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1.
Although recognized as important, measures of connectivity (i.e. the existence of high-conductivity paths that increase flow and allow for early solute arrival) have not yet been incorporated into methods for upscaling hydraulic conductivities of porous media. We present and evaluate a binary upscaling formula that utilizes connectivity information. The upscaled hydraulic conductivity (K) of binary media is determined as a function of the proportions and conductivities of the two materials, the geometry of the inclusions, and the mean distance between them. The use of a phase interchange theorem renders the formula equally applicable to two-dimensional media with inclusions of low K and high K as compared with the matrix. The new upscaling formula is tested on two-dimensional binary random fields spanning a broad range of spatial correlation structures and conductivity contrasts. The computed effective conductivities are compared to what is obtained using self-consistent effective medium theory, the coated ellipsoids approximation, and to a streamline approach. It is shown that, although simple, the proposed formula performs better than available methods for binary upscaling. The use of connectivity information leads to significantly improved behavior close to the percolation threshold. The proposed upscaling formula depends exclusively on parameters that are obtainable from field investigations. 相似文献
2.
《Advances in water resources》2004,27(10):1017-1032
This paper presents a numerical solution for the effective conductivity of a periodic binary medium with cuboid inclusions located on an octahedral lattice. The problem is defined by five dimensionless geometric parameters and one dimensionless conductivity contrast parameter. The effective conductivity is determined by considering the flow through the “elementary flow domain” (EFD), which is an octant of the unitary domain of the periodic media. We derive practical bounds of interest for the six-dimensional parameter space of the EFD and numerically compute solutions at regular intervals throughout the entire bounded parameter space. A continuous solution of the effective conductivity within the limits of the simulated parameter space is then obtained via interpolation of the numerical results. Comparison to effective conductivities derived for random heterogeneous media demonstrate similarities and differences in the behavior of the effective conductivity in regular periodic (low entropy) vs. random (high entropy) media. The results define the low entropy bounds of effective conductivity in natural media, which is neither completely random nor completely periodic, over a large range of structural geometries. For aniso-probable inclusion spacing, the absolute bounds of Keff for isotropic inclusions are the Wiener bounds, not the Hashin-Shtrikman bounds. For isotropic inclusion and isoprobable conditions well below the percolation threshold, the results are in agreement with the self-consistent approach. For anisotropic cuboid inclusions, or at relatively close spacing in at least one direction (p > 0.2) (aniso-probable conditions), the effective conductivity of the periodic media is significantly different from that found in anisotropic random binary or Gaussian media. 相似文献
3.
The hydraulic conductivity of heterogeneous porous media depends on the distribution function and the geometry of local conductivities at the smaller scale. There are various approaches to estimate the effective conductivity Keff at the larger scale based on information about the small scale heterogeneity. A critical geometric property in this ‘upscaling’ procedure is the spatial connectivity of the small-scale conductivities. We present an approach based on the Euler-number to quantify the topological properties of heterogeneous conductivity fields, and we derive two key parameters which are used to estimate Keff. The required coefficients for the upscaling formula are obtained by regression based on numerical simulations of various heterogeneous fields. They are found to be generally valid for various different isotropic structures. The effective unsaturated conductivity function Keff (ψm) could be predicted satisfactorily. We compare our approach with an alternative based on percolation theory and critical path analysis which yield the same type of topological parameters. An advantage of using the Euler-number in comparison to percolation theory is the fact that it can be obtained from local measurements without the need to analyze the entire structure. We found that for the heterogeneous field used in this study both methods are equivalent. 相似文献
4.
We consider heterogeneous media whose properties vary in space and particularly aquifers whose hydraulic conductivity K may change by orders of magnitude in the same formation. Upscaling of conductivity in models of aquifer flow is needed in order to reduce the numerical burden, especially when modeling flow in heterogeneous aquifers of 3D random structure. Also, in many applications the interest is in average values of the dependent variables over scales larger or comparable to the conductivity length scales. Assigning values of the conductivity Kb to averaging domains, or computational blocks, is the topic of a large body of literature, the problem being of wide interest in various branches of physics and engineering. It is clear that upscaling causes loss of information and at best it can render a good approximation of the fine scale solution after averaging it over the blocks.The present article focuses on upscaling approaches dealing with random media. It is not meant to be a review paper, its main scope being to elucidate a few issues of principle and to briefly discuss open questions. We show that upscaling can be usually achieved only approximately, and the result may depend on the particular upscaling scheme adopted. The typically scarce information on the statistical structure of the fine-scale conductivity imposes a strong limitation to the upscaling problem. Also, local upscaling is not possible in nonuniform mean flows, for which the upscaled conductivity tensor is generally nonlocal and it depends on the domain geometry and the boundary conditions. These and other limitations are discussed, as well as other open topics deserving further investigation. 相似文献
5.
《Advances in water resources》2005,28(11):1159-1170
The paper concerns macroscopic modeling of water flow in an unsaturated double-porosity soil consisting of highly conductive inclusions embedded in a less conductive matrix. The flow at the local scale in both sub-domains is assumed to be governed by the Richards equation. Application of the asymptotic homogenization method leads to a macroscopic flow model in the form of a single equation with two effective parameters. The effective water capacity depends on the local capacities of both sub-domains and their volumetric fractions, while the effective conductivity depends on the conductivity of the porous matrix and the local geometry of the medium. The conductivity of the inclusions does not influence the calculation of the effective conductivity. The domain of validity of the model is defined. An example of numerical simulation is presented for 1D infiltration into initially dry soil. The local geometry of the considered medium is 2D. The results obtained from homogenization are close to the fine scale solution (SWMS_2D program), where the local heterogeneous structure of the medium is explicitly represented. 相似文献
6.
We study two-dimensional flow in a layered heterogeneous medium composed of two materials whose hydraulic properties and spatial distribution are known statistically but are otherwise uncertain. Our analysis relies on the composite media theory, which employs random domain decomposition in the context of groundwater flow moment equations to explicitly account for the separate effects of material and geometric uncertainty on ensemble moments of head and flux. Flow parallel and perpendicular to the layering in a two-material composite layered medium is considered. The hydraulic conductivity of each material is log-normally distributed with a much higher mean in one material than in the other. The hydraulic conductivities of points within different materials are uncorrelated. The location of the internal boundary between the two contrasting materials is random and normally distributed with given mean and variance. We solve the equations for (ensemble) moments of hydraulic head and flux and analyze the impact of unknown geometry of materials on statistical moments of head and flux. We compare the composite media approach to approximations that replace statistically inhomogeneous conductivity fields with pseudo-homogeneous random fields.
This work was performed under the auspices of the US Department of Energy (DOE): DOE/BES (Bureau of Energy Sciences) Program in the Applied Mathematical Sciences contract KC-07–01–01 and Los Alamos National Laboratory under LDRD 98604. This work made use of STC shared experimental facilities supported by the National Science Foundation under Agreement No. EAR-9876800. This work was supported in part by the European Commission under Contract No. EVK1-CT-1999–00041 (W-SAHaRA). 相似文献
7.
《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
8.
A. Lourens F. C. van Geer 《Stochastic Environmental Research and Risk Assessment (SERRA)》2016,30(1):237-249
In many fields of study, and certainly in hydrogeology, uncertainty propagation is a recurring subject. Usually, parametrized probability density functions (PDFs) are used to represent data uncertainty, which limits their use to particular distributions. Often, this problem is solved by Monte Carlo simulation, with the disadvantage that one needs a large number of calculations to achieve reliable results. In this paper, a method is proposed based on a piecewise linear approximation of PDFs. The uncertainty propagation with these discretized PDFs is distribution independent. The method is applied to the upscaling of transmissivity data, and carried out in two steps: the vertical upscaling of conductivity values from borehole data to aquifer scale, and the spatial interpolation of the transmissivities. The results of this first step are complete PDFs of the transmissivities at borehole locations reflecting the uncertainties of the conductivities and the layer thicknesses. The second step results in a spatially distributed transmissivity field with a complete PDF at every grid cell. We argue that the proposed method is applicable to a wide range of uncertainty propagation problems. 相似文献
9.
We suggest a critical look at the epistemic foundations of the porous media upscaling problem that focuses on conceptual processes at work and not merely on form manipulations. We explore the way in which critical aspects of scientific methodology make their appearance in the upscaling context, thus generating useful effective parameters in practice. The fons et origo of our approach is a conceptual blending of knowledge states that requires the revision of the traditional method of scientific argument underlying most upscaling techniques. By contrast to previous techniques, the scientific reasoning of the proposed upscaling approach is based on a stochastic model that involves teleologic solutions and stochastic logic integration principles. The syllogistic form of the approach has important advantages over the traditional reasoning scheme of porous media upscaling, such as: it allows the rigorous derivation of the joint probability distributions of hydraulic gradients and conductivities across space; it imposes no restriction on the functional form of the effective parameters or the shape of the probability laws governing the random media (non-Gaussian distributions, multiple-point statistics and non-linear models are automatically incorporated); it relies on sound methodological principles rather than being ad hoc; and it offers the rational means for integrating the multifarious core knowledge bases and uncertain site-specific information sources about the subsurface system. Previous upscaling results are derived as special cases of the proposed upscaling approach under limited conditions of porous media flow, a fact that further demonstrates the generalization power of the approach. Our hope is that looking at the upscaling problem in this novel way will direct further attention to the methodological exploration of the problem at the length and the detail that it deserves.I would like to thank Drs. A. Kolovos and D.T. Hristopulos for their valuable comments. The work was supported by grants from the Army Research Office (Grant no. DAAG55–98–1-0289) and the National Institute of Environmental Health Sciences (P42-ES05948 & P30-ES10126). 相似文献
10.
Biofilm growth changes many physical properties of porous media such as porosity, permeability and mass transport parameters. The growth depends on various environmental conditions, and in particular, on flow rates. Modeling the evolution of such properties is difficult both at the porescale where the phase morphology can be distinguished, as well as during upscaling to the corescale effective properties. Experimental data on biofilm growth is also limited because its collection can interfere with the growth, while imaging itself presents challenges.In this paper we combine insight from imaging, experiments, and numerical simulations and visualization. The experimental dataset is based on glass beads domain inoculated by biomass which is subjected to various flow conditions promoting the growth of biomass and the appearance of a biofilm phase. The domain is imaged and the imaging data is used directly by a computational model for flow and transport. The results of the computational flow model are upscaled to produce conductivities which compare well with the experimentally obtained hydraulic properties of the medium. The flow model is also coupled to a newly developed biomass–nutrient growth model, and the model reproduces morphologies qualitatively similar to those observed in the experiment. 相似文献
11.
Renormalization group methods in subsurface hydrology: overview and applications in hydraulic conductivity upscaling 总被引：3，自引：0，他引：3
The renormalization group (RG) approach is a powerful theoretical framework, more suitable for upscaling strong heterogeneity than low-order perturbation expansions. Applications of RG methods in subsurface hydrology include the calculation of (1) macroscopic transport parameters such as effective and equivalent hydraulic conductivity and dispersion coefficients, and (2) anomalous exponents characterizing the dispersion of contaminants due to long-range conductivity correlations or broad (heavy-tailed) distributions of the groundwater velocity. First, we review the main ideas of RG methods and their hydrological applications. Then, we focus on the hydraulic conductivity in saturated porous media with isotropic lognormal heterogeneity, and we present an RG calculation based on the replica method. The RG analysis gives rigorous support to the exponential conjecture for the effective hydraulic conductivity [Water Resour. Res. 19 (1) (1983) 161]. Using numerical simulations in two dimensions with a bimodal conductivity distribution, we demonstrate that the exponential expression is not suitable for all types of heterogeneity. We also introduce an RG coarse-grained conductivity and investigate its applications in estimating the conductivity of blocks or flow domains with finite size. Finally, we define the fractional effective dimension, and we show that it justifies fractal exponents in the range 1−2/dα<1 (where d is the actual medium dimension) in the geostatistical power average. 相似文献
12.
应用模式匹配算法研究建立水平层状非均质横向同性地层中多分量感应测井响应的快速算法.首先,利用Fourier级数展开法将多分量感应响应的数值模拟转化为三个轴对称问题,并利用电阻率径向导数的奇异表达式,引入两个附加奇异微分算子,用于描述柱状分界面上的积累面电荷对共面线圈系电磁响应的影响.然后通过模式匹配算法求解轴对称问题,得到水平层状非均质横向同性地层中多分量感应磁场的半解析解以及测井响应计算方法,最后通过数值模拟结果对该算法进行检验并进一步考察阵列多分量感应仪器的响应特征. 相似文献
13.
广义混合率模型目前多应用于岩石的流变、杨氏模量等力学性质的研究,较少应用于多相介质岩石的有效电导率研究。本文利用三维有限元方法计算得到大量二相随机介质模型的有效电导率数据,引入广义混合率的有效电导率模型进行数据拟合,发现广义混合率模型参数J与两相介质电导率比值有关,并首次获得参数 J 与两相介质电导率比值之间的关系式,据此可以快速准确的预测(计算)任意二相介质的有效电导率,其结果较已有的随机介质模型和有效介质理论模型公式更为准确,为精细储集层评价奠定坚实基础。 相似文献
14.
It has been shown that convective mixing in porous media flow is important for applications such as saltwater intrusion and geological storage of carbon dioxide. In the latter case, dissolution from the injected phase to the resident brine is assisted by convective mixing, which leads to enhanced storage security through reduced buoyancy. Here, we focus on the effect of horizontal barriers on the efficiency of convective mixing. Previous investigations of the effect of heterogeneity on mixing efficiency have focused on random permeability fields or barriers of small extent compared to the intrinsic finger wavelength. The effect of horizontal barriers of larger extent, such as mudstone inclusions or thin shale deposits, has not been given sufficient attention. We perform detailed numerical investigations to represent the continuous solution of this problem in semi-infinite domains with barriers arranged in a periodic manner. The results show that mass flux into the domain, which is a measure of the efficiency of redistribution of the solute, is inversely proportional to the barrier length and proportional to the horizontal and vertical aperture between the barriers, for the cases studied. The flow structure is complex, and it depends not only on the total area of barriers but also largely on the distribution of barriers. Therefore, neither simple analytical models nor simple upscaling methods that lack information about the flow paths, can be used to predict the behavior. However, we compute the effective vertical permeability by flow-based upscaling and show that it can be used to directly obtain a first-order approximation to the mass flux into the domain. 相似文献
15.
Flow and transport take place in a heterogeneous medium made up from inclusions of conductivity K submerged in a matrix of conductivity K
0. We consider two-dimensional isotropic media, with circular inclusions of uniform radii, that are placed at random and without overlap in the matrix. The system is completely characterized by the conductivity contrast =K/K
0 and by the volume fraction n. The flow is uniform in the mean, of velocity U=const. The derivation of the velocity field is achieved by a numerical method of high accuracy, based on analytical elements. Approximate analytical solutions are derived by a few methods: composite elements, effective medium, dilute systems and first-order approximation in logconductivity variance. The latter was employed by Rubin (1995), while the dilute system approximation was used by Eames and Bush (1999) and Dagan and Lessoff (2001). Transport is solved in a Lagrangean framework, with trajectories determined numerically from the velocity field, by particle tracking. Results for the velocity variance and for the longitudinal macrodispersivity, for a few values of and n, are presented in Part 2. 相似文献
16.
The coupling upscaling finite element method is developed for solving the coupling problems of deformation and consolidation of heterogeneous saturated porous media under external loading conditions. The method couples two kinds of fully developed methodologies together, i.e., the numerical techniques developed for calculating the apparent and effective physical properties of the heterogeneous media and the upscaling techniques developed for simulating the fluid flow and mass transport properties in heterogeneous porous media. Equivalent permeability tensors and equivalent elastic modulus tensors are calculated for every coarse grid block in the coarse-scale model of the heterogeneous saturated porous media. Moreover, an oversampling technique is introduced to improve the calculation accuracy of the equivalent elastic modulus tensors. A numerical integration process is performed over the fine mesh within every coarse grid element to capture the small scale information induced by non-uniform scalar field properties such as density, compressibility, etc. Numerical experiments are carried out to examine the accuracy of the developed method. It shows that the numerical results obtained by the coupling upscaling finite element method on the coarse-scale models fit fairly well with the reference solutions obtained by traditional finite element method on the fine-scale models. Moreover, this method gets more accurate coarse-scale results than the previously developed coupling multiscale finite element method for solving this kind of coupling problems though it cannot recover the fine-scale solutions. At the same time, the method developed reduces dramatically the computing effort in both CPU time and memory for solving the transient problems, and therefore more large and computational-demanding coupling problems can be solved by computers. 相似文献
17.
Upscaling in seismics is a homogenization of finely layered media in the zero-frequency limit. An upscaling technique for arbitrary anisotropic layers has been developed by Schoenberg and Muir. Applying this technique to a stack of layers of orthorhombic (ORT) symmetry whose vertical symmetry planes are aligned, results in an effective homogeneous layer with orthorhombic symmetry. If the symmetry planes in a horizontal orthorhombic layer are rotated with respect to vertical, the medium is referred to as tilted orthorhombic (TOR) medium, and the stack composed of TOR layers in zero-frequency limit will produce an effective medium of a lower symmetry than orthorhombic. We consider a P-wave that propagates through a stack of thin TOR layers, then it is reflected (preserving the mode) at some interface below the stack, and then propagates back through the same stack. We propose to use a special modified medium for the upscaling in case of this sequential down- and up-propagation: each TOR layer in the stack is replaced by two identical TOR layers whose tilt angles have the opposite algebraic sign. In this modified medium, one-way propagation of a seismic wave (any wave mode) is equivalent to propagation of a pure-mode reflection in the original medium. We apply this idea to study the contribution from an individual layer from the stack and show how the approach can be applied to a stack of TOR layers. To demonstrate the applicability of the model, we use well log data for the upscaling. The model we propose for the upscaling can be used in well-seismic ties to correct the effective parameters obtained from well log data for the presence of tilt, if latter is confirmed by additional measurements (for example, borehole imaging). 相似文献
18.
The relationship of total dissolved solids measurements to bulk electrical conductivity in an aquifer contaminated with hydrocarbon 总被引：1，自引：0，他引：1
Eliot A. Atekwana Estella A. Atekwana Rebecca S. Rowe D. Dale Werkema Jr. Franklyn D. Legall 《Journal of Applied Geophysics》2004,56(4):281
A recent conceptual model links higher bulk conductivities at hydrocarbon impacted sites to higher total dissolved solids (TDS) resulting from enhanced mineral weathering due to acids produced during biodegradation. In this study, we evaluated the above model by investigating the vertical distribution of bulk conductivity, TDS, and specific conductance in groundwater. The results showed higher TDS at contaminated locations consistent with the above model. Further, steep vertical gradients in bulk conductivity and TDS suggest vertical and spatial heterogeneity at the site. We observed that at fluid conductivities <40 mS/m, bulk conductivity was inversely related to fluid conductivity, but at fluid conductivities >40 mS/m, bulk conductivity increased with increasing fluid conductivity. However, at fluid conductivities >80 mS/m, bulk conductivities increased without a corresponding increase in fluid conductivity, resulting in a poor correlation between bulk conductivity and fluid conductivity for the contaminated samples. This suggests that electrolytic conductivity was not completely responsible for the observed variability in bulk conductivity. We suggest two possible reasons for the inverse relationship at low fluid conductivity and poor positive correlation at high fluid conductivity: (1) geochemical heterogeneity due to biological processes not captured at a scale comparable to the bulk conductivity measurement and (2) variability in the surface conductivity, consistent with a simple petrophysical model that suggests higher surface conductivity for contaminated sediments. We conclude that biodegradation processes can impact both electrolytic and surface conduction properties of contaminated sediments and these two factors can account for the higher bulk conductivities observed in sediments impacted by hydrocarbon. 相似文献
19.
The hydraulic properties of lake beds control the interactions between lakes and ground water systems, but these properties are normally difficult to measure directly. The authors'method combines seismic reflection and electrical measurements to map the relative hydraulic conductivity of lake bed sediments. A shipboard seismic profiling system provides sediment thickness, while a towed electrical array yields longitudinal conductance and electrical chargeability. The sediment's leakance (hydraulic conductivity/thickness) can be calculated from the longitudinal conductance data. Leakance may then be converted to relative hydraulic conductivity through the seismically derived sediment thicknesses. Simultaneously acquired electrical chargeability provides an independent measure of clay content. The seismic and electrical systems are computer automated and yield production rates of approximately five line-kilometers/hour or 300 electrical soundings/hour. The systems provide continuous hydraulic information along the ship track rather than the point information derived from coring.
The procedure and systems have been used to map the bed of Lake Michigan offshore from an area of heavy pumpage. This location has been chosen to test the method because lake water has intruded the aquifer in plumes largely controlled by lake bed hydraulics. Mapping these plumes onshore permits the inference of the spatial distribution of offshore hydraulic conductivities. Offshore seepage measurements and numerical, chemical transport modeling of this site have confirmed the reliability of the geophysically derived hydraulic conductivities and have also demonstrated the improvement in numerical results achieved through the availability of spatially determined hydraulic conductivities. 相似文献
The procedure and systems have been used to map the bed of Lake Michigan offshore from an area of heavy pumpage. This location has been chosen to test the method because lake water has intruded the aquifer in plumes largely controlled by lake bed hydraulics. Mapping these plumes onshore permits the inference of the spatial distribution of offshore hydraulic conductivities. Offshore seepage measurements and numerical, chemical transport modeling of this site have confirmed the reliability of the geophysically derived hydraulic conductivities and have also demonstrated the improvement in numerical results achieved through the availability of spatially determined hydraulic conductivities. 相似文献
20.
This paper is concerned with numerical tests of several rock physical relationships. The focus is on effective velocities and scattering attenuation in 3D fractured media. We apply the so‐called rotated staggered finite‐difference grid (RSG) technique for numerical experiments. Using this modified grid, it is possible to simulate the propagation of elastic waves in a 3D medium containing cracks, pores or free surfaces without applying explicit boundary conditions and without averaging the elastic moduli. We simulate the propagation of plane waves through a set of randomly cracked 3D media. In these numerical experiments we vary the number and the distribution of cracks. The synthetic results are compared with several (most popular) theories predicting the effective elastic properties of fractured materials. We find that, for randomly distributed and randomly orientated non‐intersecting thin penny‐shaped dry cracks, the numerical simulations of P‐ and S‐wave velocities are in good agreement with the predictions of the self‐consistent approximation. We observe similar results for fluid‐filled cracks. The standard Gassmann equation cannot be applied to our 3D fractured media, although we have very low porosity in our models. This is explained by the absence of a connected porosity. There is only a slight difference in effective velocities between the cases of intersecting and non‐intersecting cracks. This can be clearly demonstrated up to a crack density that is close to the connectivity percolation threshold. For crack densities beyond this threshold, we observe that the differential effective‐medium (DEM) theory gives the best fit with numerical results for intersecting cracks. Additionally, it is shown that the scattering attenuation coefficient (of the mean field) predicted by the classical Hudson approach is in excellent agreement with our numerical results. 相似文献