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1.
The continuous time random walk (CTRW) has both an elegant mathematical theory and a successful record at modeling solute transport in the subsurface. However, there are some interpretation ambiguities relating to the relationship between the discrete CTRW transition distributions and the underlying continuous movement of solute that have not been addressed in existing literature. These include the exact definition of “transition”, and the extent to which transition probability distributions are unique/quantifiable from data. Here, we present some theoretical results which address these uncertainties in systems with an advective bias. Simultaneously, we present an alternative, reduced parameter CTRW formulation for general advective transport in heterogeneous porous media, which models early- and late-time transport by use of random transition times between sparse, imaginary planes normal to flow. We show that even in the context of this reduced-parameter formulation there is nonuniqueness in the definitions of both transition lengths and waiting time distributions, and that neither may be uniquely determined from experimental data. For practical use of this formulation, we suggest Pareto transition time distributions, leading to a two-degree-of-freedom modeling approach. We then demonstrate the power of this approach in fitting two sets of existing experimental data. While the primary focus is the presentation of new results, the discussion is designed to be pedagogical and to provide a good entry point into practical modeling of solute transport with the CTRW. 相似文献
2.
A nested workflow of multiple‐point geostatistics (MPG) and sequential Gaussian simulation (SGS) was tested on a study area of 6 km2 located about 20 km northwest of Quebec City, Canada. In order to assess its geological and hydrogeological parameter heterogeneity and to provide tools to evaluate uncertainties in aquifer management, direct and indirect field measurements are used as inputs in the geostatistical simulations to reproduce large and small‐scale heterogeneities. To do so, the lithological information is first associated to equivalent hydrogeological facies (hydrofacies) according to hydraulic properties measured at several wells. Then, heterogeneous hydrofacies (HF) realizations are generated using a prior geological model as training image (TI) with the MPG algorithm. The hydraulic conductivity (K) heterogeneity modeling within each HF is finally computed using SGS algorithm. Different K models are integrated in a finite‐element hydrogeological model to calculate multiple transport simulations. Different scenarios exhibit variations in mass transport path and dispersion associated with the large‐ and small‐scale heterogeneity respectively. Three‐dimensional maps showing the probability of overpassing different thresholds are presented as examples of management tools. 相似文献
3.
Geochemical reaction rate laws are often measured using crushed minerals in well-mixed laboratory systems that are designed to eliminate mass transport limitations. Such rate laws are often used directly in reactive transport models to predict the reaction and transport of chemical species in consolidated porous media found in subsurface environments. Due to the inherent heterogeneities of porous media, such use of lab-measured rate laws may introduce errors, leading to a need to develop methods for upscaling reaction rates. In this work, we present a methodology for using pore-scale network modeling to investigate scaling effects in geochemical reaction rates. The reactive transport processes are simulated at the pore scale, accounting for heterogeneities of both physical and mineral properties. Mass balance principles are then used to calculate reaction rates at the continuum scale. To examine the scaling behavior of reaction kinetics, these continuum-scale rates from the network model are compared to the rates calculated by directly using laboratory-measured reaction rate laws and ignoring pore-scale heterogeneities. In this work, this methodology is demonstrated by upscaling anorthite and kaolinite reaction rates under simulation conditions relevant to geological CO2 sequestration. Simulation results show that under conditions with CO2 present at high concentrations, pore-scale concentrations of reactive species and reaction rates vary spatially by orders of magnitude, and the scaling effect is significant. With a much smaller CO2 concentration, the scaling effect is relatively small. These results indicate that the increased acidity associated with geological sequestration can generate conditions for which proper scaling tools are yet to be developed. This work demonstrates the use of pore-scale network modeling as a valuable research tool for examining upscaling of geochemical kinetics. The pore-scale model allows the effects of pore-scale heterogeneities to be integrated into system behavior at multiple scales, thereby identifying important factors that contribute to the scaling effect. 相似文献
4.
We present a sequence of purely advective transport models that demonstrate the influence of small-scale geometric inhomogeneities on contaminant transport in fractured crystalline rock. Special weight is placed on the role of statistically generated variable fracture apertures. The fracture network geometry and the aperture distribution are based on information from an in situ radionuclide retardation experiment performed at Grimsel test site (Swiss Alps). The obtained breakthrough curves are fitted with the advection dispersion equation and continuous-time random walks (CTRW). CTRW is found to provide superior fits to the late-arrival tailing and is also found to show a good correlation with the velocity distributions obtained from the hydraulic models. The impact of small-scale heterogeneities, both in fracture geometry and aperture, on transport is shown to be considerable. 相似文献
5.
《Advances in water resources》1998,21(7):581-590
Advances in computer power and in reservoir characterization allow simulation of pressure transients in complex reservoirs generated stochastically. Generally, interpretation of these transient gives useful information about the reservoir hydraulic properties: a major goal is to interpret these transients in the stochastic context. First we ensemble average the pressure over all the random permeability field realizations to derive an equation which drives the ensemble averaged pressure. We use the Fourier transform in space and the Laplace transform in time, in conjuction with a perturbation series expansion in successive powers of the permeability fluctuations to obtain an explicit solution. The Nth order term of this series involves the hydrodynamic interaction between N permeability heterogeneities and after averaging we obtain an expansion containing correlation functions of permeability fluctuations of increasing order.Next, Feynman graphs are introduced allowing a more attractive graphical interpretation of the perturbation series. Then series summation techniques are employed to reduce the graph number to be summed at each order of the fluctuation expansion. This in turn gives useful physical insights on the homogenization processes involved. In particular, it is shown that the sum of the so-called ‘one-particle irreducible graphs’ gives the kernel of a linear integro-differential equation obeyed by the ensemble average pressure. All the information about the heterogeneity structure is contained in this renormalized kernel, which is a limited range function.This equation on its own is the starting point of useful asymptotic results and approximations. In particular it is shown that interpretation of pumping tests yields the steady-state equivalent permeability after a sufficiently long time for an infinite reservoir, as expected. 相似文献
6.
The spatial distribution of hydraulic properties in the subsurface controls groundwater flow and solute transport. However, many approaches to modeling these distributions do not produce geologically realistic results and/or do not model the anisotropy of hydraulic conductivity caused by bedding structures in sedimentary deposits. We have developed a flexible object-based package for simulating hydraulic properties in the subsurface—the Hydrogeological Virtual Realities (HyVR) simulation package. This implements a hierarchical modeling framework that takes into account geological rules about stratigraphic bounding surfaces and the geometry of specific sedimentary structures to generate realistic aquifer models, including full hydraulic-conductivity tensors. The HyVR simulation package can create outputs suitable for standard groundwater modeling tools (e.g., MODFLOW), is written in Python, an open-source programming language, and is openly available at an online repository. This paper presents an overview of the underlying modeling principles and computational methods, as well as an example simulation based on the Macrodispersion Experiment site in Columbus, Mississippi. Our simulation package can currently simulate porous media that mimic geological conceptual models in fluvial depositional environments, and that include fine-scale heterogeneity in distributed hydraulic parameter fields. The simulation results allow qualitative geological conceptual models to be converted into digital subsurface models that can be used in quantitative numerical flow-and-transport simulations, with the aim of improving our understanding of the influence of geological realism on groundwater flow and solute transport. 相似文献
7.
A one‐dimensional process‐based approach to study reservoir sediment dynamics during management operations 
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下载免费PDF全文 A comprehensive understanding of the dynamics of erosion and sedimentation in reservoirs under different management conditions is required to anticipate sedimentation issues and implement effective sediment management strategies. This paper describes a unique approach combining fluvial geomorphology tools and morphodynamic modeling for analyzing the sediment dynamics of an elongated hydropower reservoir subjected to management operations: the Génissiat Reservoir on the Rhône River. Functional sub‐reaches representative of the reservoir morphodynamics were delineated by adapting natural river segmentation methods to elongated reservoirs. The segmentation revealed the link between the spatial and temporal reservoir changes and the variability of longitudinal flow conditions during reservoir management operations. An innovative modeling strategy, incorporating the reservoir segmentation into two sediment transport codes, was implemented to simulate the dynamics of erosion and sedimentation at the reach scale during historic events. One code used a bedload approach, based on the Exner equation with a transport capacity formula, and the other used a suspended load approach based on the advection–dispersion equation. This strategy provided a fair quantification of the dynamics of erosion and sedimentation at the reach scale during different management operations. This study showed that the reservoir morphodynamics is controlled by bedload transport in upper reaches, graded suspended load transport of sand in middle reaches and suspended load transport of fine sediments in lower reaches. Eventually, it allowed a better understanding of the impact of dam management on sediment dynamics. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
8.
本文利用随机介质模型对复杂岩性储层进行了非均质性描述.利用模型特征量即非均质纵横比、纵向谱指数、横向谱指数以及扰动标准差等来模拟不同的随机介质.在前人工作的基础上,由某油气田的两口井资料估计储层非均质性能谱,从能谱曲线上提取储层纵向大小尺度非均质谱指数.通过将二维随机介质模拟的合成井记录互相关系数与实际井记录互相关系数进行分析比较,分别得到大小尺度非均质情况下最佳拟合时的横向谱指数和非均质性纵横比.以上求得的各种特征量从不同角度定量分析了储层非均质性的纵横向变化,为储层横向预测提供了依据. 相似文献
9.
《中国科学D辑(英文版)》2008,(Z2)
The studies on fluvial reservoir architecture are mainly aimed at outcrop and modern deposition,but rarely at the subsurface reservoir,so there are few effective methods to predict the distribution of subsurface reservoir architectures. In this paper,taking the meandering river reservoir of Guantao formation Gudao Oilfield,Jiyang depression,Baohai Gulf Basin,East China as an example,the archi-tectural modeling method of complex meandering belt reservoir is proposed,that is hierarchy con-straint,pattern fitting and multi-dimensional interaction. Architectures of meandering river reservoir can be divided into three hierarchies: meandering channel sandbody,point bar and lateral accretion body. Different hierarchies of the quantitative architecture pattern are fitted to subsurface well data (including dynamic monitoring data) in different hierarchies through one-dimensional hole,2D profiles and plane and 3D space,which are verified by each other. And then 3D model in different hierarchies is established. At the same time,the quantificational relationship between width of active river and the scale of point bar is set up,and the scale of lateral accretion sand body and shale beddings is con-firmed with horizontal well data. The study not only has significant meaning on the development of geology,but also can improve the oilfield exploitation greatly. 相似文献
10.
In subsurface porous media, the soil water retention curve (WRC) and unsaturated hydraulic conductivity curve (UHC) are two important soil hydraulic property curves. Spatial heterogeneity is ubiquitous in nature, which may significantly affect soil hydraulic property curves. The main theme of this paper is to investigate how spatial heterogeneities, including their arrangements and amounts in soil flumes, affect soil hydraulic property curves. This paper uses a two‐dimensional variably saturated flow and solute transport finite element model to simulate variations of pressure and moisture content in soil flumes under a constant head boundary condition. To investigate the behavior of soil hydraulic property curves owing to variations of heterogeneities and their arrangements as well, cases with different proportions of heterogeneities are carried out. A quantitative evaluation of parameter variations in the van Genuchten model (VG model) resulting from heterogeneity is presented. Results show that the soil hydraulic properties are strongly affected by variations of heterogeneities and their arrangements. If the pressure head remains at a specific value, the soil moisture increases when heterogeneities increase in the soil flumes. On the other hand, the unsaturated hydraulic conductivity decreases when heterogeneities increase in the soil flumes under a constant pressure head. Moreover, results reveal that parameters estimated from both WRC and UHC also are affected by shapes of heterogeneity; this indicates that the parameters obtained from the WRC are not suitable for predicting the UHC of different shapes in heterogeneous media. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
J. Zhu 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(6):447-461
A stochastic simulation is performed to study multiphase flow and contaminant transport in fractal porous media with evolving
scales of heterogeneity. Numerical simulations of residual NAPL mass transfer and subsequent transport of dissolved and/or
volatilized NAPL mass in variably saturated media are carried out in conjunction with Monte Carlo techniques. The impact of
fractal dimension, plume scale and anisotropy (stratification) of fractal media on relative dispersivities is investigated
and discussed. The results indicate the significance of evolving scale of porous media heterogeneity to the NAPL transport
in the subsurface. In general, the fractal porous media enhance the dispersivities of NAPL mass plume transport in both the
water phase and the gas phase while the influence on the water phase is more significant. The porous media with larger fractal
dimension have larger relative dispersivities. The aqueous horizontal dispersivity exhibits a most significant increase against
the plume scale. 相似文献
12.
Vertically Integrated Hydraulic Conductivity: A New Parameter for Groundwater-Surface Water Analysis
Numerical modeling of groundwater-surface water interactions provides vital information necessary for determining the extent of nutrient transport, quantifying water budgets, and delineating zones of ecological support. The hydrologic data that drive these models are often collected at disparate scales and subsequently incorporated into numerical models through upscaling techniques such as piecewise constancy or geostatistical methods. However, these techniques either use basic interpolation methods, which often simplifies the system of interest, or utilize complex statistical methods that are computationally expensive, time consuming, and generate complex subsurface configurations. We propose a bulk parameter termed “vertically integrated hydraulic conductivity” (KV), and defined as the depth-integrated resistance to fluid flow sensed at the groundwater-surface water interface, as an alternative to hydraulic conductivity when investigating vertical fluxes across the groundwater-surface water interface. This bulk parameter replaces complex subsurface configurations in situations dominated by vertical fluxes and where heterogeneity is not of primary importance. To demonstrate the utility of KV, we extracted synthetic temperature time series data from a forward numerical model under a variety of scenarios and used those data to quantify vertical fluxes using the amplitude ratio method. These quantified vertical fluxes and the applied hydraulic head gradient were subsequently input into Darcy's Law and used to quantify KV. This KV was then directly compared to the equivalent hydraulic conductivity (KT) assuming an infinitely extending layer. Vertically integrated hydraulic conductivity allows for more accurate and robust flow modeling across the groundwater-surface water interface in instances where complex heterogeneities are not of primary concern. 相似文献
13.
Laboratory Study of Air Sparging: Air Flow Visualization 总被引：15，自引：0，他引：15
Wei Ji Amine Dahmani David P. Ahlfeld Jia Ding Lin Edward Hill III 《Ground Water Monitoring & Remediation》1993,13(4):115-126
Laboratory flow visualization experiments, using glass beads as the porous medium, were conducted to study air sparging, an innovative technology for subsurface contaminant remediation. The purpose of these experiments was to observe how air flows through saturated porous media and to obtain a basic understanding of air plume formation and medium heterogeneity effects. The experiments indicate that air flow occurring in discrete, stable channels is the most probable flow behavior in medium to fine grained water saturated porous media and that medium heterogeneity plays an important role in the development of air channels. Several simulated scales of heterogeneities, from pore to field, have been studied. The results suggest that air channel formation is sensitive to the various scales of heterogeneities. Site-specific hydrogeologic settings have to be carefully reviewed before air sparging is applied to remediate sites contaminated by volatile organic compounds. 相似文献
14.
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
15.
For good groundwater flow and solute transport numerical modeling, it is important to characterize the formation properties. In this paper, we analyze the performance and important implementation details of a new approach for stochastic inverse modeling called inverse sequential simulation (iSS). This approach is capable of characterizing conductivity fields with heterogeneity patterns difficult to capture by standard multiGaussian-based inverse approaches. The method is based on the multivariate sequential simulation principle, but the covariances and cross-covariances used to compute the local conditional probability distributions are computed by simple co-kriging which are derived from an ensemble of conductivity and piezometric head fields, in a similar manner as the experimental covariances are computed in an ensemble Kalman filtering. A sensitivity analysis is performed on a synthetic aquifer regarding the number of members of the ensemble of realizations, the number of conditioning data, the number of piezometers at which piezometric heads are observed, and the number of nodes retained within the search neighborhood at the moment of computing the local conditional probabilities. The results show the importance of having a sufficiently large number of all of the mentioned parameters for the algorithm to characterize properly hydraulic conductivity fields with clear non-multiGaussian features. 相似文献
16.
A multiscale adjoint (MSADJ) method is developed to compute high-resolution sensitivity coefficients for subsurface flow in large-scale heterogeneous geologic formations. In this method, the original fine-scale problem is partitioned into a set of coupled subgrid problems, such that the global adjoint problem can be efficiently solved on a coarse grid. Then, the coarse-scale sensitivities are interpolated to the local fine grid by reconstructing the local variability of the model parameters with the aid of solving embedded adjoint subproblems. The approach employs the multiscale finite-volume (MSFV) formulation to accurately and efficiently solve the highly detailed flow problem. The MSFV method couples a global coarse-scale solution with local fine-scale reconstruction operators, hence yielding model responses that are quite accurate at both scales. The MSADJ method is equally efficient in computing the gradient of the objective function with respect to model parameters. Several examples demonstrate that the approach is accurate and computationally efficient. The accuracy of our multiscale method for inverse problems is twofold: the sensitivity coefficients computed by this approach are more accurate than the traditional finite-difference-based numerical method for computing derivatives, and the calibrated models after history matching honor the available dynamic data on the fine scale. In other words, the multiscale based adjoint scheme can be used to history match fine-scale models quite effectively. 相似文献
17.
Recent advancements in experimental techniques allow sub-core-scale heterogeneities to be quantified in a high resolution. Based on the observations of heterogeneity distributions in natural core samples, we perform simulations to study the influence of small-scale heterogeneities on large-scale CO2 migration during geological storage. We observe that even the heterogeneities at millimeter scale (the scale of a Representative Elementary Volume for sandstones) can affect large-scale buoyancy-driven upward CO2 migration. For the representative examples we study, ignoring small-scale heterogeneities can lead to an overestimation of the migration speed by a factor of two.To analyze the cause of such overestimation, we introduce a dimensionless heterogeneity factor to characterize different levels of heterogeneity. The influence on CO2 migration is quantified with respect to a variety of heterogeneity factors, correlation lengths, and fluid viscosity ratios for isotropic and anisotropic media. Our findings suggest that small-scale heterogeneities should not be ignored in core analysis, even for cores that appear relatively homogeneous and do not have distinguishable heterogeneous patterns. In addition, relative-permeability curves measured from core-flood experiments under high-flow-velocity conditions (a common practice to eliminate capillary end-effects) should not be directly used in modeling low-velocity CO2 migration if small-scale heterogeneities are present. 相似文献
18.
Multivariate grid-free geostatistical simulation with point or block scale secondary data 总被引：1，自引：1，他引：0
Yevgeniy Zagayevskiy Clayton V. Deutsch 《Stochastic Environmental Research and Risk Assessment (SERRA)》2016,30(6):1613-1633
A novel grid-free geostatistical simulation method (GFS) allows representing coregionalized variables as an analytical function of the coordinates of the simulation locations. Simulation on unstructured grids, regridding and refinement of available realizations of natural phenomena including, but not limited to, environmental systems are possible with GFS in a consistent manner. The unconditional realizations are generated by utilizing the linear model of coregionalization and Fourier series-based decomposition of the covariance function. The conditioning to data is performed by kriging. The data can be measured at scattered point-scale locations or sampled at a block scale. Secondary data are usually used in conjunction with primary data for the improved modeling. Satellite imaging is an example of exhaustively sampled secondary data. Improvements and recommendations are made to the implementation of GFS to properly assimilate secondary exhaustive data sets in a grid-free manner. Intrinsic cokriging (ICK) is utilized to reduce computational time and preserve the overall quality of the simulation. To further reduce the computational cost of ICK, a block matrix inversion is implemented in the calculation of the kriging weights. A projection approach to ICK is proposed to avoid artifacts in the realizations around the edges of the exhaustive data region when the data do not cover the entire modeling domain. The point-scale block value representation of the block-scale data is developed as an alternative to block cokriging to integrate block-scale data into realizations within the GFS framework. Several case studies support the proposed enhancements. 相似文献
19.
To more accurately predict the migration behavior of pollutants in porous media, we conduct laboratory scale experiments and model simulation. Aniline (AN) is used in one-dimensional soil column experiments designed under various media and hydrodynamic conditions. The advection-dispersion equation (ADE) and the continuous-time random walk (CTRW) were used to simulate the breakthrough curves (BTCs) of the solute transport. The results show that the media and hydrodynamic conditions are two important factors affecting solute transport and are related to the degree of non-Fickian transport. The simulation results show that CTRW can more effectively describe the non-Fickian phenomenon in the solute transport process than ADE. The sensitive parameter in the CTRW simulation process is , which can reflect the degree of non-Fickian diffusion in the solute transport. Understanding the relationship of with velocity and media particle size is conducive to improving the reactive solute transport model. The results of this study provide a theoretical basis for better prediction of pollutant transport in groundwater. 相似文献
20.
Antonio Coppola Alessandro ComegnaGiovanna Dragonetti Miles DyckAngelo Basile Nicola LamaddalenaMohamed Kassab Vincenzo Comegna 《Advances in water resources》2011,34(6):747-759
Solute transport parameters are known to be scale-dependent due mainly to the increasing scale of heterogeneities with transport distance and with the lateral extent of the transport field examined. Based on a transect solute transport experiment, in this paper we studied this scale dependence by distinguishing three different scales with different homogeneity degrees of the porous medium: the observation scale, transport scale and transect scale. The main objective was to extend the approach proposed by van Wesenbeeck and Kachanoski to evaluating the role of textural heterogeneities on the transition from the observation scale to the transport scale. The approach is based on the scale dependence of transport moments estimated from solute concentrations distributions. In our study, these moments were calculated starting from time normalized resident concentrations measured by time domain reflectometry (TDR) probes at three depths in 37 soil sites 1 m apart along a transect during a steady state transport experiment. The Generalized Transfer Function (GTF) was used to describe the evolution of apparent solute spreading along the soil profile at each observation site by analyzing the propagation of the moments of the concentration distributions. Spectral analysis was used to quantify the relationship between the solid phase heterogeneities (namely, texture and stones) and the scale dependence of the solute transport parameters. Coupling the two approaches allowed us to identify two different transport scales (around 4-5 m and 20 m, respectively) mainly induced by the spatial pattern of soil textural properties. The analysis showed that the larger transport scale is mainly determined by the skeleton pattern of variability. Our analysis showed that the organization in hierarchical levels of soil variability may have major effects on the differences between solute transport behavior at transport scale and transect scale, as the transect scale parameters will include information from different scales of heterogeneities. 相似文献