共查询到20条相似文献，搜索用时 15 毫秒
1.
Stochastic analysis is commonly used to address uncertainty in the modeling of flow and transport in porous media. In the stochastic approach, the properties of porous media are treated as random functions with statistics obtained from field measurements. Several studies indicate that hydrological properties depend on the scale of measurements or support scales, but most stochastic analysis does not address the effects of support scale on stochastic predictions of subsurface processes. In this work we propose a new approach to study the scale dependence of stochastic predictions. We present a stochastic analysis of immiscible fluid–fluid displacement in randomly heterogeneous porous media. While existing solutions are applicable only to systems in which the viscosity of one phase is negligible compare with the viscosity of the other (water–air systems for example), our solutions can be applied to the immiscible displacement of fluids having arbitrarily viscosities such as NAPL–water and water–oil. Treating intrinsic permeability as a random field with statistics dependant on the permeability support scale (scale of measurements) we obtained, for one-dimensional systems, analytical solutions for the first moments characterizing unbiased predictions (estimates) of system variables, such as the pressure and fluid–fluid interface position, and we also obtained second moments, which characterize the uncertainties associated with such predictions. Next we obtained empirically scale dependent exponential correlation function of the intrinsic permeability that allowed us to study solutions of stochastic equations as a function of the support scale. We found that the first and second moments converge to asymptotic values as the support scale decreases. In our examples, the statistical moments reached asymptotic values for support scale that were approximately 1/10000 of the flow domain size. We show that analytical moment solutions compare well with the results of Monte Carlo simulations for moderately heterogeneous porous media, and that they can be used to study the effects of heterogeneity on the dynamics and stability of immiscible flow. 相似文献
2.
This paper deals with the lower order (first four) nonstationary statistical moments of the response of linear systems with random stiffness and random damping properties subject to random nonstationary excitation modeled as white noise multiplied by an envelope function. The method of analysis is based on a Markov approach using stochastic differential equations (SDE). The linear SDE with random coefficients subject to random excitation with deterministic initial conditions are transformed to an equivalent nonlinear SDE with deterministic coefficients and random initial conditions subject to random excitation. In this procedure, new SDE with random initial conditions, deterministic coefficients and zero forcing functions are introduced to represent the random variables. The joint statistical moments of the response are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vectors and the random variables of the structural system. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. The statistical moment equations are ordinary nonlinear differential equations where hierarchy of moments appear. The hierarchy is closed by the cumulant neglect closure method applied at the fourth order statistical moment level. General formulation is given for multi-degree-of-freedom (MDOF) systems and the performance of the method in problems with nonstationary excitations and large variabilities is illustrated for a single-degree-of-freedom (SDOF) oscillator. 相似文献
3.
Power-Law Testing for Fault Attributes Distributions 总被引：2，自引：0，他引：2
This paper is devoted to statistical analysis of faults’ attributes. The distributions of lengths, widths of damage zones, displacements and thicknesses of fault cores are studied. Truncated power-law (TPL) is considered in comparison with commonly used simple power-law (PL) (or Pareto) distribution. The maximal likelihood and the confidence interval of the exponent for both PL and TPL are estimated by appropriate statistical methods. The Kolmogorov–Smirnov (KS) test and the likelihood ratio test with alternative non-nested hypothesis for exponential distribution are used to verify the statistical approximation. Furthermore, the advantage of TPL is proved by Bayesian information criterion. Our results suggest that a TPL is more suitable for describing fault attributes, and that its condition is satisfied for a wide range of fault scales. We propose that using truncated power laws in general might eliminate or relax the bias related to sampling strategy and the resolution of measurements (such as censoring, truncation, and cut effect) and; therefore, the most reliable range of data can be considered for the statistical approximation of fault attributes. 相似文献
4.
A new approximate method of solution for stochastic optimal control problems with many state and control variables is introduced. The method is based on the expansion of the optimal control into the deterministic feedback control plus a caution term. The analytic, small-perturbation calculation of the caution term is at the heart of the new method. The developed approximation depends only on the first two statistical moments of the random inputs and up to the third derivatives of the cost functions. Its computational requirements do not exhibit the exponential growth exhibited by discrete stochastic DP and can be used as a suboptimal solution to problems for which application of stochastic DP is not feasible. The method is accurate when the cost-to-go functions are approximately cubic in a neighbourhood around the deterministic trajectory whose size depends on forecasting uncertainty. Furthermore, the method elucidates the stochastic optimization problem yielding insights which cannot be easily obtained from the numerical application of discrete DP. 相似文献
5.
《水文科学杂志》2013,58(4):868-882
Abstract Non-Darcian flow in a finite fractured confined aquifer is studied. A stream bounds the aquifer at one side and an impervious stratum at the other. The aquifer consists of fractures capable of transmitting water rapidly, and porous blocks which mainly store water. Unsteady flow in the aquifer due to a sudden rise in the stream level is analysed by the double-porosity conceptual model. Governing equations for the flow in fractures and blocks are developed using the continuity equation. The fluid velocity in fractures is often too high for the linear Darcian flow so that the governing equation for fracture flow is modified by Forcheimer's equation, which incorporates a nonlinear term. Governing equations are coupled by an interaction term that controls the quasi-steady-state fracture—block interflow. Governing equations are solved numerically by the Crank-Nicolson implicit scheme. The numerical results are compared to the analytical results for the same problem which assumes Darcian flow in both fractures and blocks. Numerical and analytical solutions give the same results when the Reynolds number is less than 0.1. The effect of nonlinearity on the flow appears when the Reynolds number is greater than 0.1. The higher the rate of flow from the stream to the aquifer, the higher the degree of nonlinearity. The effect of aquifer parameters on the flow is also investigated. The proposed model and its numerical solution provide a useful application of nonlinear flow models to fractured aquifers. It is possible to extend the model to different types of aquifer, as well as boundary conditions at the stream side. Time-dependent flow rates in the analysis of recession hydrographs could also be evaluated by this model. 相似文献
6.
A Lagrangian perturbation method is applied to develop a method of moments for solute flux through a three-dimensional nonstationary flow field. The flow nonstationarity stems from medium nonstationarity and internal and external boundaries of the study domain. The solute flux is described as a space-time process where time refers to the solute flux breakthrough through a control plane (CP) at some distance downstream of the solute source and space refers to the transverse displacement distribution at the CP. The analytically derived moment equations for solute transport in a nonstationarity flow field are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. This approach combines the stochastic model with the flexibility of the numerical method to boundary and initial conditions. The developed method is applied to study the effects of heterogeneity and nonstationarity of the hydraulic conductivity and chemical sorption coefficient on solute transport. The study results indicate all these factors will significantly influence the mean and variance of solute flux. 相似文献
7.
A Simple Analogue Experiment to Account for Power-law and Exponential Decays of Earthquake Sequences
H. Ogasawara 《Pure and Applied Geophysics》2002,159(1-3):309-343
— An event rate decays either exponentially in earthquake swarms, or according to the power law in aftershock sequences, suggesting different physics for these decays. In order to investigate the physics, I measured decays in the rate of acoustic emissions (AE) that occur to relax thermal stress after turning off a home cooking apparatus. Such AE are analogous to an earthquake induced by fluid intrusion because thermo-elasticity was precisely analogous to poro-elasticity. To consider what controlled the decays, different heating rates and durations were specified in several experimental runs for which the mechanical and thermal properties were identical. Temperature decayed exponentially with the same time constant. However, both a power-law decay with a p value roughly equal to two and an exponential decay were observed. To ascertain what was occurring at the AE source, the stress and frictional strength at the AE source were numerically estimated. The stress at the AE source decayed exponentially for both power-law decay and exponential decay. In power-law decay, strength was initially very low and recovered immediately and significantly. However, in exponential decay, the change in strength during the initial stage was not as large as that in power-law decay. It was demonstrated that the time constant of exponential event-rate decay was identical to that of temperature decay if strength is constant. 相似文献
8.
阐述了大吨位双出杆粘滞阻尼器开发的数值与实验研究结果.基于硅油的幂律特性,通过对硅油介质的流态分析,介绍了非牛顿幂律流体模型对粘滞阻尼器耗能和阻尼出力的影响,与粘滞阻尼器的分析模型和计算公式.在商用流体软件平台上利用动网格技术对样品粘滞阻尼器阻尼出力进行了计算;综合实验研究结果,最终确定了大吨位土木用粘滞阻尼器设计的经验方法.另一方面,实验曲线和数值曲线基本吻和,验证了通过数值手段对粘滞阻尼器的出力特性进行预分析,从而提高开发精度、指导产品设计和缩短产品的开发周期的可行性. 相似文献
9.
Kun‐xia Yu Lars Gottschalk Xiang Zhang Peng Li Zhanbin Li Lihua Xiong Qian Sun 《水文研究》2018,32(12):1844-1857
An approach for nonstationary low‐flow frequency analysis is developed and demonstrated on a dataset from the rivers on the Loess Plateau of China. Nonstationary low‐flow frequency analysis has drawn significant attention in recent years by establishing relationships between low‐flow series and explanatory variables series, but few studies have tested whether the time‐varying moments of low flow can be fully described by the time‐varying moments of the explanatory variables. In this research, the low‐flow distributions are analytically derived from the 2 basic explanatory variables—the recession duration and the recession coefficient—with the assumption that the recession duration and recession coefficient variables follow exponential and gamma distributions, respectively; the derived low‐flow distributions are applied to test whether the time‐varying moments of explanatory variables can explain the nonstationarities found in the low‐flow variable. The effects of ecosystem construction measures, that is, check dam, terrace, forest, and grassland, on the recession duration and recession coefficient are further discussed. Daily flow series from 11 hydrological stations from the Loess Plateau are used and processed with a moving average technique. Low‐flow data are extracted following the pit under threshold approach. Six of the 11 low‐flow series show significant nonstationarities at the 5% significance level, and the trend curves of the moments of low flow are in close agreement with the curves estimated from the derived distribution with time‐dependent moments of the recession duration and time‐constant moments of the recession coefficient. It is indicated that the nonstationarity in the low‐flow distribution results from the nonstationarity in the recession duration in all 6 cases, and the increase in the recession duration is resulted from large‐scale ecosystem constructions rather than climate change. The large‐scale ecosystem constructions are found to have more influence on the decrease in streamflow than on the increase in watershed storage, thus resulting in the reduction of low flow. A high return period for the initial fixed design value decreases dramatically with an increasing recession duration. 相似文献
10.
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
11.
L. Rothenburg E. L. Matyas S. Z. Ambrus 《Stochastic Environmental Research and Risk Assessment (SERRA)》1987,1(3):217-240
This paper presents a detailed statistical analysis of Hagen-Poiseuille flow in plane random isotropic networks of interconnected channels. The emphasis is on statistico-geometrical features of networks that affect macroscopic permeability. It is shown that permeability of a network depends on its average co-ordination number, the first two moments of the channel length distribution and other explicitly identifiable geometrical features. Distributions of flow rates in channels and average flow rates are established by minimization of the rate of energy dissipation. Theoretical developments are interpreted in the context of classical statistical mechanics. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network. 相似文献
12.
《Advances in water resources》1996,19(3):133-144
A simplified stochastic infiltration model is presented, aimed at representing the rainfall-runoff transformation in the presence of heterogeneity in the soil and with precipitation as a random variable with complex temporal evolution. Such a model is based on a simple water mass balance of a surface soil layer, considered as a non-linear reservoir. The explicit inclusion of spatial heterogeneity allows the model to be used in sub-grid parametrizations at a variety of scales, from the distributed modelling of the hydrological response of small watersheds to the representation of surface mass fluxes in General Circulation Models. An approximate solution procedure is developed, which allows the estimation of statistical moments of the soil effective saturation and runoff inside discrete time steps where the hydraulic saturated conductivity and the rainfall intensity are taken as random variables with known probability density functions. As a first test of the proposed model, two different simulations, relative to two soils with different hydraulic conductivity distributions, are presented and discussed. A year long record of hourly averaged rainfall intensities, as measured by a tipping bucket gauge in Central Italy, is taken as the main input. The main finding is that the non-linear nature of the soil filter is such that, for random precipitation intensity, the coefficient of variation of the runoff is always higher than that of precipitation. Such a non-linear variability enhancement, due mainly to the threshold character of the soil mass balance equation, tends to be slightly dampened by the variability of the hydraulic saturated conductivity. 相似文献
13.
M. Riva A. Guadagnini F. Ballio 《Stochastic Environmental Research and Risk Assessment (SERRA)》1999,13(3):217-230
We consider the effect of randomly heterogeneous hydraulic conductivity on the spatial location of time-related capture zones
(isochrones) for a non-reactive tracer in the steady-state radial flow field due to a pumping well in a confined aquifer.
A Monte Carlo (MC) procedure is used in conjunction with FFT-based spectral methods. The log hydraulic conductivity field
is assumed to be Gaussian and stationary, with isotropic exponential correlation. Various degrees of domain heterogeneity
are considered and stability and accuracy of the MC procedure is examined. The location of an isochrone becomes uncertain
due to heterogeneity, and it is strongly influenced by hydraulic conductivity variance. The probability that a particle released
at a point in the aquifer is pumped by the well within a given time is identified. We propose a new expression for the probabilistic
spatial distribution of isochrones, which is formally similar to the analytical solution for a uniform medium and takes into
account the effects of heterogeneity. 相似文献
14.
15.
Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation 
下载免费PDF全文
下载免费PDF全文 In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field. 相似文献
16.
《Advances in water resources》1998,21(3):203-215
Transport of inert solutes in two-dimensional bounded heterogeneous porous media is investigated in a stochastic framework. After adopting a first-order approximation of the flow equations, analytical expressions are derived for the velocity covariances. Effects of the boundary conditions and aquifer size upon the statistical moments are analyzed. While the size of the domain is shown to have small influence on the covariances in most cases, the solutions are considerably modified by the boundaries. The results are compared with analytical solutions on infinite domains, and several discrepancies are demonstrated. For example, while the velocity variances on infinite domains are homogeneous, the present results are strongly non-stationary. Finally, the problem is solved numerically by the Monte Carlo simulation method. The results, including the behavior near the boundaries, are shown to be in close agreement with analytical solutions. 相似文献
17.
S. Yue 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(3):244-260
The open literature reveals several types of bivariate exponential distributions. Of them only the Nagao–Kadoya distribution
(Nagao and Kadoya, 1970, 1971) has a general form with marginals that are standard exponential distributions and the correlation
coefficient being 0≤ρ<1. On the basis of the principle that if a theoretical probability distribution can represent statistical
properties of sample data, then the computed probabilities from the theoretical model should provide a good fit to observed
ones, numerical experiments are executed to investigate the applicability of the Nagao–Kadoya bivariate exponential distribution
for modeling the joint distribution of two correlated random variables with exponential marginals. Results indicate that this
model is suitable for analyzing the joint distribution of two exponentially distributed variables. The procedure for the use
of this model to represent the joint statistical properties of two correlated exponentially distributed variables is also
presented. 相似文献
18.
We present a diagrammatic method for solving stochastic 1-D and 2-D steady-state flow equations in bounded domains. The diagrammatic method results in explicit solutions for the moments of the hydraulic head. This avoids certain numerical constraints encountered in realization-based methods. The diagrammatic technique also allows for the consideration of finite domains or large fluctuations, and is not restricted by distributional assumptions. The results of the method for 1-D and 2-D finite domains are compared with those obtained through a realization-based approach. Mean and variance of head are well reproduced for all log-conductivity variances inputted, including those larger than one. The diagrammatic results also compare favorably to hydraulic head moments derived by standard analytic methods requiring a linearized form of the flow equation. 相似文献
19.
《Advances in water resources》2001,24(6):607-619
Solute discharge moments (mean and variance) are computed using numerical modeling of flow and advective transport in two-dimensional heterogeneous aquifers and are compared to theoretical results. The solute discharge quantifies the temporal evolution of the total contaminant mass crossing a certain compliance boundary. In addition to analyzing the solute discharge moments within a classical absolute dispersion framework, we also analyze relative dispersion formulation, whereby plume meandering (deviation from mean flow path caused by velocity variations at scales larger than plume size) is removed. This study addresses some important issues related to the computation of solute discharge moments from random walk particle tracking experiments, and highlights some of the important differences between absolute and relative dispersion frameworks. Relative dispersion formulation produces maximum uncertainty that coincides with the peak mean discharge. Absolute dispersion, however, results in earlier arrival of the uncertainty peak as compared to the first moment peak. Simulations show that the standard deviation of solute discharge in a relative dispersion framework requires increasingly large temporal sampling windows to smooth out some of the large fluctuations in breakthrough curves associated with advective transport. Using smoothing techniques in particle tracking to distribute the particle mass over a volume rather than at a point significantly reduces the noise in the numerical simulations and removes the need to use large temporal windows. Same effect can be obtained by adding a local dispersion process to the particle tracking experiments used to model advective transport. The effect of the temporal sampling window bears some relevance and important consequences for evaluating risk-related parameters. The expected value of peak solute discharge and its standard deviation are very sensitive to this sampling window and so will be the risk distribution relying on such numerical models. 相似文献
20.
L. D. Oliver G. Christakos 《Stochastic Environmental Research and Risk Assessment (SERRA)》1995,9(4):269-296
We present a diagrammatic method for solving stochastic 1-D and 2-D steady-state flow equations in bounded domains. The diagrammatic method results in explicit solutions for the moments of the hydraulic head. This avoids certain numerical constraints encountered in realization-based methods. The diagrammatic technique also allows for the consideration of finite domains or large fluctuations, and is not restricted by distributional assumptions. The results of the method for 1-D and 2-D finite domains are compared with those obtained through a realization-based approach. Mean and variance of head are well reproduced for all log-conductivity variances inputted, including those larger than one. The diagrammatic results also compare favorably to hydraulic head moments derived by standard analytic methods requiring a linearized form of the flow equation. 相似文献