation edge by pressure differences; and (3) counter‐rotating secondary circulation cells which develop upstream of the apex of the bifurcation and move into the downstream channels, with water converging at the surface and diverging at the bed. When bedforms are not present, weak transversal fluxes characterize the upstream channel for almost its entire length, associated with clearly distinguishable secondary circulation cells, although these may be under‐estimated by the turbulence model used in the solution. In the bedform dominated case, the same hydrodynamic conditions were not observed, with the bifurcation influence restricted and depth scale secondary circulation cells not forming. The results also demonstrate the dominant effect bed discordance has upon flow division between the two distributaries. Finally, results indicate that in bedform dominated rivers. Consequently, we suggest that sand‐bed river bifurcations are more likely to have an influence that extends much further upstream and have a greater impact upon water distribution. This may contribute to observed morphological differences between sand‐bedded and gravel‐bedded braided river networks. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
10.
A. V. Desherevskii V. I. Zhuravlev A. N. Nikolsky A. Ya. Sidorin 《Seismic Instruments》2017,53(3):203-223
The first part of this work discussed the software requirements for working with geophysical monitoring data. This paper considers the technology for studying similar signals realized in the WinABD program. In contrast to many statistical analysis programs, WinABD supports a complete cycle of operations necessary for working with experimental time series. The software includes a database management system, a powerful research apparatus, and an interactive data visualization environment. The program makes it possible to analyze the structure of series and reveal dependences and interrelations between signals. There are a large number of nonstandard tools and methods necessary for everyday work with nonideal data. A moving time window technology is widely used, which makes it possible to study the development of all processes with time and reveal variations related to any events. A special “window-slamming” technology at the boundaries of a series makes it possible to carry out processing with a decreasing length of the series, which allows arbitrary combination of the applied methods. All of the procedures admit the presence of gaps in observations. For all data operations, a calendar time scale is used, which substantially improves convenience of operation. Correct joint processing of series with unidentical onset dates and noncoinciding observation periodicity is provided. 相似文献
11.
In this work, we study groundwater system temporal scaling in relation to plant water use and near‐river‐stage fluctuations in riparian zones where phreatophytes exist. Using detrended fluctuation analysis (DFA), we investigate the influence of regular diurnal fluctuations due to phreatophyte water use on temporal scaling properties of groundwater level variations. We found that groundwater use by phreatophytes, at the field site on the Colorado River, USA, results in distinctive crossovers (slope changes when the plots are fitted with straight lines) in the logarithm plots of root‐mean‐square fluctuations of the detrended water level time series versus time scales of groundwater level dynamics. For groundwater levels monitored at wells close to the river, we identified one crossover at ～1 day in the scaling characteristics of groundwater level variations. When time scale exceeds 1 day, the scaling properties decrease from persistent to close to 1/f noise, where f is the frequency. For groundwater levels recorded at wells further away from the river, the slope of the straight line fit (i.e. scaling exponent) is smallest when the time scale is between 1 and 3 days. When the time scale is < 1 day, groundwater variations become persistent. When the time scale is between 1 and 3 days, the variations are close to white noise, but return to persistent when the time scale is > 3 days. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
12.
Comparison of Daily GRACE Gravity Field and Numerical Water Storage Models for De-aliasing of Satellite Gravimetry Observations 总被引：1，自引：0，他引：1
L. Zenner I. Bergmann-Wolf H. Dobslaw T. Gruber A. Güntner M. Wattenbach S. Esselborn R. Dill 《Surveys in Geophysics》2014,35(6):1251-1266
Reducing aliasing effects of insufficiently modelled high-frequent, non-tidal mass variations of the atmosphere, the oceans and the hydrosphere in gravity field models derived from the Gravity Recovery and Climate Experiment (GRACE) satellite mission is the topic of this study. The signal content of the daily GRACE gravity field model series (ITG-Kalman) is compared to high-frequency bottom pressure variability and terrestrially stored water variations obtained from recent numerical simulations from an ocean circulation model (OMCT) and two hydrological models (WaterGAP Global Hydrology Model, Land Surface Discharge Model). Our results show that daily estimates of ocean bottom pressure from the most recent OMCT simulations and the daily ITG-Kalman solutions are able to explain up to 40 % of extra-tropical sea-level variability in the Southern Ocean. In contrast to this, the daily ITG-Kalman series and simulated continental total water storage variability largely disagree at periods below 30 days. Therefore, as long as no adequate hydrological model will become available, the daily ITG-Kalman series can be regarded as a good initial proxy for high-frequency mass variations at a global scale. As a second result of this study, based on monthly solutions as well as daily observation residuals, it is shown that applying this GRACE-derived de-aliasing model supports the determination of the time-variable gravity field from GRACE data and the subsequent geophysical interpretation. This leads us to the recommendation that future satellite concepts for determining mass variations in the Earth system should be capable of observing higher frequeny signals with sufficient spatial resolution. 相似文献
13.
《Advances in water resources》2005,28(5):451-465
This paper presents a methodology to optimise measurement networks for the prediction of groundwater flow. Two different strategies are followed: the design of a measurement network that aims at minimizing the log-transmissivity variance (averaged over the domain of interest) or a design that minimises the hydraulic head variance (averaged over the domain of interest). The methodology consists of three steps. In the first step the prior log-transmissivity and hydraulic head variances are estimated. This step is completely general in the sense that the prior variances maybe unconditional, or maybe conditioned to log-transmissivity and/or hydraulic head measurements. In case hydraulic head measurements are available in the first step, the inverse groundwater flow problem is solved by the sequential self-calibrated method. In the second step, the full covariance matrices of hydraulic head and log-transmissivity are calculated numerically on the basis of a sufficiently big number of Monte Carlo realisations. On the basis of the estimated covariances, the impact of an additional measurement in terms of variance reduction is calculated. The measurement that yields the maximum domain averaged variance reduction is selected. Additional measurement locations are selected according to the same procedure.The procedure has been tested for a series of synthetic reference cases. Different sampling designs are tested for each of these cases, and the proposed strategies are compared with other sampling strategies. Although the proposed strategies indeed reach their objective and yield in most cases the lowest posterior log-transmissivity variance or hydraulic head variance, the differences as compared to alternative sampling strategies are frequently small. For the cases considered here, a sampling design that covers more or less regularly the aquifer performs well.The paper also illustrates that for the optimal estimation of a well catchment a heuristic criterion (spreading measurement points as regularly as possible over the zone where there is some uncertainty regarding the capture probability) yields better results than a sampling design that minimises the posterior log-transmissivity variance or posterior hydraulic head variance. 相似文献
14.
《Advances in water resources》1998,22(3):223-238
Three-dimensional numerical simulations using a detailed synthetic hydraulic conductivity field developed from geological considerations provide insight into the scaling of subsurface flow and transport processes. Flow and advective transport in the highly resolved heterogeneous field were modeled using massively parallel computers, providing a realistic baseline for evaluation of the impacts of parameter scaling. Upscaling of hydraulic conductivity was performed at a variety of scales using a flexible power law averaging technique. A series of tests were performed to determine the effects of varying the scaling exponent on a number of metrics of flow and transport behavior. Flow and transport simulation on high-performance computers and three-dimensional scientific visualization combine to form a powerful tool for gaining insight into the behavior of complex heterogeneous systems.Many quantitative groundwater models utilize upscaled hydraulic conductivity parameters, either implicitly or explicitly. These parameters are designed to reproduce the bulk flow characteristics at the grid or field scale while not requiring detailed quantification of local-scale conductivity variations. An example from applied groundwater modeling is the common practice of calibrating grid-scale model hydraulic conductivity or transmissivity parameters so as to approximate observed hydraulic head and boundary flux values. Such parameterizations, perhaps with a bulk dispersivity imposed, are then sometimes used to predict transport of reactive or non-reactive solutes. However, this work demonstrates that those parameters that lead to the best upscaling for hydraulic conductivity and head do not necessarily correspond to the best upscaling for prediction of a variety of transport behaviors. This result reflects the fact that transport is strongly impacted by the existence and connectedness of extreme-valued hydraulic conductivities, in contrast to bulk flow which depends more strongly on mean values. It provides motivation for continued research into upscaling methods for transport that directly address advection in heterogeneous porous media.An electronic version of this article is available online at the journal's homepage at http://www.elsevier.nl/locate/advwatres or http://www.elsevier.com/locate/advwatres (see “Special section on vizualization”. The online version contains additional supporting information, graphics, and a 3D animation of simulated particle movement.©1998 Elsevier Science Limited. All rights reserved 相似文献
15.
ABSTRACTAmong various strategies for sediment reduction, venting turbidity currents through dam outlets can be an efficient way to reduce suspended sediment deposition. The accuracy of turbidity current arrival time forecasts is crucial for the operation of reservoir desiltation. A turbidity current arrival time (TCAT) model is proposed. A multi-objective genetic algorithm (MOGA), a support vector machine (SVM) and a two-stage forecasting technique are integrated to obtain more effective long lead-time forecasts of inflow discharge and inflow sediment concentration. The multi-objective genetic algorithm (MOGA) is applied for determining the optimal inputs of the forecasting model, support vector machine (SVM). The two-stage forecasting technique is implemented by adding the forecasted values to candidate inputs for improving the long lead-time forecasting. Then, the turbidity current arrival time from the inflow boundary to the reservoir outlet is calculated. To demonstrate the effectiveness of the TCAT model, it is applied to Shihmen Reservoir in northern Taiwan. The results confirm that the TCAT model forecasts are in good agreement with the observed data. The proposed TCAT model can provide useful information for reservoir sedimentation management during desilting operations. 相似文献
16.
In this paper, the concern of accuracy in peak estimation by the artificial neural network (ANN) river flow models is discussed and a suitable statistical procedure to get better estimates from these models is presented. The possible cause for underestimation of peak flow values has been attributed to the local variations in the function being mapped due to varying skewness in the data series, and theoretical considerations of the network functioning confirm this. It is envisaged that an appropriate data transformation will reduce the local variations in the function being mapped, and thus any ANN model built on the transformed series should perform better. This heuristic is illustrated and confirmed by many case studies and the results suggest that the model performance is significantly improved by data transformation. The model built on transformed data outperforms the model built on raw data in terms of various statistical performance indices. The peak estimates are improved significantly by data transformation. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
17.
Numerical techniques for subsurface flow and transport modeling are often limited by computational limitations including fine mesh and small time steps to control artificial dispersion. Particle-tracking simulation offers a robust alternative for modeling solute transport in subsurface formations. However, the modeling scale usually differs substantially from the rock measurement scale, and the scale-up of measurements have to be made accounting for the pattern of spatial heterogeneity exhibited at different scales. Therefore, it is important to construct accurate coarse-scale simulations that are capable of capturing the uncertainties in reservoir and transport attributes due to scale-up. A statistical scale-up procedure developed in our previous work is extended by considering the effects of unresolved (residual) heterogeneity below the resolution of the finest modeling scale in 3D. First, a scale-up procedure based on the concept of volume variance is employed to construct realizations of permeability and porosity at the (coarse) transport modeling scale, at which flow or transport simulation is performed. Next, to compute various effective transport parameters, a series of realizations exhibiting detailed heterogeneities at the fine scale, whose domain size is the same as the transport modeling scale, are generated. These realizations are subjected to a hybrid particle-tracking simulation. Probabilistic transition time is considered, borrowing the idea from the continuous time random walk (CTRW) technique to account for any sub-scale heterogeneity at the fine scale level. The approach is validated against analytical solutions and general CTRW formulation. Finally, coarse-scale transport variables (i.e., dispersivities and parameterization of transition time distribution) are calibrated by minimizing the mismatch in effluent history with the equivalent averaged models. Construction of conditional probability distributions of effective parameters is facilitated by integrating the results over the entire suite of realizations. The proposed method is flexible, as it does not invoke any explicit assumption regarding the multivariate distribution of the heterogeneity. In contrast to other hierarchical CTRW formulation for modeling multi-scale heterogeneities, the proposed approach does not impose any length scale requirement regarding sub-grid heterogeneities. In fact, it aims to capture the uncertainty in effective reservoir and transport properties due to the presence of heterogeneity at the intermediate scale, which is larger than the finest resolution of heterogeneity but smaller than the representative elementary volume, but it is often comparable to the transport modeling scale. 相似文献
18.
S. Orr S. P. Neuman 《Stochastic Environmental Research and Risk Assessment (SERRA)》1994,8(2):157-172
Operator representations of stochastic subsurface flow equations allow writing their solutions implicitly or explicitly in terms of integro-differential expressions. Most of these representations involve Neumann series that must be truncated or otherwise approximated to become operational. It is often claimed that truncated Neumann series allow solving groundwater flow problems in the presence of arbitrarily large heterogeneities. Such claims have so far not been backed by convincing computational examples, and we present an analysis which suggests that they may not be justified on theoretical grounds. We describe an alternative operator representation due to Neuman and Orr (1993) which avoids the use of Neumann series yet accomplishes a similar purpose. It leads to a compact integro-differential form which provides considerable new insight into the nature of the solution. When written in terms of conditional moments, our new representation contains local and nonlocal effective parameters that depend on scale and information. As such, these parameters are not unique material properties but may change as more is learned about the flow system. 相似文献
19.
Maps of satellite-derived estimates of monthly averaged chlorophyll a concentration over the northern West Florida Shelf show interannual variations concentrated near the coastline, but also extending offshore over the shelf in a tongue-like pattern from the Apalachicola River during the late winter and early spring. These anomalies are significantly correlated with interannual variability in the flow rate of the Apalachicola River, which is linked to the precipitation anomalies over the watershed, over a region extending 150–200 km offshore out to roughly the 100 m isobath. This study examines the variability of the Apalachicola River and its impacts on the variability of water properties over the northern West Florida Shelf. A series of numerical model experiments show that episodic wind-driven offshore transport of the Apalachicola River plume is a likely physical mechanism for connecting the variability of the river discharge with oceanic variability over the middle and outer shelf. 相似文献
20.
Nicholas J. Clifford 《地球表面变化过程与地形》1998,23(2):109-127
This paper compares flow intensity data obtained with different instruments from a variety of fluvial environments. It examines associations between the root-mean-square of longitudinal velocity fluctuations (flow intensity), local mean velocity, relative depth, and boundary resistance. Results indicate systematic differences in the behaviour of flow intensity which scale with respect to position in the boundary layer (deep sand-bedded rivers), boundary grain resistance (shallow river environments with coarse beds), and possibly form resistance (shallower sand-bedded rivers). Preliminary approaches to prediction and modelling of variations in flow intensity are suggested based upon linear regression relationships. Intensity values are also compared with theoretical and empirical limits to the use of Taylor's substitution, which allows time and frequency properties of a single-point velocity time series to be used to yield a flow length scale. In general, limits are exceeded in all environments for near-boundary flow measurements, but are met for y/d > 0·3 in most cases in sand-bed rivers, and for y/d > 0·4 in some gravel-bed environments. © 1998 John Wiley & Sons, Ltd. 相似文献